The Routledge Handbook of Properties (Routledge Handbooks in Philosophy) [1 ed.] 103215876X, 9781032158761

Table of contents :
CONTENTS
CONTRIBUTORS
INTRODUCTION
Methodology and Metaontology
1 QUANTIFICATION AND ONTOLOGICAL COMMITMENT
2 THE METHOD OF PARAPHRASE
3 PROPERTIES AS TRUTHMAKERS
4 NATURALNESS
Distinctions
5 UNIVERSALITY AND PARTICULARITY
6 ARE PROPERTIES ABSTRACT ENTITIES?
7 RELATIONS
8 INTRINSIC/EXTRINSIC
9 ESSENTIAL VERSUS ACCIDENTAL PROPERTIES
10 DETERMINATE/DETERMINABLE
Realism about Universals
11 PLATONIC REALISM
12 IMMANENT REALISM AND STATES OF AFFAIRS
13 LOCATION AND PROPERTIES
14 UNIVERSALS AND THE BUNDLE THEORY
Nominalism
15 OSTRICH NOMINALISM
16 CLASS NOMINALISM AND RESEMBLANCE NOMINALISM
17 PRIORITY AND GROUNDING NOMINALISM
18 NOMINALISM IN MATHEMATICS
Trope Theory
19 TROPE NOMINALISMS
20 TYPES OF TROPES
21 TROPE BUNDLE THEORIES OF SUBSTANCE
22 TROPE-RELATIONS
Properties in Causation, Time, and Modality
23 CAUSATION AND PROPERTIES
24 DISPOSITIONAL PROPERTIES
25 EVENTS, PROCESSES, AND PROPERTIES
26 TEMPORAL PROPERTIES
27 POSSIBLE WORLDS AS PROPERTIES
28 POWERS, POTENTIALITY, AND MODALITY
Properties in Science
29 PROPERTIES AND NATURAL KINDS
30 LAWS OF NATURE
31 EMERGENT PROPERTIES
32 QUANTITATIVE PROPERTIES
Properties in Language and Mind
33 REFERENCE TO PROPERTIES IN NATURAL LANGUAGE
34 MENTAL CAUSATION AND HIGHER-ORDER PROPERTIES
35 QUALIA AS PROPERTIES OF EXPERIENCES
36 PROPERTIES IN PERCEPTION
Properties in the Normative Realm, the Social World, and Aesthetics
37 NORMATIVE PROPERTIES
38 MORAL PROPERTIES
39 SOCIAL PROPERTIES
40 AESTHETIC PROPERTIES
INDEX

Citation preview

THE ROUTLEDGE HANDBOOK OF PROPERTIES

Philosophical questions regarding both the existence and nature of properties are ubiquitous in ordinary life, the sciences, and philosophical theorising. In philosophy, it is one of the oldest topics discussed in various intellectual traditions – East and West – reaching back to Plato and Aristotle. Today, in the analytic tradition, properties continue to be a core area of study and research. The Routledge Handbook of Properties is an outstanding reference source to this perennial topic and is the first major volume of its kind. It contains forty specially commissioned chapters written by an international team of expert contributors, and is divided into nine clear parts:

• • • • • • • • •

Methodology and Metaontology Distinctions Realism about Universals Nominalism Trope Theory Properties in Causation, Time, and Modality Properties in Science Properties in Language and Mind Properties in the Normative Realm, the Social World, and Aesthetics

The Routledge Handbook of Properties is essential reading for anyone studying and researching metaphysics, metametaphysics, and ontology, and will also be of interest to those in closely related areas such as philosophy of science, philosophy of language, philosophy of mind, ethics, and aesthetics. A.R.J. Fisher is a Lecturer in Philosophy at Gonzaga University, USA. His research focuses on the metaphysics of properties, time, and modality. He also works on the history of twentieth-century metaphysics, writing on metaphysical topics from a historical perspective. He edited Donald C. Williams’s The Elements and Patterns of Being (2018), and is presently writing a monograph on Williams’s metaphysics (forthcoming). Anna-Sofia Maurin is a Professor of Theoretical Philosophy at the University of Gothenburg, Sweden. Her research focuses on issues in (meta)metaphysics, especially tropes, unity in complexity, ontological justification, infinite regress arguments, grounding, and metaphysical explanation. Her most recent research also covers debates in social ontology. She is the author of If Tropes (2002), and Properties in the Cambridge Elements in Metaphysics series (2022).

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Routledge Handbooks in Philosophy are state-of-the-art surveys of emerging, newly re­ freshed, and important fields in philosophy, providing accessible yet thorough assessments of key problems, themes, thinkers, and recent developments in research. All chapters for each volume are specially commissioned, and written by leading scholars in the field. Carefully edited and organized, Routledge Handbooks in Philosophy provide indispensable reference tools for students and researchers seeking a comprehensive over­ view of new and exciting topics in philosophy. They are also valuable teaching resources as accompaniments to textbooks, anthologies, and research-orientated publications. Also available: THE ROUTLEDGE HANDBOOK OF PHILOSOPHY OF IMPLICIT COGNITION Edited by J. Robert Thompson THE ROUTLEDGE HANDBOOK OF THE PHILOSOPHY AND PSYCHOLOGY OF FORGIVENESS Edited by Glen Pettigrove and Robert Enright THE ROUTLEDGE HANDBOOK OF AUTONOMY Edited by Ben Colburn THE ROUTLEDGE HANDBOOK OF BODILY AWARENESS Edited by Adrian J.T. Alsmith and Matthew R. Longo THE ROUTLEDGE HANDBOOK OF INDIAN BUDDHIST PHILOSOPHY Edited by William Edelglass, Pierre-Julien Harter, and Sara McClintock THE ROUTLEDGE HANDBOOK OF PHILOSOPHY OF FRIENDSHIP Edited by Diane Jeske For more information about this series, please visit: https://www.routledge.com/RoutledgeHandbooks-in-Philosophy/book-series/RHP

THE ROUTLEDGE HANDBOOK OF PROPERTIES

Edited by A.R.J. Fisher and Anna-Sofia Maurin

Cover image: Ovanpå by Jean-Louis Maurin, 2021 First published 2024 by Routledge 4 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 605 Third Avenue, New York, NY 10158 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2024 selection and editorial matter A.R.J. Fisher and Anna-Sofia Maurin; individual chapters, the contributors The right of A.R.J. Fisher and Anna-Sofia Maurin to be identified as the author of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Fisher, A. R. J. (Anthony Robert James), editor. | Maurin, Anna-Sofia, editor. Title: The routledge handbook of properties / edited by A.R.J. Fisher, Anna-Sofia Maurin. Description: Abingdon, Oxon ; New York, NY : Routledge, 2024. | Series: Routledge handbooks in philosophy | Includes bibliographical references and index. Identifiers: LCCN 2023032205 (print) | LCCN 2023032206 (ebook) | ISBN 9781032158761 (hardback) | ISBN 9781032158815 (paperback) | ISBN 9781003246077 (ebook) Subjects: LCSH: Tropes (Philosophy) Classification: LCC BD460.T76 R68 2024 (print) | LCC BD460.T76 (ebook) | DDC 111‐‐dc23/eng/20230926 LC record available at https://lccn.loc.gov/2023032205 LC ebook record available at https://lccn.loc.gov/2023032206 ISBN: 978-1-032-15876-1 (hbk) ISBN: 978-1-032-15881-5 (pbk) ISBN: 978-1-003-24607-7 (ebk) DOI: 10.4324/9781003246077 Typeset in Sabon by MPS Limited, Dehradun

CONTENTS

Notes on Contributors

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Introduction: The Importance of Properties A.R.J. Fisher and Anna-Sofia Maurin

1

PART 1

Methodology and Metaontology

11

1 Quantification and Ontological Commitment Nicholas K. Jones

13

2 The Method of Paraphrase John A. Keller

26

3 Properties as Truthmakers Bradley Rettler

38

4 Naturalness: Abundant and Sparse Properties Elanor Taylor

48

PART 2

Distinctions

59

5 Universality and Particularity Daniel Giberman

61

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Contents

6 Are Properties Abstract Entities? Sam Cowling

72

7 Relations: Existence and Nature Fraser MacBride

82

8 Intrinsic/Extrinsic Vera Hoffmann-Kolss

92

9 Essential versus Accidental Properties Fabrice Correia 10 Determinate/Determinable Eric Funkhouser

103

115

PART 3

Realism about Universals

125

11 Platonic Realism Chad Carmichael

127

12 Immanent Realism and States of Affairs Bo R. Meinertsen

138

13 Location and Properties Nikk Effingham

148

14 Universals and the Bundle Theory Jiri Benovsky

159

PART 4

Nominalism

169

15 Ostrich Nominalism Michael Devitt

171

16 Class Nominalism and Resemblance Nominalism Gonzalo Rodriguez-Pereyra

184

17 Priority and Grounding Nominalism Guido Imaguire

195

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Contents

18 Nominalism in Mathematics Jody Azzouni

206

PART 5

Trope Theory

217

19 Trope Nominalisms Douglas Ehring

219

20 Types of Tropes: Modifier and Module Robert K. Garcia

229

21 Trope Bundle Theories of Substance Markku Keinänen and Jani Hakkarainen

239

22 Trope-Relations Anna-Sofia Maurin

250

PART 6

Properties in Causation, Time, and Modality

261

23 Causation and Properties Carolina Sartorio

263

24 Dispositional Properties Jennifer McKitrick

273

25 Events, Processes, and Properties Carlo Rossi

283

26 Temporal Properties Katarina Perović

293

27 Possible Worlds as Properties Peter Forrest

305

28 Powers, Potentiality, and Modality Barbara Vetter

315

vii

Contents PART 7

Properties in Science

325

29 Properties and Natural Kinds Alexander Bird

327

30 Laws of Nature Tuomas E. Tahko

337

31 Emergent Properties Anne Sophie Meincke

347

32 Quantitative Properties J.E. Wolff

358

PART 8

Properties in Language and Mind

367

33 Reference to Properties in Natural Language Friederike Moltmann

369

34 Mental Causation and Higher-Order Properties David Robb

383

35 Qualia as Properties of Experiences Umut Baysan

393

36 Properties in Perception Bence Nanay

403

PART 9

Properties in the Normative Realm, the Social World, and Aesthetics

415

37 Normative Properties Matti Eklund

417

38 Moral Properties Caj Strandberg

427

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Contents

39 Social Properties Dee Payton

438

40 Aesthetic Properties Sonia Sedivy

448

Index

459

ix

CONTRIBUTORS

Jody Azzouni is a Professor of Philosophy at Tufts University. He is interested in metaphysics, epistemology, philosophy of mathematics, philosophy of language, philosophy of logic, and aesthetics. He is currently writing a couple of papers on candidate semantic criteria for the identification of theories as the same ones. Umut Baysan is a Lecturer in Philosophy at the University of Oxford. He works in philosophy of mind and metaphysics, and his published work has mostly focussed on the metaphysics of mind-body relations. Jiri Benovsky is a Scientific Collaborator at the University of Geneva, Switzerland. His areas of specialization include metaphysics, meta-metaphysics, philosophy of mind, aesthetics, personal identity, perception, intuitions, vagueness, as well as Buddhist philosophy. He is the author of several books including Meta-metaphysics: On metaphysical equivalence, primitiveness, and theory choice (Springer, 2016), Mind and Matter: Panpsychism, Dual-Aspect Monism, and the Combination Problem (Springer, 2018), and Eliminativism, Objects, and Persons (Routledge, 2019). Alexander Bird is Bertrand Russell Professor of Philosophy at the University of Cambridge and a fellow of St John’s College, Oxford. His work is primarily in the metaphysics and epistemology of science, with a focus on natural kinds. He is the author of Nature’s Metaphysics: Laws and Properties (OUP, 2007) and Knowing Science (OUP, 2023). Chad Carmichael is an Associate Professor of Philosophy at Indiana University, Indianapolis. He primarily works on metaphysics and epistemology, with specific interests in Platonism and the metaphysics of material objects. Fabrice Correia holds the Chair of Analytic Philosophy at the Department of Philosophy of the University of Geneva. He is a co-founder, and is in charge, together with Kevin Mulligan,

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Contributors

of the research group in metaphysics Eidos. He has published mainly in metaphysics and philosophical logic, on topics such as essence, grounding, modality and time. Sam Cowling is an Associate Professor in the Department of Philosophy at Denison University. He works on metaphysics and the philosophy of comics. He is the author of Abstract Entities (Routledge, 2017) and Philosophy of Comics (Bloomsbury, 2022), coauthored with Wesley D. Cray. Michael Devitt is a Distinguished Professor of Philosophy at the Graduate Center of CUNY. He researches mainly in the philosophy of language and linguistics, realism, biological essentialism, and methodological issues prompted by naturalism. He is the author of several books, most recently Overlooking Conventions (Springer, 2021) and Biological Essentialism (OUP, 2023). Nikk Effingham is a Professor of Philosophy at the University of Birmingham and a Research Associate at the University of Johannesburg. His interests are ontology, the philosophy of time, and the philosophy of religion. His most recent monograph is Time Travel: Probability and Impossibility (OUP, 2020). Douglas Ehring is William Edward Easterwood Professor of Philosophy at Southern Methodist University. He is the author of Causation and Persistence: A Theory of Causation (OUP, 1997), Tropes: Properties, Objects and Mental Causation (OUP, 2011), and What Matters in Survival: Personal Identity and Other Possibilities (OUP, 2021). Matti Eklund is Chair Professor of Theoretical Philosophy at Uppsala University. He works mainly on topics in metaphysics, philosophy of language, philosophy of logic, and metaethics. He recently published Choosing Normative Concepts (OUP, 2017). A.R.J. Fisher is a Lecturer in Philosophy at Gonzaga University, USA. His research focuses on the metaphysics of properties, time, and modality. He also works on the history of twentieth-century metaphysics, writing on metaphysical topics from a historical perspective. He edited Donald C. Williams’s The Elements and Patterns of Being (OUP, 2018) and is presently writing a monograph on Williams’s metaphysics (Palgrave Macmillan, forthcoming). Peter Forrest is an Adjunct Professor at the University of New England, Australia. He works on metaphysics and philosophy of religion. His most recent book, Intellectual, Humanist and Religious Commitment: Acts of Assent (Bloomsbury, 2019), investigates the conditions for commitment in the face of intellectual dilemmas, and applies those conditions to justify commitment to Reason, to Humanism and to Theism. Eric Funkhouser is a Professor of Philosophy at the University of Arkansas. He has published several articles on the metaphysics of properties and causation, the nature of belief, and self-deception. He is the author of The Logical Structure of Kinds (OUP, 2014) and Self-Deception (Routledge, 2019).

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Contributors

Robert K. Garcia is an Associate Professor in the Department of Philosophy at Baylor University. He works primarily in analytic metaphysics and philosophy of religion, with a special interest in the metaphysics of properties, objects, and persons. He is a co-editor of Is Goodness Without God Good Enough? A Debate on Faith, Secularism, and Ethics (Rowman & Littlefield, 2009) and has published widely in journals and edited volumes. Daniel Giberman is a Senior Lecturer in Theoretical Philosophy at the University of Gothenburg, Sweden. In addition to properties, he has serious interests in persistence, mereology, fundamentality, space and time, predication, and consciousness. His latest work is a monograph-in-progress on trope bundle theory and its applications. Jani Hakkarainen is a Senior Lecturer of Philosophy at Tampere University, Finland. He has published on David Hume’s epistemology and metaphysics (his trope theory included), formal ontology and its metatheory, ontological categories, metaphysics of relations, universals, and the trope theory SNT (Strong Nuclear Theory). Hakkarainen has been Visiting Fellow to Yale University twice. Vera Hoffmann-Kolss is an Associate Professor of Philosophy at the University of Bern. Her research focuses on causal models, the metaphysics of properties, and recent debates on ontological vagueness and hyperintensionality. Guido Imaguire is a full professor of metaphysics and logic at the Federal University of Rio de Janeiro (UFRJ) in Brazil. He works on metaphysics, philosophy of language, philosophy of mathematics, and history of analytic philosophy. He is the author of Priority Nominalism (Springer, 2018), among other books and articles, and is a co-editor of the Handbook of Mereology (Philosophia Verlag, 2017). Nicholas K. Jones is an Official Fellow and Tutor at St John’s College, Oxford, as well as an Associate Professor at the University of Oxford. He works at the intersection of metaphysics with the philosophy of logic and the philosophy of language. His recent work primarily concerns applications of higher-order quantification to the metaphysics of properties, relations, and propositions. Markku Keinänen is a Senior Lecturer of Philosophy at Tampere University, Finland. He has published on formal ontology, metaphysics of relations, metaphysics of science, universal bundle theories and systematically developed trope theory SNT (Strong Nuclear Theory) in several research articles. Keinänen was Visiting Fellow at Durham University in 2012–2013. John A. Keller is an Associate Professor of Philosophy and the Rev. Joseph S. Hogan Chair at Saint Joseph’s University, Philadelphia. He has published numerous articles on the role of paraphrase in philosophical inquiry, the purpose of philosophical argumentation, the philosophy of language, and the philosophy of religion, and is the editor of Being, Freedom, and Method: Themes from the Philosophy of Peter van Inwagen (OUP, 2017). Fraser MacBride is a Professor of Philosophy at the University of Manchester. He works on metaphysics, philosophy of mathematics, philosophical logic, and the history of analytic xii

Contributors

philosophy. He is the author of On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy (OUP, 2018). Anna-Sofia Maurin is a Professor of Theoretical Philosophy at the University of Gothenburg, Sweden. Her research focuses on issues in (meta)metaphysics, especially tropes, unity in complexity, ontological justification, infinite regress arguments, grounding, and metaphysical explanation. Her most recent research also covers debates in social ontology. She is the author of If Tropes (Kluwer, 2002) and Properties (CUP, 2022). Jennifer McKitrick is the Chair of Philosophy at University of Nebraska-Lincoln. Her work focuses on metaphysics, particularly dispositions and causal powers. She is the author of Dispositional Pluralism (OUP, 2018). She is also interested in social ontology, particularly the concepts of race and gender. Anne Sophie Meincke is a Senior Research Fellow at the University of Vienna and PI of the Elise Richter-research project “Bio-Agency and Natural Freedom” funded by the Austrian Science Fund (FWF). She specialises in metaphysics, the philosophy of mind and action and the philosophy of biology, exploring in particular the intersections of these fields. Bo R. Meinertsen is an Honorary Research Fellow in philosophy at the University of Sheffield. His work focuses on metaphysics and ontology of states of affairs and their constituents (particulars, properties and relations). He is the author of Metaphysics of States of Affairs (Springer, 2018) and several articles on properties. Friederike Moltmann is a Research Director at the Centre Nationale de la Recherche Scientifique at the Université Côte d’Azur. Her research is mainly in the interface between linguistics and philosophy, especially metaphysics. She is the author of Parts and Wholes in Semantics (OUP, 1997), Abstract Objects and the Semantics of Natural Language (OUP, 2013), and Objects and Attitudes (OUP, forthcoming). Bence Nanay is a Professor of Philosophy and BOF Research Professor at the University of Antwerp, working mainly on philosophy of mind. His most recent book is Mental Imagery: Philosophy, Psychology, Neuroscience (OUP, 2023). Dee Payton is an Assistant Professor of Philosophy at the University of Virginia. They work mainly in analytic feminist philosophy and social philosophy, with a special focus on the metaphysics of social construction and methodology in analytic feminism. Katarina Perović is an Associate Professor of Philosophy at the University of Iowa. She works in metaphysics, early analytic philosophy, and philosophy of mind, and is particularly interested in meta-philosophical issues in these areas. Bradley Rettler is an Associate Professor of Philosophy at the University of Wyoming. He writes about metaphysics, philosophy of religion, and bitcoin.

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Contributors

David Robb is a Professor of Philosophy at Davidson College. He is interested in the philosophy of mind and metaphysics, especially mental causation, free will, and the nature of properties. Gonzalo Rodriguez-Pereyra is a Professor of Metaphysics at the University of Oxford and Colin Prestige Tutor of Philosophy and Senior Tutor at Oriel College, Oxford. He has written extensively on Metaphysics and Early Modern Philosophy. His main publications are Resemblance Nominalism (OUP, 2002), Leibniz’s Principle of Identity of Indiscernibles (OUP, 2014), and Two Arguments for the Identity of Indiscernibles (OUP, 2022). Carlo Rossi is an Associate Professor of the Philosophy Department at the Universidad de Santiago, Chile. His main area of research lies in metaphysics, particularly in issues pertaining to the metaphysics of material objects and other temporal entities, and intersecting areas in the Philosophy of Logic and Language, Philosophy of Physics, and Ancient Philosophy. Carolina Sartorio is a Professor of Philosophy at Rutgers University. She works at the intersection of metaphysics, the philosophy of action, and moral theory. She is the author of Causation and Free Will (OUP, 2016) and Causalism: Unifying Action and Free Action (OUP, forthcoming). Sonia Sedivy is a Professor of Philosophy at the University of Toronto Scarborough. She works primarily in aesthetics and the philosophy of perception. Her research currently focuses on connections between the two. She has written Beauty and the End of Art: Wittgenstein, Plurality and Perception (Bloomsbury, 2016) and edited Art, Representation, and Make-Believe: Essays on the Philosophy of Kendall L. Walton (Routledge, 2021). Caj Strandberg is a Professor of Practical Philosophy at the University of Oslo, Norway. He works primarily in metaethics, but also in aesthetics and normative ethics. He has published articles in Philosophy and Phenomenological Research, Oxford Studies in Metaethics, and British Journal of Aesthetics, among other places. Tuomas E. Tahko is a Professor of Metaphysics of Science at the Department of Philosophy, University of Bristol, UK. He works mainly at the intersection of metaphysics and philosophy of science. He is the author of An Introduction to Metametaphysics (CUP, 2015) and Unity of Science (CUP, 2021) and editor of Contemporary Aristotelian Metaphysics (CUP, 2012). Elanor Taylor is an Associate Professor of Philosophy at Johns Hopkins University. She works on metaphysics, particularly metaphysics of science and social metaphysics. Barbara Vetter is Professor of Theoretical Philosophy at Freie Universität Berlin. Her research concerns the metaphysics and epistemology of modality, dispositions, and abilities. She is the author of Potentiality: From Dispositions to Modality (OUP, 2015). J.E. Wolff is a Senior Lecturer in Metaphysics and Philosophy of Science at the University of Edinburgh. She has recently published The Metaphysics of Quantities (OUP, 2020).

xiv

INTRODUCTION The Importance of Properties A.R.J. Fisher and Anna-Sofia Maurin

Properties are everywhere. When Edith May Smith says this lemon is yellow, she has thereby attributed the property being yellow to the lemon. When a physicist references a law of nature she has picked out properties that exhibit some sort of instantiation pattern. When an ethicist talks about an action being right or wrong she presupposes that there are moral properties attributable to actions. When a philosopher of mind wonders about the causal efficacy of the mental state of pain she presupposes that there are mental properties. If properties are everywhere, questions about them need to be addressed at some point: do properties really exist? If they exist, what are they? What roles do they play in our theorising? How do properties figure in and impact debates in philosophy? Properties is one of the oldest topics in philosophy. It appears in various intellectual traditions and cultures – East and West – dating back to the birth of philosophy. In Ancient Greek thought, Plato proposed a theory of forms as eternal existents, while Aristotle argued that universals exist only in their instances. The Nyāya school of Hindu philosophy argued for the existence of universals over and above their instances; since instances are understood as particular qualities (tropes) the Nyāya are read as positing tropes with universals. Buddhist philosophers such as Dharmakīrti pushed back against NyāyaVaiśeṣika realism, advocating a nominalist ontology of transitory particulars (see Kumar 1997). In the Islamic tradition, Ibn Sina and Ibn Rushd developed various Aristotelian insights about properties within their own novel frameworks. In the Latin West, medieval Scholastics such as Abelard, Aquinas, Ockham, and Duns Scotus debated and occupied differing positions on the reality of universals (Spade 1994), not to mention later Scholastics such as Francisco Suarez (Ross 1962), all of whom offered theories of relations (see Henninger 1989). The Early Modern period is no different. It had its own preoccupation with universals sometimes framed in terms of general ideas; think here of such British Empiricists as Locke, Berkeley, Hume, and Mary Shepherd (see Weinberg 1965). In the nineteenth century, F.H. Bradley, in the British Idealist tradition, analysed the concept of quality and relation as given in experience and found trouble placing such things in his Absolute idealism, with the main problem being dubbed Bradley’s regress (Bradley 1893: ch. 2). In Bertrand Russell’s realist phase, he first postulated universals to account for a priori knowledge (Russell 1912: chs. 9–10) and later a bundle theory of universals DOI: 10.4324/9781003246077-1

1

A.R.J. Fisher and Anna-Sofia Maurin

according to which substances are complexes of universals (Russell 1940: 97–98). Russell’s influence forwarded discussion of properties in the Western tradition and kept alive an interest in the problem of universals. G.F. Stout’s theory of abstract particulars also proved influential in England and America (Stout 1921), impacting Donald C. Williams’s theory of tropes (Williams 1953a, 1953b), and generating further exploration of these concepts. For instance, Helen Knight’s defence of resemblance nominalism is a result of her criticism of Stout’s theory (Knight 1936), which prompted Stout to restate his theory (Stout 1936). In American philosophy, C.S. Peirce’s three-category system included qualities and relations. Other American philosophers, who are sometimes described as doing speculative philosophy, also treated these questions with importance. W.P. Montague, to give one example, argued for Platonic universals (Montague 1940: ch. 6). As we progress into the middle of the twentieth century and into the world of analytic philosophy, we reach key concepts that continue to impact philosophy today such as W.V. Quine’s conception of ontology and his efforts to salvage some coherent understanding of the debate about universals in light of ridicule from logical positivism and ordinary language philosophy (Quine 1948; for one overlooked criticism, see de Laguna 1951: 19). From this, along with the recovery of metaphysics, more and more articles and books on properties begin to appear (e.g., Loux 1970). In the second half of the twentieth century and now in the twenty-first century, the topic of properties continues to be taken seriously in the analytic tradition. The heart of the topic falls within metaphysics, but it has wide-ranging impact on and relevance to most areas of philosophy. The roles that properties play demonstrate the importance and relevance of properties. Let us distinguish between the use-question and the nature-question. The use-question asks after the way that properties are used in philosophical theorising. The nature-question asks after the nature of properties, that is, what properties are. As David Lewis remarked, a conception of something can be individuated in terms of its theoretical role. He even made this general remark in the context of properties (Lewis 1986: 55). There is not just one property-role, but rather several of them. A property-role can be specified according to explanatory interest, content or purpose. We can specify the property-role as the role of grounding resemblances among things or as the role of something that is the semantic value of an abstract, singular term. Each specified role corresponds to a distinct conception of properties. A study of the various roles that properties play and a development of a specific role in some domain of inquiry is fruitful for appreciating the explanatory pervasiveness of properties and also for shedding light on what properties are like. This in turn allows us to meet the nature-question halfway, because by filling a role a property needs to be or behave in a specific way. Thus certain candidate properties are suitable for some jobs but perhaps not for all. Finally, by showing how properties fill a variety of roles properties explain (in some sense of ‘explain’) phenomena that other philosophers beyond metaphysics find interesting. If properties (say) serve a purpose in constructing a theory of laws of nature or if properties play a crucial role in explaining social structures or processes in the social world, properties (and relations) become more relevant and even more interesting (Swoyer 1999: 101). This volume collects new essays on this perennial and sometimes sprawling topic by philosophers specialised in the field. It aims to survey and investigate properties from a methodological, conceptual, and ontological point of view. It also aims to explore what role properties play in other areas of philosophy such as philosophy of science, language, mind, ethics, aesthetics and the social world. In so doing this volume doesn’t just tell you that properties are relevant it shows you how properties are relevant and thereby important 2

Introduction

for contemporary philosophy. This volume is divided into nine parts. The first part concerns methodological issues about the existence of properties, covering metaontological principles that lead to positing properties (e.g., quantification, truthmaking). The second part is about conceptual issues, specifically the following key distinctions: universal/particular, abstract/concrete, property/relation, intrinsic/extrinsic, essential/accidental, determinate/determinable. The next three parts investigate the nature of properties, exploring the best ways to answer the nature-question: properties as universals (Platonic or Aristotelian), nominalism and its variants (from ostrich nominalism to class nominalism), and properties as tropes (varieties of trope theory). In the remaining parts of the volume, applications of properties are considered by interacting with another prominent topic in metaphysics (causation, time, and modality) or by entering an established area of philosophy: philosophy of science, language, mind, ethics, aesthetics and the social world. These latter parts of the volume address the use-question, thus explaining what work properties can and must do in philosophy. Part 1 covers methodological and metaontological considerations that arise in debates about properties. Some arguments for the existence of properties employ Quine’s criterion of ontological commitment. If to be is to be the value of a bound variable, whatever we quantify over in a suitably regimented language will be among the entities we are ontologically committed to. This cuts a number of ways. Traditionally, the nominalist has argued that since we do not need to quantify over properties to account for predication we do not need to admit properties into our ontology. The statement that a is F is regimented as there is an x such that x is F. But we might turn to the behaviour of quantifiers in other settings and find that certain claims motivate a quantificational approach to reasoning about properties after all. In Chapter 1, Nicholas K. Jones explores departures from the Quinean paradigm by probing the quantificational phrase ‘what there is’ and looks at ways in which predicates might be a source of ontological commitment. The nominalist not only has a Quinean criterion of ontological commitment in her toolbox but also the method of paraphrase. When a sentence seemingly commits us to the existence of something, say some biological species, we might offer a paraphrase such that the meaning of the seemingly committal statement is preserved in a new statement that lacks the original quantification. Paraphrasing away claims that quantify over properties allows us to avoid a commitment to properties. In Chapter 2, John A. Keller evaluates various ways that paraphrase might be used to block the existence of properties. Paraphrase raises its own questions such as how does the paraphrased statement relate to the paraphrasing statement? Why is one statement preferred when the two supposedly have the same meaning? The discussion by Keller goes some way in offering a general interpretation of the method of paraphrase that can be applied to debates beyond properties. Another metaontological tool has since been developed, stemming from the truthmaker principle first proposed in analytic metaphysics by D.M. Armstrong (1989, 2004). The intuition behind this principle is that truth depends on reality. The principle that captures this intuition usually turns out to be a principle about all truths, stating that every truth has a truthmaker. The truthmaker principle has been developed as a metaontological principle at the hands of Armstrong such that the entities admitted into our ontology are the truthmakers. In Chapter 3, Bradley Rettler considers the notion of truthmaking and the corresponding truthmaker principle when used in the service of positing properties. It seems that one use of the truthmaker principle implies that properties should serve as truthmakers. 3

A.R.J. Fisher and Anna-Sofia Maurin

Yet another methodological breakthrough that has impacted the metaphysics of properties and beyond is the distinction between natural and non-natural properties. Armstrong argued for a break between predicate and property such that it is not the case that for any predicate there is a corresponding property (Armstrong 1978b: 12). One motivation for this is a posteriori realism: science tells us the specifics of the kinds of entities that exist in our ontology, not language. With this break between semantics and ontology he realised that universals play certain roles in our theorising. For instance, universals account for genuine resemblance among particulars and account for the causal powers of things. He also used universals to explain the nature of a law. The law that all Fs are Gs is explained in part by the fact that the universals F and G are related by necessitation relation N (Armstrong 1983). Lewis noticed that the work that Armstrong’s universals do ‘must be done’ (Lewis 1983: 343), even if one holds fast to a nominalist theory. For Lewis, then, properties are classes of things (as per class nominalism) and universals are entities that carve nature at its joints. If universals are not admitted, natural properties are elite classes of things. Lewis’s goal was to systematise the concept of a natural property, thereby showing that the distinction is highly serviceable. If so, the distinction should be taken as real and as joint-carving. In Chapter 4, Elanor Taylor surveys the landscape of this fundamental distinction in theorising about properties, including the consideration that the distinction is, after all, not an objective one. Part 2 encompasses questions about basic concepts in debates about properties as well as key distinctions that are used to construct theories of properties. In debates about properties philosophers often use terms of art with distinct meanings from different perspectives. Words like ‘universal’, ‘abstract’, and even ‘property’ (along with ‘quality’, ‘attribute’, ‘character’, ‘kind’) do not always have the same meaning. As a result, terminology is a mess. If terminology is a mess, so too are the meanings of the concepts that answer to the terms. Hence, cleaning up some of the mess will go some way towards improving clarity on the topic of properties. In Chapter 5, Daniel Giberman explores different ways in which universals can be distinguished from particulars. He argues that it is difficult to say what makes a universal distinctive, because the standard proposals such as that only universals can be instantiated and that only universals can be multi-located are subject to counterexamples. In Chapter 6, Sam Cowling looks at the abstract/concrete distinction in a similar vein, concluding that it is difficult to find a trouble-free analysis of it. He also discusses whether a property if abstract is essentially abstract, which raises more complications for what is typically regarded as a less controversial distinction in debates about properties. In Chapter 7, Fraser MacBride discusses the existence and nature of relations. He argues that relations are genuine items in the world distinct from properties and that relations play a crucial role in explaining the fact that things in the world manifest relatedness. This leads to an investigation into focused topics on internal relations and asymmetric relations. In Chapter 8, Vera Hoffmann-Kolss addresses the distinction between intrinsic and extrinsic properties. She is concerned with finding an analysis of the distinction in terms of the notion of a natural property or the grounding relation. Her ultimate conclusion is that the intrinsic/ extrinsic distinction is hyperintensional and vague. In Chapter 9, Fabrice Correia explores leading approaches to the distinction between essential and accidental properties: the modal and the (Aristotelian) essence approach. He provides a nuanced discussion centred on the question of whether A-essential properties are M-essential, surveying reactions to the highly discussed objection (due to Kit Fine) that certain necessary properties of an 4

Introduction

object are not, intuitively, part of the essence of that object. In Chapter 10, Eric Funkhouser examines the relation between a determinable (red) and its determinates (crimson, scarlet, etc). He considers competing theories of this relation, namely, asymmetric necessitation accounts, property space or determination dimension models, and causal subset accounts. Part 3 consists of chapters on the realist answer to the nature-question: what is a property? The realist says that properties (and relations) are universals. Starting with the very old problem of universals, also known as the one over many, some headway can be made on the nature-question. Consider two lemons. Admittedly, they are two tokens of the same type. When we look around for other examples, we notice that the type/token distinction is everywhere and so cries out for explanation. A straightforward, perhaps intuitive, way to explain the distinction is to say that there are many tokens of the same type, where the type is a universal, a one over many (Armstrong 1978a: xiii). Realism comes in two main variants: transcendent (Platonic) realism and immanent (Aristotelian) realism. Part 3 presents standard motivations for transcendent and immanent realism as well as recent defences and criticisms of these variants. Chapters in this part also consider new routes to the existence of universals and new work on how universals are multiply located. In Chapter 11, Chad Carmichael discusses varieties of transcendent realism and defends the modal argument that the logical form of necessary truths indicates that there are Platonic universals. In Chapter 12, Bo R. Meinertsen focuses on immanent realism. On this view, universals are not subsistent in some abstract realm of being, but instead are wholly present in their instances. Such a view involves reference to the notion of a state of affairs. The state of affairs of a’s being F has an immanent universal as one component, inside the state of affairs, as it were. For someone like Armstrong, this universals theory is less problematic than others (such as Platonic variants) because the explanation for why a is F is in terms of internal, intrinsic components of the particular. If there are states of affairs, questions remain about how the components are united together. This leads to debates about relational and non-relational immanent realism. Meinertsen presents competing theories of immanent realism with the notion of a state of affairs in full view. In Chapter 13, Nikk Effingham analyses the ways in which a universal might be located. For any theory of universals, this question needs to be answered, especially because one reason that philosophers have given for arguing that universals cannot exist is that it is unclear how they exist. Compared to the locative behaviour of particulars, universals have an unfamiliar way of being located, but if it can be made more familiar then the realist about universals has batted away one line of criticism. In Chapter 14, Jiri Benovsky tackles theories of universals that attempt to construct a one-category ontology of universals. The traditional way to do this is to propose that a particular or a substance is a bundle (somehow) of universals. If each substance is a bundle of universals, there is no reason to posit substance as a fundamental ontological category. Instead, there is one fundamental category, namely, that of universal, and substances are built out of universals. One lingering question for this theory is how universals come together to ground the ‘substantial unity’, to use a phrase from A.E. Taylor (1946: 133), of the things familiar in ordinary experience such as that car or this chair. Part 4 is on the nominalist answer to the nature-question. Nominalism is the classic response to realism about universals. Nominalism either denies that there are properties at all (ostrich nominalism) or says that properties are classes, where a class is not a universal. There are many versions of nominalism, but nominalists are united behind the thesis that 5

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there are only particulars. A central motivation for nominalism is Ockham’s razor and the naturalist/empiricist reaction to universals. If nominalism works, it is in good stead against realism. Part 4 deals with arguments for varieties of nominalism (ostrich nominalism, class nominalism, resemblance nominalism) and arguments against these varieties, especially in light of recently regimented concepts in metaphysics such as grounding and fundamentality. In Chapter 15, Michael Devitt presents the latest reactions on behalf of the ostrich nominalist. The ostrich nominalist says that the contingent predication ‘a is F’ and also ‘a and b have something in common’ do not lead us to posit universals. The first statement does not need a truthmaker and no explanation is needed to say why a is F in any metaphysical sense. In Chapter 16, Gonzalo Rodriguez-Pereyra outlines class nominalism and resemblance nominalism in a truthmaker framework and tackles head on the coextension problem for both theories. To illustrate the class nominalist version of the problem: if properties are classes, the identity conditions of properties are reduced to the identity conditions of classes; but classes are individuated in terms of class-membership; hence, certain properties that are intuitively distinct will turn out identical. In Chapter 17, Guido Imaguire presents two new versions of nominalism: priority nominalism and grounding nominalism. He also explains how the problem of universals can be recast using the concept of grounding. In Chapter 18, Jody Azzouni looks at how the nominalist programme has fared in debates in the philosophy of mathematics. This front is pressing for the nominalist because of the traditional challenge from realists (such as Platonic realists) in this domain. The challenge, as Azzouni documents, is how the nominalist can find suitable referents for mathematical discourse, especially when mathematical terms seem to refer to abstract objects. Part 5 concerns the trope theoretic answer to the nature-question: properties are tropes. Trope theory is its own distinctive theory of properties for a number of reasons. In one respect it falls under nominalism because all the entities in trope ontologies are particulars. However, trope theorists accept the existence of properties. On the other hand, some trope theorists dislike the existence of Platonic entities (we won’t call them abstracta, because some trope theorists say that tropes are abstract). Trope theory, then, is a form of moderate nominalism. Some trope theorists say that a trope is a particular property of an object (substance-attribute version). Other trope theorists say that a trope is an abstract or thin particular that is a constituent of an object (bundle version). The bundle version is a onecategory ontology of tropes. Part 5 presents classic and recent interpretations of trope theory and discusses newer issues such as the question of whether there are conceptually distinct kinds of trope. In Chapter 19, Douglas Ehring surveys three trope nominalist theories: standard trope nominalism, resemblance trope nominalism, and natural class trope nominalism. These three theories differ with respect to how the nature of a trope is explained. For instance, resemblance trope nominalism says that a trope is what it is because it resembles other duplicate tropes, whereas for standard trope nominalism it is a primitive fact that a trope is what it is and so in virtue of its nature tropes ground facts of resemblance among tropes. Ehring argues for natural class nominalism, detailing how it overcomes obstacles that the other two trope nominalisms are stuck with. In Chapter 20, Robert K. Garcia points out that the concept of a trope admits of an important distinction between modifier tropes and module tropes. One difference between these two kinds of trope is that a module trope is self-exemplifying and a modifier trope is not. A red trope qua module is red, but a red trope 6

Introduction

qua modifier is not red. Garcia notes that modifier tropes do a great job of explaining some things (like powers and fundamental determinables) and that module tropes do a great job of explaining other things (like perception and causation). But neither kind of trope explains all these things, which detracts from the unity of trope theory and reveals explanatory limitations that the trope theorist should address. In Chapter 21, Markku Keinänen and Jani Hakkarainen survey different versions of the trope bundle theory of substance. Paradigmatic trope bundle theorists claim that a substance is a sum of concurring tropes contingently united in the same spacetime region. More recent trope bundle theories move away from this approach and speculate that certain tropes of some bundle must be specifically related to each other, which means that these tropes are interdependent in some modally rigid way. In Chapter 22, Anna-Sofia Maurin investigates the nature and existence of trope-relations. Among other things, she argues that to be able to handle the challenge from Bradley’s regress, relations (not just the relations posited by the trope theorist) ought plausibly to be understood as relata-specific and that relata-specific relations ought plausibly to be understood as tropes. That there are relations, she concludes, is itself a reason to be a trope theorist. Part 6 indicates the halfway mark in the volume. After examining the nature of properties, the volume turns its focus to properties in a wide variety of explanatory contexts. The remaining parts of the volume can be seen as addressing the use-question: what work can properties do and how? Part 6 investigates the role of properties in causation, time, and modality. In Chapter 23, Carolina Sartorio considers the extent to which properties figure in debates about causation, showing how properties impact answers to central questions in current conversations about causation, particularly about token causation. In Chapter 24, Jennifer McKitrick turns to dispositions, which are often thought of as ways that objects are disposed to behave in certain circumstances. One debate surveyed by McKitrick is whether dispositions are reducible to other properties such as categorical properties or whether dispositions are irreducible and so make up a distinct kind of property. She also considers the possibility that there is room for a mixed view such that some but not all dispositions are reducible. In Chapter 25, Carlo Rossi discusses the role that properties play in theories of events and processes. A well-known theory of events due to Jaegwon Kim proposes that an event is a property-instantiation at a time, which clearly gives properties the role of being one constituent of an event. Lesser known theories of events and processes stemming from Helen Steward and Rowland Stout as well as Johanna Seibt also find ways to utilise properties. Indeed, on Seibt’s theory, a process is best thought of as a determinable, so a process might be more like a universal than a particular. In Chapter 26, Katarina Perović addresses the connection between properties and time, with a focus on the problem of change. The paradigm understanding of a thing changing over time is of a thing that has a property at a time and then lacks that property at another time (the problem of temporary intrinsics). The two times in this example are often understood as instants and a thing conceived over time (whether changing or not) is understood as a thing composed of instantaneous slices. Hence, the relevant properties involved in explaining change are temporally instantaneous. Perović provides an analysis of the orthodox way of understanding the problem of temporary intrinsics against the backdrop of endurantism and perdurantism. She also alludes to an alternative way of understanding the problem by recasting the issue in terms of properties that extend over time as opposed to being at a time. Properties on this picture are not instantaneous but are rather temporally extended. In Chapter 27, Peter Forrest revisits the question of explaining 7

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modality and possibilia in terms of properties. In debates about the metaphysics of modality one competing theory to Lewis’s modal realism lets properties play the role of possible worlds. For Forrest, the thesis that worlds are properties needs unpacking and has its own challenges such as explaining the possibility of infinite complexity. In Chapter 28, Barbara Vetter continues with the theme of modality but from the perspective of someone who believes in dispositional properties or powers. Like Forrest, Vetter hopes to construct a theory of modality that only commits to actual entities and avoids merely possible objects. She proposes that if there are potentialities/powers/dispositions, they can be used to explain modality or possibilia. In Part 7, properties are shown to be relevant to science and the philosophy of science in a number of important ways. In Chapter 29, Alexander Bird considers how properties are related to the topic of natural kinds. According to E.J. Lowe’s ontology, natural kinds are sui generis and so distinct from properties or universals. Bird argues that natural kinds are better off being reductively identified with complex properties, and, in particular, with complex universals. This is a metaphysics of natural kinds that has properties at its centre. In Chapter 30, Tuomas E. Tahko surveys laws of nature in relation to properties, outlining the leading ways in which properties are used to construct theories about the laws of nature. One starting point is that a law such as all Fs are Gs expresses a connection (of some necessity) between universals, namely, being F and being G. He notes that different theories of properties impact the modal status of laws, whether laws are metaphysically necessary or just nomologically necessary. In Chapter 31, Anne Sophie Meincke traces a history of the concept of an emergent property, finding the source of today’s concept in British Emergentism of the early twentieth century. She goes on to argue that the more promising account of emergent properties involves some reference to processes. In Chapter 32, J.E. Wolff answers the question ‘what are quantitative properties?’, asserting that what makes a property quantitative (such as the mass of Jupiter) involves relational structures that are characterised by pairs of relations. This proposal is motivated in part by a representational theory of measuring quantities. Part 8 is about the role that properties play in the philosophy of language and philosophy of mind. Many philosophers have noted that properties can serve as the semantic values of terms or serve as the meanings of whole sentences. This is caught up in an ongoing debate about how natural language can be systematised using properties and how language embodies talk of abstract objects (if at all). In the philosophy of mind, a theory of properties underpins the notion of a mental property and grounds an explanation of the causal efficacy of mental properties (mental causation). Recently, philosophers have reflected on the very notion of a mental property in contrast to physical properties and how this impacts the best characterisations of what it is like to have an experience (qualia). Lastly, philosophers have studied the role of properties in perception, raising the question of whether and how properties are perceived in experience and the question of how properties can be used to flesh out theories of perception. Part 8 deals with these topics and questions. In Chapter 33, Friederike Moltmann gives a thorough linguistic analysis of places in the English language where there is explicit reference to properties. Her approach falls within descriptive metaphysics applied to intuitions that are found by using the latest methods in semantics and syntactic theory. She offers a wide range of examples that lend support to the idea that there are kinds of sentences that include quality-terms, explicit property-referring terms, etc. In certain cases, the sentence in question suggests a reference to a specific kind of property. The sentence ‘Socrates’ wisdom’ contains a trope-referring term, on her view. In 8

Introduction

Chapter 34, David Robb surveys the debate about mental causation against the backdrop of competing theories of properties. He reasons through ways in which a mental property, according to functionalism, is a second-order property and considers the question of whether second-order properties are causally efficacious, especially when it looks like firstorder properties undermine the efficacy of second-order properties. After discussing one way to overcome this problem Robb considers whether mental properties are in fact firstorder properties, which requires (he says) a trope theory of properties in order to explain their causal efficacy. In Chapter 35, Umut Baysan turns to the fact that, for certain mental states, there is something it is like to have those mental states. When a mental state is phenomenally conscious it is said to have a quale such that the quale is the relevant property for the fact that there is something it is like to have that experience. Baysan’s proposal is that qualia as properties of experiences should be understood in a neutral way whereby the conception of qualia comes with minimal commitments. In Chapter 36, Bence Nanay addresses four central questions that crop up when one thinks about properties in perception. When Edith sees a lemon what is the range of properties that she attributes to it perceptually? Are the properties represented tropes or universals? Are the properties determinates or determinables? Is there a subject involved in the representation to which the properties represented are applied? The many answers to these questions show the extent to which debates in perception involve theorising about properties. Part 9 covers the moral, social, and aesthetic aspects of reality, with an emphasis on how properties play a role in theorising about those things. In Chapter 37, Matti Eklund addresses the question of what exactly characterises a normative property, where the word ‘normative’ covers moral properties and other evaluative properties. To address this question Eklund looks at the place of the nominalist in this debate and how concepts should be connected with properties in the normative domain. Perhaps, there are normative concepts only. He assesses various accounts of what a normative property is. One account highlighted throughout his chapter is that some property P is normative just when some agent A knows that the property ascription P of x ought to motivate A in a certain way to promote x being P. Another suggestion is to pick out the playing of normative roles such that the reference of a normative concept is determined by the normative role. In Chapter 38, Caj Strandberg discusses the less general case of moral properties and asks similar questions about whether there are moral properties and what they are like. These questions send us into debates about moral realism versus moral anti-realism, naturalism versus non-naturalism, and reductionism versus non-reductionism. He stresses that realism about moral properties comes with the intuition that morality is not arbitrary. Covering the terrain on the many varieties of naturalism and non-naturalism goes a long way in showing how an action may or may not have the property of being right, especially in light of the action-guiding function of morality that stems from the reasons and motivations given for an agent to act. In Chapter 39, Dee Payton turns to the social domain and asks how a social property is to be characterised. The property of being a US one dollar bill is a social property. It appears different in kind from a property like being negatively charged, but what is this difference exactly? Her survey of the leading answers to these questions brings in cutting edge tools in metaphysics such as grounding and an essence-based approach to metaphysical analysis. One upshot is that social properties have earned the sort of attention that more traditional categories of property have received in other areas of philosophy. In Chapter 40, Sonia Sedivy considers aesthetic properties such as the cacophony of Shostakovich’s War Symphony. The literature agrees that many aesthetic 9

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properties are observable and that aesthetic properties contribute to the aesthetic value of the object. But there are various points of disagreement and open questions about other ways to conceive of aesthetic properties and other work (if any) they do in aesthetics. This bleeds into what aesthetic properties amount to: do they merely depend on non-aesthetic properties? Are attributions of aesthetic properties purely subjective? In addition to a discussion of the debate between realists and non-realists about aesthetic properties, Sedivy argues that heterogeneity and historical dependence are two important features of aesthetic properties, which boost the explanatory power of aesthetic properties. These properties, like others in other domains of inquiry traversed in previous chapters, have an important place in our theorising about the world and what it is like, which again, to sum up, shows how important properties really are.

References Armstrong, D.M. (1978a) Universals and Scientific Realism I: Nominalism and Realism. Cambridge: Cambridge University Press. Armstrong, D.M. (1978b) Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press. Armstrong, D.M. (1983) What Is a Law of Nature? Cambridge: Cambridge University Press. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (2004) Truth and Truthmakers. Cambridge: Cambridge University Press. Bradley, F.H. (1893) Appearance and Reality: A Metaphysical Essay. London: Allen and Unwin. de Laguna, G. (1951) Speculative Philosophy. Philosophical Review 60(1): 3–19. Henninger, M. (1989) Relations: Medieval Theories 1250-1325. Oxford: Clarendon Press. Knight, H. (1936) Stout on Universals. Mind 45(177): 45–60. Kumar, P. (1997) The “Nyāya-Vaiśeṣika” and the Buddhist Controversy over the Problem of Universals. East and West 47(1/4): 95–104. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Loux, M. (ed.) (1970) Universals and Particulars: Readings in Ontology. New York: Doubleday. Montague, W.P. (1940) The Ways of Things: A Philosophy of Knowledge, Nature, and Value. New York: Prentice-Hall. Quine, W.V. (1948) On What There Is. Review of Metaphysics 2(5): 21–38. Ross, J.F. (1962) Suarez on “Universals”. Journal of Philosophy 59(23): 736–748. Russell, B. (1912) The Problems of Philosophy. London: Williams and Norgate. Russell, B. (1940) An Inquiry into Meaning and Truth. London: Allen and Unwin. Spade, P. (1994) Five Texts on the Mediaeval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham. Indianapolis, IN: Hackett. Stout, G.F. (1921) The Nature of Universals and Propositions. London: British Academy. Stout, G.F. (1936) Universals Again. Aristotelian Society Supplementary Volume 15: 1–15. Swoyer, C. (1999) How Ontology Might Be Possible: Explanation and Inference in Metaphysics. Midwest Studies in Philosophy 23: 100–131. Taylor, A.E. (1946) Elements of Metaphysics. 12th Ed. London: Methuen. Weinberg, J. (1965) Abstraction, Relation, and Induction. Madison, WI: University of Wisconsin Press. Williams, D.C. (1953a) On the Elements of Being: I. Review of Metaphysics 7(1): 3–18. Reprinted in (2018) The Elements and Patterns of Being: Essays in Metaphysics, ed. A.R.J. Fisher. Oxford: Oxford University Press: 24-50. Williams, D.C. (1953b) On the Elements of Being: II. Review of Metaphysics 7(2): 171–192. Reprinted in (2018) The Elements and Patterns of Being: Essays in Metaphysics, ed. A.R.J. Fisher. Oxford: Oxford University Press: 24-50.

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PART 1

Methodology and Metaontology

1 QUANTIFICATION AND ONTOLOGICAL COMMITMENT Nicholas K. Jones

1.1 Introduction Ontology is the discipline that investigates certain highly general questions about the nature and structure of reality. Although any attempt to make this precise will inevitably be controversial, one central such question is: Ontological Question What does reality contain? Here is a two-step method for addressing this question. First, select some view(s) that one holds; e.g. the view that Tibbles is a cat. Second, figure out what the truth of the view(s) requires reality to contain; e.g. the truth of the view that Tibbles is a cat plausibly requires reality to contain the particular cat Tibbles.1 One now has a partial answer to the Ontological Question: reality contains the particular cat Tibbles. A fuller, less partial answer is obtained by applying the method to more of one’s views. Although this isn’t the only ontological method one might employ, it is both natural and popular. The method uses one’s views about other matters to inform one’s ontological views. One might thereby hope to avoid the worst excesses of unconstrained ontological speculation: “ontology the progressive research program (not to be confused with ontology the swapping of hunches about what exists)” (Yablo 1998: 229). Application of this method requires answers to two further questions, which animate my discussion below. First: Metaontological Question What is it for reality to contain something?2 Alternatively put: what is the Ontological Question about? To state the second question, let the ontological commitments of a view be what that view’s truth requires reality to contain. Then the second question is: Commitment Question What are the ontological commitments of a view?

DOI: 10.4324/9781003246077-3

13

Nicholas K. Jones

Contemporary discussion of this second question was largely initiated by W.V. Quine (1948). I discuss Quine’s answer in the next section. The Commitment Question is central not just to our two-step ontological method, but to any ontological method whatsoever. To see why, consider an arbitrary answer to the Ontological Question; e.g. reality contains cats. Now consider two rival (partial) answers to the Commitment Question. According to one, the view that reality contains cats is ontologically committed to individuals that are cats. According to the other, the view that reality contains cats is ontologically committed only to pluralities of mereological atoms in a certain complex configuration (van Inwagen 1990). These different answers to the Commitment Question convert our initial answer to the Ontological Question into two different answers. Every ontological method thus requires an answer to the Commitment Question. I have discussed the ontological commitments of views, using “view” neutrally for the bearers of ontological commitment. Let’s be clearer about what those bearers are. Candidate bearers of ontological commitment most prominently include: interpreted sentences, theories (understood as sets of interpreted sentences), utterances, statements, assertions, propositions, truth-conditions, beliefs, and speakers or theorists (i.e. people). It is often convenient to focus on sentences and theories, aiming to capture the ontological commitments of non-sentences via appropriately chosen sentences; e.g. the ontological commitments of a belief may be captured via sentences that express the belief; or the ontological commitments of people may be captured via sentences expressing their beliefs. Although it is often convenient to focus on sentences, the primary bearers of ontological commitment are not sentences themselves but the propositions or truth-conditions those sentences express. (I henceforth use “proposition” for both propositions and truthconditions.) For if the truth of a sentence requires reality to contain something, then it does so because of what the sentence says about reality; and what it says about reality is a proposition, which might also be expressed by a different sentence, or asserted, believed, denied, and so on. Our primary topic is thus the ontological commitments of propositions, irrespective of the parochial linguistic guise under which they are expressed. I do, however, discuss the commitments of both propositions and sentences below, bearing in mind that our primary topic concerns propositions. Let’s connect this with properties. One central, traditional component of the theoretical role for properties is to be what predicates express, denote, ascribe, or otherwise correspond to: properties are the ontological correlates of predicates. The existence of properties understood as occupants of this role follows from a positive answer to: Predicate Question Are predicates a distinctive source of ontological commitment? Note, however, that a negative answer does not preclude the existence of properties because they might occupy some other component of the property-role instead. The rest of this chapter discusses four answers to the Metaontological Question alongside corresponding answers to the Commitment Question, and examines their consequences for the existence of properties via the Predicate Question. An influential Quinean paradigm provides our first answer to the Metaontological Question: what reality contains is what there is. It would be hard to overstate the influence of this paradigm throughout metaphysics over the last seventy years. Insofar as there is orthodoxy about metaontology and ontological commitment, the Quinean paradigm is it. We will see that this paradigm naturally but not inevitably yields a negative answer to the Predicate Question. 14

Quantification and Ontological Commitment

Our remaining three answers to the Metaontological Question correspond to the most prominent departures from the Quinean paradigm. Our first answer employs a primitive, non-quantificational notion of existence and says: what reality contains is what exists. The Predicate Question then continues to receive a negative answer. Our second answer employs a notion of fundamentality and says: what reality contains is what’s fundamental. This leaves the Predicate Question wide open. Our final answer employs many irreducibly different forms of (higher-order) quantification and says: although what reality contains is what there is, “what there is” is ambiguous, with corresponding ambiguity in “reality” too. The Predicate Question receives a positive answer on many disambiguations.

1.2 A Quinean Paradigm Quine’s account of ontological commitment is driven by his answer to the Metaontological Question (Quine 1948: 1): Quinean Metaontology What reality contains is what there is. Quine understands “there is” here as the unrestricted existential quantifier “∃x” of firstorder logic, i.e. the quantificational logic taught in typical introductory logic courses. His discussion of ontological commitment focusses on the commitments of interpreted sentences of first-order logic, not propositions. Let’s follow Quine’s focus initially. Given Quinean Metaontology, the ontological commitments of a sentence will be what the sentence’s truth requires there to be. Quine identifies what the sentence’s truth requires there to be with what the domain of quantification needs to contain for the sentence to be true. Hence: Quinean Sentential Commitment The ontological commitments of a first-order sentence are what the domain of quantification needs to contain for the sentence to be true. This can be precisified in several ways (Bricker 2016; Rayo 2007). A theory of domains and truth is also required; any textbook version of post-Tarskian model-theoretic semantics would capture Quine’s intention. Further details aren’t necessary here. Quinean Sentential Commitment concerns the commitments of interpreted sentences of a specific kind of formal language. The commitments of sentences of other languages, including natural languages, are obtained by regimenting them into the appropriate kind of formal language. To see how Quinean Sentential Commitment works, consider a first-order sentence “Ct” where “C” regiments “is a cat”, “t” regiments “Tibbles”, and so the whole sentence regiments “Tibbles is a cat”. For “Ct” to be true, the domain of quantification needs to contain the denotation of “t”, which is Tibbles. So “Ct” is ontologically committed to Tibbles. The denotation of “t” also needs to satisfy the predicate “C” and must therefore be a cat. So “Ct” is also ontologically committed to there being at least one cat. By contrast, standard model-theoretic semantics does not require the domain to contain entities like the fact that Tibbles is a cat, or the state of Tibbles’s being a cat, or the proposition that Tibbles is a cat. So “Ct” is not ontologically committed to such entities. The Predicate Question arguably receives a negative answer under the Quinean paradigm: predicates are not a distinctive source of ontological commitment. For “Ct” to be true, 15

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standard model-theoretic semantics does not require the predicate “C” to denote an entity in the domain. It requires only that the denotation of “t” satisfy “C”, which does not require a further denotation for “C” itself in the domain.3 Quinean Sentential Commitment thus entails that predicates are not a distinctive source of ontological commitment.4 This is a central point of Quine’s (1948). It does not follow that predicates make no contribution to ontological commitment. According to Quinean Sentential Commitment, “Ct” is committed to there being at least one cat. “Ct” has this commitment partly because of what the predicate “C” means: only cats satisfy it. If “C” had meant something different, “Ct” would have had different commitments; e.g. if only dogs had satisfied “C”, then “Ct” would have been committed to there being at least one dog. One might seek a positive answer to the Predicate Question by introducing a nominalising device, which converts predicates like “C” or “is a cat” into property-names like “being a cat”. Since names require denotations in the domain, this would yield a property in the domain corresponding to each predicate. There is a real danger of inconsistency here via Russell’s paradox. Moreover, the Predicate Question still receives a negative answer. For commitment to properties arises not from predicates themselves but from their nominalisations. Removing the nominalising device removes the commitment to properties while the predicates remain. Let’s turn from sentences to propositions. This will yield a more complex perspective on the Predicate Question. Recall that the commitments of natural language are obtained by regimenting into a first-order language. Extending this idea to propositions gives the following answer to the Commitment Question: Quinean Propositional Commitment If some first-order sentence expressing a proposition p has an ontological commitment, then p has that commitment too; p has no other commitments. A variant view says that the ontological commitments of p are the commitments common to all first-order sentences expressing p. Since every proposition is expressible by a simple sentence letter, this threatens triviality: no proposition would have any ontological commitments. I therefore focus on Quinean Propositional Commitment, although parallel points apply to the variant view too.5 Quinean Propositional Commitment entangles ontological commitment with more general metaphysical questions about propositional identity; see Agustín Rayo (2007) for related discussion, and Rayo (2013: ch. 1) and Cian Dorr (2016) for the operative notion of propositional identity. For example, consider the first-order sentence: (1) Ct Here, “C” regiments “is a cat” and “t” regiments “Tibbles”. So (1) expresses the proposition: (1p) that Tibbles is a cat Consider also the first-order sentence: 16

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(2) Itc Here, “I” regiments “instantiates”, “t” regiments “Tibbles”, and “c” regiments the property-name “being a cat”. So (2) expresses the proposition: (2p) that Tibbles instantiates being a cat What are the ontological commitments of (1p)? Given Quinean Propositional Commitment, it depends whether (1) and (2) express the same proposition, i.e. whether (1p) is identical to (2p). By Quinean Sentential Commitment, (2) is committed to the property being a cat. Since (2) expresses (2p), it follows from Quinean Propositional Commitment that (2p) is committed to that property too. So (1p) is also committed to that property, if (1) expresses the same proposition as (2), i.e. if (1p) is identical to (2p). This identity follows from the popular view that necessarily equivalent propositions are identical (under natural assumptions about the existence of properties and modal behaviour of instantiation). Assuming this also holds for other typical predications, we now have a positive answer to the Predicate Question. By contrast, Quinean Propositional Commitment does not entail that (1p) is committed to being a cat, if (1) and (2) express different propositions, i.e. if (1p) is distinct from (2p). This distinctness follows from the popular view that propositions have a unique intrinsic structure analogous to the structure of sentences expressing them. This blocks the preceding argument for a positive answer to the Predicate Question. We’ve seen how Quinean Propositional Commitment entangles ontological commitment with propositional identity, and thereby with metaphysics more generally: it is not a metaphysically neutral arbiter of ontological commitment. We’ve also seen how this entanglement affects how Quineans should answer the Predicate Question. One might try to avoid entanglement by focusing on sentences instead of propositions. Yet entanglement will remain, for two reasons. First, Quinean Sentential Commitment requires a background semantic theory of domains and truth. This entangles the commitments of sentences now with semantics as well as the metaphysics of domains and truth. Following Quine, I assumed that predicates need not have denotations in the domain of quantification. But that could be contested, making predicates a distinctive source of ontological commitment. Second, recall that propositions are the primary bearers of ontological commitment and sentences have commitments because of what propositions they express. Sentences expressing the same proposition should plausibly therefore have the same commitments. This entangles the commitments of sentences too with propositional identity, contrary to Quinean Sentential Commitment.

1.3 Existence Under the Quinean paradigm, quantification cannot go beyond what reality contains. Our first departure from the paradigm rejects that assumption. A primitive notion of existence is employed to consistently say that some things exist, whereas some other things don’t. Putative non-existents include unicorns, ancient gods, Sherlock Holmes, hobbits, round squares, and largest prime numbers. This primitive notion of existence is used to answer the Metaontological Question thus: 17

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Existential Metaontology What reality contains is what exists. Notable developments of this Meinongian view have been proposed by Terence Parsons (1980), Graham Priest (2005), and Edward Zalta (1988), amongst others. This answer to the Metaontological Question delivers the following answer to the Commitment Question: Existential Propositional Commitment The ontological commitments of a proposition are whatever the proposition’s truth requires to exist. What exactly does a proposition’s truth require to exist? Does the truth of that Tibbles is a cat require Tibbles to exist, or might she instead be non-existent? One way to make progress is to follow Quine’s focus on sentences of a first-order language. We depart from Quine by enriching the language with a primitive existence predicate and a second existential quantifier: the familiar “∃” for a committal quantifier restricted to existents and “Σ” for a neutral quantifier free from restriction. The following modification of Quinean Sentential Commitment is then natural: Existential Sentential Commitment The ontological commitments of a first-order sentence are whatever must satisfy the existence predicate for the sentence to be true; which is exactly what the domain of the committal quantifier needs to contain for the sentence to be true. Like Quinean Sentential Commitment, this could be made precise in various ways and requires a background theory of domains, satisfaction, and truth. The Quinean paradigm’s complex relationship between propositional and sentential commitment carries over too, alongside the entanglement of ontological commitment with metaphysics and semantics more generally. The Quinean case for a negative answer to the Predicate Question carries over to Existential Sentential Commitment (as do the complexities surrounding that answer highlighted at the end of the last section). In fact, the case is stronger since even names can fail to generate ontological commitment. The truth of “Ct” requires that “t” have a denotation, i.e. Tibbles, in the domain of quantification; but Tibbles may belong only to the domain of neutral quantification not the domain of committal quantification, and she need not satisfy the existence predicate.6 Nominalism is the view that reality contains no properties. The present setting permits two forms of nominalism. The weaker form is committal nominalism: there (committally) are no properties, properties do not exist, and yet there (neutrally) are properties. The stronger form is neutral nominalism: there (neutrally and committally) are no properties. It is an interesting open question whether mere committal nominalism could accommodate the motivations of traditional nominalists while nonetheless providing (non-existent) properties doing much of the theoretical work that properties normally do. I close with a problem for the present setting: it departs merely terminologically from the Quinean paradigm (cf. Lewis 1990). First, the Quinean quantifier “∃” was not intended as a restricted quantifier. It therefore corresponds to the neutral quantifier not the restricted committal quantifier. Second, whatever distinction is marked by the primitive existence

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predicate, the Quinean can accept it. Quineans won’t call that distinction “existence” but can accept it as a genuine distinction. Both paradigms may therefore distinguish two questions: What (neutrally, unrestrictedly) is there? What exists, i.e. what (committally, restrictedly) is there? The paradigms differ only over which question is “really” the Ontological Question. Yet that’s a merely terminological difference. Both paradigms can incorporate the coherence of both questions and the same relationships between them.

1.4

Fundamentality

Our second departure from the Quinean paradigm begins with a hierarchical conception of reality on which some aspects of reality generate others, e.g. Tibbles and her movements are generated by the activities of the particles from which she is composed; your consciousness is generated by your neural configuration; facts about societies are generated by interactions between members of the society. The fundamental is whatever comprises the base of this hierarchy, and so generates all else. The operative notion of generation can be articulated in various ways, notably via ground (Fine 2012; Rosen 2010; Schaffer 2009), truthmaking (Armstrong 2009), naturalness (Lewis 1983), and structure (Sider 2011). Differences between these articulations won’t matter here; Nicholas Jones (2023) discusses one important such difference. This hierarchical conception of reality is naturally paired with a conception of ontology as centrally concerned with the fundamental. This suggests the following answer to the Metaontological Question: Fundamental Metaontology What reality contains is what’s fundamental. Again, there is a danger of merely terminological departure from the Quinean paradigm. The Quinean paradigm can incorporate the ideology of fundamentality and generation (although Quine himself would reject them). Two questions can thus be distinguished within both paradigms: What is there? What’s fundamental? It’s merely terminological which we call the Ontological Question. However, the ideology of fundamentality and generation brings theoretical commitment which the original Quinean paradigm lacks. Since the fundamental generates all else, each hypothesis about what’s fundamental brings a commitment to say how the generation goes: how, at least in outline, are various specific phenomena generated from the hypothesised fundamentalia? This commitment constitutes a non-terminological departure from the Quinean paradigm.

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Alongside Fundamental Ontology, we have a corresponding answer to the Commitment Question: Fundamental Commitment The ontological commitments of a proposition are whatever fundamentalia are needed to generate its truth. How to address this question? One option follows the strategy of the previous section. First, switch focus from propositions to sentences of a language containing vocabulary for fundamentality and generation. Second, investigate what the predicate “is fundamental” needs to apply to for the sentences to be true. On this approach, only sentences explicitly mentioning fundamentality possess ontological commitment. But since the non-fundamental is all generated from the fundamental, even sentences not mentioning fundamentality should be committed to the fundamentalia needed to generate their truth. Moreover, those fundamentalia may be very different from anything mentioned explicitly in the sentence. A different approach is therefore needed. The only obvious candidate is the usual method of metaphysical theorising. We formulate hypotheses about what’s fundamental and how it generates other phenomena. Then we investigate how those hypotheses cohere with our other views and compare against alternatives. The upshot is that Fundamental Commitment further entangles ontological commitment with metaphysics more generally: investigation of ontological commitment becomes a thoroughgoingly metaphysical investigation. One natural concern is that this slides away from ontology the progressive research programme, towards ontology the swapping of hunches about what’s fundamental. Optimistically, the concern is alleviated by detailed and rigorous formulation and evaluation of hypotheses about how the fundamental generates all else. Pessimistically, we may as well investigate how many angels can dance on the head of a pin. The Predicate Question is wide open under this paradigm. There is no consensus whether the best theoretical package includes ontological correlates of (at least some) predicates amongst the fundamentalia. Ontological commitment itself cannot provide independent guidance because ontological commitment has been subsumed under metaphysical theory-choice more generally. That said, Fundamental Commitment makes positive answers to the Predicate Question dangerous because they readily induce Bradleyan regress. Suppose that ordinary predication propositions R(a1, … ,an) are ontologically committed to properties. By Fundamental Commitment, properties are needed to generate the truth of those propositions. The precise method of generation is presumably that a1, … , an instantiate the property of being R, i.e.: Regression R(a1, … , an) is generated by a1 …an instantiating the relation being R, i.e. by In(being R, a1, … , an).7 Now consider an arbitrary true predication proposition F(a) and reason thus: 1 2 3 4

F(a) F(a) is generated by I1(being F, a) I1(being F, a) is generated by I2(being I1, being F, a) I2(being I1, being F, a) is generated by I3(being I2, being I1, being F, a)

⋮

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This yields an infinite “descending” chain of generation: F(a) is generated by I1(being F, a), which is generated by I2(being I1, being F, a), which is generated by … Later stages follow from their immediate predecessors by application of Regression. Fundamental Commitment and a positive answer to the Predicate Question jointly entail Regression, and thereby deliver infinite regress. How should we respond to this regress? I can only indicate the most prominent options here. First, adopt a negative answer to the Predicate Question. Second, restrict a positive answer to only certain privileged predications, excluding instantiation-propositions. Third, simply accept infinite “descending” chains of generation. Fourth, identify later stages with their predecessors and accept cyclical generation. For more on Bradleyan regresses, see Katarina Perović (2017) and Chapters 7 and 22, this volume.

1.5 Higher-Order Our final departure from the Quinean paradigm rejects Quine’s dogma that genuine (nonsubstitutional) quantification is always first-order quantification. In first-order languages, quantification is expressed by taking a sentence, replacing names with variables, and binding those variables with quantifiers; e.g. “¬Fa” yields only “∃x¬Fx”. This is first-order quantification. In higher-order languages, other kinds of expressions can also be replaced by variables and bound by quantifiers; e.g. “¬Fa” yields “∃X¬Xa”, “∃p¬p”, “∃Y(Y(Fa))”, “∃Y∃p(Yp)”, and “∃Y∃X∃x(Y(Xx))”. This is higher-order quantification. Quine held that higher-order quantification must be understood in terms of first-order quantification; e.g. “∃X(Xa)” means something like “a is a member of some set” or “a instantiates some property”. As is now widely recognised, there is little argumentative support for this dogma. We can instead permit variables of each syntactic category and quantifiers that bind them. This departure from the Quinean paradigm admits many primitive and irreducibly different forms of higher-order quantification. There are strong metaphysical reasons to embrace this apparatus. For an example, consider Saul Kripke’s (1980: 99) thesis that metaphysical necessity is necessity in the highest degree: the necessity of higher degree than every other necessity. This thesis quantifies over necessities. Since necessity is usually expressed by a monadic sentential operator, Kripke’s thesis is most naturally expressed using higher-order quantification into the position of such operators. For more on the metaphysical motivations and applications of higher-order quantification, see (Fritz and Jones forthcoming; Jones 2018; Prior 1971; Trueman 2021; Williamson 2013). Let’s assume for simplicity that higher-order quantifiers are linearly ordered: first-order, second-order, third-order, … . We then have an infinite series of answers to the Metaontological Question: First-Order Metaontology What reality contains is what there (first-order) is. Second-Order Metaontology What reality contains is what there (second-order) is. ⋮

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Although one could in principle privilege just one of these as correctly answering the Metaontological Question, there is no need to do so. One may instead regard them as equally good, non-competing ways of sharpening what “the” Ontological Question is about. That question is better conceived as an infinite series of Ontological Questions: First-Order Ontology What (first-order) is there? Second-Order Ontology What (second-order) is there? ⋮ This generalises and fragments ontology. Generalises, because ontology no longer concerns only the origin of this series, what there first-order is. Fragments, because there is no longer a single Ontological Question or a single notion of reality; there is instead an infinite series of primitive and irreducible notions of reality and corresponding Ontological Questions. Note however that the fragments are tightly interlinked, since higher-order entities apply via predication to lower-order entities; e.g. as in the view that ∃X∃y(Xy), or that ∃Y∃p(Yp). Turning to ontological commitment, we have a series of notions matching our answers to the Metaontological Question: First-Order Propositional Commitment The first-order ontological commitments of a proposition are what there first-order needs to be for the proposition to be true. Second-Order Propositional Commitment The second-order ontological commitments of a proposition are what there second-order needs to be for the proposition to be true. ⋮ Likewise for sentential commitment: First-Order Sentential Commitment The first-order ontological commitments of a sentence are what the first-order domain needs to contain for the sentence to be true. Second-Order Propositional Commitment The second-order ontological commitments of a sentence are what the second-order domain needs to contain for the sentence to be true. ⋮ As in the Quinean paradigm, each of these can be made precise in several ways and a background theory of domains and truth is required. The Quinean paradigm’s complex relationship between propositional and sentential commitment, and the entanglement between ontological commitment and metaphysics more generally (especially propositional identity) also carries over to this paradigm.

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Let’s turn to the Predicate Question. This also becomes an infinite series of questions, concerning whether predicates are a distinctive source of first-order commitment, or second-order commitment, and so on. The first-order case plays out as under the Quinean paradigm. The second-order case goes differently. According to standard semantic theories for second-order languages, the truth of a predication “Fa” requires “F” to denote an entity in the second-order domain, although this entity need not be in any other domain. The corresponding Predicate Question therefore receives a positive answer: predicates are a distinctive source of second-order ontological commitment, although not of any other order of commitment. The point generalises. The predicates of first-order languages are only the first order of predicate. Their distinctive feature is that they take names in their argument positions. The distinctive feature of second-order predicates is that they take first-order predicates in their argument positions. More generally, the distinctive feature of n-order predicates is that they take (n-1)-order predicates in their argument positions (counting names as 0-order predicates). And n-order quantification is quantification into the syntactic position of (n-1)order predicates. Let “F” be an n-order predicate and “a” be an (n-1)-order predicate. According to standard semantic theories for n-order quantification, the truth of “Fa” requires “F” to denote an entity in the domain of (n+1)-order quantification, although this entity need not be in any other domain. The answers to the many different Predicate Questions can therefore be summed up as follows: Higher-Order Commitment n-order predicates are a distinctive source of (n+1)-order ontological commitment, but not of any other order of ontological commitment. Many disambiguations of the Predicate Question thereby receive a positive answer while many other disambiguations receive a negative answer. Higher-Order Commitment systematically predicts which disambiguations receive which answers. The higher-order generalisation of the Quinean paradigm is thus congenial to realism about properties. Let me close with an objection to this argument for Higher-Order Commitment, drawing on (Skiba 2021). I’ll focus on second-order quantification as representative of higher-order quantification more generally. I said that standard semantic theories for second-order quantification have the following feature: for “Fa” to be true, “F” must have a denotation in the domain of second-order quantification (where “F” is a first-order predicate). This ensures that inferences of the following form preserve truth: (B) Fa; therefore ∃X(Xa) (B) is a second-order counterpart of the following form of inference employing first-order quantification: (A) Fa; therefore ∃x(Fx) Standard semantic theories for first-order quantification require that names denote entities in the domain of first-order quantification. This ensures that inferences of form (A) preserve truth. 23

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Now, there are systems of free first-order logic in which (A) does not always preserve truth. The view that (A) always preserves truth is a substantive logico-semanticometaphysical hypothesis, a hypothesis that might be false. Likewise, there are systems of free second-order logic in which (B) does not always preserve truth. The view that (B) always preserves truth is a substantive logico-semantico-metaphysical hypothesis. And that hypothesis too might be false. If the first hypothesis is false, names are not always a distinctive source of first-order ontological commitment. And if the second hypothesis is false, predicates are not always a distinctive source of second-order ontological commitment. The premise of (A)/(B) may then be true without the first-/second-order domain containing an ontological correlate of name “a”/predicate “F”. One might conclude that the higherorder paradigm does not guarantee any positive answer to the Predicate Question; only certain specific versions of the paradigm have that guarantee. The parallel between names and predicates is instructive here. Free logic shows how names might not always generate ontological commitment. It does not follow that names never generate commitment. Although some names might lack denotation, it is not plausible that they all do. Denotationless names are the defective case, which do not connect with reality as properly functioning names do. Higher-order metaphysicians will naturally take this same view about predicates: although some might lack second-order denotation, they are the defective case which do not connect with reality as properly functioning names do. Predicates are then typically but not universally a distinctive source of higher-order ontological commitment, just as are names for first-order ontological commitment.8

Notes 1 Truth appears here only to enable generality, so we can discuss views in general, not just particular examples. Under the intended notion of truth: for the view that p to be true is for it to be that p. Other notions of truth are irrelevant to our two-step ontological method. For example, consider a correspondence notion of truth on which: for the view that p to be correspondence-true is for reality to contain a fact that p. Employing correspondence-truth in our two-step ontological method would enable a quick yet tendentious argument that reality contains facts. Correspondence-truth is therefore not employed in our two-step ontological method. 2 The Metaontological Question concerns an identification in the sense of Dorr (2016). 3 Objection: standard model-theory assigns denotations to predicates; although those denotations needn’t belong to the domain, they should count as commitments generated by predicates. Response: this conflates the commitments of sentences with the commitments of a semantic theory about those sentences. See Rayo (2007: 431). 4 This argument primarily concerns predicates of first-order formal languages. It is plausible but not trivial that English predicates are well regimented by formal predicates. If not, English predicates may yet be a distinctive source of ontological commitment. Space prevents further discussion of good regimentation here. 5 Another variant focusses on some (or all) privileged first-order sentence(s) expressing the proposition. Privileged how? Two options stand out. First, privileged by fully capturing the proposition’s intrinsic or logical structure. But it is controversial whether propositions have intrinsic structure, and whether either kind of structure could be captured by a single sentence. Second, privileged by capturing the proposition’s metaphysically fundamental structure. This is a version of Fundamental Ontology which I discuss in Section 1.4. 6 I’m assuming a positive free logic on which non-existents can satisfy atomic predicates. One might instead adopt a negative free logic on which only existents satisfy atomic predicates. This further entangles ontological commitment with more general metaphysics and semantics. 7 We can omit truth here for the reason given in note 1.

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Quantification and Ontological Commitment 8 For helpful comments and discussion, I’m grateful to Anthony Fisher, John Keller, Fraser MacBride, Anna-Sofia Maurin, Matt Parrott, Gonzalo Rodriguez-Pereyra, Elanor Taylor, and Al Wilson, as well as attendees of the Online Properties Conference organised by Anthony and AnnaSofia.

References Armstrong, D.M. (2009) Truth and Truthmakers. Cambridge: Cambridge University Press. Bricker, P. (2016) Ontological Commitment. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Winter 2016 Edition. URL = < https://plato.stanford.edu/archives/win2016/entries/ ontological-commitment/>. Dorr, C. (2016) To Be F Is to Be G. Philosophical Perspectives 30: 39–134. Fine, K. (2012) Guide to Ground. In Correia, F. and Schneider, B. (eds.) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press: 37–80. Fritz, P. and Jones, N.K. (eds.) (forthcoming) Higher-Order Metaphysics. Oxford: Oxford University Press. Jones, N.K. (2018) Nominalist Realism. Noûs 52(4): 808–835. Jones, N.K. (2023) Against Representational Levels. Philosophical Perspectives 36: 140–157. Kripke, S.A. (1980) Naming and Necessity. Cambridge, MA: Harvard University Press. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1990) Noneism or Allism? Mind 99(393): 23–31. Parsons, T. (1980) Nonexistent Objects. New Haven, CT: Yale University Press. Perović, K. (2017) Bradley’s Regress. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Winter 2017 Edition. URL = < https://plato.stanford.edu/archives/win2017/entries/bradleyregress/>. Priest, G. (2005) Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford: Clarendon Press. Prior, A.N. (1971) Objects of Thought. Oxford: Oxford University Press. Quine, W.V. (1948) On What There Is. Review of Metaphysics 2(5): 21–38. Rayo, A. (2007) Ontological Commitment. Philosophy Compass 2(3): 428–444. Rayo, A. (2013) The Construction of Logical Space. Oxford: Oxford University Press. Rosen, G. (2010) Metaphysical Dependence: Grounding and Reduction. In Hale, B. and Hoffman, A. (eds.) Modality: Metaphysics, Logic, and Epistemology. Oxford: Clarendon Press: 109–135. Schaffer, J. (2009) On What Grounds What. In Chalmers, D. et al. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Oxford University Press: 347–383. Sider, T. (2011) Writing the Book of the World. Oxford: Oxford University Press. Skiba, L. (2021) Higher-Order Metaphysics and the Tropes Versus Universals Debate. Philosophical Studies 178(9): 2805–2827. Trueman, R. (2021) Properties And Propositions: The Metaphysics of Higher-Order Logic. Cambridge: Cambridge University Press. van Inwagen, P. (1990) Material Beings. Ithaca, NY: Cornell University Press. Williamson, T. (2013) Modal Logic as Metaphysics. Oxford: Oxford University Press. Yablo, S. (1998) Does Ontology Rest on a Mistake? Proceedings of the Aristotelian Society: Supplementary Volume 72(1): 229–262. Zalta, E.N. (1988) Intensional Logic and the Metaphysics of Intentionality. Cambridge, MA: MIT Press.

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2 THE METHOD OF PARAPHRASE John A. Keller

2.1 Introduction Sometimes the truth can be misleading. According to Max Roser (2014), (A) The average mother has 2.4 kids. Even if that’s true, it’s misleading insofar as it suggests that there’s such a thing as the average mother or that anyone has 2.4 kids. A less misleading statement of that fact is (A*) The number of children divided by the number of mothers is 2.4. According to Amie Thomasson (1999), fictional characters such as Sherlock Homes are (existing) abstract entities. If that’s right, then (E) Sherlock Holmes exists is true. Even so, it’s misleading insofar as it suggests that there is or was a detective named “Sherlock Holmes” that lived in London at 221B Baker Street with his friend Watson. A less misleading statement of that truth is (E*) There is a fictional character named “Sherlock Holmes”. Such “less misleading statements” are often called paraphrases. Paraphrase is relevant to the existence of properties because there are apparently true claims that apparently entail the existence of properties. This gives us good reason to think there are properties, unless it can be plausibly argued that at least one of those appearances is misleading. In typical (perhaps all) cases, this will involve giving a paraphrase of the apparently true claims – a less misleading restatement – that plausibly doesn’t entail the existence of properties (see, e.g., Hoffman and Rosenkrantz 2003; Jackson 1977).1

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DOI: 10.4324/9781003246077-4

The Method of Paraphrase

2.2

A Quinean Argument

Metaphysics was viewed with suspicion from the time Immanuel Kant awoke from his dogmatic slumbers in the mid-eighteenth century through the heyday of positivism in the mid-twentieth. W.V. Quine rehabilitated the reputation of metaphysics by arguing that more well-regarded areas of inquiry are inextricably tied to it: that metaphysics cannot be isolated from the pursuit of truth in other domains (Quine 1948). Quine’s argument for the unavoidability of metaphysics hinged on the fact that many of our non-metaphysical theories have ontological implications, what Quine called ontological commitments.2 But Quine didn’t just note that our non-metaphysical theories have ontological commitments: he incorporated that insight into a methodology for ontology. His most important observation was that we can leverage the evidence we have for our nonmetaphysical theories to reach conclusions about ontology. Since Quine took there to be a paucity of evidence bearing directly on ontological theses, he maintained that this indirect leveraging strategy – Quinean meta-ontology as it is often called – is the best and perhaps only legitimate method for ontological inquiry. Quine’s method – or at least the neo-Quinean method utilized by contemporary Quinean metaontologists (e.g., Burgess and Rosen 2005; Lewis 1999; van Inwagen 2023) – is illustrated by the following argument: The Quinean Argument (1) Our best scientific and mathematical theories include or entail claims that apparently entail the existence of properties. E.g.: (S) Elements in the same column of the Periodic Table often share chemical properties. (M) Addition and multiplication share important mathematical properties. (2) We are justified in believing our best scientific and mathematical theories, including claims like (S) and (M). (3) Claims like (S) and (M) do entail the existence of properties. So, (4) We are justified in believing that there are properties. (5) If we are justified in believing there are properties, we are justified in rejecting nominalism. So, (6) We are justified in rejecting nominalism.3 (1) refers to our best scientific and mathematical theories. Here, “our best theories” refers to our epistemically best theories – our most warranted or belief-worthy theories – as opposed to our “best theories” in some other sense. (Crucially, it doesn’t mean our best theory in each domain: our most belief-worthy theories about some scientific domains aren’t, in fact, worthy of belief. For example, there are no theories worthy of belief about the origins of life, a famously unsettled question. (1) refers to our most belief-worthy scientific and mathematical theories overall.) (2) says that we are justified in believing our best theories. It doesn’t say that we are rationally required to accept our best theories. Just so, The Quinean Argument concludes that we are justified in rejecting nominalism, not that we are rationally required to reject nominalism. Perhaps agnosticism about or even acceptance of nominalism is also justified. That depends on how “permissive” rationality is (Schoenfield 2019).

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Of course, we are not all justified in accepting the same things. (2) shouldn’t be read as claiming that it would be rational for every person to accept our best theories. Many people don’t have evidence, even testimonial evidence, for those theories. It’s nonetheless rational for many philosophers, including many anti-nominalists, to accept them. Many philosophers are scientifically informed, and are justified in accepting our best scientific and mathematical theories, even if only on the basis of scientific and mathematical testimony. That’s all that’s required for The Quinean Argument. Of course, some philosophers are anti-realists about even our best scientific and mathematical theories. I’ll say more about anti-realism below, but the mere fact that some people, even rational and informed people, reject the premises of an argument does not render the argument unsuccessful (Keller 2017a). (3) says, roughly, that (S) and (M) have the “logical forms” that they appear to have: that they are not misleading as to their logical or metaphysical implications, and so entail the existence of properties. This is the premise to which paraphrase can most obviously be used to object, but, as we’ll see, it isn’t the only one. Sub-conclusion (4) only follows from (1)-(3) given a closure principle that says we are justified in believing the consequences (perhaps of some restricted kind K) of things we are justified in believing. It is, however, notoriously difficult to formulate substantive closure principles that are not subject to counterexample (see, e.g., Hawthorne 2005). If we had a compelling argument that (4) was false, that would undermine this step of The Quinean Argument: instead of justifying anti-nominalism, it would cast doubt on (1)-(3). I don’t think the arguments for nominalism are strong enough to turn The Quinean Argument on its head, but some nominalists may disagree (see Burgess and Rosen 2005; Liggins 2007 for related discussion).

2.3

Rejecting (1)

How might a nominalist object to The Quinean Argument? While (1) seems difficult to deny, some philosophers take delight in denying that which is difficult to deny. However, (1) really is undeniable. If our best scientific and mathematical theories had non-transparent contents – if, say, mathematical sentences expressed propositions that would be more perspicuously expressed by sentences prefaced with “if there were abstracta” or “it’s possible that” (compare Dorr 2008; Hellman 1994) – that would undermine (3), not (1). For example, if (M) expressed the conditional proposition if there were abstracta, addition and multiplication would share important mathematical properties, that wouldn’t cast doubt on (1), precisely because “if there were abstracta” is unarticulated in (M): (M) isn’t a conditional sentence. The only way for (1) to be undermined is if it were obvious that scientific and mathematical claims like (S) and (M) have nominalistically-friendly contents. That is empirically false.

2.4

Types of Paraphrase

While (1) is undeniable, (2), (3), and (5) clearly aren’t. Paraphrase plays a role in most if not all objections to those premises. But to understand the role of paraphrase in rejecting (2), (3), and (5), it is important to distinguish between two importantly different types of paraphrase. A paraphrase is a reformulation, a new sentence that is (intended to be) less misleading than the original. But there are two types of reformulation, corresponding to two ways in which something can be misleading. Some apparently true things 28

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are false, or at least inconsistent with one’s other views. Such cases call for revising paraphrases: revisions to what is said. Revising paraphrases are sentences that (are intended to) have different and presumably better contents than the originals (i.e., true ones). In general, revising paraphrases are given when one takes some apparently true (or otherwise attractive) sentence to be false, as is the case with those that deny (2), and hence (S) and (M). A paraphrase, in this sense, is a replacement sentence that expresses a similar claim as the original, has many or all of the original’s attractive features, and is true. Revising paraphrases are (intended to be) less misleading by being more accurate: by revising what is said so that it is “strictly and literally true”. Revising paraphrases should be distinguished from reconciling paraphrases. While revising paraphrases (are intended to) replace what was originally said, reconciling paraphrases (are intended to) preserve what was originally said. Their purpose is to clarify the contents (and especially the implications) of the originals, so as to show that the original claims do not need to be revised. Reconciling paraphrases are given when one takes some sentence to be true, but misleading as to its implications. The paraphrase is intended to clarify those implications. (Recall (A) and (A*).) Reconciling paraphrases are given by those that reject (3): those who accept (S) and (M) but don’t think that they entail the existence of properties. Reconciling paraphrases are (intended to be) less misleading in the sense of being more perspicuous than the originals: by being more transparent vis-à-vis their implications. To illustrate this distinction, consider a contemporary classic of the “nominalistic paraphrase” genera, Cian Dorr’s (2008) proposal that claims apparently referring to abstract entities like (S) and (M) should be paraphrased as (S*) If there were abstracta, elements in the same column of the Periodic Table would often share chemical properties. (M*) If there were abstracta, addition and multiplication would share important mathematical properties. One might propose (S*) and (M*) as revising paraphrases of (S) and (M): as replacement sentences expressing nominalistically-acceptable claims. Dorr’s proposal is sometimes viewed in this light (see, e.g., Himelright 2020).4 However, it’s not clear that that was Dorr’s intention. He says, The superficial way of talking about numbers, properties, relations and sets is very useful … sentences get to be true or false taken superficially in virtue of what there is in the fundamental sense, and what it is like. Thus, each English sentence must have a “paraphrase”: a sentence that, when taken in the fundamental sense, says how things would have to be for the original sentence to be true in the superficial sense. (Dorr 2008: 36) On the one hand, Dorr talks about sentences like (S) and (M) being “useful”. Since useful claims are often contrasted with true ones, that might suggest that his paraphrases are revising. On the other hand, Dorr talks about such sentences being “true or false taken superficially”. If “superficial truth” is a kind of truth, that suggests that statements like (S*) and (M*) are reconciling paraphrases: statements that, if not synonymous with (S) and (M), 29

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are true in the same worlds as (S) and (M).5 If that’s correct, they show that (S) and (M) are consistent with nominalism, given that (S*) and (M*) are. (If A is consistent with B, and C is true in the same worlds as A, then C is consistent with B.) Of course, there’s no oracle that tells us when sentences express claims that are true in the same worlds. But if, for all we know, (S*) and (M*) are true in the same worlds as (S) and (M), and if, for all we know, (S*) and (M*) are more perspicuous than (S) and (M), then, for all we know, premise (3) of The Quinean Argument is false. (Two sentences true in the same worlds are unequally perspicuous if the membership conditions for the set of worlds where they are true is better reflected by the structure of one than of the other: e.g., (A*) is more perspicuous than (A).) Such ambiguity about how to interpret paraphrase proposals is commonplace: the distinction between revising and reconciling paraphrases is often neglected. But the “success conditions” for paraphrases of different kinds are different, and so it’s important to keep them distinct. For revising paraphrases to be successful, whoever offers them must take them to be adequate replacements of the originals, an inherently subjective matter that depends on one’s other views. For example, if the truth or falsity of nominalism is noncontingent, Dorr’s paraphrases will be inadequate given the orthodox account of counterfactual conditionals, according to which any conditional with an impossible antecedent is true. That account would render “if there were abstracta, 2+2 = 5” true, making it a manifestly inadequate replacement for “2+2 = 5”. Various authors have attempted to remedy this problem (e.g., Himelright 2020; Woodward 2010), but Dorr rejects the orthodox account of counterfactuals, and so doesn’t recognize the problem to begin with. But while adequacy judgements depend on one’s other commitments, there is a widely if not universally shared commitment: that the paraphrases do the “doxastic work” of the originals. “Doing the doxastic work” is fundamentally a matter of preserving the uncontroversially good inferences in which the originals figure. In the case of abstracta, there are many clearly “good” arguments about the concrete world in which claims (apparently) about abstracta seem to play an essential role: e.g., mathematics is useful for all sorts of practical purposes, and any nominalistic revision of mathematics must be able to preserve its usefulness in the practical domain. A successful nominalistic revising paraphrase must vindicate the calculations of bridge builders, bankers, and bakers. While this might seem to be a daunting requirement, recent work suggests that it isn’t insurmountable.6 The remaining challenge is an epistemological one: establishing that one is justified in rejecting the original theory and replacing it with the paraphrase. David Lewis said that “Mathematics is an established, going concern. Philosophy is as shaky as can be. To reject mathematics for philosophical reasons would be absurd” (1991: 58). That’s too strong: some mathematical claims might be rationally rejected on the basis of very well-supported philosophical claims. But it is – how should I put this? – unclear that nominalism is a “very well-supported philosophical claim”. Reconciling paraphrases face a different set of constraints. Successful reconciling paraphrases of (S) and (M) must show or at least make it reasonable to believe that those claims are consistent with nominalism: that they don’t actually entail the existence of properties. If there were sentences (S*) and (M*) that appeared both synonymous with (S) and (M) and consistent with nominalism, that would do the trick. (In the way that (A) and (A*) appear to be synonymous, but the latter appears consistent with the claim that nobody has 2.4 kids.) But synonymy is not required for a reconciling paraphrase to be successful: as we saw above, to argue that A is consistent with B (for all we know), all that is required is some C that is (for all we know) true in the same worlds as A and that is (for all we know) consistent with B. 30

The Method of Paraphrase

2.5

Rejecting (2)

Let us return now to The Quinean Argument. The two main ways in which a nominalist might object to (2) involve revising paraphrase. To deny (2) is to deny that we are justified in believing our best scientific and mathematical theories. But the claim that there is nothing right about such sentences beggars belief. (S) is clearly “more right” than falsehoods like (S2) Elements with English names that begin with the same letter often share chemical properties. Or, to consider a more prosaic example, (O) Orange is a property is clearly more right than (O2) Obama is a property. Even if we shouldn’t believe (S) and (O), there is something right about them, unlike (S2) and (O2). One natural thought is that the difference is that there are relevant truths in the neighborhood of (S) and (O), but not (S2) and (O2). To state those important truths would be to give revising paraphrases of (S) and (O): true replacements for truth-adjacent falsehoods. A superficially different strategy for denying (2) involves giving “correctness conditions” for (S) and (M) – conditions under which (S) and (M) are correct (as opposed to true) – rather than trying to identify substitute replacement truths (see, e.g., Båve 2015; Schindler 2021). One might question whether the correctness conditions approach involves paraphrase, but the two strategies are interchangeable. To illustrate this, consider (O) and (O2). Nominalists who deny (2) will likely think (O) entails the existence of properties, and is therefore false. Such nominalists will still want to say that (O) is better than (O2): (O2) has nothing going for it, while (O) is good enough to be assertible in most contexts: intelligent and informed people often say things like (O), and almost never say things like (O2). A nominalist might try to explain the differential goodness of (what she takes to be) falsehoods like (O) and (O2) by appeal to proximity to truth, arguing that (O), but not (O2), is close to being true. For example, she might say that there is a nearby replacement truth (revising paraphrase) for (O), but not (O2), since (perhaps) (O*) “Orange” is a predicate is true but (O2*) “Obama” is a predicate is false. Hence, what makes (O) false but good is its proximity to the (true) revising paraphrase (O*). That is the “revising paraphrase approach”. On a “correctness conditions approach” to explaining the differential goodness of (O) and (O2), one might argue that what makes (O)

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better than (O2) is that (O)’s correctness conditions are satisfied whereas (O2)’s aren’t. Perhaps the correctness conditions for sentences like (O) and (O2) are something like: (CCX) “x is a property” is correct iff “x” is a predicate Then (O) is false but correct (since “Orange” is a predicate), whereas (O2) is false and incorrect (since “Obama” is not a predicate). Despite the superficial differences between these approaches to explaining the differential goodness of (O) and (O2), it seems clear that they are fundamentally equivalent: the satisfaction of (O)’s correctness condition is just the truth of the revising paraphrase (O*). Revising paraphrases thus generate correctness conditions: if (O*) is a plausible revising paraphrase of (O), (O) is correct iff (O*) is true. Conversely, correctness conditions generate revising paraphrases: if (CCO) is the correctness condition for (O), then a relevant truth in the neighborhood of (O) is that (CCO) obtains.

2.6

Rejecting (3)

While some nominalists reject our best scientific and mathematical theories in favor of nominalistically-friendly replacements, others argue that our best theories do not have the anti-nominalistic entailments they appear to have, thus denying (3) rather than (2). Any such denial will involve reconciling paraphrase, implicitly if not explicitly. For example, rather than claiming that (O*) is a truth in the neighborhood of (O), one might instead claim that (O) and (O*) express the same fact, or are true in the same worlds, and hence that (O) plausibly doesn’t entail the existence of properties after all. (If (O) and (O*) express the same fact, that leaves open whether the “logical form” of the fact they express is mirrored by (O) or (O*), or neither. But that means we don’t – absent further considerations – know whether The Quinean Argument is sound.7) This strategy appears to let the nominalist have her cake and eat it too, and has thus drawn biting criticism. Consider, first, the symmetry objection: For instance, it might be maintained that (A) “There exist prime numbers greater than a thousand” is innocent because all it really means is (A*) There could exist a prime numeral greater than a thousand. or something of the sort. There are, however, two serious difficulties with such a view. For one thing, such a nominalistic translation seems to work too well. If (A) is nominalistically acceptable because “deep down” all it means is (A*), then it would seem that (B) “There exist numbers” must be acceptable, too, because all it means is (B*) There could have been numerals. But to concede (B) (and the corresponding statement about other kinds of mathematical objects) is to concede all the antinominalist maintains. (Burgess and Rosen 2005: 524) The symmetry objection was made most famously in William P. Alston (1958), but the worry is widespread: 32

The Method of Paraphrase

The notion of paraphrase has always been caught between an aspiration to symmetry – paraphrases are supposed to match their originals along some semantic dimension – and an aspiration to the opposite – paraphrases are supposed to improve on their originals by shedding unwanted ontological commitments. (Yablo 1998: fn. 47) If paraphrase is licensed by a symmetric notion like synonymy … there will be at least some opportunities for [paraphrases to undermine themselves]. (Schaffer 2009: 370) The word “paraphrase” is misleading. Intuitively, P is a paraphrase of Q if P means the same as Q. But paraphrases in this sense are useless for our purposes. How can P and Q have the same meaning whilst only one of them is committed to a certain type of entity? (Melia 1995: fn. 1) But the notion of perspicuity – of some sentences being less misleading than others – breaks the symmetry objection (Keller 2017b). A paraphrase P and an original sentence O can both express claim C, but P can be better than O by being more perspicuous: by being such that its formal implications (or the formal implications of a straightforward regimentation of it) correspond more closely to C’s actual implications than the formal implications of O. (E.g., (A*) is more perspicuous than (A).8) Paraphrases that are symmetric or equal in meaning need not be symmetric or equal with respect to the perspicuity of their implications. And of course, as stressed above, reconciling paraphrases don’t need to be synonymous (“symmetric in meaning”) to begin with, as long as they are modally equivalent. This point is even more important when it comes to the lack of scientific evidence objection: … there is a total lack of scientific evidence in favor of any such nominalistic reconstrual as a theory of what ordinary mathematical assertions mean. Or at least, no nominalists favoring such a reconstrual have ever published their suggestions in a linguistics journal with evidence such as a linguist without ulterior ontological motives might accept. (Burgess and Rosen 2005: 525) This worry is also widespread (see, e.g., Korman 2007: 332; Kripke 1980: 65). The most important response to it is to reiterate that reconciling paraphrists aren’t, or don’t need to be, making claims about synonymy. That, by itself, explains why their arguments wouldn’t generally pass muster in a linguistics journal. Of course, some reconciling paraphrists do make claims about synonymy. Perhaps they don’t really mean to or need to, or perhaps they are thinking of content as coarse grained, such that modally equivalent propositions are synonymous. But even in cases where a paraphrist intends, upon reflection, to make claims about sameness of fine-grained content, it’s false that “ulterior ontological motives” are out of bounds when it comes to linguistics. What things mean is metaphysically constrained by what there is for things to mean: no matter what Millians say, the semantic value of “Zeus” can’t be Zeus if there’s no such thing. Linguistic theories that ignore

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metaphysical constraints are based on a nonrepresentative subset of our total evidence and may need to be rejected. If we discovered that nominalism was true, nominalistic “reconstruals” of what things mean would become more linguistically plausible. We certainly wouldn’t just throw out our scientific and mathematical theories that are prima facie nominalistically unacceptable. Rather, we’d conclude that those theories should be interpreted, ultima facie, in a nominalistically acceptable manner. The truth about linguistics depends, in part, on the truth about metaphysics (see Keller 2015). Finally, consider the conflicting projects objection: There seem in fact to be two sorts of paraphrase projects that analytic philosophers have engaged in. The first is to paraphrase English sentences in such a way that intuitively valid inferences come out, on the paraphrase, formally valid. The second is to paraphrase English sentences in such a way as to represent the truths that they express more perspicuously. How do these two sorts of projects relate to one another? The first point to note is that some sentences that tend to be viewed as harmless from the point of view of the first project are not so viewed from the second – e.g., the English sentence ‘Everyone in the room casts at least one shadow.’ Secondly, it may be that pursuing the first project will be to the detriment of the second … what a priori reason is there to expect that the first project will lend itself to the second? (O’Leary-Hawthorne and Cortens 1995: 151–152) There is much to agree with here. It’s true that making intuitively valid inferences come out formally valid isn’t guaranteed to deliver the correct “logical form” of the statement: as always, theories are underdetermined by evidence. Still, the procedure is a good guide to logical form, perhaps the best guide we have. It’s also true that logic and ontology don’t necessarily march hand in hand. But all The Quinean Argument assumes is that if a statement S implies that there are Xs, then S’s truth requires the existence of Xs. That seems pretty unobjectionable. Logic, Quineans say, is an incomplete guide to ontology. That’s controversial, but not unreasonable. The conflicting projects objection assumes that logical and metaphysical perspicuity can come apart: that the project of giving logically perspicuous paraphrases can conflict with the project of giving metaphysically perspicuous ones. But why think that? Consider: “Everyone in the room casts at least one shadow”. Assume that’s true. Now, either shadows exist or they don’t. If they do, there is no conflict between the projects: the intuitive paraphrase will quantify over shadows, but shadows exist so there’s no problem. On the other hand, if shadows don’t exist, there’s no conflict either: the intuitive paraphrase formally entails that there are shadows, and that’s false. But since truths can’t entail falsehoods, this shows that the intuitive paraphrase is inadequate. Once again, there’s no conflict between the projects.

2.7

Rejecting (5)

I defined “nominalism” as the thesis that there are no abstract entities, and properties are widely taken to be paradigmatic abstracta. Hence, (5). Of course, not everything that is widely taken to be paradigmatically X actually is: peas are widely taken to be paradigmatic vegetables, but really they’re fruits. Likewise, some nominalists argue that properties are not abstracta after all. Such objections also involve paraphrase, at least implicitly.

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The Method of Paraphrase

Some nominalists argue that properties are concrete objects of some special and abundant type, such as spacetime points. Such nominalists will plausibly have to engage in paraphrase projects that mirror those of the nominalists who deny (2) or (3). Views of this kind can be worked out in different ways, but apparent truths like “Orange is a color” will need to be paraphrased as (perhaps) something like “the orange spacetime region is a subset of the colored spacetime region”. As above, this could be offered as either a revising or reconciling paraphrase (see Chapters 5, 6, and 13, this volume, for further discussion). Alternatively, some nominalists argue that nominalism isn’t the thesis that properties don’t exist, but the thesis that properties aren’t fundamental (Dorr 2008 is the locus classicus for this view; see Chapters 3 and 17, this volume, for discussion). Since the historical debate about nominalism wasn’t explicitly framed in terms of fundamentality, such nominalists will essentially be offering “properties aren’t fundamental” as a revising or reconciling paraphrase of “there are no properties”: a reconciling paraphrase if she takes herself to be participating in that historical debate, and a revising paraphrase if she doesn’t. A related approach distinguishes senses of existence (e.g., existence1 and existence2), and holds that while properties exist1, nominalism is or should be defined as the thesis that they don’t exist2. (This will be roughly equivalent to the previous option if existence2 is “fundamental existence” and existence1 is “superficial existence”.) As above, since the historical debate about nominalism wasn’t formulated in terms of existence1 and existence2, such nominalists will have to offer “properties don’t exist2” as a revising or reconciling paraphrase of “there are no properties”.

2.8 Conclusion While there is more to be said about paraphrase than fits in a short handbook entry, I hope a few key points have come through here. First, it’s important to be explicit about what sort of paraphrase one is offering: what goal one is trying to accomplish with it. Is the goal to preserve the original theory with a reconciling paraphrase, or to replace the original theory with a revising paraphrase? Second, paraphrase of some kind or another plays a central and plausibly unavoidable role in resisting arguments like The Quinean Argument. Finally, many of the popular objections to paraphrase fall flat. The legitimacy of paraphrase gives us an additional tool for philosophical theorizing. That’s the good news. The bad news is that it’s a tool for reducing “friction”: a tool for resisting conclusions, not reaching them. Without friction, it’s difficult to have much confidence in our ontological verdicts. But we should be used to that. So it has been, is, and ever shall be.9

Notes 1 Paraphrase is relevant to other debates in philosophy for similar reasons: Hawley (2001: 54) gives paraphrases of “historical” and “lingering” predicates in defense of stage theory; Lewis (1986) shows how to paraphrase away (primitive) modal operators in favor of quantification over worlds; etc. 2 According to Quine, only quantifiers have ontological implications; others have held that denoting phrases and even predicates are committing. See Chapter 1, this volume, for discussion. 3 Terminological note: I take “nominalism” to be the thesis that there are no abstract entities. Unfortunately, I have no definition of “abstract entity” to offer: see Chapters 5 and 6, this volume, for discussion.

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John A. Keller 4 Himelright, like many others, seems to assume that all paraphrases are revising. 5 Actually, other parts of the essay indicate that Dorr takes “superficial” to modify, not “true”, but “exists”: that his view is that abstracta superficially exist, but don’t fundamentally exist. See Section 2.7. Dorr’s view was anticipated by Putnam (1967). 6 There are two main ways this requirement has been instrumentalized in the literature: as a conservativeness requirement, and as a safety requirement. See Field (1980), Dorr (2008), Woodward (2010), and Skiba (2019) for discussion. 7 I take this to be a serious objection. Compare: Mind is irreducible to matter; minds exist; therefore materialism is false. Even if this argument is sound, a good objection to it is that we don’t know that it’s sound, since we don’t know whether its first premise is true. See Keller (2017a) for discussion. 8 Why think that the less committal sentence is the more perspicuous? Why think paraphrase subtracts commitments rather than adding them? The short answer is that while there’s no guarantee that the less committal sentence is the more perspicuous one, we sometimes know that it is (e.g., (A*) is more perspicuous than (A)), and even if we don’t know that it is, paraphrase can subtract rational commitments as long as we don’t know that it isn’t. See Keller (2017b) for discussion. 9 Thanks to Jody Azzouni, Chad Carmichael, Sam Cowling, Anthony Fisher, Nicholas K. Jones, Lorraine Juliano Keller, and Anna-Sofia Maurin for helpful comments.

References Alston, W. (1958) Ontological Commitments. Philosophical Studies 9(1/2): 8–17. Båve, A. (2015) A Deflationist Error Theory of Properties. Dialectica 69(1): 23–59. Burgess, J. and Rosen, G. (2005) Nominalism Reconsidered. In Shapiro, S. (ed.) The Oxford Handbook of Philosophy of Mathematics and Logic. New York: Oxford University Press: 515–535. Dorr, C. (2008) There Are No Abstract Objects. In Sider, T., Hawthorne, J. and Zimmerman, D.W. (eds.) Contemporary Debates in Metaphysics. Oxford: Blackwell: 32–63. Field, H. (1980) Science Without Numbers. Oxford: Clarendon Press. Hawley, K. (2001) How Things Persist. Oxford: Clarendon Press. Hawthorne, J. (2005) The Case for Closure. In Steup, M. and Sosa, E. (eds.) Contemporary Debates in Epistemology. Oxford: Blackwell: 26–43. Hellman, J. (1994) Mathematics Without Numbers. Oxford: Clarendon Press. Himelright, J. (2020) Paraphrasing Away Properties with Pluriverse Counterfactuals. Synthese 198(11): 10883–10902. Hoffman, J., and Rosenkrantz, G.S. (2003) Platonistic Theories of Universals. In Loux, M.J. and Zimmerman, D. (eds.) The Oxford Handbook of Metaphysics. Oxford: Clarendon Press: 46–74. Jackson, F. (1977) Statements about Universals. Mind 86(343): 427–429. Keller, J.A. (2015) Paraphrase, Semantics, and Ontology. In Bennett, K. and Zimmerman, D. (eds.) Oxford Studies in Metaphysics v. 9. Oxford: Clarendon Press: 89–128. Keller, J.A. (2017a) Philosophical Individualism. In Keller, J.A. (ed.) Being, Freedom, and Method: Themes from the Philosophy of Peter van Inwagen. Oxford: Clarendon Press: 299–323. Keller, J.A. (2017b) Paraphrase and the Symmetry Objection. Australasian Journal of Philosophy 95(2): 365–378. Korman, D.Z. (2007) Unrestricted Composition and Restricted Quantification. Philosophical Studies 140(3): 319–334. Kripke, S. (1980) Naming and Necessity. Cambridge, MA: Harvard University Press. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Blackwell. Lewis, D. (1991) Parts of Classes. Oxford: Blackwell. Lewis, D. (1999) Noneism and Allism. In Lewis, D. (ed.) Papers in Metaphysics and Epistemology. Cambridge: Cambridge University Press: 152–163. Liggins, D. (2007) Anti-Nominalism Reconsidered. Philosophical Quarterly 57(226): 104–111. Melia, J. (1995) On What There’s Not. Analysis 55(4): 223–229. O’Leary-Hawthorne, J. and Cortens, A. (1995) Towards Ontological Nihilism. Philosophical Studies 79(2): 143–165.

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The Method of Paraphrase Putnam, H. (1967) Mathematics Without Foundations. Journal of Philosophy 64(1): 5–22. Quine, W.V. (1948) On What There Is. Review of Metaphysics 2(5): 21–38. Roser, M. (2014) Fertility Rate. OurWorldInData.org. Retrieved from: https://ourworldindata.org/ fertility-rate. Schaffer, J. (2009) On What Grounds What. In Chalmers, D., Manley, D. and Wasserman, R. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Clarendon Press: 347–383. Schindler, T. (2021) Deflationary Theories of Properties and Their Ontology. Australasian Journal of Philosophy 100(3): 443–458. Schoenfield, M. (2019) Permissivism and the Value of Rationality: A Challenge to the Uniqueness Thesis. Philosophy and Phenomenological Research 99(2): 286–297. Skiba, L. (2019) Fictionalism, the Safety Result and Counterpossibles. Analysis 79(4): 647–658. Thomasson, A. (1999) Fiction and Metaphysics. Cambridge: Cambridge University Press. van Inwagen, P. (2023) Being: A Study in Ontology. Oxford: Clarendon Press. Woodward, R. (2010) Fictionalism and Inferential Safety. Analysis 70(3): 409–417. Yablo, S. (1998) Does Ontology Rest on a Mistake? Proceedings of the Aristotelian Society Supp. Vol. 72(1): 229–261.

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3 PROPERTIES AS TRUTHMAKERS Bradley Rettler

3.1 Introduction A natural thought is that what is true depends on the way the world is; everything couldn’t be exactly the way it is and yet different things be true. Most of the ways of stating this intuition are slogans, like “truths require truthmakers”, “truth supervenes on being”, “truths don’t float free of the world”, “truths must be tied down”, or the like. For any slogan, turning it into a precise truthmaker principle has been a process fraught with difficulties. A now classical way to make it precise is the following: “If something is true, then it would not be possible for it to be false unless either certain things were to exist which don’t, or else certain things had not existed which do” (Bigelow 1988: 133). But modal co-variation doesn’t seem to capture everything that the dependence language in the slogans is supposed to. Despite the challenges, many are not willing to give up the attempt to make the truthmaker intuition precise. Because of the ubiquity of supervenience talk and the work supervenience was made to do in the 1980s, metaphysicians initially looked to supervenience (plus logical relations) to help explicate truthmaking: Supervenience-Truthmaking: x makes p true =df. x exists, p is true, and necessarily, if x exists, then p is true.1 But note that Supervenience-Truthmaking doesn’t say that p is true because x exists. x’s existence entails p’s truth, but for all Supervenience-Truthmaking says, x might make p true by doing many more things other than existing; perhaps in each world, x does something, or has certain properties, that makes p true. For all Supervenience-Truthmaking says, it’s possible that in one world x makes p true by being to the left of y, and in another world x makes p true by eating ice cream, and so on. Indeed, in every world in which x exists, x has all its essential properties; so for all Supervenience-Truthmaking says, it is x’s existence and x’s having of its essential properties that makes p true. So, SupervenienceTruthmaking might be a true biconditional, but the righthand side is not a good analysis of truthmaking.

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DOI: 10.4324/9781003246077-5

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David Armstrong (2004: 6–7) endorses Supervenience-Truthmaking, and gives the following argument for its truth. Suppose x exists and makes p true, but does not necessitate p’s truth. So p is false in a world W in which x exists. But then there must be something else required to make p true – either another proposition q, or another thing y. But then x doesn’t make p true – x and y, or x and q, do. So x must not be making p true even in worlds in which x exists. It doesn’t take long to see that this argument won’t stand, because it begs the question. It says that because x doesn’t make p true in some world or other in which x exists and p is true, x doesn’t actually make p true; as Ross Cameron (2008) and others have pointed out, this assumes Supervenience-Truthmaking. There is another problem with Supervenience-Truthmaking. Necessarily, if my nose exists, then it is true that there are more than five prime numbers; after all, it is necessarily true that there are more than five prime numbers. And so if Supervenience-Truthmaking is true, then as Greg Restall (1996) first pointed out, it turns out that every thing is a truthmaker for every necessary truth. And since impossible things vacuously satisfy the antecedent of “if x exists, then p is true”, according to Supervenience-Truthmaking they are truthmakers for everything. Both of these theses – that every thing is a truthmaker for every necessary truth, and that every impossible thing is a truthmaker for every truth – are widely rejected. In light of these difficulties and other problems, philosophers departed from SupervenienceTruthmaking and began investigating other options. Here are some of them, with the new notions italicized. • Truthmaking is truth-grounding: the truthmaking relation is the relation of grounding between substance and truth (Schaffer 2010: 310; Rettler 2017: sec. 5.2). • Necessarily, if p is true, then there is some entity in virtue of which it is true (RodriguezPereyra 2005: 18). • For every sentence which is true, there must be some explanation of why it is true (McFetridge 1990: 42; Liggins 2005: 12). • A proposition is made true by some things, the Xs, if and only if it is the brutely true pure existence claim that the Xs exist or it is true in virtue of the brutely true pure existence claim that the Xs exist (Cameron 2018: 338). • p (a proposition) is true if and only if there exists a T (some entity in the world) such that T necessitates that p and p is true in virtue of T (Armstrong 2004: 17). • x makes p true iff x is intrinsically such that p (Parsons 2005: 166). None of these are equivalent to Supervenience-Truthmaking. There obviously is no widespread agreement as to the correct statement of truthmaking, so there’s nothing with which we can, without reservations, replace SupervenienceTruthmaking. What we can do, however (and what many have in fact done), is make the definiens of Supervenience-Truthmaking into a necessary condition on truthmaking, rather than a definition or a necessary and sufficient condition. This is what’s known as “Truthmaker Necessitarianism”. Truthmaker Necessitarianism: x makes p true only if, necessarily, if x exists, then p is true. Truthmaker Necessitarianism is weaker than Supervenience-Truthmaking, because it doesn’t say that truthmaking just is necessitation or that necessitation is sufficient for Truthmaking; it says that in order to do truthmaking, a thing must necessitate the truth. 39

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Many think necessitation is partly constitutive of truthmaking – that is, part of the essence of what it is to make something true is for it to necessitate the truth of it.2 This has led to Truthmaker Necessitarianism becoming orthodoxy among truthmaker theorists.3 Proponents of Truthmaker Necessitarianism, such as Cameron (2005) and Armstrong (2004), admit that they have no argument for it, but they claim that it seems intuitive to those who think truthmaking has something going for it. Truthmaker principles have been used to argue for the existence of many different kinds of things, including properties. In the remainder of this chapter, I’ll consider how truthmaking, so understood, is used to argue for the existence of properties.

3.2

A Truthmaking Argument for Properties

Armstrong (2004: 39–41) considers an argument from Truthmaker Necessitarianism to the existence of properties. The argument assumes that all true propositions have a truthmaker, a position that’s now called “Truthmaker Maximalism”. If Truthmaker Necessitarianism is true, then truthmakers for propositions necessitate the truth of those propositions. If Truthmaker Maximalism is true, then propositions of the form x is F have a truthmaker. What could such a truthmaker be? A natural thought is that the object a is the truthmaker for the proposition that a is F. But that can’t be, says Armstrong, because a could exist and not be F, and so the proposition that a is F wouldn’t be true. So a doesn’t necessitate the truth of the proposition that a is F. So, positing a as the truthmaker for the proposition that a is F violates Truthmaker Necessitarianism, and thus a isn’t a truthmaker for the proposition that a is F. But the proposition that a is F still needs a truthmaker. There are other candidates, of course. One such candidate is F. And if F were the best candidate, that would make for a very strong argument for properties, since what could F be other than a property? But F suffers from the same problem qua truthmaker for the proposition that a is F as a does – namely, F could have existed and a not been F. So Truthmaker Necessitarianism is violated yet again. So, if truthmakers necessitate their truths and propositions of the form x is F have a truthmaker, then neither x nor F is a truthmaker for the proposition that x is F. Thus, for any x and any F, neither x nor F is a truthmaker for the proposition that x is F. One way to respond is to posit properties that are essentially had by the things that have them. Then any property P can serve as a truthmaker for predications of P to things without violating Truthmaker Necessitarianism. This would only provide truthmakers for essential predications, however, and the truthmakers for accidental predications would be something altogether different.

3.3

What Kinds of Properties?

Armstrong (2004: 42) says that “truthmaking considerations … seem to favour a realism about properties”. But truthmaking considerations don’t settle the question of the nature of properties. That’s not to say, though, that any view of properties is on the table. Armstrong thinks that truthmaking considerations rule out some views, for instance, nominalism when understood as the view that there are no properties (see Part 4, this volume). But Armstrong’s argument doesn’t seem to rule out nominalism when understood as the view that there are no abstract objects, since it’s not clear abstract objects are needed to do the truthmaking. It rules out Class Nominalism, says Armstrong, because the 40

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property (which is a class) is much too big to be a truthmaker. At least, it’s much too big to be a minimal truthmaker for many sentences, and Armstrong thinks that every proposition has a minimal truthmaker (2004: sec. 3.7). For example, the red planet Mars is not necessary for making true this pen is red, but if the truthmaker is the class of red things, that includes Mars as well as the pen (Armstrong 2004: 40). It rules out Predicate Nominalism, because this pen is red would be true regardless of whether the phrase “is red” existed or not (Armstrong 2004: 40). Armstrong thinks that resemblance nominalism (see Chapter 16, this volume) fares slightly better than Class Nominalism or Predicate Nominalism, because resemblance is grounded in the natures of things. But Armstrong thinks the truthmaker argument rules out resemblance nominalism for different reasons. Namely, it posits things as truthmakers – unlike Class Nominalism, which says that classes are truthmakers, or Predicate Nominalism, which says that the predicate is involved in truthmaking. This is because resemblance is a matter of internal relations (unlike class membership or predicate application), and Armstrong says that internal relations are nothing over and above the things themselves (2004: 117). That is, the truthmakers of internal relations are just the terms of the relations themselves. But the terms of the relations include all their properties, even though all their properties aren’t necessary for making true propositions about the thing having one of those properties (Armstrong 2004: 41). This line of thinking from Armstrong is surprising. One might have thought that objects weren’t sufficient for making true propositions ascribing properties to them, but on Armstrong’s line of thinking they’re not necessary. They’re not necessary because they’re too big! They have too many extraneous properties, which they would apparently bring to the truthmaking relation. Armstrong also thinks that Platonism runs afoul of the truthmaker principle. This is because “the original insight” behind the truthmaker principle is that a should serve as a truthmaker for “a is F” and that properties should play a role in truthmaking. For Platonists these two things come apart, says Armstrong, because Platonic universals are outside of their particulars, and so things outside a are making true sentences about a. Armstrong concludes that those who accept the truthmaker principle must believe that universals are immanent in the objects that instantiate them (2004: 42). He also thinks truthmaking makes trouble for tropes. Consider two exactly similar tropes a and b. Here are two propositions: (i) a and b are distinct, and (ii) a and b are exactly similar. If tropes are truthmakers, then it’s hard to see what else other than a and b could be the truthmakers for those two propositions. And clearly (i) and (ii) aren’t the same proposition, since (ii) is consistent with the denial of (i) – identical tropes are exactly similar. But then the very same truthmakers are making true distinct propositions. Armstrong concedes that this is not a decisive argument against tropes, but he finds it “suspicious”, wondering whether tropes could really be simple if they behave in this way (2004: 43–44). But it’s not so clear what the problem is, for as much as we’ve said about truthmaking. This scenario doesn’t violate either of the principles governing truthmakers that Armstrong has laid out so far – that truthmakers necessitate their truths, and that truthmakers essentially make true the propositions for which they’re truthmakers. In order to derive a contradiction, we have to add another principle. Armstrong considers Herbert Hochberg’s (2004: 178) principle, “logically independent basic statements require different truthmakers”. That doesn’t seem to follow from the original truthmaker intuition, because we ordinarily think that the ball makes true all kinds of true propositions about it.4 This 41

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principle, which Hochberg calls “a fundamental principle of ontological analysis”, needs more argument. Kevin Mulligan et al. (1984) do not think truthmaker arguments rule out tropes, and indeed they give a truthmaking argument for tropes – following Edmund Husserl (2001[1900–1901]), they call tropes “moments”. After giving an ontological assay of tropes for several pages, in §3 of their article they turn to the question of whether tropes are truthmakers. The first bit of evidence Mulligan et al. cite is linguistic. Verbs can be nominalized – “fly” to “flight”, “born” to “birth”, “shoot” to “shooting”, and so on. So, for every sentence of the form X s , there corresponds a phrase of the form X ’s ing . They give the following argument: “If all atomic sentences contain a main verb, and all nominalisations denote moments, then it would follow, in fact, that all truth-makers are moments” (1984: 297). But the fact that we can do this with language doesn’t answer the metaphysical question: do nominalizations denote anything at all? And if so, do they denote tropes? Additionally, they don’t explicate the argument. The first two premises – (i) all atomic sentences contain a main verb and (ii) all nominalizations denote moments – don’t even mention truthmaking, so it’s hard to see how anything about truthmaking or truthmakers could follow. There is a premise missing. Constructing the argument for that premise – the one linking (i) and (ii) to truthmaking – is left entirely to the reader. Mulligan et al. identify three problems with the theory that all truth-makers are moments. One is that saying that the referents of the nominalizations of the verbs of the sentences are the truth-makers doesn’t say much about the nature of those truth-makers, so the theory isn’t very illuminating. The other is that there are some sentences that seem to be atomic sentences but have truthmakers other than moments. The first kind of sentences that seem to be atomic sentences but that seem to have truthmakers other than moments are substantial predications, like “John is a man”; maybe the things, like John, make these true. But they dismiss this idea, because John would then also be the truthmaker for “John is an animal”, and Tibbles would make true “Tibbles is an animal”, but how do we account for the fact that the truthmaker for “John is an animal” is a man and yet the truthmaker for “Tibbles is an animal” is not a man? The flatfooted response is that one of them is also a truthmaker for “John is a man” but the other is not a truthmaker for “Tibbles is a man”. But why not? Mulligan et al. suggest that the best way of answering this question is by positing humanity, which is instantiated by John but not by Tibbles. But notice that humanity is not a trope, since John instantiates it and so does Jan. I suspect that Mulligan et al. think that John and humanity aren’t enough to make it true that “John is a man” because Tibbles and humanity aren’t enough to make it true that “Tibbles is a man”. There must be some trope of John’s humanity that makes it true that John is a man, and since there isn’t such a thing as Tibbles’ humanity, there’s nothing to make it true that Tibbles is a man. The second kind of sentences that seem to be atomic sentences but that seem to have truthmakers other than moments are existential sentences, such as “John exists”. These can be made true by existence tropes, but Mulligan et al. are hesitant to posit such tropes “for reasons familiar from the tradition” (1984: 300). They are, I presume, alluding to Kant’s reasons for thinking that existence is not a property, which is that it adds nothing to the concept of a thing to say that it is; by granting that it has any other properties, one is already assuming that it exists, and saying that it exists is saying that the thing with all its properties exists.5 The third kind of sentences that seem to be atomic sentences but that seem to have truthmakers other than moments are identity sentences (John is John, Hesperus is 42

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Phosphorous). These can’t be made true by their objects (John, Venus), since such sentences are true even if the things don’t exist. Rather than positing non-existent things to do the truthmaking work, Mulligan et al. opt for a different solution. Since these sentences are true even when they don’t refer to anything, they are logical truths – and logical truths don’t require a truthmaker. So, Mulligan et al. conclude that we need no truthmakers for identity sentences, objects are truthmakers for existence sentences, and tropes are truthmakers for other atomic sentences. This furnishes us with a truthmaking argument for tropes. There are two ways a truthmaker theorist could respond to this argument and resist positing tropes. The first is to deny that predicative atomic sentences require truthmakers. But these are just the sorts of sentences people normally think require truthmakers; why is it true that the ball is red and not true that the ball is blue and not true that the ball is green and not true that the ball is purple … ? There must be something that makes the first true. The other way is to find some truthmaker other than tropes for non-existential atomic sentences. And indeed, this is the direction in which Armstrong ends up going.

3.4 Are Properties Enough? Armstrong concludes that properties as he thinks of them are not enough to be truthmakers, because, as discussed, x could have some property F and yet it’s possible that x exists and not have F; so Truthmaker Necessitarianism is violated. Because of this, Armstrong argues for the existence of states of affairs. He says: We have somehow got to get particulars and their properties together, or else somehow get the bundles tied up. Since the links needed are contingent (I am assuming for the moment), the entities to be linked cannot do the job by themselves. Truthmakers must necessitate … (Armstrong 2004: 48) Again, Armstrong doesn’t think this tells us what the nature of states of affairs is. We must posit things over and above the particulars and the properties, since neither of those can necessitate; but the nature of those things is up for debate. Says Armstrong, “The states of affairs may be bundlings of tropes, or attachments of tropes to particulars, or bundlings of universals (‘compresence’), or instantiations of universals” (2004: 49). There are options. States of affairs can be instantiations, attachments, brute, or bundlings – bundlings of tropes or universals. But these can’t merely be shorthand ways of referring to particulars and properties; an instantiation or bundling of F by x must be something over and above x and F. There is a long tradition of using the phrase “x is nothing over and above y” or “x is nothing over and above the ys”, and nearly as long of a tradition of complaining about the opaqueness of the phrase. Nearly everyone agrees that when x and y are identical, x is nothing over and above y (and vice versa). But many think that there are situations in which x is nothing over and above y despite the fact that x is not identical to y. For example, those who say that composition is identity think that an object is nothing over and above its parts, but plenty who deny that composition is identity say the same. Similarly, those who say that mental states are identical to physical states say that mental states are nothing over and above physical states, but plenty who deny that mental states are identical to physical states say the same. Some, like Kelly Trogdon and Gene Witmer (2021) suggest that where x grounds y, y is nothing over and above x. Theodore 43

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Sider (2015) surveys options for giving a precise meaning to the phrase at least as it occurs in the phrase “the whole is nothing over and above the parts”, finding each of them lacking in some way. So it’s not clear what saying “states of affairs must be something over and above their constituents” demands, beyond saying that states of affairs aren’t identical to their constituents. Armstrong wonders what happens if we discharge the assumption that the links are contingent, and assume that predication is necessary (2004: sec. 4.3). This would be to deny that it could be the case that both (i) x is F and (ii) it’s possible that x exist and not be F. He says in that case that states of affairs are not “ontological extras” – that is, they’re nothing over and above the object and property – but we still must posit them in order to have truthmakers for predications (2004: sec. 4.5). This is not because in some worlds, x and F exist and the proposition that x is F is true, but in some other worlds x and F exist and the proposition that x is F is not true because x isn’t F, since the link between x and F is necessary. But consider x and G, where x isn’t G. There are still relations that hold between x and G, and there is a mereological sum of x and G, says Armstrong. We need some sort of distinct relation between objects and properties such that the obtaining of that relation suffices to make the proposition that x is F true. Armstrong (2004: 47) thinks that relation, which he gets from (Baxter 2001), is partial identity. Partial identity isn’t the truthmaker for x is F, but when there is a partial identity relation between x and F, then the states of affairs of x’s being F is the truthmaker for the proposition that x is F. If Armstrong is right that truthmaking considerations support positing states of affairs, it’s not clear they support positing properties. The truthmaking argument for properties was that properties were necessary to do the truthmaking work, because objects couldn’t do it alone. The truthmaking argument for states of affairs is that they are necessary to do the truthmaking work, because objects and properties can’t do it together. So, suppose states of affairs are necessary to do the truthmaking work. Are they sufficient? It seems so, or we’d have another truthmaking argument for some other entity.

3.5

Are Properties Required?

So, states of affairs are necessary and sufficient for doing the truthmaking work for predication – for propositions of the form x is F . Once we’ve gone that far, it raises a crucial question: do states of affairs require properties? And it’s not obvious that the existence of states of affairs requires the existence of properties. One might think that the existence of states of affairs does require the existence of properties because states of affairs have properties as parts (or properties stand in some other quasi-parthood relation to states of affairs, like constituency). If states of affairs are bundles of properties, or bundles of an object and a property, then there are no states of affairs without properties. But not every view of states of affairs has it that they have parts or constituents. According to one theory of states of affairs (found in Plantinga 1976, 1983; Skyrms 1981: 199; Turner 2016), they are mereologically simple, lacking parts and lacking constituents. If this theory is right, then properties aren’t required to be parts of states of affairs. And so the existence of states of affairs isn’t an argument for the existence of properties. Or at least, it’s not a truthmaker argument. Similarly, Josh Parsons (1999: 325) argues that Armstrong’s truthmaker argument for realism about properties isn’t actually a truthmaker argument; nominalists can accept the truthmaker principle. To show this, he compares it to Armstrong’s (2004: 2–3) truthmaker 44

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argument against behaviorism. He begins by offering Armstrong’s truthmaker principle, which he glosses as, “For every true sentence, there is some thing such that the sentence cannot become false without a qualitative change, a non-Cambridge change, in that thing” (Parsons 1999: 327). Armstrong’s argument against behaviorism, says Parsons, is that there is nothing out in the world that maps on to the relevant dispositions posited by behaviorists; the dispositions can change without any qualitative change in anything. So, the behaviorist can’t provide truthmakers for sentences involving dispositions. Armstrong’s argument for properties is different, says Parsons. For note that there are things out in the world that map on to the relevant things for nominalists – objects. So, the nominalist can provide truthmakers – objects. The sentence “the ball is green” can’t go from true to false unless there is a qualitative change in the ball. So, the ball serves as the truthmaker for the sentence “the ball is green”. Parsons says that Armstrong needs to supplement the truthmaker argument with another principle that’s stronger than the truthmaker principle. The truthmaker principle says that for every true sentence, there is some thing such that the sentence cannot become false without a qualitative change in that thing; the truthmaker argument against nominalism, in order to rule out objects as truthmakers, must add the principle that a truthmaker for a sentence is essentially a truthmaker for that sentence. Then the ball can’t be a truthmaker for “the ball is green”, since the ball could have been blue and thus the ball would not have made it true that the ball is green. Sentences like “the ball is green” require truthmakers that, necessarily, exist only if the ball is green. The nominalist can still be a truthmaker theorist, in that the nominalist can accept the truthmaker principle. For example, the nominalist can accept that the ball makes it true that the ball is green. The truthmaker principle says that if the ball makes it true that the ball is green, then “the ball is green” cannot become false without a qualitative change in the ball. This qualitative change is a change in color, from green to something else. But the nominalist, Parsons says, cannot accept truthmaker essentialism. The ball is not essentially a truthmaker for the sentence “the ball is green”, because the ball could become some other color. Plenty of truthmaker theorists will endorse this additional truthmaker essentialism principle, and so follow Armstrong in rejecting nominalism in favor of an ontology that posits things that satisfy truthmaker essentialism – things that, necessarily, exist only if the propositions for which they’re truthmakers are true. These truthmaker theorists will need to posit properties, says Armstrong. The nature of those properties, as previously canvassed, is up for debate.

3.6 Revisiting Truthmaker Necessitarianism The intuition behind truthmaking seems to pull in favor of things – objects like balls, candles, and trees – being the truthmakers. But Truthmaker Necessitarianism rules out this intuitive view. Since objects don’t necessitate accidental predications, or most propositions that aren’t essential predications, people end up abandoning objects as truthmakers. These philosophers (like Armstrong 2004; Cameron 2008: 124; Hoffman 2006; Pendlebury 1986; Rodriguez-Pereyra 2005; Ruben 1990: 210; Russell 1918) think they need a necessitater for truths to be truthmakers, so they end up admitting facts or states of affairs into their ontologies to serve as truthmakers. Others (like Martin 1980; Mulligan et al. 1984: 295–304; and Lowe 2006: 186–187, 204–205) admit tropes. One can accept that objects are truthmakers for essential predications and still retain Truthmaker 45

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Necessitarianism, but if one wants to retain Truthmaker Necessitarianism one must admit into one’s ontology something else as truthmakers for accidental predications. If one denies Truthmaker Necessitarianism, one can accept that objects are truthmakers for predications of the form x is F . Of course, x could have existed and not been F, but that’s no problem, since truthmakers needn’t necessitate. However, F could have existed and not been instantiated by x, as well. So perhaps we can salvage a truthmaker argument for properties despite denying truthmaker necessitarianism. Truthmaker necessitarianism ended up leading Armstrong to posit facts, after which it wasn’t clear that properties were needed anymore. Denying truthmaker necessitarianism removes the need to posit truthmakers that necessitate, and so doesn’t lead all the way to facts; one can stop earlier. There’s a truthmaking relation, still, but that truthmaking doesn’t require necessitating. Maybe making true is like making bread in the following sense: I cause the bread to exist, but I don’t necessitate the existence of the bread. Perhaps some will want objects to do the truthmaking work, and others will want properties.6

3.7 Conclusion In this chapter, we’ve considered ways that truthmaking has been used to argue for properties, and what kind of properties it’s been used to argue for. Predicative sentences need truthmakers, and properties are required to either be the truthmakers, or to be constituents of states of affairs that are the truthmakers. In either case, properties must exist, if predicative sentences are to have truthmakers.

Notes 1 See Mulligan et al. (1984) and Fox (1987). 2 This stronger claim is endorsed in Armstrong (2004); Asay and Baron (2012); Fox (1987). 3 For example, Truthmaker Necessitarianism is endorsed in Armstrong (2003); Mulligan et al. (1984); Rodriguez-Pereyra (2005: 18). 4 See also Maurin (2023: sec. 2.2). 5 Unless, of course, John is a trope or a bundle of tropes. See Paul (2002) for an argument that people (and all other things) are properties. See Williams (1953) and Simons (1994) for arguments that objects are bundles of tropes, and Maurin (2010) for a defense of the view against a regress argument. 6 Thanks to Andrew M. Bailey, Anthony Fisher, Franz-Peter Griesmaier, Anna-Sofia Maurin, Lindsay Rettler, Gonzalo Rodriguez-Pereyra, Alex Skiles, Craig Warmke, and attendants at Properties: An Online Philosophy Workshop for comments and discussion.

References Armstrong, D.M. (2003) Truthmakers for Modal Truths. In Lillehammer, H. and Rodriguez-Pereyra, G. (eds.) Real Metaphysics: Essays in Honour of D.H. Mellor. New York: Routledge: 12–25. Armstrong, D.M. (2004) Truth and Truthmakers. Cambridge: Cambridge University Press. Asay, J. and Baron, S. (2012) Unstable Truthmaking. Thought 1(3): 230–238. Baxter, D. (2001) Instantiation as Partial Identity. Australasian Journal of Philosophy 79(4): 449–464. Bigelow, J. (1988) The Reality of Numbers: A Physicalist’s Philosophy of Mathematics. Oxford: Clarendon Press. Cameron, R. (2005) Truthmaker Necessitarianism and Maximalism. Logic et Analyse 48(189–192): 43–56.

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Properties as Truthmakers Cameron, R. (2008) Truthmakers, Realism and Ontology. Royal Institute of Philosophy Supplement 62: 107–128. Cameron, R. (2018) Truthmakers. In Glanzberg, M. (ed.) The Oxford Handbook of Truth. Oxford: Oxford University Press: 333–354. Fox, J.F. (1987) Truthmaker. Australasian Journal of Philosophy 65(2): 188–207. Hochberg, H. (2004) Russell and Ramsey on Distinguishing between Universals and Particulars. Grazer Philosophische Studien 67(1):195–207. Hoffman, F. (2006) Truthmaking, Recombination, and Facts Ontology. Philosophical Studies 128(2): 409–440. Husserl, E. (2001[1900-1901]) Logical Investigations. Moran, D. (ed.). Findlay, J.N. (trans.). London and New York: Routledge. Liggins, D. (2005) Truthmakers and Explanation. In Beebee, H. and Dodd, J. (eds.) Truthmakers: The Contemporary Debate. Oxford: Clarendon Press: 105–115. Lowe, E.J. (2006) The Four-Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Clarendon Press. Martin, C.B. (1980) Substance Substantiated. Australasian Journal of Philosophy 58(1): 3–10. Maurin, A.-S. (2010) Trope Theory and the Bradley Regress. Synthese 175(3): 311–326. Maurin, A.-S. (2023) Tropes. In Zalta, E.N. and Nodelman, U. (eds.) The Stanford Encyclopedia of Philosophy (Spring 2023 Edition). URL = < https://plato.stanford.edu/archives/spr2023/entries/ tropes/>. McFetridge, I. (1990) Truth, Correspondence, Explanation and Knowledge. In Haldane, J. and Scruton, R. (eds.) Logical Necessity and Other Essays. London: Aristotelian Society: 29–52. Mulligan, K., Simons, P., and Smith, B. (1984) Truth-Makers. Philosophy and Phenomenological Research 44(3): 287–321. Parsons, J. (1999) There Is No ‘Truthmaker’ Argument Against Nominalism. Australasian Journal of Philosophy 77(3): 325–334. Parsons, J. (2005) Truthmakers, the Past, and the Future. In Beebee, H. and Dodd, J. (eds.) Truthmakers: The Contemporary Debate. Oxford: Clarendon Press: 161–174. Paul, L.A. (2002) Logical Parts. Noûs 36(4): 578–596. Pendlebury, M. (1986) Facts as Truthmakers. The Monist 69(2): 177–188. Plantinga, A. (1976) Actualism and Possible Worlds. Theoria 42(1–3): 139–160. Plantinga, A. (1983) On Existentialism. Philosophical Studies 44(1): 1–20. Restall, G. (1996) Truthmakers, Entailment and Necessity. Australasian Journal of Philosophy 74(2): 331–340. Rettler, B. (2017) Grounds and ‘Grounds’. Canadian Journal of Philosophy 47(5): 631–655. Rodriguez-Pereyra, G. (2005) Why Truthmakers. In Beebee, H. and Dodd, J. (eds.) Truthmakers: The Contemporary Debate. Oxford: Clarendon Press: 17–31. Ruben, D.-H. (1990) Explaining Explanation. Abingdon, UK: Routledge. Russell, B. (1918) The Philosophy of Logical Atomism. The Monist 28(4): 495–527. Schaffer, J. (2010) The Least Discerning and Most Promiscuous Truthmaker. The Philosophical Quarterly 60(239): 307–324. Sider, T. (2015) Nothing Over and Above. Grazer Philosophische Studien 91(1): 191–216. Simons, P. (1994) Particulars in Particular Clothing: Three Trope Theories of Substance. Philosophy and Phenomenological Research 54(3): 553–575. Skyrms, B. (1981) Tractarian Nominalism. Philosophical Studies 40(2): 199–206. Trogdon, K. and Witmer, G. (2021) Full and Partial Grounding. Journal of the American Philosophical Association 7(2): 252–271. Turner, J. (2016) The Facts in Logical Space: A Tractarian Ontology. Oxford: Oxford University Press. Williams, D.C. (1953) The Elements of Being: I. Review of Metaphysics 7(1): 3–18.

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4 NATURALNESS Abundant and Sparse Properties Elanor Taylor

4.1 Introduction Consider a particular neutrino. According to an abundant conception of properties, this neutrino has a great many properties, including one corresponding to almost every predicate attributable to the neutrino. Among these abundant properties, some are fairly straightforward. For example, the neutrino has half a unit of spin, and a tiny rest mass. Others are more complicated. For example, the neutrino has no electric charge, and is a member of the set {neutrinos and tigers}. Some of the abundant properties have only an apparently tenuous connection to the neutrino itself, such as being one of the things that I am thinking about right now, or having a name coined in 1933. The proponent of sparseness acknowledges a distinction among properties such that there are important differences between those at the beginning and at the end of this list. Features of the former kind are privileged or elite, as an objective, worldly matter of fact. Among other things, the privileged properties are significant for predicting and explaining the neutrino’s behavior, they account for objective similarities between the neutrino and other entities, and they account for the neutrino’s causal powers. The features at the end of the list are not privileged in this way, and are unsuitable for these roles. To endorse this picture is to endorse the view that there are sparse properties – to endorse sparseness. To deny sparseness is to hold that there is no such worldly, objective distinction between properties. Different approaches to sparseness vary on details such as what the privileging of sparse properties amounts to, whether it is a binary distinction or a spectrum, and on the background theory of properties more generally. But overall, commitment to sparseness amounts to this idea: that there is an objective, worldly privileging of certain properties over others which makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter, I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and the roles that they attribute to sparse properties, noting that on most approaches sparse properties

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are deeply connected to inquiry. Finally, I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry.

4.2

Motivating Sparseness: Problems of Abundance

Sparseness is, at first pass, a fairly intuitive notion. Those who prefer green to green-or-atiger, or think that the neutrino’s having half a unit of spin is more significant than its being a thing I just thought of, will find sparseness appealing. However, often when philosophers endorse sparseness they do so not merely because of its intuitive appeal, but instead because of the problem-solving and system-building resources that sparseness offers. Here I will consider a set of problems that generate canonical motivations for sparseness. These ideas have a rich history going back to the ancient world, through manifestations in the medieval and early modern periods including the early modern interest in ideal languages (see Plato’s Phaedrus in Cooper 1997, Dalgarno 1661 in Cram and Maat 2001, Wilkins 1668, and discussion in Eco 1995). However, here I will bypass much of that history and begin my overview in the aftermath of logical empiricism. What I call “problems of abundance” are sceptical problems generated by the worry that some central aspect of thought and inquiry requires justification for honing in on one set of properties over another, but that this justification appears to be unavailable. Here I will consider three familiar examples – Nelson Goodman on induction, and W.V. Quine and Hilary Putnam on reference – but problems of abundance are prevalent, and appear in many different areas of philosophy. In Goodman’s new riddle of induction the same body of evidence – that all observed emeralds have been observed to be green – supports two distinct hypotheses: first, that all emeralds are green, and second that all emeralds are grue, where something is grue with respect to a future time t iff it is green and observed before t, or blue and observed after t (Goodman 1955: 71–75). When inductive generalization performs as it should it ought to take us from observations about the greenness of emeralds to a generalization about the greenness of emeralds, rather than to a generalization about the grueness of emeralds, but this requires some justification for prioritizing green over grue. We of course prefer the green hypothesis as grue is a gerrymandered and unfamiliar predicate, but without some further justification for that preference selecting the green hypothesis over the grue seems objectionably arbitrary. In Quine and Putnam’s arguments for the indeterminacy of reference, we see a similar structure. According to Quine’s behaviorism meaning ought to be determined by behavior, but, he argues, behavior fails to determine meaning. For example, our behavior around the word “rabbit” does not hone in on “rabbit” over other options such as “undetached rabbit part” or “rabbit stage” (Quine 1960: 51–56 and 1968: 188–189). This leads Quine to the conclusion that meaning, and furthermore reference, are indeterminate (Quine 1968: 191). Putnam pushes a similar worry further, showing that on some interpretations of the sentence “the cat sat on the mat” the word “cat” may refer to cherries and the word “mat” may refer to trees, without altering the truth-value of the sentence (Putnam 1981: 32–35 and Appendix). Although the background and implications of these arguments are rich and complex, their significance here is that they both reveal a problem much like Goodman’s. Determinate reference requires our words to hone in on certain features and to exclude others, but there is no apparent justification for or source of this honing-in. 49

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Goodman, Quine, and Putnam adopted different responses to these problems. Goodman held that we select the green hypothesis over the grue because we have a history of projecting the predicate “green” (Goodman 1955: 95). Quine held that there are no framework-independent facts about reference, and more generally about ontology (Quine 1968: 200–212). Putnam considered a few options including the idea that there might be primitive metaphysical truths about reference, which he dismissed as a “magical theory of reference” (Putnam 1981: 47). But this is the option closest to contemporary theories of sparseness, and the option David Lewis explicitly took up as a model for naturalness (Lewis 1984: 228–229). There are routes to sparseness beyond these sceptical problems of abundance. For example, David Armstrong was motivated to endorse a sparse theory of universals to explain genuine similarities between entities, and so endorsed versions of the One Over Many argument in cases where the cited similarities are genuine.1 Others endorse sparseness as part of an intuitively appealing realist worldview (Sider 2011: 18). However, the problems of abundance generate classic motivations for sparseness, and they illustrate much of the interesting work that sparseness can do. These problems reveal a theoretical need to privilege certain features over others, on pain of facing a kind of scepticism about central aspects of thought and inquiry. According to proponents of sparseness the world itself provides that privilege, as a matter of primitive, unexplained metaphysical fact.

4.3

Roles and Features

As we have seen, at the heart of a commitment to sparseness is the idea that there is an objective distinction among properties such that some are fit to play roles that others cannot. In this section, I will consider some important features of sparseness, and some of the roles traditionally attributed to sparseness. On all accounts, sparseness is objective. That is to say, if some property is sparse, or more sparse than some other, then this is a matter of objective fact (Lewis 1983: 347; Sider 2011: 5). The objectivity of sparseness acts as an explanatory backstop for questions about why sparse properties are appropriate for the roles attributed to them. For example, sparse properties feature in the laws of nature and in scientific explanations, they are the right classifications for inductive generalization, and they act as reference magnets. We might reasonably disagree about which properties are sparse, and this is an empirical question on most approaches. But once we have established that some property is sparse, there is no further question to ask about why it rightfully appears in our explanations and generalizations, or why it acts as a reference magnet. To be sparse just is to be the right kind of property for such roles, because sparse properties correspond to objective, worldly distinctions in reality. This idea is the source of familiar metaphors about sparseness, such as that sparse properties “carve at nature’s joints”, or that the “book of the world” is written in a language of sparse properties. Furthermore, the objectivity of sparseness has a causal aspect. For example, on Armstrong’s view, universals must perform genuine causal work, because otherwise they could not support scientific explanation or our scientific understanding of the world more generally (Armstrong 1978a: 126–132). In addition to its objectivity, sparseness is also absolute. That is to say, if a property is sparse, it is sparse in all possible worlds (Lewis 1986: 44, 60–61; see discussion in Brown and Wildman 2022, and Thompson 2016).

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Two of the most central and influential contemporary approaches to sparseness are Lewis’s naturalness (and its descendant, Sider’s structure), and Armstrong’s universals (Armstrong 1978a; Armstrong 1978b; Lewis 1983; Sider 2011). They share the basic idea of sparseness and many commitments about the roles played by sparseness, but there are significant differences between these approaches. First, the status of being a universal is not a matter of degree on Armstrong’s view, whereas Lewis’s naturalness and Theodore Sider’s structure appear on a spectrum, such that there are degrees of naturalness, running from perfectly natural to highly non-natural. Second, the background view of properties is different. Lewis endorses an abundant, nominalist view of properties and Armstrong rejects this abundance, though he does endorse structural universals, such that some universals are built out of others.2 Finally, although I group Sider with Lewis here, Sider extends his notion of sparseness beyond properties and into the logical domain, including quantifiers. Let us now consider some canonical roles for and features of sparseness. Minimality. Sparse properties form a minimal base for all other properties. Any instantiated property either is a sparse property, or else it is instantiated in virtue of certain sparse properties being instantiated. Similarity. Sparse properties are the basis of objective similarity between entities. In so far as two entities are genuinely similar, this is because they share sparse properties. Causation. Entities have the causal powers that they have in virtue of their sparse properties. Armstrong makes causal efficacy a criterion for universals, as without this universals would not feature in scientific explanations or contribute to scientific understanding. Laws. Sparse properties feature in the laws of nature, either by their corresponding predicates appearing in the axioms of the Best System, as on Lewis’s view, or by the laws themselves being relations between universals, as on Armstrong’s view. Explanation. Sparse properties feature in explanations, particularly scientific explanations. If we think of explanation as necessarily featuring laws then the connection between sparseness and explanation is mediated by the connection between laws and sparseness. Sider posits a connection between explanation and sparseness that is not necessarily mediated by the connection with laws, on which explanations are broadly speaking better the closer they get to a language of sparse properties. For Armstrong the causal role of universals accounts for their role in explanations. Reference. Sparse properties act as reference magnets, in that, roughly speaking, they are more eligible referents than non-sparse properties. Sparseness thereby resolves the Putnam/Quine concerns about the indeterminacy of reference. Induction. Sparseness provides a justification for selecting the green hypothesis over the grue hypothesis: an emerald is grue in virtue of its more sparse properties, and so our inductive reasoning should range over the more sparse properties.

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Fundamentality. Sparse properties, as a minimal base for all other properties, are fundamental. This is reflected in the idea that sparse properties on most approaches are physical. This is not an exhaustive list of roles and features, but most accounts of sparseness portray it as playing some version of these. Some further roles specific to Sider’s extended notion of structure include that structure goes into logic, such that certain quantifiers are more structural than others (Sider 2011: 85–104). Sider also holds that structure determines the substantivity or otherwise of debates (Sider 2011: 44–66). In substantive debates each side must differ with respect to how effectively the rival views capture facts about structure, otherwise the debate is not a genuine, substantive disagreement. A striking aspect of sparseness, evident from this list, is that so many of the roles for sparseness pertain to inquiry. I take inquiry to include activities such as forming lawlike generalizations, classifying phenomena, formulating explanations, formulating theories, and engaging in inductive generalization. As we can see, proponents of sparseness believe that sparseness is central to all of these activities.

4.4

Related Notions

Sparseness is traditionally understood as pertaining to properties, such that it is a property of properties. But other, related notions play similar roles. One is the natural kind. The natural kind realist, on a popular version, holds that there are worldly causal mechanisms that hold clusters of properties together, and that these property clusters are the natural kinds (Boyd 1999). The fact that there are such causal mechanisms accounts for the role of natural kinds in scientific theories, laws, and explanations, on the basis of the idea that part of what gives scientific inquiry its predictive power and explanatory success is the fact that it hones in on the kinds in this way, and so is guided by the causal structure of the world. On this view, natural kinds play an equivalent role to sparse properties in that the structure of reality guides inquiry, when it goes well, to the correct classifications for explanation and generalization. Another related notion is essence. On some versions of essentialism, essences are abundant, such that anything that has individuation conditions has an essence, including Goodman’s grue and other gerrymandered categories (Fine 1994; Correia 2006). On other versions of essentialism, however, essences are sparse, which reflects a privileged role for essences in inquiry that mirrors the privileged role of sparse properties in inquiry.3

4.5 Challenges With this overview of sparseness in hand, let us now consider some challenges to sparseness. Many reject the background realist picture behind sparseness simply because they reject realism, but some of the most interesting critical work on sparseness focuses on the combination of roles that sparseness is asked to play. In particular, Jonathan Schaffer, Cian Dorr and John Hawthorne have challenged the claim that sparseness can perform all of the roles given above, and they have done so from a broadly realist-friendly background (Schaffer 2004; Dorr and Hawthorne 2013). In this section, I follow their lead of considering challenges to sparseness that do not depend on broader scepticism about realism, 52

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or about the possibility of metaphysics. In particular, I will focus on challenges to the purported connections between sparseness and inquiry, many of which are generated by concerns about the objectivity and absoluteness of sparseness.4 Let us begin by considering the relationship between the objectivity and absoluteness of sparseness and the connections between sparseness and inquiry. As discussed in Section 4.4, a property’s status as sparse, or as more sparse than another, is determined entirely by the objective structure of reality. As such, sparseness is not affected by the features or interests of inquirers, by social or cultural context, or other potential sources of subjectivity. This is the realist aspect of sparseness, and it is of great significance to the work attributed to sparseness.5 Much of that work involves connections between sparseness and inquiry, including central roles for sparseness in laws, explanations, and inductive generalization, and the objectivity of sparseness facilitates these connections. To illustrate, consider the role of sparseness in lawhood. Lewis and Armstrong are scientific realists, and the objectivity of sparseness grounds their realism. The predicates that appear in the axioms of Lewis’s Best System correspond to perfectly natural properties, and on Armstrong’s view laws just are relations between universals. On these views, part of what it is for a law to be a law is for it to identify objective connections between joint-carving classifications. Alternatively, consider the sparseness-based solution to Goodman’s new riddle. The justification for choosing the green hypothesis over the grue hypothesis is that the world prefers it, and so sparseness offers a realist basis for generalizing over the more sparse classifications.6 In each of these cases the objectivity of sparseness funds the connection between sparseness and inquiry, in that those connections obtain at least in part because sparseness is objective. Something similar applies to the absoluteness of sparseness, the fact that any sparse property is non-contingently sparse. The absoluteness of sparseness supports the role of sparse properties in inquiry because it gives the objectivity of sparseness a robust modal status. These purported connections between sparseness and inquiry do not amount to a purely descriptive claim about how human beings in fact inquire, because (of course) people often explain, generalize, theorize, and so on in highly non-sparse terms. Instead, these connections are based on a view of the nature and function of inquiry according to which the goal of inquiry is to get to the facts about the objective, absolute structure of reality. On this view, inquiry aims to get the facts right about the structure of reality, and as such, it is and should be guided by sparseness. If it is not so guided by sparseness, then it is worse as inquiry. However, these purported connections between sparseness and inquiry face serious counterexamples. Many, though not all, of the problem cases are funded by the absence of the kind of objectivity and/or absoluteness characteristic of sparseness. In particular, cases in which the quality of inquiry is driven by more subjective or pragmatic considerations challenge the picture of sparseness as driving the quality of inquiry. Here I will consider two sources of examples: philosophy of science and inquiry into the social world.

4.5.1 Philosophy of Science A first set of cases from philosophy of science are about fundamentality. On canonical views of sparseness the sparse properties are only fundamental physical properties. On the view of sparseness as driving the quality of inquiry, it follows that explanations, theories and so on in the non-physical sciences are worse as explanations and theories than those 53

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found in physics. Any case in which we legitimately explain, theorize, or generalize in less than fundamental terms presents a challenge to this view. A number of authors have pressed this point. For example, Schaffer has argued that we should abandon the fundamentality aspect of traditional accounts of sparseness (Schaffer 2004). Jonathan Cohen and Craig Callender argue that any viable Best System Account of laws (BSA) must make room for non-fundamental special science laws. They propose an amended version of the BSA on which the predicates that appear in the laws are not necessarily perfectly natural but are instead a stipulated set of kinds, which may be selected for pragmatic reasons rather than their objective sparseness (Cohen and Callender 2009; see also Loewer 2021). These considerations also feature in traditional conversations about reductionism and nonreductionism in philosophy of science, with many philosophers of science arguing that there are autonomous non-fundamental laws, explanations, theories, and classifications (such as Fodor 1974). Proponents of sparseness have resources to push back against these concerns. If sparseness comes in degrees, then the proponent of sparseness can argue that nonfundamental sciences and non-fundamental inquiry more generally are not perfectly sparse but are relatively or fairly sparse, and that this status accounts for their legitimacy. Indeed, Sider uses this line of reasoning in his treatment of the legitimacy of inquiry into the nonfundamental sciences (Sider 2011: 21–23). Another option is to simply deny the connection between sparseness and fundamentality, as Schaffer recommends (Schaffer 2004). This issue about fundamentality need not be based on considerations about objectivity, as these cases might merely show that sparse properties are not necessarily fundamental. However, attempts to deal with this kind of problem often end up appealing to the idea that certain classifications are appropriate for inquiry for more pragmatic, practice-driven reasons (as in Cohen and Callender 2009; Loewer 2021), which indicates that considerations about objectivity drive some of these cases. This leads to a second set of problem cases from philosophy of science, in which the classifications best for inquiry are best for reasons beyond sparseness. Here I will consider the case of inquiry involving idealizations. The idea that scientific inquiry occasionally involves idealization is uncontroversial, and examples such as the frictionless plane and the perfectly rational agent are familiar. However, some philosophers of science argue that idealization is far more widespread than is standardly thought. For example, Angela Potochnik has described scientific idealization as “rampant”, “ineliminable”, and “unchecked”, arguing that idealization is a necessary and standard aspect of scientific inquiry (Potochnik 2017: 23–61). The prospect of pervasive scientific idealization generates a challenge for proponents of sparseness. One significant area is laws. Potochnik argues that most laws are idealized, including physical laws such as the laws of gravitation (Potochnik 2017: 24–33). However, idealized laws do not summarize relations between joint-carving classifications, but instead relations between idealized classifications, which are arguably non-sparse.7 If we accept that scientific idealization is pervasive, then we must also accept that most laws are idealized, which challenges general connections between sparseness and the laws of nature. These issues are complicated, and so only a summary of the potential challenges and responses can be given here. However, a proponent of sparseness could respond by arguing that rampant unchecked idealization is an artefact of our current, contingently limited conditions of inquiry, and that as we become more effective scientists, we will be able to abandon idealization. However, the pervasiveness of idealization tells against this 54

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prediction. For this prediction to be accurate, we should expect idealization to be abandoned as we proceed toward more complete and sophisticated scientific inquiry, but historically this has not been the case. Another resource is to argue that idealization is a feature of representations of laws, rather than the laws themselves. However, if scientific inquiry works with the representations, then there remains a challenge to the purported connections between sparseness and scientific inquiry as it is actually practiced. There are many other cases in which philosophers of science have argued that inquiry ranges over classifications rightfully selected for reasons other than sparseness. For example, some feminist philosophers of science have argued that the ideal of value-free science is misguided, and so that we should deliberately seek to place values into scientific practice, rather than attempt to eliminate them in pursuit of objectivity (Longino 1987). This includes the formulation of classifications, so on such views, the best scientific classifications may be best for normative reasons, rather than for their sparseness.

4.5.2

Social Inquiry

A further source of problems for these purported connections between sparseness and inquiry is inquiry into social phenomena, where our explanations and generalizations often rightly range over highly non-natural classifications. I have discussed some examples of highly non-natural classifications in social inquiry in other work, including the case of the “six-pocket woman”, a local classification significant to the anthropology of money in Papua New Guinea, and mythical classifications such as the racist controlling image of the “welfare queen” (Taylor 2016, 2020). Such classifications play a central role in social inquiry, yet are non-sparse. Furthermore, recently a number of authors have discussed the apparent non-sparseness of theories and classifications in social metaphysics, and implications for the substantivity or otherwise of social metaphysics (Barnes 2017; Sider 2017). Rather than identify further cases here, it will be useful instead to consider the features of social inquiry that drive such problem cases, and so generate problems for the purported connections between sparseness and inquiry. One potential source of non-sparseness in social inquiry is amelioration. In much social inquiry, particularly in more emancipatory branches of social metaphysics, theory choice is ameliorative in that it is driven at least in part by moral and political considerations. This feature plays a central role in debates about the metaphysics of gender, in which many participants hold that amelioration is a requirement for an adequate account of gender (Haslanger 2000; Jenkins 2016). This ameliorative aspect reflects a political tradition that takes the selection of views not only as a descriptive task but also as an action that can fund social change. However, moral and political considerations have little to do with sparseness, so theories selected for their ameliorative features are not selected for their sparseness. A second source of non-sparseness, tied to amelioration, is the contingency of the social world. Social inquiry is responsive to highly contingent social conditions which, in so far as they are socially constructed, are subject to change through changes to human thought, talk, and action. Furthermore, much social inquiry is aimed not only at accurately describing social reality but also at providing tools to change social reality for the moral and political better. In so far as classification and generalization play any role in that process, social classifications cannot be sparse, because of the objectivity and absoluteness of sparseness. 55

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4.5.3

Responses

I have mentioned some straightforward responses that the proponent of sparseness can make to these challenges to the connections between sparseness and inquiry. They can deny the cases, and deny that the generalizations, theories, and explanations given in terms of nonsparse classifications really are better than their sparser counterparts. Alternatively, they can offer resources to handle the cases, such as degrees of naturalness or relative structure. However, there are alternative, more radical responses to these problems. One route is to de-couple sparseness from inquiry. That is to say, the proponent of sparseness can endorse the view that there are sparse properties while denying that sparse properties play any significant role with respect to inquiry. Shamik Dasgupta has recently argued for an approach along these lines, rejecting the connections between sparseness and inquiry that make sparse properties the right classifications for explanation, laws, induction, and so on (Dasgupta 2018). Further modifications to this kind of approach are available, such as endorsing connections between sparseness and some kinds of inquiry, but not others. Another option is to develop tools that mirror the role of sparseness in inquiry but are more flexible than traditional sparseness, and are responsive to contingent, pragmatic, and normative factors. Two Taylors are salient here: Barry Taylor, and myself, Elanor Taylor. Barry Taylor’s cosiness offers what he calls a “vegetarian alternative” to Lewisian naturalness on which the cosiness of a predicate is relative to a theory T and is determined by its position in the axiomatized formulation of T (Taylor 2006: 109–124). My contextdependent naturalness (C-Naturalness) is intended to supplement commitment to Lewisian naturalness without over-extending the role of Lewisian naturalness in inquiry. A predicate is more C-Natural with respect to an activity when it displays a higher balance of salience and versatility with respect to that activity (Taylor 2016, 2020). These tools capture the idea that certain properties may be privileged over others with respect to inquiry, without understanding that privilege in objective, absolute terms.

4.6 Conclusion In this chapter, I have considered motivations for sparseness and for connecting sparseness to inquiry, and sketched some challenges to those connections. The traditional motivations for sparseness are rich and compelling, as are the reasons for connecting sparseness to inquiry. It is natural and appealing to think that inquiry, when functioning as it should, is guided by sparseness. However, as we have seen, often the actual business of inquiry is not so well-behaved.8

Notes 1 Armstrong describes the One Over Many argument as “The argument to universals from the apparent existence of identities of nature between different particulars” ( Armstrong 1978a: 138). For Armstrong, the need to explain similarities drives the One Over Many argument, and universals are well-placed to feature in explanations in part because of their causal significance. 2 Here I understand “nominalism” as the view that there are no universals, rather than the view that there are no properties. 3 Lowe’s view of metaphysics as “the science of essence” rests on the presumption that essences are sparse ( Lowe 2018). Some endorse a sparse view of essence to fund a defense of modalism about essence against Finean counterexamples ( Wildman 2013).

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Naturalness 4 There is much recent work on sparseness that deserves mention in a survey, but which space does not permit me to discuss here. For example, because sparseness is (typically) a property of properties it is naturally amenable to a higher-order treatment, and some authors are examining traditional issues about properties such as realism and abundance in a higher-order framework ( Jones 2018, and Chapter 1, this volume; Liggins 2021; Skiba 2021). 5 Sider discusses the objectivity of sparseness, in his case structure, and describes it as essential to the work performed by structure. “… joint-carving languages and beliefs are better. If structure is subjective, so is this betterness. This would be a disaster … If there is no sense in which the physical truths are objectively better than the scrambled truths, beyond the fact that they are propositions that we have happened to have expressed, then the postmodernist forces of darkness have won” ( Sider 2011: 65). Sparseness must also be objective to play any role in the determination of mental content ( Lewis 1983: 370–377). 6 As Lewis puts it, “… grue and bleen are inferior to the colours …” ( Lewis 1986: 61). 7 This depends on the precise locus of the idealization. One could attribute idealized properties to entities, as I suggest here. Alternatively, one could posit idealized relations between non-idealized properties. A fully developed version of this challenge will have to consider a range of different targets for idealization. 8 Thanks to Patrick Connolly, Anthony Fisher, Jacob Lettie, Nicholas Jones, Anna-Sofia Maurin, and Elizabeth Miller for helpful feedback. Thanks to participants at Properties: An Online Philosophy Workshop 16–18 May 2022 hosted by the University of Gothenburg, and to members of the WiM working group for workshopping the chapter.

References Armstrong, D.M. (1978a) Nominalism and Realism: Universals and Scientific Realism Volume I. Cambridge: Cambridge University Press. Armstrong, D.M. (1978b) A Theory of Universals. Universals and Scientific Realism Volume II. Cambridge: Cambridge University Press. Barnes, E. (2017) Realism and Social Structure. Philosophical Studies 174(10): 2417–2433. Boyd, R. (1999) Kinds, Complexity and Multiple Realization. Philosophical Studies 95(1): 67–98. Brown, J.D.K. and Wildman, N. (2022) The Necessity of Naturalness. Erkenntnis, doi: 10.1007/s1 0670-022-00567-1. Cohen, J. and Callender, C. (2009) A Better Best System Account of Lawhood. Philosophical Studies 145(1): 1–34. Cooper, J.M. (ed.) (1997) Plato: Complete Works. Indianapolis, IN: Hackett. Correia, F. (2006) Generic Essence, Objectual Essence, and Modality. Noûs 40(4): 753–767. Cram, D. and Maat, J. (2001) George Dalgarno on Universal Language: The Art of Signs (1661), The Deaf and Dumb Man’s Tutor (1680), and the Unpublished Papers. Oxford: Oxford University Press. Dasgupta, S. (2018) Realism and the Absence of Value. Philosophical Review 127(3): 279–322. Dorr, C. and Hawthorne, J. (2013) Naturalness. In Bennett, K. and Zimmerman, D. (eds.) Oxford Studies in Metaphysics: Volume 8. Oxford: Oxford University Press: 3–77. Eco, U. (1995) The Search for the Perfect Language. Oxford: Blackwell. Fine, K. (1994) Essence and Modality. Philosophical Perspectives 8: 1–16. Fodor, J. (1974) Special Sciences (or: The Disunity of Science as a Working Hypothesis). Synthese 28(2): 77–115. Goodman, N. (1955) Fact, Fiction, and Forecast. Cambridge, MA: Harvard University Press. Haslanger, S. (2000) Race and Gender: (What) Are They? (What) Do We Want Them To Be? Noûs 34(1): 31–55. Jenkins, K. (2016) Amelioration and Inclusion: Gender Identity and the Concept of Woman. Ethics 126(2): 394–421. Jones, N. (2018) Nominalist Realism. Noûs 52(4): 808–835. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1984) Putnam’s Paradox. Australasian Journal of Philosophy 62(3): 221–236.

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Elanor Taylor Lewis, D. (1986) On the Plurality of Worlds. Oxford: Blackwell. Liggins, D. (2021) Should a Higher-Order Metaphysician Believe in Properties? Synthese 199(3-4): 10017–10037. Loewer, B. (2021) The Package Deal Account of Laws and Properties (PDA). Synthese 199(1-2): 1065–1089. Longino, H.E. (1987) Can There Be a Feminist Science? Hypatia 2(3): 51–64. Lowe, E.J. (2018) Metaphysics as the Science of Essence. In Carruth, A., Gibb, S. and Heil, J. (eds.) Ontology, Modality, and Mind: Themes from the Metaphysics of E.J. Lowe. Oxford: Oxford University Press: 14–34. Potochnik, A. (2017) Idealization and the Aims of Science. Oxford: Oxford University Press. Putnam, H. (1981) Reason, Truth and History. Cambridge: Cambridge University Press. Quine, W.V. (1960) Word and Object. Cambridge, MA: MIT Press. Quine, W.V. (1968) Ontological Relativity. Journal of Philosophy 65(7): 185–212. Schaffer, J. (2004) Two Conceptions of Sparse Properties. Pacific Philosophical Quarterly 85(1): 92–102. Sider, T. (2011) Writing the Book of the World. Oxford: Oxford University Press. Sider, T. (2017) Substantivity in Feminist Metaphysics. Philosophical Studies 174(10): 2467–2478. Skiba, L. (2021) Higher-Order Metaphysics. Philosophy Compass 16(10): 1–11. Taylor, B. (2006) Models, Truth and Realism. Oxford: Oxford University Press. Taylor, E. (2016) Naturalness in Context. Inquiry 59(4): 319–342. Taylor, E. (2020) Social Categories in Context. Journal of the American Philosophical Association 6(2): 171–187. Thompson, N. (2016) Is Naturalness Natural? American Philosophical Quarterly 53(4): 381–395. Wildman, N. (2013) Modality, Sparsity, and Essence. Philosophical Quarterly 63(253): 760–782. Wilkins, J. (1668) An Essay Towards a Real Character, and a Philosophical Language. London: Printed for S. Gellibrand and John Martyn.

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PART 2

Distinctions

5 UNIVERSALITY AND PARTICULARITY Daniel Giberman

5.1 Introduction The task of distinguishing universals from particulars is difficult twice over. It faces a host of first-order challenges, since first-order proposals about the distinction (e.g., only universals are instantiable, or only universals can be multi-located) tend to be threatened by counterexamples. But it also faces formidable methodological challenges, such as how to decide whether the distinction ought to be exclusive and exhaustive. After discussing the relationships between the distinction and several pairs of pre-philosophical notions, this chapter aims to provide an instructive – albeit non-exhaustive – examination of some principal first-order approaches and methodological challenges, respectively. Socrates is a particular; his wisdom is a universal. While the foregoing is just the sort of example one might expect to kick off a handbook entry on the universal/particular distinction, its utility is limited. To see why, notice that it must be pitched at a level somewhere between pre-theoretical innocence and hyper-specialization. After all, the “folk” don’t think in terms of the philosopher’s “universal” at all, and thus will wonder why wisdom fits the bill. Indeed, many non-philosophers take “universal” to mean something like ubiquitous and rightly deny wisdom that status. In the other direction, many specialists simply reject the example, denying that any properties are universals. What’s more, audiences falling between novice and specialist will be hampered by their medial classification: their knowledge of the topic will suffice for them to understand the example, but perhaps not to understand why it’s controversial. So the situation is thrice deficient. Those most in need of examples of particulars vs. universals are apt to find them confusing, while those best equipped to assess such examples are apt to find them confused. Meanwhile, those in between likely are satisfied by the examples only because they’ve not yet learned the mitigating complications. These deficiencies notwithstanding, the Socrates/wisdom case serves as a useful entry point, since in this chapter I will discuss both whether pre-philosophical concepts shed light on the distinction between universals and particulars, and why professional metaphysicians find the distinction so unruly. The answer to the first question will be largely negative: the philosophical distinction doesn’t match any single folk distinction. The answer to the

DOI: 10.4324/9781003246077-8

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second question will be clear (I hope!), but hardly simple, as the reasons for the distinction’s unruliness are numerous and complicated. The docket: Section 5.2 contrasts the notions of universal and particular with four prephilosophical pairs of notions, namely, general/specific, repeatable/unique, property/ bearer, and type/token. Section 5.3 surveys several leading first-order criteria for drawing the universal/particular distinction, along with challenges to each. Finally, Section 5.4 considers some higher-order criteria for deciding among the approaches discussed in Section 5.3.

5.2 Pre-philosophical Distinctions in the Neighborhood of Universal/Particular This section considers a quartet of pre-philosophical concept pairings to see whether any robustly tracks the philosophical universal/particular distinction. I will conclude that none does. We will see, however, that some of these ordinary notions brush up against criteria that interest specialists. The first pair is general/specific. One immediate problem is that this dichotomy is gradient, while universal/particular is usually understood as binary and mutually exclusive. Another problem is that the general/specific distinction cuts within the class of prephilosophical particulars, as well as within the class of oft-accepted universals. Consider geographic locations, understood as physical tracts of earth or water. These are good candidates for mind-independent, pre-philosophically particular entities. Yet the northernmost quarter mile of the Mississippi River, qua geographic location, is more specific than, say, the western hemisphere. A traveler seeking direction to the former who is pointed to the latter will rightly resent his guide for furnishing too general a destination (assuming he’s not starting from Alpha Centauri). Or consider properties, which many metaphysicians take to be universals. The color property burnt umber, say, is more specific than the color property brown. A second pair worth considering is repeatable/unique. This suggestion faces two problems: possible repeatable particulars and possible unique universals. Regarding the former, think of eternal recurrence. Suppose the universe eventually implodes; however, the implosion is followed by a second Big Bang occurrence, with all the same sort of ensuing events, including second occurrences of the Mesozoic Era, the assassination of Archduke Franz Ferdinand, etc., followed eventually by the same sort of implosion, a third Big Bang occurrence, and so on. Given that future, Ferdinand and his life’s events will repeat indefinitely.1 Regarding unique universals, think of the property of being the single highest charged point particle in the universe (MacBride 1998: 218). That property appears to require uniqueness with respect to both intrinsic nature (qua highest charged) and location (qua point-sized); and yet some theorists are committed to its being a universal. Next, consider property/bearer. This pairing should be familiar, as it aligns with the opening wisdom/Socrates example. One problem here is that it’s questionable whether bearer (of properties) – taken as a general category – is really a pre-philosophical notion. (Try telling your plumber that some “property bearer” has clogged your drain.) A second is that the correct pairing ought to recognize second-order properties. After all, nonphilosophers understand what it is for, say, a color to be bright. So particularity can’t be captured by property bearing per se without risking collapse of the distinction from the getgo. In response, one might emphasize that universals are capable of being properties (even if they’re also capable of being bearers) while particulars are not. This suggestion is 62

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controversial (more below). Even if it’s sound, however, we’ve now outstripped prephilosophical considerations. Finally, consider type/token. Like bearer, token is only dubiously pre-philosophical. (“I have a token of clogged drain” won’t land well.) Moreover, thinking of universal/particular as syncing instructively with type/token raises problems similar to those plaguing instantiability as a guide to the distinction (on which more below), in that it’s already a source of disagreement whether types are anything other than particular complexes of their tokens, such as classes, sets, pluralities, or fusions. In summary, there is considerable reason to doubt that the philosophical universal/ particular distinction fits any of these pre-philosophical distinctions, nor is it to be understood as beholden to any of them. Still, the extent to which it ought to be allowed to stray from them may be a source of disagreement among theorists. For example, even if one doesn’t want to identify universals with properties and particulars with bearers, one might hold that, necessarily, if there are universals then they are properties.

5.3

First-Order Criteria for Drawing the Distinction

What, then, of philosophers’ attempts to characterize the distinction? In this section, I will survey and opine on some key specialized approaches. According to the repetition approach, universals are repeated or repeatable; particulars are not.2 Versions of the approach are common, including in recent research articles (e.g., Jones 2018: 825). I incorporate under this heading the treatment of universals as that which objects may have “in common”, since the implication there is that universals alone are capable of repeating across disjoint particulars (Perry et al 2022: 808).3 The disjointedness qualification is crucial, since two particulars can overlap in the sense of having a third in common. When he played both professional American football and professional baseball, Bo Jackson was a particular that the distinct rosters of the Los Angeles Raiders and Kansas City Royals had in common. Moreover, trope theorists can agree that objects “share” properties, and even tropes, without holding that properties or tropes are universals. An apple and its skin are numerically distinct; but the trope theorist is free to hold that they share one redness trope (Giberman 2022a). While disjointedness is important, it isn’t the only qualification needed. To see why, notice that plausible particulars repeat in the sense of having multiple alike constituents, each disjoint from the others. Consider the repetition inherent in checkerboards, chants, and shampoo applications. One familiar fix is to focus on the status of being wholly repeatable, which is achieved when the whole entity repeats, as opposed to when distinct proper parts or other constituents collectively yield repetition. Strictly speaking, however, no mereological commitment is needed. What matters is numerical identity: being lone repeatable. Disjoint black squares repeat collectively on a checkerboard, but no lone black square repeats. Blackness, by contrast, is thought to be lone repeatable, in that it is numerically identical across many black squares. Along what dimension does this lone repeatability obtain? The checkerboard example just described is ambiguous. Does the blackness repeat across its instantiations by the squares (Hoffman and Rosenkrantz 2003: 53)? Or rather across the locations of the (surfaces of the) squares (Armstrong 1978)? Or along some other dimension? The ambiguity avoids favoring immanent over transcendent universals, as the criterion might seem to do if repeatability concerns location. 63

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Return to the idea that blackness lone repeats across the checkerboard squares – that they “have it in common”. Suppose that idea is correct. Does it follow that blackness is a universal? Not obviously. For it may be that the trope theorist’s or class nominalist’s collection of blackness tropes or black objects itself lone repeats across the squares, its status as a collection notwithstanding. By analogy, consider Australia’s Olympic representatives and Australian Embassy representatives in Paris in 2024. The Australian Olympians and embassy officials are (I’ll assume) numerically distinct from each other, but the numerically selfsame whole nation of Australian citizens – that citizenry alone – is repeated in its role across the games and the embassy, its status as a collection (of persons) notwithstanding. Similarly, one might suggest, it’s the very same whole/entire collection/class/set/plurality/fusion of black tropes/objects that’s represented or exemplified at each of the checkerboard’s various black squares. For it’s the same property, blackness, that’s involved; and these theorists hold properties to be complexes of tropes or objects. (I will use “complex” as generic shorthand for the disjunctive “collection/class/set/plurality/fusion”.) One might suggest that the relevant lone repeater must somehow reside within each node of repetition, as blackness plausibly resides within each black square. The thought is that, since the entire complex of black tropes or objects is not appropriately within each square, non-universal conceptions of blackness fail the criterion. But again it isn’t obvious that this thought is correct. It really is the entire nation of Australian people that’s instanced/represented/involved “within” the Australian embassy in Paris. When application of some national policy occurs there, for example, its status as national is not limited to the involvement of people who happen to be in the embassy building that morning – it relevantly involves all Australians. Maybe the same is true of blackness and checkerboard squares. To be sure, it isn’t the entire Australian citizenry or the entire complex of black things/tropes that is spatially located within the relevant instances. But the question is whether the entire complex is involved at that instance in whatever sense of involvement property possession can neutrally be taken to require. If location is really what matters for universality, then lone repeatability per se is insufficient. One might try next to interpret “lone” in lone repeatability as entailing that the repeater has no internal membership or constituency structure. After all, collections, classes, sets, pluralities, and fusions (not to mention citizenries) all can have internal constituent structure, but plausibly universals cannot. Unfortunately, however, counterexamples for this version of the approach are not far to seek. Numbers – which are standardly taken to be particulars – are plausibly structureless lone repeaters across extensions with their cardinality: two plausibly is lone repeated across pairs of hands, pairs of bicycle wheels, etc. Furthermore, there debatably are metaphysically possible lone structureless repeated spatial objects, which are not plausibly universals. For example, consider a multiply located point-sized entity whose only intrinsic qualitative nature is some physical magnitude F. Qua multiply located, it repeats; yet qua point-sized and qualitatively limited to one property, it has no internal constituency. Finally, understanding the criterion via constituent-free lone repeatability would require either the flat rejection of structural universals or an understanding of structural universals as devoid of internal constituent structure. Given these complications, one might suggest characterizing universals as lone repeatable properties.4 However, nominalists about universals deny that properties are universals and, as we’ve seen, may allow that particular properties (understood perhaps as complexes of tropes or objects) are lone repeatable; but they do not deny that universals are definable. 64

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Consider next the instantiation approach, according to which universals are instantiated or instantiable, or perhaps multiply instantiated or instantiable, while particulars are not. This proposal is also fairly mainstream (Blackburn 1994: 387). Naturally, proponents of this approach must explicate instantiation – a non-trivial task. Instantiation, at least as applied to properties, is commonly understood as equivalent to possession, such that to be instantiated is to be possessed by a bearer. One problem with this common understanding for the present proposal is that universal-averse ontologists of properties allow that properties may be (or must be) possessed by bearers. The standard trope theorist (e.g., Campbell 1990) may hold that blackness is a complex of blackness tropes, that complexes of tropes are not universals, and that blackness is possessed by some checkerboard squares. Thus the proposal risks identifying the standard trope theorist’s properties with universals even though the standard trope theorist explicitly rejects that identification. Perhaps at this point, another appeal to wholeness or entirety would be useful, the idea being that to be a universal is to be wholly or entirely instantiable. One could then argue that complexes of tropes or objects are not ever wholly or entirely instantiated. Rather, the thought goes, they are merely instantiated by proxy: one of their constituents is directly related to the relevant property bearer, but nothing from the trope ontology is ever wholly/entirely instantiated by the bearer. Thus the black checkerboard square is, on trope theory, importantly related to one blackness trope from the complex of blackness tropes; but the square wholly/ entirely instantiates neither the trope (since only properties are instantiated) nor the complex (since the complex is too “big” to be wholly/entirely instantiated by the square). But again the issue turns on fine details about what instantiation is. As we saw above, it is clear that the entire complex of blackness tropes is not located at the black square. However, it is unclear that the blackness trope’s being a constituent of the black square (being in the square’s “bundle”) is not precisely what it is for the complex of blackness tropes to be instantiated – even entirely or wholly so – by the square (at the relevant place and time). Consider once more the Australian citizenry and its whole/entire involvement vis-à-vis the Australian embassy in Paris. There is no clear sense in which the citizenry is too “big” to be entirely/wholly involved in the embassy. Location simply is not part of the issue, as most Australians remain in Australia throughout their relevant involvement. If it turns out that location is crucial to the notion of being too “big” at work above, then instantiation per se is an insufficient criterion of universality. Yet if location is not what bars the trope theorist’s complexes of blackness tropes from being wholly/entirely instantiated by the checkerboard square, then the proponent of the present proposal owes a non-question-begging explication of what does. A third specialized approach to the distinction is based on discernibility. On this approach, universals satisfy (or can satisfy) the identity of indiscernibles; particulars do not (or cannot). Put differently, all and only particulars may have a qualitatively identical twin. This criterion has been endorsed by John Wisdom (1934), D.C. Williams (1953), and Douglas Ehring (2004, 2011). It is an important proposal, since it avoids many of the worries raised so far. Unfortunately, however, it faces its own putative counterexamples. First, distinct universals plausibly may be indiscernible, especially if there are good theoretical roles for such universals to play, such as allowing particulars to be bundles of universals (Rodriguez-Pereyra 2017). Second, it may be that some distinct universals are indiscernible because some abstracta (i.e., non-spatiotemporal entities) plausibly are intrinsically qualitatively empty: they’re bare ontological primitives that do certain explanatory work (say, being the semantic values of predicates).5 Third, it may be that some 65

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metaphysically possible particulars are discernible from everything else. Plausible examples here include gods, numbers, and the totality of modal space. Finally, if universals do have intrinsic natures but cannot have qualitative twins then an arbitrary plurality of universals will be discernible from everything else; yet pluralities of universals plausibly are not themselves universals, but rather particulars; so some particulars necessarily lack qualitative twins (Giberman 2016). These putative counterexamples bring out issues of higher order desiderata and methodology, including questions about topic neutrality and exhaustion (see Fisher 2020: fn 28 for helpful discussion). For example, must we decide whether numbers or gods exist in order to discern universals from particulars? Must universals have a qualitative nature? And if so, must no two of them exactly resemble? Are pluralities of universals really particulars or merely non-universals? Answering these questions is a task for future research. Moving on, a yet further approach is based on location. According to the most general version of this proposal, universals are (or can be) multiply located; particulars are not (or cannot be). This approach too is common, with versions appearing in work by David Armstrong (1978), Keith Campbell (1981, 1990), David Lewis (1986), and Jonathan Schaffer (2001: 248). As with repetition, the unqualified suggestion of multiple location is unpromising. Many particulars are multiply located in the unqualified sense. The Mona Lisa is in different places that correspond to its different parts: it is located (in the unqualified sense) both where its subject’s smile is represented and where her eyes are represented. Moreover, the whole painting counts (I assume) as having been located in different places over time, such as at Da Vinci’s workspace and (later) at the Louvre.6 Thus it is whole multiple exact location in space at some one time that matters for the present approach, and which its advocates usually intend. The Mona Lisa is neither wholly nor exactly where the eyes of its subject are represented, nor is it ever in Italy and France at the same time. And again, the mereological machinery isn’t required. The key idea is strict numerical identity: lone multiple exact spatial location at a given time. Even with these wrinkles ironed, there remain at least two senses of lone multiple exact spatial location that could underlie the approach. On the first, an entity can have the relevant status by being exactly located at two disjoint regions, even if it is not exactly located at some of the regions at which its parts or constituents are exactly located. On the second, if an entity has the relevant status then all of its parts or constituents are exactly located everywhere that any of them are exactly located. So, deploying the first sense, a relevantly multiply located watermelon might be exactly located at two disjoint watermelon-shaped-and-sized regions at the same time, but it cannot be exactly located where any of its seeds are exactly located. It is simply too big for that. By contrast, deploying the second sense, a relevantly multiply located watermelon is exactly located both at a watermelon-shaped-and-sized region and at each of its sub-regions, including every region at which any of the watermelon’s parts/members/constituents is exactly located, even the seed-sized ones. (The second sense allows that a multiply located watermelon might also be located at two watermelon-shaped-and-sized regions; it is the bit about being located also at sub-regions of watermelon-shaped-and-sized regions that matters.) The second sense is thus more extreme than the first. This extremity may benefit the location approach to the universal/particular distinction, if it could be established that universals plausibly satisfy the second sense. After all, the second sense, qua more extreme than the first, is better equipped to bar particulars from its graces. 66

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As with previous proposals, there are a number of known problems for the location approach. One was noted already: the property of being the highest charged point particle in the universe seems to be necessarily singly located (MacBride 1998). A second problem is that the location approach appears to rule out unduly the Platonic/transcendent ontology of universals, since those universals have no spatial location whatsoever (MacBride 2005; Russell 1911). Other problems concern particulars that seem capable of the relevant kind of multiple location. Consider, for example, a time-travelling enduring material object that travels to a time at which it already is present (Gilmore 2003; MacBride 1998). Such an entity would seem to be multiply located by being exactly and wholly at two places at once. Or consider so-called multi-locator extended simples: material objects that lack proper parts and yet exactly occupy some extended region and each of its sub-regions. Since material objects seem not to be universals, such objects pose a serious threat to the location approach (Ehring 2011; MacBride 1998). Whether these problems can be addressed adequately will turn once again on a number of further issues, such as whether spatial location of the relevant sort must be physical location, whether no universal can be a material object, and whether the more or less extreme sense of lone multiple location is what’s really behind the best version of the approach (some of these questions are addressed in Giberman 2022b). Another approach is based on predication. On this proposal, universals are predicated or predicable (either of particulars or of other universals); particulars are not. The relevant notion of predication is not contingent on linguistic facts, but rather concerns the mindindependent phenomenon of applying to or being true of subjects. While viewing predication as central to universality dates back at least to Aristotle, the bare appeal to predication per se is perhaps less common in the contemporary literature than appeals to repetition, instantiation, or location. Still, contemporary theorists no doubt treat predication as important to universality (see Carmichael 2010; see also Chapter 11, this volume). Similar concerns arise here as arose for the instantiation approach: properties seem to meet the predication condition, but many ontologists think that properties are not universals, but rather complexes of tropes or material objects. Of course, a proponent of the proposal would likely deny that complexes of tropes or objects are relevantly predicable. The question, then, is whether there are compelling independent reasons for this denial. Again, settling the ensuing debate(s) is a task for future research. There are more specialist proposals than I have space for here. I will close this section by briefly noting three further approaches, which respectively invoke qualitative simplicity, abstractness, and necessary existence as distinctive markers of universality. Regarding simplicity: some particulars, e.g., spacetime points, plausibly are qualitatively simple (Sider 2006); moreover, structural universals may be viewed as qualitatively complex. Regarding abstractness: taking abstractness to be non-spatiotemporality appears to rule out immanent universals; and taking it as involving acts of mental isolation of abstracta seems at odds with certain isolable entities that plausibly are particulars, such as dents (abstractable from bumpers) and smiles (abstractable from faces). Finally, regarding necessary existence: many immanent universals (if they exist) seem to lack it, while certain plausible particulars, such as gods or numbers (if they exist), seem to have it.

5.4 Second-Order Criteria This final section will consider some second-order criteria for adjudicating among the firstorder proposals. Due to spatial constraints, I will focus on only three. The first concerns 67

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direction of influence: should the distinction inform theoretical roles for universals and particulars, or vice versa? The second concerns the semi-formal properties of the distinction, such as whether it must turn out to be exclusive and exhaustive. Finally, the third concerns how neutral we must try to be when suggesting approaches to the distinction. Is it okay to foreclose certain debates? Or does doing so undermine a given approach to the distinction? All three are thorny issues, and I will not try to solve them here. My aim is to make their significance vivid. First, direction of influence: do we start with a stipulated theoretical role for, say, universals, and then draw the distinction so as to respect that role? Or is the distinction to enjoy final say over what the theoretical roles are? Suppose Anne requires universals to be properties, but accepts multi-locator extended simple material objects. Suppose further that she’s tempted toward the location approach to the distinction. What should Anne do at this point: give up multi-locator extended simple material objects? Start denying that all universals are properties? Accept that some properties are material objects? Or consider all this and decide in the end against the location approach? Or consider Bennie, who (i) doubts that particulars are (lone) predicable or (lone) repeatable and (ii) finds arguments for the discernibility approach compelling. Suppose he also takes seriously the contention that the entirety of modal space is characterized by a single modal-space-sized trope. Furthermore, he thinks that this trope, if it exists, necessarily lacks a qualitative twin and cannot lone repeat. Should Bennie then deny that it is a trope after all, since it is not a particular (given the discernibility approach)? And if he does so, should he allow that it’s predicable of modal space, since it seems to characterize modal space? Or should he continue to view it as a particular given its inability to lone repeat? Finally, should he simply deny that all tropes are particulars? Again, I have no advice on how to tackle these questions of direction of influence. But I hope their importance is clear. Second, the semi-formal contours of the distinction: must it be exclusive and/or exhaustive? It’s helpful to distinguish between weak and strong senses of exclusivity: (Weak Exclusivity) For any entity x and world w, if x is a particular at w then x is not a universal at w. (Strong Exclusivity) For any entity x, if x is a particular at any world then there is no world at which x is a universal. We can also ask whether the putative exclusivity is individual-specific or sortal-specific, as opposed to maximally general. For example, perhaps some relatively exotic kinds of entities like gods or fictional characters could be both universal and particular, even if no ordinary material object could be. Exhaustion can also come in more than one strength: (Weak Exhaustion) There is no entity x such that at every world at which x exists, x is neither a particular nor a universal. (Strong Exhaustion) There is no entity x at any world such that x is neither a universal nor a particular.

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Perhaps certain exotica are counterexamples to exhaustion. Consider a mereological fusion of an abstract (i.e., non-spatiotemporal) multiply instantiable color property and the Chrysler building. Call it “Pattie”. Is Pattie universal or particular? One might think the best answer is “neither”, since Pattie has elements that particulars are supposed to lack, as well as elements that universals are supposed to lack. In response, one might constrain exhaustion so that it applies only to fundamentalia: (Constrained Exhaustion) There is no entity x at any world such that (i) x is fundamental and (ii) x is neither a universal nor a particular. Note, however, that even Constrained Exhaustion might not fit with certain views, such as a maximal version of priority monism, understood as taking not just the spatiotemporal universe as fundamental, but the mereological fusion of everything that exists (including Platonic universals) as fundamental (on general priority monism, see Schaffer 2010). On this view, the one fundament is a candidate counterexample even to Constrained Exhaustion, since it enjoys both non-universal-ish and non-particular-ish features. Third, neutrality: how partisan, with respect to other issues in philosophy, is the universal/particular distinction allowed to be? Again a bifurcation between weak and strong notions is helpful. In the case of weak partisanship, those who endorse a given approach to the distinction strip one side of an (erstwhile) independent debate of certain arguments, intuitive results, or other dialectical resources that it otherwise enjoys. Below are three examples of weak partisanship. (Weak 1) The location approach may be endorsed in a way that keeps friends of extended simple material objects from being able to maintain that they’re functionally or categorially material objects, since their being universals might call those statuses into question. (Weak 2) The instantiation approach may be endorsed in a way that requires friends of tropes to give up the claim that trope complexes can usefully play the needed theoretical roles of properties. (Weak 3) The friend of exclusivity might endorse it in a way that requires gods to be either necessarily particular or necessarily universal. In the case of strong partisanship, those who endorse a given approach to the distinction leave one side of a debate completely untenable, often by outright rejecting the entities it defends. Below are three examples of strong partisanship, each corresponding to one of the earlier examples of weak partisanship. (Strong 1) The location approach may be endorsed in a way that simply rejects wholly multiply locatable material objects, thereby rejecting multi-locator extended simple material objects. (Strong 2) The instantiation approach may be endorsed in a way that simply rejects tropes. (Strong 3) The friend of exclusivity might simply reject the metaphysical possibility of gods. 69

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It seems generally better to be only weakly partisan, if one cannot manage complete neutrality. Unfortunately, however, the weakly partisan positions tend to result in difficult trade-off cases. In closing, my two cents is that these and many other issues that surround the universal/ particular distinction are important for a variety of topics in metaphysics and beyond. Yet attributing such value to the subject is compatible with acknowledging that there may be no ultimate core conception of the universal/particular dichotomy that is uniquely correct or even uniquely beneficial. What is uncontroversially worthwhile is the goal of increased clarity about the surrounding issues, consequences, and potential problems for certain ways of characterizing universality and particularity.7

Notes 1 Quibble: isn’t each of the recurring Archduke Franz Ferdinands a distinct, rather than a repeated, particular? Maybe. But then what does “Archduke Franz Ferdinand” refer to when we talk of each Archduke Franz Ferdinand? A universal? It’s far from clear that that’s the best interpretation of the eternal recurrence thought experiment. 2 “Non-repeatable” and “unique” are not appropriately synonymous here, since specialists often take universals to have unique natures or theoretical roles, and thus to be unique, while also relevantly repeatable. 3 Other discussions of “common” factors or natures (e.g., Campbell 1990: 30–31; or Maurin 2002: ch. 5) do not take repetition to be sufficient for universality. 4 Something like this approach appears in Kim et al (2012: 269) and Rosen et al (2018: 457). In fairness, these authors are introducing the notions and don’t portray their contribution as final. 5 On the abstract/concrete distinction, see Chapter 6, this volume. 6 This “counts as” locution indicates neutrality regarding the persistence debate. 7 Thank you to the participants in the Online Properties Conference (16–18 May 2022) for this volume for helpful discussion and feedback.

References Armstrong, D.M. (1978) Universals and Scientific Realism v. 1: Nominalism and Realism. Cambridge: Cambridge University Press. Blackburn, S. (1994) The Oxford Dictionary of Philosophy. Oxford: Oxford University Press. Campbell, K. (1981) The Metaphysic of Abstract Particulars. Midwest Studies in Philosophy 6: 477–488. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Carmichael, C. (2010) Universals. Philosophical Studies 150(3): 373–389. Ehring, D. (2004) Distinguishing Universals from Particulars. Analysis 64(4): 326–332. Ehring, D. (2011) Tropes: Properties, Objects, and Mental Causation. Oxford: Oxford University Press. Fisher, A.R.J. (2020) Abstracta and Abstraction in Trope Theory. Philosophical Papers 49(1): 41–67. Giberman, D. (2016) Indiscernibility Does Not Distinguish Particularity. Thought 9(1): 51–57. Giberman, D. (2022a) Ostrich Tropes. Synthese 200(1): 1–25. Giberman, D. (2022b) Whole Multiple Location and Universals. Analytic Philosophy 64(4): 245–258. Gilmore, C. (2003) In Defence of Spatially Related Universals. Australasian Journal of Philosophy 81(3): 420–428. Hoffman, J. and Rosenkrantz, G. (2003) Platonistic Theories of Universals. In Loux, M. and Zimmerman, D. (eds.) The Oxford Handbook of Metaphysics. Oxford: Oxford University Press. 46–74. Jones, N. (2018) Nominalist Realism. Noûs 52(4): 808–835.

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Universality and Particularity Kim, J., Korman, D., and Sosa, E. (eds.) (2012) Metaphysics: An Anthology, 2nd Ed. Malden, MA: Wiley-Blackwell. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. MacBride, F. (1998) Where Are Particulars and Universals? Dialectica 52(3): 203–227. MacBride, F. (2005) The Particular-Universal Distinction: A Dogma of Metaphysics? Mind 114(455): 565–614. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. Perry, J., Bratman, M., and Fischer, J.M. (eds.) (2022) Introduction to Philosophy: Classical and Contemporary Readings, 9th Ed. Oxford: Oxford University Press. Rodriguez-Pereyra, G. (2017) Indiscernible Universals. Inquiry 60(6): 604–624. Rosen, G., Byrne, A., Cohen, J., Harman, E., and Shiffrin, S. (eds.) (2018) The Norton Introduction to Philosophy, 2nd Ed. New York: W.W. Norton. Russell, B. (1911) On the Relations of Universals and Particulars. Proceedings of the Aristotelian Society 12: 1–24. Schaffer, J. (2001) The Individuation of Tropes. Australasian Journal of Philosophy 79(2): 247–257. Schaffer, J. (2010) Monism: The Priority of the Whole. Philosophical Review 119(1): 31–76. Sider, T. (2006) Bare Particulars. Philosophical Perspectives 20: 387–397. Williams, D.C. (1953) On the Elements of Being: I. The Review of Metaphysics 7(1): 3–18. Wisdom, J. (1934) Problems of Mind and Matter. Cambridge: Cambridge University Press.

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6 ARE PROPERTIES ABSTRACT ENTITIES? Sam Cowling

6.1 Introduction When introducing the metaphysics of properties – usually in class, but sometimes on airplanes – we often find ourselves in the awkward position of having to explain what kinds of things properties are in the broadest possible sense. Faced with this challenge, a first strategy is to enumerate examples: redness, humanity, fragility. A second strategy is to describe their theoretical role: they are the ways things are or could be, but not the things that have them. Understandably enough, some remain quite confused even at this point. It is tempting, then, to launch into a third, more ambitious strategy, which begins by sketching a picture of reality according to which there are, on the one hand, elbows and alligators and, on the other hand, numbers and possibilities. The former are concrete entities. They can be created or destroyed. They have more or less specific locations. They can be known through perception. In contrast, the latter are abstract entities. They aren’t created or destroyed (though our words for and thoughts about them are). They aren’t located anywhere (or at least not in any familiar way). They can be known, but such knowledge is secured only through peculiar means like mathematical intuition or rational reflection. Our introduction to the metaphysics of properties now continues: properties are like numbers and possibilities, not elbows and alligators. They are abstract entities, not concrete things. So, just as mathematical inquiry into numbers is a distinctive enterprise that requires mathematical expertise, metaphysical inquiry into properties is similarly complicated and, among other things, it requires a clear understanding of this distinction between abstract and concrete entities (on this picture and competing views of the abstractconcrete distinction, see Burgess and Rosen 1997 and Szabo 2003). As we’ll see shortly, every part of this third strategy is the subject of metaphysical controversy. Even so, the view sketched above enjoys a plausible claim to being the standard one and regularly serves as the backdrop against which dissenting views are characterized. By way of preview, there are some who deny that there is a significant distinction between the abstract and the concrete. There is also widespread disagreement about the features that are distinctive to abstract entities – e.g., about whether they have locations or causal powers. And, finally, there are many philosophers who deny that

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properties are abstract entities and instead claim that they are no less concrete than your coffee mug. This chapter explores some of these disagreements in order to understand how the abstract-concrete distinction bears upon the metaphysics of properties and vice versa. Before proceeding, let me mark two assumptions that narrow our field of inquiry. First, I assume that the general commitments of views on which properties are universals, tropes, or sets are well understood, and, given length constraints, I focus mostly on the interaction of these three views with the abstract-concrete distinction. I therefore assume the mindindependent existence of properties which is a shared commitment of these views. I will, however, briefly consider the interaction of the abstract-concrete distinction with views that deny the existence of properties in the final section. Second, I assume the separability of the abstract-concrete distinction from the nearby distinction between particulars and universals. Universals are standardly taken to be general entities that are in some sense shareable. In contrast, individuals like Napoleon are standardly held to be particular entities. If one adopts an ontology solely of universals and ordinary individuals and holds universals to be abstract entities, our two distinctions would coincide. Notice, however, that if one posits the existence of numbers in addition to ordinary individuals, these distinctions crosscut reality: some particulars like the number seven are abstract but others like Napoleon are concrete. Further complexity results from the fact that trope theories are regularly described as holding properties to be abstract particulars rather than universals. The complicated relationship between these two distinctions is therefore a product of both ontological disagreement – namely, disagreement about what exists – and categoreal disagreement – namely, disagreement about what ontological categories entities fall within. In debates about the metaphysics of properties, the particular-universal distinction arguably occupies pride of place over the abstract-concrete distinction. It has a more extensive historical pedigree and plays a key role in understanding the differences between contemporary views of tropes and universals. A careful account of how it informs the current debate over properties is provided in Chapter 5, this volume.

6.2

The Abstract-Concrete Distinction

The abstract-concrete distinction is often held to partition reality as follows. It is both an exhaustive distinction, requiring that each entity is abstract or concrete, and an exclusive one, permitting no entities to be both abstract and concrete. The abstractness or concreteness of an entity is an absolute matter: entities are not merely abstract (or concrete) relative to something else; they instantiate a monadic property of being abstract (or being concrete). Moreover, this status is invariant: entities are not abstract at some world or time and concrete at others. They have their status essentially and permanently. Finally, abstractness and concreteness do not admit of degree, so entities cannot be more or less abstract even if some entities might be more or less controversial candidates for being abstract (on these and related features of the abstract-concrete distinction, see Cowling 2017). Suppose that the abstract-concrete distinction partitions reality in the way just described. What determines which entities fall on either side of the metaphysical line? One way to answer this question is to provide an analysis of what it is for an entity to be abstract.1 A reductive analysis of the abstract-concrete distinction would offer informative and non-trivial necessary and sufficient conditions for being abstract. Such analyses can be formulated using the following schema: necessarily, x is an abstract entity if and only if _____. A plausible 73

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analysis of abstractness would be valuable for several reasons, but most immediately it promises a recipe for sorting reality into the separate domains of the abstract and the concrete. In order to clarify his notorious doctrine of modal realism, David Lewis (1986: 81–86) examines a handful of ways in which philosophers purport to distinguish the abstract and the concrete. Several of these “ways” can be developed into reductive analyses of the distinction. For present purposes, we will focus on three of them and their consequences for the question of whether properties are abstract entities. According to what we can call the Way of Location, necessarily, x is an abstract entity if and only if x lacks spatiotemporal location.2 If our concern is solely with numbers and their status as paradigmatic abstract entities, the Way of Location seems a promising way to define abstractness. It would be bizarre to ascribe the number seven a specific spatial location and, while the relationship of numbers to time is a vexed matter, it is plausible to hold such entities to be “outside” of time rather than, say, existing at all times.3 Depending on which ontology one adopts, the Way of Location delivers quite different verdicts on the abstractness of properties. If properties are held to be transcendent or Platonic universals, they are abstract in virtue of existing outside of space and time. On views that take universals to be immanent or Aristotelian entities – located wherever they are instantiated – they turn out to be concrete entities (on universal theories, see Armstrong 1978). The same holds true for tropes which are usually held to be located where their bearers are (on trope theories, see Campbell 1990; Ehring 2011). Additionally, if properties are identified with sets of entities and impure sets – roughly, sets with concrete individuals as members – are located where their members are, the Way of Location entails that properties are concrete rather than abstract (on set-theoretic views of properties, see Armstrong 1978; Lewis 1983). The Way of Location ties the abstract-concrete distinction to the weighty matter of whether something is found within spacetime, but it is far from clear that lack of spatiotemporal location is a genuine mark of abstractness. Consider, for example, the prospect of physical theories according to which there is a fundamental level of reality more basic in our physical explanations than spacetime. In such a scenario, there is little temptation to think the relevant posits would be properly categorized alongside numbers as abstract solely because they are non-spatiotemporal. Ultimately, facts about spatiotemporal location seem inadequate for characterizing the abstract-concrete distinction. The same goes for modal facts about necessary or contingent existence. Although natural numbers are paradigmatic abstract entities and are regularly held to be necessary existents, mere necessary existence seems to be neither a necessary nor sufficient condition for abstractness. A necessarily existing Abrahamic God is a distinctive kind of concrete posit, and, if transcendent universals existed only contingently, this seems irrelevant to their standing as abstract entities (see Adams 1981). Although more complex modal-spatiotemporal properties like being essentially non-spatiotemporal might better comport with intuitions about abstractness and concreteness, it will be useful to turn now to approaches that draw upon different core notions – most notably, causal structure. According to the Way of Causation, necessarily, x is an abstract entity if and only if x is non-causal – i.e., x does not or cannot stand in ordinary causal relations to individuals. Roughly speaking, the Way of Causation takes abstract entities to be outside of the causal structure of creation, destruction, and change that pervades concrete reality. Like the Way of Location, this analysis takes a feature plausibly ascribed to numbers – being non-causal – as 74

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the mark of abstractness.4 It is, however, unclear whether causal inactivity is a plausible sufficient condition for being abstract. Consider the case of what Peter Forrest (1982) calls an “epiphenomenalon” – a physical yet causally inert particle. Since such an entity seems conceivable but not intuitively abstract in nature, it is unclear that causation is the right tool for marking the abstract-concrete divide. When we turn to the verdicts the Way of Causation delivers about properties, it proves difficult to extract a clear answer. This is partly because, on many views, properties occupy a crucial role in providing explanations of causal phenomena. The blackness of the surface is what causes it to retain heat. The mass of the particle is what causes it to decelerate. To deny that properties are potential, though perhaps only partial, causes of events would be to significantly undermine a standard way to defend their existence and theoretical importance. But, if we revise the Way of Causation by stipulating that properties are not causal in the sense relevant for being concrete, it is unclear how this would differ from simply insisting that properties are abstract and objects are not. It is more plausible for defenders of tropes and universals to reject the Way of Causation altogether. Views on which properties are sets are in a similar position. For, while it is tempting to assume that sets are non-causal in virtue of being mathematical entities like numbers, some sets enter into what are arguably causal relationships: impure sets come into being only when their concrete members do and, upon the destruction of their members, presumably cease to exist. Given such cases, any verdict the Way of Causation might offer on properties will be a tendentious one. The preceding reductive analyses focus on features that abstract entities allegedly lack like locations and causal powers. In contrast, what Lewis (1986: 85) calls the Way of Abstraction holds abstract entities to be those things that “result from somehow lacking specificity, so that an incomplete description of the original concrete entity would be a complete description of the abstraction.” Given this rough but intuitive characterization, abstractions do sound rather like properties. We can talk, for example, about the property of mass being only an “abstraction” from massive things. But, while some abstractions seem suitable for identification with tropes or universals, Lewis (ibid.) argues that the Way of Abstraction cannot be used to demarcate properties in general: But we cannot just identify abstractions with universals or tropes. For why can we not abstract some highly extrinsic aspect of something - say, the surname it bears? Or its spatiotemporal location? Or its role in some causal network? Or its role in some body of theory? All these are unsuitable candidates for genuine universals or tropes, being no part of the intrinsic nature of the thing whence they are abstracted. Lewis’s argument here assumes that tropes and universals are relatively sparse: only certain predicates – namely, those concerning the intrinsic and relatively natural features of objects – express properties. In contrast, abundant views – roughly, views that hold all (non-paradox inducing) predicates express properties – reject this assumption by positing a trope or universal for each of the highly extrinsic features Lewis mentions (see Chapter 4, this volume). But, while such abundant views are theoretical options, it remains difficult to reconcile abundantism with the assumptions about location and constituency that trope and Aristotelian universal views standardly adopt. Although redness and mass might be envisioned as constituents of red things and particulars, it is not clear how to account for the location or constituency of properties such as being to the left of a thing with the same last name. 75

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The Way of Abstraction faces additional extensional challenges (e.g., regarding propositions and natural numbers), but it does prove useful for marking the historical connection between abstract entities and the cognitive process of abstraction which is often thought to underwrite our epistemic access to properties (see also Fisher 2020 on the relationship between abstraction and trope theory). And, as noted in Section One, some philosophers have argued that we enjoy a distinctive kind of epistemic rapport with mathematical entities that is radically unlike our ways of knowing concrete entities. Despite the regularity with which abstract entities have been claimed to have a unique epistemological status, there is no viable strategy for marking the abstract-concrete distinction in purely epistemic terms, especially since many views assert that we are perceptually aware of properties. Independent of concerns about properties, all of the preceding approaches for reductively analyzing the abstract-concrete distinction face challenges. Taken together, they deliver conflicting verdicts about the abstractness or concreteness of properties, depending upon both how the analyses are implemented and, of course, what one takes properties to be. Perhaps the strongest conclusion that can be drawn is that, if one takes properties to be non-causal transcendent entities, their affinity with mathematical entities make them likely to be counted as abstract. For some philosophers, the ambiguity of talk about abstract and concrete entities, coupled with its limited theoretical usefulness, suggests that we are best served to dispense with it as a piece of metaphysical theory. In slogan form, the case for this kind of eliminativism about the distinction might be put as follows: if we are not sure which things are abstract, why they are abstract, or why it would matter, then we should stop talking about abstractness and concreteness altogether. I return to the prospects for eliminativism in the final section.

6.3 Must Properties Be Abstract Entities? Our understanding of the abstract-concrete distinction is not an all or nothing affair nor is it wholly dependent upon the availability of a reductive analysis. As with other kinds of entities, we can learn much that is useful by discovering certain necessary or sufficient conditions for being an abstract entity. On primitivist views, the distinction is an ineliminable piece of theory, but one that cannot be reductively explained. And, for would-be primitivists, a crucial question is whether being a property is a sufficient condition for being an abstract entity. As we saw above, analyses of the distinction offer competing verdicts about the abstractness of properties. In some cases, the proposed analyses seem to misclassify entities. For instance, if the Way of Location deems impure sets concrete in virtue of being located, we are better served to simply reject the Way of Location (or deny that impure sets are located). In other cases, especially ones regarding tropes and universals, matters are much less clear. This is likely due to the peculiar theoretical grasp we have of tropes and universals. Our grounds for positing them and, in turn, our understanding of them, flows almost exclusively from the metaphysics of properties. In this respect, tropes and universals are importantly different from sets, which we know best via our mathematical theories. Given this difference, one might conclude that the relationship of tropes and universals to the abstract-concrete distinction is a negotiable matter: we can assign them whatever status best serves our metaphysical purposes. In stark contrast, however, many philosophers posit an affinity between properties, propositions, and mathematical entities and take their 76

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abstractness to be self-evident. On such views, the abstractness of properties is far from negotiable. It is instead held to be a conceptual necessity that being a property turns out to be a sufficient condition for being an abstract entity. But why think that properties, regardless of their ontological category, are abstract entities? I take it that the best available argument runs roughly as follows. The essential theoretical role of properties revolves around their conferral of qualities upon individuals – in short, properties explain why things have the qualities that they do. Crucially, this distinctive species of metaphysical explanation is radically unlike the explanations which concrete entities can enter into. If properties were concrete entities, they would be incapable of accounting for the conferral of qualities. Perhaps they figure into some metaphysical explanations, but the conferral of qualities simply isn’t the kind of thing that concrete reality can explain. So, unless properties occupy a radically different ontological category – namely, that of abstract entity – they cannot accomplish the essential explanatory work required of them. The preceding argument assumes a view of properties and their explanatory value that can be resisted in several ways, but, for our purposes, the key question is whether it is the abstractness of properties that makes them suitable for occupying this theoretical role. One way to show that abstractness is not required for properties to serve as the conferrers of qualities is to show that there are credible views that identify properties with concrete entities. Importantly, this cannot be accomplished by simply insisting that one could categorize tropes or universals as concrete, since the plausibility of doing so is precisely what is at issue. We must instead draw from ontological categories that are not introduced or grasped solely via the metaphysics of properties. One view of properties that might serve this role is mereological nominalism, according to which properties are concrete objects or the mereological sums thereof. Roughly put, such a view takes humanity to be identical with the mereological sum of all humans (on mereological nominalism, see Effingham 2020). While such a view warrants broader consideration, it is poorly suited as a tool for rebutting the argument set out above. The explanatory role of the properties in question is their status as the explanans of the qualities of concrete objects, so positing yet more concrete objects and pointing toward their qualities seems to send us into an explanatory circle. An alternative metaphysics of properties that is better suited to rebutting the above argument is locationism, according to which properties are identical with regions or locations. On such a view, properties are to be distinguished from the category of concrete objects and from the category of abstract entities. They are, instead, concrete locations (on locationism, see Cowling 2014). Where more familiar species of property realism posits distinctive relations like instantiation, compresence, or exemplification, locationism holds that the relation between objects and properties is of the same ideological kind as the occupation relation that objects bear to regions of spacetime. Just as objects are extended in virtue of occupying certain regions of spatiotemporal locations, objects are massive in virtue of occupying certain locations in quality-space. The resulting framework aims to unify the metaphysics of properties with the metaphysics of location and dispense with separate primitive notions. For instance, the phenomenon of intrinsic qualitative change is to be understood in terms of objects moving through quality-space in analogy with how changes in the position of objects can be understood in terms of their pattern of spatiotemporal location (on the role of locationism in interpreting physical theory, see Arntzenius and Dorr 2012). 77

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The case for locationism draws partly on theoretical conservatism: we have an independent grasp on and case for positing the existence of locations, so accounting for property-theoretic phenomena like change and similarity via locations is preferable to admitting sui generis entities like tropes or universals. Moreover, since locations are immanent, contingent, known through perception, and play causal roles in our best physical theories (e.g., the curvature of spacetime explaining facts about acceleration), there is adequate reason to believe they are concrete. There is therefore no barrier to holding that concrete locations can provide the metaphysical explanations distinctive to properties – namely, conferring qualities upon objects. Those committed to the view that being a property is a sufficient condition for being abstract might object that locations are, contrary to what one might expect, abstract entities. And, while one finds remarks in Carnap (1950) suggestive of the view that spacetime points are abstract entities, the causal, immanent, and contingent character of spatiotemporal explanations in our best physical theories is reason to believe that, if spatiotemporal locations exist, they are concrete in nature. A more fine-grained objection is that, unlike spatiotemporal locations, the locations that confer qualities upon objects – namely, regions of quality-space – are abstract entities even if spatiotemporal locations are concrete. Against this objection, notice that locationism is premised upon the thesis that location is an ontological category that subsumes species like spatiotemporal location as well as spatial location and temporal location. But all locations – quality-space included – have the capacity to supply certain kinds of causal explanations. In particular, the kinds of explanations that invoke quality-space concern qualities like mass and colour rather than, say, shape and size. Since there is no non-question begging reason to insist upon the abstractness of quality-space, locationism serves as a useful counterexample to the view that properties are by definition abstract entities. Whether or not we find locationism ultimately appealing, we should nevertheless deny that being a property is a sufficient condition for being abstract.

6.4 Uses and Abuses of the Abstract-Concrete Distinction Let’s conclude with what the abstract-concrete distinction cannot do for us. Consider the following argument one sometimes encounters: Abstract entities are, by their very nature, entities of kind K (e.g., non-spatiotemporal, necessarily existing) and properties are abstract entities, so properties are, by their very nature, entities of kind K. Arguments of this form should leave most of us unconvinced, given the substantial challenges each premise faces. As a result, there is little reason to believe that we can credibly rely upon the abstract-concrete distinction to settle debates about whether properties are located, noncausal, necessarily existing, or what have you. We should also be wary of nominalist arguments that invoke abstractness in order to make a case against the existence of properties. A plausible argument against properties ought to establish a claim regarding the specific nature of properties (e.g., that they lack spatiotemporal location) and then show that entities of such nature are problematic (e.g., because of epistemic worries about non-spatiotemporal entities). Appeals to the abstractconcrete distinction are not a replacement for either of these steps especially given our tentative grip on the distinction and where properties fall relative to it. In general, arguments against the existence of properties are usually more tendentious and therefore less 78

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convincing to the extent that they rely upon general claims regarding abstract-concrete distinction. Upon closer scrutiny, the limited value of the abstract-concrete distinction for deriving insights about properties should be unsurprising. Notice that the kind of phenomena properties are often held to explain (e.g., resemblance, laws, causation) seem conceptually prior to the abstract-concrete distinction. These phenomena generate more urgent philosophical concerns than the project of sorting through our hazy sense of what abstract entities are really like. Our best theories about properties should not be hostage to our hunches about abstractness. We should also be suspicious of efforts to ward off concerns about properties by simply announcing that they are concrete rather than abstract. If we cannot determine the nature of properties on the basis of their claimed abstractness, we cannot sanitize them against metaphysical or epistemological objections simply by claiming they are concrete. As we have seen, there is a lot that the abstract-concrete distinction cannot do. Indeed, the fact that it affords us so little assistance seems to be a point in favor of eschewing the distinction entirely. At such points, the assessment offered by Theodore Sider (2013: 287) seems apt: The abstract/concrete distinction behind this objection is a relic of a certain theory. According to this theory, reality divides into two realms—abstract and concrete—in a way that is significant on various fronts. Epistemic: we know about the abstract a priori. Modal: facts about the abstract are necessary. Causal: the abstract is causally inert. Spatial: abstract entities are not in space and time. But this is just a theory, nothing more. It’s not sacrosanct; nothing supports it other than tradition; and it should stand aside if it obstructs an attractive simplification of ideology. There are, however, two reasons to think that we cannot yet dispense with the abstractconcrete distinction. First, as noted earlier, the lack of unanimity about abstractness and concreteness does not mean that, within a specific metaphysical theory, it cannot be put to productive albeit theoretically partisan use. It is, for example, open to a realist about properties or numbers to hold that abstract entities have distinctive metaphysical features in virtue of their abstractness or, more boldly, to claim that such entities are graspable via rational intuition precisely because of their abstractness. Clearly, this would be a controversial and highly partisan stance toward abstractness, but if the resulting theory proved powerful and otherwise attractive, it might emerge as the most reasonable way to conceive of the distinction. Like many other theoretical “relics”, it is the explanatory value of abstractness within a specific metaphysical theory rather than its non-negotiable place in our scientific or folk theories that proves significant. While the abstract-concrete distinction may be of little interest when we aspire to neutrality between competing theories, it is potentially a valuable tool when put to work in a fully articulated metaphysics of properties. Second, the question of whether we should retain, or jettison certain distinctions and concepts is often answered by looking solely at their place in our fully articulated theories. On such an approach, if a property does not occur in our canonical, formal expression of our theory, then, other things being equal, we can simply disregard its significance and avoid invoking it. But, obviously, we present our theories in classrooms, on airplanes, and at conferences in a host of informal and often quite peculiar ways – e.g., by using the 79

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propaedeutic with which this chapter began. In some cases, the extent to which theories can be grasped at all might depend upon the heuristic use of concepts that ultimately fall away in our final formulations. While our ideological commitments, narrowly understood, do not extend to whatever we talk about when we present novel theories to the uninitiated, it would be a mistake to focus our metaphysical attention solely upon formalized theories. When we turn our attention to heuristic, informal roles of this kind, the abstractconcrete distinction turns out to be quite powerful. For all its imprecision, it does allow us to sort potential ontological commitments into categories that are unified by similar philosophical concerns. Similarly, it permits us to sift through metaphysical theories that exhibit substantial agreement with each other on account of whether they posit similar entities. So, while it is a highly imperfect tool for taxonomy, it is nevertheless an expedient way to set our philosophical agenda when it comes to investigating different kinds of entities and evaluating different sorts of theories. For instance, to identify a metaphysics of properties as platonist is, in part, to indicate that its distinctive posits have more in common with paradigmatic abstracta like natural numbers than ordinary individuals. This in turn conveys that its theoretical challenges and its vices and virtues have an affinity with certain “platonist” views in the philosophy of mathematics. In these admittedly vague ways, the abstract-concrete distinction exerts influence over metaphysical practice as an informal, agenda-setting apparatus. Depending on how one views the broader trajectory of the metaphysics of properties, this influence might be seen as vicious or virtuous. Importantly, however, its competitor is not the outright elimination of heuristic uses of concepts and distinctions; the practice of metaphysics can hardly do without them. Its natural rival is, instead, some altogether different suite of undefined concepts and murky distinctions that are almost certainly subject to comparable controversy.5

Notes 1 Alternatively, one could analyze concreteness and then analyze abstractness. If the distinction is assumed to be exclusive and exhaustive, these strategies can be treated as largely interchangeable. 2 This is one of several ways to refine what Lewis (1986) calls “the Way of Negation” which distinguishes abstract entities by what they lack relative to concrete ones. What I call “the Way of Causation” is a competing version of Lewis’ Way of Negation. 3 I set aside complications about the distinction between spatiotemporal location versus spatial location and temporal location for present purposes. See Hoffman and Rosenkrantz (2003). 4 The causal isolation of mathematical entities is an abiding theme in contemporary philosophy of mathematics due in part to Benacerraf (1973). For discussion, see Leng (2010). 5 Thanks to Justin Mooney and Kelly Trogdon for helpful comments and discussion.

References Adams, R.M. (1981) Actualism and Thisness. Synthese 49(1): 3–41. Armstrong, D.M. (1978) Universals and Scientific Realism. Vols I and II. Cambridge: Cambridge University Press. Arntzenius, F. and Dorr, C. (2012) Space, Time, and Stuff. Oxford: Oxford University Press. Benacerraf, P. (1973) Mathematical Truth. Journal of Philosophy 70(19): 661–679. Burgess, J.P. and Rosen, G. (1997) A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford: Clarendon Press. Campbell, K. (1990) Abstract Particulars. Oxford: Blackwell.

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Are Properties Abstract Entities? Carnap, R. (1950) Empiricism, Semantics, and Ontology. Revue Internationale de Philosophie 4(11): 20–40. Cowling, S. (2014) Instantiation as Location. Philosophical Studies 167(3): 667–682. Cowling, S. (2017) Abstract Entities. London: Routledge. Effingham, N. (2020) Mereological Nominalism. Philosophy and Phenomenological Research 100(1): 160–185. Ehring, D. (2011) Tropes: Properties, Objects, and Mental Causation. Oxford: Oxford University Press. Forrest, P. (1982) Occam’s Razor and Possible Worlds. The Monist 65(4): 456–464. Fisher, A.R.J. (2020) Abstracta and Abstraction in Trope Theory. Philosophical Papers 49(1): 41–67. Hoffman, J. and Rosenkrantz, G. (2003) Platonistic Theories of Universals. In Loux, M.J. and Zimmerman, D.W. (eds.) Oxford Handbook of Metaphysics. Oxford: Oxford University Press: 46–74. Leng, M. (2010) Mathematics and Reality. Oxford: Oxford University Press. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Sider, T. (2013) Against Parthood. Oxford Studies in Metaphysics 8: 237–293. Szabo, Z. (2003) Nominalism. In Loux, M.J. and Zimmerman, D.W. (eds.) Oxford Handbook of Metaphysics. Oxford: Oxford University Press: 11–45.

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7 RELATIONS Existence and Nature Fraser MacBride

7.1 Introduction Here are four metaphysical questions which need to be asked about relations. What are they supposed to be? What are they supposed to do? How are they supposed to do it? Are there any? Epistemic, semantic, and logical questions also need to be asked about relations. How are relations given to us? How do we talk about them? What logic is required to reason about them? I’m going to focus on the metaphysics of relations. But that’s not because I think metaphysics has some kind of foundational significance. Far from it. Epistemology, semantics, and logic are never far away and typically close by. And we need answers to all these questions about relations, answers which hang illuminatingly together, before we can legitimately claim to truly understand the nature of relations. I’ll start by considering what relations are supposed to do. Why start there? Because relations are hypothesised to do what they’re supposed to do. Let me elaborate in a preliminary way. We take relations to be a certain kind of entity designed to fulfil a certain brief. Hence if there is a need for something to fulfil that brief and nothing else can do it better, then we have reason to believe relations exist. But if there isn’t a need for anything to do what they’re supposed to do, or there is a need but other things can fulfil that brief better, then we don’t have reason to believe they exist. Thereby we navigate a path from considering the design brief of relations to considering what they are, if there are any, and thence to considering whether there are any. Why do we also need to consider how they do what they are supposed to do? Because if we can’t understand how it’s possible for relations to fulfil their design brief then that’s another kind of reason not to believe in them. And if one theory of what relations are, T1, can explain how it’s possible for them to fulfil their design brief whereas another, T2, cannot, that’s a reason for us to favour T1 over T2 as an account of the nature of relations. That’s an abstract description of some of the most significant theoretical choice points which we will have to negotiate enroute to a theory of relations worth taking seriously. Although abstract it’s a description that will help us find our way.1 Along the road I consider examples couched in ordinary language or regimentations thereof, rather than

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examples couched in the language of mathematics and science. That’s not a shortcoming because the need for a metaphysics of relations, whether aye or nay, is already evident from examples couched in ordinary language and more theoretical discourse still presupposes a grasp of ordinary language.

7.2

The General Design Brief of Relations

What are relations supposed to do? There’s more to say but the simple answer is that relations are supposed to explain the fact that the world consists of related things. That’s an answer which is liable to sound uninformative. There are two systematic reasons for this. One is that ordinary language doesn’t sharply distinguish talking about one thing being related to another and there being a relation between them. About, for example, a medical condition and a given symptom we might say that they are closely related. But we might just as well say that there is a close relation between them – without thereby meaning something different, the difference being merely a matter of literary style. The other reason is that talk of relatedness and relations is pretty much basic, so there’s no elucidating relatedness or introducing relations without ultimately circling back to where we started. How then are we ever to get started on the metaphysics of relations? We can draw upon the knowledge implicit in our understanding of familiar English verbs. This doesn’t mean turning our attention away from the world to language. Because by reflecting on what our descriptions of the world require of the world to be true, we can find out what the world must be like if our descriptions are true. Consider the verbs ‘glue’, ‘fasten’ and ‘tie’ and the preposition ‘to’. We use them to describe (truly or falsely) how one thing is glued to or fastened to or tied to another thing. We have ‘connect’ as well. Using ‘connect’ and ‘to’, we are able to state in more generic terms what is common between things which are glued or fastened or tied together – that this one is connected to that one, this other one to that other one, and so on. But this is only the beginning. English has an extraordinary supply of vocabulary for describing the myriad ways in which things are connected to one another. It’s hardly surprising that our language has these resources because if it didn’t, we’d lose the capacity to describe features of ourselves that are most dear to us and features of our environment which are critical for our survival. For example, we have other verbs such as ‘admire’ and ‘remember’ to describe how thinking agents are connected by way of thought and emotion with other persons, things, and events, ‘push’ and ‘ignite’ to describe how they are causally related, and ‘touch’ and ‘follow’ to describe how they are connected in space and time. And we also have ‘compare’ and ‘contrast’ which we use to describe other more abstract forms of connection whereby the characteristics of one thing are said to be similar to, or strikingly differ from, the characteristics of another thing even if they’re things that aren’t otherwise connected. So far we have considered transitive verbs which enable us to describe how two things are connected. But there are also verbs such as ‘gave’ and ‘travels’ which together with ‘from’ and ‘to’, enable us to describe how three things are connected – when, for example, someone gave such-and-such to someone else or someone travelled from here to there. More generally still, we are able to use complex predicates whose parts include verbs and prepositions to describe patterns of connection which obtain between even greater numbers of things – when for example, someone bought something from someone else for a certain sum. 83

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Now cast your cognitive net wide and contemplate the totality of everything that we truly say about the world using these descriptive resources. Contemplate the relatedness that everywhere surrounds us and runs through us. Now you can understand what relations are for. The design brief of relations is to explain all of this. Perhaps that explanatory ideal cannot be fully realised because it may turn out there are cases of relatedness that need no explaining or need explaining differently. I’ll call the total phenomenon given to us, relatedness-in-general. We can expect at least this much from relations if they exist: to contribute to an explanation of relatedness-in-general by explaining some – even if not all – cases of relatedness in particular. Ordinary language does not draw a sharp boundary between being related and there being a relation. If we just stick with ordinary language, it makes no sense to explain relatedness in terms of relations, because relatedness and relations come to the same thing – hence one cannot explain the other. So to understand how relations can explain relatedness-in-general we need there to be a sharp boundary between them and this is where we need to start talking the technical language of Metaphysicians’ English – although bear in mind that this is a language we might choose to stop speaking later if it turns out that there are unwelcome consequences of speaking that way. Metaphysician’s English is a language in which ‘relation’ occurs as a noun which yields to articles and pluralization in a strict semantic sense, as, for example, ‘dog’ does in English. What do I mean by this? To understand ‘dog’ we must grasp how much of what’s out there counts as a dog and how much as another dog and so the difference between one dog and many dogs. Similarly, to understand ‘relation’ in Metaphysicians’ English requires grasping what counts as a relation and what counts as another relation and thereby the difference between one relation and many relations. So, speaking Metaphysicians’ English, if there are relations, they are circumscribed denizens of reality. By contrast, whilst ‘relation’ in English is grammatically capable of taking the plural in certain contexts, its plural occurrence typically only acts as a shorthand device for summing up the various ways in which things can be relevantly related. Imagine hearing that the Secretary General of the UN has normalised relations with such-and-such hitherto rogue state. This doesn’t ontologically commit the speaker to the existence of relations conceived as circumscribed denizens of reality – because understanding what’s been said doesn’t presuppose a grasp of relations as circumscribed denizens. Why? Because what’s been said is just shorthand for the statement that the Secretary-General is allowing the state in question to send a representative to the UN, allowing negotiations between diplomatic missions, and so on – as per the Vienna Convention on diplomatic relations. Metaphysicians (speaking their language) differ with respect to what exactly counts as a relation and indeed they differ with respect to whether there are any relations. But this much is agreed. If there are such entities then, qualifications aside, there are cases in which things are related together because there is something else, a relation, which performs the role of mediating or standing between them. That’s how, in general terms, a relation is supposed to explain relatedness. It’s because there’s a gap between claiming (a) that some things are related, and claiming (b) that there is a relation which stands between them, that (b) is a candidate for explaining (a). We have reason to believe that there really are such entities if the best explanation of such-and-such things being related is that there’s a relation responsible for their being related. This doesn’t imply that all cases of relatedness are explained by relations nor that there is a unique relation for each case of relatedness that is explained by relations. 84

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7.3 Specialised Design Briefs It’s the general design brief of relations to explain some – even if not all – cases of relatedness. But there are different dimensions to relatedness. Each kind of relatedness is classifiable under a number of different headings and different kinds of relatedness are classified differently under these headings. Specific kinds of relations are introduced to explain these different kinds of relatedness. We can formulate the different headings as questions the answers to which determine how a given kind of relatedness should be classified. Here I give four headings but there are others. 1 How many things are related? Consider situations in which one thing is tied to another. In each such situation, two things are related. So in that case the relatedness in question is classified as binary. Situations in which one person gives something to someone else are situations in which three things are related. In that case, the relatedness is classified as ternary. Situations in which one thing is more similar to another than a further thing is similar to yet another thing are classified a quaternary. And so on. By contrast different numbers of things may be so related as to form rigid bodies; sometimes it might be three, sometimes four etcetera. In that case, the relatedness in question has variable arity. 2 What sorts of entities are related? Take a given wire and the true statement that its electrical resistance is directly proportional to its length. What is said to be related are the resistance and length of the wire. So if we take the resistance and length to be properties of the wire then what is related are properties. Hitherto we have exclusively considered cases involving, persons, physical bodies, and events rather than their properties. So these are classified as cases of lower-order relatedness. But because what’s related here are properties of the wire rather than the wire itself, this is a case of higherorder relatedness. More generally, situations in which n-order entities are related are cases of n-order relatedness. 3 Does the relatedness of certain things follow from what properties they have? Suppose that someone is more susceptible to ill health than someone else. That’s a consequence of their respective medical conditions – their inner natures or intrinsic properties. This kind of relatedness is classified as internal. By contrast, someone’s having more access to health care than someone else depends on the respective circumstances in which they find themselves – on what’s available outside of them. Hence things’ being related in this respect isn’t a consequence of how they are intrinsically. This kind of relatedness is classified as external. More generally, some things are internally related if their being related is a consequence of how they are intrinsically whilst an extrinsic relationship is a relationship that isn’t internal. 4 How are the related things related? Answers to (4) depend upon answers to (1) whilst answers to (2) and (3) are independent. Consider Alexander’s being married to Roxanne, so a case of binary relatedness. How they’re related is classified as a case of symmetric relatedness because if someone is married to someone else, it’s also the case that they are married to them – hence Roxanne is married to Alexander too. By contrast, someone’s seeing something else, another binary case, is classified as non-symmetric because there’s no guarantee that whenever someone sees something else that that something else sees them. Someone’s drinking something is classified as a special case of non-symmetry; it’s asymmetric because whatever they drink can’t drink them.

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Now so far this only indicates how binary cases are to be classified. To appreciate how this classificatory scheme may be developed to cover relations of greater arity consider a regimented language in which predicates occur at the beginning of atomic sentences. In such a language a sentence of the form ‘R(a,b)’ describes a symmetric relationship between what ‘a’ and ‘b’ pick out just in case the following condition obtains: for all x and y if R(x,y) then R(y,x). It describes a non-symmetric relationship just in case that condition fails to hold and an asymmetric relationship just in case the following condition holds: for all x and y if R(x,y) then it’s not the case that R(y,x). Now consider ternary relationships. Here distinctions between full and partial symmetry can be drawn which don’t apply to binary relationships. A sentence of the form ‘R (a,b,c)’ describes (i) a fully symmetric relationship just in case: for all x, y, and z if R(x,y,z) then R(x,z,y) and R(y,x,z) and R(y,z,x) and R(z,y,x) and R(z,x,y). Example: a, b and c form a tripod.2 (ii) a partially symmetric relationship just in case: it doesn’t describe a fully symmetric relationship and for all x, y, z if R(x,y,z) then R(x,z,y) or for all x, y, z if R(x,y,z) then R(y,x,z) or for all x, y, z if R(x,y,z) then R(y,z,x) or for all x, y, z if R(x,y,z) then R(z,x,y) or for all x, y, z if Rxyz then Rzyx. Example: d is between e and f.3 (iii) an asymmetric relationship just in case: for all x, y and z if R(x,y,z) then it’s neither the case that R(x,z,y) nor R(y,x,z) nor R(y,z,x) nor R(z,x,y) nor R(z,y,x). Example: d inherits h from i. The scheme extends in the obvious way to cover quaternary relationships etcetera. Metaphysicians introduce different kinds of relations to explain these different kinds of relatedness. How are these relations supposed to fulfil their specialised design briefs? By logically echoing the relatedness they are introduced to explain. Binary relations which hold between two things are introduced to explain cases of binary relatedness, ternary relations which hold between three things are introduced to explain ternary relatedness, and so on. Higher-order relations which hold between lower-order relata are introduced to explain cases in which the properties of lower-order things are related, or if relations are admitted, cases in which relations of lower-order things are related. Internal relations whose holding is determined by the intrinsic properties of the things between which they hold are introduced to explain internal relatedness; external relations whose holding isn’t so determined are introduced to explain external relatedness. Symmetric relations are introduced to explain cases of symmetric relatedness – for example, a symmetric relation which, so to speak, holds indifferently between Alexander and Roxanne once they are married. Whereas non-symmetric relations are introduced to explain cases of nonsymmetric relatedness – for example, a non-symmetric relation which when someone sees something there is a relation between them and what they see, a relation which isn’t guaranteed to hold the same way between what they see and them. And so on.

7.4 Why Believe in Relations? Relations are in the business of explaining relatedness by holding between related things. Now if we know anything we know that there are related things. Just look around and see. In fact, we don’t even need to look around to be certain of this because the kind of consciousness which is typical of us consists of successive interpenetrating mental episodes. 86

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Hence, if believing in relations provides the best explanation that we can devise of such things being related – assuming that the best explanation is explanatory enough to make it worth taking seriously and not just the best of a bad lot – then that gives us good reason for supposing relations to exist. Other reasons have been put forward for supposing relations to exist. I don’t want to rule them out as genuine but they are less revealing of the nature and significance of relations. It wouldn’t be wrong per se to say, for example, that pairs or triples of things resemble one another, and that we need to appeal to the existence of binary and ternary relations to explain the resemblance between pairs and triples. Suppose that A is above B, C is above D and E is above F. Then there are three pairs which resemble one another by virtue of their sharing the above-below mode of arrangement. And this can be explained by positing a relation which these pairs, and indefinitely many other pairs, share as a common nature. Now this way of conceptualising relations has the advantage that it’s a generalisation of a familiar way of thinking about properties – that properties conceived as common natures are posited to account for the fact that there are things which taken singly, rather than as pairs or triples, resemble one another. But this way of conceptualising relations fails to keep in focus their significance, if there are relations, for the structure of reality, the series and patterns in which things and events are arranged – in other words for the relatedness of things. But conceiving relations as the common natures of pairs or triples presupposes relatedness because a pair or a triple is two or three things related together – so the relatedness is packed into the pairs or triples but isn’t explained.

7.5

Are There Relations?

It’s a feature of the general design brief of relations to do better than pairs or triples in this respect. But can they do what they’re supposed to do? There’s a regress argument – better: a family of arguments – owed to or inspired by F.H. Bradley.4 Here’s one version. Let A be related to B. To explain their relatedness, introduce a relation R1. But it’s not enough to have R1 out there somewhere. To explain their relatedness, R1 needs to actually hold between them. But holding between two things is just a way of being related to them. Hence an explanation of the relatedness of A and B in terms of R1 presupposes that R1 is related to A and B – if R1 weren’t related to A and B then R1 would be adrift from them, an irrelevance to their relatedness. Since the intention was to explain the relatedness of A and B, it follows that the explanation of their relatedness in terms of R1 is incomplete – we need to also explain the fact that R1 is related to them. But this explanatory shortfall cannot be made good by positing a further relation, R2, which holds between R1, A, and B because this presupposes that R2 is related to R1, A, and B. And introducing a further relation, R3, to explain the relatedness of R2, R1, A, and B just introduces a further relatedness which stands in need of explanation before our explanation of A being related to B can be completed. We are launched on a vicious regress, vicious because an explanation of relatedness is always close but always out of reach. Responses to Bradley’s regress are legion. I’ll sketch a framework for comparing and evaluating them. I don’t claim completeness but only indicate significant fault lines. Consider the following radical nominalist response to Bradley’s regress – nominalist because it disavows relations, radical because it so thoroughly disavows them. Bradley’s argument shows relations can’t do what they’re supposed to do, explain relatedness – hence we’re better off without them.5 We should abandon the theoretical ambition of 87

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explaining relatedness as misguided wishfulness and instead embrace the varieties of relatedness for themselves, as what they are, because they stand without need of explanation. We are entitled to use verbs and predicates to describe relatedness without supposing such linguistic units stand for anything – because relatedness is ultimate and irreducible. There are related things and our language has resources to describe how they are related, but nothing more metaphysical need be said. Distinguish the ontology of a theory T, what T says or implies exists, from the ideology of T, the linguistic resources that T relies upon to describe what it says or implies exists, resources which, at least from the perspective of T, are unanalysable. Then the envisaged nominalist response comes to this. The ideology of relatedness which is an extraordinarily pervasive feature of ordinary language, indeed essential to the expression of the world view embodied in that language, has no corresponding ontology. Contrast the realist response that Bradley’s regress isn’t vicious because the relatedness of A and B actually is explained in terms of R1; there’s no unfinished business in this respect, even though there’s always more business to be done, because what’s really happening is that each stage of the alleged regress discloses more and more rarefied consequences of A and B’s being related, relatedness which in turn admits of explanation in terms of further relations. But the fact that there’s always more to explain doesn’t compromise the adequacy of the explanation of A and B’s relatedness in terms of R1.6 It’s integral to this line that a specific piece of ideology, viz. the specialised vocabulary of Metaphysicians’ English which is used for describing the obtaining of relations, for example ‘holds between’, does have a corresponding ontology: relations which not only hold between ordinary things but hold between the relations that hold between them etcetera. Between these two extreme responses to Bradley’s regress lie a range of intermediate positions according to which some but not all of the relevant ideology corresponds to an ontology of relations – for example, views according to which the specialised vocabulary of Metaphysician’s English equips us to describe the contribution relations make to the structure of the world by holding between things but without thereby incurring a commitment to further relations. This is a feature common to positions which hold relations are universals and positions which hold relations are particular – so regardless of whether relations are capable of holding between different things or essentially bespoke to things that bear them.7 From either point of view it is simply in the nature of relations to hold between things without benefit of further relations – that’s simply what they do and nothing more need or can be said. It doesn’t follow that a compelling case has been made that Bradley’s regress is thereby stymied. To do so we would need to establish that one of these theories, depending upon its distinctive blend of ontology and ideology, is explanatorily adequate and superior to any alternative we can envisage.

7.6 Internal and External Relations The distinction between internal and external relatedness adds another dimension to this picture. Things are internally related when their being related is determined or necessitated by their having the properties they do – otherwise, they’re externally related. Now typically statements describing how things are internally related aren’t reducible to statements describing what properties they have. Suppose, for example, that A is taller than B because A has some height m and B some height n and m>n. Now A’s having m and B’s having n 88

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suffices for A’s being taller than B. Hence A and B are internally related. But their having their respective heights isn’t necessary for A’s being taller than B – because they could have had different heights and still A be taller than B. So the vocabulary used to describe internal relatedness cannot in general be replaced by descriptions of the properties things have. But it doesn’t follow that the ideology of internal relatedness requires a corresponding ontology of relations. Distinguish the following two positions. (1) A’s being taller than B supervenes upon what heights they have – more generally, there’s no difference in internal relatedness without a difference in what properties the related things have. Since what supervenes is not something ontologically more than what it supervenes upon, it follows that internal relatedness supplies no ‘addition to the world’s furniture’.8 (2) The statement that A is taller than B is ‘made true’ by A’s having m and B’s having n, i.e., non-relational facts about what properties they have. More generally, relational truth-makers aren’t required as truth-makers for statements describing internal relatedness. What exists is determined by what truth-makers there are. Ergo there are no internal relations.9 By contrast, (1) and (2) take external relatedness, if there is any and qualifications aside, to implicate an ontology of external relations because, ex hypothesi, external relatedness doesn’t supervene upon what properties things have, nor are statements of external relatedness made true by facts about what properties things have. A position (3), contrary to (1) and (2), builds on the reflection that we can intelligibly ask why A’s being taller than B supervenes upon what heights they have and why A’s having its height and B’s having its height makes it true that A is taller than B. We can furnish answers because it’s not just a brute fact that they do. If A is taller than B that’s because A’s height is greater than B’s height. If it ceases to be the case that A is taller than B that’s because whatever height B then has is greater than or equal to the height then had by A. There’s no difference in whether A is taller than B without a difference in their respective heights because it’s their respective heights under a linear ordering (greater than or equal) which are responsible for whether or not one is taller than the other. But this answer to our first ‘why’ question presupposes that the heights are themselves internally related under that ordering. Similarly, A’s having its height and B’s having its height makes it true that A is taller than B but only because the height of A is greater than the height of B. Since internal relatedness reappears in the answer to our second ‘why’ question too, neither supervenience nor truthmaking can be called upon to establish that internal relatedness lacks a corresponding ontology.10 According to (3) the more compelling view is that internal relatedness has a corresponding ontology of relations just as external relatedness does.

7.7

How Do Relations Relate?

Our world consists of structures, extraordinary arrangements of related things, perhaps even a single encompassing structure. The distinctive formal features of these structures, the abstract manner of their arrangement, is determined by whether the relatedness characteristic of them is symmetric, non-symmetric, asymmetric etcetera. Grant that there are corresponding relations fulfilling their respective specialised design briefs. How are these relations able to do what they are supposed to do? The stakes couldn’t be higher. If we can’t understand how relations perform a role in generating structure then we must give up on relations. Focus on asymmetric binary relations. For any two things, a and b, such a relation R must be capable of holding one of two different ways between them – the aRb way or the 89

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bRa way but never both. Which way R holds, if it holds, between them will determine where in a series the related things occur. So what’s the difference between aRb and bRa? The ontology-ideology framework also has service for comparing answers to this question. Again, I don’t aim for completeness. The radical ideological answer here is (i) that there is no discursive illumination to be had into the nature of this difference for arbitrary R. The difference between aRb and bRa is ultimate and irreducible. It’s a distinction which we cannot get underneath to better understand because it is always with us, always presupposed – only having the wrong explanatory settings make us grasp for more. We must acknowledge the difference between aRb and bRa in all our reasoning and recognise the difference when we see it – recognise whether, for example, a is to the left of b or b to the left of a. But it doesn’t illuminate matters to try and break this difference down into something simpler or more basic because there is nothing that’s simpler or more basic in general.11 It’s a quite different ideological answer to hold (ii) that the difference between aRb and bRa can be understood at a deeper level of analysis by employing a primitive notion of direction. The idea is that the difference is to be understood in terms of two different ways R may travel between a and b. In one case R travels from a to b, in the other case R travels from b to a.12 But, other recherché difficulties aside, this is only a metaphor and it’s unclear what literal truth the metaphor conveys – over and above the fact that there are two different ways for R to hold between a and b, the aRb way and the bRa way. Contrast two more ontologically involved accounts of the difference between aRb and bRa which deny relations have direction but hold that there is genuine discursive insight to be had into the difference between aRb and bRa. According to (iii), R has an inner structure – it’s because relations have this inside them that structures in the world, things-in-relation, are possible. Because it has this inner structure, R is more perspicuously represented like this: ( )#R( )%. Here brackets are used to indicate ‘gaps’ in the relation, the different subscripts indicating that they are different gaps, two gaps because R is binary. Facts or states result from things ‘filling’ the gaps. When a fills ( )# and b fills ( )% the result is aRb. When b fills ( )# and a fills ( )% the result is bRa.13 It’s because they arise from having their gaps filled differently that aRb and bRa are different. It’s a further consequence, however, that even a symmetric relation S will have two gaps (because its binary), ergo there will be two different ways of filling its gaps for two relata, ergo the fact that aSb will be different from bSa – even when, for example, S is the marriage relation. Alongside ontological scruples about whether ‘gaps’ are bona fide entities, an unwillingness to accept that a symmetric relation is capable of giving rise to more than one fact from the same relata motivates the contrary position (iv) that the difference between aRb and bRa isn’t to do with R’s inner nature but outward-facing ‘substitutional’ connections between these facts and other facts of which R is a constituent, say cRd.14 Take aRb and simultaneously substitute c for a and d for b. The result is cRd. But perform the same simultaneous substitution on bRa and the result is dRc. Hence aRb is distinct from bRa because they yield different outcomes when subjected to the same substitutional operation. But because, prima facie, substitution is itself a relation, it is questionable whether (iv) facilitates an understanding of how relations do what they’re supposed to do in more basic terms. Nevertheless, here’s the good news. It’s still wide-open which account of relations is the best account we have. Here’s the bad news. That’s because we don’t have an agreed procedure for deciding between balances of ontology and ideology.15 90

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Notes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

For a general account of the debate, see MacBride (2020). Full symmetry should not be confused with Fine’s ‘strict symmetry’ ( 2000: 17). Note there are other eligible definitions of partial symmetry. See Bradley (1897: 25–34, 572–584). See Fisk (1972: 139–143). See Maurin (2015) for objections. See Grossmann (1992: 55–56) and Maurin (2010: 321–323). And MacBride (2011: 170–174) for objections. See Armstrong (1997: 87). See Simons (2010: 204–205). See MacBride (2011: 163–166). See MacBride (2014). See Russell (1903: §94). See Fine (2000: 10–16) for objections and Orilia (2011) for a fuller development and defence. See Fine (2000: 16–32) and Leo (2014) for an alternative development. See MacBride (2007: 44–53) for objections. Thanks to Chris Daly, Frederique Janssen-Lauret, Joop Leo, and Alan Weir.

References Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Bradley, F.H. (1897) Appearance and Reality. 2nd Edition. London: Swan Sonnenschein. Fine, K. (2000) Neutral Relations. Philosophical Review 109(1): 1–33. Fisk, M. (1972) Relatedness without Relations. Noûs 6(2): 139–151. Grossmann, R. (1992) The Existence of the World. London: Routledge. Leo, J. (2014) Thinking in a Coordinate-Free Way about Relations. Dialectica 68(2): 263–282. MacBride, F. (2007) Neutral Relations Revisited. Dialectica 61(1): 25–56. MacBride, F. (2011) Relations and Truthmaking. Proceedings of the Aristotelian Society 111: 161–179. MacBride, F. (2014) How Involved Do You Want To Be In A Non-Symmetric Relationship. Australasian Journal of Philosophy 92(1): 1–16. MacBride, F. (2020) Relations. In Zalta, E. (ed.) Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/relations/>. Maurin, A.-S. (2010) Trope Theory and the Bradley Regress. Synthese 175(3): 311–326. Maurin, A.-S. (2015) States of Affairs and the Relation Regress. In Galluzzo, G. and Loux, M.J. (eds.) The Problem of Universals in Contemporary Philosophy. Cambridge: Cambridge University Press: 195–214. Orilia, F. (2011) Relational Order and Onto-Thematic Roles. Metaphysica 12(1): 1–18. Russell, B. (1903) The Principles of Mathematics. London: George Allen and Unwin. Simons, P. (2010) Relations and Truthmaking. Proceedings of the Aristotelian Society Supplementary Volume 84: 199–213.

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8 INTRINSIC/EXTRINSIC Vera Hoffmann-Kolss

8.1 Introduction A property is intrinsic iff individuals have it in virtue of how they themselves are, not in virtue of the relations in which they stand to other individuals; a property is extrinsic iff it is not intrinsic, that is, iff there are individuals that have it in virtue of standing in certain relations to other individuals. Having a mass of 3 kg, being cubical, and being an electron are examples of intrinsic properties; having two children, being next to a cube, and being repelled by an electron are examples of extrinsic properties. In many cases, it is intuitively clear und uncontroversial whether a property is intrinsic or extrinsic. However, the details of the debate on the intrinsic/extrinsic distinction are more controversial. A first crucial question is whether the intrinsic/extrinsic distinction can be analysed in terms of other, better-understood notions and if so, what such an analysis should look like. A major part of the debate on the intrinsic/extrinsic distinction revolves around this question. A second question that has come increasingly into focus in recent years is what the general characteristics of the intrinsic/extrinsic distinction are. It is now widely agreed, for instance, that the distinction is hyperintensional, that is, that there are cointensional properties P and Q (properties P and Q having the same extension in all possible worlds), such that P is intrinsic, and Q is extrinsic. Another general characteristic concerns the formal properties of the distinction. The intuitive definition given above suggests that the distinction is exhaustive and exclusive, that is, that a property is either intrinsic or extrinsic, but not both. However, this assumption is called into question if the intrinsic/extrinsic distinction is vague, that is, if there are properties for which it is indeterminate whether they are intrinsic or extrinsic. Obviously, such general characteristics of the intrinsic/extrinsic distinction have implications for the first question of what an analysis of the distinction should look like. For instance, if there are reasons to assume that the intrinsic/ extrinsic distinction is hyperintensional, then an analysis of the distinction should be compatible with this. This chapter is organized as follows: in the next section, Section 8.2, I set the stage for the argumentation of the other sections. I briefly describe the role that the intrinsic/extrinsic

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distinction plays in philosophical debates and distinguish it from other conceptually related distinctions, in particular the distinction between relational and non-relational properties and the distinction between having a property intrinsically and having a property extrinsically, that is, the so-called ‘local’ version of the intrinsic/extrinsic distinction. I then address the two questions mentioned above in turn. I first describe several attempts to define the intrinsic/extrinsic distinction: Section 8.3 deals with the well-known loneliness test proposed by Rae Langton and David Lewis, Section 8.4 with combinatorial accounts and approaches based on the notion of grounding. I sketch the debate about how adequate these approaches are and point out that every successful analysis of the intrinsic/ extrinsic distinction invokes notions based on substantial metaphysical assumptions, such as the notion of grounding or the notion of a natural property. In Section 8.5, I tackle the question of what the general characteristics of the intrinsic/extrinsic distinction are. I describe recent arguments to the effect that the distinction is hyperintensional and argue that there is reason to think that the intrinsic/extrinsic distinction is vague. Section 8.6 provides a brief summary and points out some open research questions.

8.2

Setting the Stage

The applications of the intrinsic/extrinsic distinction span a number of philosophical debates. A classic field of application is the distinction between intrinsic and extrinsic value, where an action or a state of affairs has intrinsic value iff it is good in itself and extrinsic value iff it is not good in itself, but has consequences that have intrinsic value (Moore 1903: 21). In the metaphysics of science, a crucial question is whether Humeanism is true, where Humeanism (in its most radical form defended by Lewis) is an ontological position, according to which all properties and relations as well as the laws of nature and other modal necessitation relations supervene on the distribution of fundamental intrinsic properties over space-time points (Lewis 1986a). In the philosophy of mind, there is a distinction between internalism and externalism about mental states. According to internalism, all mental properties supervene on the intrinsic properties of an individual, whereas, according to externalism, there are mental properties that supervene partially on the extrinsic properties of the individual (Burge 1979). These debates usually invoke a more or less intuitive notion of intrinsicality, and often they can benefit from a more precise understanding of the intrinsic/extrinsic distinction. As suggested by the working definition and the examples given at the beginning, the standard understanding is that the intrinsic/extrinsic distinction applies to first-order properties (i.e., properties instantiated by individuals). Accordingly, being intrinsic and being extrinsic are considered second-order properties, that is, properties of first-order properties. However, the distinction can be applied to other entities as well. For instance, one can distinguish between intrinsic and extrinsic relations. A binary relation R is intrinsic iff whether individuals x and y stand in R to each other does not depend on what individuals other than x and y are like. Otherwise, R is extrinsic. And analogous definitions can be given for n-place relations applying to n-tuples of individuals. The being taller than relation is a paradigmatic example of an intrinsic binary relation. Being siblings is an extrinsic binary relation, since whether individuals are siblings crucially depends on their relationship to other individuals, viz. on whether they have the same parents (or at least one identical parent). In a similar vein, one can distinguish between intrinsic and extrinsic facts, where intrinsic facts are constituted by intrinsic properties only, whereas extrinsic facts are at 93

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least partially constituted by extrinsic properties. However, since the standard analyses of the intrinsic/extrinsic distinction apply to first-order properties and since it is usually possible to derive other applications from these analyses, I will, in what follows, focus on definitions of the distinction between intrinsic and extrinsic first-order properties. Dividing the class of first-order properties into two dichotomous categories is a common approach in many philosophical debates. Many of these categorizations are independent of the intrinsic/extrinsic distinction. It is now rather uncontroversial, for instance, that the distinction between dispositional and categorical properties is logically independent of the intrinsic/extrinsic distinction. There are intrinsic categorical properties, such as being cubical, and extrinsic categorical properties, such as being next to a cube. In addition, there are intrinsic dispositional properties, such as being fragile, and extrinsic dispositional properties, such as being able to open a red door (applied to a key). The category of extrinsic dispositions has first been introduced and described by Jennifer McKitrick (2003, see also Chapter 24, this volume). Other categorizations are more closely related to the intrinsic/extrinsic distinction. Some properties are relational: their instantiation by some individual x always consists in x’s standing in a certain relation to other individuals. Extrinsic properties are always relational in this sense. For instance, an individual’s instantiating the extrinsic property of having two children consists in her standing in a certain relation to the individuals that are her children. However, some intrinsic properties are also relational. For instance, the property of having a broken leg is intuitively intrinsic: whether an individual has it only depends on what she herself is like, that is, on whether the bones in one of her legs are fractured, but not on what other individuals are like. At the same time, the property is relational: an individual’s having it consists in her standing in the part-whole relation to a leg that is broken. In general, the class of extrinsic properties is a proper sub-class of the class of relational properties. Some authors argue that one can exploit this relationship and define a property as extrinsic iff it is relational and satisfies some further condition. The basic idea here is that the instantiation of an extrinsic property by an individual x does not only consist in x’s standing in a certain relation to arbitrary individuals, but to individuals that are wholly distinct from x (Francescotti 1999; Hoffmann-Kolss 2010b; Khamara 1988: 144). However, whether this approach leads to an adequate analysis of the intrinsic/extrinsic distinction is controversial. In any case, the distinction between relational and nonrelational properties (without further conditions or assumptions) cannot simply be equated with the intrinsic/extrinsic distinction. Another closely related categorization of properties is what is often called the ‘local’ version of the intrinsic/extrinsic distinction. This distinction can be illustrated by the following example: the disjunctive property of being cubical or next to a cube is intrinsically had by cubical individuals and extrinsically had by individuals that are next to a cube. This means that it is locally intrinsic to cubical individuals and locally extrinsic to individuals that are next to a cube. Note that the local version of the intrinsic extrinsic distinction is not exclusive and that a property can be had both intrinsically and extrinsically by the same individual at the same time. The notion characterized by the intuitive definition given at the beginning is usually called the ‘global’ version of the intrinsic/extrinsic distinction. The property of being cubical or next to a cube is globally extrinsic, since it is not the case that all individuals having it instantiate it in virtue of what they are like in themselves – some individuals instantiate it in virtue of being next to a cube. 94

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A standard way to relate the two notions is to define a property as globally intrinsic iff necessarily, whenever an individual has it, it has it intrinsically (Humberstone 1996: 228; Marshall and Weatherson 2018). This implies that a property is globally extrinsic iff it is possible that an individual has it extrinsically. Whether this systematic relationship can be used to reduce the global version of the intrinsic/extrinsic distinction to the local version or vice versa is controversial. Carrie Figdor argues, for instance, that there is reason to be sceptical about this close interdefinitional relationship and that the local version of the intrinsic/extrinsic distinction can do more explanatory work than the global version (Figdor 2008). In general, the relationship between the local and the global version of the intrinsic/extrinsic distinction is still underexplored. In what follows, I will only focus on the global version.

8.3 Duplication Accounts of Intrinsicality Lewis has famously argued that the intrinsic/extrinsic distinction is closely related to the distinction between natural and non-natural properties (see Chapters 4 and 29, this volume). He assumes that some properties are perfectly natural, and that these perfectly natural properties are always intrinsic. However, the opposite is not true. There are intrinsic properties that are not perfectly natural, for instance, the disjunctive property of being red or cubical (Lewis 1983: 355–358; 1986b: 61). If the assumption that all perfectly natural properties are intrinsic is accepted, one can use it to give the following reductive definition of the intrinsic/extrinsic distinction: two individuals x and y are duplicates iff x and y instantiate exactly the same perfectly natural properties.1 A property is intrinsic iff it can never differ between duplicates; otherwise, it is extrinsic (Lewis 1986b: 61–62). This definition belongs to a class of definitions which are called ‘duplication accounts’ of intrinsicality and which rely on the idea that intrinsic properties are ones that cannot differ between duplicate individuals. Although Lewis’s approach assumes that all perfectly natural properties are intrinsic, it can also deal with the observation that there are intrinsic properties that are not perfectly natural, such as being red or cubical. The underlying idea is that an individual x’s perfectly natural properties determine whether or not x has the colour red and whether or not x has cubical shape. But then x’s perfectly natural properties also determine whether x has the property of being red or cubical. A possible problem for this approach is that it is not conceptually illuminating enough. It relies on the assumption that there is a class of perfectly natural properties and that the members of this class are all intrinsic but does not provide a further explication or analysis of what it means for a property to be intrinsic (or extrinsic). A more conceptually illuminating duplication account of intrinsicality is based on the so-called ‘loneliness test’, later developed by Lewis in a joint paper with Langton. The intuition underlying this test is that the instantiation or non-instantiation of an intrinsic property by some individual x does not have any implications for the existence of any individuals other than x. Consequently, intrinsic properties can be had (or lacked) by individuals independently of whether they are lonely or accompanied in the following technical sense: an individual is accompanied iff it coexists with a contingent individual completely distinct from itself and lonely iff it is not accompanied. A property passes the loneliness test iff it satisfies the following definition: Independence of accompaniment: A property P is independent of accompaniment iff the following four conditions are satisfied (Langton and Lewis 1998: 334): 95

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(a) (b) (c) (d)

a lonely individual can have P an accompanied individual can have P a lonely individual can have not-P an accompanied individual can have not-P.

Many intrinsic properties pass the loneliness test. Being cubical is independent of accompaniment, since it can be instantiated by lonely as well as by accompanied individuals, and the same applies to its negation. The disjunctive intrinsic property of being red or cubical is also independent of accompaniment. By contrast, the extrinsic property of having children is not independent of accompaniment, since it cannot be instantiated by lonely individuals. The loneliness test is conceptually illuminating, since it offers a systematic analysis of a basic intuition about the intrinsic/extrinsic distinction, that is, the intuition that the instantiation of an intrinsic property by an individual x is independent of the relations in which x stands to other individuals. If whether x instantiates P is independent of the relations in which x stands to other individuals, then x’s instantiation of P is in particular independent of whether x stands in the co-existence relation to other individuals. The loneliness test captures this intuition. However, the loneliness test cannot be considered an adequate reductive definition of intrinsicality. An immediate problem is that it is not only passed by intrinsic properties, but also by certain extrinsic properties. The property of being either cubical and lonely or else non-cubical and accompanied is intuitively extrinsic, since at least some individuals have it in virtue of standing in the coexistence relation to other individuals. But it is independent of accompaniment: a lonely cube has it, and an accompanied non-cubical individual also has it, that is, conditions (a) and (b) are satisfied; moreover, a lonely non-cubical individual lacks it, and so does an accompanied cube, that is, conditions (c) and (d) are also satisfied (Langton and Lewis 1998: 335). Langton and Lewis are aware of this problem and apply the loneliness test not to every logically complex property, but only to non-disjunctive properties. They define a property as disjunctive iff it is not a perfectly natural property and can be expressed as a disjunction of natural properties, or of properties which are much more natural than itself (Langton and Lewis 1998: 335–336). Being either cubical and lonely or else non-cubical and accompanied is disjunctive, since it is a disjunction of properties more natural than itself. This then leads to another version of the duplication account. A property P is defined as basic intrinsic iff P is independent of accompaniment and both P and not-P are nondisjunctive (in the sense just described). Two individuals x and y are duplicates iff x and y instantiate exactly the same basic intrinsic properties. A property is intrinsic iff it can never differ between duplicates; otherwise, it is extrinsic (Langton and Lewis 1998: 336–337). Given that being either cubical and lonely or else non-cubical and accompanied is a disjunctive property, it is correctly classified as extrinsic, since it is not basic intrinsic and there can be cubical duplicates, one of which has it (because it is lonely), whereas the other one lacks it (because it is accompanied). The duplication account faces a number of difficulties. One problem is that it relies crucially on the distinction between disjunctive and non-disjunctive properties, which in turn relies on the assumption that properties can be ordered by degree of naturalness. The latter assumption is controversial, and even if one accepts it in principle, there can still be intuitive disagreement about whether specific example cases of properties are disjunctive or not (Langton and Lewis 2001; Marshall and Parsons 2001). 96

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A further problem is that duplication accounts can only be applied to a rather limited class of properties, that is, to contingent qualitative properties. If a property is not contingent, it is either a necessary property, such as being such that 6 is divisible by 3, or a contradictory property, such as being a married bachelor. Non-contingent properties are all automatically classified as intrinsic by duplication accounts, since they can never differ between duplicates (Langton and Lewis 1998: 340). However, this implication contradicts the intuition that some non-contingent properties – for instance, being such that 6 is divisible by 3 – are extrinsic, since individuals have them not in virtue of what they are like themselves, but in virtue of what other individuals are like. On the other hand, certain nonqualitative properties, in particular identity properties, such as being identical to David Lewis, are automatically classified as extrinsic, since they always differ between duplicates that are not numerically identical. However, there is reason to think that such properties are intrinsic (Eddon 2011: 316–317). One possibility to deal with this is consequence is to conclude that both non-contingent properties and non-qualitative properties fall outside the scope of duplication accounts (Langton and Lewis 1998; for discussion, see Marshall 2021). However, since duplication accounts also raise other problems (see, e.g., Bader 2013; Shumener 2022; Sider 2001; Wilhelm 2022), several authors have proposed that this approach should be abandoned altogether. The most common approaches that do not rely on the notion of duplication are described in the following section.

8.4 Combinatorial Accounts and Grounding-Based Approaches Several authors have tried to develop definitions of the intrinsic/extrinsic distinction that have a broader scope than duplication accounts and can adequately deal with the standard examples and at least some of the possible problem cases. One such attempt is the approach already mentioned in Section 8.2 of considering extrinsic properties as a certain type of relational property (Francescotti 1999). An alternative option is to invoke combinatorial considerations. The possible patterns of instantiation of intrinsic properties over individuals are characteristically different from the possible patterns of instantiation of extrinsic properties. If x instantiates a certain intrinsic property, then this does not have any implications for what intrinsic properties other individuals have. However, if x instantiates some extrinsic property, this often has implications for the distribution of (intrinsic or extrinsic) properties over other individuals. For instance, if x instantiates the extrinsic property of being next to a cube, then there must be a cubical object in the vicinity of x (Denby 2006; Weatherson 2001; for further discussion of Denby’s account see Denby 2010; Hoffmann-Kolss 2010a). A special variant of the combinatorial approach is based on the intuition that P is intrinsic iff an individual x instantiating P would not lose P if the world inhabited by x was either contracted by removing individuals or extended by adding individuals (Vallentyne 1997; Yablo 1999). However, regardless of how successful these analyses are in capturing concrete example cases of intrinsic and extrinsic properties, the entire approach of definitionally reducing the intrinsic/extrinsic distinction to other notions is called into question by a theoretical argument given by Dan Marshall, according to which it is impossible to define the intrinsic/ extrinsic distinction in terms of broadly logical notions. Roughly speaking, broadly logical notions are notions from first-order predicate logic, including the notion of identity, as well as notions from possible world semantics, set theory, and mereology (Marshall 2009). Marshall’s argument then is that (given certain assumptions) the properties of being an 97

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electron and being either a lonely positron or an accompanied electron ‘have the same pattern of instantiation through logical and mereological space’ (Marshall 2009: 653). This means that the way in which the first of these two properties is distributed over individuals and their proper parts in all possible worlds is structurally isomorphic to the way in which the second property is distributed. Marshall proves that definitions using only broadly logical notions can only distinguish between properties that have different patterns of instantiation through logical and mereological space. Therefore, given that being an electron is intuitively intrinsic, whereas being either a lonely positron or an accompanied electron is intuitively extrinsic, these two properties (and properties structurally analogous to them) provide a counterexample to any definition of intrinsicality that uses only broadly logical notions. One possible reaction to this difficulty is a primitivist approach, according to which one should accept that the intrinsic/extrinsic distinction is primitive in the sense of not being further analysable.2 Another possible reaction is to abandon the requirement that analyses of the intrinsic/extrinsic distinction should only use broadly logical notions. It should be noted that Langton and Lewis’s definition can in fact deal with the properties of being an electron and being either a lonely positron or an accompanied electron in an adequate way. Being an electron is non-disjunctive and independent of accompaniment. Therefore, it is classified as basic intrinsic and a fortiori as intrinsic. Being either a lonely positron or an accompanied electron is disjunctive and therefore not basic intrinsic. Moreover, there are duplicate individuals, for instance, two electrons, that can differ in whether they have this property. It follows that being either a lonely positron or an accompanied electron is correctly classified as extrinsic. This only works, however, because Langton and Lewis’s definition presupposes the notion of perfectly natural property, which is not a broadly logical notion in Marshall’s sense and which is needed to define the notion of disjunctive property. A more recent attempt to define the intrinsic/extrinsic distinction using a notion that is not broadly logical, but is based on substantial metaphysical assumptions is to understand the in-virtue-of relation occurring in intuitive definitions of intrinsicality as the grounding relation. A paradigmatic definition of this type has been given by Gideon Rosen (Rosen 2010: 112; I here use a reformulation from Marshall 2013: 7–8): Grounding-based definition of the intrinsic/extrinsic distinction: P is intrinsic iff necessarily, for any x and y, the following two conditions are satisfied: (a) If the ascription of P to x is grounded by a fact that has y as an individual constituent, then y is part of x. (b) If the ascription of not-P to x is grounded by a fact that has y as an individual constituent, then y is part of x.3 For instance, if x instantiates the intrinsic property of having a mass of 3 kg, then this fact is grounded by facts about x itself (note that x is a part of x) and facts about the proper parts of x, and the same is true if x does not instantiate having a mass of 3 kg. By contrast, if x instantiates the extrinsic property of having two children, then this fact is not only grounded in facts about x and the proper parts of x, but also in facts about other individuals. Unlike duplication accounts, the grounding-based approach can deal with noncontingent properties and identity properties. If x has the extrinsic necessary property of being such that 6 is divisible by 3, then this fact is grounded by facts about (abstract) individuals that are totally distinct from x – the numbers 6 and 3. If x has the identity 98

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property of being identical to David Lewis, then this fact is only grounded by facts about x, not by facts about other individuals, and the property is correctly classified as intrinsic. A further advantage of the grounding-based approach is that it is adequate even if the intrinsic/extrinsic distinction turns out to be hyperintensional. I discuss this point in the next section.4

8.5 General Features of the Intrinsic/Extrinsic Distinction: Hyperintensionality and Vagueness As pointed out in Section 8.1, there is a debate not only about how to define the intrinsic/ extrinsic distinction, but also about what its general characteristics are. Maya Eddon argues that the distinction is hyperintensional. There are cointensional properties, that is, properties having the same extension in all metaphysically possible worlds, that fall ‘on different sides of the intrinsic/extrinsic divide’ (Eddon 2011: 334). One of Eddon’s arguments runs as follows: the intrinsic property of being David Lewis is necessarily coextensional with a disjunctive property of the form having such-and-such-features-and-soand-so-relations to other things_(w1) or having such-and-such-features-and-so-and-sorelations to other things_(w2) or having such-and-such-features-and-so-and-so-relations to other things_(w3) or… … This complex property is supposed to consist of all the characteristics uniquely instantiated by David Lewis in all those possible worlds in which he exists (Eddon 2011: 334, fn 31). Since it is plausible to assume that this complex property is extrinsic, the example shows that there is an intrinsic property, the property of being David Lewis, which is cointensional with some extrinsic property. It follows that the intrinsic/extrinsic distinction is hyperintensional. One might object to this argument on the grounds that it relies on a rather technical and far-fetched example. However, there are further examples showing that the intrinsic/extrinsic distinction is hyperintensional (and Eddon 2011 also provides a further argument supporting this conclusion). The intrinsic property of being cubical, for instance, is cointensional with the property of being cubical and such that 6 is divisible by 3, which is arguably extrinsic. And the intrinsic property of being 324 m high is cointensional with the extrinsic property of being as high as the Eiffel Tower in the actual world in 2022 (for further discussion, see Hoffmann-Kolss 2015). Hyperintensionality raises problems for duplication accounts of intrinsicality. To see this, suppose that P is classified as intrinsic by the duplication account and that Q is cointensional with P. Given that P is classified as intrinsic, any duplicate individuals x and y either both have P or both have not-P. Given that P is cointensional with Q, this implies that any duplicate individuals either both have Q or both have not-Q. But then, any property Q that is cointensional with some intrinsic property is also intrinsic. It follows that duplication accounts are problematic, if the intrinsic/extrinsic distinction is hyperintensional. The observation that the intrinsic/extrinsic distinction is hyperintensional is often taken as a central motivation for a grounding-based approach, which allows for more finegrained distinctions between types of properties. For instance, the fact that x has the extrinsic property of being cubical and such that 6 is divisible by 3 is partially grounded by a fact about individuals that are completely distinct from x, that is, the numbers 6 and 3, whereas the fact that x has the intrinsic property of being cubical is only grounded by facts about x and the proper parts of x. 99

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Another feature of the intrinsic/extrinsic distinction that has not been addressed in the literature to date is that the distinction can be vague. As pointed out above, one standard assumption is that the distinction is exhaustive and exclusive, that is, that each property is either intrinsic or extrinsic, but not both. This assumption is called into question, if there are borderline cases of intrinsicality. Intuitive characterisations often imply that properties of physical objects are intrinsic iff individuals have them in virtue of what goes on inside their physical boundaries. However, if the physical boundaries of individuals can be vague, this implies that there are properties for which it is indeterminate whether they are intrinsic. It is plausible to assume, for instance, that clouds have vague physical boundaries: there are water molecules for which it is indeterminate whether they are proper parts of the cloud. Consider the property of being a cloud such that the water molecules at its vague physical boundary have a temperature of -5°C. If it is indeterminate whether the water molecules at the vague physical boundary of a cloud are proper parts of the cloud, it is indeterminate whether an individual having this property has it in virtue of what it itself and its proper parts are like. But then it is indeterminate whether the property is intrinsic. One might object that this indeterminacy just arises, because the term ‘cloud’ is semantically vague and that the example does not show that the metaphysical distinction between intrinsic and extrinsic properties is indeterminate. However, there seems to be a stable intuition that it is indeterminate whether certain properties are intrinsic when vague objects come into play. The question of how to deal with this intuition and what other examples of vague intrinsicality might be found is currently underexplored.

8.6 Summary and Directions for Future Research Let’s take stock: A central question regarding the intrinsic/extrinsic distinction is whether it can be reduced to other notions. The debate of the past fifty years shows that such a reductive definition cannot be had on the cheap. It is not possible to reduce the intrinsic/ extrinsic distinction to broadly logical notions. Rather, notions relying on substantial metaphysical assumptions are required, such as the grounding relation or at least the notion of natural property. Duplication accounts, which use the notion of natural property, turn out to be limited in scope, since they were only designed to handle contingent qualitative properties. Grounding-based approaches have a broader field of application, but obviously presuppose the notion of grounding, which some philosophers find objectionable (e.g., Wilson 2014). The more recent debate is moving in a slightly different direction and focusses on general features of the intrinsic/extrinsic distinction rather than on coming up with more and more sophisticated reductive analyses. For instance, it is now widely accepted that the intrinsic/ extrinsic distinction is hyperintensional. Grounding-based definitions can capture this feature. However, it is an open question what a hyperintensional definition of the intrinsic/ extrinsic distinction that is not based on the notion of grounding should look like. Further questions that might be important for future research concern the question of whether the distinction can be vague, and how the relationship between the local and the global version of the distinction should be understood. Finally, there is a methodological issue that arises in many metaphysical debates but has not been discussed much in the context of the debate on intrinsicality. The adequacy of an analysis of a metaphysically relevant notion is often measured by intuitive examples. The 100

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more intuitive examples an analysis can cover, the more adequate it is. This approach raises several questions. Whose intuitions should be taken into account, only those of the members of some expert community, or those of people not having any philosophical training, or both? How should we proceed in cases of conflicting intuitions? Should certain intuitions carry more weight than others? What are the alternatives to this intuition-based reasoning? These and related questions provide ample opportunity for further discussion and research.

Notes 1 Strictly speaking, Lewis’s definition of duplicate individuals is more complex: x and y are duplicates iff x and y instantiate exactly the same perfectly natural properties and there is a one-one mapping between the proper parts of x and those of y, such that the parts assigned to each other by this mapping have exactly the same perfectly natural properties and stand in exactly the same perfectly natural relations ( Lewis 1986b: 61). 2 An argument to the effect that the intrinsic/extrinsic distinction is primitive is given by Skiles (2014). Hoffmann-Kolss argues that the intrinsic/extrinsic distinction cannot be reductively defined, since the intuitive distinction between intrinsic and extrinsic properties is implicitly circular and therefore non-reductive ( Hoffmann-Kolss 2018). 3 A predecessor of this account relying on both the notion of independence of accompaniment and the notion of grounding has been developed by Witmer, Butchard, and Trogdon (2005). Bader proposes a grounding-based definition that takes the local version of the intrinsic/extrinsic distinction as more basic than the global version ( Bader 2013). 4 All attempts to define the intrinsic/extrinsic distinction described in this and the previous section presuppose that neither the class of intrinsic properties nor the class of extrinsic properties are empty. This assumption can be called into question. One can argue, for instance, that all properties are constituted by an object’s standing in certain relations to something else and are therefore extrinsic (a historical argument in this direction is provided by McGilvary 1930) or that at least all properties instantiated by the fundamental physical particles are extrinsic ( Esfeld 2014). To explore how one might then explain the intuitive distinction between intrinsic and extrinsic properties is beyond the scope of this chapter.

References Bader, R.M. (2013) Towards a Hyperintensional Theory of Intrinsicality. Journal of Philosophy 110(10): 525–563. Burge, T. (1979) Individualism and the Mental. Midwest Studies in Philosophy 4: 73–121. Denby, D.A. (2006) The Distinction between Intrinsic and Extrinsic Properties. Mind 115(457): 1–17. Denby, D.A. (2010) Intrinsic and Extrinsic Properties: A Reply to Hoffmann-Kolss. Mind 119(475): 773–782. Eddon, M. (2011) Intrinsicality and Hyperintensionality. Philosophy and Phenomenological Research 82(2): 314–336. Esfeld, M. (2014) Physics and Intrinsic Properties. In Francescotti, R. (ed.) Companion to Intrinsic Properties. Berlin: De Gruyter: 253–269. Figdor, C. (2008) Intrinsically/Extrinsically. Journal of Philosophy 105(11): 691–718. Francescotti, R.M. (1999) How to Define Intrinsic Properties. Noûs 33(4): 590–609. Hoffmann-Kolss, V. (2010a) Denby on the Distinction between Intrinsic and Extrinsic Properties. Mind 119(475): 763–772. Hoffmann-Kolss, V. (2010b) The Metaphysics of Extrinsic Properties. Frankfurt: Ontos Verlag. Hoffmann-Kolss, V. (2015) On a Sufficient Condition for Hyperintensionality. Philosophical Quarterly 65(260): 336–354.

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Vera Hoffmann-Kolss Hoffmann-Kolss, V. (2018) Why Intrinsicness Should Be Defined in a Non-reductive Way. Grazer Philosophische Studien 95(1): 1–14. Humberstone, I.L. (1996) Intrinsic/Extrinsic. Synthese 108(2): 205–267. Khamara, E.J. (1988) Indiscernibles and the Absolute Theory of Space and Time. Studia Leibnitiana 20(2): 140–159. Langton, R. and Lewis, D. (1998) Defining “Intrinsic”. Philosophy and Phenomenological Research 58(2): 333–345. Langton, R. and Lewis, D. (2001) Marshall and Parsons on “Intrinsic”. Philosophy and Phenomenological Research 63(2): 353–355. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986a) Introduction. In D. Lewis (ed.) Philosophical Papers vol. 2. Oxford: Oxford University Press: ix–xvii. Lewis, D. (1986b) On the Plurality of Worlds. Malden, MA: Blackwell. Marshall, D. (2009) Can “Intrinsic” Be Defined Using Only Broadly Logical Notions? Philosophy and Phenomenological Research 78(3): 646–672. Marshall, D. (2013) Intrinsicality and Grounding. Philosophy and Phenomenological Research. Marshall, D. (2021) Intrinsicality and the Classification of Uninstantiable Properties. Philosophical Studies 178(3): 731–753. Marshall, D. and Parsons, J. (2001) Langton and Lewis on “Intrinsic”. Philosophy and Phenomenological Research 63(2): 347–351. Marshall, D. and Weatherson, B. (2018) Intrinsic vs. Extrinsic Properties. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/archives/spr2018/ entries/intrinsic-extrinsic/>. McGilvary, E.B. (1930) A Tentative Realistic Metaphysics. In Adams, G.P. and Montague, W.P. (eds.) Contemporary American Philosophy. New York: Macmillan: 109–132. McKitrick, J. (2003) A Case for Extrinsic Dispositions. Australasian Journal of Philosophy 81(2): 155–174. Moore, G.E. (1903) Principia Ethica. Cambridge: Cambridge University Press. Rosen, G. (2010) Metaphysical Dependence: Grounding and Reduction. In Hale, B. and Hoffmann, A. (eds.) Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press: 109–135. Shumener, E. (2022) Intrinsicality and Determinacy. Philosophical Studies 179(11): 3349–3364. Sider, T. (2001) Maximality and Intrinsic Properties. Philosophy and Phenomenological Research 63(2): 357–364. Skiles, A. (2014) Primitivism About Intrinsicality. In Francescotti, R.M. (ed.) Companion to Intrinsic Properties. Berlin: De Gruyter: 221–252. Vallentyne, P. (1997) Intrinsic Properties Defined. Philosophical Studies 88(2): 209–219. Weatherson, B. (2001) Intrinsic Properties and Combinatorial Principles. Philosophy and Phenomenological Research 63(2): 365–380. Wilhelm, I. (2022) Intrinsicality and Entanglement. Mind 131(521): 35–58. Wilson, J.M. (2014) No Work for a Theory of Grounding. Inquiry: An Interdisciplinary Journal of Philosophy 57(5–6): 535–579. Witmer, D.G., Butchard, W. and Trogdon, K. (2005) Intrinsicality without Naturalness. Philosophy and Phenomenological Research 70(2): 326–350. Yablo, S. (1999) Intrinsicness. Philosophical Topics 26(1–2): 479–505.

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9 ESSENTIAL VERSUS ACCIDENTAL PROPERTIES Fabrice Correia

9.1 Introduction The distinction between properties that are essential and those that are accidental (i.e., non-essential) is central to philosophy. One important reason why this is so, albeit by far not the only one, is that many of the “big questions” in philosophy – What is truth? What is knowledge? What is it for an action to be good? etc. – ask for essential features of the items they mention. In this chapter, I try to give a fair snapshot of the contemporary discussions on the topic, focusing more on the theory of essentiality and accidentality but without neglecting the applications of these notions. Before moving on to issues that shape the current debates about the essential vs accidental distinction, let me briefly elaborate on a question that is largely left aside in these debates but which is nevertheless of importance, namely: What is it, exactly, that is essential or accidental? Consider a typical essentialist statement like (1) Being human is an essential property of Socrates On the face of it, (1) makes reference both to Socrates and to another entity, the property of being human. Is this first impression to be taken seriously? More generally, is the essential vs accidental distinction tied to talk of properties understood in an ontologically serious way? Both “yes” and “no” are coherent answers to this question. If talk of properties is taken seriously, then there naturally arises the question of whether one’s views about what sort of entities properties are may have an impact on one’s views about which properties are essential to what. The reply to this question is certainly affirmative. For suppose that Socrates is essentially human. Then consider the claim that the universal property of being human is essential to Socrates. Granted that there is the universal property of being human, the claim would seem to be a good way of cashing out the initial assumption. But now consider the claim that the humanity-trope that inheres in Socrates is essential to him. Granted that there is such a thing as Socrates’s humanity-trope, this claim is not a good way of cashing out the initial assumption. For it rules out a view that is not ruled out by the assumption, namely the view, which looks

DOI: 10.4324/9781003246077-12

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perfectly coherent, that Socrates has distinct humanity-tropes at distinct worlds. (I am here assuming that essential properties are necessary; this is a widely accepted view, but it is nonetheless a view that has been questioned. See later in this chapter.) Thus, properties-quauniversals and properties-qua-tropes are not on a par when it comes to claims of essentiality. Similar considerations hold for other pairs of conceptions of the nature of properties. If talk of properties is not taken seriously, then how is a statement like (1) to be understood? One may invoke predicates or concepts instead of properties. Thus, one may take (1) to be an informal version of (2) or (3), where (2) is taken to be ontologically commited to Socrates and the predicate “is human” and to nothing else, and (3) is taken to be committed to Socrates and the concept of being human and to nothing else: (2) Socrates essentially satisfies the predicate “is human” (3) Socrates essentially falls under the concept of being human A further, more radical view is that (1) is an informal version of (4) and that (4) is committed to Socrates and to nothing else: (4) Socrates is essentially human On this view, (4) states that Socrates is essentially a certain way, but it does not do it by stating that Socrates is related to a certain entity – a predicate, a property, a concept, or whatnot.1 In what follows, I will very often use the idiom of essential and accidental properties, but except for special occasions that I will explicitly flag, I will be neutral on whether talk of properties should be taken at face value or whether, alternatively, one of the other options just discussed (or even further options) should be chosen instead.

9.2

The Aristotelian Notion and the Modal Notion of Essence

Analytic philosophers have used the label “essential property” and cognate expressions (“essentially”, “it is essential to”, …) in two distinct ways. There is first a use of these expressions for a notion that philosophers have thought about and used throughout the history of philosophy and which Aristotle has systematized to a great extent. This notion – Aristotelian essentiality or A-essentiality, as I will call it – is tied to what are sometimes called “what-questions”, questions such as (a) (b) (c) (d) (e) (f)

What What What What What What

is it to be human? is knowledge? is the nature of knowledge? does truth consist in? is Socrates? is the nature of Socrates?

A-essentialist claims, at least the most basic among them, are answers, intended to be full or only partial, to such questions. Following Aristotle (Metaphysics Z 5, 1031a11–12; Aristotle 1984), we may call such claims “definitions” (bearing in mind that some of them may only be partial).2

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The second use corresponds to a purely modal notion – modal essentiality or Messentiality, as I will call it. An M-essential property of an object is simply a property that the object has as a matter of necessity, and more generally, M-essentiality is basically just necessity. Although “essential”, “essentially”, etc. have been massively used by philosophers, including analytic philosophers, to express A-essentiality, a non-negligible number of influential analytic philosophers have used them to express M-essentiality.3 A-essentiality and M-essentiality are, on the face of it, quite distinct notions. Yet they are plausibly intimately connected: it is indeed very plausible to hold that every A-essential property is M-essential (but see the discussion below). It is therefore somewhat unfortunate that the same labels have been used for both notions, since this creates the risk of failing to understand which notion is at stake in certain contexts. The risk is actually exacerbated by the fact that some much-discussed accounts of A-essentiality are modal accounts (again, see below). In what follows, I will take on board both notions. For some of the topics to be discussed, the difference between the two notions will not matter, or at least not much. For some other topics, the difference will matter to a significant extent. There is an important distinction that needs to be made already here because it will shape the structure of the rest of this chapter. The distinction shows up in the list of whatquestions above. The last two questions are clearly about a given object, namely Socrates. The first question does not seem at all to be about an object. For the remaining questions, impressions can go both ways. On one hand, they contain names – “knowledge”, “truth” – and for this reason it is tempting to understand them as being about certain objects. But on the other hand, it is easy to paraphrase them into questions that do not contain names, questions of the same form as the first question on the list: “What is it for someone to know something?” in the case of questions (b) and (c), and “What is it for a proposition/sentence/ belief/… to be true?” in the case of question (d). Following terminology introduced in (Correia 2006), I will call questions (e) and (f) and questions (b)–(d) understood as being about specific objects objectual, and question (a) and questions (b)–(d) understood according to the paraphrases mentioned above generic. I will come back to the objectual vs generic distinction in the very last section of the chapter. Until then, with the exception of a short passage in Section 9.6, when talking about Aessence I will exclusively focus on the objectual notion – that is, on the notion involved in the objectual questions, namely that of an object being A-essentially so and so. Likewise, when talking about M-essence, I will exclusively focus on the notion of an object being Messentially so and so.

9.3 Variations on M-Essentiality An M-essential property is a necessary property. There are two slightly different ways of making this idea precise: (M1) x is M-essentially F iff necessarily, x is F (M2) x is M-essentially F iff necessarily, x is F if x exists Necessity is here metaphysical necessity, as opposed to, say, logical or conceptual necessity. The existence predicate may be understood in various ways. The two standard options in theories of modality, in particular in quantified modal logic, are (i) to take “exists” to be

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synonymous with “is identical to something” and (ii) to take “exists” to express a primitive notion. (M1) and (M2) are equivalent if x is a necessary existent. If x is a contingent existent, (M1) requires that no M-essential property of x is existence-entailing. (M2) makes no such requirement. Thus, if you believe that Socrates only contingently exists, that he is M-essentially human and that being human is existence-entailing, then you cannot take M-essentiality to be characterized along the lines of (M1) – you must opt for (M2). However, it is possible to opt for (M1) and still take humanity to be M-essentially tied to Socrates despite his being a contingent object: just claim that what is M-essential to him is not the property of being human, but the property of being human if existing. Bernard Linsky and Edward N. Zalta (1994, 1996) and Timothy Williamson (1998, 2000) argue that existing, in the sense of being identical to something, is a necessary property. For them, (M1) and (M2) are therefore equivalent for any x. However, they all agree that objects like Socrates are in some sense contingent. They cash out contingency in terms of “concreteness” instead of existence: whereas Socrates is actually concrete, he could have failed to be so (he would have been non-concrete had no living beings populated the universe, say). On such an account, the spirit of original contrast between (M1) and (M2) is still present, but it takes the form of a contrast between (M1) and (M2) with “exists” replaced by “is concrete”. (M1) and (M2) can be further refined by plugging in one’s favourite account of de re modal claims. On David Lewis’s (1968) counterpart theory, for instance, assuming that F makes no reference to any particular object (unlike, for instance, “is bigger than the Eiffel Tower”), (M1) gets translated into the following biconditional: (M3) x is M-essentially F iff for any possible world and any counterpart y of x in that word, y is F The general case goes as follows, where R is any predicate that makes no reference to any particular object: (M4) x is M-essentially such that Rxx′x′′ … iff for any possible world and any counterparts y, y′, y′′, … of x, x′, x′′, … , respectively, in that world, Ryy′y′′ On Lewis’s account, just like on the views of Linsky and Zalta (1994, 1996) and of Williamson (1998, 2000) but for a very different reason, (M1) and (M2) are equivalent.

9.4

The Simple Modal Accounts of A-Essentiality and Some Objections against Them

I previously stressed that it is plausible to hold that A-essential properties are M-essential. What about the converse? The view that it also holds has a certain prima facie plausibility. It is therefore tempting to hold that a property is A-essential just in case it is M-essential. Given the two ways of precisely cashing out what an M-essential property is (see above), this yields two modal accounts of A-essentiality: (A1) x is A-essentially F iff necessarily, x is F (A2) x is A-essentially F iff necessarily, x is F if x exists

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The prima facie plausibility of these accounts does not stand up to examination. There is one obvious problem that they face: they deem A-essential every property that is trivially necessarily had by everything, whereas at least some of these properties are intuitively not A-essential to everything. Being red or not red and being such that 7 is prime are example of such properties. Another, slightly less obvious problem affects (A2): whereas it may be held that an elite group of objects enjoy A-essential existence – say certain divinities or purely mathematical entities – it is counterintuitive to hold, pace (A2), that absolutely everything does. Kit Fine (1994) criticizes the modal accounts of A-essence using the previous arguments and further counterexamples to (A1) and (A2). Granted that numerical distinctness is necessary, the two accounts imply that, say, Socrates is A-essentially distinct from the Eiffel Tower. But this is counterintuitive: surely, claiming that Socrates is distinct from the Eiffel Tower is not giving an answer, even partial, to the question of what Socrates is. Or consider the relations between Socrates and {Socrates}, the set-theoretic singleton whose member is Socrates. The view that Socrates is A-essentially a member of {Socrates} is counterintuitive: surely, what Socrates is has nothing to do with {Socrates}, and more generally with sets. Yet given principles of modal set-theory that are very plausible if not compelling, (A1) and (A2) both imply that Socrates is A-essentially a member of the singleton. Fine’s objections are, in effect, objections to the view that M-essentiality is sufficient for A-essentiality, and he is explicit that he has no problem with the view that the former is necessary for the latter. Others have also questioned this latter view – see for instance Joseph Almog (1991), Penelope Mackie (2020) and Jessica Leech (2021), and also a recent paper of mine on non-modal conceptions of essence (Correia forthcoming) for further references. This position is far from being orthodox, but it certainly deserves to be taken seriously. Fine’s objections have triggered a massive set of reactions. Some philosophers have tried to save the spirit of the modal accounts of A-essentiality, others have put forward nonmodal accounts. I discuss the first move in Section 9.5, and the second move in Section 9.6.

9.5 Sophisticated Modal Accounts of A-Essentiality Being red or not red is, in an intuitive sense, a property that does not really characterize anything; and if being such that 7 is prime perhaps really characterizes 7, intuitively it does not really characterize, say, Socrates. Why not modify the modal account by simply enforcing a requirement that guarantees that the A-essential properties of an object do really characterize the object? Two suggestions which go in that direction have been made in the literature. One of them has it that a property is A-essential iff it is M-essential and “carves reality at the joints” (see Cowling 2013; De Melo 2019; Wildman 2013). The other one has it that a property is A-essential iff it is M-essential and intrinsic (see Bovey 2021; Denby 2014). The corresponding accounts are thus as follows: (A1.a) x is A-essentially F iff (i) necessarily, x is F & (ii) being F is joint-carving (A2.a) x is A-essentially F iff (i) necessarily, x is F if x exists & (ii) being F is joint-carving

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(A1.b) x is A-essentially F iff (i) necessarily, x is F & (ii) being F is intrinsic to x (A2.b) x is A-essentially F iff (i) necessarily, x is F if x exists & (ii) being F is intrinsic to x There is no doubt that these suggestions allow one to get rid of some of the Finean counterexamples. Thus, for instance, being red or not red is not joint-carving – on any reasonable understanding of “joint-carving” – and therefore both (A1.a) and (A2.a) predict that nothing A-essentially has this property. Likewise, being such that 7 is prime is not intrinsic to Socrates – on any reasonable understanding of “intrinsic” – and therefore both (A1.b) and (A2.b) predict that that property is not A-essential to Socrates. However, it is doubtful that the proposals are immune from all the Finean counterexamples. It is plausible to hold that set-membership is joint-carving. Taking this for granted, how can it be denied that being a member of {Socrates} is also joint-carving? (To make the argument more convincing, one may change the example and replace Socrates with some fundamental particle.) Granted that that property is joint-carving, (A1.a) and (A2.a) are in no better position than (A1) and (A2). And is it not tempting to follow Theodore Sider (2011) and hold that existence carves at the joints? Granted that existence does carve at the joints, (A2.a) is in no better position than (A2). (A1.b) and (A2.b) perform better with the singleton example: intuitively, being a member of {Socrates} is not intrinsic to Socrates. But it is not clear that (A2.b) does any better than (A2) with respect to the existence example: it seems that one can hold, consistently, that existence is a primitive property that is intrinsic to anything that has it, and that Socrates does not A-essentially exist. And it is not clear either that (A1.b) and (A2.b) perform well with the example involving the property of being red or not red, or rather with a variant thereof. The property of having this particular H20 molecule as a part is an intrinsic property of me. It seems to follow that having this particular H20 molecule as a part or not having it as a part is also an intrinsic property of me. This is a property that I necessarily have, and yet, intuitively, it is not one of my A-essential properties. The modal accounts of A-essence just discussed simply (conjunctively) add a further condition to the original modal condition. In reaction to Fine’s objection to the original account, another strategy has been pursued to defend the view that A-essentiality is a modal notion: invoking non-standard modal concepts. In (Correia 2007), I appeal to a concept of strict implication whose logic is three-valued, and Berit Brogaard and Joe Salerno (2007) put to work a counterfactual conditional that is not trivialized when applied to impossible conditions.

9.6 Non-Modal Accounts of A-Essentiality In reaction to Fine’s objections to the modal account of A-essentiality, many philosophers have taken the notion to be primitive, or have worked on the assumption that it is or could be primitive. Those who did so in print include Fine himself (1995a, 2015), Correia (2006, 2012), Boris Kment (2014), E.J. Lowe (2008, 2012), Kathrin Koslicki (2012) and Bob Hale (2013). See Correia (forthcoming) for further references. Others have put forward accounts of A-essentiality in non-modal terms. There have been very few proposals of that sort.4 Michael Gorman (2005, 2014) advocates the following account: 108

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(A3) x is A-essentially F iff (i) being F is a property which really characterizes x and (ii) it is not the case that being F really characterizes x in virtue of the fact that another given property really characterizes x Condition (i) is meant to secure that properties like being red or not red and being such that 7 is prime are not A-essential to Socrates. The locution “in virtue of” in (ii) expresses metaphysical grounding, or something close to it (see Correia and Schnieder 2012 and Raven 2020 on that notion). Agustín Rayo (2013) and Correia and Alexander Skiles (2019) defend an account of Aessentiality in terms of a generalized notion of identity, a notion that can be expressed by means of statements of type “To be F is to be G” or “There is no difference between being F and being G”. The account goes through an account of generic A-essentialist claims of type “To be F is part of what it is to be G”, which goes as follows: (G) To be F is part of what it is to be G iff there is no difference between being both F and G and being G The account of A-essentiality can then be formulated as follows, with the caveat that what comes after “iff” is to be understood along the lines of (G): (A4) x is A-essentially F iff to be F is part of what it is to be x where “to be x” may be understood as synonymous with “to be identical to x”.5 Do these accounts fall prey to the Finean counterexamples? Primitivism has no problem with them. If you share Fine’s view that, intuitively, all the properties he invokes in the counterexamples – existing, being a member of {Socrates}, and so on – can be deemed Aaccidental to the relevant objects, then taking the notion of an A-essential property to be primitive will not prevent you from holding that these properties are indeed, or at least can be taken to be, A-accidental to these objects. (Of course, arguments can convince a primitivist that contrary to first impression, this or that property invoked by Fine turns out to be A-essential, but this is another story.) On the face of it, Gorman’s account is both too liberal and too restrictive. It seems too liberal regarding the Finean counterexamples. As we saw, condition (i) of the account gets rid of trivial properties such as being red or not red. But what about the properties of existing and of being a member of {Socrates}? Don’t they “really characterize” Socrates? If not, why not? A proper assessment would require an account of what real characterization is, and Gorman does not give such an account. The account seems too restrictive because of condition (ii). Why should grounded properties of Socrates ipso facto fail to be A-essential to him? Mars is A-essentially spherical (let us suppose), and from this we are inclined to infer that it A-essentially has a shape. But if, as grounding orthodoxy about the connections between determinables and determinates has it (see for instance Rosen 2010), Mars’s being spherical grounds its having a shape, then by (ii) the inference is not valid. Facing the choice between giving up grounding orthodoxy on this point and rejecting condition (ii), it seems that doing the latter is most natural. Whether the account defended by Rayo (2013) and Correia and Skiles (2019) fares well with respect to the Finean counterexamples depends on one’s conception of generalized 109

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identity. Rayo is happy to endorse the view that statements of type “To be F is to be G” are equivalent to modal statements of type “Necessarily, all and only Fs are G”. On this account, (A4) is equivalent to, and hence trivially fares no better than, (A2). But Rayo’s deflationary view is implausible – see Øystein Linnebo (2014) and Correia and Skiles (2019) – and on a more robust conception of generalized identity, it can be argued that (A4) is immune to the counterexamples (see Correia forthcoming for some elaboration). The sophisticated modal accounts of A-essence (see Section 9.5), just like the standard modal accounts, have it that A-essential properties are necessary (or necessary if the object exists), and are therefore in conflict with the views of Mackie (2020), Leech (2021) and others (see Section 9.4). What about the non-modal accounts discussed in this section? As Gorman (2014) stresses, his account prima facie leaves room for there being contingent Aessential properties. The Rayo-Correia and Skiles account differs in this respect. On Rayo’s conception of generalized identity, A-essential properties must be necessary. Correia and Skiles (2021) argue for the same conclusion on their own conception of generalized identity.

9.7 Further Topics In this last section, I briefly run through a number of further topics. Some pertain again to the theory of essence, others to applications of the notion. Individual essences. Socrates is essentially human (let us suppose). Yet being human is not a property that is specific to him: many other objects have it. Is there any essential property of Socrates that is not had by other objects? Being identical to Socrates is a plausible candidate. It is indeed plausible to hold that necessarily, no object distinct from Socrates has that property. Being identical to x is a so-called individual essence of x – a property P of x such that (i) P is essential to x and (ii) necessarily, no object distinct from x has P. It is a non-qualitative property, for it makes reference to a particular object – namely x. Are there qualitative individual essences, i.e., individual essences which make no reference to any particular objects? If so, what kind of properties are they? These are much-debated philosophical questions. See Mackie (2006: chs. 2 and 3) for a substantial discussion. The definition of individual essence that I formulated above is not specific about the question of which of A-essentiality and M-essentiality is involved in clause (i). Typically, if not always, people discussing individual essences have M-essentiality in mind. It is not clear whether working with A-essentiality instead would bring anything new – or better: anything both new and interesting – to the relevant debates. Which properties are essential to what? There is serious disagreement among philosophers about which properties are essential to what. More so when essentiality is understood as A-essentiality than when it is understood as M-essentiality, but even in the latter case disagreement is significant. G.W. Leibniz defended the extreme view that every property of every object is both Aessential and M-essential to it (see, e.g., Leibniz 2020). At the other extreme are the view that no property is A-essential to anything and the view that no property is M-essential to anything. The second view is untenable: compelling principles of modal logic guarantee that everything is necessarily red or not red, and necessarily self-identical (or self-identical if existing), for instance. The first view also seems untenable, at least granted that objects of certain kinds exist: the number 7, for instance, if there is such a thing, is certainly A-essentially an integer. Between the Leibnizian extremes and its opposites stand a wide range of options. 110

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Being self-identical, being identical to Socrates and being red or not red are all very plausibly M-essential properties of Socrates. The first two are perhaps A-essential to him, and so is perhaps even the third one. In any case, those of these properties which are essential to him, whichever they may be, are certainly trivially essential to him. Putative examples of non-trivial essential properties have been thoroughly discussed in the literature: (A) Being a member of a (natural or artefactual) kind (see Wiggins 1980, and the discussion in Mackie 2006: chs. 7 and 8). (B) Having one’s actual biological or material origin (see Kripke 1980, and the discussions in Mackie 2006: ch. 6 and Robertson Ishii and Atkins 2020). (C) Having some particular object as a part/component/constituent (see Chisholm 1973 and Fine 2010). (D) Having members with such and such internal/microphysical structure (the intended bearers of these properties are intended to be natural kinds) (see Kripke 1980, Putnam 1975, and the discussion in Bird and Tobin 2022). Most people who have been engaged in the related discussions had M-essentiality in mind, but in many contexts this is immaterial. It would actually be interesting to investigate in detail where and how the A-essentiality/M-essentiality distinction could potentially impact these discussions. A-essence as an ingredient in accounts of other notions. The notion of A-essence has been used to define or characterize other notions of philosophical interest. Fine (1994) suggests that metaphysical necessity can be understood in terms of A-essence, and many philosophers have been since then seduced by this idea (see Correia forthcoming for a short survey and discussion). Fine (1995b) and others suggest characterizations of ontological dependence in terms of A-essence (see Correia 2008 for a thorough survey). In Correia (2013), I explore the possibility of giving characterizations of metaphysical grounding in terms of A-essence. Fine (2015), Rosen (2015) and Correia (2017) propose accounts of real definition where A-essence plays a central role. Generic essence, and beyond. The notion of essence that has been at the centre of the discussion so far in this chapter is that of objectual essence – the notion of generic essence has only been mentioned as an ingredient in an account of objectual A-essence (Section 9.6). It should be clear that taking the generic notion seriously would have a significant impact on the previous discussion at various important junctures. For instance, if the Finean view that metaphysical necessity must be understood in terms of A-essence is on the right track, then surely both objectual and generic A-essence should be invoked. Or again, consider the Kripke-Putnam claims about the essence of natural kinds. They are usually cashed out in objectual terms: a given object, e.g., the kind water, is said to be essentially so and so – in this case, say, such that any sample of substance that belongs to the kind is made of H2O molecules. But is it necessary to endorse an ontology of kinds in order to formulate such claims? On the face of it, the most natural formulations are generic. Thus, the previous claim about water seems to be most naturally formulated in something like the following way: it is part of what it is to be a sample of water that samples of water are made of H2O molecules. The objectual/generic distinction manifests itself in language in the form of the name/ predicate distinction. It is tempting to hold that further logico-grammatical categories 111

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correspond to further notions of essence. Correia (2013), and to a greater extent Correia and Skiles (2019), advocate the view that the space of notions of essence goes beyond the objectual and the generic. Andreas Ditter (2022) puts forward a logic of essentialist claims framed in a higher-order, typed language where the subjects of essentialist attribution can be of arbitrary grammatical categories. Scepticism and anti-realism about essence. There is a vast literature on scepticism about de re metaphysical modality (roughly, the view that such modality is unintelligible/ irremediably obscure) and anti-realism about it (roughly, the view that although such modality is conceptually in order, modal truths are nevertheless in some sense “mind-dependent”) (see Bueno and Shalkowski 2021: part 3 for a recent survey). Since M-essentialist claims are special cases of de re modal claims involving metaphysical modality, each of these two views is at least indirectly a view about M-essentiality. If being A-essential entails being M-essential, then plausibly, scepticism / anti-realism about M-essentiality yields scepticism / anti-realism about A-essentiality. Interestingly, one’s view about objectual essence may be quite different from one’s view about generic essence (or about further notions of essence one may wish to countenance). Thus, for instance, Lewis (1986) is explicitly anti-realist about objectual M-essentiality. Whether an object is M-essentially F, according to him, is a matter of how we describe or think about the object in question: some ways of doing it pick out counterpart relations that deliver the result that the object is M-essentially F, while other ways pick out counterpart relations that deliver the opposite result. Yet this view about objectual Messentialist statements is certainly compatible with a fully realist attitude towards (at least certain) generic questions of type “What is it to F?” and cognates. Lewis himself often uses expressions of type “what it is for something/an F to G” in claims that he makes, and there is no reason, at least in most cases I think, to doubt that he understands them in their standard, Aristotelian sense.6

Notes 1 The view that (2), (3) or (4) shows in a more perspicuous way the ontological commitments of (1) is a view on which (2), (3) or (4) constitutes what Keller (Chapter 2, this volume) calls a “reconciling paraphrase” of (1). 2 Given the central role that questions of that kind play in Plato’s Socratic dialogues, I could have used “Socratic essentiality” instead of “Aristotelian essentiality” for the notion at stake. I chose the latter because of Aristotle’s hugely influential work on the notion. 3 Clear examples are Plantinga (1978) and Forbes (1985). The case of some other philosophers, for example, Kripke (1980), is less clear. See Correia (forthcoming) for more on the issue. Cowling (2013) advocates a modal reduction of a notion of essence that is distinct from both A-essence (which he calls “nature”) and M-essence, but it is not clear what his target notion is. 4 Zalta (2006) proposes a non-modal definition of essential properties for abstract objects, but it is not clear that he intends it to be an account of A-essential properties for these objects. See Correia (forthcoming) for a discussion. 5 On the face of it, “To be F is to be G” is a correct sort of answer to the question “What is F?”, and accordingly it is tempting to hold that the Rayo-Correia and Skiles account is primitivist after all. I do believe that instances of “To be F is to be G”, in the intended sense, are essentialist statements. But even taking this for granted, the account is not primitivist since it characterizes the target notion, that of an object being A-essentially such and such, in terms of a distinct notion. 6 Work on this chapter was funded by the Swiss National Science Foundation (project 100012_197172).

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References Almog, J. (1991) The What and the How. Journal of Philosophy 88(5): 225–244. Aristotle (1984) Metaphysics. In Barnes, J. (ed.) The Complete Works of Aristotle: The Revised Oxford Translation, vol. II. Princeton: Princeton University Press. Bird, A. and Tobin, E. (2022) Natural Kinds. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Spring 2022 Edition), URL = < https://plato.stanford.edu/archives/spr2022/entries/ natural-kinds/>. Bovey, G. (2021) Essence, Modality, and Intrinsicality. Synthese 198(8): 7715–7737. Brogaard, B. and Salerno, J. (2007) A Counterfactual Account of Essence. The Reasoner 1(4): 4–5. Bueno, O. and Shalkowski, S. (eds.) (2021) The Routledge Handbook of Modality. New York: Routledge. Chisholm, R.M. (1973) Parts as Essential to Their Wholes. Review of Metaphysics 26(4): 581–603. Correia, F. (2006) Generic Essence, Objectual Essence, and Modality. Noûs 40(4): 753–767. Correia, F. (2007) (Finean) Essence and (Priorean) Modality. Dialectica 61(1): 63–84. Correia, F. (2008) Ontological Dependence. Philosophy Compass 3(5): 1013–1032. Correia, F. (2013) Metaphysical Grounds and Essence. In Hoeltje, M., Schnieder, B. and Steinberg, A. (eds.) Varieties of Dependence. Munich: Philosophia Verlag: 271–291. Correia, F. (2017) Real Definitions. Philosophical Issues 27(1): 52–73. Correia, F. (forthcoming) Non-Modal Conceptions of Essence. In Koslicki, K. and Raven, M. (eds.) The Routledge Handbook of Essence. New York: Routledge. Correia, F. and Schnieder, B. (2012) Grounding: An Opinionated Introduction. In Correia, F. and Schnieder, B. (eds.) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press: 1–36. Correia, F. and Skiles, A. (2019) Grounding, Essence, and Identity. Philosophy and Phenomenological Research 98(3): 642–670. Correia, F. and Skiles, A. (2021) Essence, Modality, and Identity. Mind 131(524): 1279–1302. Cowling, S. (2013) The Modal View of Essence. Canadian Journal of Philosophy 43(2): 248–266. De Melo, T.X. (2019) Essence and Naturalness. Philosophical Quarterly 69(276): 534–554. Denby, D. (2014) Essence and Intrinsicality. In Francescotti, R. (ed.) Companion to Intrinsic Properties. Berlin: De Gruyter: 87–109. Ditter, A. (2022) Essence and Necessity. Journal of Philosophical Logic 51(3): 653–690. Fine, K. (1994) Essence and Modality. Philosophical Perspectives 8: 1–16. Fine, K. (1995a) Senses of Essence. In Sinnott-Armstrong, W. (ed.) Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus. Cambridge: Cambridge University Press: 53–73. Fine, K. (1995b) Ontological Dependence. Proceedings of the Aristotelian Society 95(1): 269–290. Fine, K. (2010) Towards a Theory of Parts. Journal of Philosophy 107(11): 559–589. Fine, K. (2015) Unified Foundations for Essence and Ground. Journal of the American Philosophical Association 1(2): 296–311. Forbes, G. (1985) The Metaphysics of Modality. Oxford: Clarendon Press. Gorman, M. (2005) The Essential and the Accidental. Ratio 18(3): 276–289. Gorman, M. (2014) Essentiality as Foundationality. In Novotný, D.D. and Novák, L. (eds.) NeoAristotelian Perspectives in Metaphysics. New York and London: Routledge: 119–137. Hale, B. (2013) Necessary Beings. An Essay on Ontology, Modality, and the Relations Between Them. Oxford: Oxford University Press. Kment, B. (2014) Modality and Explanatory Reasoning. Oxford: Oxford University Press. Koslicki, K. (2012) Essence, Necessity, and Explanation. In Tahko, T. (ed.) Contemporary Aristotelian Metaphysics. Cambridge: Cambridge University Press: 187–206. Kripke, S. (1980) Naming and Necessity. Harvard: Harvard University Press. Leech, J. (2021) From Essence to Necessity via Identity. Mind 130(519): 887–908. Leibniz, G.W. (2020) Discourse on Metaphysics (Trans. G. Rodríguez-Pereyra). Oxford: Oxford University Press. Lewis, D. (1968) Counterpart Theory and Quantified Modal Logic. Journal of Philosophy 65(5): 113–126. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Blackwell.

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Fabrice Correia Linnebo, Ø. (2014) ‘Just is’-Statements as Generalized Identities. Inquiry: An Interdisciplinary Journal of Philosophy 57(4):466–482. Linsky, B. and Zalta, E.N. (1994) In Defense of the Simplest Quantified Modal Logic. Philosophical Perspectives 8: 431–458. Linsky, B. and Zalta, E.N. (1996) In Defense of the Contingently Non-Concrete. Philosophical Studies 84(2-3): 283–294. Lowe, E.J. (2008) Two Notions of Being: Entity and Essence. Royal Institute of Philosophy Supplement 62: 23–48. Lowe, E.J. (2012) What Is the Source of Our Knowledge of Modal Truths? Mind 121(484): 919–950. Mackie, P. (2006) How Things Might Have Been. Oxford: Oxford University Press. Mackie, P. (2020) Can Metaphysical Modality be Based on Essence? In Dumitru, M. (ed.) Metaphysics, Meaning, and Modality: Themes from Kit Fine. Oxford: Oxford University Press: 247–264. Plantinga, A. (1978) The Nature of Necessity. Oxford: Clarendon Press. Putnam, H. (1975) The Meaning of ‘Meaning’. In Gunderson, K. (ed.) Minnesota Studies in the Philosophy of Science VII: Language, Mind and Knowledge. Minneapolis, MN: University of Minnesota Press: 131–193. Raven, M.J. (2020) Introduction. In Raven, M.J. (ed.) The Routledge Handbook of Metaphysical Grounding. New York: Routledge: 1–19. Rayo, A. (2013) The Construction of Logical Space. Oxford: Oxford University Press. Robertson Ishii, T. and Atkins, P. (2020) Essential vs. Accidental Properties. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Winter 2020 Edition), URL = < https://plato.stanford.edu/ archives/win2020/entries/essential-accidental/>. Rosen, G. (2010) Metaphysical Dependence: Grounding and Reduction. In Hale, B. and Hoffman, A. (eds.) Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press: 109–136. Rosen, G. (2015) Real Definition. Analytic Philosophy 56(3): 189–209. Sider, T. (2011) Writing the Book of the World. Oxford: Oxford University Press. Wiggins, D. (1980) Sameness and Substance. Oxford: Blackwell. Wildman, N. (2013) Modality, Sparsity, and Essence. Philosophical Quarterly 63(243): 760–782. Williamson, T. (1998) Bare Possibilia. Erkenntnis 48(2–3): 257–273. Williamson, T. (2000) The Necessary Framework of Objects. Topoi 19(2): 201–208. Zalta, E.N. (2006) Essence and Modality. Mind 115(459): 659–694.

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10 DETERMINATE/DETERMINABLE Eric Funkhouser

10.1

Introduction

This chapter is about the relationship between a determinable and its determinate properties – the determination relation. Properties related by determination belong to a category or family, such as the colors, shapes, temperatures, and so on. While this vocabulary was not coined until W.E. Johnson (1921), the distinction was more or less anticipated in Aristotle’s logical and metaphysical works (e.g., Categories, Metaphysics) and in various taxonomic works since. The determination relation has been applied to different entities – properties (universals, tropes), predicates, events, classes, concepts, and so on. This chapter confines itself to property determination, but most of the points made here extend to these other applications.

10.2

Specification

Everyone accepts that the conceptual core of determination is the idea that determinates are specific ways of instantiating a determinable property – e.g., scarlet is a specific way of being red, or measuring 5 kilograms is a specific way of having mass. This specification involves two directions of necessitation. First, determinates necessitate their determinables in the sense that, say, being scarlet guarantees being colored. Second, the instantiation of a determinable necessitates the instantiation of some determinate or other. No object is simply colored; it always must be blue, red, yellow, or some other determinate shade. To be colored is to be some specific color. This latter claim is somewhat controversial, however, and Jessica Wilson (2013) has argued that determinables can sometimes be instantiated without the instantiation of a unique determinate or any maximally specific determinate at all. For example, a mountain might have a determinable shape without having a maximally determinate shape. Not every kind of specification counts as determination, however. Theorists have made great efforts to distinguish true determinates from other types of specification, namely: i) species of a genus and ii) disjuncts of an arbitrary disjunction. Species are defined by two terms – one a generic essence and the other a differentia. Humans are rational animals, say, where animal is the genus and rationality the differentia. But red is not supposed to be a species of color. This is because to be red is not to be

DOI: 10.4324/9781003246077-13

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colored plus some other quality. Rather, redness is somehow contained in color and needs no external qualification such as are provided by differentia. Red specifies color along dimensions that are internal to the categorization of color. The species-genus relation primarily applies to substances. These substances can fall under many different kinds, allowing them to take on external properties (e.g., animals instantiate properties that have no bearing on biological taxonomies). The determination relation, in contrast, applies to abstractions like properties or predicates – what Johnson called adjectives. These abstractions cannot take on external properties. For example, Johnson (1921: 174) distinguishes statements like “Red is a color” from “Plato is a man”. We can put the point by saying that red can be nothing but a color, but Plato can be more than a man (e.g., an animal, a physical object, etc.). While arbitrary disjunctions are specified by their disjuncts, this is not sufficient for determination. Yellow is not a determinate of the disjunction yellow-or-angry, even though it is a more specific variety of it (Searle 1959: 141). Yellow-or-angry is not a unified kind that can count as a determinable that admits of determinates. Our discussion of comparison and exclusion will explain why this is so. Determination is more than mere specification. There also are formal differences in specification even among the properties that are actually related by determination: Simple/complex: Some properties are determined along only one dimension – e.g., mass along the dimension measured in kilograms, or temperature by degrees. Other properties are determined along more than one dimension – e.g., color along the dimensions of hue, brightness, and saturation. Bounded/unbounded: Some determinables have bounded values, as temperature has a lower bound (absolute zero) and speed has an upper bound (the speed of light). Other determinables can be specified without bounds (e.g., number itself). There also are determinables that are bound in the sense of being limited, but not in a way that can be ordered or quantified. For example, truth and falsity might be the limited options for the determinable property of having a truth value. Continuous/discrete: Mass can take any value along a continuum. But economic value and truth value are determined by discrete units (pennies or satoshis, true or false). Many gradable adjectives have continuous determinates. But there are discrete determinates (e.g., true or false) which show that determination does not necessarily involve a difference in degree or grade. While there are determinables that are not gradable, it is likely that all gradable properties have determinates. Levels and relativity of determination: Determination is relative in the sense that a property (red) can be determinable relative to one property (scarlet) but determinate relative to another (color). Specification is asymmetric and transitive, as is the determination relation itself. At the extremes, we can speak of maximal determinates (a precise shade of scarlet) which cannot be further specified and maximal determinables (color) which are not determinates of any further determinable. It is also common to speak of determinates that reside “at the same level”, such as yellow and blue, or circle and square.

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10.3 Comparison Determinates do not simply specify their determinables; they do so “in a certain respect” or they characterize “the same adjective” (Johnson 1921: 175; Prior 1949: 13). Red and yellow characterize with respect to color, where this is supposed to be a real basis for comparison. In contrast, yellow and angry are not determinates that characterize a common determinable with respect to being yellow-or-angry, as there is no such real basis for comparison (Armstrong 1978: ch. 14). While determination can be thought of in terms of disjunction (i.e., a determinable might be identified with the disjunction of its maximal determinates), not just any combination of disjuncts gives rise to a determinable property. Rather, determinates must compose a real unity. Here we see a connection between determinables and resemblance. Determinable properties pick out real resemblances, and these might also be described as natural. The determinates of a common determinable make up a family of properties that allow for a special kind of comparison. These comparisons often generate an ordering. For example, objects can be placed in order according to their mass, height, temperature, color, and so on. Several of these kinds have a unique, privileged ordering (e.g., mass), but color shows that there can be various ways to order determinates without any ordering being uniquely privileged. All of these comparative judgments seem to make sense only under a common determinable – e.g., red is more similar to orange than it is to yellow, but it makes no sense to ask whether red is more similar to 5 kilograms than it is to square. Not all determinables give rise to a comparative ordering, however. Truth value might be a determinable with true and false as its determinates (Searle 1959: 152), but there is no ordering here. Well-defined orderings might also be missing for determinables with many determinates, such as beliefs which are determined by content. There are no privileged relationships between many beliefs – say, beliefs about world capitals, the periodic table, and high fashion – but for the fact that they are all specific beliefs. Determinables might be the categories that are necessary for any comparison, and incommensurability would then be the outcome whenever there is no shared determinable. It is an interesting insight that comparative difference seems to require sameness. Determinates differ from one another in a comparative way – not simply in virtue of being “other” – only because they share the same determinable. Johnson (1921: 176) claimed that determinates are better understood in terms of having a special kind of difference rather than similarity. But it is probably better to treat equally the roles played by difference and similarity/sameness (Elder 1996: 151–154). Without a shared determinable, comparisons between properties and substances are likely futile (assuming that every property falls under some determinable). We have been talking of comparisons between properties (e.g., red properties being similar to orange properties), but the point also applies to substances themselves. Stop signs and apples are comparable because they instantiate determinates of the determinable red. The concept of a determinable can be used to mark the oft-drawn boundary between a difference of degree and a difference of kind. A difference of degree occurs only for properties under a common determinable (e.g., two masses or two colors that differ in degree). A difference of kind occurs when properties fall under distinct maximal determinables (e.g., masses are different in kind from colors) (Funkhouser 2014: 113–114). A special kind of comparison that logicians and metaphysicians have frequently emphasized is that of a contrary. Contraries are exclusive and opposite – like being hot instead

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of cold, red rather than blue. Different determinates at the same level are contrary and opposed to one another, offering contrasts under a determinable. Some have claimed that properties necessarily offer such contrasts in the sense that whenever a property is instantiated it must belong to a family of properties that offers at least one contrary alternative. Indeed, Ruth Garrett Millikan (1984: 268) goes so far as to say that the identity of a property is given by the identity of its contraries. Relating this to our topic, the claim is that every property must be either a determinable or a determinate, and every property is then defined by these relationships. One justification for this is that property ascriptions always introduce contrastive characterizations. An alternative metaphysical picture, perhaps worth considering, is that there are “orphan” properties that do not admit of specification (hence, are not determinable) and are not themselves determinates of a determinable. Such properties would be “orphan” in the sense that they do not belong to a family of comparative and contrastive alternatives. It would be an interesting and deep fact about properties if it instead turns out that every property must be a determinable or a determinate.

10.4 Exclusion Expanding on the topic of contrariness, some of the most prominent treatments of determination have claimed that determinates are not only incompatible with one another but stand in outright opposition (Elder 1996; Johnson 1921; Prior 1949; Searle 1959). Many properties are incompatible simply because the substances instantiating them are incapable of instantiating each kind of property. For example, nothing can be both green and prime (in the mathematical sense) because numbers cannot be colored. So, those properties are incompatible. Determinates (at the same level) – while supposedly incompatible with one another – are different. This is often put by saying that determinates exclude, oppose, compete with, or are contrary to one another. An object that is scarlet could be crimson, yet its being scarlet excludes its being crimson at that place and time. Indeed, substances often continuously transition from determinate to determinate, though those determinates are incompatible with one another. Think of how objects change their color, shape, mass, temperature and so on – there is a succession of different determinates under a determinable. This relates to a point raised by Ludwig Wittgenstein about properties that come in degrees, gradables such as temperature and mass. Something can be more or less hot, more or less massive. Plausibly, the different grades of a kind – the various temperatures, say – are determinates of a common determinable. Wittgenstein (1929) claimed that these different grades/determinates exclude one another, violating his previous claims about the independence of atomic facts. Significantly, Wittgenstein claimed that this incompatibility was not due to a logical contradiction. Something other than logical exclusion was supposed to be at work, an explanation that we might now describe as metaphysical. The idea is that there is something in the nature of temperature or mass that makes it impossible for a substance to instantiate more than one at a time, though this incompatibility cannot be established by reason. One could certainly challenge Wittgenstein’s claim that such exclusion is not due to a logical contradiction. If temperature is something like average kinetic energy, then it seems that there is a contradiction in something being both 80 and 90 degrees. The same is true of mass, especially if we attend to the ways that scientists operationalize these measurements 118

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(e.g., balancing on a scale). Still, it may turn out that some determinate exclusion does not involve a contradiction. For those cases, it is interesting to consider if another form of explanation is available or if instead the exclusion should be accepted as primitive. We also might want to rethink the claim that determinates exclude one another. Belief is a plausible candidate for a determinable kind. No one can just believe simpliciter, as we must instead always have some specific belief or other. But people can simultaneously have beliefs with many different maximally determinate contents. There are other possible counterexamples with this same form. For example, you cannot just “select” simpliciter, that is, without making any determinate selection (e.g., the beef, the chicken). Yet, many times you can make more than one selection. Once again, multiple determinates of a determinable appear to be instantiated at once. These are mundane cases of multiple instantiation, but some might argue that even radical property “piling” can occur – say, distinct colors instantiated by the same object (in the same place, at the same time, and so on). There are moves that one could make to salvage the exclusion thesis, though. First, one could maintain that every determinable does have only one corresponding determinate. In these cases, then, there must be distinct determinable properties (e.g., belief simpliciter) instantiated for each determinate. Yet, except for clear cases of “piling”, this seems redundant or at least profligate. Second, one could deny that these non-excluding cases are really cases of determination after all, flatly insisting that determinates must exclude one another (say, by conceptual necessity). Nevertheless, we should hope that there is a principle behind this insistence. Perhaps the supposed examples of non-exclusive determinates actually involve different substantival kinds, say, rather than adjectival kinds. Regardless, we should want to know why these cases should not be included as examples of determination.

10.5 Models and Theories The pioneering work situating determinables and determinates in conceptual space occurred in the 1920s-1950s. Interest in the determination relation was then rekindled in the 1990s, largely driven by applications to mental properties and mental causation (Ehring 1996; MacDonald and MacDonald 1986; Yablo 1992). By that time, a cottage industry had already emerged on the topics of reduction and mental causation. Can mental properties be identified with physical properties? And can mental causation find a place in a world of physical causation? Some turned to the determination relation for help. Theorists who followed in this tradition grew more serious about metaphysical questions related to what might otherwise be only a logical distinction. (David Armstrong’s (1978) landmark work on property realism initiated a metaphysical climate that tolerated such forays.) The questions that emerged included: What is the relationship between the instantiation of a determinable property and its corresponding determinate? Is one more fundamental than the other? For that matter, do determinable property instances even exist? And how do determinables and determinates fare against one another when it comes to causal efficacy and causal explanation? Stephen Yablo advocated for an unorthodox account of determination such that the realization of mental states by physical states could be assimilated to it. His account is unorthodox because it is not concerned with distinguishing determination from speciesgenus or disjunct-disjunction relations and the like. Perhaps more to the point, Yablo did not attend to the idea that determination is an adjectival characterization or a specification 119

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“in a respect”. To be fair, Yablo did say that instantiating a determinate is “a specific way” of instantiating a determinable. But this specificity was accounted for in simple modal terms: determination is asymmetric necessitation. Strictly speaking, Yablo (1992: 253, fn 23) acknowledges that asymmetric necessitation is distinct from determination, because otherwise conjunctions would determine their conjuncts. Yet, he offered no account of what more is necessary for determination beyond asymmetric necessitation. In fact, he claimed that two widely accepted doctrines – the supervenience of the mental on the physical and the multiple realization of the mental by the physical – entail (or at least strongly suggest) that mental properties are determinable relative to the physical realizations that are the determinates. The idea is that each physical realization is a specific way of being in that mental state just like scarlet is a specific way of being red. On this simple modal account, multiple realization is embraced as a form of determination. Each realization necessitates the realized property (supervenience); and while some realization is necessary in order to instantiate the higher-level property, no particular realization is necessitated (multiple realizability). Why did Yablo propose such a simple, perhaps even crude, test for determination? A driving force was his explicit rejection of the relatively a priori or conceptual accounts of determination that preceded his. In particular, Yablo’s account contrasts with John Searle’s (1959: 148) contention that determinates are logically related to one another. In support of Searle’s view, we should recognize that it often does seem to be a largely conceptual point that some properties are related as determinates of a common determinable. Even when we confine ourselves to our armchairs, it is difficult not to recognize scarlet and crimson as determinates of the same determinable, or 5 kilogram and 6 kilogram as specifying the same determinable. And it is hard to imagine empirical discoveries that would convince us otherwise. But Yablo properly notes that, in a post-Kripkean world, we should acknowledge that not even all identities can be known a priori. If identity statements can be a posteriori, then it is reasonable to expect that there are a posteriori determination relations as well. Just as being H2O does not entail being water by conceptual necessity, Yablo expects that there will be determination relations that can be discovered only through empirical means. For these reasons, Yablo favors what he calls a metaphysical, rather than a conceptual, understanding of the determination relation. But remember that determinates qualify “in respect of” the determinable (Prior 1949), and this condition might not be met by physical realizations of mental kinds. Just as disjuncts fail to qualify (arbitrary) disjunctions in some real, unitary, and shared respect, the multiple realizations of a higher-level kind might fail to qualify it in a real, unitary, and shared respect. Intuitively, realization properties belong to different families of properties than do the properties they realize. Neuroscientific properties realize cognitive psychological properties, say, but these families of properties seem to pick out different resemblances, with different orderings, studied using different tools and methodologies. With these points in mind, non-reductive physicalists often tout the autonomy of the special sciences with respect to the realization-level sciences. But the study of a determinable kind is not autonomous with respect to its determinates – e.g., one must study red, blue, and yellow to study color (Funkhouser 2014: 113). Yet it may be that the whole point of Yablo’s rejection of a conceptual account of determination is that we sometimes must reject what seems intuitively or a priori correct. If mental properties are determined by the physical properties that realize them, then these mental and physical properties do belong to the same family. It is just that we needed to do empirical investigation to discover this 120

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fact. This result is somewhat paradoxical given that Yablo started with the core commitments of a non-reductive physicalist – supervenience plus multiple realizability. Douglas Ehring (1996) provided the first substantial counter to Yablo’s assimilation of realization to determination. Ehring argued that, unlike determinates, same-level physical realizations do not exclude one another. Nor does the ordering of physical realizations properly correspond to the ordering of the (supposedly) determinable mental property – e.g., radically different physical realizations of pain might not differ much as pains. (These points should generalize beyond the mental-physical to other kinds of realization.) Perhaps even more damaging to the determination thesis, the idea of multiple realizability allows (if not demands) that a maximally determinate mental property – a very specific kind of pain, say – can have multiple realizations. By the thesis that realization is determination, these would be determinates of that very specific kind of pain. But this contradicts the assumption that this is a maximally determinate pain kind. The main problem that emerges is that distinct physical realizations need not differ qua mental kind – or the physical differences at least do not properly correspond to mental differences – as is required of determinates under a common determinable. I have elaborated on Ehring’s insights and put forth a model of determination aimed at capturing the notion of specification “in a respect” (Funkhouser 2006, 2014). Again, Ehring’s main point was that different determinates always characterize their determinables in the same respect – e.g., the different determinates of color all differ with respect to color. But the different realizations of a mental kind do not necessarily differ with respect to their mentality! This is implicit in Hilary Putnam’s (1967) classic formulation of the multiple realizability thesis: radically different animals (mammals, reptiles, and mollusca) are said to instantiate the same pain. And this is a consequence of functionalism more generally: realization differences do not necessarily make for mental differences. But different determinates always are different in respect of that determinable. To represent this fact, I argued that every maximal determinable constitutes a property space structured by determination dimensions. Determination dimensions are supposed to be respects in which a kind can vary and be specified qua that maximally determinable kind. For example, there is a determination dimension for mass. Picture this as a line, and every instantiation of mass corresponds to a unique point on this line. Mass has a linear property space, so to speak. Segments of this line pick out determinate (and determinable!) mass properties (i.e., ranges of mass); points on the line pick out maximal determinates of mass. Other determinable kinds are multidimensional in the sense that they can vary along more than one dimension. Color can be used as a toy example with three supposed determination dimensions: hue, brightness, and saturation (Funkhouser 2014). These dimensions generate a three-dimensional property space with maximally determinate color properties mapped to points in this space. These points represent specific values for each of the three dimensions of variation. The idea is that the different families of properties – say, the psychological and the neuroscientific – have their own property spaces. If property instances map on to unique points in a property space, then properties from distinct families cannot share an instance – that kind of identity is thwarted. But the distinctness of these property spaces is not always a conceptual or a priori truth. Rather, the epistemology depends on the kind in question. The kinds posited by the empirical sciences likely have determination dimensions – ways in which they can be specified – that cannot be known a priori. Indeed, we can think of these dimensions as constituting at least part of the essence for these kinds, essences which may be discoverable only by empirical means (as touted by Kripke, Putnam, Yablo, and many 121

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others). But there might be other determinable kinds that have determination dimensions that can be known a priori – think of the properties studied in logic, math, and philosophy. Determination dimensions allow us to distinguish determination from species-genus relations as well as arbitrary disjunct-disjunction relations. Whereas species of the same genus are distinguished by external differentia, determinates are distinguished from one another along internal dimensions that (at least partially) characterize the essence of their determinable kinds. Further, arbitrary disjunctions of properties – like yellow-or-angry – have instances that correspond to distinct property spaces (i.e., color or emotion) structured by differing determination dimensions. But determinates of the same determinable always map on to the same property space (e.g., color). On my model, every token property (e.g., trope) corresponds to a unique point in a property space. In that sense, every token property is maximally determinate. Yet, each property token is also an instance of every other determinate and determinable kind that includes that point in its property space. Suppose that a football jersey is a particular shade of scarlet. The point (i.e., hue, brightness, and saturation value) that property maps to is also contained in the larger segment of the property space that corresponds to red. That is, the space for scarlet is a proper subset of the space for red. It also is contained in the property space of color itself. There are various carvings of the property space of color, and a given instance of color is an instance of all these different kinds – e.g., this instance of scarlet is simultaneously an instance of red and color. Determination is primarily a type-level relation. But properties can be understood as either types or tokens. If we think of properties as types – say, universals or classes – then it is clear that, in that sense, determinable properties are distinct from determinate properties. The class of red things is larger than the class of scarlet things, after all. And for parallel reasons, the universal for redness cannot be one and the same as the universal for scarletness. But properties can also be conceived as tokens, along the lines of trope theory. Again, one could argue that while determinables and determinates are distinct at the type level, the tokens are nevertheless identical – e.g., a particular football jersey’s being red might be identical to its being scarlet. One could also accept the truth of such a statement on a nominalist reading that rejects properties altogether. The identity theory for determinable and determinate instances agrees with Ehring (1996). But others have argued that the world contains only determinate properties. Such claims need clarification given the distinction between properties understood as types or tokens. For example, Carl Gillett and Bradley Rives (2005) argue for the “non-existence of determinables”. Yet what they really argue against is the existence of determinable property instances that are distinct from determinate property instances. Their arguments are perfectly compatible with the existence of determinable property types or with determinable property instances that are identical to determinate property instances (as on the Ehring-Funkhouser model). Wilson (2012) counters Gillett-Rives and makes the case for “fundamental determinables”, where these are real property instances distinct from the corresponding determinate property instances. While denying that determinable property instances are identical to their corresponding determinate instances, she does admit a kind of partial identity. Following Sydney Shoemaker (2001), Wilson claimed that determinables and determinates are defined by their causal powers, with the former having a proper subset of the powers of the latter. Questions remain whether we go with a determination dimension model or a model that defines determinables as having a proper subset of the causal powers of their determinates. Determination dimension models fare well at accounting for the “specification in a 122

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respect” worry. Determination dimensions just are such respects. However, the model does not seem to offer a reductive explanation, at least for simple determinables. In effect, the view holds that determinate masses vary in their mass, determinate temperatures vary in temperature, and so on. One might also deny that determinables – like color – possess unique determination dimensions (Wilson 2009). But the causal powers view has loose ends of its own. Perhaps foremost, what distinguishes causal power overlap that is a genuine case of determination from cases that are not (e.g., mere realization relations)? Nor is it clear that there always is a common power shared by all determinates of a kind. And the causal power account does not extend to non-causal determinables. Finally, neither model seems to explain why the instantiation of one determinate excludes its contrary alternatives (though this might not be a defect). These models do a pretty good job of explaining specification and comparison, but more could be said regarding exclusion. Why does one realization exclude another, or why can’t a substance instantiate distinct property space points from the same property space?

10.6

What’s Next?

While it is hard to anticipate how philosophical tools will be used, I envision four main areas in which future work on the determination relation will likely be applied. Property theory: Most significantly, investigations of the determination relation can yield deep insights into the metaphysics of properties more generally. Of special interest, we should aim to settle the question of whether all properties must be either determinable or determinate. If every property must be determinable or determinate, then determination should tell us quite a bit about the roles that properties essentially play. Determination gets at adjectival characterization, which is central to the work of properties. Indeed, some models of property determination yield quite general conditions for the individuation of properties (Funkhouser 2014). We also should seek explanations for why determinates exclude one another when they do, as that might shed light on the nature of properties – or their functional role – more generally. Ontological reduction and causation (especially mental-physical): Determination will continue to be used in attempts to explain mental-physical relations or to provide a contrast (e.g., with realization). Much more could be said about whether and why determinates and determinables compete (or not) for causal efficacy and as causal explanations, especially if no reduction or identity holds between them. Metaphysical and epistemic indeterminacy: Determinables are, by their nature, unspecified. They have natural applications, then, to all manner of metaphysical and epistemic indeterminacy (Wilson 2013). This includes philosophical treatments of vagueness, the future, modality, and laws of nature. Grand metaphysical projects: Determination will continue to have a place in metaphysical projects that aspire to provide the grounds, fundamental base, or a comprehensive inventory of the world. Many assume that the world is fundamentally determinate, but it may be that no account of the world is complete without countenancing irreducible determinable properties (Wilson 2012). 123

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We have seen that the determination relation is essentially intertwined with some of the most central work performed by properties: specification, comparison, and exclusion. For these reasons, any comprehensive property theory should do justice to the logic and metaphysics of determination.

References Armstrong, D.M. (1978) Universals and Scientific Realism. Cambridge: Cambridge University Press. Ehring, D. (1996) Mental Causation, Determinables and Property Instances. Noûs 30(4): 461–480. Elder, C. (1996) Realism and Determinable Properties. Philosophy and Phenomenological Research 56(1): 149–159. Funkhouser, E. (2006) The Determinable-Determinate Relation. Nous 40(3): 548–569. Funkhouser, E. (2014) The Logical Structure of Kinds. New York: Oxford University Press. Gillett, C. and Rives, B. (2005) The Non-Existence of Determinables: Or, a World of Absolute Determinates as Default Hypothesis. Noûs 39(3): 483–504. Johnson, W.E. (1921) Logic, Part I. Cambridge: Cambridge University Press. MacDonald, C. and MacDonald, G. (1986) Mental Causes and Explanation of Action. Philosophical Quarterly 36(143): 145–158. Millikan, R.G. (1984) Language, Thought, and Other Biological Categories. Cambridge, MA: MIT Press. Prior, A. (1949) Determinables, Determinates, and Determinants. Mind 58(229): 1–20. Putnam, H. (1967) Psychological Predicates. In Capitan, W.H. and Merrill, D.D. (eds.) Art, Mind, and Religion. Pittsburgh, PA: University of Pittsburgh Press: 37–48. Searle, J. (1959) On Determinables and Resemblance. Proceedings of the Aristotelian Society Supp. Vol. 33: 141–158. Shoemaker, S. (2001) Realization and Mental Causation. In Proceedings of the 20th World Congress in Philosophy. Cambridge: Philosophy Documentation Center: 23–33. Wilson, J. (2009) Determination, Realization and Mental Causation. Philosophical Studies 145(1): 149–169. Wilson, J. (2012) Fundamental Determinables. Philosophers’ Imprint 12(4): 1–17. Wilson, J. (2013) A Determinable-Based Account of Metaphysical Indeterminacy. Inquiry 56(4):359–385. Wittgenstein, L. (1929) Some Remarks on Logical Form. Proceedings of the Aristotelian Society Supp. Vol. 9: 162–171. Yablo, S. (1992) Mental Causation. Philosophical Review 101(2): 245–280.

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PART 3

Realism about Universals

11 PLATONIC REALISM Chad Carmichael

Realism about properties is the thesis that there are properties. Platonic realism is the thesis that at least some properties are platonic. So what is a property, and what is it for a property to be platonic?

11.1

What Is a Property?

Properties are also sometimes called qualities, features, attributes, characteristics, states, traits, kinds, sorts, types, or aspects. (These terms can also be used to mark various distinctions between different kinds of property.) Putative examples of properties include: redness circularity philosopherhood the property of having mass the property of being a toaster. Of course, not all realists about properties believe in the existence of every putative example. The most restrictive or sparse form of realism will accept only the most fundamental properties, such as perhaps the property of having mass and similar posits of fundamental physics. By contrast, an abundant form of realism accepts a wider range of properties, including even properties like the property of being a toaster – or, even weirder, the “disjunctive” property of being either a toaster or a black hole. Whether to think of properties sparsely or abundantly is the sort of thing realists disagree with each other about (see Chapter 4, this volume).1 As with many philosophical terms, there is no consensus about how best to define “property”. A traditional idea is that properties are things that are or could be had in common by many particular objects, as for example a red ball, a red tomato, and a red hat all have the property redness in common. But some realists about properties hold that there are properties that have exactly one instance of necessity: the property of being an even prime number, for example. One might have thought that properties can be defined as DOI: 10.4324/9781003246077-15

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those things that have (or could have had) instances – i.e., they are instantiables. But some realists think that there are properties that cannot have instances: the property of being a round square, for example. A somewhat more metaphysically neutral conception of properties is as follows. Let’s say that something is a predicable just in case it is capable of being either true or false of something. Various linguistic items are predicables: for example, the predicate “is a dog” is a predicable that is true of each dog. But predicates are not properties. So what is the difference between a property and a predicate like “is a dog”? The answer is that, unlike a predicate, a property is mind-independent in the sense that it does not depend for its existence or its status as a predicable on the existence or activity of any minds. On this view, then, properties are mind-independent predicables. This account is neutral on a wide range of metaphysical disputes about properties: whether properties are sparse or abundant, whether they can exist uninstantiated, whether they can be uninstantiable, whether they stand in causal relations, whether they are located in the physical world, and so on.2 In any case, irrespective of what conclusion one comes to on these and other controversies, one will presumably agree that if there were mindindependent predicables, they would be pretty good candidates for being properties.

11.2 What Is a Platonic Property? Some realists about properties hold that all properties are located in their instances. On this view, if there is such a property as blueness, then blueness itself is located where each blue object is located. Call the view that properties are located in their instances immanent realism.3 One thing that it could mean to say that a property is platonic is that it is not immanent but transcendent: it is incapable of spatial location. In another terminology, to say that properties are platonic in this sense is to say that they are abstract objects. This is a form of platonic realism on any reasonable understanding. But I want to suggest that there are also weaker forms of platonic realism. For example, one might claim that some properties exist uninstantiated, and that they are therefore unlocated and rather abundant. But one might also think that all properties with instances are located in their instances, and that uninstantiated properties are all such that they could have had an instance, and would have been located in their instances if they had any. Such a position does not embrace the idea that there are properties that could not have had a location. Is this a form of platonic realism? Yes, at least in the sense that this view embraces properties without spatial locations (for more about this view, see Section 11.12 and Carmichael 2022). In short, then, I will understand platonic properties as properties that (perhaps contingently) lack locations. And platonic realism is therefore the idea that there are mind-independent predicables that lack locations. I now turn to some arguments for platonic realism.

11.3 The “One over Many” Argument We often make claims, in both ordinary and scientific contexts, which appear to entail that properties exist. If any of these claims is true, and the apparent entailment is genuine, then properties exist. A common sort of argument for realism is that, in one or another of these cases, opponents of properties have no plausible analysis that renders the relevant claim false or the entailment merely apparent. 128

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Perhaps the most well-known argument like this is the so-called “one over many” argument. Different versions of the argument focus on slightly different claims related to having features in common; here is a sampling: 1 2 3 4 5 6

a and b “partake of a common nature” (Russell 1912: 143). a and b “have something in common” (Quine 1948: 29). a and b are “of the same type” (Armstrong 1978a: xiii). a and b “have the same property, F-ness” (Devitt 1980: 434). a and b “have some common property” (Lewis 1983: 355). “Spiders share some of the anatomical features of insects” (van Inwagen 2004: 114).

Claims 4 and 6 at least apparently have the existence of properties or features as a logical consequence. In the other cases, the entailment is something more tenuous, going by way of the claim that the “type” or “common nature” or “thing in common” must be a property since it is hard to see what else it could be. The argument crucially depends on denying that opponents of properties might devise a paraphrase of these claims which reveals that, despite appearances, they are either false or do not entail the existence of properties (for more on the idea of paraphrases, see Chapter 2, this volume). This argument has been endorsed by proponents of platonic and non-platonic theories of properties alike.4 This is at least initially puzzling. Nearly every presentation of the argument appeals to cases that involve properties that only abundant realists accept: the property of being red, for example. If the argument is successful, then, it appears to establish a relatively abundant form of realism that typically appeals to platonists.5 One reason for this appeal is that, once we opt for a relatively abundant view of properties, we are faced with the question of how abundant properties are, and the natural answers entail that they are abundant enough to include some platonic properties. For the argument, if successful, establishes the existence of properties that are, or are equivalent to, disjunctive properties. For example, suppose that the property of being jade is the disjunctive property of being either F or G. Then if all the samples of jade that were F but not G were eliminated, but there were still samples of jade that were G, then the property of being jade, along with its two disjuncts F and G, would still exist. In that case, though, the property F would exist uninstantiated. So the argument tends to favor a platonic view. In response to the “one over many” argument, David Lewis (1983) notes that it requires a (perhaps unmotivated) rejection of the idea of primitive resemblance, since primitive resemblance seems to afford opponents of properties a paraphrase of at least claims 1–3 and 5. In addition, Michael Devitt (1980), following W.V. Quine (1948), argues that claim 4 can be paraphrased as “a and b are both F”, which he analyzes, in turn, as equivalent to “a is F and b is F”. Both Quine and Devitt argue that the latter claim does not require realism (on this exchange, see Chapter 15, this volume). Claim 6 is perhaps more challenging, as it seems to require a more specific relationship of anatomical resemblance, which is apparently equivalent to resemblance by virtue of sharing anatomical properties. The opponents of properties do not want a distinct primitive for every respect in which things can resemble one another; what then should they say about anatomical resemblance and similar notions that involve similarity-in-a-specific-respect? Lewis (1983: 347–348) proposes that the relevant notion of primitive resemblance is variably polyadic and contrastive, so that we say “x1, x2, … resemble one another and do not likewise resemble y1, y2, …”. Using this predicate, the thought goes, we can uniquely 129

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capture the anatomical resemblance of spiders and insects, without invoking properties, by means of the contrast between the manner in which they resemble one another and the manner in which they do not resemble everything else. Another approach, due to Gonzalo Rodriguez-Pereyra (2002: ch. 4), has it that primitive resemblance is a dyadic relation (rather than a variably polyadic one), and that it comes in degrees. Then the idea is that, for each anatomical feature the realist believes in, there is a set of things S = {x1, x2, … } such that each pair of the xs resemble each other to a specific degree. The opponent of properties then claims that this precisely captures the fact that the xs resemble each other in the specific respect for which the realist accounts by posting a shared anatomical feature. Claim 6 above would then be understood to mean: each (actual) spiderinsect pair is such that its members are both members of some such sets.

11.4

Lewis’s Argument

Lewis (1983: 348–351) gives a similar argument for platonic realism, but one which appeals to a broader range of statements apparently about properties. Lewis claims that properties are needed in order “to provide an adequate supply of semantic values for linguistic expressions” (1983: 348). The idea here is that there are a wide variety of plausibly true and certainly meaningful sentences whose semantic analysis seems to require properties. Lewis cites these examples (among others): Red resembles orange more than it resembles blue Red is a colour Redness is a sign of ripeness Grueness does not make for resemblance among all its instances He has the same virtues as his father. Lewis also claims that we need properties for the purpose of “characterizing the content of our intentional attitudes” (1983: 351). Only abundant properties can fill these roles, Lewis thinks, since the relevant semantic values, and the content of our intentional attitudes, are so numerous. Plausibly, some such abundant properties must be platonic in our sense, since some of them will end up being uninstantiated. Lewis’s argument and the “one over many” argument make a prima facie case for platonic realism. Given the lack of consensus about how the opponent of properties should proceed, the elegance and naturalness of a realist position, and the failure of standard objections to abundant platonic realism (see below), these arguments have won some converts to platonic realism. Still, these arguments have an open-ended character, in effect placing a bet that their opponents cannot find a plausible account of the above claims and of mental content.6 But it is hard to be confident about what clever opponents of realism might devise in the future. Arguably, then, these standard arguments are less convincing than one might have hoped.

11.5

A Modal Argument for Realism

In my view (Carmichael 2010), a more convincing argument derives platonic realism from considerations involving necessary truth. The first step of this argument proceeds from the idea that there are necessary truths, and that every necessary truth is a truth that would 130

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have been true in any possible situation. Given that something cannot be true without existing, it follows that actual necessary truths had to exist.7 The second step of the argument says that these necessarily existing truths are structured entities with logical form, and specifically that they have predicable constituents that they could not exist without. Thus, there are necessarily existing predicables. The third step is the claim that necessary existence entails mind-independence.8 From this, it follows that there are mindindependent predicables, which is my favored definition of a property, as discussed earlier. Finally, if one can argue that these properties are platonic in one of the senses I identified, one can conclude that platonic realism is true. This style of argument faces a number of challenges; let’s look at a few of them.

11.6

“True At”

One common challenge says that a necessary truth is not a truth that would have been true in any possible situation. Instead, the idea is that a necessary truth is a truth that is true at every possible world, where “true at” is understood in such a way that a necessary truth can sometimes be true at a world even though that truth does not exist in that world. The thought here is that a truth can describe a possible world “from the outside”, so to speak, and if it correctly describes every world, then it is necessary without existing necessarily, contrary to the modal argument. This view faces a problem involving iterated modality. Suppose that it is necessary that everything is self-identical. On the present view, this is necessarily equivalent to the claim that it is true at every possible world that everything is self-identical. But of course it is also necessary that it is necessary that everything is self-identical. So, on the present view, it follows (by substitution of necessarily equivalents) that it is necessary that it is true at every possible world that everything is self-identical. It is impossible for something to be true at every possible world without existing. (A necessary truth can be true at every world without existing in every world, on the present view, but it cannot be true at every world without existing simpliciter.) Thus, it follows that the necessary truth that everything is self-identical exists necessarily. One could respond by denying that there are any iterated modal truths such as “it is necessary that it is necessary that everything is self-identical”. But this is pretty implausible. One could also deny that “it is necessary that everything is self-identical” is necessarily equivalent to “it is true at every world that everything is self-identical”. In that case, either there could be a necessary truth that is not true at every world, or there could be something that is true at every world without being a necessary truth. Neither claim is very plausible. But more importantly, this view is dialectically out of line: the interest we have in truth at every world is precisely undermined by its alleged non-equivalence with necessity. For, given its non-equivalence with necessity, proponents of this reply can no longer claim to provide an alternative to the idea that necessary truths just are truths that would have been true in any possible situation.9

11.7 Second-Order Quantification Here is a different sort of objection having to do with second-order quantifiers.10 Secondorder quantification is quantification into non-nominal (e.g., predicate or sentential) position, as in: 131

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∃F Jack is F ∃p it is true that p. On the view I have in mind, one should not interpret these claims to mean, respectively, There is a property F such that Jack has F There is a proposition p such that p is true. For, so interpreted, the higher-order quantifiers are really just first-order quantifiers, which effectively (at least in a semantic sense) quantify into nominal position and range over a restricted domain. The idea that recent enthusiasts of the second-order framework have in mind is more radical than this: the thought is that higher-order quantifiers are sui generis and cannot be reduced to first-order quantification in this way.11 This sort of view can be used to object to the modal argument for realism. The idea is that the starting point of the argument – that there are necessary truths – is ambiguous. On the first-order reading, it means: ∃x □ x is true. But, on the second-order reading, it means: ∃p □ it is true that p. The objection has it that the first reading is false, while the second reading is true but does not serve our argument. For, the thought goes, on the second reading, to get the necessary existence of a proposition, we would require a premise which says something like: ∀p □ (it is true that p → p exists). However, this is ill-formed, since “p” is a higher-order variable and therefore cannot take nominal position, as it does in the consequent of the embedded conditional. So the modal argument is blocked. My response: if primitive higher-order quantification makes sense, then so does higherorder identity. And, if we have an expression for higher-order identity, say “≡”, then we can express the existence of a given necessary truth – say the proposition that everything is self-identical – using a second-order quantifier: ∃p (p ≡ everything is self-identical). Now we can formulate the needed premise like this: □ (it is true that everything is self-identical → ∃p (p ≡ everything is self-identical)). And now, given that

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□ it is true that everything is self-identical we may derive: □ ∃p (p ≡ everything is self-identical). Thus we end up with my conclusion: that necessary truths necessarily exist. The argument can then go through as before. One could try to claim that there is no intelligible notion of higher-order identity. But this is not particularly plausible. Primitive higher-order quantification is about as intelligible as primitive higher-order identity. And enthusiasts of primitive higher-order quantification are already committed to being open-minded about our ability to understand higher-order ideology. One could also reply that “∃p (p ≡ ___)” does not express a notion of existence that is of interest in ontology. But ontology is at least in part about what there is. So, if “there is” can express second-order quantification, then ontology is (in part) about what there is in the second-order sense. One might try to claim that “there is” does not in any sense express secondorder quantification, but this is inconsistent with the present objection, which maintains that “there are necessary truths” can be given a second-order reading. One could reformulate the objection, claiming instead that there really are no necessary truths, but that this is not as absurd as it sounds because “∃p □ it is true that p” – a claim that is uninterpretable in natural language – is true. This is an unpersuasive response: if a claim is uninterpretable in natural language, then its truth is ill-suited to explain our attraction to the thesis that there are necessary truths. Moreover, if the modal argument shows that platonic realism is as plausible as the claim that there are necessary truths, then it is a successful argument.

11.8

Necessary Truths and Logical Form

The modal argument says that necessarily existing truths have logical form. Why think this? Let’s call necessarily existing truths “propositions”. There certainly are such things as logical truths: for example, it is a truth of logic that everything is self-identical. If this truth of logic is not a proposition, then we must have in mind that the sentence “Everything is self-identical” is a truth of logic. On this view, only sentences have logical form. Call this “the sentence view”. Here are three problems with the sentence view: 1 On the sentence view, which logical truths there are is a contingent matter, since any given sentence of natural language might not have existed. But it does not seem contingent which logical truths there are: it seems necessary, for example, that it is logically true that everything is self-identical. 2 Each truth of logic is true by virtue of (or grounded in) its logical form. On the sentence view, therefore, we can correctly say that the fact that it is true that everything is selfidentical is grounded in the fact that “Everything is self-identical” has logical form f. As Jonathan Schaffer (2016: 58) observes, grounded facts are typically counterfactually dependent on their grounds. But it would have been true that everything is self-identical even if the sentence had never existed. So counterfactual dependence does not hold in this case, contrary to the sentence view. 133

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3 Sentences do not play the right doxastic and epistemic role to be the sole bearers of logical form: when we deductively justify belief in a logical truth, we logically deduce the content of our belief, which is not a sentence. But to be logically deduced, the content of our belief (a proposition) must have logical form. For these reasons, I conclude that the sentence view is false. Since propositions are the other salient candidates for being the primary bearers of logical truth, they must have logical form after all.

11.9

Does the Modal Argument Establish Platonic Realism?

It seems so. For suppose that there could have been properties that have no actual instances. If the modal argument succeeds, then, had there been such a property F, there would have been a necessarily existing proposition involving F, such as the proposition that either something is F or nothing is F. Since that proposition would have existed necessarily, it would exist in the actual world, and therefore – again assuming the success of the modal argument – the property F would actually exist as well, and would by hypothesis be actually uninstantiated. So to avoid the actual truth of platonic realism, given the success of the modal argument, one would have to deny that there could have been properties that have no actual instances. But this is implausible: plainly there could have been such properties given realism about properties. So the modal argument, if successful, establishes not just realism but platonic realism.

11.10

The Benacerraf-Field Argument

I now briefly turn to some standard arguments against platonic realism. Perhaps the most famous of these is the Benacerraf-Field argument (Benacerraf 1973; Field 1989: 25–30), which is usually posed against abstract objects generally, but which can be directed, in particular, against platonic properties. According to this argument, if there were eternally uninstantiated properties, then it would be hard to see how they could stand in an appropriate explanatory relationship to our beliefs about them. For example, they would seem to be causally isolated. This apparent lack of an appropriate explanatory relationship, according to the argument, defeats our justification for any beliefs we hold about such properties. Let’s focus for a moment on the belief that platonic properties exist. Suppose that one rests this belief on the modal argument above. The premises of that argument are about the nature of necessary truth and logical truth. To undercut this basis for belief in the existence of properties, then, one would have to press the Benacerraf-Field objection against these modal and logical beliefs. Of course it is true that we should try to develop an epistemology of logic and modality, and the details of such an epistemology are a matter of ongoing controversy. But the failure of philosophers to conclusively establish an epistemology of logic and modality is not an adequate reason to embrace skepticism about these beliefs. So, on this understanding of our basis for realism, the Benacerraf-Field objection is an interesting philosophical problem to be solved rather than a serious objection to realism. On the other hand, what if one rests belief in realism on the “one over many” argument? Then the situation is not so clear. For the premises in that case are, according to the realists themselves, quantifications over properties. For example, the premise that “a and b have 134

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something in common” is, according to realism, a simple existential generalization over properties. And so, according to the Benacerraf-Field objection, there are serious concerns, specific to realism itself and not generalizable to a wider class of modal and logical beliefs, about our justification for such beliefs. And the same remarks apply to Lewis’s argument for realism. However, those who rest their realism on these arguments can still take advantage of the response to the Benacerraf-Field argument that I discuss in Section 11.12.

11.11

Parsimony Arguments

Another standard argument against platonic realism appeals to considerations of parsimony. As David Armstrong (1978a: 130) puts the point: A spatiotemporal realm of particulars certainly exists (it includes our bodies). Whether anything else exists is controversial. If any entities outside this realm are postulated, but it is stipulated further that they have no manner of causal action upon the particulars in this realm, then there is no compelling reason to postulate them. Occam’s razor then enjoins us not to postulate them. If this is right, then parsimony may provide a reason to reject platonism in favor of the sort of “immanent realism” that Armstrong favors.12 Of course, something has to do the work of properties; we do not want the simplest theory simpliciter, but rather the simplest theory that explains all that needs explaining. As I argued in Sections 11.3 and 11.4, the “one over many” argument and Lewis’s argument, if successful, require a relatively abundant conception of properties, including platonic properties, to account for the truth (or meaningfulness) of a number of ordinary claims that are apparently about properties. Furthermore, as we saw above, if the modal argument is correct, theories that reject platonic realism fail to account for the modal facts, and especially the facts involving alien properties. So, if these arguments for realism are correct, then parsimony does not favor a theory like Armstrong’s, because such theories are too sparse to explain all that needs explaining.

11.12

Weak Platonism

In addition to the above replies to these standard objections to platonic realism, I want to propose that what I call weak platonism provides an additional defense against these objections. By “weak platonism” I have in mind a theory with the following three tenets, each of which it accepts as necessary: (Platonism) There are properties without locations (specifically: uninstantiated ones) (Instantiability) Each property could have had an instance (Immanence) Each instantiated property is located in each of its instances. A theory that incorporates these three tenets is by my definition still a version of platonic realism because it accepts properties that have no location. But it helps to alleviate the epistemic and parsimony worries by appealing to Instantiability and Immanence. Let me briefly explain.13 First the parsimony worry. Lewis (1973: 87) distinguishes between quantitative and qualitative parsimony: roughly, the distinction between reducing the number of things 135

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(quantitative) and reducing the kinds of things (qualitative). Lewis argues with some plausibility that qualitative parsimony is what we should care about reducing when we are concerned with parsimony, at least in ontology. The ontology of weak platonism differs from that of traditional immanent realism (e.g., Armstrong’s view) only in that it embraces properties that are unlocated but could have had a location. So the key question is whether the elimination of properties that are contingently unlocated amounts to a gain in qualitative parsimony. Arguably, the answer is no. The contingently unlocated properties are not a natural or essential kind, but rather a gerrymandered grouping of the sort whose elimination is not normally regarded as constituting a gain in qualitative parsimony. For this reason, given weak platonism, I think this sort of parsimony-based worry about platonism is not convincing. Second, the epistemic worry. On weak platonism, each property is such that, had it been instantiated, it would have been located. Thus, a wide range of counterfactual conditionals about the physical world concern these properties. For example: if there is no object of mass M, then we would nevertheless know that, had there been an object of mass M in location L, the property of being mass M would have been located in L. If we suppose that there is no epistemic problem about our knowledge counterfactuals about the physical world, then this rescues a wide range of beliefs about uninstantiated properties – in addition to the existential beliefs I defended above – from the epistemic worry.14

Notes 1 Armstrong (1978b, 1989) favors a sparse conception. Russell (1912: ch. IX), Bealer (1993), van Inwagen (2004), and Carmichael (2010, 2022) favor an abundant conception. Lewis (1983) suggests a view on which there are sparse property-like things that he calls “universals” (conceived along Armstrong’s lines) as well as abundant sets of possibilia, which he calls “properties”. 2 Lewis (1983, 1986: sec. 1.5) identifies properties with sets of possibilia. Is his theory consistent with my view that properties are predicables? I think so. Lewis’s theory entails that sets can have instances and properties can have members. If Lewis is willing to say these things, I think he should also be willing to say that sets can be predicables. 3 Sometimes immanent realists also hold that properties are parts or constituents of their instances, and that each property is wholly located where each instance is located, so that properties with multiple instances are multiply located. 4 Russell (1912: ch. IX) and van Inwagen (2004) are platonists who endorse the argument. Armstrong (1978a) is a non-platonist who endorses the argument. 5 And, in particular, an abundant realism on which properties are more abundant than typical nonplatonic views such as Armstrong’s would have it. Armstrong might try to paraphrase “all the red things have something in common” by “all the red things either have F or G or H or …”, where F, G, and H are sparse properties which entail that their bearers are red. However, for this to be an adequate paraphrase, its truth must explain the (at least) apparent truth of “all the red things have something in common”. But, in that case, one would expect “all the toasters and black holes have something in common” to be apparently true, since it could be given a similar “disjunctive” paraphrase. 6 Lewis makes an even more specific prediction: any such account will be “piecemeal” in a way that “threatens systematic semantics” ( 1983: 350). 7 Sentences exist contingently and can be necessary truths. But they are only necessary in a secondary sense, by virtue of expressing truths that are necessary in the primary sense, which is the sense under discussion in the text. 8 One might reply to this step by saying that necessarily existing predicables are mind-dependent because they are concepts in the mind of a necessarily existing God. See Plantinga (1982).

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Platonic Realism 9 Speaks (2012) responds that “p is necessarily true” is necessarily equivalent to “every world instantiates Cp”, where Cp is the “truth condition” associated with p. Since Speaks thinks of truth conditions as properties, this idea secures contingently existing propositions at the cost of admitting my desired conclusion that there are (necessarily existing) properties. 10 For discussions of this idea, see Jones (2018), Cameron (2019), and Liggins (2021). 11 They are also not supposed to be substitutional quantifiers, since “∃p it is true that p” would have been true even if there had been no languages. 12 Schaffer (2015) argues that parsimony has to do with what is fundamental. If he is right, then Carmichael (2016), which defends a fundamental ontology consisting only of properties, actually favors platonic realism on grounds of parsimony. 13 See my ( 2022) for further details. 14 Thanks to Anthony Fisher, Dan Korman, John Keller, Anna-Sofia Maurin, and participants of the Online Properties Workshop in May 2022.

References Armstrong, D.M. (1978a) Universals and Scientific Realism I: Nominalism and Realism. Cambridge: Cambridge University Press. Armstrong, D.M. (1978b) Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Bealer, G. (1993) Universals. Journal of Philosophy 60(1): 5–32. Benacerraf, P. (1973) Mathematical Truth. Journal of Philosophy 70(19): 661–679. Cameron, R. (2019) Truthmaking, Second-Order Quantification, and Ontological Commitment. Analytic Philosophy 60(4): 336–360. Carmichael, C. (2010) Universals. Philosophical Studies 150(3): 373–389. Carmichael, C. (2016) Deep Platonism. Philosophy and Phenomenological Research 92(2): 307–328. Carmichael, C. (2022) Immanence in Abundance. Erkenntnis, doi: 10.1007/s10670-022-00594-y. Devitt, M. (1980) “Ostrich Nominalism” or “Mirage Realism”? Pacific Philosophical Quarterly 61(4): 433–439. Field, H. (1989) Realism, Mathematics, and Modality. Oxford: Blackwell. Jones, N. (2018) Nominalist Realism. Noûs 52(4): 808–835. Lewis, D. (1973) Counterfactuals. Cambridge, MA: Harvard University Press. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Blackwell. Liggins, D. (2021) Should a Higher-Order Metaphysician Believe in Properties? Synthese 199(3-4): 10017–10037. Plantinga, A. (1982) How to be an Anti-Realist. Proceedings and Addresses of the American Philosophical Association 56(1): 47–70. Rodriguez-Pereyra, G. (2002) Resemblance Nominalism. Oxford: Oxford University Press. Quine, W.V. (1948) On What There Is. The Review of Metaphysics 2(5): 21–38. Russell, B. (1912) The Problems of Philosophy. London: Williams and Norgate. Schaffer, J. (2015) What not to Multiply Without Necessity. Australasian Journal of Philosophy 93(4): 644–664. Schaffer, J. (2016) Grounding in the Image of Causation. Philosophical Studies 173(1): 49–100. Speaks, J. (2012) On Possibly Nonexistent Propositions. Philosophy and Phenomenological Research 85(3): 528–562. van Inwagen, P. (2004) A Theory of Properties. Oxford Studies in Metaphysics 1: 107–138.

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12 IMMANENT REALISM AND STATES OF AFFAIRS Bo R. Meinertsen

12.1

Introduction

This chapter considers a central aspect of the relationship between immanent realism and states of affairs. Immanent realism, or Aristotelian realism, is the view that properties are universals, and that universals are somehow present ‘in’ their instances. In Scholastic terms, they are universalia in rebus. They contrast with transcendent universals, the universals of transcendent or Platonic realism, which ‘transcend’ their instances (universalia ante rem). If, like me, you are attracted to both realism about universals and naturalism (the doctrine that every entity exists in space and/or time), immanent realism is appealing, since it pulls universals out of ‘Plato’s heaven’ and brings them ‘down to earth’. A question worth asking is how they are brought down to earth, as it were. I call it the hosting question. This is a special case of the general issue of what it is for a universal to be instantiated. One traditional answer is that they are hosted by being constituents of ‘bundles of universals’ (see Chapter 14, this volume). In this chapter, I shall explore the answer that they are hosted by being constituents of the states of affairs that result from their instantiations. I shall pay particular attention to two competing specific answers found in David Armstrong’s middle period (late 1970s to late 1990s). For as well as being quite accessible, Armstrong of this period is, by far, the most important contemporary author on both immanent universals and states of affairs. ‘Universal’ is a well-known term. Roughly, a universal is a property or relation construed as a ‘one over many’ which is shared by the things that instantiate it (its instances). The notion of a ‘state of affairs’ is perhaps less familiar. In the most general sense, a state of affairs can be said to exist ‘if and only if a particular […] has a property or, instead, a relation holds between two or more particulars’ (Armstrong 1997: 1).1 For instance, the tomato’s being red and John’s loving Sam are states of affairs. The plan for the chapter is as follows. First, in Section 12.2, I contrast immanent universals with transcendent universals, and consider whether they are concrete or abstract. This is an important matter: if they are abstract, they are not really brought down to earth from Plato’s heaven, and hence the hosting question is a non-issue for them. Next, in Section 12.3, I introduce the notion of states of affairs and the main relevant features of

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them. This leads to distinguishing two kinds of ‘compositional’ states of affairs, which, roughly, correspond to two versions of immanent realism in Armstrong. Then, in Section 12.4, I present and discuss Armstrong’s first version, showing that it lacks a coherent formulation; and finally, in Section 12.5, I sketch his second version and suggest that (an extension of) it might answer the hosting question.

12.2 Abstract versus Concrete Universals Traditionally, immanent universals are construed as concrete (spatiotemporal), unlike the abstract (non-spatiotemporal) universals of transcendent or Platonic realism. Due to transcendent universals being abstracta, transcendent realism is committed to a two-realm ontology: the abstract realm of universals and the concrete realm of particulars. A Platonic universal, when instantiated, is abstract even though the particulars instantiating it are concrete. Since Platonic universals are abstracta, they are unacceptable to naturalists, such as Armstrong. But perhaps less obviously, it makes the instantiation of a universal by concrete particulars rather mysterious: it has to bridge a chasm between two profoundly different realms, the world of abstracta and the world of concreta (Vallicella 2016a). This bridging seems mysterious because instantiation is neither internal nor intentional. Cases of internal relations bridging these realms (e.g., being a member of holding between Socrates and his singleton {Socrates}) seem unproblematic. So do cases of intentional relations crossing the chasm (e.g., thinking of holding between Socrates and the number 4). Plato himself spoke of instantiation involving the particulars as ‘copies’ of the Forms. This rather obscure ‘copy theory’ of instantiation was probably a result of his idiosyncratic view that Forms characterize themselves (Red is red, Large is large, etc.), so that they are able to resemble particulars. In any event, in the tradition of transcendent realism following Plato, it seems no one has provided an illuminating account of instantiation. In short, transcendent realism as traditionally understood faces a bridging problem owing to the abstractness of its universals, which immanent realism does not; conversely, immanent realism has a hosting problem, which transcendent realism is free from. However, at least two influential philosophers maintain that immanent universals are not concrete. If they are right, then immanent realism does not really bring universals down to earth from Plato’s heaven, and its universals do not encounter the hosting question. (Of course, we can still ask the corresponding general question of what it is for such universals to be instantiated.) One proponent of immanent universals, E. J. Lowe (2006), argues that they are not concrete, and eo ipso he is committed to their being abstract. He does not, however, seem to acknowledge this commitment. In contrast, another proponent of immanent universals, Reinhardt Grossmann (1983, 1992), is explicit and unabashed that they are abstract. Grossmann rejects concrete universals as part of a general criticism of naturalism (1992: 12–13, 22–29), whereas Lowe’s discussion is relevant to our purposes in this chapter. Lowe’s argument focuses on an issue for immanent realism that arises when reflecting on its notion of ‘instance’. The instance of a universal is the particular that instantiates it. As mentioned, an immanent universal exists ‘in’ its instances. This intimacy between an immanent universal and its particular instances is encapsulated in the so-called ‘principle of instantiation’. Here is a formulation of this principle: (PI) For each n-adic universal U, there exist at least n particulars such that they are U. (Armstrong 1978: 137)

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An immanent universal is nothing without its instances, so to speak. By itself, however, this principle tells us nothing about how an immanent universal is ‘in’ its instances. According to the concretist approach, on which concrete immanent universals are hosted by concrete states of affairs, the way in which a universal is ‘in’ its instances is rather literal. Roughly, a universal is ‘in’ its instances both in the sense that (i) it is a constituent of them and in the sense that (ii) it is co-located with them. Now, the first sense can only really be presented when the notion of a state of affairs has been explained, which is not until the following section. But the second sense may be introduced at this point. An immanent universal is co-located with its instances, as it is wholly present ‘in’ each of them. For example, the redness of our tomato is co-located with each red tomato (of the same shade of red), and indeed with every other particular that is red (of that shade), since all of the universal is ‘in’ each instance. The description ‘wholly present’ is important: it is not the case that a part of the universal is in each of its instances, the way a scattered particular is, say, a sail covering a group of people, to use Plato’s example from the Parmenides (131e–c). Such a universal (scattered particular) only has parts, each of which is co-located with a part of the instance: one part of it (part of the sail) is where one particular (person) is; another part of it is where another particular (person) is; and so on. An immanent universal is wholly located in different places (if its instances are). This distinctive locatedness of immanent universals is known as ‘multiple location’. This is a highly controversial issue, and understandably so: multiple location is radically different from the locatedness of particulars familiar to us pre-theoretically. It is precisely multiple location that Lowe (2006: 99) singles out in his argument against concrete universals. Lowe objects that, since the universal is wholly located in each of its instances, it appears that the location of any one of its instances must coincide spatially with the universal. But if so, two instances, say, two flowers instantiating the same shade of red, must be co-located, despite ex hypothesi being in different locations. Now, proponents of concrete universals have responded to this objection that it smacks of being a category mistake, due to its applying the exact same principles that hold for locatedness of particulars to universals, two entirely different categories of entity (Armstrong 1988; Meinertsen 2018: 123–124). But Lowe is unconvinced by this type of reply: [I]t needs to be explained to us how they can behave so differently, despite genuinely being located in space and time. And I have never yet come across a satisfactory explanation of this purported fact. As it stands, then, it seems to be nothing more than a piece of unsupported dogma. (Lowe 2006: 99) For this reason (and another, which we need not go into), Lowe formulates and endorses what he calls a ‘weak’ notion of immanence, the ‘strong’ one in his view being the one requiring multiple location. This weak notion is simply adherence to the principle of instantiation. The resultant view, Lowe says, implies that a universal instantiated by concrete particulars ‘must have particular instances which exist “in” space and time, but it doesn’t imply that the universal itself must literally exist “in” space and time’ (2006: 99). In this way, Lowe ‘softens’ immanent realism, ridding it of the difficulties of multiple location. However, due to its commitment to abstracta, Lowe’s (and Grossmann’s) position is unpalatable to metaphysicians of a naturalist bent. Thus, naturalists had better stick to immanence in the strong sense and deal with the location consequences, as it were 140

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(for discussion of the location of properties, see Chapter 13, this volume). Moreover, even if naturalism is false and we were to accept abstract immanent universals, we would still need to address the bridging challenge, just like proponents of transcendent universals – a fact which neither Lowe nor Grossmann seem to acknowledge.

12.3 States of Affairs As it stands, the above definition of a state of affairs as a particular’s having a property or two or more particulars’ standing in a relation is so underspecified that it compatible with a wide variety of usages of the term ‘state of affairs’. Fortunately, they fall into two broad categories. Within the first category, the word ‘state of affairs’ is used for abstract (nonconcrete), proposition-like states of affairs, sometimes called ‘propositional facts’ (see Betti 2015: chs. 4–6). On some theories, e.g., Chisholm’s (1970; 1971), these entities are barely distinguishable from propositions; on other theories, notably Reinach’s (1982[1911]), they are more clearly distinguished from propositions, but still abstract (see Meinertsen 2022). Within the second category, the word ‘state of affairs’ expresses the idea of a compositional state of affairs. These entities are complexes consisting of particulars and properties or relations, and perhaps something that binds them together. States of affairs in this sense are mostly construed as concrete and worldly entities, as much part of the terrestrial world as tables and chairs and plants and animals. For example, the states of affairs of the tomato’s being red or John’s being next to Sam are concrete entities alongside their constituent particulars (the tomato, John and Sam). Russell (1972[1918]), Wittgenstein (1961[1921]), Bergmann (1967) and Armstrong (1997) are classic advocates of this conception of states of affairs. Let us call this the ‘concretist’ view of compositional states of affairs. Alternatively, proponents of compositional states of affairs may construe them in an ‘abstractist’ fashion. This is a rather rare view: to my knowledge, the only (well-known) philosopher to defend it is Grossmann (1983; 1992). As mentioned, Grossmann also considers immanent universals to be abstract, so his states of affairs (which he calls ‘facts’) involving concrete particulars like our tomato are ontologically hybrid complexes. While Grossmann’s states of affairs are abstract, just like propositional states of affairs, they can be the ‘hosts’ of abstract immanent universals, precisely because they are compositional: they can have them as constituents. In any case, in effect, this is Grossmann’s answer to the general question of what it is for an immanent universal to be instantiated. Unfortunately for Grossmann, abstract compositional states of affairs do not survive William Vallicella’s devastating objection to them (Vallicella 2016a: 127–128). Concrete compositional states of affairs (henceforth just ‘states of affairs’) are nonmereological complexes, in two separate senses. First, unlike the parts of a mereological sum, the constituents of a state of affairs can co-exist without the state of affairs existing. To illustrate, consider the constituents of a’s being F: a might instantiate another universal and F might be instantiated elsewhere. Second, the same constituents can make up distinct states of affairs. For example, if R is a non-symmetrical relation, a’s having R to b and b’s having R to a are distinct states of affairs. That is, the arrangement of the constituents of a states of affairs is important. Specifically, it is vital to the identity conditions of states of affairs: (SI) For all states of affairs s, s1 = s2 if and only if s1 and s2 have the same constituents and these constituents are arranged in the same way.2

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Being non-mereological complexes, states of affairs face what has been called ‘the problem of complexity’: the problem of how the many parts or constituents of a complex give rise to one unified entity, the complex or whole (Mertz 1996: 16). In the context of states of affairs ontology, this problem is often known as ‘the problem of unity’ or ‘the unity problem’. Roughly, it is the question of what is necessary and sufficient for some particulars and universals to make up a certain state of affairs, as opposed to not making one up.3 An intuitive way of answering this question is to posit as a constituent of a state of affairs a unifying relation that ties together its components, i.e., links together the particular and universal. We might call such a conception of states of affairs relationalism. On my own view, which I call ‘relational internalism’, this relation is internal or intrinsic to the state of affairs in the sense of being a constituent of it. This relation contrasts with a nonconstituent unifier, which is external or extrinsic to the state of affairs; for example, (a relation to) God in the state of affairs ontology of Vallicella (2002: ch. 7). Well-known contemporary examples of relational internalism are the state of affairs ontology of Bergmann (1967) and Grossmann (1983; 1992), where the unifying relation is known as ‘the fundamental tie’ and ‘nexus of exemplification’, respectively. Which relation might do the unifying on relational internalism? Perhaps, it is the relation of instantiation, i.e., the relation that holds between a particular and the universal it instantiates. However, this view – and indeed any view that construes instantiation as a relation – is associated with one or more issues known as ‘the problem of instantiation’. Of these, the most well-known is that the view leads to Bradley’s regress. One of many versions of this regress is this: if instantiation, R1, relates the particular and universal in a state of affairs, it surely must be related to them by a further relation, R2. This new relation in turn seems to require a third relation, R3, to relate it to its relata, and so on to infinity. This regress is widely held to be vicious, and hence the view that the unifying link in a state of affairs is the instantiation relation is often held to be a non-starter. In contrast, on non-relationalism, states of affairs are not unified by a relation, neither inside nor outside them. Initially, in his 1978 book, Armstrong defends a version of immanent realism which he calls ‘non-relational realism’, on which a particular’s instantiation of a universal does not involve a relation between the particular and universal. On what he calls ‘relational realism’, by contrast, this relationship does involve a relation. In the present context, I shall take it that these versions of realism pair up with the two approaches to the unity of states of affairs in a straightforward way (and that the terms for them can be used interchangeably). That is, I shall assume that (NR) Non-relational realism is true if and only if non-relationalism about states of affairs is true. Conversely, I shall assume that (RR) Relational realism is true if and only if relationalism about states of affairs is true. Given the outcome of the two preceding sections, then, we can now specify the hosting question as this: are immanent universals constituents of relationalist or non-relationalist states of affairs? Equivalently, is relational realism or non-relational realism true? Let us first look at the latter option. 142

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12.4

Non-Relational Realism

Armstrong insists that his version of immanent realism be a non-relational immanent realism (1978: 107). As mentioned, by this he means that the relationship of instantiation between particular and universal should not be construed as a relation. Instead, he contends, it should be conceived as a ‘more intimate union […] than mere relation’ (1978: 107). What could the desired ‘more intimate than mere relation’ relationship between particular and universal be, according to Armstrong?4 In a somewhat witty passage, he adduces Scotus’s formal distinction and his example of ‘the simultaneous unity and distinguishability of the members of the Holy Trinity’ (1978: 110), suggesting that a relatable analogy may be the relationship between size and shape. He claims that: ‘Size and shape are inseparable […] yet they are not related [by an external relation]. At the same time they are distinguishable, and particular size and shape vary independently’ (1978: 110). This is a thought-provoking analogy. Size and shape are indeed analogous to particular and universal in the sense that while the determinable size and shape of an object necessarily go together – no object can have a shape without also having a size (that is, they are ‘inseparable’) – the determinate sizes are independent of the determinate shapes of the object (that is, they ‘vary independently’). Is Armstrong’s analogy reasonable? In general, I think that for an analogy to be reasonable, the analogue, i.e., the analogous thing, should not be too dissimilar to the ‘topic’, i.e., the thing claimed to be analogous to the analogue (see Meinertsen 2015). In this particular case, then, the shape/size relationship should not be too dissimilar to the particular/universal relationship. Unfortunately for Armstrong, however, the analogue he puts forward is highly dissimilar to the topic. For the analogue concerns a relationship between entities of the same ontological kind or category (properties), whereas the topic concerns a relationship between entities of different ontological kinds or categories (particulars and universals). So, his analogy is not reasonable. Armstrong’s first attempt at formulating non-relational realism is unconvincing. Not long after this, he embarks on his occasional ‘abstractionist’ tack of describing particulars and universals as ‘abstractions’ from states of affairs, see e.g., (1983: 84). He does not intend with this locution to imply that they are mere mental entities: ‘The factors of particularity and universality are really there in states of affairs’ (1983: 84). Their ontological status is similar to the one in his non-relationalism. Personally, however, I think it sounds odd on a compositional model of states of affairs to have the components be ‘abstractions’ from what they compose. The bricks of a brick wall are surely not ‘abstractions’ from it even if, let us assume, they cannot exist separately from it (perhaps they are ‘magic’ bricks). Indeed, construing particulars and universals as ‘abstractions’ from states of affairs fits in perfectly with an extant non-compositional view of states of affairs (De Rizzo and Schnieder 2023). So, it seems plain that this ‘abstractionist’ assertion is not an alternative formulation of non-relational realism. In any case, as we shall see below (in Section 12.5), Armstrong actually rejects nonrelational realism in his 1989 book. In 1997, however, he reverts to it. He expresses it using the Fregean notion of unsaturatedness, in effect using this concept as an analogy of the particular/universal relationship. He claims that universals are ‘unsaturated’ entities that are ‘saturated’ by particulars: ‘Frege’s copula is the bringing together of a particular or particulars, on the one hand, and “concepts” on the other, by inserting the particulars in

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the unsaturated structure’ (1997: 29). Closely related to this idea of universals as ‘unsaturated’, he construes the universal as a ‘gutted state of affairs’: ‘The universal is a gutted state of affairs; it is everything that is left in the state of affairs after the particular particulars involved in the state of affairs have been abstracted away in thought’ (1997: 28–29). Specifically, he considers universals to be state of affairs types with placeholders (‘blanks’) ready to be ‘saturated’ by particulars. More formally, universals are represented as _’s being F, _’s being G, _’s being F & G, _’s standing in R to _, etc., where the blanks are ‘saturated’ by particulars in states of affairs. This view may be said to correspond to Frege’s conception of his Begriffe as essentially ‘unsaturated’ entities. Armstrong seems to be justified when he says universals on this view are conceived in a ‘Fregean-Aristotelian’ manner as state of affairs types (1997: 202). Unfortunately for Armstrong, however, Fregean unsaturatedness does not provide him with a better analogy than the size/shape relationship. For, once again, the analogue concerns a relationship between entities of the same ontological kind or category (‘blanks’ of general terms being ‘filled’ with singular terms – or something to that effect), while the topic concerns a relationship between entities of different ontological kinds or categories (particulars and universals). Hence, speaking of universals as unsaturated entities saturated by particulars does not provide a coherent formulation of non-relational realism.5

12.5

Relational Realism

In his 1978 book, Armstrong is adamant that attempts to posit a unique relation that links the particular and universal without leading to Bradley’s regress do not succeed. He thinks this is a major point in favour of non-relational realism. In support of his verdict, Armstrong cites, inter alia, Bergmann as a proponent of non-relational realism (1978: 110). (He merely takes issue with Bergmann’s use of the term ‘tie’, which he thinks is indicative of the very relational realism that Bergmann – in Armstrong’s view – sought to distance himself from.) However, as indicated in Section 12.3, I consider Bergmann to be a classic relationalist/relational realist. True, the unifying relation he posits, ‘the fundamental tie’, is very different from ordinary relations; but it is still a relation.6 It is rather ironic that Armstrong’s initial case for non-relational realism in this way misconstrues an important example of relationalism.7 It is, therefore, pleasing to see Armstrong espouse relational realism in 1989. With a nod to Bergmann and Grossmann, he even formulates it by mentioning ‘the fundamental tie’ and ‘nexus’: The state of affairs of a’s being F exists if and only if a instantiates F because these are two ways of talking about the same thing. Similarly, if R is a symmetrical relation, then a’s having R to b is the same thing as a and b instantiating R. […] The fundamental tie, or nexus, in a Universals theory is nothing but the bringing together of particulars and universals in states of affairs.8 (Armstrong 1989: 110) However, Armstrong did not retain this position: in 1997, we again find him propounding non-relational realism. Perhaps, he was once more mainly motivated by Bradleyan reasons. This would be ironic, since he now proposes a response to Bradley’s regress (Armstrong 1997: 118–119). Roughly speaking, he claims that only the first step in the regress requires the postulation of a state of affairs (truthmaker), whereas the following 144

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steps are necessitated by this state of affairs. He compares it to the truth regress (let

be a contingent truth; it is true that

is true; it is true that it is true that

is true, and so on ad infinitum) and therefore considers it to be just as non-vicious. In the truth regress, there is likewise only one truthmaker required (the one for

), with each of the subsequent truths entailed by its existence (1997: 119). Even if the difficulty of Bradley’s regress can be met in this way, relational realism/ relationalism faces the challenge posed by the problem of unity. Armstrong seems not to be cognisant of the latter problem and so his 1989 position is not entirely satisfactory. The problem of Bradley’s regress (how to avoid it) is different from the problem of unity: a regress-blocker is not eo ipso a unifier (Vallicella 2004: 163). Relying on Vallicella (2002; 2004; 2016a) in particular, I have addressed this issue in detail and proposed a relationalist solution to it that takes into account the distinction between Bradley’s regress and the problem of unity (Meinertsen 2018: chs. 9–10). According to this solution, the unifying relation, call it U*, in the state of affairs of a’s being F is related to the particular a and the universal F in virtue of U* being related to a and F as well as itself. It is in the nature of U* to relate itself to the particular and the universal. Hence, the truthmaker for is U*’s standing in U* to F and a. If this solution is correct, then this self-relating fundamental tie not only solves the problem of unity but also avoids Bradley’s regress. Space does not permit us to explore this version of relationalism here in further detail. Nonetheless, it seems plausible that relational realism, at least potentially, answers the hosting question, whereas non-relational realism does not.9

12.6 Conclusion This chapter has considered the question of how immanent universals are hosted by compositional states of affairs. In particular, given the result that immanent universals are concrete, it has explored the view that they are hosted by being constituents of concrete compositional states of affairs. These states of affairs are either relationalist or nonrelationalist. Equivalently, either relational realism or non-relational realism is true. I explained how Armstrong, in his middle period, defends first the latter, then the former, and finally the latter again. Unfortunately for Armstrong, his version of non-relationalism is unconvincing, but his relationalism, or rather, a suitably expanded version of it, may be viable.10

Notes 1 Strictly speaking, a first-order state of affairs. Second-order states of affairs are when first-order states of affairs have properties or stand in relations (e.g., the tomato’s being blighted causing it to be discarded), or when first-order properties and relations have properties or stand in relations (e.g., redness being a colour); and similarly for higher orders. As is common in the literature, this chapter deals only with first-order states of affairs. 2 Identity conditions for states of affairs of this kind are sometimes known as ‘structural’. It is noteworthy that Grossmann, despite not subscribing to states of affairs in the present sense, puts forward what, in effect, amounts to (SI) for the category of entities he calls structures ( 1983: 242). 3 A different approach to the problem of unity, which appears to be Armstrong’s own (see e.g., 1989: 88), sees it as a problem which states of affairs solve, rather than a problem for them. As such it is closely related to the problem of what makes true contingent truths and the positing of states of affairs as truthmakers for such truths. For a discussion of this approach, see Maurin (2015).

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Bo R. Meinertsen 4 Although non-relationalist proponents of states of affairs include a number of philosophers, the clearest formulation of the approach is arguably Armstrong’s own. For other non-relationalist conceptions of states of affairs, see Olson (1987) and Hochberg (1999). 5 For further criticism of the notion of unsaturatedness in connection with particulars and universals, see Simons (1981). 6 More recently, metaphysicians have defended such a relation in novel ways. For example, Betti (2015: 89) maintains that relations are what she calls ‘relata-specific’, where a relation is relataspecific ‘if and only if it is in its nature to relate specific relata’. This thesis is uncontroversial if relations are tropes (see Maurin 2010). But Betti holds that it also makes sense if they are universals (see Vallicella 2016b and O’Connaill 2020 for objections to this claim). 7 Incidentally, later on in his career, Bergmann might have agreed with Armstrong – at any rate, he eventually abandoned the fundamental tie (see Tegtmeier 2018). 8 An alternative interpretation of this passage is that it suggests a view that Armstrong would later formulate as the thesis that there is ‘no relation of instantiation over and above the states of affairs themselves’ and that ‘the instantiation of universals by particulars is just the state of affairs itself’ (1997: 118, 119). For this thesis seems to mirror the claim in the quoted passage that instantiation and state of affairs expressions are ‘two ways of talking about the same thing’. I am not sure what exactly this view amounts to; but, like his ‘abstractionist’ remarks (which were covered in Section 12.4), it appears contrary to a compositional conception of states of affairs. 9 The later Armstrong (2004 and onwards) would have been unenthusiastic about any attempt at developing relational realism. For in his late period, he abandoned both relational and nonrelational realism, proposing instead a completely different view of the relationship between particulars and universals. On his new position, following Leibniz, he considers all apparently contingent predication to be in reality necessary ( Armstrong 2004; 2006). In this new theory, instantiations of universals by particulars are still called ‘states of affairs’. However, its view of predication makes it similar to bundle theory ( Armstrong 2004: 46; see also Brink and Maurin 2005: 18). In fact, I think it is more bundle theory than state of affairs ontology, and hence consider it to fall outside the province of this chapter. 10 For many comments on earlier drafts of this chapter, I am grateful to Nikk Effingham, Anthony Fisher, Anna-Sofia Maurin, Donnchadh O’Connail, Eric Olson, and Erwin Tegtmeier.

References Armstrong, D.M. (1978) Nominalism and Realism (Vol. I of Universals and Scientific Realism). Cambridge: Cambridge University Press. Armstrong, D.M. (1983) What Is a Law of Nature? Cambridge: Cambridge University Press. Armstrong, D.M. (1988) Can a Naturalist Believe in Universals? In Ullmann-Margalit, E. (ed.) Science in Reflection. Dordrecht: Kluwer: 103–115. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Armstrong, D.M. (2004) Truth and Truthmakers. Cambridge: Cambridge University Press. Armstrong, D.M. (2006) Particulars Have Their Properties of Necessity. In Chakrabarti, A. and Strawson, P.F. (eds.) Universals, Concepts and Qualities: New Essays on the Meaning of Predicates. Burlington, VT: Ashgate: 239–248. Bergmann, G. (1967) Realism: A Critique of Brentano and Meinong. Madison, WI: University of Wisconsin Press. Betti, A. (2015) Against Facts. Cambridge, MA: MIT Press. Brink, I. and Maurin, A.-S. (2005) Revisionary Metaphysics: An Interview with D.M. Armstrong. Theoria 71(1): 3–19. Chisholm, R. (1970) Events and Propositions. Noûs 4(1): 15–24. Chisholm, R. (1971) States of Affairs Again. Noûs 5(2): 179–189. De Rizzo, J. and Schnieder, B. (2023) States of Affairs and Fundamentality. Philosophia 51(1): 411–421. Grossmann, R. (1983) The Categorial Structure of the World. Bloomington, IN: Indiana University Press.

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Immanent Realism and States of Affairs Grossmann, R. (1992) The Existence of the World: An Introduction to Ontology. London: Routledge. Hochberg, H. (1999) Complexes and Consciousness. Stockholm: Library of Theoria. Lowe, E.J. (2006) The Four-Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Oxford University Press. Maurin, A.-S. (2010) Trope Theory and the Bradley Regress. Synthese 175(3): 311–326. Maurin, A.-S. (2015) States of Affairs and the Relation Regress. In Galluzo, G. and Loux, M.J. (eds.) The Problem of Universals in Contemporary Philosophy. Cambridge: Cambridge University Press: 195–214. Meinertsen, B.R. (2015). A Method for Evaluation of Arguments from Analogy. Cogency 7(2): 109–123. Meinertsen, B.R. (2018) Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley’s Regress. Singapore: Springer. Meinertsen, B.R. (2022) Reinach and Armstrongian State of Affairs Ontology. Axiomathes 32(3): 401–412. Mertz, D.W. (1996) Moderate Realism and Its Logic. New Haven, CT: Yale University Press. Olson, K.R. (1987) An Essay on Facts. Chicago: University of Chicago Press. O’Connaill, D. (2020) In Defence of Facts. Dialectica 74(1): 95–123. Reinach, A. (1982[1911]) On the Theory of the Negative Judgment. Trans. B. Smith. In Smith, B. (ed.) Parts and Moments: Studies in Logic and Formal Ontology. Munich: Philosophia Verlag: 315–377. Russell, B. (1972[1918]) The Philosophy of Logical Atomism. In Pears, D. (ed.) Russell’s Logical Atomism. London: Fontana/Collins: 31–142. Simons, P. (1981) Unsaturatedness. Grazer Philosophische Studien 14(1): 73–96. Tegtmeier, E. (2018) Bergmann’s Universal Realism: With and Without Fundamental Tie. American Philosophical Quarterly 55(2): 121–129. Vallicella, W.F. (2002) A Paradigm Theory of Existence: Onto-Theology Vindicated. Dordrecht: Kluwer. Vallicella, W.F. (2004). Bradley’s Regress and Relation-Instances. The Modern Schoolman 81(3): 159–183. Vallicella, W.F. (2016a) Facts: An Essay in Aporetics. In Calemi, F.F. (ed.) Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. Berlin: De Gruyter: 105–132. Vallicella, W.F. (2016b). Review of Ariana Betti, Against Facts. Metaphysica 17(2): 229–241. Wittgenstein, L. (1961[1921]) Tractatus Logico-Philosophicus. Trans. D. Pears and B. McGuinness. London: Routledge and Kegan Paul.

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13 LOCATION AND PROPERTIES Nikk Effingham

13.1

Introduction

This chapter: (i) introduces the philosophy of location, before discussing (ii) reasons to locate properties in spacetime and (iii) where in spacetime properties would be located.

13.1.1

Chorology

‘Chorology’ is the study of location. Two chorological relations are relevant: exact location and weak location. Exact Location: Things exactly occupy those regions that are their ‘shadows in substantival space’. For instance, a ball would be exactly located at a ball-shaped region (Parsons 2007: 203). If something has multiple exact locations, we say it is ‘multiply located’. Weak Location: Objects weakly occupy regions that are not entirely free of them. For instance, I am weakly located in Britain and the Milky Way, but not Mongolia or Jupiter. How these relations inter-relate is a good question, though not one which is important here; what is important is clarifying the difference between ‘temporally relativized chorology’ and ‘spatiotemporal chorology’. Temporally relativized chorological relations are three-place relations between an object, a spatial region, and a time. For instance, the Statue of Liberty is weakly located in New York at the present moment whilst, in 1884, it was weakly located in Paris. Spatiotemporal chorological relations are instead two-place relations between an object and a spacetime region. For instance, since I exist at instants in 1995, I am weakly located at the spacetime region we would identify with 1995. Or another example: Our solar system traces a path through spacetime (its ‘worldline’); I would be weakly located at that region.

13.1.2

Tropes and Universals

By ‘properties’ we may mean ‘properties proper’ (e.g., Red, the singular entity instantiated by red things) or ‘property instantiations’ (e.g., the individual instances of Red). For each, 148

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we may: (i) deny their existence; (ii) identify them with entities already in our ontology (e.g., identifying properties proper with classes of instances or classes of tropes, or identifying property instantiations with states of affairs); or (iii) take them to be irreducible. If the entities in question do not exist, clearly there are no issues about whether, nor where, they are located. Similarly, we can side-line discussing cases of (ii) because questions about the location of such entities are immediately settled by your existing view about the location of entities from the salient ontological category. For instance, a class nominalist identifying Red with the class of all red things should say of Red’s location what they say of the location of classes in general (e.g., that they are unlocated, or what have you). (Although see Effingham (2020b: 173–175) for issues that arise when identifying ‘properties proper’ with material objects.) That leaves only case (iii). Assuming ‘properties proper’ are irreducible, i.e., that they are universals, are they located and if so where? Similarly, assuming ‘property instantiations’ are irreducible, i.e., that they are tropes, the same questions arise.

13.2 Are Properties Located in Spacetime? There are two camps concerning the location of universals: Platonists believe they are unlocated whilst ‘immanent realists’ instead believe that they are located. Whereas trope theorists have but one camp, uniformly believing that tropes are concrete entities located in spacetime (Giberman 2014; Küng 1967; Maurin 2002: 17) (although there’s nothing in principle ruling out abstract tropes). This section canvasses two motivations for believing that properties are in spacetime.

13.2.1

Naturalism and Causation

Naturalism is the thesis that everything is located in spacetime; universals/tropes must then be in spacetime (Armstrong 1988; Schaffer 2001: 251). But presumably the naturalistic motivation itself follows from some underlying principle(s) e.g., an epistemic motivation (we can only have epistemic access to spatiotemporal things) or a causal motivation (existing things must be causally active and only spatiotemporal entities are causally active (Armstrong 1988: 104; 1989a: 7–8; Giberman 2022; Oliver 1996: 8–9)). Connected to this causal motive, we might also locate properties because we believe (i) that properties are causal relata and also (ii) that causal relata are necessarily located. However, such a motivation tells more in favour of the location of tropes than universals. If the sharpness of the knife causes me to bleed, trope theorists can interpret that literally, saying that a sharpness trope is the causal relatum (Campbell 1981; 1990). Vis-à-vis universals, this argument becomes rather less persuasive. Unlike tropes, universals are unsuited to be causal relata; rather, it is states of affairs – which have universals as constituents – that are the causal relata e.g., the states of affairs of the knife instantiating Sharpness is what causes me to bleed (Armstrong 1997: 204–206; Oliver 1996: 17). That requires only that states of affairs are located, not the universals themselves; we only get located universals if we further believe: CONSTITUENT LOCATION:

If x is located then the constituents of x are located.

Discussion of whether CONSTITUENT LOCATION is true or not leads naturally into the next motivation to locate properties.

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13.2.2

Properties as Constituents

Many metaphysicians believe that some things, e.g., objects, events, concrete states of affairs etc., are ‘built-up’ out of properties, having them as metaphysical constituents; properties might be their sole constituents (equating to ‘bundle theory’, whereby, say, an electron is a construction out of mass and charge properties) or alongside a bare particular. Given CONSTITUENT LOCATION, properties would then be located. So is CONSTITUENT LOCATION true? Consider two motivations. The first is an intuition that unlocated properties are too ‘insubstantial’ to constitute located things (Keinänen et al. 2016: 79; Kriegel 2021). But I doubt that such ‘intuitions’ can be trusted. I agree that intuitions can play a role in philosophical theory choice, but I would have in mind firm intuitions like sadistic torture being immoral or Harry Potter not actually existing; it’s hard to see how CONSTITUENT LOCATION is on a par with those intuitions. (Who told you CONSTITUENT LOCATION was true? Mister Rogers?) The second is to see the world as fundamentally being nothing but a sea of located properties (or, alternatively, located properties plus substrata); in that case, location may play a crucial role in the bundling of properties.1 The standard view is to say that ‘compresent’ properties constitute further things. ‘Compresence’ may be treated as a primitive, but some have argued that it can be analyzed chorologically, saying that it is bundles of co-located properties that constitute a further thing (Lafrance 2015; O’Leary-Hawthorne and Cover 1998: 214fn 7; Williams 1953: 11–12). In that case, compresence requires located properties. This analysis has problems, though – at least, it does if we assume that co-location is possible. Imagine a ghost passes through a wall. The ghost exactly occupies a spatial region also exactly occupied by a portion of brick. Thus, physical properties (belonging to the wall) are co-located with ethereal properties (belonging to the ghost). Given the chorological analysis of compresence, there is but one object at that region, namely an object that is partially physical and partially ethereal – and that is contrary to our hypothesis that there were two things exactly occupying that region. (And we needn’t rope in the possibility of ghosts to get this problem for it is enough that lumps of clay constitute statues or that bosons can be co-located.)2

13.2.3

Trope Individuation

Consider a red statue with a red-trope, ts, and a red ball with a red-trope, tb. What makes ts and tb distinct? That is: What individuates tropes? If objects are more fundamental than tropes, we can individuate them by their instances, i.e., ts and tb are distinct because different objects instantiate them. But many trope theorists say instead that objects depend upon their tropes, closing off this route. In that case, whilst we could take individuation to be primitive (Campbell 1990; Ehring 2011; Maurin 2002), if we wanted an informative analysis of individuation we might endorse a chorological analysis, individuating perfectly resembling tropes in virtue of their exactly occupying different regions (Campbell 1981; Schaffer 2001).3 That obviously requires located tropes. Whether this chorological analysis works or not quickly leads into a discussion of David Armstrong’s ‘swapping and piling’ problems (Armstrong 1978: 86; 1989b: 131–32). Because other chapters in this handbook discuss those problems in detail (see for example Chapter 19, this volume), I will not discuss the individuation of tropes any further.

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13.2.4

Self-Instantiation

If properties instantiate themselves, they will be located. Were Red red, it must be located for nothing unlocated can be red; if Charge were charged then it must be located, for abstracta are not subject to attractive forces; if Mass of 0.51 MeV instantiated itself then it must be located, for mass belongs only to spatiotemporal things. Nor is it unusual to believe that properties self-exemplify. For instance, it helps play a role in explaining the resemblance of properties. Given red is more similar to orange than blue, we might explain that by saying that Red is red, Orange is orange, and Blue is blue, so of course those resemblances hold. Similarly, trope theorists usually believe tropes resemble; their self-instantiating would explain that resemblance. Self-instantiation is admittedly not the only option for explaining such resemblances. If we accepted either a primitivist approach (whereby there is no explanation for why properties resemble) or an ersatz approach (whereby properties have ‘ersatz’ intrinsic natures that somehow resemble one another, similar to how ersatz possible worlds can stand in differing degrees of closeness to one another) then this would avoid self-instantiation. Having canvassed motivations for why we should locate properties, I now turn to questions about where tropes/universals would be located, were they located.

13.3 The Location of Universals 13.3.1

Multiple Location and Wholly Present

Usually, located universals (‘immanent universals’) are said to be multiply located, being exactly located wherever any instance of the universal is exactly located. For instance, Charge is exactly located at ~1080 different regions, namely each region that a charged object exactly occupies. Because lingo like ‘exact location’ is so recent, few philosophers have explicitly committed to this view, although doubtlessly it’s what most immanent realists previously had in mind (Effingham 2015: 847–48). In the literature, there is talk of universals instead being ‘wholly present’ at each region exactly occupied by an instance. Some philosophers clearly intend ‘wholly present’ to just be a different way of phrasing ‘multiply located’ as I defined it in the previous paragraph. Others instead intend merely a mereological claim: x is wholly present at r iff no part of x can be found anywhere other than r. (Though, since universals are usually thought to be mereologically simple, it’s just trivial that they are ‘wholly present’ wherever they are located.) So be aware of the ambiguous ways that philosophers talk about immanent universals. Even when immanent universals are (implicitly or explicitly) indicated as being multiply located, an ambiguity usually remains: are they multiply located in the spatiotemporal sense or the temporally relativized sense? There are three ways to resolve that ambiguity: • Universals are multiply located in both senses. This would be the view of, say, the perdurantist. Universals would inhere in instantaneous temporal parts, exactly occupying the spacetime regions exactly occupied by those parts; thus, universals are spatiotemporally multiply located. Further, since each such region is an intersection of a spatial region with an instant, universals are also exactly located at multiple spatial regions at those instants; thus, universals are also multiply located in the temporally relativized sense. 151

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• Universals are only multiply located in the temporally relativized sense. They would be similar to time travellers given a Josh Parsons-style view of persistence (whereby persisting objects exactly occupy one spacetime region yet nevertheless lack temporal parts (Parsons 2000)). Parsons-style time travellers could nevertheless be multiply located in the temporally relativized sense e.g., if they were a time traveller who returned to stand next to themselves. On this option of the multiple location of universals, universals would be similar to those time travellers: exactly occupying only one spacetime region but standing in temporally relativized exact location to multiple spatial regions at any one time. • Universals are only spatiotemporally multiply located. In the temporally relativized sense, at any given instant the universal would be exactly located only at the spatial region composed of every spatial region that its instances exactly occupy at that instant. Whilst, in the spatiotemporal sense, the universal would be exactly located at the intersection of that (singular and scattered) spatial region and the relevant instant. Thus – assuming that the universal exists at many instants – it would be spatiotemporally multiply located.

13.3.2

The Possibility of Multiple Location

Does it even make sense to say that something has multiple exact locations? Reinhardt Grossmann (1992: 13) explicitly worries about such multiple location; as do others, thinking this worry favours (singularly located) tropes (Campbell 1981: 477; Garcia 2015: 646; Mertz 1987: 177). The plausibility of multiple location may vary depending upon what type of exact location one has in mind. The possibility of temporally relativized multiple location looks quite plausible. Imagine a time traveller coming back in time and standing next to themselves. It seems natural to describe that as a case of exactly occupying two spatial regions at the same time (Effingham 2020a: 29–34; MacBride 1998: 222–223). But the possibility of spatiotemporal multiple location looks trickier; certainly, there’s no similar example justifying the possibility of spatiotemporal multiple location (though this does not mean that it isn’t possible). That said, consider three arguments that have been explicitly advanced against the possibility of multiple location. The Barker-Dowe problem: Consider O, an object spatiotemporally multiply located at regions r1, r2… …rn. Assume that each such region is temporally unextended (i.e., instantaneous) but that they compose a temporally extended region, R. Since O exactly occupies only temporally unextended regions, O is temporally unextended. Where ‘om’ is whichever object that exactly occupies rm, o1, o2 …on compose a further thing that exactly occupies R. Since R is temporally extended, that composite object is temporally extended. But that composite object appears to be identical to O – after all, every one of o1, o2 …on are identical to one another and so it is natural to think that what they compose is simply identical to O (for the same reason that, strictly speaking, Nikk Effingham composes Nikk Effingham). We now have a contradiction: O is both temporally extended and unextended (Barker and Dowe 2003). This problem has been well-discussed (Barker and Dowe 2005; Beebee and Rush 2003; Calosi 2014; Calosi and Costa 2015; Daniels 2013; Eagle 2016; Garret 2017; Jarrott 2014; McDaniel 2003; Smith 2008). The solution depends upon whether you are attracted to endurantism or perdurantism. 152

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Assume endurantism. Just as chorological relations have temporally relativized and spatiotemporal versions, mereological relations (e.g., composition) do too. Temporally relativized composition is commonplace e.g., my atoms compose me at this moment. But spatiotemporal composition (e.g., temporal parts composing a perduring entity) is alien to the endurantist. Endurantists will be ‘spatiotemporal mereological nihilists’, denying that spatiotemporal composition occurs. Given such a denial, there is no reason to believe o1, o2 …on compose a temporally extended object. Problem solved! (This is Jarrott’s (2014) solution.) Assume perdurantism. Perdurantists believe in spatiotemporal composition and so cannot deny that o1, o2 …on spatiotemporally compose a further thing. Instead, they should deny that O is identical to the thing composed of o1, o2 …on. Whilst a numerically identical entity usually only composes itself, a multiply located (yet numerically identical) entity can compose a distinct thing. Compare to an analogous case of temporally relativized multiple location where a time travelling brick is multiply located at adjoining spatial regions, stacked together to compose a wall. It seems wrong to think that the wall which results is identical to the brick (Effingham and Robson 2007) (although see Daniels 2014 and Eagle 2010: 67–81 for dissent). If the wall is not identical to the brick, then we similarly should deny that o1, o2 …on compose O. Problem solved! The More-Ehring problem: The next worry is that multiply located entities apparently have contradictory shape properties and/or stand in contradictory distance relations. This worry first appears in 1671, in More’s Enchiridion metaphysicum (Pasnau 2011: 341); more recently, it has been pressed by Douglas Ehring (2002). Imagine a red statue and two red balls; the statue is 1 m away from one ball and 10 m away from another. If universals are multiply located, then the following is true: Red is 10 m away from Red That’s weird. But weirder still is that Red is also 1 m away from Red. Assuming that if x is 1 m away from y then x is not 10 m away from y, it follows that: ¬ Red is 10 m away from Red Thus, we have a contradiction. (Similarly, given multiple location, Red would be both ball-shaped and statue-shaped; again, an impossibility!) Consider three responses: the relativization response; the weird occupation response; and the bullet-biting response. The ‘relativization’ response adds extra relata to the problematic relations in order to avoid the contradiction. This is Cody Gilmore’s (2003) strategy. Where we standardly believe that ‘__ is 1 m apart from__’ is a dyadic relation, Gilmore says it’s quadadic. The relation is instead of the form ‘__ (at region __) is 1 m apart from __ (at region __)’; so, there are four-relata: two for the objects and two for the locations which they exactly occupy. In the statue-ball case, the following facts are therefore true (where rstatue, rball1, and rball2 are regions exactly occupied by the relevant objects): Red (at rstatue) is 1 m apart from Red (at rball1) ¬ (Red (at rstatue) is 10 m apart from Red (at rball1))

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Red (at rstatue) is 10 m apart from Red (at rball2) ¬ Red (at rstatue) is 1 m apart from Red (at rball2) And those facts are consistent. (We could say the same of shape: Red is statue shaped at rstatue and ball shaped at rball1, which is, again, not contradictory.) Here’s an objection: No sense can be made of these ‘extra-relativized’ relations. Imagine I said that the monogamous marriage relation – standardly thought to be two-place – is instead a three-place relation relativized to a transfinite cardinal. How absurd! Sentences like ‘Will and Jada are married relative to beth-seven’ would just be gibberish! My worry is that Gilmore’s relations have the same problem. We could avoid the problem if locutions of the form ‘x (at region R)’ were the names of different entities. But those entities would just be different property instantiations; were ‘Red (at rstatue)’ a name, it’d name something like a trope. And then it would be tropes that were located, not universals – and tropes are singularly located! We would have ‘solved’ the problem only by giving up on the multiple location of properties. Gilmore does say something about how to understand these relations other than as names. Elsewhere, we find it entirely natural to ‘add’ relativizations to a spatiotemporal location. For instance, it is common to say ‘Socrates is standing’ expresses the dyadic relation of Socrates standing relative to a particular time (and, thus, a region – at least if we treat times as spacetime regions). Gilmore suggests something similar is going on when we are faced by the More-Ehring problem. However, the natural way to understand the ‘addition’ of relativizations to locations is that the addition somehow restricts our attention to a certain region – for instance, we pay attention only to an instant at which Socrates stands. Or consider: In the Arctic there are no motorways i.e., when we restrict our attention only to the Arctic, we see that no motorways exist. That said, consider facts involving two relativizations: Socrates is standing at midday in Athens. The city of Medan lies in Indonesia in the northern hemisphere. To make sense of those claims, we restrict our attention to the intersections of the named regions. Where the instant of time that is midday intersects with Athens, Socrates stands! Where the northern hemisphere intersects with Indonesia, we find Medan! But if this is right, Gilmore has a problem since Gilmore must commit to: Red (at rstatue) is 1 m apart from Red (at rball1) Since rstatue and rball1 do not overlap, they have no intersection, and so no sense can be made of asking whether Red is apart from itself at that intersection.4 The second solution to the More-Ehring problem is to deny that universals stand in the relations other located objects stand in; whilst objects are both located and distant from one another, somehow/someway universals are merely located and are not distant from one another (Meinertsen 2018: 119–130). But I struggle to make any sense of rstatue and rball1 being 1 m apart, Red exactly occupying them, and yet Red failing to inherit that spatial separation. Similarly for shape: if Red exactly occupies a ball-shaped region surely it must be ball-shaped? To think otherwise is to misunderstand what ‘exact location’ means in the first place (Gilmore 2006: 200). 154

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One option is to deny that universals are exactly located anywhere, whilst maintaining that they are nevertheless located somewhere. Again, this move doesn’t ‘solve’ the MoreEhring problem so much as abandon the multiple location of universals entirely; nevertheless, the suggestion is interesting enough in its own right to merit discussion. Consider: EXACTNESS:

If a thing is weakly located at some region, then that thing is exactly located at (at least) one region.

There are reasons to think EXACTNESS is false (Kleinschmidt 2016; Nolan 2006; Parsons 2007: 205–210). Were it false, universals could be weakly located where each of their instances are whilst failing to have any exact location. Call this ‘weak immanent realism’. Since universals would then have no exact location, they would have no shape, avoiding the shape problem. Similarly, the distance problem is solved: consider the scattered composite of the statue and the balls; that composite is weakly located at rstatue, rball1 and rball2 without any troublesome fact about it being some distance away from itself; were weak immanent realism true, Red would be in a similar position. But, as already noted, weak immanent realism abandons the multiple location of universals. With an eye on retaining such multiple location, consider the final solution: Deny that there is any contradiction in the first place. Being both 1 m away from yourself and 10 m away from yourself is strange, but not impossible; similarly, being both statue-shaped and ball-shaped is odd, but not strictly speaking contradictory. As I argue elsewhere (Effingham 2020a: 27–36) (see also Barker and Dowe (2003: 108 n5), Mahlan (2018: 40–41, 41 n4), and Peacock (2016: 63–66)) the possibility of time travel shows exactly this of temporally relativized multiple location: if a tall time traveller visits her shorter earlier self, then (at that time) she will be both short and tall – but that does not imply the contradictory claim that she is short and not short (or tall and not tall). In cases of multiple location apparently contradictory properties (e.g., short/tall or ball-/statue-shaped) turn out not to be contradictory at all. The suggestion would be that the same applies when we consider multiply located universals. E.J. Lowe’s problem: Co-location is a transitive relation (for if Abigail is in the same place as Bronia and Bronia is in the same place as Claire, surely Abigail is in the same place as Claire?). Assuming that co-location holds between two things exactly occupying the same region, multiply located universals lead to absurdity. Red exactly occupies rstatue, as does the statue, so they are co-located. Red exactly occupies rball1 as does the first ball, so they are co-located. Since co-location is transitive, the ball is therefore co-located with the statue. But that’s clearly false! (Lowe 1998: 156; 2006: 24, 98–100). We might solve this problem in ways analogous to the More-Ehring problem e.g., by adding relativizations or denying universals are exactly located (and, thus, not colocated with anything). But by far the easiest response is to deny that co-location is transitive, at least in cases where multiple location is involved. Compare to a case where a ghost is co-located with a human in New York at time t. Imagine that the ghost travels back in time to time t, managing to co-locate with a second human in Sydney. Were colocation transitive, the two humans would be co-located, which is false. The lesson to draw is that, in cases involving multiple location, the transitivity of co-location fails (Effingham 2013). 155

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13.3.3

Singularly Located Properties

As the example of weak immanent realism shows, not everyone need believe that immanent universals are multiply located. Another competing understanding to the multiple location view is that universals are singularly located, being exactly located at (and only at) the region composed of all of the regions that its instances exactly occupy. Whilst less common than the multiple location view, it has received explicit endorsement (Bigelow 1988: 18–22; Effingham 2015; Parsons 2007). Again, it would have both temporally relativized and spatiotemporal versions. (And note that, assuming universals have no parts, singularly located universals would still be ‘wholly present’ – for some interpretation of that phrase – wherever they were found.) You might be driven to the singular location view over and above the multiple location view because you believe multiple location is impossible (Parsons 2007). But even were multiple location possible, we might nevertheless prefer singular location. I have elsewhere argued that if there is no good reason in favour of thinking universals are multiply located, we should opt for singular location; further, I argued that there is no such good reason (Effingham 2015).

13.4

The Location of Tropes

Uncontroversially, tropes are singularly located, being exactly located where their instances are exactly located. Again, because the chorological lingo is a recent introduction, it is rarely explicitly stated in such terms, but I suggest that it’s what most trope theorists have in mind. As with universals there are some questions about whether one means tropes are singularly located in the temporally relativized or spatiotemporal sense (or both). If tropes persisted then tropes might be multiply located in either sense. If they endured, they would exactly occupy only one spatial region at any time, but would be spatiotemporally multiply located throughout time, like any other endurant. And if tropes could travel in time, they could (like any time traveller) be multiply located in the temporally relativized sense. So we should not define the difference between tropes and universals as properties capable (or not) of being multiply located. There is also a potential problem with thinking that tropes exactly occupy the region exactly occupied by their instance. Assume that bundle theory is true and that objects are composites of their tropes; this conflicts with: SIZE:

If x has y as a proper part then the region y exactly occupies is a proper part of the region that x exactly occupies.

For instance, the statue and its red trope both exactly occupy rstatue, but that conflicts with SIZE if we are to think the trope is (in some sense) a proper part of the statue. Trope theorists might deny SIZE, although a bald-faced denial would be extreme. A more sophisticated strategy would be to say that it’s true of material parthood, but no such principle is true of the relation holding between (e.g.,) a statue and its tropes. This strategy, however, would weaken any proposed analogy between parthood and metaphysical constituency. Alternatively, the trope theorist might adopt an analogue of weak immanent realism (saying that tropes are only weakly located where their instances are) or deny that they are located at all (and revisit the suggestion above that they are mere abstracta). I know of no trope theorist who has considered such options, but as the contemporary developments in chorology gain traction, this may well change.

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Notes 1 Located properties also follow if we accept an ‘eliminativist’ bundle theory. Standard bundle theorists believe in bundles of properties constituting objects (and events etc.); eliminativists believe only that the properties exist, not that they constitute anything ( Robb 2005: 468). Since something is located, and the only things that exist – either derivatively or fundamentally – are properties, then properties are located. 2 This motivation also ties in with another: analyzing instantiation. A chorological analysis would be: an object instantiates a property iff it is co-located with it ( Russell 1912: 23). See Effingham (2015: 852-53) and Peacock (2016: 55) for discussion. 3 The individuation condition is not purely chorological, being ‘sullied’ by a restriction to perfectly resembling tropes. This is because, standardly, tropes can be co-located e.g., a mass and a charge trope being co-located to form an electron. One trope theorist, the fourth-century Buddhist philosopher Vasubandhu (in Abhidharmakośabhāsya) is an exception; Vasubandhu believed tropes could not be co-located ( Goodman 2004: 400), which leaves open a ‘purely chorological’ individuation condition. 4 As an alternative, note that Bowers (2017: 126) relativizes the relations to property instantiations instead of locations. (Not that it helps because I can’t make sense of that relativization either!)

References Armstrong, D.M. (1978) Nominalism and Realism: Universal and Scientific Realism Volume I. Cambridge: Cambridge University Press. Armstrong, D.M. (1988) Can a Naturalist Believe in Universals? In Ullmann-Margalit, E. (ed.) Science in Reflection. London: Kluwer Academic Publishers: 103–115. Armstrong, D.M. (1989a) A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press. Armstrong, D.M. (1989b) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Barker, S. and Dowe, P. (2003) Paradoxes of Multi-Location. Analysis 63(2): 106–114. Barker, S. and Dowe, P. (2005) Endurance is Paradoxical. Analysis 65(1): 69–74. Beebee, H. and Rush, M. (2003) Non-Paradoxical Multi-Location. Analysis 63(4): 311–317. Bigelow, J. (1988) The Reality of Numbers: A Physicalist’s Philosophy of Mathematics. Oxford: Clarendon Press. Bowers, J. (2017) A Simple Dialogue. Thought 6(2): 122–128. Calosi, C. (2014) Extensionality, Multilocation, Persistence. Dialectica 68(1): 121–139. Calosi, C. and Costa, D. (2015) Multilocation, Fusions and Confusions. Philosophia 43(1): 25–33. Campbell, K. (1981) The Metaphysic of Abstract Particulars. Midwest Studies in Philosophy 6(1): 477–488. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Daniels, P. (2013) Endurantism and Paradox. Philosophia 41(4): 1173–1175. Daniels, P. (2014) Occupy Wall: A Mereological Puzzle and the Burdens of Endurantism. Australasian Journal of Philosophy 92(1): 91–101. Eagle, A. (2010) Perdurance and Location. Oxford Studies in Metaphysics 5: 53–94. Eagle, A. (2016) Multiple Location Defended. Philosophical Studies 173(8): 2215–2231. Effingham, N. (2013) Impure Sets May Be Located: A Reply to Cook. Thought 1(4): 330–336. Effingham, N. (2015) The Location of Properties. Noûs 49(4): 846–866. Effingham, N. (2020a) Time Travel: Probability and Impossibility. Oxford: Oxford University Press. Effingham, N. (2020b) Mereological Nominalism. Philosophy and Phenomenological Research 100(1): 160–185. Effingham, N. and Robson, J. (2007) A Mereological Challenge to Endurantism. Australasian Journal of Philosophy 85(4): 633–640. Ehring, D. (2002) Spatial Relations Between Universals. Australasian Journal of Philosophy 80(1): 17–23.

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Nikk Effingham Ehring, D. (2011) Tropes: Properties, Objects, and Mental Causation. Oxford: Oxford University Press. Garcia, R. (2015) Two Ways to Particularize a Property. Journal of the American Philosophical Association 1(4): 635–652. Garret, B. (2017) Endurantism Endures: Rejoinder to Barker and Dowe. Manuscrito 40(3): 29–32. Giberman, D. (2014) Tropes in Space. Philosophical Studies 167(2): 453–472. Giberman, D. (2022) Ostrich Tropes. Synthese 200(1): 1–25. Gilmore, C. (2003) In Defence of Spatially Related Universals. Australasian Journal of Philosophy 81(3): 420–428. Gilmore, C. (2006) Where in the Relativistic World Are We? Philosophical Perspectives 20: 199–236. Goodman, C. (2004) The Treasury of Metaphysics and the Physical World. Philosophical Quarterly 54(216): 389–401. Grossmann, R. (1992) The Existence of the World: An Introduction to Ontology. New York: Routledge. Jarrott, J. (2014) Currently Persisting Paradoxes: Getting Clear about Endurantism. Res Cogitans 5(1): 59–76. Keinänen, M., Hakkarainen, J. and Keskinen, A. (2016) Why Realists Need Tropes. Metaphysica 17(1): 69–85. Kleinschmidt, S. (2016) Placement Permissivism and Logics of Location. Journal of Philosophy 113(3): 117–136. Kriegel, U. (2021) The Concreteness of Objects: an Argument Against Mereological Bundle Theory. Synthese 199(1-2): 5107–5124. Küng, G. (1967) Ontology and the Logistic Analysis of Language. Dordrecht: D. Riedel. Lafrance, J. (2015) A Bundle of Universals Theory of Material Objects. Philosophical Quarterly 65(259): 202–219. Lowe, J. (1998) The Possibility of Metaphysics: Substance, Identity, and Time. Oxford: Oxford University Press. Lowe, J. (2006) The Four-Category Ontology. Oxford: Oxford University Press. MacBride, F. (1998) Where are Particulars and Universals? Dialectica 52(3): 203–227. Mahlan, J. (2018) Can Universals be Wholly Located where Their Instances are Located? Metaphysica 19(1): 39–55. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. McDaniel, K. (2003) No Paradox of Multi-Location. Analysis 63(4): 309–311. Meinertsen, B. (2018) Metaphysics of States of Affairs. Singapore: Springer. Mertz, D. (1987) Particularism, Exemplification, and Bradley’s Regress. Journal of Speculative Philosophy 1(3): 177–205. Nolan, D. (2006) Stoic Gunk. Phronesis 51(2): 162–183. O’Leary-Hawthorne, J. and Cover, J. (1998) A World of Universals. Philosophical Studies 91(3): 205–219. Oliver, A. (1996) The Metaphysics of Properties. Mind 105(417): 1–80. Parsons, J. (2000) Must a Four-Dimensionalist Believe in Temporal Parts? The Monist 83(3): 399–418. Parsons, J. (2007) Theories of Location. Oxford Studies in Metaphysics 3: 201–232. Pasnau, R. (2011) Metaphysical Themes 1274-1671. Oxford: Oxford University Press. Peacock, H. (2016) Where are Universals? Metaphysica 17(1): 43–67. Robb, D. (2005) Qualitative Unity and the Bundle Theory. The Monist 88(4): 466–492. Russell, B. (1912) On the Relations of Universals and Particulars. Proceedings of the Aristotelian Society 12: 1–24. Schaffer, J. (2001) The Individuation of Tropes. Australasian Journal of Philosophy 79(2): 247–257. Smith, D. (2008) How to Endure an Alleged Paradox. Journal of Philosophical Research 33: 285–292. Williams, D.C. (1953) On the Elements of Being: II. Review of Metaphysics 7(2): 171–192.

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14 UNIVERSALS AND THE BUNDLE THEORY Jiri Benovsky

14.1

Introduction

In short, the bundle theory with universals view says that an object is a bundle of universals. The debate concerning the bundle theory with universals has been shaped, for better or worse, by the discussion of the possibility of two perfectly identical spheres, following Max Black’s (1952) scenario. I will discuss it in the last section of this chapter. Before we get there, the plan is the following: first, briefly articulate the distinction between platonic universals and immanent universals; second, articulate in detail what the bundle theory is and how it can combine with the view that properties are universals; third, articulate some objections (and replies) to the bundle theory with universals view, not in order to reject it, but rather to provide a deeper understanding of the theory; and finally, articulate the objection from the principle of the Identity of Indiscernibles with the two identical spheres scenario, to see what possible lessons can be learnt from it. This chapter being concerned with the bundle theory as combined with the view that properties are universals, I shall leave entirely aside the view according to which objects are bundles of tropes. Let it here simply be noted that this latter view is arguably the more popular one (see Chapter 21, this volume as well as Benovsky 2008, where I compare in detail bundle theories with tropes and bundle theories with universals).

14.2

Platonic versus Immanent Universals

Tracing back to Plato, the idea of platonic universals, to put it briefly, amounts to the claim that properties are non-spatio-temporal entities (sometimes labelled as abstract entities, in this sense of “abstract”) which are related to spatio-temporal (“concrete”) objects by a relation of instantiation (or “exemplification”) in such a way that they (the properties) are multiply instantiable. One version or another of such a view can be found in many pieces of philosophical writing throughout the history of philosophy; useful introductory and committed readings in order to get a better understanding of the view include Bertrand Russell (1912) and David Armstrong (1978, 1989). The core idea of the nature of objects and universals consists thus in the claim that an object, say a chair, stands in a suitable

DOI: 10.4324/9781003246077-18

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relation with a non-spatio-temporal universal, say redness, and that this is what it means to say that the chair is red. Different objects, say many different chairs, can stand in this suitable relation with the very same universal of redness, and this is what it means to say that the universal (the property of redness) is multiply instantiable – this is how different objects can share the same property, for instance how different chairs can all be red. The relation of instantiation is typically understood as a primitive relation, not further defined. Immanent universals, on the other hand, are things of this world. They are spatiotemporal entities, exactly as the material objects that instantiate them. According to this view, material objects also have their properties by standing in a suitable (primitive) relation to their universals, in a structurally similar way as this is done under the platonic universals view, with the notable difference that the relation of instantiation relates here only concrete things (concrete objects and concrete universals). Immanent universals, although being spatio-temporal, have the capacity of being multiply instantiated which, in this case, means that they can be multiply located, that is, they can be wholly present in many places at the same time (say, the spatio-temporal property of redness can be wholly present in many chairs, tomatoes and Ferraris at the same time). This capacity, also, is a primitive postulate of the theory.

14.3

Substratum Theory versus Bundle Theory

In the quick formulation of what universals are in Section 14.2, the (standard) background assumption was not the bundle theory but rather the substratum theory (also sometimes referred to as “the substance-attribute view”; I shall not use the term “substance” in order to avoid possible confusion with the view according to which objects are Aristotelian substances). The substratum theory, as combined with the view that properties are universals, claims, as we have seen above, that objects like chairs are substrata (sometimes referred to as “bare particulars”) which stand in a relation of instantiation to their properties – universals. Both versions, that is, both the view that universals are spatiotemporal and that they are non-spatio-temporal, are available here. In the substratist view, in order for an object to exist, three types of components are thus needed: the substratum, the universals, and the instantiation relation. The substrata-cum-universals view is the standard view when it comes to understanding properties in terms of universals (instead, say, of embracing tropes or a kind of nominalism). The bundle theory denies the existence and the theoretical need for substrata. According to a bundle-theoretic understanding of the nature of material objects such as chairs, objects are not substrata standing in a relation to universals, rather objects are composed directly of the universals themselves. What there is, at the fundamental ontological level, are merely universals. Objects are constructions out of those. In this sense, the bundle theory is a more parsimonious view than the substrata-cum-universals view since it postulates only one category of entities, namely, properties. As bundle theorists see it, substrata are unnecessary and under-defined, rather mysterious, entities, and metaphysicians are better off without them. Since the bundle theory does not postulate the existence of a substratum, it needs something else to hold together the different universals of a single object. A typical Ferrari is a bundle of properties such as being red, being fast, and having four wheels. These properties are, under the bundle-theoretic framework, held together not by an underlying substratum but rather by a special relation, typically understood as an n-adic relation 160

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(n being the number of properties of the given object). This relation has been given many names, but perhaps the one that is the most popular is the term “compresence”, following Russell’s idea that the universals are simultaneously present, at a given time, in a bundle. While the substratum theory is straightforwardly compatible with both the view that universals are platonic (non-spatio-temporal) and immanent (spatio-temporal) entities, the bundle theory does not seem to work as easily with both options. If combined with the view that universals are non-spatio-temporal, it could have the unpalatable consequence that ordinary material objects such as chairs or Ferraris are non-spatio-temporal as well. Perhaps friends of the bundle theory can find some way out of this trouble, but typically the bundle-theory-cum-universals view comes in combination with the view that universals are immanent, spatio-temporal, concrete, entities – and so are then the objects that are made of them. In short, the bundle-theory-cum-universals view amounts then to the claim that material objects are collections (bundles) of immanent (concrete, spatio-temporal) universals. At the bottom of the bundle theorist’s ontology, there is then only the one category of immanent universals – the special relation of compresence being itself an immanent universal. Perhaps it is this kind of parsimony and simplicity which marks the bundle theory as being an elegant view and which attracts its followers. A tricky part of this endeavour concerns the special relation of compresence. In order to try to get a better grip on how the compresence relation does its job – compresence being officially an undefined primitive – L.A. Paul (2002) suggests that we can understand it in mereological terms. She thus puts forward a property mereology view. In this view, properties – immanent universals – are, literally, mereologically speaking – parts of the objects which have them. For instance, a Ferrari contains redness, fastness and fourwheelness as parts.

being located at place1 and time1

being located at place2 and time2

R having four wheels

being located at place3 and time3 being round

R: the property of being red

In this figure, the Ferrari is thus understood as a mereological sum of its components, its qualitative parts. Objects are thus defined as fusions of properties. Paul refers to them as “logical parts” instead of “qualitative parts” since properties need not always be qualitative (say, in the case of location properties, for instance). These logical parts being universals, they can be parts of many different objects – a Ferrari, a tomato, or a chair – which can in this way overlap. As Paul puts it, in line with what we already saw above, her reason 161

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to favour the bundle theory lies in its simplicity and elegance. Understanding the compresence relation in terms of a more familiar relation of mereological parthood can then perhaps make it even simpler in terms of its ontological commitments. However, it should be noted that, as for the relation of compresence and as for the substratum, the fundamental relation of parthood is here a primitive not-further-defined relation, postulated by the theory with the function of gluing together properties of a single objects (in Benovsky 2008, 2016, I explore the meta-theoretical consequences of the fact that all these theories appear to be using a functionally same primitive notion to be able to do their job). One motivation and perhaps a theoretical advantage of Paul’s version of the bundletheory-cum-universals view is that it explains the mystery of multiple location in terms of overlap. Objects often have the same property. A Ferrari and a tomato are both red. In the traditional immanent universals view, this means that redness is bi-located, it is in two places at the same time (though see Chapter 13, this volume for some qualifications of this claim). This is (again) a primitive theoretical postulate of the theory, and while it is of course admissible that a theory appeals to primitive notions, this one has sometimes faced an incredulous stare, perhaps lacking a deeper and plausible understanding in a crucial place. In Paul’s view, redness is not in two places at once. Rather, as illustrated on the figure above, it is part of different groups of properties – of different bundles. Whether such a notion of property overlap is more or less open to a possible incredulous stare and whether it is more or less plausible than multiple location of universals is open to debate, but at least it should be recognized that Paul’s property mereology view tries to address the hard questions facing the friend of the bundle theory with immanent universals view. Paul (2002: 583) thus claims that her view “combine[s] the benefits of tropes and universals without their attendant problems” (for a discussion of this view, see Le Bihan 2018). To sum up: the bundle theory is to be combined with the view that universals are immanent (not platonic); it appeals to a primitive relation which ties together the properties of a single object (in Paul’s version this is a mereological relation); it is a one-category ontology; it insists on ontological parsimony and simplicity.

14.4

Objections and Replies

The purpose of this section is to get a better grip on the bundle-theory-cum-universals view by going through some objections to it as well as possible replies. Objection 1: the glue problem. We have already quickly seen this point above: how to understand the nature of the ontological glue which holds together properties of a single bundle? The unity of objects is what is at stake here. The bundle theorist’s reply appeals to a primitive tool (for meta-theoretical consequences of this, and for a comparison with competing theories about the nature of objects and properties, see Benovsky 2008, 2016). This primitive notion is the relation of “compresence” which amounts roughly to the idea of the properties “being together”, and which goes around under various names, including “collocation”, “combination”, “coactuality”, and others. Whatever its name, its theoretical functional role is always the same: it has the (primitive) function to take properties and, by bundling them together, to give rise to objects. Armstrong (1978: 90–91) puts it thus, focusing on Russell’s view (but what he says applies easily to all other versions as well): “Russell’s fundamental device is to introduce an unanalysable, symmetrical, non-transitive relation which holds between some, but not all, pairs of properties”. A bundle of properties (universals) corresponding to an object is thus a complete complex of compresence: a 162

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group of properties where each member is compresent with each other and where there do not exist other properties (outside the bundle) which would be compresent with each member. The objector might then insist precisely on what the proponents of the bundle theory want to put forward: namely that the proposed solution here amounts to embracing an under-explained primitive tool. Other technical issues might also be raised, such as regress problems (see Chapter 22, this volume). Objection 2: change. It appears that under the bundle theory no objects can ever change. Indeed, if an object is a bundle of properties, then if one of its properties is replaced by another, the bundle is not the same bundle anymore, and so the object is not the same object anymore – it did not change, it has simply been replaced by another object. To deal with the notion of change, the bundle theorist can appeal here to a perdurantist (fourdimensionalist) account of change, where change across time is understood not in terms of one and the same object existing at different times and having different properties but rather in terms of different temporal parts existing at different times and having different properties (the temporal parts, of course, need to be suitable related). What we learn here is that the bundle theory turns out to be bundle-bundle theory (second level bundles grouping together first-level bundles which are the temporal parts (this is a perdurantist “worm view” version of this view)). It thus seems that the bundle theory is committed to either such a perdurantist worm view or to a version of temporal counterpart theory (i.e., the view that objects persist through time by having suitably related temporal counterparts at different times; for our present purposes, both the worm view and temporal counterpart theory can do the job equally well). Philosophical literature on perdurantism and on temporal counterpart theory is vast, Ted Sider (2001) provides an excellent discussion. What about endurantism? Endurantism is the view according to which objects do not have temporal (counter)parts but rather persist through time by being wholly present at all times at which they exist (see, inter alia, van Inwagen 2001). It appears that the bundle theory cannot be combined with it. Let us see why. Suppose a bundle theorist wanted to combine her view with endurantism. She needs to account for the problem of change and for the problem of temporary intrinsics: objects change their properties, they have different properties at different times. Say that a Ferrari is red at t1 and that it is then painted yellow, so later at t2 it is yellow. In the endurantist view, one and the same numerically identical object, the Ferrari, exists at t1 and at t2 and has two incompatible properties: being red and being yellow. To avoid the threat of a contradiction, the endurantist might want to appeal to an indexicalist view where properties are spatio-temporally indexed (I discuss the need for a spatial index, in addition to the temporal index, in Benovsky 2008, 2009): Ferrari Fast-at-l1-t1 Red-at-l1-t1 Red-at-l2-t2 Blue-at-l3-t3 …

In this view, there is no contradiction since the two properties “Red-at-l1-t1” and “Blueat-l3-t3” are not incompatible, given that they are indexed. In this view, objects do not have their properties simpliciter, they always have spatio-temporally indexed properties. But 163

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then, such indexed properties are tropes, not universals. No property, under indexicalism, can be multiply instantiated, since it is always spatio-temporally bound, so such a view simply has no room for universals. As a consequence, the bundle theory with universals is not compatible with endurantism at least if the endurantist embraces an indexicalist-type strategy to deal with the problem of change and the problem of temporary intrinsics. The point to take home is then the following: among the theoretical commitments of the bundle theory there is also one version or another (worm view or counterpart theory) of perdurantism. Objection 3: modal properties. As we shall now see, the bundle theory needs not only to be a bundle-bundle theory but in fact it has to be a bundle-bundle-bundle theory. The reason for this is the modal analogue of the problem of change we have seen above. Here it is: bundles are constituted by their properties, and so it seems that any property of any bundle is essential to it. Indeed, if you change one property, the bundle is not the same bundle any more. This then precludes objects of having some properties only contingently – all and any properties of any object turn out, under the bundle theory, to be essential to it. A red Ferrari is thus necessarily red. To avoid this unpalatable consequence of her view, the bundle theorist can appeal to the same type of strategy as when she was responding to the problem of change above – namely, she can embrace one version or another of modal perdurantism, which typically takes the form of a modal counterpart theory. In this way, a Ferrari is constituted of first-level bundles which are the temporal parts of an object in the actual world, then it is a temporal bundle of those first-level bundles (understood either in temporal counterpart-theoretic terms or in terms of a perdurantist temporal worm view), and then it is a bundle of those second-level bundles (typically understood in terms of modal counterparts). As a cumulative conclusion stemming out of objections 2 and 3, we thus see that the bundle theory is committed to both perdurantism and modal counterpart theory (in one version or another). Depending on what you think for independent reasons about the counterpart theory and about perdurantism, you might welcome this as a fruitful interaction with interesting and appealing pieces of metaphysics, or you might view this as a type of a reductio ad absurdum. (For what it is worth, let me say that I am sympathetic to the former reaction.) Objection 4: ontological autonomy/independence. According to the bundle theory, properties – universals – are not, strictly speaking, had by anything. They simply exist, by themselves, and that’s it. They “float free”, as the objectors put it, insisting on the implausibility of such a claim. Properties, according to the objectors, need something, like a substratum, to bear them, they cannot just float around, free of any ontological attachment (see Armstrong 1997). The reason why this objection is expressed here in somewhat metaphoric terms is that it is often expressed in this way. And the reason for that lies in the fact that there is not much of an argument behind the objection. The objection merely, but strongly, insists on the sheer implausibility of what the bundle theorist wants us to swallow: a world of properties, not had by any substance or substratum. Just the properties, variously related to each other and bundled together, with nothing to support them. Perhaps less metaphorically, the objector’s claim amounts to the idea that properties are not ontologically independent enough entities to be able to exist without an underlying bearer. They are not, so to speak, substantial enough. 164

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As a reply to such an objection, perhaps the best (and probably the only) thing the bundle theorist can do, is to switch the burden of proof (Hawthorne and Cover 1998: 207): Perhaps some philosophers will claim to find it just self-evident that universals are had by something. We don’t have much to say to such philosophers. We do note, however, that the polemic against the bundle theory has rarely taken the form ‘It is simply self-evident that anything quality-like is directly or indirectly predicated of something that isn’t like a quality […]’. If opponents of […] the Bundle Theory wish to retreat to this form of an incredulous stare, so be it. In a similar vein, bringing in possible considerations coming from physics, Galen Strawson argues that the objection is perhaps not really justified (Strawson 1997: 427): ‘But if there is a process, there must be something – an object or substance – in which it goes on. If something happens, there must be something to which it happens, something which is not just the happening itself’. This expresses our ordinary understanding of things, but physicists are increasingly content with the view that physical reality is itself a kind of pure process – even if it remains hard to know exactly what this idea amounts to. The view that there is some ultimate stuff to which things happen has increasingly ceded to the idea that the existence of anything worthy of the name ‘ultimate stuff’ consists in the existence of fields of energy – consists, in other words, in the existence of a kind of pure process which is not usefully thought of as something which is happening to a thing distinct from it. This objection is dialectically important since it lies at the core of the motivation for the substratum theory. If this objection fails, there does not seem to be much of a reason to postulate substrata in one’s ontology. Substrata are there, supposedly, to be the bearers of properties. If properties need no bearers (i.e., if it is enough for them to be bundled together), the metaphysician needs no substrata. The dispute here seems to be one opposing two types of incredulous stares: free-floating (“merely” bundled) properties on the one hand, and bare under-defined substrata on the other. Both have been, and continue to be, stared at, rather strongly, by the two disagreeing sides of the debate (see Benovsky 2008 for a meta-theoretical analysis of this dialectical dead-end and its consequences).

14.5

The Objection from the Principle of Identity of Indiscernibles

I devote a special final section to this objection, given the important role it has played in the discussion of the bundle theory with universals view. The objection, simply put, is the following: the bundle theory with universals is committed to the principle of the Identity of Indiscernibles, but this principle is false, so the bundle theory is false. Here is the principle of the Identity of Indiscernibles:

( x) ( y) (( F) (Fx

Fy)

(x = y))

Black (1952) has provided a famous scenario to illustrate this principle and articulate this objection. The bundle theory says that objects are bundles of properties. Black asks us then to consider the case of two objects which are qualitative duplicates of each other, and 165

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to make his case as strong as possible he asks us to imagine a universe which contains only two objects, namely two entirely qualitatively identical spheres. They have the same size, same colour, same mass, and they are located at, say, one meter from each other. There is nothing else in this universe, except the two spheres, so the spheres have no relational properties which could make a (relational) difference between them. Given this scenario, Black argues, since the properties of the two spheres are universals, the spheres have the very same properties not only in a qualitative sense but also in a numerical sense. For instance, the universal of being spherical is one and the very same entity – the numerically same universal – involved in the two spheres. This is the case for all properties of the spheres. But let us not forget that the two spheres are nothing but bundles of their properties and that they are individuated by their properties. As a consequence, in this situation, not only their universals, but the two spheres themselves are numerically identical: in fact, they are then not two but rather one sphere. This is indeed exactly what the principle of Identity of Indiscernibles says. But, the objector argues, contra this principle, it is possible there to be two qualitatively identical spheres. So, the principle is false, and the bundle theory with universals view is then false as well. In the rather abundant literature concerning this argument, it has been tried to distinguish the two spheres by their location properties or by their haecceistic properties like “being sphere S1”, but such strategies often lead to even less palatable places than the problem with the Identity of Indiscernibles principle in the first place. Haecceities, for instance, seem to be closer to a cheap magician’s trick than to a genuine solution to a problem. John O’Leary-Hawthorne (1995) provides both a bold and interesting answer to Black’s argument. In short, he suggests that given the fact that, under the bundle theory with universals view, objects are made of universals (and nothing else), they can inherit the behaviour of universals. So, he makes the proposal that not only can universals be multiply located but that objects can be multiply located as well. Thus, a sphere in Black’s universe, which is a bundle of universals, can be bi-instantiated: it can be bi-located at, say, one meter from itself. Boldly but not unreasonably, O’Leary-Hawthorne argues that any strangeness of this proposal comes from the fundamental strangeness of the idea that anything can be multiply located. But if one accepts such an idea in the case of universals, as the bundle theory with universals does, it is then no stranger, but rather a natural consequence, to claim that bundles of universals can be multiply located as well. Such a view then collapses the distinction between objects and properties. However shamelessly elegant such a move can be, here is an objection to it, raised by William Vallicella (1997): the problem with this proposal lies in the fact that in order to be multiply located a bundle of universals would require to be (multiply) instantiated, but this is not possible under the bundle theory. As Vallicella argues, universals are instantiated by being in a bundle with other universals, but if a bundle (say, a sphere) is already a complete bundle of universals, it cannot then be bundled together with other universals. Instantiation, in this situation, does not make sense for the bundle theorist. Perhaps we can see a simpler way out of trouble here. Perhaps we can argue that it is the compresence relation which can do the job. The two spheres may be entirely qualitatively identical, but the two bundles, the two spheres, can be tied together by two different compresence relations – why not? The two compresence relations would need to be numerically distinct, albeit not being qualitatively distinct of course, but remember that the compresence relation is a primitive tool postulated by the theory. As such, as a primitive 166

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tool, it can very well be granted the possibility of being numerically distinct while being qualitatively identical. After all, this is exactly what the substratum theorist says about the substratum, and if this works for her, there is no reason why the bundle theorist could not appeal to such a (primitivist) strategy as well. Primitive distinctness seems then to be something that both sides require to take on board.

References Armstrong, D.M. (1978) Universals and Scientific Realism. Cambridge: Cambridge University Press. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Black, M. (1952) The Identity of Indiscernibles. Mind 61(242): 153–164. Benovsky, J. (2008) The Bundle Theory and the Substratum Theory: Deadly Enemies or Twin Brothers? Philosophical Studies 141(2): 175–190. Benovsky, J. (2009) On (Not) Being in Two Places at the Same Time: An Argument Against Endurantism. American Philosophical Quarterly 46(3): 239–248. Benovsky, J. (2016) Meta-Metaphysics: On Metaphysical Equivalence, Primitiveness, and Theory Choice. Dordrecht: Springer. Le Bihan, B. (2018) Priority Monism Beyond Spacetime. Metaphysica 19(1): 95–111. O’Leary-Hawthorne, J. (1995) The Bundle Theory of Substance and the Identity of Indiscernibles. Analysis 55(3): 191–196. O’Leary Hawthorne, J. and Cover, J.A. (1998) A World of Universals. Philosophical Studies 91(3): 205–219. Paul, L.A. (2002) Logical Parts. Noûs 36(4): 578–596. Russell, B. (1912) The Problems of Philosophy. New York: Henry Holt. Sider, T. (2001) Four Dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press. Strawson, G. (1997) The Self. Journal of Consciousness Studies 4(5/6): 405–428. Vallicella, W. (1997) Bundles and Indiscernibility: A Reply to O’Leary-Hawthorne. Analysis 57(1): 91–94. van Inwagen, P. (2001) Ontology, Identity and Modality. Cambridge: Cambridge University Press.

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PART 4

Nominalism

15 OSTRICH NOMINALISM Michael Devitt

15.1 What Is Ostrich Nominalism? David Armstrong introduced the term “Ostrich Nominalism” in his book, Nominalism and Realism (1978), when discussing the One over Many (OoM) problem. He describes this venerable problem as that of explaining in virtue of what “many different particulars can all have what appears to be the same nature … all be of the same type” (1978: xiii). He identifies the OoM problem with the “problem of universals” (1978: 41).1 After outlining five reductive Nominalist responses to the problem, Armstrong mentions the Quinean response, under the name “Ostrich Nominalism”, as a possible sixth. This pejorative name aptly captures what Armstrong thinks of this response.2 Ostriches are reputed to ignore problems by burying their heads in the sand, and doubtless many Realists and other metaphysicians think that is just what Quineans are doing. For, the distinctive feature of the Quinean response to the OoM problem is, in Armstrong’s words, seeing “no need for any reductive analyses of the sorts just [mentioned]. There are no universals but the proposition that a is F is perfectly all right as it is” (1978: 16). Where other Nominalists offer reductive analyses to explain the sameness-of-nature without positing universals, the Quinean sees no need for any explanation. Where other Nominalists take the OoM problem seriously and try to solve it, the Quinean dismisses the problem as pseudo.3 We have identified the OoM problem as the problem of explaining sameness-of-nature. That there is sameness-of-nature is the OoM premise of Armstrong’s Realist OoM argument (1978: xiii). That argument explains the premise by positing universals: a and b have the same nature in virtue of instantiating a certain universal. So, the Realist accepts both the problem and the argument to universals. The five reductive Nominalists accept the problem and premise but reject the argument to universals by urging different explanations of the premise. The Quinean accepts (a version of) the premise but rejects the very problem of explaining this sameness-of-nature and hence, of course, rejects the argument to universals.4 My paper, “‘Ostrich Nominalism’ or ‘Mirage Realism’?” (1980), was a reply to Armstrong, defending the Quinean response. I rejected the pejorative “ostrich” label for this response because, I argued, there is nothing ostrich-like about ignoring a problem that

DOI: 10.4324/9781003246077-20

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isn’t there. Indeed, I charged, adopting Realism because of such a pseudo problem, as Armstrong largely does, deserves the pejorative label “Mirage Realism”. Still, sometimes the victims of a slur embrace it; think of homosexuals embracing “queer”. And philosophers sympathetic to the Quinean response have embraced “ostrich”; as Howard Peacock says, “the label of ‘Ostrich Nominalist’ has recently been adopted as a badge of honour by nominalists who wish to emphasize their disdain for realists’ arguments” (2009: 184; see Guillon 2021; Imaguire 2018; Mantegani 2015; Summerford, 2003; Van Cleve 1994). So “Ostrich Nominalism” has become a fairly neutral way of referring to the Quinean response, with no slur intended. And that is how I shall use it. To say more about Ostrich Nominalism (the Quinean response), we need first to say more about the OoM. Alex Oliver is a big help. He points out that Armstrong vacillates between “various versions” of the OoM (Oliver 1996: 48). There are six different types of fact which demand an account according to Armstrong: 1 2 3 4 5 6

a a a a a a

and b are of the same type/ have a common property and b are both F and b have a common property, F has a property is F has the property F (Oliver 1996: 49)

We should think of these as different premises that Armstrong is requesting us to account for in OoM arguments. But what exactly is Armstrong requesting? Oliver thinks this is unclear, detecting “three possible interpretations”: First, the request is for a conceptual analysis …. Second, the request is for a specification of the ontological commitments of the sentences. Third, the request is for a specification of the truth-makers of the sentences. (Oliver 1996: 50) My paper addressed only ontological commitments. The truthmakers request has loomed large in recent discussions. I shall consider it at some length in Sections 15.6–15.7. The Ostrich simply dismisses the request for conceptual analysis, for reasons I shall but briefly indicate now (but see Devitt 2014). Conceptual analysis is usually understood as an a priori examination of concepts in order to discover something about the world. The analysis is supposed to have the same “content” as the concept analyzed; the analysis is supposed to “define” the concept (Oliver 1996: 50–53). From the Quinean naturalistic perspective of the Ostrich (Devitt 2010), the search for such an analysis is totally misguided. The study of concepts and meanings is, or should be, an entirely empirical enterprise, on which progress is very hard. And, importantly, such progress as we have made provides novel information about concepts, not novel information about the world the concepts are about. Return to ontological commitments. In effect, I took (3) to be Armstrong’s premise. I rejected it immediately because of its commitment to properties, replacing it with the Quinean paraphrase, (2) (1980: 434–435). (Quinean paraphrasing will be discussed in Section 15.8.) So, (2) is the OoM sameness-of-type premise that the Ostrich accepts. And the alleged OoM problem becomes that of explaining in virtue of what (2) holds. The 172

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Ostrich has a swift response, as Quine brings out in his famous discussion of red things: “That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible” (1961[1953]: 10). And (2) has no commitment to the universal F-hood. Alternatively, the Ostrich might treat explaining (2), as I did, as “a trivial problem” that is solved by (5), the Quinean paraphrase of (6), together with its like companion, “b is F”. I anticipated an objection from Armstrong: “In virtue of what is a (or b) F?” (1980: 435).5 If there were a OoM problem it would be answering this question. But there is no problem: in Quine’s words, the predication is “ultimate and irreducible”. David Lewis soon entered the fray and agreed. He had these choice words on this question about “predication in general”: it is not “answerable at all … [it] deserves our neglect. The ostrich that will not look at it is a wise bird” (1983: 352; see also Summerford 2003: 103). And (5) has no commitment to the universal F-hood. In sum, the Ostrich rejects (6) but accepts (5) as a paraphrase, and claims that (5) needs no explanation. The Ostrich rejects (3) but accepts (2) as a paraphrase, and claims either that it needs no explanation or that it is trivially explained by (5) and its like companion which, as just noted, need no explanation. (5) and (2) do not posit universals, That, in brief, is the Ostrich’s response to versions of the OoM starting from premises (2), (3), (5), and (6). I will say more in support of this response in the course of discussing objections to Ostrich Nominalism. I will also respond to versions of the OoM starting from (1).

15.2 Armstrong’s Caricature Armstrong’s paper, “Against Ostrich Nominalism” (1980), is a response to mine. He claims that sameness of type is “a Moorean fact” that needs an account. He then simply repeats the charge that Quine is an ostrich for not giving such an account, for “refusing to answer a compulsory question” (1980: 441). But, of course, the Quinean point is precisely that the question needs no answer. I had emphasized that the Quinean indeed takes predicates “with ontological seriousness”, as Armstrong demands (1978: 16), and does not deny that an object “really is F (or G, or whatever)” (Devitt 1980: 435). Armstrong is unmoved, insisting that, on the Quinean view, “particulars are a sort of structureless blob … they lack real internal structure” (1980: 446). Decades later, I responded to Armstrong in a “Postscript” to a reprint of my paper: This is a caricature. It foists on the Quinean an ontological framework that is motivated by the One over Many problem, just the problem that the Quinean rejects. So the problem does not lead the Quinean to traffic in “bare particulars”, “mere thisnesses”, and the like; as I remarked, “he sees no need to play that game”. Suppose that, according to the Realist, an object has an internal structure F-ness. Then, according to the Quinean, it really is F, said as firmly as you like. Nothing more need be said. (Devitt 2010: 26–27) This rejection of “old-time” metaphysics is the crux of Ostrich Nominalism. Yet the Ostrich’s critics tend to just insist on her joining what she regards as a pointless game. Thus, Armstrong’s habit of distinguishing “thin particulars” from “thick particulars” (1978: 114; 1989: 94–96) “invites the Ostrich Nominalist to start a game that she simply cannot play” (Calemi 2016: 41; see also Melia 2005: 72). 173

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15.3

The “less definite” OoM of Lewis and Van Cleve

As already noted, Lewis is sympathetic to the Ostrich. Indeed, he agrees (1983: 354) with much of my 1980 paper. He finds Armstrong’s OoM argument “unconvincing” (1983: 351). He notes that if Armstrong’s vivid criticism – “Quine gives the predicate what has been said to be the privilege of the harlot: power without responsibility” (Armstrong 1980: 443) – applied to Quine, it would apply equally to Armstrong himself. For, Armstrong’s “non-relational Realism” accepts at least one predicate without analysis, “the predicate ‘instantiates’ (or ‘has’), as in ‘particular a instantiates universal F’” (Lewis 1983: 353–354).6 Nonetheless, Lewis thinks that my taking (3), which is about “some specific F”, as the OoM premise, makes the problem “too easy” (p. 354). There is another OoM problem concerned with the “less definite” a and b have some common property (are somehow of the same type). I owe an account of that (p. 355). A decade later, James Van Cleve, made the same criticism (1994: 586–587). They are both drawing attention to a OoM argument with a premise that is item (1) on Oliver’s helpful list. In my “Postscript”, I offered this paraphrase of the likes of the “less definite”, and rather trivial, (1): a and b resemble each other. (Devitt 2010: 28) But there is a problem with this, neatly demonstrated to me by Jonathan Schaffer: “where ‘some’ can live, any quantifier can live”. Thus, the Ostrich needs to paraphrase not only (1)’s claim that a and b share some common properties but also the more interesting claims that they share all, many, seven, or … properties. The way forward is to note that whenever a and b resemble each other it will be because (S) a and b are both F, for some substitution of the schematic “F”. So, we adopt (S) as our paraphrase of (1). Then the paraphrases for the other quantifications are easily obtained by substituting “all”, “many”, “seven”, or … for “some”.

15.4 Peacock’s Similar but Different Problem Peacock sees “a pressing problem for the Ostrich Nominalist” in dealing with the claim that a and b are “qualitatively the same” “in one respect” but “qualitatively different” in another (2009: 203). He examines five ways for the Nominalist to avoid quantifying over respects and finds them all “unsatisfactory” (2009: 204). One of those ways is, in effect, what I shall now offer. We paraphrase the sameness claim with (S) and the difference claim with: (D) a is F but b is not, or a is not F but b is, for some substitution of the schematic “F”. Peacock takes three problems to “immediately threaten this position”. First, it may require a “higher-order quantification” leading to “ontological commitment to properties”

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(2009: 208). But there is no such requirement and the commitment is only to the predicates that serve as substitutions. Second, and more interesting: A nominalist who says that “Fa and Fb” is a schema which has instances will have to say things like “sentences S1 and S2 are instances of the same schema“. But if one and the same schema has different sentences as instances, it sounds like a schema is a kind of type, and types were precisely what the nominalist was hoping to do without. This argument is parallel to an objection raised repeatedly in Armstrong’s criticism of rival nominalist theories. (Peacock 2009: 208–209) Peacock is right about Armstrong: Armstrong is very fond of this sort of argument. Indeed, he used it in criticizing my Ostrich paper: where Peacock talks of “same schema”, Armstrong talked of “same predicate” (1980: 442). And the Ostrich is very fond of the following sort of response, which indeed I used (Devitt 2010: 26) in responding to Armstrong. The Ostrich’s treatment of sameness of type is quite general: it applies not only to sameness of the type red, but also to sameness of the type schema “F”substitutions. So, the Ostrich follows Quine’s example by saying that various expressions “are all of them” schema “F” substitutions. No types there. Finally, Peacock finds some schema substitutions unsuitable; for example, “a disjunctive predicate like ‘ … is spherical or is a philosopher’ can be true of two particulars without those two particulars exhibiting any qualitative sameness at all” (2009: 209). So, presumably, Peacock does not count sharing the property spherical-or-a-philosopher as “qualitative sameness”. The Ostrich then awaits Peacock’s specification of the sorts of properties that do not thus count. This can then be turned easily into a specification of the sorts of predicates that do not count as substitutions.

15.5

Pickel and Mantegani on Ontological Parsimony

Bryan Pickel and Nicholas Mantegani (“PM”) introduce a “box world” of “a blue sphere”, “a green cube”, “an orange sphere”, and “a blue cone” (2012: 1). They quote (2012: 2) my Occamist criticism of the Realist: “In ontology, the less the better. Therefore this sort of Realist makes us ontologically worse off without explanatory gain” (Devitt 1980: 437). I am implying, as PM note, that the Ostrich’s theory is more parsimonious. PM think that this is “simply wrong”. By comparing theories of the box world, PM argue that “the ostrich’s commitments using Quine’s criterion yields a less parsimonious ontology than that of her realist rivals” (2012: 2). Using that criterion, we see immediately that the Ostrich is committed to six sorts of things: blue things, spheres, green things, cubes, orange things, and cones. Yet, PM argue, the Realist is committed only to four sorts: “particulars, universals, instantiating things, and instantiated things” (2012: 19). PM’s grasp of Quine’s criterion strikes me as excellent. But they misunderstand the Ostrich’s parsimony claim. This misunderstanding is revealed in two ways. (I), in the rival “theories” that PM attribute to the Ostrich and the Realist. PM call these “description[s]” of the box world (2012: 2) and that is apt because that is all they are; thus, the Ostrich’s “theory” is simply the claimed existence of the four objects, “a blue sphere”, “a green cube”, etc. Neither of these “theories” explain anything. Yet what the Ostrich claims to be more parsimonious is not a mere description of the world but a theoretical explanation of 175

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it. As I said, the Realist is less parsimonious in that he adds entities “without explanatory gain”. (II), the misunderstanding is also revealed in PM’s box world. PM say: “This world is supposed to share crucial features with our own” (2012: 1). And so it does; both have spheres, for example. But there is a crucial difference: in the box world, nothing happens. The Ostrich compares theories that attempt to explain the causal structure of the world; to explain why things are as they are and interact as they do. The box world has no such structure. PM’s descriptions of the box world are “mock theories”, not real theories. The distance between PM’s mock theories and real theories can be brought out simply. The Ostrich’s theory of the real world posits Fs because being an F explains phenomena. Any Realist rival must also explain these phenomena. The Realist’s mock theory of the box world posits “particulars, universals, instantiating things, and instantiated things”. These posits will not explain any phenomena of scientific interest. In Section 15.1, we noted Oliver’s “three possible interpretations” of Armstrong’s “request” in posing his OoM problems. One of these, “conceptual analysis”, was quickly dismissed. I have now concluded my presentation of the Ostrich’s response to the “ontological commitments” request.7 I turn to the “truthmakers” request.

15.6

Interpreting Truthmaking

The dominant development in the universals debate since Armstrong introduced Ostrich Nominalism has been the turn to truthmakers: “the idea that truthmakers are the explanans demanded by the Problem of Universals has become a sort of new orthodoxy” (Imaguire 2018: 31). Armstrong attributes “the truth-maker principle” to C. B. Martin and expresses it as follows: … there must be something in the world that makes [a contingent truth] true. “Something” may be taken as widely as may be wished. The “making” … is that in the world in virtue of which the truth is true. (Armstrong 1989: 88) The talk of “truth” in the name of, and motivation for, the truthmaker principle leads Armstrong to interpret the principle as semantic: “The [truth-making] relation … is a crosscategorial one, one term being an entity or entities in the world, the other being … true propositions” (2004: 5).8 Indeed, a semantic interpretation of truthmaking is standard. Thus, Oliver assesses “the truth-maker principle” as “a sanitised version of a correspondence theory of truth” (1996: 69). Despite this, the truthmaker principle can be interpreted as metaphysical. The truth term is very tricky, as many works have shown (e.g., David 1994; Devitt 2001; Horwich 1990; Kirkham 1992). What Martin is really motivating is a metaphysical principle. Consider Armstrong’s counterfactual example of something that needs a truthmaker: “If you had not put your foot on the brake so promptly just then, there would have been a nasty accident” (Armstrong 2004: 1). What we need to explain is something entirely worldly. We want to know why would there have been a nasty accident if you had not put your foot on the brake so promptly just then. What in the world made that so? Martin is right to demand an explanation. But any semantic property of sentences or propositions, including truth, is irrelevant to the explanation. Of course, it can be convenient to use “true” to pose that very same metaphysical question. Thus, if we name Armstrong’s 176

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counterfactual “CF”, then we can ask Martin’s question: “What made CF true?” More importantly, if we want to generalize the question, we have to use “true” (or some similar device). Armstrong is illustrating this in asking for “some way that the world is in virtue of which these [counterfactual] truths are true” (2004: 1). This question about counterfactuals in general is no more semantic than the one about CF in particular. In the apt words of Lewis, the use of “true” is just a way of “making a long story short” (2001: 278); the question “is not at all about truth” (2001: 279). My claims here are simply drawing attention to the oft-noted “disquotational” role of a truth term. This role stems from the “equivalence thesis”: all appropriate instances of the “equivalence schema” s is true iff p hold, where an appropriate instance substitutes for “p” a translation of the statement referred to by what is substituted for “s”. Deflationists like Paul Horwich (1990) think that this is all there is to “true”. But the rest of us who think that there is more to “true” than this – for example, that “true” has an explanatory role in semantic theory – should nonetheless accept the equivalence thesis and hence accept that the truth term has the disquotational role exploited above. The question, “In virtue of what is ‘Snow is white’ true?” can be just another way of asking the metaphysical, and entirely non-semantic, “In virtue of what is snow white?” So, despite its talk of truth, Martin’s principle can be understood as purely metaphysical.9 And, that is how it has to be understood if the Ostrich is to take it seriously. If the principle is understood in the standard semantic way, the Ostrich dismisses it as a misguided attempt to derive a metaphysics from a semantics. Such attempts are wrong in principle (Devitt 1984; 2010). They are particularly wrong where the semantics in question is the unpromising truthmaker principle. So, uses of “true” in what follows should always be understood disquotationally.

15.7 The Metaphysical Request for a Truthmaker The Ostrich is enthusiastic about Martin’s metaphysical principle, understood naturalistically. So, in claiming that “(5) needs no explanation”, the Ostrich is not denying that there is a need for a scientific explanation of what it is for a to be F. Indeed, there obviously is a need unless a being F is a fundamental physical fact. So, for an example, there is a need for a scientific explanation of what it is for a to be red. The Ostrich is denying that there is any need for some non-scientific explanation of a being F;10 there is no need for a metaphysical “grounding”, to use a term that is popular in analytic metaphysics (Schaffer 2009). I summed up the Quinean position: What we are denying can be brought out vividly by taking “F“ to be a fundamental predicate, say a physical predicate. Then … we have nothing to say about what makes a F, it just is F; that is a basic and inexplicable fact about the universe … . Why be dissatisfied with this? Explanation must stop somewhere. What better place than with a fundamental physical fact of our world?11 (Devitt 1980: 436) That is the Ostrich’s response to the OoM request for an ontological commitment, but it works just as well in response to the present request for a truthmaker: the Ostrich simply 177

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dismisses the request; the OoM is still a pseudo problem. Yet the Ostrich’s critics think that the move to truthmakers makes all the difference. Consider Gonzalo Rodriguez-Pereyra: Since the Problem of Universals is the problem of giving a philosophical or metaphysical explanation of how the facts expressed by (1)-(6) are possible … the sort of account in question cannot be one about their ontological commitments. (Rodriguez‐Pereyra 2000: 261) Why not? The Ostrich has no problem at all explaining how it is possible that, say, this rose is red, without positing anything but the rose. We simply look to science for an explanation of how roses can actually be red. Indeed, nothing else is appropriate. Clearly Rodriguez-Pereyra disagrees: Is it not possible to reproduce the ostrich’s strategy about truthmakers? No, for even if ostrich nominalism works for ontological commitments, the truthmaker version is untenable … (Rodriguez‐Pereyra 2000: 267) Why? Rodriguez-Pereyra’s position reflects a crucial move from the principle that Martin motivated to what Peacock calls “the Strong Truthmaker Principle” (2009: 189). Where our “weak” principle demands an explanation of a being F, Rodriguez-Pereyra’s “strong” Principle demands an explanation that is simply in terms of the existence of entities: (TM) Necessarily, if

is true, then there is some entity in virtue of which it is true. (Rodriguez-Pereyra 2005: 18; see also his 2000: 259; Armstrong 2004: 5, 17) Calemi draws out the consequence of moving to (TM): In truthmaker theory only existence matters; but according to the Ostrich Nominalist, it is not the case that such predicative truths as (3) [Socrates is wise] are true solely by virtue of the existence of some entity … . (3) is true if and only if (i) Socrates exists and (ii) he is wise. (Calemi 2016: 42) On the one hand, (TM)’s insistence on a grounding in “existence facts” rather than “predicative facts” (Guillon 2021) is fatal to the Ostrich, as Rodriguez-Pereyra demonstrates: … the truthmaker version of ostrich nominalism fails simply because a sentence like “a is F” may be contingently true. If so, then a does not suffice to make it true that it is F, since “a exists” does not entail “a is F” … Therefore a is not the truthmaker of “a is F”. (Rodriguez‐Pereyra 2000: 267–268) On the other hand, (TM) yields a case for universals, though far from a decisive one; think of tropes. (TM) demands the existence of some entity other than a. The universal, Fness, will spring immediately to the Realist’s mind:

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… it becomes entirely natural and reasonable to postulate that [a] has properties that are objectively there, and that one or more of these properties is the truthmaker. (Armstrong 2004: 41) Yet the existence of F-ness, even along with the existence of a, won’t suffice to ground a being F: a might not instantiate F-ness. So, as Oliver points out (1996: 71–72), the Armstrongian Realist is likely to take the truthmaker to be a “state of affairs” that includes F-ness. In sum, the response to the Ostrich’s dismissal of the truthmaker interpretation of the OoM rests entirely on the strong (TM). But why accept (TM)? The question is particularly pressing given that, as Helen Beebee and Julian Dodd nicely remark, “from a Quinean perspective”, (TM) yields such “ontological exotica” as “states of affairs or tropes” (2005: 3). The Ostrich totally rejects (TM) as just another bit of unnatural metaphysics. As Peacock says, “what ‘makes it true’ that a is F is simply the existence of a particular that is a certain way, i.e., is F” (2009: 189). Speaking for the Ostrich, Lewis rightly says, such predications are “true not because of whether things are, but because of how things are” (1992: 216). Rodriguez-Pereyra has responded to doubts about (TM) with two arguments.12 First: But if being how it is is what makes the proposition that the rose is red true, being how it is is also what makes the proposition that the rose is light true, the proposition that the rose is fragrant true, and so on. But this is wrong. For what makes true that the rose is red is not what makes true that the rose is light. What makes true that the rose is red is that it is red, while what makes true that the rose is light is that it is light. (Rodriguez‐Pereyra 2005: 23) When the Ostrich says that it is how (the way) the rose is that makes it red, of course she does not mean that it is how the rose is in general that does the making. She means that it is how the rose is in particular, without being specific. If specificity is demanded, she can follow Rodriguez-Pereyra: “What makes true that the rose is red is that it is red”. That’s trivial, of course. If more is demanded, the Ostrich directs us to the science of colors. “What makes the rose light?” The Ostrich has a different trivial answer, backed up by a different science. To point out these differences is not, contrary to Rodriguez-Pereyra, to “quantify over ways” (2005: 23); there is no mention of ways. In sum, nothing here ruffles the Ostrich’s feathers. This is the appropriate place to consider Rodriguez-Pereyra’s claim that the truthmaker approach “transforms the Problem of Universals” from our OoM “into the Many over One, that is, the problem of explaining how the same particular can have different properties” (2000: 255). To the Ostrich, this is just another pseudo problem: the rose can be red without being light and vice versa. Nothing more needs to be said beyond the scientific explanations of being red and being light. Rodriguez-Pereyra’s second argument for (TM) is as follows: 1 2 3 4

Truth is grounded. Grounding is a relation. Relations link entities. Therefore, truth is grounded in entities. (2005: 25)

The Ostrich accepts (1) provided it is understood as the claim that non-fundamental facts are scientifically explicable in terms of other facts. Take the case of the rose. The Ostrich 179

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thinks that the rose is red because, according to the science of colors, it is P (and not, spuriously, because it is red). That’s all there is to the idea of grounding that RodriguezPereyra nicely motivated earlier (2005: 21). So, (2) is false: grounding is not a relation. Rodriguez-Pereyra’s argument to the contrary (2005: 26–31), with its uncalled-for talk of “propositions” and “facts”, simply begs this question. The only entity that we need to talk about here is the rose, just as the Ostrich always thought.

15.8 Imaguire’s “Priority Nominalism” I turn finally to Guido Imaguire’s “Priority Nominalism” (2018). Imaguire admires Ostrich Nominalism but thinks that it needs supplementation with “a new tool of analytic metaphysics”, grounding (2018: ix; see Chapter 17, this volume, for details). “Fundamental” truths have no grounds. Imaguire’s dramatic break with the Ostrich is his claim that “only fundamental truths are really ontologically committing” (2018: ix); “some sentences can be considered true, but their commitment may be neglected as merely apparent” (2018: 90). Consequently, properties (like tropes and states of affairs) are derivative and, therefore, they do not really exist, i.e., they “exist” just in a “misleading” and not in an ontologically regulated manner of speaking. From a strict ontological perspective, there are only particulars. (Imaguire 2018: 40) I shall not argue against this unwelcome departure from Quinean orthodoxy, but rather consider its motivation. The motivation comes from an old objection (Alston 1958) to the Quinean strategy of avoiding the unwanted ontological commitments of S by adopting a paraphrase S* that lacks those commitments. Imaguire raises the objection like this: “Why should we suppose that it is S and not S* that deceives us?” (2018: 29). Thus, in Section 15.1, I offered (5), which has no commitment to universals, as a paraphrase of (6), which has. But why prefer (5) to (6)? Imaguire claims that such a preference is “apparently arbitrary” (2018: 87). He thinks that we need Priority Nominalism to solve this “serious problem” (2018: 88) for the Ostrich: the priority nominalist solves it by means of the notion of grounding: compare the facts expressed by S and S* in terms of ontological fundamentality and apply the commitment criterion only to the most fundamental one (Imaguire 2018: 29) The persistent paraphrase objection stems from a misunderstanding of what Quine has in mind in talking of paraphrases. Quine does not have in mind that S and S* “have to have the same meaning”, “express the same informational content”, or be “made true by the same truthmakers” (Imaguire 2018: 88). Nor do Mellor and Oliver have Quine right in the following discussion (cited by Imaguire 2018: 87): Suppose we have a sentence S, apparently committed to some entity e, and an equivalent sentence [S*] which is said to be uncommitted to e. This, it is said, shows that S is only apparently committed to e. (Mellor and Oliver 1997b: 15) 180

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Paraphrasing is best thought of as a sort of theory choice. Suppose that e is a novel posit, for example, a universal: so, our theories are not already committed to universals. Suppose that a theorist is entertaining S, which is really, not just “apparently”, committed to e, but finds a paraphrase S*, which has no such commitment. Suppose, finally, that S yields no explanatory gain over S*. Then the theorist should choose S*; that’s the dictate of Quine’s Occamism (Section 15.5). As I said in response to Mellor and Oliver, [S*] will serve his purposes well enough. He thus “frees himself from ontological commitments of his discourse” (Quine 1961[1953]: 103). His commitment to e is only apparent not real: it arose from “an avoidable manner of speaking” (Quine 1961[1953]: 13). (Devitt 2010: 25) To emphasize, S is really committed to e, but S* is not. And that is why the theorist prefers S*, thus removing his own commitment to e. There is nothing in the least “arbitrary” about the replacement: it is guided by an Occamist principle that plays a major role in scientific theory choice. In sum, the Ostrich has no need of grounding to keep out universals.13

Notes 1 In one brief chapter ( 1978: 58–63), Armstrong rightly acknowledges some other arguments for universals arising from apparent references to a universal, as in “Red is a color”, and apparent quantifications over them, as in “He has the same virtues as his father”. 2 “Ostrich Nominalism has been treated with disdain” ( Imaguire 2018: xiii). 3 But Quineans do not dismiss the problems and arguments alluded to in note 1. Indeed, it is because Quine (1980) thinks that our best theories have to quantify over universals that Quine himself is not a nominalist. 4 Oliver remarks, “Terminology is a mess here” ( 1996: 44, n. 46), before offering some useful clarifications. Suffice it to say, the Quinean rejection of the OoM as an argument for “universals” should be taken as a rejection of it as an argument for Platonic universals, Aristotelian universals, properties, attributes, classes, etc. I shall talk simply of “universals”. 5 This is Campbell’s “A question”; (2) raises his “B question” ( 1990: 29). 6 Consider also: “In the end, even Armstrong himself cannot afford to take predicates with the same ontological seriousness that he nonetheless demands from the Ostrich Nominalist” ( Calemi 2016: 39). 7 Calemi (2016) has a neat criticism of the Ostrich based on an assumption about anaphora. But the assumption is false, as the phenomenon of copredication shows. 8 Mulligan et al. 1984, which seems to have introduced contemporary talk of “truthmakers”, takes the concern of truthmaker theory to be with “the complex and bewildering difficulties of the relations between language and the real world” (1984: 288). 9 Hornsby notes that “truthmakers have two different agenda”, one “ontological”, one the nature of “truth” ( 2005: 33). Melia notes that “Armstrong frequently treats truthmaking as a supervenience relation holding between different states of affairs, rather than a relation holding between states of affairs and sentences” ( 2005: 79). 10 As Melia’s “sensible nominalist” also denies ( 2005: 70). 11 As Guillon points out, everyone in the debate stops somewhere ( 2021: 84–86). According to Giladi “Hegel’s realism can be read as directly opposed to Devitt’s claim that the best terminus for explanation is ‘a fundamental physical fact of our world’”. (2014: 738) 12 Armstrong offers no argument, seeming to find (TM) obvious ( 1989: 89; 2004: 42). 13 My thanks to the following for comments on a draft: Francesco Calemi, Anthony Fisher, Paul Giladi, Jean-Baptiste Guillon, Guido Imaguire, Anna-Sofia Maurin, Howard Peacock, Bryan Pickel, Gonzalo Rodriguez-Pereyra, and Jonathan Schaffer.

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References Alston, W. (1958) Ontological Commitments. Philosophical Studies 9(1-2): 8–17. Armstrong, D.M. (1978) Nominalism and Realism I: Universals and Scientific Realism. New York: Cambridge University Press. Armstrong, D.M. (1980) Against ‘Ostrich Nominalism’: A Reply to Michael Devitt. Pacific Philosophical Quarterly 61(4): 440–449. Reprinted in Mellor and Oliver 1997a: 101-111. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (2004) Truth and Truthmakers. Cambridge: Cambridge University Press. Beebee, H. and Dodd, J. (eds.) (2005a) Truthmakers: The Contemporary Debate. Oxford: Oxford University Press. Beebee, H. and Dodd, J. (2005b) Introduction. In Beebee and Dodd 2005a: 1–16. Calemi, F.F. (2016) Ostrich Nominalism or Ostrich Platonism? In Calemi, F.F. (ed.) Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. Berlin: De Gruyter: 31–49. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. David, M. (1994) Correspondence and Disquotation: An Essay on the Nature of Truth. Oxford: Oxford University Press. Devitt, M. (1980) ‘Ostrich Nominalism’ or ‘Mirage Realism’? Pacific Philosophical Quarterly 61: 433–439. Reprinted in Mellor and Oliver 1997a: 93-100. Reprinted in Devitt 2010 with new Postscript: 13-30. Devitt, M. (1984) Realism and Truth. 2nd ed. 1991. Oxford: Basil Blackwell. Devitt, M. (2001). The Metaphysics of Truth. In Lynch, M. (ed.) The Nature of Truth. Cambridge, MA: MIT Press: 579–611. Reprinted in Devitt 2010: 155-181. Devitt, M. (2010) Putting Metaphysics First: Essays on Metaphysics and Epistemology. Oxford: Oxford University Press. Devitt, M. (2014) We Don’t Learn About the World by Examining Concepts: A Response to Carrie Jenkins. In Neta, R. (ed.) Current Controversies in Epistemology. New York: Routledge: 23–34. Giladi, P. (2014) Ostrich Nominalism and Peacock Realism: A Hegelian Critique of Quine. International Journal of Philosophical Studies 22(5): 734–751. Guigon, G. and Rodriguez-Pereyra, G. (eds.) (2015) Nominalism about Properties: New Essays. New York: Routledge. Guillon, J.-B. (2021) A Common Sense Defence of Ostrich Nominalism. Philosophia 49(1): 71–93. Hornsby, J. (2005) Truth without Truthmaking Entities. In Beebee and Dodd 2005a: 33–47. Horwich, P. (1990) Truth. 2nd ed. 1998. Oxford: Clarendon Press. Imaguire, G. (2018) Priority Nominalism: Grounding Ostrich Nominalism as a Solution to the Problem of Universals. Cham: Springer Nature. Kirkham, R. (1992) Theories of Truth: A Critical Introduction. Cambridge, MA: MIT Press. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Reprinted in Mellor and Oliver 1997a: 188-227. Lewis, D. (1992) Critical Notice of David Armstrong, A Combinatorial Theory of Possibility. Australasian Journal of Philosophy 70(2): 211–224. Lewis, D. (2001) Forget about the ‘Correspondence Theory of Truth’. Analysis 61(4): 275–280. Mantegani, N. (2015) Avoiding Ad Hoc Ontology. In Guigon and Rodriguez-Pereyra 2015: 189–207. Melia, J. (2005) Truth-Making without Truth-Makers. In Beebee and Dodd 2005a: 67–84. Mellor, D.H., and Oliver, A. (eds.) (1997a) Properties. Oxford: Oxford University Press. Mellor, D.H. and Oliver, A. (1997b) Introduction. In Mellor and Oliver 1997a: 1–33. Mulligan, K., Simons, P., and Smith, B. (1984) Truth-Makers. Philosophy and Phenomenological Research 44(3): 287–321. Oliver, A. (1996) The Metaphysics of Properties. Mind 105(417): 1–80. Peacock, H. (2009) What’s Wrong with Ostrich Nominalism? Philosophical Papers 38(2): 183–217. Pickel, B. and Mantegani. N. (2012) A Quinean Critique of Ostrich Nominalism. Philosophers’ Imprint 12(6): 1–21. Quine, W.V. (1961[1953]) From a Logical Point of View. Cambridge, MA: Harvard University Press. Quine, W.V. (1980) Soft Impeachment Disowned. Pacific Philosophical Quarterly 61(4): 450–451. Rodriguez-Pereyra, G. (2000) What is the Problem of Universals? Mind 109(434): 255–273.

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Ostrich Nominalism Rodriguez-Pereyra, G. (2005) Why Truthmakers. In Beebee and Dodd 2005a: 17–31. Schaffer, J. (2009) On What Grounds What. In Chalmers, D., Manley, D., and Wasserman, R. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Oxford University Press: 347–383. Summerford, J. (2003) Neither Universals nor Nominalism: Kinds and the Problem of Universals. Metaphysica 4(1): 101–126. Van Cleve, J. (1994) Predication Without Universals? A Fling with Ostrich Nominalism. Philosophy and Phenomenological Research 54(3): 577–590.

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16 CLASS NOMINALISM AND RESEMBLANCE NOMINALISM Gonzalo Rodriguez-Pereyra

16.1

Introduction

I take the Problem of Universals to be the problem of accounting for the truthmakers of predications attributing so-called sparse or natural properties to particulars (for the distinction between sparse and abundant properties see Lewis 1983; Schaffer 2004; Chapter 4, this volume; for my interpretation of the Problem of Universals as a problem about truthmakers see Rodriguez-Pereyra 2000 and 2002: 14–30). On this interpretation of the problem, theories of universals and theories of tropes make universals and tropes, respectively, part of the truthmakers of predications attributing sparse properties to particulars. But Class and Resemblance Nominalism reject both universals and tropes. Instead, Class Nominalism identifies sparse properties with natural classes (or sets), where being natural is a primitive feature of certain classes. For instance, assuming for simplicity that being red is a sparse property, such a property is the class of red things according to Class Nominalism. Accordingly, the truthmakers of propositions predicating redness of certain things are the facts that the things in question belong to the class of red things. If a certain apple, call it a, is red, the truthmaker of the proposition that a is red is the fact that a belongs to the class of red things. Philosophers who have expressed sympathy for different versions of Class Nominalism include Anthony Quinton (1957) and David Lewis (1986: 50–53, 1983: 344–351), although neither Quinton nor Lewis adhered to my interpretation of the Problem of Universals. The central idea of Resemblance Nominalism is that resemblance is basic in the account of commonality of sparse properties. Thus, suppose that being red is a sparse property (a supposition I will continue to make hereafter), and that there are two red apples. Resemblance Nominalism says that they are red because they resemble each other, not that they resemble each other because they are red. Resemblance Nominalism can be taken to be the theory that sparse properties are resemblance classes, that is, classes such that their membership conditions can be stated in terms of resemblance. According to Resemblance Nominalism – at least according to the version of Resemblance Nominalism I am now considering – the property of being red is the class of red things. Accordingly, the

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truthmakers of propositions predicating redness of certain things are the facts that the things in question belong to the class of red things. If a certain apple, call it a, is red, the truthmaker of the proposition that a is red is the fact that a belongs to the class of red things, but since the class of red things is a resemblance class, the truthmaker is the fact that a resembles certain things and fails to resemble other things. Different versions of Resemblance Nominalism have been held by Rudolf Carnap (1967) and Gonzalo Rodriguez-Pereyra (2002). There are also philosophers who have felt the attraction of Resemblance Nominalism, without having accepted it; these include H.H. Price (1953) and W.V. Quine (1969).1 Thus Class Nominalism and Resemblance Nominalism – at least given how I have represented them so far – are akin in that both identify sparse properties with classes. But while in Resemblance Nominalism resemblance plays an essential role in the characterization of such classes and thus in distinguishing the classes properties are from other classes, resemblance plays no such role in Class Nominalism – instead, as I said, what makes natural classes natural is a primitive fact about them. Given the affinity between Class Nominalism and Resemblance Nominalism some suspect, and others think, that they are two formulations of one and the same theory (see Lewis 1983: 348, fn. 9; Guigon 2009: 189, fn. 1; Busse 2016: 693, and 2018: 447–448). Whether they are two formulations of one theory or whether they are two different theories depends both on issues of theory individuation – issues I cannot discuss here – and what versions of Class Nominalism and Resemblance Nominalism one is considering. Thus I shall remain non-committal on this question, but it is clear that even if they are two different theories, there is a considerable affinity between them. At this point someone might doubt the nominalistic pedigree of these two theories. For classes are abstract objects, and doesn’t Nominalism consist in the rejection of abstract objects? The answer is that “Nominalism” is an ambiguous word. In one sense it means the rejection of abstract objects. This sense of the word dates back to the 1940s, to the work of Nelson Goodman and Quine (1947). In another sense the word means the rejection of universals, and this usage goes back to the Middle Ages. Class Nominalism and Resemblance Nominalism are nominalistic theories in the latter sense. They reject universals. But they don’t need to reject abstract objects. And they don’t reject them if, as there is reason to think, classes are abstract objects. As we shall see later, the identification of properties with classes presents a serious problem for Class Nominalism and Resemblance Nominalism, but the problem is not that classes are abstract objects. Indeed, it has been argued that Resemblance Nominalism need not identify properties with classes, since it need not identify them with anything (Rodriguez-Pereyra 2002: 61). This version of Resemblance Nominalism says that what makes true, or grounds, that a certain particular is, say, red, is that it resembles other particulars – but it refuses to identify properties with classes or anything else. This version of Resemblance Nominalism is eliminativist about properties. I used to prefer this version of Resemblance Nominalism (Rodriguez-Pereyra 2002: 61). But now I think properties must be accepted in one’s ontology, although they are not classes or sets. Thus, I shall sketch in Section 16.4 a way in which both Class and Resemblance Nominalism can be developed so that they admit properties without identifying them with classes. If these theories can indeed be developed in this way, they have the resources to cope with a problem that has been thought to be lethal to them, namely the problem of coextensive properties.

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16.2

Some Problems for Class and Resemblance Nominalism

There are many problems that Class Nominalism and Resemblance Nominalism face. Some of them have to do with the identification of classes and properties, and I shall consider the most important of these below, in Section 16.4. Resemblance Nominalism also faces additional problems having to do with taking resemblance as a primitive. For instance, David Armstrong has argued that Resemblance Nominalism must take the formal properties of resemblance (reflexivity, symmetry, and non-transitivity) and exact resemblance (reflexivity, symmetry, and transitivity) as primitive, while the Theory of Universals can derive such formal properties from those of sharing some universal with and sharing all universals with (see Armstrong 1997: 23). It is not clear how forceful this objection is, since every theory will have its own primitive and some features of the primitive will have to be primitive too. Nevertheless, it has been argued that such formal properties of resemblance and exact resemblance can be derived from more basic principles (Rodriguez-Pereyra 2002: 72–79). Another issue having to do with the properties of resemblance is its adicity: does resemblance ever link more than two particulars? The opinions are divided: I argue that this is not the case (Rodriguez-Pereyra 2002: 80–81), while Ghislain Guigon (2009: 29–62) and Ralf Busse (2018: 453–454) argue that resemblance can link more than two particulars. The issue is important because if resemblance is “collective”, i.e., if it can link more than two particulars, a very famous problem for Resemblance Nominalism, the so-called Imperfect Community Difficulty, does not really arise. The problem consists in characterizing classes in terms of resemblance that do not apply to classes whose members resemble pairwise but that, intuitively, do not share any property. For instance, the class formed by three things as follows: a yellow, square, and hard thing, a yellow, round, and soft thing, and a red, square, and soft thing. The Imperfect Community difficulty, however, can be solved using a “dyadic” resemblance relation (i.e., one that links at most two particulars), but this predicate must apply not only to concrete particular things but also to their pairs (see Rodriguez-Pereyra 2002: 156–176 for details). Another issue is whether the resemblance relation invoked by Resemblance Nominalism is contrastive or not. A contrastive resemblance relation is one that holds between particulars that resemble each other and particulars they don’t resemble: “x1, x2 … resemble each other and do not equally resemble any of y1, y2, …” is a predicate expressing a variably polyadic contrastive resemblance relation. Busse (2018) adopts a contrastive resemblance relation (see also Lewis 1983), while Rodriguez-Pereyra (2002) adopts a noncontrastive resemblance relation. A contrastive resemblance relation permits one to deal in a straightforward manner with the so-called Companionship Difficulty. This difficulty arises when all the Fs are G but not vice versa. In this case, there are things outside the class of Fs, namely the Gs that are not F, that resemble all the Fs. The problem then is to specify resemblance conditions satisfied by all classes corresponding to properties, including classes, like the class of Fs in this example, which are properly included in other such classes. A contrastive resemblance relation solves the Companionship Difficulty since the Fs resemble one another in contrast to Gs that are not F (see Paseau 2015: 106). But this is not necessary, since the Companionship Difficulty can also be solved using a non-contrastive resemblance relation, provided this relation comes in degrees. Briefly, the idea is that there is a lowest degree of resemblance to which the members of classes corresponding to properties resemble each other, and that no class C1 corresponding to a property is

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included in another class C2 corresponding to a property such that the lowest degree to which any two members of C1 resemble each other is the lowest degree to which any two members of C2 resemble each other. Assuming that the class of Fs is properly included in the class of Gs (and that the class of Gs is not properly included in any other class corresponding to a property), the lowest degree to which the Fs resemble each other is 2 and the lowest degree of resemblance to which the Gs resemble each other is 1. This is the basic idea, and a simplification of the actual solution to this difficulty, which is more complicated (see Rodriguez-Pereyra 2002: 177–185 for details). There are, as it should be expected, different views about how to measure the degrees of resemblance between two particulars (or more particulars, for those who believe in “collective” resemblance). For discussion see Rodriguez-Pereyra (2002: 65–69) and Ben Blumson (2018 and 2022). A traditional objection to Resemblance Nominalism is Bertrand Russell’s infinite regress of resemblance. According to Russell, if resemblance is not a universal, there must be a different resemblance for each pair of resembling things; but then these resemblances will have to resemble each other. Thus either one embarks on an infinite regress or one has to admit that resemblance is a universal (Russell 1997: 48). What is vicious, however, is Russell’s argument, for it implicitly reifies resemblance. Indeed, without the reification of resemblance it makes no sense to claim that individual resemblances resemble each other. But the Resemblance Nominalist does not reify resemblance: in the Resemblance Nominalist ontology there are resembling entities, but their resemblance is not a further entity. Once this is pointed out, there is no opportunity for a regress of resemblances to arise (see Rodriguez-Pereyra 2001; 2002: 105–123, and 2004 for a fuller discussion of Russell’s regress).

16.3 Advantages of Class and Resemblance Nominalism What are the advantages of Class Nominalism and Resemblance Nominalism over alternative theories, specifically over the Theory of Universals and the Theory of Tropes? Since classes are particulars, it is sometimes held that their advantage over the Theory of Universals consists in ontological economy: while Class Nominalism and Resemblance Nominalism admit particulars and only particulars in their ontology, the Theory of Universals admits both particulars and universals in its ontology. But not only will this not work against the Theory of Tropes (since it also only admits particulars in its ontology), it does not really work against all versions of the Theory of Universals, since some versions of it are eliminativist about particulars. Such versions of the Theory of Universals admit only universals. There are many respects in which metaphysical theories can be compared, and different philosophers will assign different weights to different respects. For instance, those who think that preserving intuitions and accepted opinions is the preeminent parameter of theory comparison might think that Class Nominalism and Resemblance Nominalism are inferior to the Theory of Universals and the Theory of Tropes. This is because, for instance, according to Resemblance Nominalism it is because two apples resemble each other that they are red, while the common intuition is that they resemble each other because they are red. Similarly, according to Class Nominalism, whether something has a certain property must be an extrinsic fact about it, since whether something is a member of a class (at least of a non-singleton class) must be an extrinsic fact about it, and yet the common intuition is that whether something has a property can be an intrinsic fact about it. It should be noted that not every alternative to Class Nominalism and Resemblance Nominalism is free from 187

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problems with intuitions. Some versions of the Theory of Universals, for example, violate the intuition that entities cannot be located at many places at the same time. However, although I cannot argue the point at length here, it seems to me that Class Nominalism and Resemblance Nominalism are more counterintuitive than the Theory of Universals and the Theory of Tropes. Nevertheless, when the comparison is between metaphysical theories postulating a definite ontology, preserving intuitions and common opinions cannot be the preeminent parameter of comparison, since intuitions and such opinions are no more than uncritical beliefs and there is no reason to expect them to be true. In this sense, Metaphysics is like Physics, a discipline in which it makes little sense to respect intuitions and pre-theoretical opinions. On the other hand, in any area of research – whether philosophical or not – it is of the utmost importance to have as much independent evidence as possible for the entities postulated by theories. This is done by avoiding, in so far as possible, ad hoc ontology, i.e., avoiding, in so far as possible, the postulation of entities whose only or main reason to believe in is that they solve one or more particular problems or play one or more particular theoretical roles. Thus, given that there is more independent evidence for concrete particulars and classes than there is for universals and tropes, Class Nominalism and Resemblance Nominalism are superior to the Theory of Universals and the Theory of Tropes. For further discussion of this and related points, see Rodriguez-Pereyra (2002: 199–221). For a dissenting voice, see Nicholas Mantegani (2015).2 Which one of Class Nominalism and Resemblance Nominalism is better? Here the difference cannot consist in a difference in ontology, since both theories have the same ontology. In my view, Resemblance Nominalism is superior to Class Nominalism because it is explanatorily more powerful. Since Class Nominalism takes the naturalness of natural classes to be a primitive fact about them, Class Nominalism cannot explain what distinguishes natural from non-natural classes: certain classes are natural and others are not, and that’s all there is to it. Resemblance Nominalism, on the other hand, can explain that difference: classes are natural if and only if their members satisfy certain resemblance conditions. For further discussion of these points see Rodriguez-Pereyra (2002: 222–226).

16.4

The Coextension Difficulty

The best-known difficulty for both Class and Resemblance Nominalism is the Coextension Difficulty. Suppose that the class of Fs is a property, the property F. And suppose that the class of Fs is the class of Gs. Then that class is also the property G. So the properties F and G are one and the same. But for many substitution instances of “F” and “G”, this is wrong. The classical example is that in which “is a cordate” and “is a renate” are substituted for “F” and “G”. Clearly, the properties of being a cordate and being a renate are not one and the same property. I actually think this is a bad example, since class and resemblance nominalists should identify being a cordate and being a renate with different classes (see Rodriguez-Pereyra 2002: 97–98). But it doesn’t matter. Even if being a cordate and being a renate are not coextensive properties, it is likely that there are other examples, for example the mass and the charge of electrons. In any case, even if there are no actual cases of coextensive properties, it is clear that there could have been different but coextensive properties (see Rodriguez-Pereyra 2002: 98 for an argument), and this is enough to cause trouble for Class and Resemblance Nominalism. 188

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One possible solution to this problem is to adopt Lewisian Modal Realism. If F and G are not necessarily coextensive, there could have been Fs which are not G, or Gs which are not F. On Lewisian Modal Realism this means that there is a possible world where there are Fs which are not G and/or there is a possible world where there are Gs which are not F. And on Lewisian Modal Realism this means that there are Fs which are not G and/or there are Gs which are not F, if the quantifier is used without restricting it to the actual world. Thus the Class Nominalist and the Resemblance Nominalist can identify the property F with the class of all Fs, including those existing in other possible worlds. Similarly, they can identify the property G with the class of all Gs, including those existing in other possible worlds. In this way they can avoid the identification of the properties F and G, since those classes are two distinct classes. These are the classes Lewis identifies properties with, and in my book on Resemblance Nominalism I argued that Resemblance Nominalists should be modal realists of the Lewisian variety, precisely in order to solve the Coextension Difficulty (Rodriguez-Pereyra 2002: 99). I was then a committed Lewisian modal realist. But if the modal realist solution works at all, it can only work for contingently coextensive properties. Couldn’t there be necessarily coextensive properties? I used to think that there are no necessarily coextensive properties, and that any apparent example of necessarily coextensive properties was a case of semantically different predicates applying in virtue of one and the same property (Rodriguez-Pereyra 2002: 100). But I have come to see, finally, that Lewisian Modal Realism is wrong. Why? Basically because, as many have pointed out, those enormous island universes Lewis calls possible worlds have nothing to do with modality. There is no reason why a horse in one of those universes should be a merely possible horse (van Inwagen 2001: 226). Additionally, I now find the rejection of necessarily coextensive properties unpersuasive. So, can Class and Resemblance Nominalism avoid the Coextension Difficulty without adopting Lewisian Modal Realism? Yes, and this is what I shall argue now. There is a variety of proposals about how Class or Resemblance Nominalism can deal with the Coextension Difficulty in an actualist setting. Here I shall sketch what I take to be the most promising option. But first let me indicate why I find some of the other proposals more or less unsatisfactory. First, it will not do to postulate ersatz possible worlds, i.e., abstract objects – whatever they may be – that play the role of possible worlds. Typically, the objects in those ersatz possible worlds are abstract objects, and no abstract object is red, or square, or has some of the other properties for which Class and Resemblance Nominalism try to account for. So the objects in those ersatz possible worlds cannot be the members of the classes Class and Resemblance Nominalism single out as properties. This point might be thought to be too quick, since one might take ersatz possible worlds to be Lagadonian set-theoretical constructions in which every object functions as a name for itself and every property or relation functions as a name for itself. This is the proposal suggested by Busse (2016), although he does not advance it to deal with the co-extension difficulty. But in Class Nominalism and Resemblance Nominalism properties are classes, so if properties F and G are coextensive they will be one and the same class and therefore one and the same property. The set-theoretical construction will be the same as and so there is no way of differentiating coextensive properties F and G on this proposal. Another way of getting around the Coextension Difficulty has been proposed by Guigon (2015). He proposes that the Resemblance Nominalist should adopt Counterpart Theory in an actualist setting. Thus, although property F may be one and the same with property G, the F-counterparts of the actual F/Gs need not be the same as their G-counterparts. And 189

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so the Class Nominalist and the Resemblance Nominalist can maintain the identity of properties F and G while at the same time accounting for the strong intuition that something could have been F without being G. But even if this proposal accounts for such an intuition, it cannot account for the intuition, also a strong one, that F and G, or being F and being G, are two distinct properties. Indeed, the account assumes that coextensive properties are identical. One could also appeal to degrees of similarity and say that in cases of coextension, the particulars having the coextensive properties resemble to a degree higher than 1 (see for example Paseau 2015: 108). If there are coextensive properties, then this allows one to distinguish a case where certain particulars share just one property, from a case where particulars instantiate two coextensive properties (they resemble to degree 2), from a case where certain particulars instantiate three coextensive properties (they resemble to degree 3), and so on. But if properties are classes, as they are in the version of Resemblance Nominalism we are considering, then this is not enough, for it does not allow one to distinguish two coextensive properties F and G: if the class of Fs is the same as the class of Gs, then they are one and the same property, and so the Fs/Gs resemble to degree 1 (assuming the class of Fs/Gs is not included in a class corresponding to another property, which, even if it is the case, does not affect the substantive point I am making, namely that merely introducing degrees of resemblance does not help with the present problem if properties are classes). Let me now sketch a different solution to the Coextension Difficulty. Predicates predicate conditions, and such predicable conditions are what properties, in the primary sense of the term, are.3 Thus, in this sense of the term, the property of being human is what the predicate “is human” predicates of things. Clearly a property understood in this way cannot be a class (or a universal, or a trope), for a class (or a universal, or a trope) is not a predicable condition. Being a class (universal/trope) is of course a predicable condition, but a class (universal/trope) is not being a class (universal/trope) but what satisfies the predicable condition being a class (universal/trope). How does a class stand to the corresponding predicable condition? On both Class and Resemblance Nominalism classes are the correlates of the relevant (i.e., sparse) predicable conditions in the sense that particulars must relate to them in a particular way – they must belong to them – for those particulars to satisfy the corresponding predicable condition. It is only in this sense that it makes any sense to call classes (or universals, or tropes) properties: they are what particulars must be related to for them to satisfy properties in the sense of predicable conditions. But classes are not really properties: they are the correlates of properties, that is, of predicable conditions. Now, there is no reason why different predicable conditions cannot necessarily have the same correlates. Indeed, if there is a necessary connection between two predicable conditions, and nothing can have one without having the other, why should it not be the case that what particulars must be related to in order to satisfy those two predicable conditions cannot be the same thing? Thus, if class and resemblance nominalists take classes to be the correlates of predicable conditions, necessarily coextensive properties present no problem at all. There is no wrong identification of two different properties here. There are two predicable conditions, that is, two properties, having one and the same correlate. Now what I have just said about necessarily coextensive properties can be extended to contingently coextensive properties. For there is no reason why contingently coextensive predicable conditions should not have the same correlate. Thus, if classes are the correlates 190

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of predicable conditions, contingently coextensive properties present no problem at all. There is no wrong identification of two different properties here. There are two predicable conditions, that is, two properties, having one and the same correlate. But is this really plausible in the case of contingently coextensive properties? If two properties are only contingently coextensive, they are independent, and therefore an explanation might be demanded of why what makes particulars satisfy them should be one and the same fact. Shouldn’t one expect that independent predicable conditions are always grounded in different facts, as in the Theory of Universals? No, one shouldn’t expect such a thing in theories like Class and Resemblance Nominalism. Indeed, it is easy to see that according to these theories it is possible that the satisfaction of two independent predicable conditions is grounded in one and the same fact – in other words, it is possible that the truthmaker for propositions stating that a certain object satisfies independent predicable conditions is one and the same fact. Take the properties, that is, predicable conditions, of being red and being square. They are not coextensive, and according to Class and Resemblance Nominalism what makes particulars satisfy being red is that they belong to a certain class and what makes particulars satisfy being square is that they belong to a different class. Now, since particulars are contingent entities, there must be a possibility in which the only particulars that are red are the particulars that are actually red and square, and the only particulars that are square are the particulars that are actually red and square. This is a possibility in which the properties of being red and being square are coextensive. If that possibility obtained, what would make anything satisfy being red would be exactly the same as what would make it satisfy being square, namely being a member of one and the same class: the class of red particulars, that is, the class of square particulars. The key to this solution is the distinction between properties, as predicable conditions, and their correlates, which Class and Resemblance Nominalism take to be classes and other theories take to be universals or tropes. But can Class and Resemblance Nominalism accept properties in the sense of predicable conditions? Why not? Well, presumably such predicable conditions are abstract, and Nominalism rejects abstract objects. But as it was pointed out in Section 16.1, Class and Resemblance Nominalism are nominalistic theories in the sense that they reject universals, not abstract objects; indeed it is perfectly possible for them to accept abstract objects. Someone might argue that predicable conditions are, basically, universals. After all, many of them can be satisfied by many different particulars. But they are not universals. Nor are those predicable conditions that can be satisfied by only one particular trope. First, tropes, and universals on Aristotelian conceptions of them, are located in space and time, while predicable conditions are not located in space or time. Tropes and universals thus conceived are concrete, while predicable conditions are abstract. Of course, universals can be conceived Platonically as abstract objects. But even here there is a crucial difference: universals and tropes, whether abstract or concrete, are supposed to be what makes particulars satisfy certain predicable conditions – alternatively, they are what account for the fact that particulars satisfy certain predicable conditions. Thus they cannot be predicable conditions. But on the view of properties as predicable conditions, properties are not classes. So, can Class and Resemblance Nominalism really adopt this solution? Yes, because Class and Resemblance Nominalism are theories of what makes particulars satisfy predicable conditions, and what they say is that belonging to certain classes is what makes particulars 191

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satisfy predicable conditions. Thus the identification of properties with classes is not essential to them. Similarly, the Theory of Tropes and the Theory of Universals are also theories of what makes particulars satisfy predicable conditions, and thus the contrast between these theories is still the same: where other theories postulate universals and tropes, Class and Resemblance Nominalism postulate classes. Note, also, that on this conception Class and Resemblance Nominalism are still theories of sparse properties – or, more strictly, theories of the correlates of sparse properties. For although not every predicable condition plays the roles usually associated with sparse properties, some of them do; and it is about these that Class and Resemblance Nominalism say that their correlates are classes. But if properties are predicable conditions, what is the role of classes in these theories? To account for what makes particulars satisfy predicable conditions. When something is red, it satisfies the predicable condition of being red, and what makes it satisfy it is that it belongs to a certain class. Thus classes, in so far as they are the correlates of predicable conditions, form part of the truthmakers of propositions stating that a certain particular satisfies a certain predicable condition, e.g., the proposition that a is red. Before closing, there are two things I would like to note. The first is that the solution here sketched is likely to commit the Class or Resemblance Nominalist to the rejection of Truthmaking Necessitarianism, the idea that, necessarily, if the truthmaker of a certain proposition exists, that proposition is true. For particulars are contingent and many of their sparse properties are had contingently; think of shapes for instance. Then it is easy to show that it could have been the case that all the square particulars could have been the only round particulars. If that possibility had been the case, the proposition that a is square (where a is an actual square particular) would have been false, and yet what makes it true according to Class and Resemblance Nominalism would have existed anyway: the class of actual particulars would have existed and would have been natural, and the particulars that are actually square would have satisfied the relevant resemblance condition. I say that the solution here advocated is likely to commit the Class and Resemblance Nominalist to the rejection of Truthmaker Necessitarianism because it is open to the Class and Resemblance Nominalist to have a metaphysics that maintains that particulars are not contingent entities, or that, although they are contingent entities, they have their sparse properties necessarily. But some resemblance nominalists might not take this line and will want to admit that it is possible that all square particulars had been the only round particulars. How bad is this consequence? On the one hand, although it is an appealing doctrine, there seem to be no generally accepted arguments for Truthmaker Necessitarianism. On the other hand, Class and Resemblance Nominalists will have to provide a plausible explanation of how this particular violation of Truthmaker Necessitarianism is possible: how can it be that belonging to the same class, or resembling the same things, makes something square but could have failed to make it square? Note that in the classical cases of violation of Truthmaker Necessitarianism – negative existential truths and affirmative universal ones – the explanation seems to be at hand: “How can it be that what makes it true that these are all the birds on this tree could have failed to make it true?” Easy: “Because there could have been a further bird on the tree”. The second thing to note is that Class and Resemblance Nominalism need not be committed to the idea that properties are predicable conditions to implement the essentials of this solution to the Coextension Difficulty. For the record, I do think that properties are predicable conditions, but my point now is that Class and Resemblance Nominalism can be 192

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eliminativist about properties. Indeed, they can maintain that properties do not exist. But they cannot reject predicable conditions. And once they accept predicable conditions, what they have to say is that classes are the correlates of predicable conditions, and that what makes true propositions stating that certain particulars satisfy certain predicable conditions is that such particulars belong to the corresponding classes. Needless to say, there are many more issues that need discussing in relation to the solution to the Coextension Difficulty than I have presented. But I cannot be exhaustive here, and so I have limited myself to sketching the idea.4

Notes 1 Although, as I have noted in other publications, Leibniz sometimes says things that are suggestive of a version of Resemblance Nominalism, his theory is a version of so-called Ostrich Nominalism rather than Resemblance Nominalism (see Rodriguez-Pereyra 2014: 198–199); thus, I do not interpret Leibniz as a resemblance nominalist. 2 Mantegani maintains that Resemblance Nominalism’s commitment to resembling particulars arises from a purely theoretical motivation, and therefore such a commitment is ad hoc ( Mantegani 2015: 201). Yes, the commitment to resembling particulars in Resemblance Nominalism arises from a purely theoretical motivation, that of accounting for the truthmakers of predications attributing so-called sparse or natural properties to particulars. But this does not mean that such a commitment is ad hoc, since the entities Resemblance Nominalism postulates (resembling particulars) are not entities whose only or main reason to believe in is that they solve any particular problems or play any particular theoretical roles. 3 Different philosophers have adopted theories of properties like this (see, for instance, Hale 2015: 37–40; Jubien 2009: 54–57; van Inwagen 2004: 131-38). See also Rodriguez-Pereyra (2022: 9–13) for more on this conception of properties and, in particular, for the relation between predicable conditions and meanings. 4 Material on which this chapter is based was presented to conferences or seminars at Eidos, Theorema, and the Conference for the Routledge Handbook of Properties. Many thanks to the many people who contributed to the paper by discussing it at those events, to Nick Jones for conversations about the topics of this paper, and to Paul Audi and Ralf Busse for written comments on a previous draft of the paper.

References Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Blumson, B. (2018) Two Conceptions of Similarity. Philosophical Quarterly 68(270): 21–37. Blumson, B. (2022) Does Everything Resemble Everything Else to the Same Degree? Asian Journal of Philosophy 1(1): 1–21. Busse, R. (2016) Class Nominalism, Wolterstorff’s Objection, and Combinatorial Worlds. Philosophical Quarterly 66(265): 680–700. Busse, R. (2018) The Adequacy of Resemblance Nominalism About Perfect Naturalness. Philosophy and Phenomenological Research 96(2): 443–469. Carnap, R. (1967) The Logical Structure of the World. Trans. Rolf George. London: Routledge and Kegan Paul. Goodman, N. and Quine, W.V. (1947) Steps Toward a Constructive Nominalism. Journal of Symbolic Logic 12(4): 105–122. Guigon, G. (2009) The Metaphysics of Resemblance. Thèse de doctorat ès lettres. Université de Genève. Guigon, G. (2015) Coextension and Identity. In Guigon, G. and Rodriguez-Pereyra, G. (eds.) Nominalism about Properties: New Essays. Abingdon and New York: Routledge: 135–155. Hale, B. (2015) Necessary Beings. Oxford: Oxford University Press. Jubien, M. (2009) Possibility. Oxford: Oxford University Press.

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Gonzalo Rodriguez-Pereyra Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Mantegani, N. (2015) Avoiding Ad Hoc Ontology. In Guigon, G. and Rodriguez-Pereyra, G. (eds.) Nominalism about Properties: New Essays. Abingdon and New York: Routledge: 189–207. Paseau, A.C. (2015) Six Similarity Theories of Properties. In Guigon, G. and Rodriguez-Pereyra, G. (eds.) Nominalism about Properties: New Essays. Abingdon and New York: Routledge: 95–120. Quine, W.V. (1969) Natural Kinds. In Quine, W.V. (ed.) Ontological Relativity and other Essay. New York: Columbia University Press: 114–138. Quinton, A. (1957) Properties and Classes. Proceedings of the Aristotelian Society 58: 33–58. Price, H.H. (1953) Thinking and Experience. London: Hutchinson’s University Library. Rodriguez-Pereyra, G. (2000) What is the Problem of Universals? Mind 109(434): 255–273. Rodriguez-Pereyra, G. (2001) Resemblance Nominalism and Russell’s Regress. Australasian Journal of Philosophy 79(3): 395–408. Rodriguez-Pereyra, G. (2002) Resemblance Nominalism. A Solution to the Problem of Universals. Oxford: Oxford University Press. Rodriguez-Pereyra, G. (2004) Paradigms and Russell’s Resemblance Regress. Australasian Journal of Philosophy 82(4): 644–651. Rodriguez-Pereyra, G. (2014) Leibniz’s Principle of Identity of Indiscernibles. Oxford: Oxford University Press. Rodriguez-Pereyra, G. (2022) Two Arguments for the Identity of Indiscernibles. Oxford: Oxford University Press. Russell, B. (1997[1912]) The World of Universals. In Mellor, D.H. and Oliver, A. (eds.) Properties. Oxford: Oxford University Press: 45–50. Schaffer, J. (2004) Two Conceptions of Sparse Properties. Pacific Philosophical Quarterly 85(1): 92–102. van Inwagen, P. (2001) Two Concepts of Possible Worlds. In van Inwagen, P. (ed.) Ontology, Identity, and Modality: Essays in Metaphysics. Cambridge: Cambridge University Press: 206–242. van Inwagen, P. (2004) A Theory of Properties. In Zimmerman, D. (ed.) Oxford Studies in Metaphysics, vol. 1. Oxford: Oxford University Press: 107–138.

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17 PRIORITY AND GROUNDING NOMINALISM Guido Imaguire

17.1

Introduction

In recent years new formulations and solutions to the Problem of Universals (PU) have been offered that are based on the notions of grounding and fundamentality. In this chapter, I will first (this section) list and briefly explain the main – new and old – formulations of the problem. Then, I shall propose a novel solution called priority nominalism (Section 17.2) and show how it answers each of the proposed questions (Sections 17.3 and 17.4). Finally, in Section 17.5, I shall present and discuss a similar grounding-oriented solution, viz. grounding nominalism. There are many formulations of PU. Each formulation states a different question. Thus, I take ‘Problem of Universals’ as a label of (at least) four different but interrelated questions: F1. F2. F3. F4.

Are there universals? How is it possible that, at the same time, a and b are both F? Given that a is F, in virtue of what is a F? Are universals fundamental or derivative?

F1 is the question of existence, which is the traditional way to formulate the PU. Notice that F1 is not an ordinary question of existence such as whether or not there are unicorns, but rather a categorial question, that is whether universals make up a fundamental category of being. So, F1 does not ask whether or not the category of universals has some instances, but rather asks about the ontological status of the whole category of universals, i.e., entities like redness, roundness and all other F-nesses. F2 states the puzzle known as the One over Many: ‘how can two (or more) different particulars share the same nature?’ or, a bit more perplexing, ‘how can a and b be identical and different at the same time?’ Some think that the distinction between qualitative and quantitative identity is sufficient for solving the puzzle (see e.g. MacBride 2002; Wieland 2008).1 For others, F2 states an argument for realism rather than a problem (see Armstrong

DOI: 10.4324/9781003246077-22

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1978: 65). According to realism, we can only explain sameness or shareability of nature, if we accept the existence of properties qua shareable entities. F3 asks for the fundamentality profile of first-order facts.2 It was proposed by Keith Campbell in addition to F2, which he considered biased insofar as it assumes that if they are both F, then a and b simply ‘must’ have something in common (Campbell 1990: 29). F3 asks what must happen in the deep structure of reality in order to establish that a is F. Finally, F4 was proposed by Jonathan Schaffer in his (2009) and Peter Schulte in his (2019) and follows a new trend in contemporary metaphysics. The proposal is not simply to supplement, but rather to replace the question of existence with the question of fundamentality. According to Schaffer, ‘both the realist and nominalist accept the existence of general properties. The dispute is over whether they are fundamental, or whether they are derivative’ (2009: 362). Plausibly, any full-blooded solution to the PU has a more or less substantial answer to each of these questions. And since the questions are relevantly related to each other, any solution should ideally present a coherent and unified answer. Of course, since F4 is a formulation in terms of the very recent grounding jargon, we cannot expect that solutions proposed before this trend would be explicit about it. In this chapter, I argue that Priority Nominalism has not only substantial, but also highly plausible and coherent answers to all four formulations of the PU.

17.2

Priority Nominalism

Priority nominalism is the new ostrich nominalism: it is ostrich plus grounding. The pejorative label ‘ostrich’ was introduced by D.M. Armstrong (1978: 16) to indicate what he considered more a ‘dismissive’ attitude – viz. W.V. Quine’s attitude in his (1948) – than properly a solution to the PU. For Armstrong, the ostrich refuses to recognize the problem and fails to take predication with ontological seriousness. However, some have been sympathetic to this position and have tried to defend it, in particular Michael Devitt (1980, 2010, and Chapter 15, this volume) and James van Cleve (1994). James Summerford (2003), Joseph Melia (2005) and Peter Forrest (2021) are likewise not far from this position. Roughly, the ostrich nominalist assumes that (i) universals do not exist, (ii) questions of existence should be decided by means of the principle of ontological commitment, and (iii) first-order facts cannot be explained (that a is F is a brute fact). Grounding is meanwhile, for better or worse, a common good of contemporary metaphysics.3 Although the nature of grounding is contested, I will here assume – in line with the orthodoxy – that grounding is a relation of metaphysical non-causal explanation and priority. It is usually expressed by terms like ‘because’, ‘in virtue of’ or ‘grounds’. Grounding is a many-one relation: x1, x2, … may together ground y. In this case, we say that x1, x2, … are each a partial ground for y. For some, it is a genuine relation, for others it is an operator. According to orthodoxy, the adequate relata of grounding connections are facts or true propositions. Grounding expresses a kind of ontological priority: when x grounds y, x is more fundamental than y. According to orthodoxy, grounding is a strict partial order, i.e., nothing grounds itself, if x grounds y, y does not ground x and if x grounds y, and y grounds z, then x grounds z. Grounding entails necessity: if x grounds y, then necessarily, if x then y. But grounding is more than simple necessitation or modal covariance: it is a hyperintensional connection. Even if x and y are necessarily equivalent, like the fact that Socrates exists and the fact that the singleton Socrates exists, x and y may not be substitutable salva veritate in any grounding context (as for instance in the 196

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grounding claim ‘the singleton Socrates exists because Socrates exists’). All this will simply be assumed in the following. There are grounding enthusiasts and grounding sceptics. For the sceptics, grounding is not intelligible and/or not useful. The old ostrich, it should be noted, is a grounding sceptic, and this is the main point of contention between her and the priority nominalist. In the following, I will simply assume that grounding is an intelligible and useful metaphysical tool (in fact, this claim could be seen as a desideratum of this chapter).

17.3

The Fundamentality of First-Order Facts

That grounding is relevant for solving the PU is particularly evident if we consider formulations F3 and F4, for both explicitly refer to the notion of grounding and fundamentality. I will start with F3 and leave F4 for the very end. F3 asks for the ground of a first-order fact like a is F. There are two possible nondismissive reactions to F3: one may claim that a is F has no ground because it is fundamental, or one may claim that this fact is grounded in some other fact. In the first case, the proponent ideally should present arguments for supporting the fundamentality of this fact. In the second case, the proponent should present the more fundamental fact which is supposed to ground it. And here comes the famous divide: while realists offer a ground which involves participation or instantiation of universals, nominalists appeal to facts that refer only to particulars (resembling particulars, class membership, etc.). Traditional ostrich nominalism was accused of being a dismissive position, because it did not offer any explanation (including grounding) for such first-order facts. Indeed, Devitt (see Chapter 15, this volume) explicitly rejects talk of grounding. Quine, so far as I can see, never appealed to grounding, and we may plausibly suppose that he would not be sympathetic to this piece of old Aristotelian ideology: although, eloquently enough, he claimed (1948: 30) that sentences like ‘a is F’ express ‘ultimate and irreducible’ truths.4 Nor does the priority nominalist offer a ground for the fact that a is F. And this is not because she is a grounding sceptic, but rather because she considers it a fundamental fact. And this is not a dismissive answer, since plausibly any solution has the right to propose its own fundamental fact. As we have seen, Campbell considered F2 a biased formulation and suggested F3 instead. But his F3 (‘in virtue of what is a F?’) is also biased, for it implicitly assumes that there ‘must be’ a ground for the fact that a is F. A better, non-biased, formulation would be: F3*. Given the fact that a is F, is it fundamental or derivative? If derivative, what grounds it? For the priority nominalist, the fact that a is F is fundamental just because there is no fact p which grounds it. However, there is an ambiguity that must be clarified at this point. Take the fact that: (1) this ball is red. F3* asks: is (1) fundamental or not? There are two different ways to answer this. According to what may be called a ‘non-categorial explanation’, (1) is grounded in: (2) this ball is scarlet. 197

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Here the grounding profile of a first-order fact is determined by means of its relation to other first-order facts. Now, according to what I call a ‘categorial explanation’, one may claim that (1) is grounded in (3a) this ball participates in (or instantiates) redness, or (3b) this ball is a member of the class of red things, or (3c) this ball is similar to other red things, etc. Exactly this kind of explanation is at the center of the debate over the PU: realists defend (3a), class nominalists (3b), resemblance nominalists (3c), etc. And all these answers seem to be adequate moves in the dialectic of the debate. Importantly, the priority nominalist does not claim that all first-order facts like (1) are fundamental. For she accepts that (1) is grounded in (2). Now, suppose that everyone, including realists and nominalists alike, agrees that (2) is not further grounded in the non-categorial sense. Maybe better: assume that (2) is your favorite fundamental firstorder fact, such as perhaps the fact that this particle is negatively charged. Then, one may still ask whether (2) is categorially fundamental, or whether it is grounded in a further ‘categorial’ fact (e.g., this electron participates in negative chargedness, or is a member of the class of negatively charged things, etc.). At this point, plausibly only sparse properties are at stake (see Chapter 4, this volume). And here comes a new divide: while ‘most’ realists5 and most nominalists agree that (2) is grounded in another categorial fact, the priority nominalist rejects this. That this particle is negatively charged is categorially fundamental. Why does the priority nominalist assume that the fact that this particle is negatively charged is fundamental? The main reason is the regress argument. The literature on the regress argument is vast and cannot be discussed in detail here (see Chapter 22, this volume). It should be sufficient to sketch the core idea of the argument in its grounding version. Any explanation of the kind ‘a is F because …’ has on the right side a fact – after all, grounding is a relation between facts. Indeed, a categorial fact like (3a-c) is also a fact. And so, it has to be constituted by the original object a and an additional predicative part, which is constituted by a relation: a is R-related (instantiates/is a member of/is similar) to x (where x is a universal, a class, another particular, etc.). Now, why should we take this new fact [a is R-related to x] as fundamental? No plausible answer has been given so far.6 For notice that what is at stake here is not a ground for the object, or for the property, but for the instantiation, i.e., for the ‘mysterious tie’ which connects a and F. And any further explanation in terms of ‘[a is R-related to x] because …’ just introduces a new mysterious tie between a and the R-relation to.

17.4 The Existence of Universals and the One over Many It is not obvious how the issues of existence (F1) and the One over Many (F2) are connected to grounding. In fact, according to some grounding enthusiasts (in particular Schaffer 2009), the grounding agenda is introduced exactly for the purpose of replacing the ‘obsolete’ existence program. However, interest in grounding does not necessarily require us to neglect the issue of existence. For the priority nominalist, grounding should rather be seen as a useful – even necessary – additional tool for resolving some predicaments arising from the question of existence. 198

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Like the old ostrich, the priority nominalist does not believe in universals. The priority nominalist accepts Quine’s principle of ontological commitment for deciding questions of existence, which says roughly that we have to accept the existence of the entities we quantify over in the sentences we consider true and unavoidable.7 I say ‘unavoidable’ because if we accept as true a sentence S, which entails quantification over entity E, but we are able to present a theoretically equivalent sentence S* which does not commit to E, we are justified to drop the commitment to E. Concerning the very fact that a is F, the answer of both the ostrich and the priority nominalist is straightforward. Since ‘a is F’ only entails quantification over particulars, the conclusion is that there are only particulars. Now, the addition of the grounding tool helps the nominalist solve two predicaments of the old ostrich. The first predicament concerns the One over Many argument (F2): if (4) a is F and (5) b is F are both true, then it is also true that (6) a and b have something in common, viz. F-ness. And since (6) entails quantification over universals, we should conclude that universals exist. Quine’s reaction to this is unfortunately dismissive: for him, (6) is just a ‘popular and misleading manner of speaking’ (Quine 1948: 29). He does not bother to say why. The priority nominalist can say more: (6) is neither false nor a mere façon de parler. In fact, it is literally true. But – and this is the main point – it is a derivative and not a fundamental truth. For, (6) is fully grounded in (4) and (5), and not the other way around. A red house and a red rose have something in common because both are red (a similar point is made by Melia 2005: 78ff). And, says the priority nominalist, we should only accept the entities we quantify over in fundamental truths. This is the Principle of Grounded Ontological Commitment: To be is to be the value of a bound variable of a fundamental truth. Let me briefly mention two reasons for accepting this principle. The first is a recognition that there are too many ways – too many true sentences we may use – to describe the same phenomenon. In fact, (6) is theoretically equivalent to (4) and (5). (6) entails an addition of entities without any explanatory gain. Curiously, we do not really need the One over Many phenomenon to make us accept the existence of universals: examples could be ‘a has something b does not have, F-ness’ (in cases where only a is F) and ‘there is something that neither a nor b have, viz. F-ness’ (in cases where nothing is F!). This way you can trivially introduce the existence of whatever you want. To recall an old Quinean example: if we consider all derivative truths seriously, we should believe in the existence of odd entities like the ‘average woman’ or the ‘average child’, for it is statistically true that ‘the average woman has 2.4 children’. Not all truths should be taken seriously in formulating our ontology. And here grounding helps us. The average woman has 2.4 children because of certain facts about real women with real children. 199

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Here the second, somewhat surprising, reason. When we analyze the whole debate on the PU, we see that all proposed solutions, explicitly or not, agree on something like this principle. Just take, for instance, transcendental realism and class nominalism. The transcendental realist does not say ‘a is F, therefore there are universals’, but instead ‘a is F because a participates in F-ness, therefore there are universals’. The class nominalist does not say ‘a is F, therefore there are classes’ but instead ‘a is F because a is a member of the class F, therefore there are classes’. Thus, in the whole dialectic of the debate the commitment to entity x is justified on the basis of the appeal to a fundamental fact whose expression entails quantification over x (‘a participates in x’, ‘a is a member of x’). The ontology of each theory is decided on its fundamental level. Note that the priority nominalist is not sweeping unwelcome entities under the rug by manipulating language, or by creating odd paraphrases to avoid certain commitments. Quite the opposite: all realists and nominalists, except for the priority nominalist, create new entities or ‘mirages’ by constructing superfluous paraphrases or groundings. In contrast, the priority nominalist only ‘de-paraphrases’: back to the fundamental ‘a is F’ – that’s all.8 The second predicament of the old ostrich concerns what has been considered the main argument against ostrich nominalism, viz. the problem of abstract reference in truths like: (7) red is a color and (8) orange is more similar to red than blue. These sentences entail quantification over properties. The difficulty of offering plausible first-order paraphrases of such sentences has led some metaphysicians to the conclusion that quantification over universals – and that entails here: realism – is unavoidable. Quine himself (1960: 121–123) and Devitt (1980, 2010, and Chapter 15, this volume) recognized these difficulties. Since the grounding nominalist only accepts the entities we quantify over in fundamental truths, the decision about the existence or non-existence of universals depends on whether such second-order truths are fundamental or not. Fortunately, there are quite reasonable grounds for such second order truths: (7*) for any x, whenever x is red, x is colored in virtue of x being red (8*) for any x, y and z, whenever x is red, y is orange and z is blue, if x is more similar to y than to z, then x is more similar to y than to z, partly in virtue of x being red, y being orange and z being blue. Plausibly, the fact that x is red grounds the fact that x is colored. After all, the first fact necessitates and relevantly explains the second fact. Further, it seems plausible that the facts that x is red, y is orange and z is blue partly (but not fully) ground the fact that x is more similar to y than to z, i.e., this particular color distribution contributes to a greater similarity between x and y (independently of how similar or dissimilar x, y and z are overall). Of course, second-order truths are still a threat to the priority nominalist, for her success depends on the open agenda of offering grounds for all such truths.9

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17.5 Grounding Nominalism Let’s turn, finally, to F4. Similar to F3, F4 explicitly states the PU as a problem about fundamentality: are universals fundamental or not? As with F3, one may be dismissive or not about it. Further, as with F3, one may be dismissive simply by adopting grounding skepticism. But there is also another way to be dismissive about F4. As we saw above, according to grounding orthodoxy, the only adequate relata of grounding connections are facts or true propositions.10 Therefore, it is not strictly adequate to say about any nonfactual entities, in particular objects and properties, that they are fundamental or derivative. Claims like ‘universals are derivative’ or ‘universals are grounded in particulars’ are inadequate, at least insofar as a special relation of grounding is not defined for the category of universals and particulars. But, is there anyone who explicitly claims that universals are derivative? Yes, there is: the grounding nominalist. Like priority nominalism, grounding nominalism is a new grounding-based solution to the PU. It was proposed by Schulte in ‘Grounding Nominalism’ (Schulte 2019). Like ostrich and priority nominalists, the grounding nominalist accepts the principle of ontological commitment in order to decide questions of existence. Further, he takes a is F to be an ungrounded fact and proposes grounds for truths with abstract reference, using the resources of grounding (such as (7*), for instance). However, contrary to the priority nominalist, the grounding nominalist assumes that (universal or particular) properties (or relations) are real, i.e., they exist in the same sense in which particulars exist. After all, we quantify over them in sentences like (6) and (7). However, according to Schulte, grounding nominalism is a kind of nominalism insofar as it claims that only concrete objects are fundamental, while properties are derivative. Roughly speaking, universals are grounded in concrete particulars that instantiate them. Since different particulars can instantiate the same universal, overdetermination is allowed: each particular red thing fully grounds redness. Schulte proposes the following defining principle for grounding nominalism: (GN) For every (first-order) property or relation x, a (true) grounding explanation of the form ‘x exists because p’ is available, where ‘p’ only makes reference to particular things. The idea is clear: if F-ness exists, this is so because some particular x is F. This formulation overcomes the mentioned difficulty of applying grounding to non-factual entities. For the claim here is not, strictly speaking, that ‘this apple grounds redness’, but rather that ‘redness exists because this apple is red’, which is a case of grounding between facts. Schulte’s proposal entails an implicit rule for deriving the fundamentality profiles of nonfactual entities from purely factual grounding: an entity x is fundamental if (i) x exists and (ii) there is no grounding explanation for ‘x exists’ (and conversely, an entity is derivative if it exists and there is such an explanation).11 So far, the answers of grounding nominalism to F1, F3 and F4 are clear: universals do exist (F1) but are derivative (F4), and first-order facts like a is F are fundamental (F3). Schulte is not explicit about F2, the One over Many, but he does not have to be. For it is clear that the grounding nominalist does not appeal to the phenomenon of sameness of nature in order to justify the existence of universals: one single red thing is sufficient to establish the existence of redness.

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The major difference between grounding nominalism and all other forms of nominalism, including priority nominalism, is that it accepts the existence of universals.12 Peculiar advantages and difficulties of this position emerge from this difference. Schulte claims the following advantage over traditional nominalism: since the grounding nominalist does accept the existence of properties, he is free from the obligation to offer paraphrases for true sentences in which we quantify over properties. While this may be true, at the same time he is obligated, like the priority nominalist, to offer grounding explanations for all those truths, because this is required by (GN). The first, most obvious difficulty consists in the fact that grounding nominalism is radically revisionist concerning the label ‘nominalism’. No previous brand of nominalism accepts the existence of universals. Schulte himself (2019: 487) recognizes that grounding nominalism may sound to some like ‘nominalism in name only’. He tries to justify the label ‘nominalism’ by claiming that this position preserves the nominalist intuition that particulars and properties are not on a par or that at the fundamental level there are only particulars. Now, Aristotelian realism is sometimes characterized in these terms: universals exist insofar they are grounded in their instances. Thus, grounding nominalism seems to be rather a variant of immanent realism. Further, since grounding nominalism accepts the existence of universals, it is not as parsimonious as traditional nominalism, unless one – as Schulte explicitly does – rejects the traditional principle of the razor (do not multiply entities without necessity) and accepts instead Schaffer’s (2015) alternative laser (‘do not multiply fundamental entities without necessity’), which is a controversial matter.13 Here there is a second difficulty. Without any restriction of the domain of quantification, (GN) entails that there are unicorns. For being a unicorn is a first-order property and (GN) entails that there must be a fact p (something like ‘this is a unicorn’) which grounds the existence of being a unicorn. I suppose Schulte presupposes a principle of instantiation, such that ‘every property’ strictly means ‘every instantiated property’. But there is a similar problem concerning abundant properties: without any restriction to fundamental properties or truths, (GN) entails that there are properties like being bigger than my nose, since it is true that this table is bigger than my nose. Finally, we may wonder about the motivation for grounding nominalism: why should we believe that universals are grounded in particulars, and not the other way around? Or that both are equally fundamental? While Schulte leaves these questions open, Alexandre Declos (2020) proposes an argument for it, viz. ‘the argument from abstraction’: objects, insofar as they are concrete (‘complete’) entities, must be prior to properties such as abstract (‘incomplete’ or ‘created by a process of abstraction’) entities. This is a plausible line of reasoning which deserves a detailed analysis. In any case, it is far from clear how we can – if we can do this at all – derive the fundamentality profile of fact constituents from the fundamentality profiles of the facts they constitute. Some may claim that when a is F is a fundamental fact, this only means that F is a fundamental property.14 For others, all constituents of a fundamental fact must be fundamental15; and since a is F is considered fundamental, both a and F are expected to be equally fundamental. In order to maintain the thesis that universals are not fundamental, the grounding nominalist depends not only on the open agenda of offering grounding explanations for all second-order facts, but also on a convincing argument for the mentioned principle to derive the fundamentality profiles of non-factual entities from strict fact-grounding.

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Notes 1 Some metaphysicians have been proposing alternative puzzles: For Rodriguez-Pereyra (2000), not the one over many, but the Many over One (‘how is it possible that a is F and G at the same time?’) is the pressing problem, while Peacock (2009) suggests the Many over Many (‘how is it possible that a and b are at the same time similar – both are F – and different – one is G the other is non-G – at the same time?’). 2 By a ‘first-order fact’ I mean an atomic fact constituted by a first order relation of arity n (including 1) and n-many objects. 3 The contemporary notion was introduced by Fine (1994, 1995, 2001), Schaffer (2009), Rosen (2010), and Raven (2012). For an overview, see Correia and Schnieder (eds.) (2012) and Hoeltje et al. (2013). For a defense of the orthodox view, see Schaffer (2009), Raven (2013), and Cameron (2016); against orthodoxy, see Jenkins (2011), Schaffer (2012), Litland (2013), Correia (2014), Thompson (2016), and Rodriguez-Pereyra (2015). 4 Quine did not explain the expression ‘ultimate and irreducible’, but it was certainly not meant as equivalent to the notion of fundamental (in the sense of grounding), which goes against the spirit of his naturalism. This is the main difference between the original ostrich and the priority nominalist. The priority nominalist is not an enemy of the ‘old Aristotelian metaphysics’. But still, this passage makes clear that Quine had some intuition about some kind of primitiveness of firstorder facts. 5 I say ‘most’ realists, because a realist may accept the existence of universals and, at the same time, that a is F is a fundamental fact. Frege plausibly defended such a view: ‘The logically primitive relation is the relation of an object falling under a concept’ ( Frege 1983: 128). Dixon (2018) argued in a recent paper that a realist may accept ‘upward grounding’, i.e., that the fact that a is F grounds the fact that a instantiates F-ness. So, the realist may accept the existence of universals independently of accepting that a is F in virtue of an instantiation fact. 6 For a detailed discussion of all attempts to avoid the regress, see Imaguire (2018: ch. 4). 7 For those who prefer to decide the question of existence in terms of truth-making, the priority nominalists, following Lewis (2003), offer particulars and the way they are, as the only truthmakers for fundamental truths ( Imaguire 2018: 102–103). 8 The priority nominalist does not claim to know a general rule for deciding in each particular case in which direction the grounding relation goes. She only claims that, generally, first order facts are more fundamental than second order facts. 9 For the favorable prospects of this agenda, see the grounding explanations for many kinds of such truths in Imaguire (2018: ch. 6). 10 As far as I can tell, only Schaffer’s (2009) defended a tolerant view, according to which entities of any category may be grounding related. For grounding as a relation between facts, see Correia and Schnieder (2012: 11) and Schnieder (2020). 11 Schulte in conversation. 12 I suppose that, in the end, one may wonder whether the difference between grounding and priority nominalism is substantial or only verbal. After all, it seems that what the grounding nominalist calls ‘existent and fundamental’ is designated by the priority nominalist as ‘existent’, and what the former calls ‘derivative’ the latter designates as ‘not really existent’. This is an important question which requires additional analysis and depends on certain fundamental issues concerning the relation between the notions of existence and grounding. 13 For a critical discussion of Schaffer’s (2015) arguments, see Fiddaman and Rodriguez-Pereyra (2018). For arguments against the laser, see Da Vee (2020) and Thunder (2021). 14 Grounding claims are typically based solely on the fundamentality profiles of properties. See for instance: a is red because a is scarlet, here the particular a works as a variable, for its nature is completely irrelevant for the grounding link. Because of this, some metaphysicians suggest that only properties play a role in grounding connections (see e.g. Rosen’s ‘Weak Formality’ in his 2015:198; see also Audi 2012: 693). 15 See e.g., the ‘principle of purity’ in ( Sider 2012: 126).

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References Armstrong, D.M. (1978) Universals and Scientific Realism: Nominalism and Realism. Cambridge: Cambridge University Press. Audi, P. (2012) Grounding: Toward a Theory of the In-Virtue-Of Relation. Journal of Philosophy 109(12): 685–711. Cameron, R. (2016) Do We Need Grounding? Inquiry 59(4): 382–397. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Correia, F. (2014) Logical Grounds. The Review of Symbolic Logic 7(1): 31–59. Correia, F. and Schnieder, B. (eds.) (2012) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press. Da Vee, D. (2020) Why Ockham’s Razor Should be Preferred to the Laser. Philosophical Studies 177(12): 3679–3694. Declos, A. (2020) More Grounds for Grounding Nominalism. Philosophia 49(1): 49–70. Devitt, M. (1980) ‘Ostrich Nominalism’ or ‘Mirage Realism’? Pacific Philosophical Quarterly 61(4): 433–439. Reprinted in Devitt, M. (2010) with new “Postscript”: 13–30. Devitt, M. (2010) Putting Metaphysics First: Essays on Metaphysics and Epistemology. Oxford: Oxford University Press. Dixon, T.S. (2018) Upward Grounding. Philosophy and Phenomenological Research 97(1): 48–78. Fiddaman, M. and Rodriguez-Pereyra, G. (2018) The Razor and the Laser. Analytic Philosophy 59(3): 341–358. Fine, K. (1994) Essence and Modality. Philosophical Perspectives 8: 1–16. Fine, K. (1995) Ontological Dependence. Proceedings of the Aristotelian Society 95(1): 269–290. Fine, K. (2001) The Question of Realism. Philosophers’ Imprint 1(1): 1–30. Forrest, P. (2021) Fictional Possibilities Grounded in Foundational Nominalism. Philosophia 49(1): 1–16. Frege, G. (1983) In Nachgelassene Schriften und Wissenschafticher Briefwechsel, edited byH. Hermes, F. Kambartel, and F. Kaulbach. Hamburg: Felix Meiner Verlag. Hoeltje, M., Schnieder, B. and Steinberg, A. (eds.) (2013) Varieties of Dependence: Ontological Dependence, Grounding, Supervenience, Response-Dependence. Munich: Philosophia Verlag. Imaguire, G. (2018) Priority Nominalism. Cham: Springer. Jenkins, C. (2011) Is Metaphysical Dependence Irreflexive? The Monist 94(2): 267–276. Lewis, D. (2003) Things qua Truthmakers. In Lillehammer, H. and Rodriguez-Pereyra, G. (eds.) Real Metaphysics: Essays in Honour of D. H. Mellor. London: Routledge: 25–33. Litland, J.E. (2013) On Some Counterexamples to the Transitivity of Grounding. Essays in Philosophy 14(1): 19–32. MacBride, F. (2002) The Problem of Universals and the Limits of Truth-Making. Philosophical Papers 31(1): 27–37. Melia, J. (2005) Truthmaking Without Truthmakers. In Beebee, H. and Dodd, J. (eds.) Truthmakers: The Contemporary Debate. Oxford: Clarendon Press: 67–84. Peacock, H. (2009) What’s Wrong with Ostrich Nominalism? Philosophical Papers 38(2): 183–217. Quine, W.V. (1948) On What There Is. Review of Metaphysics 2(5): 21–38. Quine, W.V. (1960) Word and Object. Cambridge, MA: MIT Press. Raven, M. (2012) In Defence of Ground. Australasian Journal of Philosophy 90(4): 687–701. Raven, M. (2013) Is Ground a Strict Partial Order? American Philosophical Quarterly 50(2): 191–199. Rosen, G. (2010) Metaphysical Dependence: Grounding and Reduction. In Hale, B. and Hoffman, A. (eds.) Modality: Metaphysics, Logic, and Epistemology. New York: Oxford University Press: 109–136. Rosen, G. (2015) Real Definition. Analytic Philosophy 56(3): 189–209. Rodriguez-Pereyra, G. (2000) What is the Problem of Universals? Mind 109(434): 255–273. Rodriguez-Pereyra, G. (2015) Grounding is Not a Strict Order. Journal of the American Philosophical Association 1(3): 517–534. Schaffer, J. (2009) On What Grounds What. In Chalmers, D., Manley, D. and Wasserman, R. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Oxford University Press: 347–383.

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Priority and Grounding Nominalism Schaffer, J. (2012) On Some Counterexamples to the Transitivity of Grounding. In Correia, F. and Schnieder, B. (eds.) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press: 122–138. Schaffer, J. (2015) What Not to Multiply Without Necessity. Australasian Journal of Philosophy 93(4): 644–664. Schnieder, B. (2020) Grounding and Dependence. Synthese 197(1): 95–124. Schulte, P. (2019) Grounding Nominalism. Pacific Philosophical Quarterly 100(2): 482–505. Sider, T. (2012) Writing the Book of the World. Oxford: Oxford University Press. Summerford, J. (2003) Neither Universals nor Nominalism: Kinds and the Problem of Universals. Metaphysica 4(1): 101–126. Thompson, N. (2016) Metaphysical Interdependence. In Jago, M. (ed.) Reality Making. Oxford: Oxford University Press: 38–56. Thunder, S. (2021) There is No Reason to Replace the Razor with the Laser. Synthese 199(3–4): 7265–7282. Van Cleve, J. (1994) Predication Without Universals? A Fling with Ostrich Nominalism. Philosophy and Phenomenological Research 54(3): 577–590. Wieland, J.W. (2008) What Problem of Universals? Philosophica 81(1): 7–21.

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18 NOMINALISM IN MATHEMATICS Jody Azzouni

18.1

Introduction

The debate between Platonists and nominalists (the NP debate) is often presented as one of the oldest in philosophy. This isn’t one debate, however – stretching from ancient times until now. I won’t show this in proper historical detail; but this chapter will illustrate, by sketching the many options, how there have been many debates distinguished by changing concerns and commonly-held assumptions. This concomitant material surrounds the bare question “Do Platonic objects exist?” and drastically alters the resources available to opponents to support their positions. There are themes, nevertheless, broadly structuring the specific debates that are often grouped as falling under the NP debate. I’ll craft this chapter around those themes, give a little history and focus on the narrower set of options still living among contemporary philosophers of mathematics. My aim in this chapter, largely, isn’t to argue. I’m primarily surveying philosophical landscape, although I will indicate several lines of argument and venture opinions about which ones are right. NP debates overlap, but only modestly, with concurrent debates over the existence of properties or universals. For Plato, the issues are the same, and his arguments for why there are mathematical objects are the same as his arguments for why there are properties or universals. This is largely true of contemporary debates as well. But the two kinds of debate are potentially separate for linguistic reasons – and so arguments for and against properties/universals can differ from those about mathematical abstracta. Properties correspond to parts of speech codifiable as predicates, although we can always (sometimes awkwardly) nominalize them – “John is running”, “John exemplifies the property of running”. “That table is red”, “Red is a color”. Many mathematical terms, number terms notably, are already nouns – indeed, mathematical discourse is grammatically complete, and pure mathematical discourses are isolatable both from one another and from the rest of our discourse. This motivates certain nominalist programs in mathematics that don’t straightforwardly apply to debates about universals/properties. In what follows, I’ll continue to focus only on NP debates in mathematics.

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18.2

Metaphysical and Epistemological Characterizations of the Objects Nominalists and Platonists Argue about

Let’s start with nomenclature questions: What is nominalism? What is Platonism? Definitions are hard to give, at least ones neatly characterizing these opposing positions – even if the debate is restricted to mathematics. This is because there are many ways to demarcate “nominalistically-acceptable objects” (N-objects). Still, there are two broad ways of contouring N-objects: epistemically and metaphysically. Historically speaking, these are both moving targets. A first epistemic stab is this: Consider everything we can access via our senses. Nominalism is the view: that’s everything there is. Platonism demurs: more exists than that because there’s also what’s available through the use of our minds – this includes items referred to by terms in mathematical discourse: numbers and functions of them, as well as geometric objects, points, lines, etc. As I mentioned, this is an epistemic distinction: what we have access to via the senses and what’s available by intellectual means or by recollection (Plato 1963a). An objection: the nominalist demanding that what there is be accessible via the senses is too parochial because there are objects inaccessible to our senses but otherwise identical to what we sense, except that they’re small or far away or otherwise inaccessible. This can be, more or less, patched by expanding “the observable” to what’s observable in principle (van Fraassen 1980); but one can still complain of any epistemically-induced set of N-object contours that it misses the point because an epistemic distinction isn’t an appropriate basis for anyone, nominalists included, to deny the existence of something. A response is that the epistemic distinction the nominalist relies on isn’t meant to supply a metaphysical faultline; instead, the faultline is between what – epistemically – we may responsibly commit ourselves to as existing, and what we can’t (Azzouni 2004). Metaphysical faultlines are drawn for epistemic reasons. So this nominalist corrects the remark one paragraph back; we can’t responsibly take to exist anything that, in principle, can’t be sensed. Regardless, metaphysical N-object contours can be drawn using ontological categories, for example, space and time. Call concreta everything in space and time. Nominalists claim: only concreta exist; Platonists think more exists than that, and among those additional items are what are referred to by the terms in mathematical discourse. We can also consider other metaphysical characterizations of concreta: for example (along Plato’s lines) the changeable (versus the eternally unchanging) or – a downstream suggestion from this original Platonic one – the causal (versus the acausal): David Armstrong (1980) calls this the Eleatic Principle (Colyvan 2001: ch. 3). These are candidate criteria for what exists; the nominalist argues for and adopts one of these and denies the existence of anything that doesn’t fall under the chosen criterion. Characterizations of the NP debate in terms of space and time or causality require these ontological categories be fundamental, at least for the class of objects the nominalist intends to restrict everything that exists to. This also motivates the picture of Platonic objects as different – as outside of time and space, as therefore unchanging – and as acausal. In addition, most contemporary metaphysicians see them as necessary objects: in standard applications of modal logic, for example, they’re treated as present in every possible world. These are common contemporary metaphysical characterizations of abstracta – not only are numbers and other mathematical objects so treated, so too, often, are universals and properties. Recent theorizing in physics (quantum theories, string theories), however, suggests that space and time and causation aren’t fundamental ontological categories: perhaps other

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geometric notions function as the background framework for everything there is, or perhaps nothing geometric at all functions as a background framework for physical ontology. Contemporary scientific success motivates a different NP distinction. The “scientific world picture” provides us with our current “physical ontological basket”: basic physical items are characterized (fundamental particles and/or fields … .), and larger items constituted of such (squirrels, galaxies …) are also treated as existing, unless one’s a metaphysical nihilist (van Inwagen 1990; Rosen and Dorr 2002). This kind of nominalist, someone who invokes “naturalism”, claims that what’s in the physical ontological basket is all and only what exists; Platonists claim more than that exists, and that the more is referred to by mathematical terms. There are at least two ways to understand “naturalism”. The first treats science as metaphysically central: what science requires to exist is what exists. The debate then turns to the question of what science ontologically requires. The second approach is epistemic: science employs the currently best epistemic methods for determining what exists. Thus the scientific world picture epistemically justifies our belief in the entities it requires and no others. A related epistemic nominalist strategy turns on arguing that our resources for knowing about objects only allow us to commit ourselves to objects via certain means. Supernatural means of access to the objects we thus know about is ruled out: ruled out is that God has imprinted knowledge of abstracta in our minds; equally ruled out are mystical methods of access to metaphysically remote denizens of the universe. Epistemic naturalists argue that we can only know about objects that we (can) causally interact with; this, in turn, may require such objects to be themselves causally active; and that, in turn, can exclude our responsibly committing ourselves to such objects (Azzouni 2008; Benacerraf 1973; Callard 2007; Callard 2023). Jody Azzouni and Benjamin Callard debate over whether causal interaction with acausal Platonic objects is possible. Once it’s accepted that we can know about items we haven’t any causal access to – e.g., objects outside our light cone – a descendent condition can emerge, a reliability condition: there must be reliable processes by which we come to know about any objects we come to know about. There are two ways to understand “reliable processes”, locally and globally. Local reliable processes are specified to individual entities. Someone knows about a specific entity, the chair they’re looking at, because they see the chair, and seeing chairs is sufficiently reliable for them to know there’s a chair in front of them. Global reliable processes don’t require reliable processes to connect the knower to each item they know about. Rather, global methods of knowing capture entire classes of objects reliably. Well-establishing a scientific theory, for example, is a reliable process that enables proponents of that theory to know about the entire class of objects that theory is ontologically committed to. Those who require local reliable processes for knowledge correspondingly argue that knowledge of typically described Platonic objects – ones outside of space and time, and acausal – is ruled out (Field 1980). They understand this epistemic condition as licensing our knowledge of all the objects in the physical ontological basket, but nothing more. Platonists, however, can argue that included among the commitments of well-established theories are those to mathematical objects. They may do so by arguing that local reliable processes are too narrow for knowledge-commitments. After all, even physical objects – certain fundamental particles, they may argue – are ones physicists are committed to even though, if there are instances of specific particles established by local reliable processes, this isn’t true of all the particles belonging to a type. Or, they may argue, on independent grounds, that Quine’s criterion for what a discourse is committed to (Quine 1980[1953]) 208

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suffices to commit those who take scientific discourse seriously (i.e., take it to be true) to Platonic objects (see Section 18.3 below; see also Chapters 1 and 11, this volume). Unless the metaphysical contours for N-objects are simply asserted as there – as not needing argument to be established – the epistemic approach to N-object demarcation is more fundamental than the metaphysical approach. This is because metaphysical distinctions – and more specifically, metaphysical contours around what exists – aren’t givens: they have to be argued for: we must satisfy ourselves (epistemically) that the metaphysical requirements on what exists are justified. Regardless of this last point, NP disagreements depend on antecedent and concomitant metaphysical/epistemic views, about what there is and what the legitimate ways of learning about what there is are; there’s a lot that philosophers disagree over before they even start an NP debate; arguably any such debate is so affected by these antecedent commitments that, as I suggested in Section 18.1, we shouldn’t speak of the NP debate, but pluralize it as I’ve been doing: there are many NP debates. In any case, I’ll return to these differing views in their contemporary settings in later sections.

18.3 The Referential Thesis and Quine’s Criterion In the Sophist, Plato writes this (1963b, 237d–237e): STRANGER:

THEAETETUS: STRANGER: THEAETETUS: STRANGER: THEAETETUS: STRANGER: THEAETETUS: STRANGER:

Surely we can see that this expression “something” is always used of a thing that exists. We cannot use it just by itself in naked isolation from everything that exists, can we? No. Is your assent due to the reflection that to speak of “something” is to speak of “some one thing”? Yes. Because you will admit that “something” stands for one thing, as “some things” stands for two or more. Certainly. So it seems to follow necessarily that to speak of what is not “something” is to speak of no thing at all. Necessarily. Must we not even refuse to allow that in such a case a person is saying something, though he may be speaking of nothing? Must we not assert that he is not even saying anything when he sets about uttering the sounds “a thing that is not”?

The issue raised is how we’re to talk of something that doesn’t exist; the concern is that trying to do so is incoherent. Not only is a person failing to speak sensibly in such cases (because there isn’t anything she has succeeded in talking about), but because truths are always truths about things, it doesn’t seem possible to say something true about something that doesn’t exist. Even to say “Hercules doesn’t exist” (which, surely, is true), is, despite how we seem to understand the statement, not to say anything about it. This raises philosophical issues all on its own (how do we manage to say sensible true things about fictions – not just negative claims like “Hercules doesn’t exist”, but positive ones like, “Sherlock Holmes is more famous than Hercules”?) It also, however, motivates a default position vis-à-vis all meaningful truth-apt discourses: the words in these discourses must refer to existents, and the 209

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truth values of the sentences in these discourses must have the truth values they have because they’re true (respectively, false) of the items the terms in them refer to. Until the twentieth century, mathematics was universally assumed to be a meaningful true discourse – one, moreover, which is invaluable empirically. The one evident fact is that as sciences progress, mathematics becomes more entrenched in them; this isn’t only true of physics it’s also true of biology, chemistry, and even the social and psychological sciences. Therefore (one naturally thinks) mathematical terms refer to existents. Until the very late twentieth century, as I mentioned, nominalists and Platonists didn’t challenge this referential thesis about mathematical discourse; only then did they, more or less concurrently, challenge the idea that mathematics is true. And then, using newly invented logical tools, they could challenge either the referential thesis or its application to presumed-true mathematical discourse, and on that basis design new nominalist programs, as I’ll discuss in Sections 18.5 and 18.6. Let’s consider those NP debates that arise if debaters presuppose the referential thesis – this is to discuss the bulk of the late-twentieth-century philosophy of mathematics. Consider geometry. There are nouns, “point”, “line”, “triangle”, etc. as well as truths that these nouns appear in – ones established by proof or recognized as self-evident. In arithmetic, similarly, there are nouns “one”, “two”, “three”, as well as the truths those nouns appear in. What do such nouns refer to? The nominalist who accepts the referential thesis must find appropriate objects, among the nominalistically-acceptable objects, for mathematical terms to refer to. Call this a reference program (for there are many): the success or failure of nominalism – given the referential thesis – turns on the success of one or another reference program. Many nominalists and Platonists (still) accept Quine’s criterion (1980[1953]) for what a discourse is committed to (and therefore, what a sincere speaker asserting that discourse is derivatively committed to). This is a specification and refinement of the referential thesis. Upon “regimentation” of the discourse(s) of mathematics in first-order logic, whatever falls under the quantifiers is ontologically committed to by that discourse. Paraphrase (see Chapter 2, this volume) is the technique of rewriting discourse that’s apparently committing (e.g., to “sakes”, as in “John did it for Peter’s sake”) to discourse that isn’t so apparently committing (“John did it to help Peter”). That is, if sentences of certain forms (primarily, “there are [Noun-phrase]”, or “[Noun-phrase] exist”) containing noun-phrases – “number”, “10”, “Hilbert space” – that purportedly refer to abstracta can’t be transliterated to sentences without such terms (can’t be “paraphrased”), the discourse containing those sentences are ontologically committed to what those terms refer to. One may claim that global reliable processes – specifically those used to well-establish scientific theories – rely on methods of confirmation. But confirmation, it can be argued, doesn’t similarly affect all the sentences of a theory; specifically, the mathematical theories involved in any particular scientific theory aren’t confirmed by whatever it is that confirms the science since the mathematics is already taken to be true (Sober 1993; Azzouni and Bueno 2016 for criticism). This approach evidently requires a theory of confirmation – which we (currently) don’t have. The Platonist can argue that, insofar as we accept confirmation holism, all of a scientific theory (including the mathematics involved) is confirmed when confirmation of the theory is to be had (Colyvan 2001; Maddy 1992; Resnik 1997). It also requires a sentence-by-sentence separation of scientific discourse from mathematical discourse. But there are reasons (discussed in Section 18.5 below) to think that a sentence-bysentence distinction between mathematical and empirical content isn’t available. 210

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Until philosophers who rejected Quine’s criterion started drawing broader lessons about mathematical discourse (Azzouni 2004), Quine’s criterion structured NP debates via a corollary of it: the indispensability thesis (Azzouni 2009; Colyvan 2001; Panza and Sereni 2016; Putnam 1975a; Quine 1980[1953]). Scientific discourse is committed to whatever mathematical objects are the relata of noun phrases that appear in mathematics that’s indispensable to that discourse, where here “indispensable” means the discourse in question can’t be paraphrased in a way that eliminates those mathematical noun phrases. Quine, and many other philosophers, decided on the basis of Quine’s criterion, and the indispensability thesis, that mathematical terms refer. Taking the reference program to fail, they became – reluctantly in Quine’s case – Platonists (Goodman and Quine 1947). Subsequent philosophers, as we’ll see, think the reference program is still viable.

18.4

Reference Programs

I mentioned in Section 18.3 a maneuver open to the nominalist, especially the nominalist who accepts Quine’s criterion. This is to find nominalistically-acceptable objects that can serve as the referents for the mathematical terms that appear in mathematical discourse. Or, at least (given the nominalist in question accepts the indispensability thesis), nominalistically-acceptable objects for those mathematical terms that appear in mathematical discourse that’s scientifically indispensable. This project is dependent on exactly how – epistemically or metaphysically – the nominalist demarcates what’s nominalistically acceptable. This too is (historically) a moving target. One or another version of conceptualism has often arisen as a possible reference program for mathematical terms, and this is true for universals as well: Mathematical objects are ideas or concepts, where ideas or concepts are psychological or mental entities. This is open to the mismatch objection (Frege 1953): mathematical objects and psychological entities don’t have the same properties. It also suffers from a related problem, the infinity obstacle: there aren’t enough psychological entities to be the relata for mathematical language – not, anyway, if we want to preserve (all the) mathematical truths. It can be argued that we have a potential infinity of thoughts – and therefore, a potential infinity of entities is nominalistically acceptable. This licenses the counting numbers being psychological entities: we can always think of a next one. But all mathematics that relies on “completed infinities” is excluded: we can’t mathematically study the functions on the counting numbers – prove properties about the set of all such functions – because there are too many of them. This is shown by standard diagonalization proofs (Cantor 1996[1891]). A drastic solution is to curtail the mathematical entities themselves: there are no higher infinities of mathematical entities; for example, the standard (classical) real number line is replaced. Accompanying this drastic solution, for some, are modifications in logic too (Troelstra 1991). A cousin of conceptualism (sometimes described as Formalism) is to take mathematical notation itself as supplying the desired entities. The numerals are impounded as numbers, notational points (e.g., penciled dots on paper) are impounded as mathematical points; indeed, for geometry, the idea is that the mathematical objects are the very diagrammatic objects that are sketched in Euclidean pictorial proofs. This still faces the mismatch objection and the infinity obstacle: the diagrammatic items haven’t the same properties mathematical items have: points have no dimension, lines have only one dimension. And there isn’t enough notation to go around – to provide relata for all abstracta. This is especially the case, given that the contemporary characterization of the points in the space211

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time manifold are continuum-many in number; thus the functions on such manifolds are even higher in number. Modern mathematical/logical tools to the rescue: When I described Quine’s criterion in Section 18.3, I characterized it in terms of first-order logic. Many philosophers accept Quine’s criterion but deny that the framework logic the criterion is used within must be first-order (Boolos 1984; Boolos 1985; Chihara 2004; Field 1980; Hellman 1989; Lewis 1991; Putnam 1975b). Because plural quantifiers, modal logic, and higher-order logics strictly differ from first-order logic in their expressive strength, paraphrasing scientific discourse into a language with one of these logical frameworks, instead of first-order logic, enables the elimination of what look otherwise like ontological commitments to mathematical entities: there’s a tradeoff of ontology for enriched ideology. For example, the plural-quantifier statement, “There are some Cheerios in the bowl” looks intuitively like it’s committed to and only to the Cheerios in the bowl; render it first-order, and additional commitments emerge, perhaps to a set (Azzouni 2019; Boolos 1984). There have been heated debates about whether differences in expressive strength show that ontological commitments – to mathematical entities – are still present but disguised (Azzouni 2019; Boolos 1985; Quine 1970). It would be a surprise if expressive strength didn’t involve ontological supplementation – this seems otherwise far too easy a route to nominalism. The point made above about the manifold being mathematically rich enough to induce the infinity obstacle invites an approach of taking concreta itself (the spacetime manifold) or aspects of concreta to have enough structure to isomorphically embed mathematical ontology in it – and in this way to deny that “Platonic objects” have nominalistically unacceptable properties. This approach has roots in ancient Greek philosophy. (Contemporary versions: Arntzenius and Dorr 2012; Field 1980). Such a manifold embedding strategy, the nominalist can argue, should be nominalistically-responsible. The idea is that this nominalist strategy shouldn’t ontologically cheat by illegitimately building into the manifold itself more structure than is otherwise licensed by the science itself. The thought is that the space-time manifold, studied in cosmology, is physical. But applied mathematics is intimately involved in standard characterizations of the properties of the manifold – this is true in Newtonian cosmology, and it remains true to this day; it’s therefore easy to see why nominalists, especially ones who argue for nominalism along epistemic lines, might not accept that all the properties practicing science attributes to the items it studies, especially space-time manifolds, are nominalistically acceptable. Consider, for example, the curvature of space-time. This has been instrumentally established – more than that: locally measured! Contrast that with the space-time manifold having continuummany points – it’s a dense complete field with specific topological and metrical properties. Its density and completeness have not been established by the science at all: rather, it’s a given of the mathematics of manifolds – it’s part of the mathematics that’s applied to the phenomena studied by physics. Cosmologists, for example, don’t establish – they don’t even consider trying to establish – that the dimensionless points the space-time manifold is (mathematically) constituted of are structured as the applied mathematics understands them to be (i.e., continuum dense, …). This distinction is recognized when it comes to certain applications of mathematics. Consider the simple application of Euclidean geometry with a metric to a chalkboard. The theory quantifies over chalky diagrammatic figures: it successfully characterizes their areas and angle properties and attributes useful numeric/geometric properties to these things. We know that the implicit assumptions about the space these figure live on (and the implicit 212

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assumptions about the figures themselves) aren’t true. A flat continuum structure that we know to be false is imposed on them and on the space itself. The best way to describe the situation is to say that the chalk figures (which are real) are treated as having an internal structure that isn’t real by the imposition of a branch of applied mathematics to them. (The contours of the figures, in particular, are described as lines and curves with a continuum point structure.) This internal structure, the epistemic nominalist argues, doesn’t correspond to anything real – the entities posited (points and regions of curves and lines) don’t exist. They stand in for – they “code” for – the ultimately quantum-mechanical internal structure that these things do have. It isn’t that all the geometrical part-posits, which this application of geometry attributes to chalky figures, aren’t real. Rather, there are a moderate number of sub-regions of the chalky figures that can be treated as real, just as the chalky figures themselves are. Consider a surprisingly similar case: fluid dynamics and rational continuum mechanics (Truesdell 1991; Truesdell and Rajagopal 2000). Here, too, substantial (but known to be false) geometric and topological assumptions are made about various materials – specifically, about the topological, metrical, and geometrical properties of their posited parts. Accompanying these mathematical assumptions are rich structural embeddings of Platonic objects. The theory is empirically adequate; but the embedded Platonic objects aren’t, in any sense, instrumentally tested for. The epistemic nominalist, therefore, suggests this: consider the standard mathematical/ physical description of a scientifically-studied phenomenon. Distinguish the nominalisticallyacceptable properties/elements of the phenomenon as those that the science treats as instrumentally-testable (Azzouni and Bueno 2016). This isn’t an operational characterization: “instrumentally-testable” should be understood as a theoretically-informed interaction with the phenomenon in question – one that’s methodologically open-ended in the sense that new tools/theories are treated as ones that may emerge in the future (e.g., for studying black holes). Describe the Platonistic properties/elements as those that the science doesn’t treat as instrumentally-testable (e.g., spacetime points). This distinction isn’t one of dividing sentences that characterize a physical phenomenon into those that are nominalistically acceptable and those that aren’t. Rather, putting the matter linguistically, it divides the predicates taken to hold of physical objects into those that are nominalistically acceptable and those that aren’t. Curvature, for example, is a nominalistically acceptable property of the space-time manifold. The speed at which a (gravitational) field propagates in time and space is a nominalistically acceptable property of fields. That a field is mathematically structured of changing spacetime points isn’t a nominalistically acceptable property of fields. Manifold-embedding strategies face the challenge of characterizing mathematical structures and entities only via the nominalistically-acceptable elements/properties of manifolds and not all their elements/properties. This is a high bar, one that’s currently unmet by contemporary work. (Here I’m stating my opinion.)

18.5

Field’s Program

For a systematic understanding of various reference programs, it’s suitable to separate discussions of various maneuvers, as I’ve done. In practice, philosophers help themselves to several strategies simultaneously. This is especially true of Field’s ongoing nominalist program, which helps itself both to non-first-order logical tools and manifold-embedding strategies (and faces technical obstacles because of this). 213

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The idea is to take advantage of the fact that some mathematical applications to empirical phenomena evidently and neatly separate descriptions of the mathematics from descriptions of the empirical phenomena – for example, our applications of arithmetic to a group of zebras or the applications in ordinary life of geometry to surfaces. In both cases, presumably, the zebras and the surfaces are described in discourses that are mathematicsfree, and the geometry and arithmetic applied to them are branches of pure mathematics. Let E be the empirical subject area the pure mathematics M is applied to. Claim 1: all and only the empirically desirable results are ones in the vocabulary of E. Claim 2: The application of M to E is conservative: For any sentence s of E that follows by proof from sentences of M and E* (where E* are sentences about E known to be true), there is a proof of s from sentences of E* alone. Claim 1 and Claim 2 – if right – provide a response to the indispensability thesis apparently exhibited by the application of M to E: M isn’t essential to the proofs of the desired results of E; in particular, there’s no essential deductive relationship between the sentences of M and the results E that we use the sentences of M to deduce. We can thus take the sentences of M to be false (and therefore we needn’t be committed to what the terms of the sentences of M purportedly refer to). Current and long-standing consensus is that the program fails because of a tsunami of technical obstacles (Azzouni 2009; Azzouni 2019; Bueno 2013; Malament 1982; Melia 2006; Shapiro 1983; see Field 1989 for defense and attempted patches). A sketch of these: because the program requires a non-first-order logic and it employs a manifold-embedding strategy, it faces the objections both those strategies face. But further, and relatedly, it fails to make good on the needed separation between purely mathematical content and nominalistically-acceptable empirical content. This creates problems with establishing the needed conservation result: build enough mathematical structure into the empirical target – e.g., that the empirical target is a space-time manifold and its contents – and the applied mathematics will not be conservative. These last two problems are very application-specific: any successful case of Field’s program with respect to a specific scientific subject areas (and branch of mathematics) doesn’t generalize because of the very different mathematics involved as well as differences in the empirical content that mathematics is applied to.

18.6 Conclusions It’s barely an exaggeration that twentieth-century analytic metaphysics – this is true of the latter half of the last century and much of this one (so far, anyway) – is the exploration of numerous nominalist reference programs: via alternative logics and explorations of how nominalistic candidates, especially concreta, can be taken to have sufficient structure to proxy for mathematical entities. There are still other routes to nominalism currently being explored, ones using pretense or “weaseling”: these treat indispensable mathematics as false. This chapter could have easily been three times the size it is. Reasons of space also preclude discussion of another strategy: denying Quine’s criterion, but treating the sentences of applied mathematics as true nevertheless (Azzouni 2004). If a term-sensitive nominalist/Platonist distinction can be drawn, then it will enable a distinction between what we can responsibly take to exist and what we needn’t – despite the apparently-referential terms of applied mathematics. Without Quine’s criterion, there’s no reason to think these terms refer. My opinion: this is the most promising route for nominalists. 214

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References Armstrong, D.M. (1980) The Nature of Mind. Brighton, UK: Harvester Press. Arntzenius, F. and Dorr, C. (2012) Calculus as Geometry. In Arntzenius, F. (ed.) Space, Time, and Stuff. Oxford: Oxford University Press: 213–278. Azzouni, J. (2004) Deflating Existential Consequence: A Case for Nominalism. Oxford: Oxford University Press. Azzouni, J. (2008) A Cause for Concern: Standard Abstracta and Causation. Philosophia Mathematica 16(3): 397–401. Azzouni, J. (2009) Evading Truth Commitments: The Problem Reanalyzed. Logique et Analyse 52(206): 139–176. Azzouni, J. (2019) The Challenge of Many Logics: A New Approach to Evaluating the Role of Ideology in Quinean Commitment. Synthese 196(7): 2599–2619. Azzouni, J. and Bueno, O. (2016) True Nominalism: Referring Versus Coding. British Journal for the Philosophy of Science 67(3): 781–816. Benacerraf, P. (1973) Mathematical Truth. Journal of Philosophy 70(19): 661–679. Boolos, G. (1984) To Be is to be a Value of a Variable (or to be Some Values of Some Variables). Journal of Philosophy 81(8): 430–449. Reprinted in Jeffrey, R.C. (ed.) Logic, Logic, and Logic. Harvard: Harvard University Press: 54–72. Boolos, G. (1985) Nominalist Platonism. Philosophical Review 94(3): 327–344. Reprinted in Jeffrey, R.C. (ed.) Logic, Logic, and Logic. Harvard: Harvard University Press: 37–53. Bueno, O. (2013) Nominalism in the Philosophy of Mathematics. In Zalta, E.N. (ed.) Stanford Encyclopedia of Philosophy, URL = < http://plato.stanford.edu/archives/fall2013/entries/ nominalism-mathematics/> Callard, B. (2007) The Conceivability of Platonism. Philosophia Mathematica 15(3): 347–356. Callard, B. (2023) Can Math Move Matter? Inquiry 66(3): 355–380. Cantor, G. (1996[1891]) On an Elementary Question in the Theory of Manifolds. In Ewald, W. (ed.) From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford: Oxford University Press: 920–922. Chihara, C. (2004) A Structural Account of Mathematics. Oxford: Oxford University Press. Colyvan, M. (2001) The Indispensability of Mathematics. Oxford: Oxford University Press. Field, H. (1980) Science Without Numbers: A Defence of Nominalism. Princeton, NJ: Princeton University Press. Field, H. (1989) Realism, Mathematics and Modality. Oxford: Blackwell. Frege, G. (1953[1893]) The Foundations of Arithmetic. Trans. J.L. Austin. 2nd ed (revised). Evanston, IL: Northwestern University Press. Goodman, N. and Quine, W.V. (1947) Steps Toward a Constructive Nominalism. Journal of Symbolic Logic 12(4): 105–122. Hellman, G. (1989) Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford: Oxford University Press. Lewis, D. (1991) Parts of Classes. Oxford: Blackwell. Maddy, P. (1992) Indispensability and Practice. Journal of Philosophy 89(6): 275–289. Malament, D. (1982) Review of “Science Without Numbers: A Defence of Nominalism”. Journal of Philosophy 79(9): 523–534. Melia, J. (2006) The Conservativeness of Mathematics. Analysis 66(3): 202–208. Panza, M. and Sereni, A. (2016) The Varieties of Indispensability Arguments. Synthese 193(2): 469–516. Plato (1963a) Phaedo. In Hamilton, E. and Cairns, H. (eds.) The Collected Dialogues of Plato. Princeton, NJ: Princeton University Press: 40–98. Plato (1963b) Sophist. In Hamilton, E. and Cairns, H. (eds.) The Collected Dialogues of Plato. Princeton, NJ: Princeton University Press: 957–1017. Putnam, H. (1975a) Philosophy of Logic. In Putnam, H. (ed.) Mathematics, Matter and Method. Cambridge: Cambridge University Press: 323–357. Putnam, H. (1975b) Mathematics Without Foundations. In Putnam, H. (ed.) Mathematics, Matter and Method. Cambridge: Cambridge University Press: 43–59.

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Jody Azzouni Quine, W.V. (1980[1953]) On What There Is. In Quine, W.V. (ed.) From a Logical Point of View. Cambridge, MA: Harvard University Press: 1–19. Quine, W.V. (1970) Philosophy of Logic. Englewood Cliffs, NJ: Prentice Hall. Resnik, M. (1997) Mathematics as a Science of Patterns. Oxford: Oxford University Press. Rosen, G. and Dorr, C. (2002) Composition as a Fiction. In Gale, R.M. (ed.) The Blackwell Guide to Metaphysics. Oxford: Blackwell: 151–174. Shapiro, S. (1983) Conservativeness and Incompleteness. Journal of Philosophy 80(9): 521–531. Sober, E. (1993) Mathematics and Indispensability. Philosophical Review 102(1): 35–57. Troelstra, A.S. (1991) History of Constructivism in the 20th Century. In Kennedy, J. and Kossak, R. (eds.) Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Cambridge: Cambridge University Press: 150–179. Truesdell, C. (1991) A First Course in Rational Continuum Mechanics. Vol. 1. Boston, MA: Harcourt Brace Jovanovich. Truesdell, C. and Rajagopal, K.R. (2000) An Introduction to the Mechanics of Fluids. Berlin: Birkhäuser. van Fraassen, B. (1980) The Scientific Image. Oxford: Oxford University Press. van Inwagen, P. (1990) Material Beings. Ithaca, NY: Cornell University Press.

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PART 5

Trope Theory

19 TROPE NOMINALISMS Douglas Ehring

19.1

Introduction

Traditional Metaphysical Realists assert that there are both universals in the form of properties and particulars. Nominalists affirm that there are only particulars (see Rodriguez-Pereyra 2019 for other senses of “nominalism”).1 Although Trope Nominalists agree with Realists that there are properties, they deny that properties are universals. Trope Nominalists, on the other hand, also reject the claim that properties are sets of unstructured objects, a view held by a number of object-based Nominalists. Properties are tropes. A trope is both a property and a particular although a trope is not composed of, or constituted by, a property and a distinct particular. As such tropes are not exemplifications of universals by particulars. Tropes are categorially simple with no non-trope constituents. Examples of tropes include the wisdom of Plato and the spin property of this electron.2 As particulars, tropes are generally characterized as being incapable of being wholly present at different places at the same time, the most common conception of particulars.3 The mass property of this electron here is numerically distinct from the mass property of a distant electron even though these mass properties are exactly similar. Additionally, for Trope Nominalists, tropes are the sole building blocks of all that exists. Trope Nominalists, for instance, reject the view that a concrete object consists in a substratum in which tropes inhere (for substrata-trope theory see Heil 2003 and Martin 1980). Concrete objects are bundles, all the constituents of which are tropes (for a discussion of bundle theories, see Chapters 14 and 21, this volume). And property types, such as charge in general, are sets of tropes.4 In short, for the Trope Nominalist, (1) there are no universals, (2) property instances and property types are fully analyzable in terms of tropes, and (3) individual objects are bundles of tropes (see Bacon 1995; Campbell 1990; Ehring 2011; Maurin 2002; Stout 1921–1923 and 1923; Williams 1953a, 1953b, and 1986). Trope Nominalists argue that Trope Nominalism is superior to its two- and onecategory rivals. Keith Campbell, for example, argues that the main two-category alternative to Trope Nominalism, with an ontology of particulars and universals, faces difficulties not faced by Trope Nominalism, including misgivings about universals, objections to the substratum or bare particular component of concrete particulars, as well as objections to

DOI: 10.4324/9781003246077-25

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the relation of instantiation that is supposed to bind the items from the two categories together in concrete particulars (Campbell 1990). It has also been claimed that Trope Nominalism provides better metaphysical accounts of various phenomena than does an ontology of universals and particulars, including perception (Williams 1953a: 16–17), causal relata (Campbell 1990: 23; Denkel 1996: 185; Ehring 1997 and 2009: 406-407; Williams 1953b: 172: chs. 3 and 4), events (Bennett 1988: 90; Campbell 1990: 22), mental causation (Ehring 2011; Robb 1997: 186–188: ch. 5), various linguistic phenomena (Moltmann 2007: 363; Wolterstorff 1960: 187), structural properties (Campbell 1990: 46), property persistence (Ehring 1997: 91–115) and stationary versus moving properties (Ehring 2011: 50–68). Trope Nominalists further suggest that even if Trope Nominalism and its two-category Realist rival were of equivalent explanatory power (and equally internally defensible), Trope Nominalism would be preferable on the basis of Occam’s Razor (Campbell 1990: 17). Finally, Trope Nominalists maintain that the main onecategory alternatives to Trope Nominalism, including Resemblance Object Nominalism, Substratum-Trope Theory, and a one-category Universalism, face insurmountable objections not faced by Trope Nominalism (Campbell 1990: 17–20, 32–34). In the following, I will first outline three versions of Trope Nominalism and three different accounts of trope individuation. I will then defend a specific version of Trope Nominalism, Natural Class Trope Nominalism, along with a specific account of trope individuation, a primitivist account. Finally, I will consider certain objections to Trope Nominalism including Natural Class Trope Nominalism.

19.2

Three Trope Nominalisms

A key question that a Trope Nominalist must answer is what, if anything, determines the nature of a trope. Different answers to this question give rise to different forms of Trope Nominalism. According to the most popular version of Trope Nominalism, which I will call Standard Trope Nominalism (STN), the nature of a trope is not determined by its resemblance relations to other tropes nor by its membership in natural classes of tropes. “What is it about charge in virtue of which it is charge? It is being what it is” (Campbell 1990: 30). A trope’s nature determines its relations of resemblance to other tropes and its membership in natural classes of tropes. Resemblance between tropes is an internal relation grounded in the intrinsic nature of those tropes, which is not determined by anything else. Resemblance Trope Nominalism (RTN) differs from STN with respect to how the nature of a trope is determined. For RTN, the nature of a trope is determined by that trope’s resemblance relations to other tropes, not the other way around. And resemblance among tropes is not further reducible. This is the trope analogue to object-based Resemblance Nominalism. For the Natural Class Trope Nominalism (NCTN), the nature of a trope is determined by its memberships in natural classes of tropes (Ehring 2011: 175; Stout 1921–1923: 3–4). What is it about a charge trope in virtue of which it is a charge trope? It is its membership in a certain natural class of charge tropes. The notion of a natural class is taken as a primitive and the naturalness of a class of tropes is not grounded in the nature of tropes or in the resemblance relations between tropes nor otherwise grounded.5 Resemblance among tropes consists in co-membership in a natural class. For STN, similarity across concrete particulars – attribute agreement – is explained by reference to the similarity of the non-identical tropes that each object possesses. For RTN, attribute agreement across concrete particulars is also explained by reference to the 220

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similarity of non-identical tropes that each object possesses, but on the assumption that resemblance between tropes is not determined by the intrinsic nature of the tropes. For NCTN, the similarity of objects is explained by reference to co-membership of nonidentical tropes that each object possesses in a common natural class. For STN, fully determinate property types are maximal classes of exactly resembling tropes such that the trope members of that class exactly resemble each other and there are no tropes outside that set that exactly resemble those tropes. The same is true for RTN on the assumption that trope-trope resemblance is not reducible. For NCTN, a fully determinate property type, F-ness, is the maximal and perfectly natural class of F-tropes.6 For STN, RTN and NCTN, a concrete particular is a bundle of tropes with no nonproperty constituent, such as a substratum or bare particular, and uniting tropes into a bundle is the relation of compresence. “o is F” (excluding some “F’s” such as “does not exemplify itself”) is true if and only if the bundle of tropes that constitutes o overlaps the set of tropes that make up the F-ness property type. STN and RTN agree that true sentences involving abstract reference, such as “courage is a virtue”, are generally accounted for as follows. “Courage” operates as a name, naming the maximal set of resembling courage tropes and this sentence is true because the set of courage tropes, which is the property type “courage”, is a subset of the set of virtue tropes. RTN, however, differs from STN in rejecting the claim that resemblance between tropes is determined by the intrinsic nature of the tropes. For NCTN, “courage” operates as a name, naming a natural class of courage tropes, and the sentence asserts that the set of courage tropes is a subset of the natural class of virtue tropes.7 A further dimension of variation across Trope Nominalisms depends on how trope individuation is specified. There are three accounts of how to individuate tropes that are intrinsically exactly similar to each other. (Tropes which are not intrinsically exactly similar are automatically distinct.) According to the Primitivist Principle (PI), intrinsically exactly similar tropes in the same world are numerically distinct tropes if and only if they are numerically distinct (Campbell 1990: 69; Ehring 2011: 76). The Spatio-Temporal Principle (SI) is that intrinsically exactly similar tropes in the same world are numerically distinct if and only if there is non-zero distance between them (Schaffer 2001: 249). The Object Principle (OI) says that exactly similar tropes in the same world are distinct just in case they characterize wholly distinct objects. OI is not well-suited to Trope Nominalism given that the latter includes a trope-bundle theory of concrete particulars. On a bundle theory, the individuation of an object depends on the individuation of the elements, the tropes of the bundle, generating circularity on this principle (Ehring 2011: 77; Lowe 1998: 206; Schaffer 2001: 249). OI is also incompatible with the possibility of free-floating, “object-less” tropes, which are allowed for by some proponents of tropes (Campbell 1990: 21; Schaffer 2003: 134–138; Williams 1953b: 179).8

19.3

Natural Class Trope Nominalism and the Primitivist View of Trope Individuation

Which form of Trope Nominalism is preferable? There are reasons to think that the answer is Natural Class Trope Nominalism combined with a primitivist view of trope individuation. Although SI and PI are each compatible with Trope Nominalism, the balance of arguments seem to favor PI over SI. First, SI excludes, but PI does not, the possibility of non-spatio-temporal tropes. Second, SI, but not PI, rules out the possibility of all forms 221

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of trope piling. Trope piling consists in the presence of at least two exactly similar tropes, t1 and t2, in the same location at the same time. In one form of trope piling, trope pyramiding, there are differences in the causes/effects of such a pile when compared to the presence of t1 alone or t2 alone. ST excludes the possibility of trope pyramiding since it is a form of trope piling. However, excluding trope pyramiding cannot be justified by the principle that a difference that does not make a causal difference is not possible since trope pyramids do make a causal difference. Furthermore, excluding trope piling generates an explanatory lacuna for ST. Consider that ST does not exclude the possibility of “imperfect trope piling”, piles of inexactly similar tropes, say, in the form of imperfect trope pyramiding. ST allows, for example, for the possibilities of an imperfect trope pyramid consisting of a mass trope of 1 gram and a 1.00001 gram trope and of a trope pyramid of a 1 gram trope with a .9999 gram trope, while excluding the possibility of trope pyramid of two exactly similar 1 gram tropes. It is hard to see how ST might explain why the latter is excluded if the former is not excluded.9 As for the variants of Trope Nominalism, there is a reason to reject STN. As noted, Trope Nominalists hold that tropes are categorially simple, lacking constituents that are not tropes either in the form of bare particulars, concrete particulars or universals. A trope is not a “union of distinct elements, one particularizing and the other furnishing a nature” (Campbell 1990: 20). In addition, for the proponent of STN, the nature of a trope is determined solely by the trope itself, not by any relations among tropes as are the natures of RTN and NTCN tropes. The desideratum of categorial simplicity, combined with the non-relational determination of their natures, however, gives rise to a serious objection to STN (see Armstrong 2005: 310; Ehring 2011: 174–187; Hochberg 2001: 178–179; 2004: 39; Moreland 2001: 70–71. For a comparison of the Hochberg and Armstrong versions of this argument see Maurin 2016). Here is one version of this objection. If a redness trope t1 and redness trope t2 resemble each other and are non-identical to each other, and both of these relations are internal relations, as per STN, grounded in intrinsic aspects of these tropes, t1 and t2 must each have two different intrinsic aspects, a particularizing (a thisness) and a nature-giving aspect (redness) (For this and other versions of this line of objection, see Ehring 2011: 175–187). This objection does not apply to RTN or NCTN. For RTN and NCTN, the nature of a trope is not determined by the trope itself. For RTN, the nature of a trope is not an intrinsic matter but is grounded in resemblance relations among tropes. For NCTN, the nature of a trope is also not an intrinsic matter but is grounded in its membership in various natural classes of tropes. Hence, this objection cannot get started against RTN and NCTN. Various responses to this line of argument are grounded on either the claim that “formal” classifications do not have ontological implications or the claim that formal distinctions do not track ontological differences. (1) Jani Hakkarainen and Markku Keinänen argue that particularity is a “formal feature” of a trope, not an “ontologically content-ful feature”, and that formal features are not “entities”, so they are not identical to nor distinct from anything. There is no intrinsic aspect of a trope that is a particularizing aspect of the trope (Hakkarainen and Keinänen 2017: 462). So, “… internal relations may differ arbitrarily without rendering their relata non-simple, due to the difference between … ‘ontological content’ and ‘ontological form’” (2017: 651). For this objection to be convincing, however, an acceptable explication of the distinction between “ontological 222

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content” and “ontological form” must be formulated but, as Kevin Mulligan points out, this distinction may “sound good” until we try to characterize it (1998: 343). Furthermore, on this view, formal predicates such as “is a particular” do not express ontological aspects of entities even when truly predicated of them. One then wonders why one would not extend this thesis to non-formal predicates such as “is red”. The result would be Austere or Extreme Nominalism (Griffith 2015: 28–29). (2) Campbell suggests that the distinction between the nature and particularity of a trope is merely a formal distinction or a “distinction by abstraction”, and though these aspects of a trope can be separated in the mind by abstraction, in reality they are identical (1990: 56–57). For this response to be persuasive, however, we would need an account of “abstracting” that has this implication. Certain obvious candidates do not have this implication. If abstracting is selectively attending to one feature rather than attending to another, non-identical feature, this appeal to abstraction will not provide a basis for rejecting this kind of argument. And if abstraction means thinking of something not as falling under a species but as falling under a genus, it will not be relevant since, for example, crimsonness is not a species of particularity. So it is at least not clear that there is an adequate account of a distinction by abstraction that will do the work Campbell assigns to it. Although both NCTN and RTN are immune to this “simplicity” objection, there are advantages to NCTN over RTN. (1) RTN does not preserve the intuitively plausible claim that that resemblance among tropes is determined by the nature of tropes. For RTN, the nature of a trope is logically posterior to its resemblance relations to other tropes. NCTN does preserve this claim. (2) According to RTN, the formal characteristics of the resemblance relation must be taken as primitive. These features include the reflexivity, symmetry and transitivity of exact resemblance and the reflexivity, symmetry and non-transitivity of inexact resemblance. These features of resemblance, however, should be explainable (Armstrong 1989: 102–103). For NCTN, they are. A NCTN trope’s resemblance relations to other tropes depends on their joint membership in various natural classes of tropes and the formal features of resemblance can be explained or derived from the membership of tropes in natural classes (Ehring 2011: 187–193).

19.4 Objections to Natural Class Trope Nominalism I turn now to various objections to NCTN, some of which apply to all variants of Trope Nominalism and some to NCTN but not all variants. I will begin with the former. A number of objections to Trope Nominalism focus on the modality of properties. Consider, first, what might be called the “One-Over-Fewer” objection (see Wolterstorff 1970: 80). Suppose that a property type is a class of actual tropes and that the property type “redness” is the class of all actual redness tropes. Given that a class has its membership essentially, the class of all actual red tropes would not have existed had even just one actual red trope not existed. If the type “redness” is identical with that class, then it would seem to follow that had even a single member of the class of red tropes not existed, then there would have been no such thing as the “redness” property type, or the property type “redness” would have been different. But this disjunctive implication is false.10 One response to this objection involves combining Trope Nominalism with Modal Realism. The One-Over-Fewer objection cannot get a footing if property type “redness” is identical to the class of both actual and merely possible red tropes. However, Modal Realism is not widely accepted. An alternative combines Trope Nominalism with a counterpart theory for 223

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properties in the context of an actualist account of modality, say, in the form of linguistic ersatzism. It could, then, be claimed that there is a world w that includes a representation of a “type” counterpart to the actual class of redness tropes (“redness”) which is represented as lacking one member of that class but as otherwise no different than the class of actual red tropes although w lacks a representation of a “class” counterpart to that class. So it is true that “redness could have had one fewer instance” since there is a world in which there is a type counterpart to the type “redness” but no class counterpart to the class of actual red tropes (Ehring 2011: 206–214). A second objection to Trope Nominalism, also involving modality, charges that Trope Nominalism is not consistent with the fact that determinates necessitate their determinables. Suppose that the property type “redness” is a class R of actual red tropes and that the property type “crimson” is a subclass of tropes, C, of R. If none of the actual noncrimson red tropes had existed, then R would not have existed (since R consists solely of actual red tropes), and if R had not existed, but C had, the property type “crimson” would not have been a determinate of the property type “redness”. Thus, according to Trope Nominalism, determinates do not necessitate their determinables (Ehring 2011: 229). In response one might expand the “redness” class to include both actual and merely possible redness tropes, but, again, that requires Modal Realism. Alternately, the Trope Nominalist can adopt a counterpart theory for properties in the context of an actualist account of modality such as linguistic ersatzism. The Trope Nominalist can, then, argue that in the closest possible world w in which there is type counterpart to C, C’, but no type counterparts to any of the other shades of red, C’ is itself a type counterpart to R and the only such counterpart. If none of the non-crimson red tropes had existed, the property type “crimson” would still have been a determinate of the property type “redness”. Another general objection to Trope Nominalism, also having to do with the modality of properties, is the “trope coextension objection”. Trope Nominalists have historically claimed that their theory is exempt from the “coextension objection” to object-based Resemblance Nominalism, but Trope Nominalism may face its own co-extension objection (Manley 2002: 83–84). Suppose that all red objects are crimson, so that the class of actual red tropes is identical to the class of actual crimson tropes. If the property types are classes of actual tropes only, then “redness” is identical to the property type “crimsonness”. However, it is possible for there to be instances of the property type “redness” that are not instances of the property type “crimsonness”. Hence it is possible for the type “redness” and the type “crimsonness” not to be identical. But it is not possible for the type “crimsonness” not to be identical to the type “crimsonness”. Therefore, the property type “redness” is not identical to the property type “crimsonness”. In response we might again bring into play Modal Realism, expanding the relevant property types to include both actual and merely possible tropes. Or we can make use of a counterpart theory for properties combined with an actualist account of modality such as linguistic ersatzism (Ehring 2015: 125–127). The property type “redness” and the property type “crimsonness” denote the same property type in our case, but the property type “redness” invokes a different counterpart relation than does the property type “crimsonness”. It is false that there is a possible world with a unique “crimsonnness” counterpart, X, of the property type “crimsonness” and a unique “crimsonness” counterpart, Y, of the property type “crimsonness” such that X and Y are not identical. But it is true that there is a world, w, in which there is a “redness” counterpart to the class of actual redness tropes that is not identical to the “crimson” counterpart in w to that same class. Something could have been 224

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red and not crimson and that is consistent with the claim that “redness” is identical to “crimsonness” in our case. (For a different response, see Jaworski 2016: 48–49.) Another objection that is also focused on modality is the swapping objection. The swapping objection is supposed to show that properties cannot be tropes (Armstrong 1989: 131–132). If properties are tropes, not universals, then it should be possible that two properties that are exactly similar to each other could have occupied swapped locations. But property swapping is not genuinely possible.11 Property swapping is not possible because it would consist in a difference without a causal difference. One response to the trope swapping objection is to deny that trope swapping would not give rise to a causal difference: “… it is not true to say that the swap produces absolutely no difference in the situation. But there is a difference in individuation. The natures of the effects are exactly similar … But … these effects are now the effects of F2 rather than F1. The individuality of their aetiology has been changed. So the difference that the swap produces is not spurious and the objection fails” (Campbell 1990: 72; “F1” and “F2” refer to swapped qualitatively indistinguishable tropes). Another response is to point out, first, that this objection would seem to give rise to a broader objection to particulars in general not just tropes. Since it is possible for two particulars, tropes or not, to be qualitatively indistinguishable, it is possible that those particulars could have been swapped without making a causal difference. If a difference that does not make a causal difference is not possible, it follows that there are no particulars. So unless one rejects the possibility of qualitatively indistinguishable particulars generally by, for example, adopting a one-category Universalism, every theory of properties will face some version of this objection and, hence, it is not a reason for rejecting Trope Nominalism in particular and for adopting some other theory of properties. There are a number of objections to NCTN which do not necessarily apply to other variants of Trope Nominalism. I mention two. The first has to do with the role of properties in causation. According to this objection, if a trope’s being of a certain sort is a matter of its membership in a certain natural class of tropes as per NCTN, then when a thing x acts in virtue of having a trope, t, of a certain nature, that thing’s efficacy will require the relevancy of that trope’s membership in at least one natural class of tropes, C, and, thus, the causal relevancy of the other members of that class, which is highly implausible (this objection is based on Armstrong’s objection to object-based Natural Class Nominalism; Armstrong 1989: 49–50). This objection can be restated as follows: (1) Even if t had not been a member of C, solely in virtue of the absence of some of the other non-t members of C, x would still have caused e. Hence, from (1), (2) even if t had not been a T-type trope, solely in virtue of the absence of some of the other non-t members of C, x would still have caused e. Hence, from (2), (3) t’s being a T-type trope is irrelevant to x’s causing e in virtue of t. In fact, if Natural Class Trope Nominalism is combined with property counterpart theory, then it is not necessarily true that if some of the members of C had not existed, nothing would have been a T-type trope. We can reasonably assume that there is a “type” counterpart relation that differs from a “class” counterpart relation opening up the possibility of worlds in which there is a type counterpart to T but no class counterpart to T. It would only automatically follow from Natural Class Trope Nominalism that t’s being a 225

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T-type trope is causally irrelevant from the fact that the non-t members of T are irrelevant if it automatically followed that had some of the non-t members of T not existed, then t would not have been a T-type trope. Another objection to NCTN is an “order of explanation” objection. According to this objection, NCTN is inconsistent with the plausible claim that membership in a natural class is determined by that trope’s nature not the other way around. In response, one might argue that although this consequence is counterintuitive, NCTN may still be the best of our options among the three variations of Trope Nominalism. Although STN avoids this order of explanation objection, the tropes of STN fail to be categorially simple. And the tropes of RTN are subject to their own order of explanation objection in that the resemblance relations of RTN tropes are not determined by their natures, but the other way around. Since both NCTN and RTN are subject to an order of explanation objection, we should opt for NCTN over RTN since the former makes the logic of resemblance non-primitive.

Notes 1 Austere or Extreme Nominalists claim that there are no properties (or relations) and deny that there is ever anything that metaphysically accounts for object o’s being F ( Devitt 1980). Moderate Nominalists generally, but not without exception, affirm that there are properties and hold that properties are reducible to sets of concrete particulars meeting certain conditions such as mutual resemblance. 2 The properties at issue in discussions of Trope Nominalism are generally restricted to “sparse properties” rather than “abundant properties”. Whereas there is an abundant property for “any condition we could write down…” sparse properties are picked out, primarily, by reference to their role in accounting for similarity among concrete particulars and accounting for the causal powers of concrete particulars ( Lewis 1986: 59–60). Not every abundant property is a sparse property (for a discussion of sparse and abundant properties, see Chapter 4, this volume). 3 On the “Aristotelian” characterization of the universal/particular distinction, universals exist in space and time, but can be wholly present in more than one location at the same time, unlike particulars. On an alternative way of making the distinction, exactly similar universals cannot fail to be identical, but exactly similar particulars can fail to be identical ( Ehring 2011: 32–35; Williams 1986: 3; for objections to this view, see Rodriguez-Pereyra 2017 and Giberman 2016). On this alternative, a trope could be wholly present at more than one place at the same time, but still be a particular as long as exact similarity does not guarantee identity. 4 In addition, since tropes ordinarily occur in clusters, they can only generally be “brought before the mind … by a process of selection, of systematic setting aside, of these other qualities…” ( Campbell 1990: 2). 5 The naturalness of a natural class of tropes comes in degrees. 6 A different view is found in Williams for whom the distinction between a case and a property type or kind “is not a difference in the category but in rule for counting” ( Campbell 1990: 44). “Entities … not subject to the identity of indiscernibles, are cases or particulars; entities … subject to the identity of indiscernibles, are ‘general’ entities, that is, kinds or universals” ( Williams 1986: 8). For Williams, a property type or kind is not a set of similar tropes but a trope considered under a counting rule that takes perfectly qualitatively indistinguishable tropes as identical. As Campbell says, when describing Williams’s view, “[t]his one thing is not a new thing but our familiar tropes now treated in a way that gives them some of the distinctive features of universals” ( Campbell 1990: 45). 7 Alternately, Trope Nominalists might read these sentences as involving plural reference ( Jaworski 2016: 39 footnote 2.). 8 If objects have substrata and free-floating tropes are not possible, OI is a serious possibility. 9 A further reason for rejecting ST is that it rules out the possibility of a time-traveling, enduring trope that meets itself. Such a trope would be at a distance from itself. (For further reasons for rejecting ST and a critique of some arguments in favor of ST, see Ehring 2011: ch. 3).

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Trope Nominalisms 10 This objection has a further implication for NCTN and RTN. For NCTN and RTN, the nature of a red trope depends on its membership in the class of redness tropes. So if the latter includes all and only actual redness tropes, then had a single red trope, r1, not existed, this color trope, r2, of this red ball would not have been a redness trope and so nothing would have been red including this ball. 11 Property swapping is not possible if properties are universals.

References Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder: Westview. Armstrong, D.M. (2005) Four Disputes about Properties. Synthese 144(3): 309–320. Bacon, J. (1995) Universals and Property Instances: The Alphabet of Being. Oxford: Blackwell. Bennett, J. (1988) Events and Their Names. Oxford: Oxford University Press. Campbell, K. (1990) Abstract Particulars. Oxford: Blackwell. Denkel, A. (1996) Object and Property. Cambridge: Cambridge University Press. Devitt, M. (1980) Ostrich Nominalism’ or ‘Mirage Realism’? Pacific Philosophical Quarterly 61(4): 433–439. Ehring, D. (1997) Causation and Persistence: A Theory of Causation. New York: Oxford University Press. Ehring, D. (2009) Causal Relata. In Beebee, H., Hitchcock, C. and Menzies, P. (eds.) Oxford Handbook on Causation. Oxford: Oxford University Press: 387–423. Ehring, D. (2011) Tropes: Properties, Objects and Mental Causation. Oxford: Oxford University Press. Ehring, D. (2015) The Trope Coextension Problem. In Rodriguez-Pereyra, G. and Ghislain, G. (eds.) Nominalism about Properties: New Essays. New York: Routledge: 121–134. Giberman, D. (2016) Indiscernibility Does Not Distinguish Particularity. Thought: A Journal of Philosophy 5(4): 249–256. Griffith, A. (2015) Do Ontological Categories Exist? Metaphysica 16(1): 25–35. Hakkarainen, J. and Keinänen, M. (2017) The Ontological Form of Tropes – Refuting Douglas Ehring’s Main Argument against Trope Nominalism. Philosophia 45(2): 647–658. Heil, J. (2003) From an Ontological Point of View. Oxford: Oxford University Press. Hochberg, H. (2001) Individuation and Individual Properties: A Study of Metaphysical Futility. The Modern Schoolman 79(2–3): 107–135. Hochberg, H. (2004) Relations, Properties, and Particulars. In Hochberg, H. and Mulligan, K. (eds.) Relations and Predicates. Frankfurt: Ontos Verlag: 17–53. Jaworski, W. (2016) Structure and the Metaphysics of Mind: How Hylomorphism Solves the MindBody Problem. Oxford: Oxford University Press. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Lowe, E.J. (1998) The Possibility of Metaphysics: Substance, Identity, and Time. Oxford: Clarendon Press. Martin, C.B. (1980) Substance Substantiated. Australasian Journal of Philosophy 58(1): 3–10. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. Maurin, A.-S. (2016) Tropes: For and Against. In Calemi, F.F. (ed.) Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. Berlin: De Gruyter: 85–104. Manley, D. (2002) Properties and Resemblance Classes. Noûs 36(1): 75–96. Moltmann, F. (2007) Events, Tropes, and Truthmaking. Philosophical Studies 134(3): 363–403. Moreland, J.P. (2001) Universals. Kingston, ON: McGill-Queen’s University Press. Mulligan, K. (1998) Relations: Through Thick and Thin. Erkenntnis 48(2–3): 325–353. Robb, D. (1997) The Properties of Mental Causation. Philosophical Quarterly 47(187): 178–194. Rodriguez-Pereyra, G. (2017) Indiscernible Universals. Inquiry 60(6): 604–624. Rodriguez-Pereyra, G. (2019) Nominalism in Metaphysics. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, URL = < https://plato.stanford.edu/archives/sum2019/entries/ nominalism-metaphysics/>. Schaffer, J. (2001) The Individuation of Tropes. Australasian Journal of Philosophy 79(2): 247–257.

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Douglas Ehring Schaffer, J. (2003) The Problem of Free Mass: Must Properties Cluster? Philosophy and Phenomenological Research 66(1): 125–138. Stout, G.F. (1921-3) The Nature of Universals and Propositions. Proceedings of the British Academy 10: 157–172. Stout, G.F. (1923) Are the Characteristics of Particular Things Universal or Particular? Proceedings of the Aristotelian Society, Supplementary Volume 3: 114–122. Williams, D.C. (1953a) On the Elements of Being I. Review of Metaphysics 7(1): 3–18. Williams, D.C. (1953b) On the Elements of Being II. Review of Metaphysics 7(2): 171–192. Williams, D.C. (1986) Universals and Existents. Australasian Journal of Philosophy 64(1): 1–14. Wolterstorff, N. (1960) Qualities. Philosophical Review 69(2): 183–200. Wolterstorff, N. (1970) On Universals: An Essay in Ontology. Chicago: University of Chicago Press.

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20 TYPES OF TROPES Modifier and Module Robert K. Garcia

20.1

Introduction

According to trope theory, properties exist but are non-shareable, or “tropes”. Unlike universals, tropes are non-sharable in that it is impossible for a trope to characterize distinct objects at the same time.1 For example, if c1 is the cubicity trope of cube a at time t, then no object wholly distinct from a is characterized by c1 at t. If a distinct cube b also exists at t, then there is a cubicity trope, c2, such that c1 and c2 are exactly similar but numerically distinct. In characterizing an object, a trope plays the role of a character-grounder. In our example, a is cubical in virtue of having c1 and b is cubical in virtue of having c2. We thus have the general concept of a trope, that of a non-shareable charactergrounder. As we will see, this general concept is ambiguous in a way that allows a distinction between two more specific concepts: modifier tropes and module tropes. After distinguishing these types of tropes (Section 20.2) I will go on to show how they are unequally suited for metaphysical work. Modifier tropes have advantages concerning powers (Section 20.3) and fundamental determinables (Section 20.4), whereas module tropes have advantages concerning perception and causation (Section 20.5). In addition, each resulting trope theory faces unique implications and challenges concerning charactergrounding. Modifier trope theory faces challenges concerning the inscrutability of predication and the incompatibility with bundle theory (Section 20.7), whereas module trope theory faces challenges concerning character overdetermination and a collapse into austere nominalism (Section 20.8).

20.2

Modifier Tropes versus Module Tropes

We can arrive at the distinction by considering a specific trope and using the law of excluded middle to ask a question about the character of the trope itself. Consider a range of putative tropes that one might find in either abundant or sparse trope ontologies. Applying the law of excluded middle, we can ask: Is a negative charge trope itself negatively charged? Is a mass trope itself massive? Is a salinity trope itself saline? Is a sphericity trope itself spherical? Is a fragility trope itself fragile? Is a hotness trope itself hot? Is a hardness trope

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itself hard? Is a redness trope itself reddish? Is a courage trope itself courageous? Is a value trope itself valuable? And so on. In each case, the two ways of answering the question map onto two different conceptions of a trope: the affirmative answer yields what I call a module trope, the negative a modifier trope. It is desirable to move from specific questions about putative tropes to a general question that delivers the module/modifier distinction. Because tropes are character grounders, one way to frame the general question is in terms of whether tropes have the character they ground (Garcia 2015b; Maurin 2023); here we might say that a module trope has the character it grounds whereas a modifier trope does not. Alternatively, we could frame the general question in terms of whether tropes are self-exemplifying; here we might say that a module trope is self-exemplifying whereas a modifier trope is not (Garcia 2016). I take these ways of framing the question to be equivalent. However, both are potentially misleading and require caveats. On the one hand, the relational language (“have” and “exemplify”) might lead you to conclude that where there is a module trope there are two entities: the trope (which has or exemplifies the character) and the relevant character (which is had or exemplified by the trope). But that would be a mistake. A module trope is simple and not composed of one trope characterizing another trope. On the other hand, the language of self-exemplification should not be taken to imply that a module trope is charactered logically posterior to (and as a result of) it functioning as a character-grounder. That would be a mistake for two reasons. First, it would assume that character grounding is possibly reflexive, which is at least controversial if not false (see Rodriguez-Pereyra 2015 and Schaffer 2009). Second, tropes are supposed to be fundamental entities and character-grounders of everything else. Thus, the character and nature of a trope is determined logically prior to its functioning as a character grounder. For example, a sphericity module trope is spherical logically prior to its functioning as a character grounder; it is not the case that a sphericity module trope is spherical in virtue of grounding its own character or as a logical result of exemplifying itself. Thus, to ask whether the sphericity trope is self-exemplifying (or has the character it grounds) is really to ask whether the trope itself is spherical logically prior to its functioning as a character grounder. To frame the question more generally, to ask whether a trope is selfexemplifying (or has the character it grounds) is to ask whether the trope itself is charactered in the relevant way logically prior to its functioning as a character grounder. So much for the caveats on “having character” and “self-exemplification”. Let them be understood in what follows. Nevertheless, in so far as it is feasible, perhaps it is best to avoid speaking of a trope “exemplifying” or “having” character and, instead, to speak of a trope “being charactered”. In keeping with this, I suggest we frame our general question as follows: is a trope itself charactered in the way of being charactered that it is supposed to ground? Or, where F-ness names a trope and F-ish is the adjective for the way of being charactered that F-ness grounds, we could also put it this way: Is F-ness itself F-ish? The two ways of answering this question disambiguate the general concept of a trope into two types. A yes gives you the concept of a module trope and a no gives you the concept of a modifier trope. To set the stage for considering their relative merits, it will be helpful to more closely consider each type of trope in turn. A modifier trope is comparable to an immanent non-self-exemplifying universal, the difference being that only the latter is sharable. Like the universal, the modifier trope does 230

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not exemplify, have, or bear the character it grounds. Instead, a modifier trope grounds the character of its bearer: it characterizes its bearer in some single and specific way. On this view, a billiard ball is hard in virtue of its hardness trope and spherical in virtue of its sphericity trope, but the hardness trope is not itself hard and the sphericity trope is not itself spherical. The sphericity modifier trope is a non-shareable, non-spherical, spheremaker or spherizer. Thus, a modifier trope is what we might call a character-maker in that it makes something else charactered but the trope is not itself charactered in that way. The latter qualification is important because it is misleading to say that a modifier trope isn’t charactered at all. For example, although a sphericity modifier trope isn’t naturally charactered (e.g., it isn’t spherical), it is charactered both formally (being a property, being selfidentical, being nonshareable, etc.) and functionally (being a sphere-maker). A module trope is comparable to an immanent self-exemplifying universal, again, the difference being that only the latter is sharable. A module trope is also comparable to a modifier trope in that both are character grounders. Like a modifier trope, a module trope grounds the character of its bearer in some single and specific way. But unlike the modifier trope, the module trope is itself charactered in that way. On this view, a billiard ball is hard in virtue of its hardness trope and spherical in virtue of its sphericity trope, but the hardness trope is itself hard and the sphericity trope is itself spherical. Note that, aside from the character that it grounds, a module trope has no other natural character. A sphericity module trope, for example, is spherical but not otherwise (naturally, non-formally) charactered; being spherical is the only way in which it is charactered: it is not also (say) massive or negatively charged. Thus, in effect, a module trope is a primitively singlypropertied object. A sphericity module trope is a primitively merely spherical object. With the modifier/module distinction in hand, we will now consider how modifier and module tropes are unequally suited for metaphysical work (Sections 20.3–20.5) and fare differently with respect to character-grounding (Sections 20.6–20.8).

20.3 Powers Unlike modifier tropes, module tropes are not eligible to be the powers (or dispositions) of objects. Module tropes can play the role of powers only if powers can be selfexemplifying. Presumably, a self-exemplifying power would be a self-disposing power – a power that disposed itself in some way. However, in the literature on powers, the tacit but well-motivated assumption is that powers are not self-empowering or self-disposing, whatever that might mean. Rather, the natural and usual way to understand a power is to take a power to dispose its bearer in a certain way (Marmodoro 2010: 1). Thus, magnetism is not itself magnetic and fragility is not itself fragile; rather, magnetism disposes its bearer to attract nearby ferrous metals and fragility disposes its bearer to break under certain conditions. The assumption that powers are not self-disposing is especially clear and plausible in the analysis of higher-level powers, such as the power to roll down an inclined plane. An object has the latter power in virtue of having other (perhaps dispositional) properties including sphericity, rigidity, and heaviness. This requires each of the latter properties to dispose something other than itself – a distinct bearer that is jointly disposed by lower-level powers and thereby has the higher-level power to roll down a plane. Thus, these lower-level powers are non-self-disposing; if they are tropes, they must be modifier tropes. In sum, in so far as powers are non-selfdisposing, a trope ontology of powers will require modifier tropes. 231

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20.4

Fundamental Determinables

Unlike modifier tropes, module tropes are not eligible to play the role of fundamental determinables. Determinables are less-than-fully-specific properties like mass, color, and shape. Fully determinate properties “fall under” the latter and are properties like mass 1 kg, scarlet, and sphericity. A fundamental determinable is a determinable property that is distinct from and irreducible to fully determinate properties (Wilson 2012: 5; for more on the determinate/determinable distinction, see Chapter 10, this volume). On module trope theory, a fundamental determinable would seem to be impossible. Suppose that triangularity is a fundamental determinable trope. On module trope theory, triangularity would be self-exemplifying: triangularly shaped, but not in any fully determinate way. It would be three-sided and three-angled, but none of the angles would have a specific degree and none of the sides would have a specific length. Thus, triangularity would be a triangle but it would be neither equilateral, isosceles, nor scalene. Such a module trope seems impossible. Likewise for other fundamental determinables, such as mass, color, and charge. If they exist, it seems impossible that they are self-exemplifying and so they could not be module tropes. However, they could be modifier tropes. On modifier trope theory, triangularity is not self-exemplifying. Here, the trope is not itself triangularly shaped – neither indeterminately triangularly shaped nor fully determinately triangularly shaped. Thus, there is nothing impossible about triangularity being a modifier trope. Likewise for other fundamental determinables. In sum, for the modifier trope theorist, postulating fundamental determinables is a live option; for the module trope theorist it is not. This is a pro tanto advantage for modifier trope theory in so far as a case can be made for fundamental determinables. Here the jury is out. Although some trope theorists reject fundamental determinables and, instead, identify them with property-classes of fully-determinate tropes (Campbell 1990; Ehring 1996, 2011; Williams 1953), others argue that an adequate trope theory will require them (Garcia 2015b; Wilson 2012). If the case succeeds, then trope theory requires modifier tropes.

20.5

Perception and Causation

Unlike modifier tropes, module tropes are eligible to play a direct role in perception and causation – to be the immediate objects of perception and the terms of causal relations. With respect to perception, consider the greenness trope of a leaf. On module trope theory, the trope is itself colored. As such, it is the sort of entity that you could directly perceive by attending to the leaf. In contrast, on modifier trope theory, when you attend to the leaf, the colored entity that you directly see is not the greenness trope but its bearer, which the trope colorizes. The greenness modifier trope is not colored and thus is not the sort of entity you can directly perceive. But the greenness modifier trope is not unique in this regard. On modifier trope theory, a sweetness trope is not sweet, a temperature trope is not (say) hot, a smoothness trope is not smooth, and so on. Thus, unlike module tropes, modifier tropes are ineligible to play a direct role in perception. With respect to causation, consider the hotness trope of a stove. On module trope theory, the hotness trope is itself hot. As such, it is the sort of entity that could directly cause a burn on your hand. In contrast, on modifier trope theory, when you burn your hand on the stove, the hot entity that causes the burn is not the hotness trope but its bearer. Although the stove is hot in virtue of its hotness trope, the trope itself is not hot and thus is

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not the sort of entity that could directly cause the burn. But hotness modifier tropes are not unique in this regard. On modifier trope theory, mass tropes are not massive, charge tropes are not charged, and so on. Thus, unlike module tropes, modifier tropes are ineligible to play a direct role in causation. The ineligibility to play a direct role in perception and causation marks an important disadvantage of modifier tropes. According to many trope theorists, a principal motivation for preferring tropes to universals is the fact that tropes, unlike universals, are suited to be the immediate objects of perception and the terms of causal relations (Campbell 1981; Ehring 1997; Lowe 2006; Schaffer 2001; Williams 1953). On modifier trope theory, this motivation is lost.

20.6

Thin and Thick Character

In the remainder I will consider how each type of trope fares with respect to charactergrounding. For this it will be useful to draw a distinction concerning character. I take it to be a Moorean fact that there are naturally charactered entities. By “entity” I mean object or thing in the most general sense. By “naturally charactered” I mean ways of being charactered that “carve the world at the joints” – characteristics in virtue of which entities objectively resemble each other or have fundamental causal powers (Koons and Pickavance 2015: 116). There is no consensus on which characteristics are natural, but for the sake of the argument I will presume they include being negatively charged, being spherical, and being hard. We can distinguish two related phenomena concerning natural character. First, there is the phenomenon of thin-character. There is thin-character if there is an entity x such that x is (predicatively) F, where F is a non-formal and (non-conjunctive) natural property. Note that an object can be thinly-charactered without being merely thinly-charactered. In its role as a character-grounder, each trope is supposed to account for thin-character. In the case of a billiard ball, there is an x such that x is spherical. The ball’s sphericity trope accounts for the latter case of thin-character. Second, there is the phenomenon of thick-character. This occurs when there is an entity that is thinly-charactered in more than one way. That is, there is thick-character if there is an entity x such that x is F and x is G, where F and G pick out distinct (non-conjunctive) natural properties. As character-grounders, tropes are supposed to jointly account for thick-character. In the case of a billiard ball, there is an x such that x is spherical and x is hard. The ball’s sphericity trope and hardness trope jointly account for the latter case of thick-character. Thick-character is a pervasive feature of the manifest world (Garcia 2016). It is also a central explanandum in disputes about the existence and nature of properties. As it involves one entity being naturally charactered in many ways, Gonzalo RodriguezPereyra (2002) calls the need to account for it the “Many Over One” problem and argues that it is the essence of the perennial Problem of Universals.2

20.7

Modifier Tropes as Character-Grounders

As character-grounders, modifier tropes would seem to be more mysterious and less parsimonious than module tropes. I will consider each implication in turn. The first implication concerns the inscrutability of character-grounding. On modifier trope theory, an object is thinly-charactered in some way in virtue of having a trope that is not itself charactered in that way. A sphericity modifier trope is not itself spherical, yet 233

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somehow makes its bearer is spherical. Thus, on modifier trope theory, there are two important aspects of character grounding. First, a modifier trope must be numerically distinct from the bearer it characterizes. That is, modifier tropes engage in irreflexive character-grounding, or what I call character-making. Second, character grounding produces something at the object-level that bears no qualitative resemblance to anything at the trope-level. This threatens to make character grounding rather mysterious. In contrast, module trope theory can at least mitigate the mystery. Here, the fact that the module trope is itself thinly-charactered provides the trope theorist with at least a minimal resource for explaining how the trope grounds the sphericity of its bearer. She might, for example, deny that character grounding is irreflexive and simply take the bearer’s being spherical to amount to nothing more than the bearer’s having a proper part (a trope) that is spherical (Garcia 2016). In sum, unlike modifier tropes, module tropes go some distance toward dispelling what D.C. Williams calls “the ancient mystery of predication” (Williams 1953: 11). The second implication concerns parsimony. Trope theory is often advantageously paired with a bundle theory of substance. According to bundle theory, an object is a whole whose constituents are all and only properties, suitably interrelated in some way (for more on trope bundle theory, see Chapter 21, this volume). Not all trope theorists adopt bundle theory (Heil 2012; LaBossiere 1994; Lowe 2006; Martin 1980). However, those who do adopt it do so partly on the grounds that, unlike universals, tropes do not require an additional category of differentiating entities (substrata or bare particulars3) to individuate qualitatively indiscernible objects (Campbell 1990; Ehring 2011; Maurin 2002; and Schaffer 2001). Thus, tropes are said to have the advantage over universals of allowing for a parsimonious mono-category ontology while avoiding mysterious and paradoxical substrata (Schaffer 2001: 248). This advantageous pairing is thwarted by modifier tropes. Although neither version of trope theory needs substrata to differentiate substances, there is other work for substrata to do for which modifier tropes are not suited. As a character-grounder, a trope is supposed to account for the fact that something is thinly-charactered. For example, a sphericity trope is supposed to account for the fact that something is spherical. On module trope theory, because the trope qua spherical is itself thinly-charactered, there is the option of identifying it with the trope-bearer – with the “something” that is spherical.4 On modifier trope theory, this is not an option because the trope is not itself spherical. Thus, the entity which is spherical (in virtue of the modifier trope) must be (i) numerically distinct from the trope and (ii) the sort of entity that not only can be spherical but can be made to be spherical. In other words, the trope-bearer must be a distinct and characterizable sort of entity. Thus, to account for character – thin or thick – a modifier trope theory requires, in addition to the category of tropes, a category of trope-bearers – not to differentiate substances, but to be the literal subjects of characterization. This is one of the traditional roles played by a substratum – an entity of notorious repute. Indeed, as noted, avoiding substrata is a central motivation for preferring tropes to universals. Unfortunately, it is doubtful that modifier trope theory enjoys this motivation. A modifier trope bundle theory seems to be a non-starter.

20.8 Module Tropes as Character-Grounders Module trope theory faces its own challenges concerning character. To see this we need to complicate the above distinction between thin and thick character and revisit our original concept of a module trope. With respect to the degree to which a module trope is itself 234

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naturally charactered, there seem to be three options. First, it might be merely thinly charactered: naturally charactered in exactly one way. Second, it might be maximally charactered: naturally charactered in all the ways that its bearer is naturally charactered. Third, it might be middlingly charactered: more than merely thinly charactered but less than maximally charactered. Call the view that module tropes are maximally charactered maximal trope theory. Presumably, no one will be tempted towards this view, but it will be instructive to consider why. First, the trope would be a complete qualitative duplicate of its bearer, putting them in causal competition and threatening causal overdetermination (see below for more on this type of problem). Second, and more instructively, the view would be equivalent to austerenominalism-plus-tropes. The austere nominalist accounts for maximal character without postulating properties; instead, she takes it to be primitive and at the level of the ordinary object. The maximal trope theorist deploys the same strategy, but at the trope level: her trope would be a primitively maximally charactered entity. However, if you accept primitive maximal character at the trope level, you might as well accept it at the ordinary object level and eschew tropes altogether. Thus, the maximal theory is both unmotivated and extravagant. This leaves the module trope theorist with a choice between adopting middling trope theory and merely thin trope theory.5 Either option faces challenging implications. The first implication is that both options require character-making and trope bearers. On neither will the existence of module tropes suffice to account for maximal character. If module tropes are merely thinly charactered, then a plurality of tropes only gives you the coexistence of merely thinly charactered entities. Similarly, if module tropes are middlingly charactered, then a plurality of tropes only gives you the co-existence of middlingly charactered entities (see Garcia 2016 and 2020 for relevant discussion). Thus, by themselves, module tropes cannot account for maximal character – the character of ordinary objects. Rather, on either option, for maximal character, module tropes must be character-makers and must jointly characterize a distinct and characterizable bearer, thereby making it maximally charactered. In this way, like modifier tropes, module tropes require trope-bearers. The second implication concerns character duplication and the threat of causal overdetermination. The above requirement on maximal character raises a unique difficulty for both options within module trope theory. Consider a maximally charactered object, O, which is spherical and hard (etc.). On trope theory, O is spherical in virtue of its sphericity trope and hard in virtue of its hardness trope. On modifier trope theory, the hardness trope is not hard and the sphericity trope is not spherical, so between O and its tropes there is only one hard entity and one sphere (and they are one and the same). However, on module trope theory, the hardness trope is hard and the sphericity trope is spherical, so between O and its tropes there are two hard entities and two spheres. Indeed, wherever there is a sphericity module trope that is a character-maker, there are two numerically distinct spheres: the trope and the bearer which is spherical in virtue of that trope. This generalizes: whether they are middlingly or merely thinly charactered, module tropes can account for maximal character only if they are character-makers and thus, wherever you have an F-ness trope, you will have two numerically distinct F-things.6 In this way, accounting for maximal character seems to saddle module trope theory with the systematic duplication of character. It is generally thought that character duplication is an unwelcome result. To take one example7, consider the dispute about material constitution and its puzzle concerning the statue and the clay. On the constitution view, Michelangelo’s David and the marble that composes it are numerically distinct but share exactly the same material parts. This is alleged 235

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to have the unwelcome implication that each weighs 6 tons. But suppose you put David on a digital scale. What quantity is shown on the scale’s display? And what causes that effect? Just one of the 6-ton entities, or both? The answers are vexed but one implication is clear: character duplication is unwelcome because it forebodes causal overdetermination. Unfortunately, it is not clear how to avoid causal overdetermination on a module trope theory that accounts for maximal character. Reconsider our maximally charactered object, O, which is spherical and hard. Suppose O is resting on a pillow. In this case, it is natural to say that the sphericity of the ball is directly causing the pillow top to have a concave shape. But if tropes are module tropes and character makers, then there are two spheres on the pillow: the sphericity trope and its bearer. Presumably, at least one of the spheres is directly responsible for the concavity of the pillow top. But which? Or is it both? Again, the answers are vexed. If both spheres cause the concavity, then there would be causal overdetermination. If only the trope causes the concavity, then O would be epiphenomenal. But between the trope and O, O is the only maximally charactered entity. Generalizing from this case would lead to the implausible implication that maximal character in general is epiphenomenal.8 If only O causes the concavity, then the trope would be epiphenomenal. Generalizing, this would mean that module tropes cannot, after all, play a direct role in causation and perception, thereby losing the above-noted central motivation for trope theory. Of these three alternatives, there is no obvious winner. Thus, whether module tropes are middlingly or merely thinly charactered, the verdict is out on whether and how they can account for maximal character while avoiding character duplication or causal overdetermination (see Giberman 2022 for a promising attempt). The third implication concerns a dilemma between middling trope theory and merely thin trope theory. It is not clear that the former is significantly better than maximal trope theory in avoiding a collapse into austere nominalism (or worse). The austere nominalist and middling trope theorist ultimately deploy the same strategy: postulate primitively multiply naturally charactered entities. Notice that the latter display the many over one phenomenon – an explanandum that arguably is the central motivation for postulating properties (as noted above). Thus, in effect, the shared strategy denies that the many over one requires an analysis. It is strange, then, that unlike the austere nominalist, the middling theorist takes the character of maximally charactered objects – ordinary objects – to require an analysis and meets that requirement by taking maximal character to be grounded in less-than-maximally but multiply charactered tropes. This additional step seems unmotivated. If the shared strategy works for middlingly charactered entities, then it is not clear why it would not work for maximally charactered entities. But if it works for the latter, then we don’t need the former. In this way, middling trope theory seems to collapse into austere nominalism. A module trope theorist might try to forestall this collapse by taking tropes to be merely thinly charactered. Here, a sphericity trope is primitively and merely spherical. This strategy has the significant advantage of not denying that the many over one requires an analysis; it thus leaves intact a primary motivation for postulating tropes. However, the viability of this approach is threatened by what I call thickening principles. These have the following form: an entity is charactered under one determinable only if it is also charactered under another determinable. Plausible examples include an entity is colored only if it is shaped and an entity is shaped only if it is extended. Although whether and which thickening principles are true depends on numerous considerations, that there are true thickening principles is tacitly assumed by prominent advocates and critics of trope 236

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theory.9 Here, Jonathan Schaffer’s (2003) view is instructive. He argues for the metaphysical possibility of a mass trope that is massive but not otherwise charactered. Such a module trope would be merely thinly charactered. If such a trope is possible, then there are no thickening principles concerning mass. However, the possibility of such a trope does not secure the viability of a merely thin trope theory because viability requires that all natural character is free from thickening principles – and perhaps even that all possible natural character is free (Garcia 2015b: 649). Such freedom is far-fetched. To sum up the third implication, the choice between middling trope theory and merely thin trope theory poses a dilemma: the former threatens to collapse into austere nominalism whereas the latter implausibly requires that natural character is free from thickening principles.

20.9 Conclusion As we’ve seen, the general concept of a trope admits of a distinction between modifier tropes and module tropes. The distinction has wide-ranging implications. Modifier tropes are uniquely eligible to be powers and fundamental determinables, whereas module tropes are uniquely eligible to play a direct role in perception and causation. Moreover, each type of trope theory faces unique challenges concerning character-grounding. Modifier trope theory faces challenges concerning the inscrutability of predication and the incompatibility with bundle theory, whereas module trope theory faces challenges concerning character overdetermination and a collapse into austere nominalism. These differences indicate that the modifier/module distinction divides the advantages of general trope theory and thus presents the trope theorist with a pivotal choice.

Notes 1 This synchronic non-shareability is distinct from diachronic non-shareability, which is denied by some trope theorists. For example, on Douglas Ehring’s view (1997), tropes are “transferable” in that a trope can characterize distinct objects at different times. 2 Keith Campbell (1981) calls it “the problem of concrete individuals”. 3 For more on bare particulars, see Bailey 2012, Garcia 2014, and Pickavance 2014. 4 I call this thaumatrope theory ( Garcia 2016). 5 Indeed, the literature displays ambivalence on these options; see Garcia 2015b. 6 To forestall the trouble that awaits this conclusion, one might hold that the sense in which the trope-bearer is (made to be) charactered is not the same as the sense in which its character-maker is (primitively) charactered. I call this an equivocation strategy. Here, a sphericity trope is spherical and its bearer is spherical, but they are not spherical in the same sense; we equivocate when attributing “spherical” to them. Unfortunately, equivocation strategies have significant problems. For discussion, see Garcia 2016. 7 Other examples include a character duplication problem for bare particulars (see Bailey 2012 and Pickavance 2014) and the “Two Many Thinkers” problem for psychological approaches to personal identity. 8 See Garcia 2016 for further discussion of these alternatives. 9 For discussion, see Denkel 1997: 604; Garcia 2015a, MS; Koons and Pickavance 2015: 99, 108, and 121.

References Bailey, A.M. (2012) No Bare Particulars. Philosophical Studies 158(1): 31–41. Campbell, K. (1981) The Metaphysic of Abstract Particulars. Midwest Studies in Philosophy 6(1): 477–488.

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Robert K. Garcia Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Denkel, A. (1997) On the Compresence of Tropes. Philosophy and Phenomenological Research 57(3): 599–606. Ehring, D. (1996) Mental Causation, Determinables and Property Instances. Noûs 30(4): 461–480. Ehring, D. (1997) Causation and Persistence: A Theory of Causation. New York: Oxford University Press. Ehring, D. (2011) Tropes: Properties, Objects, and Mental Causation. New York: Oxford University Press. Garcia, R.K. (2014) Bare Particulars and Constituent Ontology. Acta Analytica 29(2): 149–159. Garcia, R.K. (2015a) Is Trope Theory a Divided House? In Loux, M.J. and Galluzzo, G. (eds.) The Problem of Universals in Contemporary Philosophy. Cambridge: Cambridge University Press: 133–155. Garcia, R.K. (2015b) Two Ways to Particularize a Property. Journal of the American Philosophical Association 1(4): 635–652. Garcia, R.K. (2016) Tropes as Character-Grounders. Australasian Journal of Philosophy 94(3): 499–515. Garcia, R.K. (2020) La Bundle Theory y el Desafío del Carácter Denso [Bundle Theory and the Challenge of Thick-Character], translated into Spanish by C. Rossi. Revista de Humanidades de Valparaíso 16: 111–136. An English version of this article is available upon request. Garcia, R.K. (MS) Moderate Nominalism: Tropes vs. Tropers. Unpublished manuscript. Giberman, D. (2022) Ostrich Tropes. Synthese 200(1): 1–25. Heil, J. (2012) The Universe as We Find It. New York: Oxford University Press. Koons, R.C., and Pickavance, T.H. (2015) Metaphysics: The Fundamentals. West Sussex, UK: WileyBlackwell. LaBossiere, M. (1994) Substances and Substrata. Australasian Journal of Philosophy 72(3): 360–370. Lowe, E.J. (2006) The Four-Category Ontology: A Metaphysical Foundation for Natural Science. New York: Oxford University Press. Marmodoro, A. (2010) The Metaphysics of Powers: Their Grounding and their Manifestations. New York: Routledge. Martin, C. (1980) Substance Substantiated. Australasian Journal of Philosophy 58(1): 3–10. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. Maurin, A.-S. (2023) Tropes. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Spring 2023 Edition. URL = < https://plato.stanford.edu/archives/spr2023/entries/tropes/ Pickavance, T. (2014) Bare Particulars and Exemplification. American Philosophical Quarterly 51(2): 95–108. Rodriguez-Pereyra, G. (2002) Resemblance Nominalism: A Solution to the Problem of Universals. New York: Oxford University Press. Rodriguez-Pereyra, G. (2015) Grounding is Not a Strict Order. Journal of the American Philosophical Association 1(3): 517–534. Schaffer, J. (2001) The Individuation of Tropes. Australasian Journal of Philosophy 79(2): 247–257. Schaffer, J. (2003) The Problem of Free Mass: Must Properties Cluster? Philosophy and Phenomenological Research 66(1): 125–138. Schaffer, J. (2009) On What Grounds What. In Chalmers, D., Manley, D., and Wasserman, R. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. New York: Oxford University Press: 347–383. Williams, D.C. (1953) On the Elements of Being: I. Review of Metaphysics 7(1): 3–18. Wilson, J.M. (2012) Fundamental Determinables. Philosophers’ Imprint 12(4): 1–17.

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21 TROPE BUNDLE THEORIES OF SUBSTANCE Markku Keinänen and Jani Hakkarainen

21.1

Introduction

This chapter is an opinionated introduction to contemporary theories according to which substances or objects are bundles of tropes. “Substance” and “object” are taken as interchangeable in this context. Substances are spatiotemporally located, particular, and persisting individual entities that bear properties. Substances can be illustrated by ordinary objects like trees, dogs, and houses, but some theories consider elementary particles better examples of substances (such as electrons and quarks). Tropes are natures, which may be taken either primitively or derivatively. Moreover, tropes are particulars, although different trope theorists have different conceptions of particularity. We think the best examples of particular natures are basic physical quantities like determinate electric charges, but some other theorists take colors and shapes as tropes (too). Tropes are simple: if tropes have parts, all these parts are tropes and it is standardly assumed that substances are ultimately constructed out of mereologically simple tropes. Nonetheless, tropes are parts, as will be seen below. Tropes form the only fundamental ontological category. They are also considered as located in spacetime. Finally, tropes are individuals: they have numerical identity and are unities (each trope is one entity). In his The Elements of Being (2018a[1953]), D.C. Williams coined the term “trope” for the ontological category of simple or thin particular natures (“occurrences of essences”). In addition to constructing substances out of tropes, he introduced tropes to eliminate the fundamental object-property dichotomy (2018a[1953]: 30–31) and hence substances and properties as fundamental ontological categories. The trope bundle theories considered in this chapter follow Williams’ insight: they take tropes to form the sole fundamental ontological category. Therefore, these theories eliminate substances as a fundamental category. Accordingly, this category is (formal ontologically) analyzed reductively. This results in a ground-breaking insight by Williams: analyzing substances and inherence (that is, a substance having a particular property) reductively go hand in hand in trope bundle theories. Therefore, we examine analyses of substances as trope bundles from the point of view of analyses of inherence, too. The first and most important question for each trope bundle theory is then the problem of unification: how are individual tropes unified into an individual substance? This

DOI: 10.4324/9781003246077-27

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unification can be considered synchronically, diachronically, and counterfactually. Second, since a substance is spatiotemporally located, we need an explanation about how the tropes that are its parts determine its location. Third, our best science suggests that many substances are members of natural kinds but there are only a limited number of these natural kinds (e.g., kinds of elementary particles). Accounting for this is a reasonable requirement for trope bundle theories. Relatedly, the number of the kinds of tropes constructing substances is also restricted. Why this is so is a further question involved in the substance construction out of tropes. As will be seen below, different theories give different answers, with their merits and problems, to these questions. Each of these trope bundle theories introduces exactly one fundamental ontological category, which gives categorial ontological economy and parsimony with respect to different kinds of formal ontological relations.1 Categorial ontological economy in the service of solving key metaphysical problems is a good reason to hold a trope bundle theory (cf. Ehring 2011: 45ff.). In what follows, we start by discussing Williams’ and Keith Campbell’s (1990) paradigmatic trope theories, especially as they pertain to substance, and highlight some problems with these theories (Section 21.2). This sets us up, in Section 21.3, to present two recent developments of trope bundle theory that attempt to address these problems (Ehring 2011; Maurin 2002). These recent developments maintain, like the paradigmatic theories, that nonrelational tropes are existentially rigidly independent beings. Hence, we label them independence theories. Finally, in Section 21.4, we present two alternative trope bundle theories that suppose non-relational tropes are dependent existents, dependence theories, namely, Arda Denkel’s (1996, 1997) Saturation theory and our Strong Nuclear Theory.

21.2

Paradigmatic Trope Theories

Williams outlined a systematic trope theory in which tropes are considered existentially independent fundamental entities. According to him, substances are mereological sums of concurrent, that is, spatiotemporally exactly co-located tropes. In the beginning chapters of his Abstract Particulars (1990), Campbell develops further the idea of tropes as particular natures, members of a single fundamental category, and independent existents. There are some interesting differences between Williams’ and Campbell’s views, which we will discuss later in this section. Nevertheless, Williams’ and Campbell’s trope theories are usually grouped together under the label of “classical trope theories” (Fisher 2018, 2020; Maurin 2023). We begin this section by describing the common ground of their views. Williams and Campbell use the terms “abstract” and “concrete” in a fashion that deviates from the currently standard use: spatiotemporal versus non-spatiotemporal. Tropes are “abstract” in the specific sense of being able to be exactly spatiotemporally co-located (concurrent, compresent) with other tropes. Substances are mereological sums of mutually co-located tropes, which thereby “monopolize” their locations (Campbell 1990: 3; Williams 2018a [1953]: 28–29). Substances are “concrete” in the sense of monopolizing their locations.2 For instance, suppose substance i is a micro-particle which is constituted by three determinate quantity tropes, t1, t2, and t3. Let us say t1 is a -e charge trope, t2 a determinate mass trope, and t3 a spin trope. One may now propose the following analysis of inherence: [CI]: Trope t is a property of substance i if and only if t is a part of i and t is exactly spatiotemporally co-located with i.

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Thus, substance i has -e charge trope t1 as its property because t1 is a part of i and is exactly spatiotemporally co-located with i. Both Williams (2018a[1953]: 30–31) and Campbell (1990: 59) accept a similar analysis to [CI], although they present it as a part of an analysis of exemplification, that is, of objects’ possessing properties as general entities.3 Thus, the advocates of paradigmatic trope theories assume that tropes are particular natures, fundamental particulars, and individuals (that is, countable unities with numerical identity), which have some specific spatiotemporal location. The additional assumption is that every plurality of mutually exactly co-located tropes forms a certain kind of individual, namely, their mereological sum. Moreover, any such mereological sum is a substance (cf. Campbell 1990: 21; Williams 2018a[1953]: 29–30). In standard cases, substances are complex individuals typically constituted by two or several tropes. However, free individual tropes are allowed for and they are limiting cases of inherence, objects having exactly one property. There are several interesting differences between Williams’ and Campbell’s trope theories. First, according to Williams (2018b[1960]: 52–55), every substance is an occupant of a four-dimensional manifold (place-time), which he calls a “plime” (Fisher 2020: 45). Williams also adopts a four-dimensionalist conception of persistence: substances and tropes exist at different times by dividing into temporal parts (Williams 2018b[1960]: 53). Because he adopts classical extensional mereology, Williams can also construe temporally extended tropes as mereological sums of their temporal parts (Williams 2018a[1953]: 29). By contrast, Campbell (1990: 3, 24, 131) seems to leave open the possibility that temporally persisting substances divide into temporal parts and occasionally considers substances and tropes as if they were endurants (Campbell 1990: 132, 141). Campbell’s view is perhaps best interpreted as leaving open the question of whether tropes/substances are endurants, perdurants or exdurants. Second, Williams and Campbell disagree, at least as a theoretical ideal, about the existence of relations. Williams (2018c[1963]: 108ff) considers spatiotemporal relations credible examples of external relations. It seems that we need to introduce entities additional to their relata such as particular relations to account for the holding of these relations. According to Campbell (1990: ch. 5), preserving trope theory as a one-category ontology requires that we find non-relational truthmakers for all relational truths, including contingent ones. The third difference between Williams’ and Campbell’s views is perhaps the most interesting. According to Williams (2018a[1953]: 28), concurrence is a “limiting value of location”, namely, exact spatiotemporal co-location. If one adopts this view, one might think that the spatiotemporal relations that determine the relative locations of tropes also determine which tropes are concurrent with each other. The way in which Campbell formulates his trope theory in the first 58 pages of his Abstract Particulars is consistent with taking compresence as a limiting value of location as suggested by Williams in the case of concurrence. Nevertheless, toward the end of Abstract Particulars, Campbell starts to treat compresence as a fundamental relation connecting tropes which are parts of a single substance. Campbell considers such relations of compresence the best candidates for particular relations, which one is obliged to postulate unless one is willing to introduce specific field tropes (Campbell 1990: 58–59, 69, 130–133). Of the recent trope theorists, Anna-Sofia Maurin (2002) and Douglas Ehring (2011) follow the later Campbell by taking compresence as primitive (see Section 21.3 below).

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If successful, Williams’ paradigmatic trope theory would constitute a metaphysician’s paradise because of its simplicity and categorial ontological economy. There is only one fundamental ontological category (tropes), which is determined by comparatively transparent formal ontological relations such as identity and parthood. By analyzing inherence by means of parthood and exact co-location, trope theory avoids the fundamental dichotomy between characterizing (properties) and characterized entities (substances). An account of the spatiotemporal location of tropes, which is required in any case, provides us with substances having certain properties in different locations as a by-product. Nevertheless, Williams’ paradigmatic trope theory faces a series of difficulties. First, both Williams and Campbell are Humean trope theorists who thus deny existential dependencies between wholly distinct individual tropes that constitute a substance. According to them, it is a matter of contingent fact that tropes standardly occur in “concurrent/compresent groups” (Campbell 1990: 21; cf. Williams 2018a[1953]). However, there is “an explanatory gap” between this official view and the fact that we encounter things belonging only to a limited number of natural kinds. If the building blocks of physical reality (e.g., fundamental particles) are trope bundles, they seem to be constituted by a very limited set of different kinds of tropes determining their natural kind. It seems that, minimally, the trope theorist should be able to say which kind of explanation – metaphysical or, perhaps, empirical – would shed light on the issue of why substances are constituted only by a highly restricted number of different kinds of tropes in a limited number of combinations. Another closely related problem is that, while allowing for freefloating individual tropes, paradigmatic trope theories have not given any answer to the question of why we do not encounter such beings in actual physical reality. Second, because he takes substances as mereological sums of co-located tropes and analyzes inherence by means of [CI], Williams’ paradigmatic trope theory rules out mutually co-located substances such as mutually co-located micro-particles. This is a serious limitation as it binds the trope theoretical account of substances to our commonsense intuitions about macro-objects as rigid impenetrable physical bodies. However, co-located micro-particles are possible if not actual (cf. Keinänen 2011: 433). Trope metaphysics aiming at some conception of micro-particles or, more generally, substances that do not fulfill the standards of macroscopic impenetrable bodies cannot rule out mutually co-located substances. Third, Williams is explicitly committed to the perdurantist view of persistence of tropes and substances. By this move, he avoids the standard problem addressed to an endurantist trope theorist of specifying the persistence conditions of a substance over some period of time (that is, the temporal identity conditions of a substance) by means of endurant tropes. Nevertheless, four-dimensionalism (perdurantism or exdurantism) is not without its problems and one might ask whether it is possible to develop a viable endurantist trope bundle theory. Finally, Williams admits the need to introduce relations to account for (at least) spatiotemporal locations of tropes. However, the claim that relations considered particulars (particular relations) are sui generis entities adhering to two or more objects/tropes reintroduces the primitive distinction between characterizing and characterized entities in trope theory. It also undermines the goal of constructing a one-category trope ontology. In order to preserve this goal the trope theorist should eliminate relations from their ontology (as Campbell (1990) attempted to do) or else attempt to generalize the analysis of inherence to adherence.4 For reasons of space, we set aside problematic issues concerning relations 242

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and will concentrate on the first three issues in this chapter (for more on particular relations, see Chapter 22, this volume).

21.3

Independence Theories

In the final two sections of this chapter, we assess different trope bundle theories on the basis of their being capable of solving these first three difficulties posed to paradigmatic trope theories. We begin with two trope theories inspired by Campbell’s trope theory, Maurin’s (2002) and Ehring’s (2011) accounts. We label them “independence theories” because they, like Williams and Campbell, strive to construct substances without introducing existential dependencies between standard, non-relational tropes. As does Campbell (1990), Maurin (2002: ch. 2) calls the relation that binds tropes together so as to form a single substance “compresence” and considers it an external relation between tropes (Maurin 2002: 129, 133). In other words, it holds contingently between its relata. Maurin (2002: 163–166) introduces the relations of compresence considered particulars that account for the holding of compresences between tropes. Maurin (2010, 2011) further defends the idea of compresences as particular relations that necessarily relate their relata in a certain specific way if they exist.5 Ehring (2011: ch. 4) rejects existential dependencies between wholly distinct tropes. He takes compresence to be a sui generis type of relation which is not reducible to anything else and thus not reducible to spatiotemporal co-location. If the substances constituted by the mutually compresent tropes are spatiotemporal, compresence entails co-location, but the converse does not hold (Ehring 2011: 98). Because he takes compresence as sui generis in this way, Ehring can allow for mutually co-located substances. Like Maurin (2002: 163–168), Ehring binds the tropes constituting a substance by means of compresence relations considered particulars, which hold contingently between their relata. Nevertheless, Ehring (2011: 119–135) considers compresences as “self-relating relations”, which are themselves parts of the bundles of mutually compresent tropes.6 Compresence relations are instantaneous. Ehring (2011: 46–50) claims that tropes provide the best explanation for the phenomenon of qualitative persistence in terms of trope endurance. In other words, tropes are endurants that explain persistence of properties in time and serve as mediators of the physical connection between causes and effects (Ehring 1997: ch. 5; Ehring 2011: 48). Given that substances are constituted by enduring non-relational tropes and the fact that compresence relations exist instantaneously, the resulting substances are instantaneous (Ehring 2011: 100–107). Thus, Ehring uses trope bundle theory to combine his endurantist conception of tropes with four-dimensionalism about substances: substances are perdurants or exdurants.7 Assuming perdurantism with respect to substances, if a substance exists longer than an instant, it is constituted by distinct instantaneous adherences of distinct relations of compresence to a certain group or groups of endurant tropes. Thus, what we might take as a single substance having slightly different properties at different times is actually a series of trope bundles bound together by distinct compresence relations. Like Williams, Ehring avoids what is generally considered a problem for all trope/universal bundle theories, namely, to provide diachronic identity conditions for endurant substances that can change their properties (Ehring 2011: 100). By the same token, Ehring introduces enduring tropes. According to him, they provide us with the only viable account of qualitative persistence (Ehring 2011: 66). 243

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Therefore Ehring’s trope theory avoids a potential problem of a perdurantist trope ontology: to specify the conditions in which a sequence of instantaneous stage-like tropes constitute a temporally continuous trope. Nevertheless, like paradigmatic trope theories, Ehring’s theory also has “an explanatory gap” between individual tropes and their contingent compresences, on the one hand, and the arrangement of tropes only into certain kinds of substances, on the other. If the explanation is supposed to be empirical, the trope theorist should be able to specify what kind of explanation it is.8 Recall that for the purpose of allowing for mutually co-located substances and to avoid the second difficulty that we posed to paradigmatic trope theories, Ehring considers compresence a sui generis relation not reducible to spatiotemporal co-location. The introduction of primitive compresence would entail the following analysis of inherence by means of compresence: [CAI]: Trope t is a property of substance i if and only if t is a part of i and t is compresent with all and only the other parts of i. Because of the transitivity of compresence and the fact that a bundle of mutually compresent tropes constitutes a substance, [CAI] entails that t is a property of i if and only if t is compresent with i. The problematic status of [CAI] becomes apparent if one asks what compresence is. Ehring answers that it is primitive and not reducible to exact spatiotemporal co-location. According to Ehring, in the case of tropes existing in space and time, compresence entails co-location at a time. Compresence has three basic functions in Ehring’s trope theory: first, to unify tropes into a single substance; second, to account for the spatiotemporal colocation of concrete tropes constituting a substance; and third, to make substances (trope bundles) instantaneous and located at a point of time. Nevertheless, our main worry is that it is unclear whether compresence is intelligible enough. Even in the case of primitives, one needs to be able to say something with affirmative content to make them sufficiently intelligible. Particular compresence relations are assumed to relate tropes in a primitive compresent way to unify tropes which are parts of the same substance (Ehring 2011: 98). In Ehring’s trope theory, the two additional functions are by-products of this basic function. Unifying is the role that substrata play in some theories alternative to trope bundle theory. It is supposed to be the nature of compresence relations to play this basic role. This leaves us in the dark about the nature of compresence relations, except perhaps that they are entities introduced to replace substrata. In addition, in [CAI], the primitive adherence of the relations of compresence to non-relational tropes replaces the inherence of the latter to a substratum or substance. We have argued elsewhere that adherence (i.e., a particular relation relating two or more entities) is an even more problematic primitive formal ontological relation than inherence (Hakkarainen and Keinänen 2023a; cf. Lowe 2016). For these two reasons, Ehring pays a high price for allowing for co-located substances and the other suggested benefits of primitive compresence.

21.4

Dependence Theories

According to what we call “dependence theories”, (some or all) tropes are existentially dependent beings; tropes are rigidly or generically dependent on certain or certain kinds of 244

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distinct tropes that are not their proper parts. Dependence theories construct substances by means of modal existential dependencies between all distinct non-relational tropes constituting substances, whereas independence theories do not invoke such dependencies. Irrespective of their existentially dependent status, tropes are considered fundamental entities in dependence theories. Unlike stronger dependence relations such as identity dependence or essentialist ontological dependence, these modal existential dependence relations are not considered to have any direct bearing to the fundamentality of their relata. The former, but not the latter, introduce asymmetric determination relations (like the identity conditions of entity x being determined by the identity conditions of y) between dependent existents and their dependees.9 Denkel’s (1996, 1997) Saturation theory constructs substances by means of a single relation he calls “saturation”. Any trope t falls under some determinable D1 (color, mass, charge, etc.) and is, necessarily, saturated by additional tropes falling under certain additional determinables D2, …, Dn. Saturation entails co-location at a time. Substances are pluralities of tropes which saturate each other completely. Although Denkel considers saturation a primitive substance-making relation, it can be analyzed by means of spatial co-location at a time and generic dependence.10 To illustrate this, we may take Matteo Morganti’s (2009) application of Saturation theory to fundamental micro-particles. According to Morganti, every fundamental trope t falling under a certain specific determinate (such as a -e charge trope) is generically dependent on tropes falling under certain distinct determinables (such as some mass trope, some spin trope). Moreover, these additional tropes are co-located with t at certain moment(s) of time. Micro-particles are aggregates of mutually fully saturated tropes, that is, aggregates of mutually co-located tropes in which all their generic dependencies are fulfilled. Morganti considers a conception of trope bundling that is based on generic dependencies to be superior to every conception based on rigid dependencies (cf. below) because it allows for “substantial changes” in Denkel’s sense, that is, migration of tropes from a particle to a new particle replacing the earlier one: every trope, say a -e charge trope of a muon, can continue its existence but start out accompanied by different kinds of tropes falling under the same determinables (such as mass and spin). For instance, a -e charge trope of a muon can continue its existence and come to be a part of a trope bundle that forms an electron (see Morganti 2009: 189–190 for a similar example). In the version of the theory considered above, Saturation theory takes tropes as endurants. Like in Williams’ paradigmatic trope theory, substances are mereological sums of mutually co-located tropes. By restricting the formation of trope bundles by means of generic dependence, Saturation theory seems to provide a partial explanation for why tropes figure only as parts of substances (cf. micro-particles in the example above) belonging to a limited group of natural kinds. Moreover, like Ehring, the advocate of Saturation theory might consider substances perdurants leaving the burden of explaining the qualitative continuity in the world to endurant tropes. However, because it analyzes inherence by means of [CI], Saturation theory rules out mutually co-located substances. The second major drawback of this view is that it offers no detailed account of the contingent relations that make tropes parts of a single substance. Peter Simons (1994) presents what he calls Nuclear Theory according to which substances are built from tropes solely by means of formal ontological relations of rigid and generic dependence.11 In standard cases, there is a group of mutually rigidly dependent tropes forming the tropes necessary to a substance, its nuclear tropes. Moreover, there 245

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might be additional tropes on which the nuclear tropes are generically dependent. Tropes are parts of a substance by being rigidly dependent on its nuclear tropes. Substances are aggregates of tropes in which all their rigid dependencies on distinct tropes are fulfilled; their dependence closures. Unlike other trope theories discussed in this chapter, Nuclear Theory does not constrain the relative spatiotemporal locations of tropes constituting a substance in any manner (cf. Keinänen 2011: 431–433). Therefore, it remains a schematic construction which can be supplemented in different ways to bring tropes together into a single location, in order to function as properties of a substance. For instance, Simons (2000: 148–149) suggests that the nuclear tropes of a substance usually take the same location as a matter of contingent fact. However, he does not develop this idea any further. The Strong Nuclear Theory (SNT), which we have defended in a series of articles,12 is inspired by Simons (1994). However, it takes a slightly different line than all the trope theories described above. In SNT, the main strategy is, first, to construct different kinds of trope bundles by means of the formal ontological relation of rigid dependence. As in Simons (1994), substances are identified with dependence closures of tropes with respect to their rigid dependencies. Second, for the purpose of the analysis of inherence, SNT provides an account of the spatiotemporal location of tropes relative to the location of the entire substance. Here, the basic idea is that certain pluralities of tropes constitute individuals (that is, singular entities) that stand in basic spatiotemporal relations. The locations of these trope bundles determine the locations of individual tropes. According to SNT, tropes divide into different types depending on how they stand in the relation of rigid dependence: [NT]: Trope t is a nuclear trope if and only if t is rigidly dependent on certain distinct tropes which are also rigidly dependent on t, or alternatively, t is not rigidly dependent on any other trope. [CT]: Trope t is a c-trope if and only if t is rigidly dependent on certain nuclear trope (s), but the converse does not hold. Trope t is not rigidly dependent on any other trope. Intuitively, nuclear tropes are necessary properties of a substance. Examples of nuclear tropes are -e charge, certain determinate mass, or spin tropes necessary to a micro-particle. On the other hand, c-tropes are tropes contingent to a substance such as spin direction or color charge tropes contingent to a micro-particle. To achieve these results, SNT states that every plurality of nuclear tropes constitutes an individual, an n-bundle. Similarly, each c-trope and the nuclear tropes on which it is rigidly dependent form a further individual, a c-bundle. Distinct nuclear tropes necessarily fall under distinct determinables (mass, charge, spin, etc.), which brings certain qualitative diversity to most substances. If a given trope t is a part of simple substance i (a substance that does not have any other substances as its proper parts), t is either the single nuclear trope of i or t is rigidly dependent on the nuclear tropes of i, which individuate substance i. Nevertheless, we still need an account of the location of tropes relevant to the analysis of inherence. Here, SNT proposes that n-bundles and c-bundles, not individual tropes, are the minimal entities that occur in the basic spatiotemporal relations. The spatiotemporal location of an n-bundle determines the location of its constituent nuclear tropes. Similarly, the location of an n-bundle determines the location of the substance in which it occurs as a part. 246

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The n-bundles form functional unities with a certain qualitative diversity: groups of different kinds of tropes necessary to a substance that determine its causal powers – like mass, spin, and charge tropes. Necessarily, they are co-located with each other and the substance if and only if they exist. Similarly, the location of each c-trope is determined by the location of the c-bundle in which it occurs as a part. If we assume that both tropes and the substances they constitute are endurants, SNT needs a separate account of the location of every c-bundle in relation to the location of the n-bundle of a substance. We have argued elsewhere that every c-bundle of a substance is spatially co-located with the n-bundle at each moment in which they both exist (Keinänen 2011: sec. 3). According to SNT, aggregates of tropes closed under rigid dependence are simple substances: substances that do not have other substances as their proper parts. A simple substance typically contains an n-bundle as its part and, possibly, some c-bundles as its proper parts. On this basis, we obtain the following analysis of inherence in SNT: [AI]: Trope t is a property of substance i if and only if, necessarily, if t exists, t is a part of i, and t is exactly co-located with i at every moment of t’s existence. In the limiting case, t is a nuclear trope and exactly spatiotemporally co-located with i. However, if t is a c-trope, its temporal location is a proper or improper part of the temporal location of i, but t is spatially co-located with i during the time of its existence. Nuclear tropes and c-tropes fulfill the conditions of [AI] in relation to the simple substances they constitute. Like [CI], [AI] provides us with a reductive analysis of inherence. According to [AI], spatial co-location, or in the case of nuclear tropes, spatiotemporal co-location is not sufficient for inherence. Additionally, [AI] states that, necessarily, if t exists, substance i exists, and t is a part of i. Since these claims are consequences of t’s being rigidly dependent on the nuclear tropes of i and a new account of the determination of the location of tropes, SNT analyzes inherence in terms of co-location, parthood, and rigid dependence. SNT provides new answers to the three problems that plague paradigmatic trope theories. First, in the standard case, tropes are parts of a certain kind of substance determined by its nuclear tropes. Here, the explanation of why tropes are properties of certain kinds of substances is assumed to be metaphysical and determined by the existential dependencies between tropes. Second, SNT allows for mutually co-located substances, which should be a possibility allowed for in any trope bundle account of fundamental substances. Finally, by means of c-bundles, SNT can provide a trope theoretical conception of endurant substances, which are identical through change of contingent tropes. Nevertheless, SNT is not committed to endurantism: in a perdurantist version of SNT, it is enough to suppose that the locations of c-bundles are determined by the locations of n-bundles and that these locations are instantaneous.13

Notes 1 Formal ontology is the branch of metaphysics that analyzes ontological categories by ontological forms (forms of being), which correspond to different formal ontological relations like being a part of or being existentially dependent on ( Hakkarainen and Keinänen 2023b). 2 See Fisher (2020: 44–45) for a detailed description of Williams’ abstract/concrete distinction.

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Markku Keinänen and Jani Hakkarainen 3 We distinguish between exemplification, i.e., an object possessing general properties (universals or their substitutes), and inherence, i.e., an object having properties taken as particulars. 4 Cf. Keinänen (2018: sec. 2). Here, adherence stands for the formal ontological relation between a particular relation and its relata (“relating”). 5 Cf. Keinänen (2018) and Hakkarainen and Keinänen (2023a). 6 Moreover, Ehring (2011: 123) rejects relata specific particular relations Maurin introduces, but we ignore this difference in this chapter. 7 Ehring (2011: 105) ends up preferring exdurantism to perdurantism, but due to space, we ignore this subtlety in his theory. 8 See Schaffer (2003) for an attempt to provide such explanation. 9 See Tahko and Lowe (2020) for an excellent discussion of different kinds of dependence relations. 10 See Keinänen (2005: 352–369; 2011: 430–431) for discussion. 11 The formal ontological relation of rigid dependence is characterized modal-existentially and as follows: RD(e,f) = ¬(□ E!f) & □ ((E!e → E!f) & ¬(f ≤ e)). 12 Hakkarainen (2018); Hakkarainen and Keinänen (2017); Keinänen (2011, 2018); Keinänen and Hakkarainen (2010, 2014). 13 We are grateful to Kone Foundation for financially supporting this research.

References Campbell, K. (1990) Abstract Particulars. Oxford: Blackwell. Denkel, A. (1996) Object and Property. Cambridge: Cambridge University Press. Denkel, A. (1997) On the Compresence of Tropes. Philosophy and Phenomenological Research 57(3): 599–606. Ehring, D. (1997) Causation and Persistence: A Theory of Causation. New York: Oxford University Press. Ehring, D. (2011) Tropes: Properties, Objects and Mental Causation. Oxford: Oxford University Press. Fisher, A.R.J. (2018) Instantiation in Trope Theory. American Philosophical Quarterly 55(2): 153–164. Fisher, A.R.J. (2020) Abstracta and Abstraction in Trope Theory. Philosophical Papers 49(1): 41–67. Hakkarainen, J. (2018) What Are Tropes, Fundamentally? A Formal Ontological Account. In Kuorikoski, J. and Toppinen, T. (eds.) Action, Value and Metaphysics, Acta Philosophica Fennica 94. Helsinki: Societas Philosophica Fennica: 129–159. Hakkarainen, J. and Keinänen, M. (2017) The Ontological Form of Tropes – Refuting Douglas Ehring’s Main Argument against Trope Nominalism. Philosophia 45(2): 647–658. Hakkarainen, J. and Keinänen, M. (2023a) Bradley’s Regress and the Inadequacy of the RelataSpecific Answer. Acta Analytica 38(2): 229–243. Hakkarainen, J. and Keinänen, M. (2023b) Formal Ontology. Cambridge: Cambridge University Press. Keinänen, M. (2005) Trope Theories and the Problem of Universals. Helsinki: University of Helsinki. Keinänen, M. (2011) Tropes — The Basic Constituents of Powerful Particulars? Dialectica 65(3): 419–450. Keinänen, M. (2018) A Trope Theoretical Analysis of Relational Inherence. In Kuorikoski, J. and Toppinen, T. (eds.) Action, Value and Metaphysics, Acta Philosophica Fennica 94. Helsinki: Societas Philosophica Fennica: 161–189. Keinänen, M. and Hakkarainen, J. (2010) Persistence of Simple Substances. Metaphysica 11(2): 119–135. Keinänen, M. and Hakkarainen, J. (2014) The Problem of Trope Individuation: A Reply to Lowe. Erkenntnis 79(1): 65–79. Lowe, E.J. (2016) There Are Probably No Relations. In Marmodoro, A. and Yates, D. (eds.) The Metaphysics of Relations. Oxford: Oxford University Press: 100–112. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. Maurin, A.-S. (2010) Trope Theory and the Bradley Regress. Synthese 175(3): 311–326. Maurin, A.-S. (2011) An Argument for the Existence of Tropes. Erkenntnis 74(1): 69–79.

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Trope Bundle Theories of Substance Maurin, A.-S. (2023) Tropes. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Spring 2023 Edition), URL = < https://plato.stanford.edu/archives/spr2023/entries/tropes/>. Morganti, M. (2009) Tropes and Physics. Grazer Philosophische Studien 78(1): 185–205. Schaffer, J. (2003) The Problem of Free Mass: Must Properties Cluster? Philosophy and Phenomenological Research 61(1): 125–138. Simons, P. (1994) Particulars in Particular Clothing: Three Trope Theories of Substance. Philosophy and Phenomenological Research 54(3): 553–575. Simons, P. (2000) Identity through Time and Trope Bundles. Topoi 19(2): 147–155. Tahko, T.E. and Lowe, E.J. (2020) Ontological Dependence. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), URL = < https://plato.stanford.edu/archives/ fall2020/entries/dependence-ontological/>. Williams, D.C. (2018a[1953]) The Elements of Being. In Fisher, A.R.J. (ed.) The Elements and Patterns of Being. Oxford: Oxford University Press: 24–50. Williams, D.C. (2018b[1960]) Universals and Existents. In Fisher, A.R.J. (ed.) The Elements and Patterns of Being. Oxford: Oxford University Press: 51–66. Williams, D.C. (2018c[1963]) Necessary Facts. In Fisher, A.R.J. (ed.) The Elements and Patterns of Being. Oxford: Oxford University Press: 104–124.

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22 TROPE-RELATIONS Anna-Sofia Maurin

22.1

Introduction

When trope theorists introduce their basic posits, the examples they use tend to refer to the – particularized – properties of a thing: the shape and color of this lollipop (Williams 1953: 4f.), the temperature of that wire, the solidity of this bell (Campbell 1990: 3), or the snubbedness of Socrates’ nose (Mulligan et al. 1984: 291). Much more rarely is there mention of such things as the being to the left of (e.g., of this lollipop vis-à-vis that one), the being attached to (of the wire to the bell), or the being larger than (of Socrates’ nose as compared to Aristotle’s). If the being to the left of, the being attached to, or the being larger than are tropes, they are trope-relations. This chapter investigates what trope-relations are as well as to what extent trope theory does, ought to, or even can include trope-relations among its basic posits.1

22.2

The Existence of (Trope-)Relations

When trope theorists ask whether trope-relations exist, what they’re inquiring about is in all likelihood not whether these (and similar, relational) statements are (or can be) true: This lollipop is to the left of that one. That wire is attached to that bell. Socrates’ nose is larger than Aristotle’s. Rather, what they are asking is whether, given that these (and similar, relational) statements are true: does reality have to contain (trope-)relations? The key to answering this question, say most trope theorists, is to be found in the distinction between internal and external relations. G.E. Moore famously held that a relation is internal (in his words: a property is an internal relational property) (1919: 47) ‘if it can always be truly asserted of any term x which has that property, that any term which had not had it would necessarily have been different from x’. D. M. Armstrong (1978b: 85) accepted the importantly different view that ‘[t]wo or more particulars are internally

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related if and only if there exist properties of the particulars which logically necessitate that the relation hold’. And according to David Lewis (1986: 62), ‘[a]n internal relation is one that supervenes on the intrinsic natures of its relata: if X1 and Y1 stand in the relation but X2 and Y2 do not, then there must be a difference in intrinsic nature either between the Xs or else between the Ys’. Specifics aside, the difference between internal and external relations lies in how they relate to what they relate: internal relations are (and external relations are not) in some sense fixed by or founded in their relata (either by being fixed or founded in the existence or essential nature of those relata (à la Moore) or by being fixed or founded in their (contingent) nature (à la Armstrong or Lewis)). Suppose the relations invoked by the statements above are all internal relations. Then, according to Armstrong (1978b: 86), those relations are ‘nothing more than the possession by the particulars of the properties which necessitate the relation[s]’. And according to E.J. Lowe (2016: 106): [W]e shouldn’t seriously believe in the real existence of so-called ‘internal’ relations, even if it is sometimes convenient to talk as if they existed. There are no ‘internal’ relations, then. There are just certain relational truths that are made true by monadic entities of certain types, whether these be concrete objects or tropes. Are all (trope-)relations internal relations? According to one prominent trope theorist – Keith Campbell – they just might be: given plausible background assumptions (the plausibility of which will be briefly considered below) all relations are founded relations, either by being essential to the identity of their relata (what Campbell calls ‘internal’) or by being determined by their contingent nature (what he calls ‘external-founded’). The thesis that all relations are either internal or external-founded – the thesis that no relation exists – Campbell calls Foundationism. In his defense of Foundationism, Campbell considers three types of relations – causation, spatiotemporal relation, and compresence – which all appear to be glaring examples of unfounded (external) relations, but which he believes can be construed as founded. Causation, first, appears unfounded only so long as you accept a Humean view of causation. If causation is instead grounded in the powers of its relata (see e.g., Yates 2016) – the view of causation Campbell prefers – it is external-founded (Campbell 1990: 124). Similarly for spatiotemporal relations. These are unfounded, says Campbell, only to the extent that spacetime is relational. If spacetime is substantive – the view on spacetime Campbell prefers – spatiotemporal relations are (also) external-founded (see Simons 2010 for a similar view). We need not bother with the details of Campbell’s arguments, nor with whether we find them persuasive or not. It is enough to note that even if he is right, and causation as well as spatiotemporal relation can be understood as founded types of relations, the ontological and theoretical cost is – to many perhaps prohibitively – high. And even if that cost were deemed acceptable there remains Campbell’s third example of a seemingly unfounded relation: compresence. Accounting for how compresence can be a relation founded in its terms is – and Campbell agrees – where the real challenge lies. According to a majority of trope theorists – Campbell included – compresence is the relation which holds the tropes that make up a concrete object together (see Chapter 21, this volume, for further discussion). Compresence is hence a relation between tropes, not objects. And this matters. As we have seen, according to Campbell, if a relation is internal, 251

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it is essential to the identity of its relata, which means that, if those relata are tropes, it is essential to the identity of those tropes: Internal: if those tropes did not stand in that relation, those tropes would not exist. Moreover, according to Campbell, if a relation is external-founded, it is determined by the – contingent – nature of its relata, which means that, if those relata are tropes, it is determined by the nature of those tropes: External-founded: if those tropes did not stand in that relation, they would have to have a different nature from the nature they in fact have. According to a majority of trope theorists, tropes are their (simple) natures. But if they are, tropes cannot have a nature other than the nature they in fact have/are. Which means that the only way for compresence to not be external, is if it is internal: if t and t′, are compresent, t and t′ could not exist and not be compresent. But this is problematic. For, says Campbell, in most cases, it does not seem as if compresent tropes must be compresent in order to exist. Thinking that they must would place ‘altogether too harsh restriction on what is possible’ (Campbell 1990: 132). Therefore, it does not seem as if compresence can be either external-founded or internal. Therefore, Foundationism is in trouble. Is all lost for Foundationism? Not according to Campbell. For if the world is a world of mutually (and necessarily) interconnected (trope-)fields – Space-Time and The Field – and if The Field is compresent with Space-Time by being necessarily ‘variegated across SpaceTime but containing no real, detachable parts’ (ibid.), Campbell believes we can say that compresence is founded in its trope-relata. The cost of accepting this worldview is a radical departure from the world of common-sense objects that move across space and change over time. For those of us who think philosophy should contradict common-sense as little as possible, this price is (much) too high. Let’s conclude, therefore, with a hypothetical: whatever we may think of the nature of causation or of spacetime, if we want our ontology to be able to accommodate at least some of our common-sense beliefs, at least one (external) relation exists: compresence.

22.3

The Existence of Trope-Relations?

We have now seen that the trope theorist who does not accept a radically revisionist view of reality will most likely have to posit the existence of at least one (trope-)relation. But why not more? That the trope theorist might conceivably get away with accepting the existence of just compresence hinges on her not having to posit the existence of internal relations. In this Section, I revisit the question of why that is the case. Additionally, given that defeasible reasons exist for thinking that internal as well as external relations exist, I consider, but in the end dismiss, a challenge to the trope theoretical view: an argument to the effect that what exists when an internal relation (of resemblance) exists must be a universal. Are all internal relations ‘no addition to being’? One – the(?) – reason for saying yes is parsimony. Most agree that you should not posit entities beyond necessity. Internal relations are relations which obtain in virtue of the 252

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nature and/or existence of their relata: if those terms exist/have the natures they do, their being related is entailed. Which means that, if someone (God?) wanted to account for all truths, including all relational truths, all he (she, it, they) would have to do is create those relata (being the way those relata are). But then positing relations on top of those relata arguably amounts to positing something beyond necessity. Suppose you agree that you should not posit entities beyond necessity. Indeed, suppose you agree that to posit internal relations to account for (internal) relational truths would be beyond necessity. Then only if there is some other ‘job’ – other than making true all relational truths, that is – relations are needed for, do we have a reason to posit internal relations (for a good introduction to this way of thinking of reasons for positing (internal) relations, see MacBride 2011: 162; 2020: Sec. 3). What ‘job’ might that be? According to Herbert Hochberg (2013: 232), (internal) relations are needed for the job of objects of perception. This is because Hochberg thinks that we – ‘obviously’ – perceive not just the relata of relations, but the relations themselves. More precisely, Hochberg argues, even if e.g., spatiotemporal relations turn out to be founded in (and so internal to) their relata, ‘[s]urely one does not perceive a temporal trope of priority to B that is inherent in (the nature of) A or a trope of being-beneath-D that is inherent in C’ (ibid.: 231). Rather, what one perceives when one perceives that A is before B or that C is beneath D, says Hochberg, is, besides A and B or C and D (and their respective natures), the relations of being prior to and being beneath. But then (ibid.: 232): Whether such relations are needed, along with facts, to account for the truth of the relational statements, they are certainly required to deal with the account of the apprehensions of something beneath something else, and something occurring before something else. According to Bertrand Russell (1903: sec. 214, see also MacBride 2011 and Bigelow and Pargetter 1990: 55–56), (internal) relations are needed for the job of explaining why some relations are founded in (the nature of) their terms (e.g., why they are internal). To see why that is, consider the following (so-called ‘comparative’) relational truth: a is taller than b. This statement is true in virtue of the (contingent) natures of a and of b: because a is the height it is and b is the height it is, a is taller than b (which makes being-taller-than external-founded in Campbell’s sense). Now, suppose the natures in virtue of which a is taller than b are: a is 2 meters tall (F), and b is 1 meter tall (G). Then we can ask: in virtue of what do these natures make a taller than b? The answer could of course be that it’s primitive. A much more satisfying answer is however that a’s

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being F and b’s being G makes a taller than b because F is greater than G. But now we have accounted for why the natures of a and b make true the relational statement that a is taller than b by invoking another (internal) relation: being-greater-than. Does this relation (have to) exist? If explanation requires that it does, then arguably yes. In any case, what explanation requires is something about which reasonable people disagree. Which might make one think that so is whether internal relations exist. Suppose for the sake of argument that internal relations exist. Suppose, more precisely, that the internal relation of resemblance exists. Then according to some, if resemblance exists it must be a universal – which would be bad news for the trope theorist. An argument for the conclusion that if resemblance exists, it must be a universal was first formulated by Russell (1956[1911]; cf. Hochberg 1980). Russell’s argument was directed against a (somewhat) classic nominalism, but it doesn’t seem far-fetched to think that a version of the argument could be formulated against the trope view. Here’s one such version (this one from Johansson 2009): suppose the world contains precisely three exactly similar tropes a, b, and c. Why are those tropes exactly similar? The only available answer (if the trope theorist wants to remain a trope theorist), says Ingvar Johansson, is that they are exactly similar because they belong to the same similarity class. But this explanation makes use of the following three claims: a and b are exactly similar a and c are exactly similar b and c are exactly similar. And since ‘this construction employs three instances of similar’, it implicitly presupposes the existence of a relational universal: similarity. The trope theorist could point to another resemblance class: that consisting of the resembling similarities (joined by a – second order – relation of resemblance). But this answer leads to an infinite regress. And this infinite regress is vicious, because (Johansson 2009: 82): The threatening similarity universal is, so to speak, always pushed a step forward. In other words […] in the case of the resemblance classes at hand, what comes first is for its definition dependent on what comes afterwards. In such a case, an infinite regress is vicious. I don’t think this regress is vicious, however. At least, I don’t think it is if the view from which it is generated is ‘standard’ trope theory. Standard trope theory is a view according to which tropes have the natures they do primitively (not ‘in virtue of’ something else) and it is a view according to which tropes resemble each other ‘in virtue of’ their nature. That this is not the trope theory Johansson is objecting to seems clear if we consider what he thinks will be the case in a situation where there is but one spherical-shape trope (and no universal sphericity). In that case, he argues (ibid: 83): Since there is no instance of the relational universal exact similarity of shapes that can be used in a construction of a nominalistic resemblance class, this implies that this lonely thing cannot truly be described as being spherical.

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Only if tropes have the natures they do in virtue of belonging to this or that resemblance class would it follow that ‘this lonely thing cannot truly be described as being spherical’. Tropes do not have the natures they do in virtue of belonging to this or that resemblance class, however. Therefore, ‘this lonely thing’ can be truly described as being spherical! And this matters. For, not only does Johansson claim that a regress analogous to that generated for ‘classic’ nominalism can be generated for the trope view. He also claims that this regress is vicious. Why? Because (to paraphrase Johansson) what comes first in it is dependent on what comes afterwards. Johansson is here making the (I believe quite reasonable) point that whether a regress is vicious has to do with what ‘pattern of dependence’ it instantiates. More precisely, it has to do with if it instantiates a pattern of dependence where what exists ‘first’ depends for its existence on what exists ‘next’ in the regress order, etc. ad infinitum (where ‘first’ and ‘next’ should be read atemporally). But then the question becomes: Which pattern of dependence does the trope-version of the regress instantiate? If tropes resemble in virtue of their (primitive) natures, the trope version of the regress will instantiate a pattern of dependence according to which: a, b, and c resemble each other in virtue of the (primitive) natures of a, b, and c, the resemblances holding between a, b, and c resemble each other in virtue of the (primitive) natures of those resemblances, the resemblances holding between the resemblances holding between a, b, and c resemble each other in virtue of the (primitive) natures of those resemblances. And so on ad infinitum. But then, even if reasons (e.g., perception or explanation) exist for thinking that every instance of resemblance generated in the regress exists, and even if, if one resemblance-trope exists, an infinity of resemblance tropes exist, this is no reason to think that the resulting regress is vicious. For that regress does not instantiate a vicious-making pattern of dependence.2 Which means that we can (tentatively) conclude that even if internal relations exist, trope theory is not in trouble.

22.4 The Existence of (Trope-)Relations? So (trope-)relations (external, possibly also internal) (must) exist. But can they? According to a line of argument going back to F.H. Bradley (1893; cf. Parmenides; for a more recent version, see Della Rocca 2020) they cannot. The argument (at least in Bradley’s version) proceeds on the assumption that relations, if they exist, must be either founded (in Campbell’s words: internal or external-founded) or unfounded (external). It proceeds in two steps. The first step shows why no relation can be founded in its terms. The second shows why no relation can be unfounded in its terms. The conclusion follows immediately: if a relation, to exist, must be either founded or unfounded but can be neither, relations do not (indeed cannot) exist. Here’s the argument in a bit more detail. Consider a lump of sugar. This lump, let’s suppose, is white, sweet, and hard. Pondering over the nature of the lump may lead us to wonder: 1 How is the lump related to its many qualities? 2 How are its many qualities related to each other? Bradley first investigates if (1) could be answered by saying of the lump that it is identical to (and thereby founded in) its qualities. Then this must be either because the lump is identical 255

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to its qualities ‘taken separately’ or because it is identical to its qualities ‘taken collectively’ or, finally, because it is identical to them ‘united’. Clearly, the lump – which has many qualities – cannot be identical to each of its qualities taken separately, or there will be contradiction. And it cannot be identical to its qualities taken collectively, for (1893: 16, emphasis added): ‘[s]ugar is obviously not mere whiteness, mere hardness, and mere sweetness; for its reality lies somehow in its unity’. If the lump is founded in its qualities by being identical to them, therefore, it must be identical to those qualities united. Saying that it is does not lead to contradiction, and it doesn’t mistakenly identify sugar with its qualities, which is good. The success of this answer does however depend on our being able to come up with an answer to (2): only if we can say how the many qualities of the lump are related to each other – how they are united – can we answer (1) by saying that the lump is founded in its qualities by being identical to those qualities united. Bradley’s first attempt to answer (2) is by saying that the qualities of the lump are related to each other by being founded in each other either by being identical to each other or by being what he calls predicated of each other. Neither answer works, however. Whiteness isn’t hardness (or sweetness… ), nor does whiteness have the property of being hard (or sweet… ). Bradley next considers answering (2) by introducing a relation holding between the qualities of the lump by ‘being predicated of’ them (an internal relation, in other words). If the relation is internal in this sense, Bradley notes, the qualities of the lump would be related ‘by nature’. Yet Bradley (very reasonably!) doesn’t think that whiteness is by nature such that it is related to hardness, or that hardness is by nature such that it is related to whiteness, etc. Rather, whiteness, hardness, and sweetness, although they happen to make up the lump didn’t have to do so. Which means that, if there is a relation in which they stand, that relation must be external. Can the relating of the qualities of the lump be accomplished by adding an external relation to them? Not according to Bradley (and this is perhaps the most famous part of his argument). If the relating of the qualities of the lump is unfounded or external, those qualities could exist without being related. But then (1893: 18): … [t]he relation C has been admitted different from A and B, and no longer is predicated of them, Something, however, seems to be said of this relation C, and said, again, of A and B. And this something is not the ascription of one to the other. If so, it would appear to be another relation, D, in which C, on one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process. The new relation D can be predicated in no way of C, or of A and B; and hence we must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another, F; and so on, indefinitely. Which means that we cannot answer (2) by saying that the qualities of the lump are externally related. Which means that we cannot answer (2), period. Thus we cannot answer (1). Which, according to Bradley, means that relations cannot exist.

22.5

The Existence of Trope-Relations!

Bradley’s argument is very much discussed. Most agree that it cannot be right. And most disagree about exactly why that is.3 Some (e.g., Armstrong 1997) reject the argument on 256

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the grounds that the regress it generates is in fact benign. However, if you accept that a regress is vicious if it instantiates a pattern of dependence going from ‘later’ to ‘earlier’ in the regress order, (as above, these terms refer to where in the regress order something occurs and so should be read atemporally) those people must be wrong: what the argument shows is that lump’s existence depends on the existence of lump’s qualities related, that lump’s qualities being related depends on there being relations in which they stand, that there being relations in which they stand depends on there being relations in which those relations stand, and so on ad infinitum. This is a pattern of dependence going from ‘later’ to ‘earlier’. Which was precisely what we didn’t want. Some (e.g., Blanshard 1986, Broad 1933, Grossmann 1992) reject the argument on the grounds that it wrongly posits an infinite regress when in fact there is none. Because it is in the nature of relations to relate, these philosophers point out, adding an (external) relation to the qualities of the lump will make those qualities related. No further relations relating the relation to its relata required! This response is fine as far as it goes. But does it go far enough? Many believe that it does not. Bradley’s argument is reasonably interpreted as a challenge to whoever wants to defend the ‘relating power’ of relations. Saying that ‘it is in the nature of relations to relate’ is then not enough. To truly stand up to the challenge the proponent of the ‘it’s in the nature of relations to relate’ response must also come up with an answer to the following question: How do relations relate? Again, there are many different responses on offer in the literature (e.g., Keinänen 2011; Meinertsen 2018; Vallicella 2000). Here, and for reasons that will hopefully become clearer as we proceed, I will focus on just one: the so-called relata-specific solution (see Betti 2015; Maurin 2002, 2010, 2011; Simons 2010; Wieland and Betti 2008; see Hakkarainen and Keinänen 2023 for a more recent critique). The way Bradley sets things up, proponents of this solution point out, the regress gets going only if we accept that something like the following intuition needs preserving: Intuition: some things exist in virtue of the existence of their qualities united, yet those qualities might exist and not be united (with each other). Intuition concerns how the relata of a relation can (or cannot) depend on each other. The distinction between internal (founded) and external (unfounded) relations, on the other hand, concerns how a relation can (or cannot) depend for its existence on its relata. Bradley, and many after him, have simply assumed that if a relation is internal to its relata, those relata must be internal to it and that, if a relation is external to its relata, those relata must be external to it. But what if those things could come apart? More precisely, what if the relata of a relation could exist and not be related, yet the relation in which they stand, to exist, had to relate those relata? Then, says the proponents of the relata-specific solution, there will be no regress: if a relation is relata-specific, once it exists so does its relata (related). Yet because the existence of the relation is contingent (it doesn’t have to exist, and so its relata do not have to be related) Intuition is nevertheless preserved. Suppose (possibly counterfactually) that the relata-specific solution is a good one: if relations are relata-specific, the Bradleyan problem goes away. Then we must ask: What exists when a relata-specific relation exists? 257

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This is a question about the categorial home of relata-specific relations. One possible answer to this question is that what exists when a relata-specific relation exists is a trope. Suppose this possible answer is also the best answer. Then if relations are relata-specific, trope theory is true. Is what exists when a relata-specific relation exists a trope? I’ll end this section with some reasons for thinking that it is. Suppose (as we shall see, counterfactually) that relata-specific relations are universals, and suppose that objects are substrates in which universals are instantiated (a view famously championed by Armstrong 1978a). Then the substrate in which e.g., lump’s properties are instantiated will be distinct from the substrate in which clump’s properties are instantiated (clump being lump’s rather unfortunate cousin). Which, given that relations are relata-specific, means that the relation (R) uniting lump’s constituents must be distinct from the relation (R’) uniting clump’s constituents. On this view, then, no two objects could ‘share’ the relation that plays a role in making each of them up. This proposal, therefore, makes relations universal in name only. Suppose relations are universals and objects are bundles of their (universal) properties. In this case, if lump and clump are qualitatively identical, they could in principle ‘share’ the R playing a role in making each of them up. The problem with this view is, first, that if the R uniting the constituents of lump is identical to the R uniting the constituents of clump, we cannot distinguish indiscernible bundles from each other with respect to their distinct ‘bundling mechanisms’. But then how are we to distinguish them? Second, if lump’s R is identical to clump’s R, clump exists given the existence of lump, and vice versa. But what do those two things have to do with each other? Suppose, finally, that you’re a (classic) nominalist. On this view, there are concrete particulars only. Nominalists – at least those who accept that some things exist in virtue of their parts (so, most nominalists!) – must also come up with a solution to the Bradley problem. If the only – or best – solution to that problem is the relata-specific solution, nominalism is straightforwardly contradicted: even if relations are particular, they are not concrete. So what are they? Although far from conclusive, what the above indicates is that relations, if they exist, are tropes.

22.6 Summary In this chapter, I have argued that good reasons exist for thinking that at least one (external) relation exists (compresence), that even if internal relations (also) exist, this need not worry the trope theorist, and that the fact that relations exist might be taken as a reason to think that trope theory is true.

Notes 1 For a nice discussion of relations not guided by the ‘special interest’ of trope theory, see Chapter 7, this volume. 2 That the same goes for (contemporary versions of) ‘classic’ nominalism has been convincingly argued by Rodriguez-Pereyra (2001). 3 I will not be mentioning all attempts to solve the Bradley problem here. For fuller run-throughs, see e.g., Maurin (2012) and Perovic (2017). Cf. also Cameron (2022).

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References Armstrong, D.M. (1978a) Universals and Scientific Realism I: Nominalism and Realism. Cambridge: Cambridge University Press. Armstrong, D.M. (1978b) Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Betti, A. (2015) Against Facts. Cambridge, MA: MIT Press. Bigelow, J. and Pargetter, R. (1990) Science and Necessity. Cambridge: Cambridge University Press. Blanshard, B. (1986) Bradley on Relations. In Manser, A. and Stock, G. (eds.) Philosophy of F.H. Bradley. Oxford: Oxford University Press: 211–226. Bradley, F.H. (1893) Appearance and Reality. Oxford: Clarendon Press. Broad, C.D. (1933) Examination of McTaggart’s Philosophy. Cambridge: Cambridge University Press. Cameron, R. (2022) Infinite Regress Arguments. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), URL = < https://plato.stanford.edu/archives/fall2022/entries/ infinite-regress/>. Campbell, K. (1990) Abstract Particulars. Oxford: Blackwell. Della Rocca, M. (2020) Parmenidean Ascent. Oxford: Oxford University Press. Grossmann, R. (1992) The Existence of the World. London and New York, NY: Routledge. Hakkarainen, J. and Keinänen, M. (2023) Bradley’s Relation Regress and the Inadequacy of the Relata-Specific Answer. Acta Analytica 38(2): 229–243. Hochberg, H. (2013) Nominalism and Idealism. Axiomathes 23(2): 213–234. Hochberg, H. (1980) Russell’s Proof of Realism Reproved. Philosophical Studies 37(1): 37–44. Johansson, I. (2009) Proof of the Existence of Universals – and Roman Ingarden’s Ontology. Metaphysica 10(1): 65–87. Keinänen, M. (2011) Tropes – The Basic Constituents of Powerful Particulars. Dialectica 65(3): 419–450. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Lowe, E.J. (2016) There Are Probably No Relations. In Marmodoro, A. and Yates, D. (eds.) The Metaphysics of Relations. Oxford: Oxford University Press: 100–112. MacBride, F. (2011) Relations and Truth-Making. Proceedings of the Aristotelian Society 111: 161–179. Maurin, A.-S. (2002) If Tropes. Dordrecht: Kluwer. Maurin, A.-S. (2010) Trope Theory and the Bradley Regress. Synthese 175(3): 311–326. Maurin, A.-S. (2011) An Argument for the Existence of Tropes. Erkenntnis 74(1): 69–79. Maurin, A.-S. (2012) Bradley’s Regress. Philosophy Compass 7(11): 794–807. Meinertsen, B. (2018) Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley’s Regress. Singapore: Springer. Moore, G.E. (1919) External and Internal Relations. Proceedings of the Aristotelian Society 20: 40–62. Mulligan, K., Simons, P, and Smith, B. (1984) Truth-Makers. Philosophy and Phenomenological Research 44(3): 287–321. Perovic, K. (2017) Bradley’s Regress. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), URL = < https://plato.stanford.edu/archives/win2017/entries/bradley-regress/>. Rodriguez-Pereyra, G. (2001) Resemblance Nominalism and Russell’s Regress. Australasian Journal of Philosophy 79(3): 395–408. Russell, B. (1903) The Principles of Mathematics. London: George Allen and Unwin. Russell, B. (1956 [1911]) On the Relations of Universals and Particulars. In Logic and Knowledge: Essays, 1901–1950. London: George Allen and Unwin. Simons, P. (2010) Relations and Truthmaking. Aristotelian Society Supplementary Volume 84(1): 199–213. Vallicella, W.F. (2000) Three Conceptions of States of Affairs. Noûs 34(2): 237–259. Wieland, J.W. and Betti, A. (2008) Relata-Specific Relations: A Reply to Vallicella. Dialectica 62(4): 509–524. Williams, D.C. (1953) On the Elements of Being I. Review of Metaphysics 7(1): 3–18. Yates, D. and Marmodoro, A. (2016) Introduction. In Marmodoro, A. and Yates, D. (eds.) The Metaphysics of Relations. Oxford: Oxford University Press: 1–18.

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PART 6

Properties in Causation, Time, and Modality

23 CAUSATION AND PROPERTIES Carolina Sartorio

23.1

Introduction

Properties play an important role in theorizing about causation. This is particularly clear when it comes to the kind of causation that relates event types (“type causation”). For example, consider the type-causal claim “Smoking causes lung cancer”. This is a generalization that states that events of a certain type cause, or tend to cause, events of another type. But it’s natural to understand event types as properties shared by events – such as the property of being an act of smoking, or the property of suffering from lung cancer. As a result, type causation is a form of causation that seems to involve properties in a central way. Arguably, however, the most fundamental causal concept is one that involves tokens, not types. For it’s natural to think that generalizations are grounded in the instances they are generalizations of, and thus, that causation between types is grounded in causation between tokens. For example, “Smoking causes lung cancer” arguably holds in virtue of the specific instances where smoking leads to lung cancer (see, e.g., Hausman 1998). In any case, my focus here will be token causation. I will consider questions such as: do properties also play an important in theorizing about token causation? And, if so, how? Although the role that properties play is less immediately obvious in this case, I’ll argue that it’s still important. Mainly, this is because properties allow us to make fine-grained causal discriminations that we wouldn’t otherwise be able to make – at least not as naturally. As I’ll aim to show, those fine-grained causal discriminations are important for the sake of causal theorizing itself, but also given the conceptual link that exists between causation and moral responsibility. The chapter discusses a range of topics where properties play a central role. They include the debate over the causal relata, the debate over the transitivity of causation, the debate over an alleged asymmetry between hasteners and delayers, and the debate over switches.

23.2

The Motivations: The Role of Properties in Token Causation

Consider the following example: Compassionate Doctor: A doctor gives morphine to a terminally ill patient before he dies in order to alleviate the pain. The patient dies peacefully as a result. DOI: 10.4324/9781003246077-30

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Intuitively (assuming the morphine didn’t significantly alter the time and cause of the patient’s death but only made it less painful), we would like to be able to say that the doctor didn’t cause her patient’s death; instead, she only caused it to be a peaceful or painless death. Intuitively, the latter doesn’t entail the former. Otherwise, as David Lewis once put it, “Who would dare be a doctor?” (Lewis 1986a: 250). The most natural way to understand this claim is in terms of the distinction between causing an event and causing an event’s property (or: causing an event to have a certain property, or something of the sort). What is the relation between causing an event and causing an event’s property? Again, intuitively, it’s not a very tight relation. Just like the compassionate doctor can cause the death to be painless without causing the death itself, I can cause a meeting to be boring – or to start late – without causing the meeting itself, the presence of clouds in the sky can cause a sunset to be beautiful without causing the sunset itself, etc. Arguably, it’s only when we think of properties that events have essentially that we can reliably predict that causing an event to have that property will go hand in hand with causing the event itself. For example, if a death by poisoning essentially involves the relevant poison (that is to say, it wouldn’t have been the same token event without it), then administering the poison both causes the death and the death’s being a death by poisoning. But events (or the events that we care to talk about in ordinary language) have most properties only accidentally. As a result, it’s easy to think of examples where causing an event’s property doesn’t also result in causing the event. Effects are quite “robust”, in this sense. In many or most cases where we cause effects to have certain properties, we cause them to happen in certain ways without causing them to happen (Lewis 1986a; Sartorio 2006). Now, as it turns out, Lewis himself in later work (Lewis 2000) proposed an account of causation (causation as “influence”) that tracks difference-making or counterfactual dependence along different dimensions, where these dimensions include whether an event happens (regular counterfactual dependence), but also when and how an event happens. On this view, anything that has that kind of influence – anything that helps determine whether, when, or how an event happens – can be seen as a cause, to some degree. But, as many have pointed out (see, e.g., Collins 2000; Kvart 2001; Schaffer 2001; Silver 2019), this view is extremely counterintuitive. Importantly, the distinction between causing an event and causing an event to have a certain property seems to underlie our ordinary attributions of moral responsibility. For example, we may want to say that the compassionate doctor isn’t responsible for her patient’s death because she didn’t cause his death. At the same time, we may want to say that the compassionate doctor is responsible for a property of the death, because she did cause the death to have that property – for example, we may want to praise her for the death’s being a peaceful and painless one. It seems that we need these causal discriminations in order to ground the corresponding responsibility attributions. This is a distinction at the level of effects. But, arguably, there is a similar distinction at the level of causes. It’s the distinction between an event’s causing an effect and an event’s property causing an effect (or: an event’s causing an effect in virtue of having a certain property, or something of the sort). To illustrate, consider this other example: Clumsy Terrorist: A terrorist has planted a bomb that needs to be triggered by pushing a button. Since he is right-handed, he would have normally pressed the button with his right hand. However, on his way to the triggering device the terrorist 264

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falls and injures his right hand. As a result, when he gets to the button, he pushes it with his left hand. The bomb goes off as planned. Here we would like to draw a similar distinction, but at the level of causes: we would like to say that the cause of the explosion was the terrorist’s pushing the button, and not the terrorist’s pushing the button with his left hand. (Or that the terrorist’s act caused the explosion by virtue of being a button-pushing event, and not by virtue of being a buttonpushing event where the left hand was involved.) Again, these causal discriminations are connected with our moral responsibility attributions. For example, we may want to say that the terrorist is responsible for the explosion in virtue of pressing the button and not in virtue of pressing the button with the left hand. For what makes him responsible for the explosion is his having pressed the button, not his having pressed the button in a particular way (with the left hand). Clumsy Terrorist can also be used to illustrate how the causal discriminations at the level of effects and causes can come together, and in a way that can be used to shed light on a puzzle about causation. The puzzle that I have in mind arises as follows (here I follow Paul 2000). Consider the following three events that obtain at successive times T1, T2, and T3: E1: The terrorist’s fall E2: The terrorist’s pushing the button with the left hand E3: The explosion If all we have are these three events and nothing more fine-grained than that, then we seem to be forced to say that E1 caused E2, which then caused E3. But then, assuming causation is transitive (if A causes B and B causes C, then A also causes C – an assumption that is quite intuitive, since one way in which we establish causal relations is by tracing causal chains), it follows that E1 also caused E3. However, this seems clearly wrong: the terrorist’s fall didn’t cause the explosion! In contrast, if we have the more fine-grained tools provided by properties and propertyinvolving causation, we can make discriminations that allow us to avoid this result and thus solve the puzzle (this is the solution proposed by L.A. Paul herself). We can say, for example, the following: • E1 caused E2 to have a certain property P: the property of being done with the left hand. • But, when E2 caused E3, it did so in virtue of a different property Q: the property of being a button-pushing. Arguably, this is compatible with the transitivity of causation. For, presumably, once property-involving causation is introduced in this way, it’s natural to assume that the transitivity of causation only applies when the intermediate property is the same. In other words: the conditions under which we can infer that E1 causes E3 are conditions where E1 causes E2 to have a certain property and where that very same property (or E2’s having that property) also causes E3. Otherwise, there is a mismatch of properties and transitivity doesn’t apply. It doesn’t apply because there is no pressure to say that the causal influence that E1 had on E2 transfers onto E3 when the property that is causally relevant in each case is a different one. 265

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More on the transitivity claim later, in Section 23.4. In this section, we’ve seen that there are important motivations for thinking that properties are relevant to theorizing about token causation. But how, exactly, can we make sense of property-involving causation? I turn to this in the next section.

23.3 How to Accommodate Properties within Token Causation: The Debate over the Causal Relata Causation theorists have aimed to capture the relevance of properties in a number of different ways. Most radically, some have argued that causation is, at the most fundamental level, a relation between properties, not a relation between events. A bit more precisely, it’s a relation between property instantiations (“aspects”, as in Paul 2000) or tropes (Campbell 1990 and Ehring 1997, 2011). In other words, these views claim that property instantiations or tropes are the causal relata – or, at least, the most fundamental causal relata. When we attribute causal powers to events, those causal powers are grounded in the causal powers of some of their properties (events are only causally efficacious in virtue of their having certain properties). For example, according to these views, what caused the explosion in the clumsy terrorist case is not an event – such as the terrorist’s pushing the button – but an event’s aspect – such as the event’s instantiating the property of being a button-pushing. Similarly, the terrorist’s fall didn’t cause an event – such as the event of the terrorist’s pushing the button – but an event’s aspect – such as its instantiating the property of being done with the left hand. Aspects and tropes are concrete particulars: roughly, they are instantiations of properties in physical objects or in regions of space-time. They are things like this redness and that redness, or this particular instantiation of redness and that particular instantiation of redness. As a result, a potential advantage of conceiving of causation as a relation between (most fundamentally) tropes or aspects is that we can make the fine-grained causal discriminations we need without giving up the idea that causation is a relation between particulars. On the other hand, the claim that tropes or property instantiations, not events, are the most fundamental causal relata is quite unorthodox, and many metaphysicians aren’t comfortable with it (see Maurin 2023: sec. 4.1 for further discussion). Other theorists have, either explicitly or implicitly, made room for the relevance of properties in more indirect ways. Those who haven’t given up on events as the basic causal relata have instead postulated an enriched ontology of events that allows us to make similar causal discriminations. This enriched ontology typically includes spatiotemporally coincident events that differ in their essential properties (as in Hausman 1992; Lewis 1986a; Yablo 1992). On these views, causation is still a relation between events, but only between events that have the right kinds of essences. And properties play the key role of specifying what those essences are. For example, according to these views, there are two (and in fact more) button-pushing events occurring after the terrorist fell and injured his right hand, and they both occupy the exact same spatiotemporal location. One is essentially left-handed (it wouldn’t have occurred if the terrorist had pushed the button with the right hand) but the other one isn’t (it’s only accidentally left-handed: it would still have occurred if the terrorist had pushed the button with the right hand). The terrorist’s fall caused the event that is essentially lefthanded, but not the one that is accidentally left-handed. 266

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As noted above, these views allow us to hold on to the idea that causation is a relation between events. But they do that at the expense of a heavily bloated event ontology that not everybody is comfortable with (Paul and Hall 2013: 239ff.). As we have seen, properties still play a role in these views, but in a more indirect and less explicit way. They play the role of specifying the essences of the events that enter in the causal relations, and thus they help us distinguish between those events that are causes and effects and those that aren’t. Stephen Yablo has argued that this way of thinking about causation has a very significant payoff, in that it can shed light on the problems of mental causation and causal exclusion (Yablo 1992). Mental properties, Yablo argued, are not causally excluded by their physical realizers (and thus retain their causal efficacy) because they have the right amount of specificity for their effects. This is because, given the multiple realizability of the mental by the physical, the physical properties are typically too specific to be doing the relevant causal work. On Yablo’s view, mental events and physical events are just another example of coincident events that differ only in their essential properties, and paying attention to those essential properties and the causal work that they do and don’t do is the key to vindicating the causal relevance of the mental (for discussion, see Chapter 34, this volume). So far, we have reviewed views of causation on which properties are the causal relata and views where properties play the more indirect role of determining the essences of the events that enter in causal relations. But the list doesn’t end there. For yet others have suggested that causes and effects aren’t concrete particulars (things like events or tropes) but facts (see, e.g., Mellor 2004). And part of the motivation for those views is precisely the ability to make fine-grained causal discriminations while avoiding a bloated event ontology. Here, again, properties play the more indirect role of specifying the relevant facts that work as causes or effects (on some views of facts, properties are constituents of facts). For example, the fact that the drilling of a tooth was made under anesthesia causes the fact that the dental procedure was painless (or, perhaps more naturally: the procedure was painless because it was done under anesthesia; Mellor 2004: 320–321). On D.H. Mellor’s view, this explains how we can “affect” an event without causing it. Again, an advantage of this view is that, by appealing to facts, we can naturally account for these causal discriminations without having to postulate a myriad of events that differ only in their essential properties. On the flipside, the price we have to pay is, of course, that we must give up the natural view that events are the causal relata (and, according to Mellor, the view that causation is a relation in the first place). Finally, others have abandoned the idea that causation is a binary or two-place relation (Hitchcock 1996; Maslen 2004; Schaffer 2005). These philosophers have suggested that causation is a contrastive relation that involves more than two actual events. On this picture, instead of the simple schema “C causes E” (involving two actual events), we have something more complex like “C rather than C* (a contextually specified counterfactual event) causes E rather than E* (another contextually specified counterfactual event)”. This is another quite unorthodox view that abandons what many consider to be a truism about causation: the claim that causation is a relation between two actual events. On the flipside, the view gives us the flexibility we need when we want to say that the doctor caused the patient’s death to be painless without causing the death, or that the dentist caused the procedure to be painless without causing the procedure itself. This is captured by the relevant contrasts in each case. For example, the doctor’s administering the morphine rather than a different substance (one without the same pain-relieving powers) caused the death to be painless rather than painful. As we can see, properties become 267

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relevant in this view at the time of specifying the contrasts that apply in each case. Again, their role is more indirect, but still important. We have seen that the relevance that properties have for theorizing about causation can be captured in a number of different ways. Which view one is likely to find most plausible is something that will depend on our take on the causal relata and other similar issues in the metaphysics of causation. But these views have at least this in common: properties are needed, in some way or other, to distinguish what is causally relevant from what is not. Otherwise, the resulting picture of causation is too crude to make the fine-grained causal discriminations that seem appropriate in many cases. Moreover, as we have seen, this isn’t only important for the purposes of causal theorizing itself, but also for the more practical purposes of grounding our moral responsibility attributions. So far, I have discussed the general issue of how properties are relevant to (token) causation. In the remainder of the chapter, I turn to more specific debates about causation where properties play a central role. I discuss the debate over the transitivity of causation, the debate over an alleged asymmetry between hasteners and delayers, and the debate over switches.

23.4

The Transitivity of Causation Revisited

Let me turn once again to our discussion of the transitivity of causation. As we have seen in Section 23.2, properties and property-involving causation can be invoked to rescue transitivity from some apparent counterexamples. But, should we think that causation is, in fact, transitive? Although some think it is (see, e.g., Lewis 1986b and 2000; Hall 2000), others think it’s not (see, e.g., Hitchcock 2001 and Yablo 2002). I’m in this last camp. Let me briefly explain why. Consider this new case: Remorseful Assassin: A professional assassin is about to shoot his victim but changes his mind at the last minute. Unfortunately, the assassins-for-hire company doesn’t take any chances: they always send a backup assassin to make sure that the job is done. When the remorseful assassin backs down, the backup assassin steps up and kills the victim. This case involves an apparent failure of the transitivity of causation. For, arguably, the remorseful assassin’s backing down caused the backup’s assassin shooting, and the backup assassin’s shooting caused the victim’s death; however, the remorseful assassin’s backing down didn’t cause the victim’s death. Moreover, note that property-involving causation cannot help here. For intuitively this case doesn’t involve an aspect or property “mismatch” in the intermediate step, as there was in the clumsy terrorist case from Section 23.2. The backing down by the remorseful assassin resulted in the shooting by the backup assassin, and that same shooting behavior resulted in the victim’s death. Intuitively, what matters in each case is simply that there was shooting done by the backup assassin, and this is the same aspect or property throughout. As a result, there seem to be recalcitrant counterexamples to the transitivity of causation, and property-involving causation cannot disarm them all. But this is how I think it should be. For cases like that of the remorseful assassin strike me as genuine counterexamples to transitivity. And, in that case, property-involving causation can still be 268

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helpful, although in a different way: it can help us distinguish the genuine transitivity failures from the merely apparent ones (the merely apparent transitivity failures would be the ones that involve a mismatch of properties, and the genuine ones would be the ones that don’t). Finally, note that there is another connection with responsibility here. In cases of genuine transitivity failures that involve moral agents, there is a corresponding responsibility failure: the agent fails to be responsible for the outcome. Moreover, the most natural explanation of that lack of responsibility is the lack of causation, which seems to entail a transitivity failure. The remorseful assassin case illustrates this point. The remorseful assassin is not responsible for the victim’s death, and the most natural explanation of his lack of responsibility is that he didn’t cause the death. However, he did seem to have caused something that caused the death: the shooting by the backup assassin. Thus, the most natural explanation of the remorseful assassin’s lack of responsibility seems to be one that illustrates the failure of the transitivity of causation (Sartorio 2005).

23.5 Hasteners and Delayers Another interesting debate in the causation literature is the one over the alleged asymmetry between hasteners and delayers. This is another debate that concerns properties – in this case, temporal properties of events. Jonathan Bennett once pointed out that there is an intuitive difference between causing an event to happen a bit earlier (hastening it) and making it happen a bit later (delaying it). Intuitively, hastening an event is typically enough for causing it to happen, but delaying it is not. Bennett’s main example involves a forest fire: in one scenario, the forest fire is hastened by lightning; in another scenario, it is delayed by heavy rains. Intuitively, the lightning strike causes the fire to happen, but the rains do not (Bennett 1987: 373). In other words, hasteners seem to cause what they hasten (at least typically), but delayers don’t seem to cause what they delay (at least not typically). Some have accepted this asymmetry as a genuine causal asymmetry and have tried to accommodate it within their general theories of causation (see, e.g., Toubourg 2018 and Yablo 2004; see also Paul 1998 – but see the comments in fn. 10). Others have been more skeptical of it or have rejected it as a mere appearance (they include Bennett himself in later work: Bennett 1988: 69–72; Lewis 2000; Mackie 1992; Schaffer 2005; Sartorio 2006). If one wanted to reject the hasteners/delayers asymmetry, there are different ways in which one could try and explain away the appearances. For example, Schaffer suggests a pragmatic explanation that appeals to the fact that hasteners close opportunities for further intervention, whereas delayers leave them open. He argues that, although this doesn’t result in a real causal asymmetry, it could help explain why we tend to perceive it as such (Schaffer 2005). Others have drawn attention to the fact that prevention plays a more prominent role for delayers than for hasteners (delayers cause a later occurrence of an event only by preventing an earlier occurrence) and note that this can potentially be used to explain away the appearances (Bennett 1988: 71; Lewis 2000; Mackie 1992; Sartorio 2006). Notice that here, too, responsibility considerations could become relevant, especially when we’re dealing with agential cases of hastening and delaying. Most typically, hasteners go along with an intention to cause an event, but delayers do not – if anything, they tend to go along with an intention to prevent the event from happening. For example, I may call my friend to remind them of our lunch date, thinking that they’d most likely had forgotten 269

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about it, and only manage to hasten her arrival by a few minutes (she hadn’t forgotten, but decided to come a little earlier after getting the reminder). Here my intention was to cause the lunch date to happen, but I only managed to hasten it a little. Compare this with a doctor who was trying to save her patient’s life but only managed to delay it a little – the doctor was trying to prevent the death from happening, not to make it happen. This difference in intention could explain why there is typically more of a temptation to think that hasteners are causes than to think that delayers are. (At least for agential cases. Maybe there is a way of extending the explanation to non-agential cases too, but I won’t get into this here.)

23.6

Switches

By “switches” I mean events that help determine the properties of the causal history of an effect without (seemingly) causing the event itself. Notice that I am no longer focusing on properties of the effect itself, but on properties of the causal history leading up to the effect. In other words, these are properties that determine how an effect was caused. Again, philosophers debate whether switches really aren’t causes or whether this is a mere appearance. Some believe that contributing to the specific causal route is enough for causing, and want to explain away the appearances, but others disagree. Here is an example of a switch (taken from Sartorio 2013): Hat: Each morning Jimmy flips a coin to decide whether to wear his hat that day (heads, he wears it; tails, he doesn’t). Jimmy’s friends, Suzy and Billy the vandals, have secretly come up with the following plan: if Jimmy wears the hat that morning, Suzy will throw a rock at a window and make it shatter, and otherwise Billy will. The coin comes up heads, so Jimmy wears the hat that morning, Suzy then throws her rock at the window, and the window shatters. Is Jimmy’s wearing the hat that morning a cause of the shattering? It seems not: intuitively, Jimmy’s wearing the hat helped determine the causal route to the window shattering (that is to say, whether it happened via Suzy or Billy) without thereby causing the shattering. However, on many theories of causation, Jimmy’s wearing the hat comes out as a cause. This is connected with our prior discussion of transitivity. For, arguably, Jimmy’s wearing the hat caused Suzy’s throw, and Suzy’s throw caused the window shattering. If causation is transitive, it follows that Jimmy’s wearing the hat caused the window shattering (see, e.g., Hall 2000 and Lewis 1986b). Again, this is a highly counterintuitive result. Plus, there is another problem: it seems to follow from this that, regardless of what Jimmy does at the time (if he wears the hat or if he doesn’t), he causes the shattering to obtain. But this, again, seems wrong. Moreover, it has unwanted implications for responsibility. For, intuitively, Jimmy is not responsible for the shattering simply because he didn’t cause it to happen, and not because he would have caused the shattering no matter what (as in: he had no alternative possibilities of action). But, if switches are causes, this natural explanation of Jimmy’s lack of responsibility isn’t available, for his putting on the hat is, in fact, a cause of the shattering (Sartorio 2005). In contrast with Hat, there are cases where contributing to the properties of the causal history of an effect does seem to be enough to cause the effect, even without making a difference to the effect itself. These are cases where there is more than one potential route to 270

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an effect, and where the different causal routes are importantly different from each other. To illustrate, consider the following case by Ned Hall (2000): Kiss: One day, Suzy kisses Billy passionately instead of greeting him with the usual handshake. Billy is thrilled and whistles a happy tune on his way back home. Had Suzy not kissed Billy, Billy would have gone into a store where he would have heard the same tune, the tune would have stuck in his head, and he would have ended up whistling the tune on his way back home all the same. As Hall points out, here we are much more likely to see the kiss as a cause of Billy’s whistling the tune. For we tend to regard the kiss as preempting the other potential cause (hearing the tune in the store), and thus as a cause of the whistling. But, assuming there is a real difference between switches and causes, what does that difference amount to? It’s hard to say for sure, as distinguishing switches from causes turns out to be one of the most difficult challenges that we’re likely to face in theorizing about causation. Again, some end up suggesting that there is no real difference (it’s a mere appearance; see Hall 2000 and Paul 2000), but others think the distinction is real (Hall 2006; Sartorio 2005; Yablo 2004). Notice that, here too, embracing the distinction as real has the added advantage that it can help us ground our responsibility judgments. For, in contrast with Jimmy in the Hat case, here Suzy seems to be responsible for Billy’s whistling the happy tune (and for him being in a good mood, etc.). This is so even if Billy would have whistled the same happy tune (and been in an equally good mood, etc.) in the absence of her kiss. Moreover, the reason Suzy is responsible in Kiss and Jimmy is not in Hat is, arguably, that Suzy is a cause and Jimmy isn’t. In sum: arguably, contributing to the properties of an effect’s causal history is sometimes enough for causing the effect itself. But other times it’s not. And whether it is or isn’t enough is something that depends on the specific properties in question.1

Note 1 Thanks to Anthony Fisher, Anna-Sofia Maurin, and the participants at the Online Properties Workshop (16–18 May 2022), where I presented an outline of this chapter.

References Bennett, J. (1987) Event Causation: The Counterfactual Analysis. In Tomberlin, J.E. (ed.) Philosophical Perspectives 1: Metaphysics. Atascadero, CA: Ridgeview Publishing Company: 367–386. Bennett, J. (1988) Events and Their Names. Indianapolis, IN: Hackett. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Collins, J. (2000) Preemptive Preemption. Journal of Philosophy 97(4): 223–234. Collins, J., Hall, N. and Paul, L.A. (eds.) (2004) Causation and Counterfactuals. Cambridge, MA: MIT Press. Ehring, D. (1997) Causation and Persistence: A Theory of Causation. New York, NY: Oxford University Press. Ehring, D. (2011) Tropes: Properties, Objects, and Mental Causation. Oxford: Oxford University Press. Hall, N. (2000) Causation and the Price of Transitivity. Journal of Philosophy 97(4): 198–222.

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Carolina Sartorio Hall, N. (2006) Structural Equations and Causation. Philosophical Studies 132(1): 109–136. Hausman, D. (1992) Thresholds, Transitivity, Overdetermination, and Events. Analysis 52(3): 159–163. Hausman, D. (1998) Causal Asymmetries. Cambridge: Cambridge University Press. Hitchcock, C. (1996) The Role of Contrast in Causal and Explanatory Claims. Synthese 107(3): 395–419. Hitchcock, C. (2001) The Intransitivity of Causation Revealed in Equations and Graphs. Journal of Philosophy 98(6): 273–299. Kvart, I. (2001) Counterexamples to Lewis’ ‘Causation as Influence.’ Australasian Journal of Philosophy 79(3): 411–423. Lewis, D. (1986a) Events. In Lewis, D. (ed.) Philosophical Papers, Volume II. New York, NY: Oxford University Press: 241–269. Lewis, D. (1986b) Causation. In Lewis, D. (ed.) Philosophical Papers, Volume II. New York, NY: Oxford University Press: 159–213. Lewis, D. (2000) Causation as Influence. Journal of Philosophy 97(4): 182–197. Mackie, P. (1992) Causing, Delaying, and Hastening: Do Rains Cause Fires? Mind 101(403): 483–500. Maslen, C. (2004) Causes, Contrasts, and the Nontransitivity of Causation. In Collins, J., Hall, N. and Paul, L.A. (eds.) Causation and Counterfactuals. Cambridge, MA: MIT Press: 341–357. Maurin, A-S. (2023) Tropes. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), URL = < https://plato.stanford.edu/archives/spr2023/entries/tropes/>. Mellor, D.H. (2004) For Facts as Causes and Effects. In Collins, J., Hall, N. and Paul, L.A. (eds.) Causation and Counterfactuals. Cambridge, MA: MIT Press: 309–323. Paul, L.A. (1998) Keeping Track of the Time: Emending the Counterfactual Analysis of Causation. Analysis 58(3): 191–198. Paul, L.A. (2000) Aspect Causation. Journal of Philosophy 97(4): 223–234. Paul, L.A. and Hall, N. (2013) Causation: A User’s Guide. Oxford University Press. Sartorio, C. (2005) Causes as Difference-Makers. Philosophical Studies 123(1-2): 71–96. Sartorio, C. (2006) On Causing Something to Happen in a Certain Way without Causing It to Happen. Philosophical Studies 129(1): 119–136. Sartorio, C. (2013) Making a Difference in a Deterministic World. Philosophical Review 122(2): 189–214. Schaffer, J. (2001) Causation, Influence, and Effluence. Analysis 61(1): 11–19. Schaffer, J. (2005) Contrastive Causation. Philosophical Review 114(3): 327–358. Silver, K. (2019) Avoiding Late Preemption with the Right Kind of Influence. Philosophia 47(4): 1297–1312. Toubourg, C.T. (2018) Hasteners and Delayers: Why Rains Don’t Cause Fires. Philosophical Studies 175(7): 1557–1576. Yablo, S. (1992) Cause and Essence. Synthese 93(3): 403–449. Yablo, S. (2002) De Facto Dependence. Journal of Philosophy 99(3): 130–148. Yablo, S. (2004) Advertisement for a Sketch of an Outline of a Prototheory of Causation. In Collins, J., Hall, N. and Paul, L.A. (eds.) Causation and Counterfactuals. Cambridge, MA: MIT Press: 119–137.

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24 DISPOSITIONAL PROPERTIES Jennifer McKitrick

24.1

Introduction

By the middle of the twentieth century, much of Anglo-American philosophy was under the sway of logical empiricism, a school of thought that eschewed discussion of anything that was not empirically verifiable. In this philosophical milieu, metaphysics was disparaged. Causal dispositions, which had been ridiculed by Molière and derided by David Hume, seemed to be in the dustbin of philosophical history (Hume 1978: book I, part III, sec. XIV; Molière 1931). However, by the late twentieth century, metaphysics has regained respectability, and dispositional properties have resurged as a topic of philosophical interest. It is tempting to see this recent episode of philosophical history as a debate between two clearly delineated camps, neo-Humeans who continue to seek reductive analyses of dispositional properties, and neo-Aristotelians who embrace dispositions as a fundamental part of their ontology. However, the situation is more complicated. There are various motives and methods for reducing dispositional properties. Furthermore, there is no comprehensive “dispositions metaphysic” that all dispositions theorists share. Indeed, there is no consensus about what the term “dispositionalism” means. The term is used to refer to the view that dispositions exist, the view that all properties are dispositions, the view that dispositions are irreducible, the view that modality is grounded by dispositions, the view that some philosophical concept such as belief or value can be analyzed in terms of dispositions, and the view that human behavior can be explained in terms of psychological dispositions as opposed to situations. This failure to differentiate various views about dispositions suggests that all theories that posit some role for dispositional properties are of a piece. On the contrary, believing that there are dispositions leaves many unanswered questions and topics for debate. In what follows, I will pose a few of those questions and explore the range of answers, most of which have been defended in recent literature. These questions include: “What are dispositions?”; “With respect to debates about dispositions, what kinds of properties are there?”; and “Are dispositions reducible?”. I will close by mentioning further unsettled questions and concluding that there is much room for disagreement among dispositional realists.

DOI: 10.4324/9781003246077-31

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24.2

What are Dispositions?

According to dispositions theorists, one of the ways that an object can be is to be disposed to behave in certain ways. So, if dispositions exist, they are a kind of property. Theories of dispositions will differ depending on whether the theorist takes properties to be tropes, universals, classes of objects, or something else. Examples of dispositions include inflammability, explosiveness, electrical charge, gravitational mass, and of course, fragility. While it is difficult to give a theory-neutral characterization of dispositions, most philosophers would agree that something having a disposition has further consequences that go beyond what is actually currently occurring. These consequences are the manifestation of the disposition. For example, something being flammable has consequences regarding the possibility of a fire happening, and fire is the manifestation of flammability. We associate dispositions with activity and change, at least conceptually. An object with a disposition is disposed to do something or make something happen. Terms such as “power”, “potency”, and “potentiality” are often used as synonyms or near-synonyms for “disposition”. On some views, dispositions are primitive and undefinable (Martin 1994: 7; Mumford and Anjum 2011: 193). On other views, dispositions are associated with possibility: if something is flammable, then it can burn (Vetter 2015: 14; see also Chapter 28, this volume). Others associate dispositions with conditionals: if the flammable object were ignited, then it would burn (Goodman 1983: 34).

24.3

Which Kinds of Properties Exist?

Philosophers hold various views about the kinds of properties that exist with respect to whether they are dispositions or not. Properties that are not dispositions are often called “categorical properties”. Assuming that properties exist, the main options are: all properties are categorical; all properties are pure dispositions; some properties are dispositions and some are categorical; and, all properties are “powerful qualities”. Let us consider each of these options in turn.

24.3.1

All Properties are Categorical

Call the view that all properties are categorical “categorical monism” (Armstrong 1996: 18). On this view, thing’s categorical properties are only contingently related to future possibilities. Something having a categorical property does not necessitate anything beyond its current actual state. For example, the categorical properties of a wine glass do not necessitate its breaking. If all properties are categorical, there are no “necessary connections” between properties (Hume 1978: 82). Hume rejected dispositions for epistemic reasons, arguing that causal powers were never observed, nor properly inferred from anything that is observed (Hume 1978: 75). Some contemporary philosophers reject dispositions, and thus subscribe to categorical monism, for reasons that go back to Molière (Molière 1931). If dispositions are posited to explain their manifestations but fail to do so, then we have no reason to suppose that dispositions exist. For example, saying that opium is disposed to cause sleep does not explain why opium causes sleep. On the contrary, it is said that it is the “causal basis” of the disposition that is causally relevant and real (Prior et al. 1982: 255). Another reason some philosophers are suspicious of dispositions is that if they existed, they would be

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properties that, in some sense, “point” beyond themselves toward future, non-actual possibilities, and these philosophers find this notion dubious (Armstrong 2005: 314). Assume that the dispositional/categorical distinction is exclusive and exhaustive, if one rejects dispositions, then all properties must be categorical. However, categorical monists are often pressed to say more about these nondispositional properties which they favor. Stripped of all causal dispositions, it is difficult to say what the essence of a categorical property consists of. While mass might seem like a good candidate for being a categorical property, what is left of mass once we divorce it from the dispositions to attract other massive bodies, to warp space time, and to resist acceleration? Just its being the particular property that it is. For these reasons, categorical properties are sometimes dismissed as being mere “quiddities” (Black 2000: 91).

24.3.2

All Properties are Pure Dispositions

The opposite extreme of categorical monism is the view that all properties are pure dispositions (Mumford and Anjum 2011: 3). Saying that properties are “pure dispositions” means that the nature of these properties is exhausted by their dispositionality. Philosophers call this view “dispositional monism”, or “pan-dispositionalism”. One reason for thinking that all properties are dispositions is that categorical properties would be inert and undetectable. They would not be able to explain change and activity in the world. Even if such properties did exist, they would not make any difference, and we could never know about them (Shoemaker 1980: 118). Consequently, there is no reason to suppose that they exist. Another reason in favor of dispositional monism is that physicists describe fundamental features of reality in dispositional terms, such as energy, force, and potential for motion (Mumford 2006: 476). On the other hand, other philosophers argue that if the nature of every property were exhausted by its consequences for non-actual occurrences, then objects would have no occurrent characteristics. In other words, if each property was a disposition for some other property to be instantiated, then that newly instantiated property must also be a disposition for some other property to be instantiated, and so on (Armstrong 1997: 80). This consequence of dispositional monism is sometimes called “the regress of pure dispositions”, which is a bug or a feature, depending on your point of view (Mumford and Anjum 2011: 5).

24.3.3 Some Properties are Categorical and Others are Dispositional A third option is that both dispositions and categorical properties exist. Dispositions theorists call this “the mixed view” or “property dualism” (Molnar 2003: 111).1 According to mixed views, the universe contains dispositional properties, such as charge, as well as categorical properties, such as having a hexagonal structure. Saying that both dispositions and categorical properties exist is consistent with saying that dispositions and categorical properties are both fundamental, or dispositions are grounded by nondispositions, or vice versa. Property dualism captures the intuition that objects have intrinsic, occurrent features, and also the potential to bring about some future state of affairs. Another advantage is that it is not subject to the regress of pure dispositions objection to dispositional monism, since a manifestation can involve the instantiation of a categorical property and not merely dispositions for further manifestations. However, property dualists face critics on both flanks – dispositional monists who claim that there is 275

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no good reason to posit categorical properties and categorical monists who remain suspicious of dispositions.

24.3.4

All Properties are Powerful Qualities

The fourth view is that all properties are powerful, however, they are not pure dispositions, because they are both dispositional and qualitative (Heil 2003: 111). Note that advocates of this view do not make the incoherent claim that properties are both dispositional and non-dispositional (categorical), but instead contrast “dispositional” with “qualitative”. What it means for a property to be qualitative is given by examples of qualities like sweetness and whiteness (Heil 2003: 28). However, since these, like all properties, are dispositional on this view, such examples cannot illustrate what is meant by “qualitative” without ambiguity. On the positive side, this view escapes some of the criticisms raised against pure dispositions and categorical properties. A property’s nature is not exhausted by its consequences for future possibilities, for it has a qualitative side. What’s more, a property is not a mere quiddity, since its powerful side is essential as well. Furthermore, on this view, dispositions do not compete with their casual bases for causal relevance, since these are but aspects of a single property. However, the idea that one property has different sides or aspects is a bit puzzling. One possible view is that a powerful quality itself has properties – a disposition and a qualitative property. Or, perhaps a powerful quality is a conjunction of a disposition and a qualitative property. However, such proposals just rearrange dispositions and qualities, turning the view into a version of property dualism. If there are problems with property dualism that powerful qualities are meant to solve, those problems will reappear. So, a powerful quality must be a single, unitary property that is identical to both its dispositionality and its qualitativeness. But since the qualitiativeness of a property is neither dispositional nor categorical, the nature of qualitativeness remains obscure (McKitrick 2018: 108).

24.4

Are Dispositions Reducible?

Now that we have canvased different answers to the question “Which kinds of properties exist?” let us turn to the next question, regarding whether dispositions are fundamental or reducible to something else. In order to explore answers to this question, we must first consider the questions: “What does it mean to be fundamental?”; “Does the fundamental consist of the smallest constituents of matter/energy, or does it consist of the universe as a whole?”; and, “Is there a fundamental level at all, or does each thing reduce to another thing ad infinititum?” Since these debates carry on independently of the nature of dispositions, for the purposes of this discussion, I will adopt what I take to be a common twentyfirst-century assumption, micro-reductionism, according to which there is one fundamental level, that it is the ultimate reduction base of everything that is reducible, and it is at the micro-level. So, the question under consideration is: “What kinds of properties are in the fundamental reduction base?” (Or, if properties are reducible: “Are dispositions at the lowest level at which properties appear?”) We also need to consider the nature of reduction. For our purposes, it will suffice to make a distinction between two different concepts that the term “reduce” often conveys. 276

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According to metaphysical reduction, entities of a given kind are explained in terms of entities of another simpler or more basic kind. Reduction in this sense is similar to grounding. Roughly speaking, when A grounds B, the existence of A determines that B exists and determines B’s nature. An entity can also partially ground another when it is but one of multiple factors that determine the existence and nature of the grounded entity. Grounded entities ultimately bottom out in a fundamental ground which is not itself grounded. Everything that is not fundamental is grounded. Unless one holds an extremely sparse theory on which only fundamental entities exist, grounded entities also exist. Grounded entities need not be eliminated from our ontology. Saying that a molecule is grounded by a particular arrangement of constituent atoms is not a reason to think that the molecule does not exist. The idea that dispositions are reducible/grounded is consistent with realism about dispositions. Semantic reduction, on the other hand, is typically part of a “translate and eliminate” project whereby expressions which apparently denote some kind of entity are paraphrased in terms of expressions denoting other entities (on paraphrase, see Chapter 2, this volume). Consider the claim: “The average American family has 2.5 children”. There is no entity that is the average American family that has a half of a child as one of its members. “The average American family” is an expression that does not refer to an entity at all, but is just shorthand for a statistical summation over real, individual families. The average American family is reduced to individual families, and thus we do not need to posit the existence of an average family over and above the real, individual families. If dispositions are reducible/ eliminable, then expressions that seem to refer to dispositions actually refer to something else, supporting anti-realism about dispositions. (Of course, this does not entail the following inverse claim: if we cannot semantically reduce disposition expressions, then dispositional properties are ineliminable.) When philosophers argue about whether dispositions are reducible, it is not always clear whether they mean that they are eliminable and thus do not really exist, or that they are grounded but still real. It is important to keep those options in mind. Now that we have some idea what “reduction” means, let us examine three answers: all dispositions are reducible; All dispositions are irreducible; and Some dispositions are reducible while others are fundamental.

24.4.1

All Dispositions are Reducible

The first option we will consider is semantic reduction of disposition ascriptions. According to the most common version of this approach, saying something has a disposition is tantamount to asserting a certain conditional statement (Carnap 1936: 440). On a simple conditional analysis, the disposition ascription “the glass is fragile” just means “if the glass were struck, it would break”. No dispositions are mentioned in the second sentence, and so fragility has been reduced and apparently eliminated. So, conditional analyses are typically in service of a “translate and eliminate” project. Of course, the above translation is too simple and liable to all sorts of exceptions. One must assume that the glass is struck with a certain force with a sufficiently rigid object and that the glass is not reinforced in some way or magically changed at the last instant (Lewis 1997: 147). So, proponents of reduction develop more sophisticated conditionals, or more sophisticated interpretations of the conditionals, in an effort to capture what is conveyed by saying that something has a disposition (Contessa 2013: 406). 277

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If a conditional analysis of a disposition claim were successful, then the conditional would be true if and only if the associated disposition claim were true. If this could be accomplished, it would be fair to ask the reductionist: “What makes your conditional statement true?” If she says “nothing”, then she has asserted the conditional as a brute fact, which some philosophers find doubtful (Mumford 2009: 170). Alternatively, she can appeal to patterns of categorical properties. However, if categorical properties have nothing but contingent relations to future states, it is not clear how the history of instantiations of categorical properties can explain the truth of a statement which has implications for what might happen in the future. Consequently, metaphysicians often talk about these conditionals in terms of possible worlds (Lewis 1973: 16). Roughly, “if the glass were struck, it would break” means that, in the closest possible world in which the glass is struck, it breaks. However, if we take possibleworlds semantics literally, dispositions have been eliminated in favor of merely possible entities across multiple, non-actual worlds. For many, that does not seem like a good trade (Vetter 2015: 6). If we do not take possible-worlds talk literally, then it, too, must be semantically reduced to something else, and the reductionist has more work to do in order to explain what dispositions ultimately reduce to. Another reductionist idea is that a disposition is a second-order property, more specifically the property of having a categorical basis that plays a certain causal role (Johnston 1992: 229). The reason that the categorical property is supposed to be a suitable reduction base for the disposition is that the categorical property is such that it would cause the manifestation in certain circumstances. For example, opium is soporific because it has some chemical property that would produce sleep if it were ingested. However, if a property is such that it would cause a manifestation, then it seems dispositional (McKitrick 2009: 36). If the categorical reduction base is indeed powerless, then the categorical monist needs to explain why we should say that it would cause anything. Another reductionist view is that dispositions are reducible to categorical properties governed by laws of nature (Armstrong et al. 1996: 17). Call this the “Nomological view”. For example, suppose that a match is flammable – it is disposed to ignite when struck. According to a Nomological view, the match has some property P which, together with the laws of nature, entails that it will ignite when struck. “Flammability” might be a way to refer to P – a way we use for convenience, especially if we have not identified the categorical property that figures in the law. In that case, the disposition “flammability” has been eliminated. The Nomological view denies that properties can be intrinsically powerful and instead locates the source of change in the natural laws. Nomological accounts must be fleshed out with an account of the metaphysics of natural laws and how they govern (for more on properties in laws, see Chapter 30, this volume). David Armstrong, a well-known proponent of the Nomological view, holds that laws are necessitation relations between categorical properties (Armstrong 1983: 85). However, some question whether he successfully eliminates dispositions (Handfield 2005: 452). Armstrong’s universals are in rebus, that is, in the objects that instantiate them. So consider a particular x that is F, where properties F and G stand in the Necessitation relation. If the Necessitation relation is in rebus, it must be located where x is. Hence, x is intrinsically necessitated to yield G. If being intrinsically necessitated to yield G is distinct from having the power to produce G, it may seem like a distinction without a substantial difference. In other words, the idea that salt is intrinsically necessitated to dissolve in water might not be importantly different from the idea that salt is disposed to dissolve in water. 278

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24.4.2

All Dispositions are Irreducible

Now that we have considered the view that all dispositions are reducible, let us consider the opposite views according to which all dispositions are irreducible. There are at least three things one might mean by saying that all dispositions are irreducible. First, one might mean that dispositions are among the fundamental properties of the ultimate constituents of matter and that there are no other dispositions. Second, one might mean that all dispositions, from charge on up to courage, are equally irreducible. Third, one might mean that no disposition is reducible to anything that is not itself a disposition. On the anti-reductive first view, dispositions are part of the ultimate reduction base and there are no grounded dispositions (Williams 2019: 18). These dispositions may be construed as either pure dispositions or powerful qualities. The idea that all dispositions are irreducible can be combined with dispositional monism or property dualism. Regardless, if all dispositions are irreducible, then other apparent dispositions of macro-entities such as fragility or courage must be non-dispositional or eliminable. (This is not to say that macroentities cannot have irreducible dispositions, such as charge or mass. However, dispositions such as fragility and courage do not seem to be good candidates for being fundamental properties.) Some of the reasons in favor of pan-dispositionalism that we saw above also support the idea that dispositions are irreducible. If all properties are dispositions, and there is a fundamental level, then some dispositions must be fundamental. What is less clear is why one would think that there are no higher-level dispositions that are grounded by lower-level dispositions. For example, salt is soluble because its sodium and chlorine atoms are held together by ionic bonds. Being ionically bonded is grounded in electric charge, so arguably solubility is grounded in electric charge. If electric charge is a fundamental power, it exists. But on this austere dispositions view, solubility does not really exist because it is reducible. The second anti-reductive view is that all dispositions of micro- and macro-entities, from the charge of an electron to the fragility of a glass, to the courage of a lion, to the volatility of a market, are all irreducible. If all of these dispositions were fundamental, this would run counter with the assumption of micro-reductionism that we made above, according to which the fundamental properties are properties of micro-entities studied by subatomic physics. On the view currently under consideration, a property such as the volatility of a commercial market is a fundamental property, and this is very counterintuitive. Alternatively, perhaps macro-level dispositions can be irreducible without being fundamental. One way to be irreducible is to be resistant to “translate and eliminate” strategies. The objections and counterexamples posed against attempts at semantic reduction of dispositions offer some reasons to think that we cannot reduce dispositions in this way (Mumford and Anjum 2011: 193). Perhaps this means that these macro dispositions are not fully grounded by more fundamental properties. On the view that dispositions at various levels are irreducible, macro dispositions emerge from configurations of micro properties, without being reducible to them (Mumford and Anjum 2011: 103). On the other hand, even if all dispositions talk is semantically ineliminable, it does not follow that the dispositions so denoted are not fully grounded (Bird 2016: 349). According to the third anti-reductive view, dispositionality is not reducible to anything that is not itself dispositional (Vetter 2015: 25). If views discussed above according to which there are no grounded dispositions or there are emergent dispositions are problematic, this interpretation is more plausible than the claim that all dispositions are

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irreducible full stop. Strictly speaking, this is a view that allows some dispositions are reducible – it is just that they are reducible to other dispositions. Consequently, this view is consistent with the third answer to the reducibility question, according to which some dispositions are reducible while others are not.

24.4.3

Some Dispositions are Reducible while others are not

Our third answer to the question “Are dispositions reducible?” is that some dispositions are grounded in other properties, but the ultimate grounds include fundamental irreducible dispositions. This answer has both pandispositionalist and property dualist variants. On the pandispositionalist variant, macro dispositions are grounded by micro dispositions, but the fundamental ground is constituted by fundamental, irreducible dispositions. For example, table salt being nutritious is partially grounded in its solubility, and its solubility is grounded in the electrostatic charges of its constituents, and perhaps those electrostatic charges are irreducible. If this is an alternative to the view that all dispositions are fundamental, then we must allow that reducible/grounded dispositions exist. If both dispositions and categorical properties exist, as the property dualist would have it, there are several other possibilities, depending on whether non-dispositions appear only at the fundamental level, only at non-fundamental levels, or at both fundamental and nonfundamental levels, further complicated by the various grounding relations which could possibly hold between the different kinds of properties. One option is that the fundamental ground is constituted by dispositions, and they ground both categorical properties and dispositions. Another is that the fundamental ground includes dispositions and categorical properties, and they jointly ground macro-level properties of all types.

24.5 Conclusion There are many varieties of dispositional realism. There are many views according to which dispositions exist – they are the only kind of property, they exist alongside categorical properties, all properties have a powerful side, they are fundamental, they are emergent, are grounded, or there are some of each. A realist can endeavor to explain dispositions in terms of categorical properties, possibilities, or counterfactuals, or they can reject the call for explanation altogether and deem dispositions primitive. A realist can hold that dispositions are the only kind of property, that dispositions and categorical properties are equally real, or that all properties have a dispositional side. Additionally, realists can maintain that dispositions are fundamental, emergent, grounded, or varied in their dependence relations. There are a number of further issues on which dispositional realists can and do disagree. Some theorists claim that dispositions are directly observable (Mumford and Anjum 2011: 195), while others claim that dispositions can only be inferred by regular observation of their manifestations (McKitrick 2018: 233). Many theorists hold that dispositions manifest in certain circumstances – that is, they have circumstances of manifestation or “triggers” (Schrenk 2015: 396). However, there are some who argue that dispositions do not have triggers (Vetter 2015: 131). A further point of contention is whether each disposition necessarily manifests in a distinctive way, or whether some dispositions can manifest in various ways (Bird 2007: 21). In other words, they disagree about whether dispositions “single-track” or “multi-track”. If each disposition has a distinctive manifestation, one 280

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might construe a disposition’s manifestation or “exercise” as one contribution to an overall effect, rather than the effect itself (Cartwright 2007: 195). However, others criticize such views for being unparsimonious (McKitrick 2018: 110). Yet another unsettled issue is the role of laws of nature in a dispositional realist ontology. Some argue that dispositions render laws superfluous (Mumford 2005: 397), while others argue that dispositions render laws metaphysically necessary (Ellis 2001: 219). While this chapter is an overview of views about dispositional properties in contemporary thought, it also has a thesis: rejecting Humean skepticism about dispositions does not entail a particular theory, but instead opens up a large range of possibilities, across different issues. Debates between dispositions theorists and neo-Humeans are ongoing, but the debates among dispositional realists are at least as lively.

Note 1 This should not be confused with property dualism in the philosophy of mind, according to which sentient beings have mental parts or properties that are distinct from their physical ones ( Robinson 2020).

References Armstrong, D.M. (1983) What Is a Law of Nature? Cambridge: Cambridge University Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Armstrong, D.M. (2005) Four Disputes about Properties. Synthese 144(3): 309–320. Armstrong, D.M., Martin, C.B., and Place, U.T. (1996) Dispositions: A Debate. Ed. Crane, T. London: Routledge. Bird, A. (2007) Nature’s Metaphysics: Laws and Properties. Oxford: Oxford University Press. Bird, A. (2016) Overpowering: How the Powers Ontology Has Overreached Itself. Mind 125(498): 341–383. Black, R. (2000) Against Quidditism. Australasian Journal of Philosophy 78(1): 87–104. Carnap, R. (1936) Testability and Meaning. Philosophy of Science 3(4): 419–471. Cartwright, N. (2007) What Makes a Capacity a Disposition? In Kistler, M. and Gnassounou, B. (eds.) Dispositions and Causal Powers. Farnham: Ashgate: 195–206. Contessa, G. (2013) Dispositions and Interferences. Philosophical Studies 165(2): 401–419. Ellis, B. (2001) Scientific Essentialism. Cambridge: Cambridge University Press. Goodman, N. (1983) Fact, Fiction, and Forecast. 4th ed. Cambridge, MA: Harvard University Press. Handfield, T. (2005) Armstrong and the Modal Inversion of Dispositions. Philosophical Quarterly 55(220): 452–461. Heil, J. (2003) From an Ontological Point of View. Oxford: Clarendon Press. Hume, D. (1978) A Treatise of Human Nature. Ed. Nidditch. Oxford: Oxford University Press. Johnston, M. (1992) How to Speak of the Colors. Philosophical Studies 68(3): 221–263. Lewis, D. (1973) Counterfactuals. Oxford: Blackwell. Lewis, D. (1997) Finkish Dispositions. Philosophical Quarterly 47(187): 143–158. Martin, C.B. (1994) Dispositions and Conditionals. Philosophical Quarterly 44(174): 1–8. McKitrick, J. (2009) Dispositions, Causes, and Reduction. In Handfield, T. (eds.) Dispositions and Causes. Oxford: Oxford University Press: 31–64. McKitrick, J. (2018) Dispositional Pluralism. Oxford: Oxford University Press. Molière. (1931) Le Malade Imaginaire, Comédie-Ballet. Ed. Vanbourdolle, R. Paris: Librairie Hachette. Molnar, G. (2003) Powers: A Study in Metaphysics. Oxford: Oxford University Press. Mumford, S. (2005) Laws and Lawlessness. Synthese 144(3): 397–413. Mumford, S. (2006) The Ungrounded Argument. Synthese 149(3): 471–489.

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Jennifer McKitrick Mumford, S. (2009) Ascribing Dispositions. In Damschen, G., Schnepf, R., and Stüber, K.R. (eds.) Debating Dispositions: Issues in Metaphysics, Epistemology and Philosophy of Mind. Berlin: Walter de Gruyter: 168–185. Mumford, S. and Anjum, R.L. (2011) Getting Causes from Powers. Oxford: Oxford University Press. Prior, E.W., Pargetter, R. and Jackson, F. (1982) Three Theses about Dispositions. American Philosophical Quarterly 19(3): 251–257. Robinson, H. (2020) Dualism. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), URL = < https://plato.stanford.edu/archives/fall2020/entries/dualism/>. Schrenk, M. (2015) Trigger Happy: Ein Kommentar zu Barbara Vetter’s Potentiality. Zeitschrift für Philosophische Forschung 69(3): 396–402. Shoemaker, S. (1980) Causality and Properties. In van Inwagen, P. (ed.) Time and Cause: Essays Presented to Richard Taylor. Dordrecht: Reidel: 109–135. Vetter, B. (2015) Potentiality: From Dispositions to Modality. Oxford: Oxford University Press. Williams, N.E. (2019) The Powers Metaphysic. Oxford: Oxford University Press.

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25 EVENTS, PROCESSES, AND PROPERTIES Carlo Rossi

25.1

Introduction

Talk about properties pervades the contemporary debate about the nature of events and processes. Much of that debate follows the view developed by Jaegwon Kim, according to which events are exemplifications of properties at times (Kim 1966, 1969, 1973, 1976). Here it is most obvious that properties play an intimate role in a theory of events by properties serving as an important constituent of events. Yet, it has been objected that Kim’s fine-grained criterion of identity results in an overabundant ontology of events and that his account treats events as structured particulars, making them almost indiscernible from states of affairs (Bennett 1984; Dodd 2009; Steward 1997). Given that problematic result, in this chapter, I will discuss for the most part different approaches that also have an important place for properties in a theory of events and processes. Many of them follow a line of argument that can be traced back to Alexander Mourelatos (1978) and has received renewed attention recently (Galton and Mizoguchi 2009; Steward 2013; Stout 1997, 2015). According to this line of thought, certain properties can be used to draw a distinction between mass-noun and count-noun expressions that allows us to articulate the ontological divide between events and processes. Thus, in virtue of such properties, events are regarded as countable and temporally bounded entities, whereas processes are regarded as closer to massy non-countable entities, making them similar in some aspects to properties (Crowther 2018; Seibt 2018) but also similar to continuants in some others (Stout 2015). Accordingly, this chapter has the following structure. In Section 25.2, I introduce Kim’s theory and some of its shortcomings. In Section 25.3, I briefly present the distinction between continuant and occurrent entities. Then, I turn my attention to Mourelatos’s argument, which draws on issues of aspect and the nominalization of sentences that refer to events and processes. Mourelatos’s argument will be relevant later for a number of discussions examined in Sections 25.4 and 25.5. In Section 25.4, I discuss some recent proposals that attempt to draw a distinction between processes and events on the basis of their modal properties, such as the property of being modally robust in virtue of form (Steward 2013, 2015). Finally, in the last section, I explore certain consequences of what has been

DOI: 10.4324/9781003246077-32

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said about events and processes in Sections 25.3 and 25.4, particularly the alleged status of events as falling under the category of particulars and processes under the category of nonparticulars. Special attention will be paid to the implication that if processes are nonparticulars, then they turn out to be closely similar to universal properties.

25.2

Events as Property Exemplifications

Kim’s account of events is a paramount example of the role that properties play in accounting for the nature of events and other temporally extended entities. The canonical notation stipulated by Kim for representing events is triples of the form of

[s, P, t], where s stands for a substance, P for a property, and t for a time or an interval of time. The identity condition that Kim proposes for events is, unsurprisingly, the following:

[s, P, t] = [s , P , t ] iff s = s , P = P and t = t . Lastly, given that not every triple that could represent an event actually exists and events are supposed to be represented by triples of some sort, they have the following existence condition (Kim 1976): [s, P, t] exists or occurs iff s has P at t. Now, it is difficult not to regard events as some form of state of affairs if we follow this account. Kim seems not too bothered by this charge, as he explicitly admits that he uses the term ‘event’ as a blanket term not only to refer to events but also to states, states of affairs, phenomena, and conditions, among other entities (1969: 213). Yet, such an admission would hardly persuade those who consider events to be temporal particulars and not some sort of abstract entity. Whether it is ultimately successful or not, Kim postulates the following central features for the view. First, events are non-repeatable concrete particulars, with a single spatiotemporal location. Second, events may exemplify a wide array of properties, but there is only one property – what Kim calls the constitutive property – which individuates an event. Third, event-types are obtained by regarding the constitutive property as a generic event, whereas event-tokens are obtained by the exemplification of the constitutive property by an object at a time or period of time. Lastly, events are not meant to be taken as identical to triples or to any other set-theoretic construction, but rather they are represented by them in Kim’s theory. Reading Kim as charitably as possible, the first and fourth features should distinguish events from other types of entities which also fall under the blanket term ‘event’ but have more dubious credentials as particulars. On the other hand, the second and third feature attempt to address a concern raised by Kim’s fine-grained criterion of identity that results in an overabundant ontology. For example, given that the event of Brutus killing Cesar is individuated by a different property than the event of Brutus stabbing Cesar multiple times in the Theatre of Pompey on the Ides of March, both events, which plausibly are identical, are two different ones. Yet, Kim would reply that we could still regard them as identical as long as they possess the same constitutive property. According to Kim, we may refer to an event with descriptions that involve different properties, such as taking place in the Theatre

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of Pompey or during the Ides of March. What cannot be the case in Kim’s view is to refer to the same event with descriptions that involve different constitutive properties, that is, the property of which events are an exemplification. Notwithstanding all these caveats, Kim’s view looks ill-suited for providing us with a proper understanding of the categories of events and processes and the role that properties would have in drawing a distinction between them. Besides the notorious difficulties of not regarding events as abstract entities, it is not clear how to account for processes on this view. Are processes a peculiar kind of event? If not, which identity conditions are we meant to stipulate for them? In the next few sections, I will explore a different path to answer some of these questions, a path not exempt from shortcomings but arguably more promising than the framework provided by Kim.

25.3

Occurrence, Aspect, and Nominalizations

According to W.E. Johnson (1924: xx–xxi), continuants exist over extended periods of time and may change their properties, whether intrinsic or extrinsic, while occurrents need not continue to exist over periods of time, that is, they may be instantaneous existents, and are not capable of undergoing change. Looking at the temporal character of particular entities, i.e., the way in which the entity in question fills a period of time, this category distinction gives us a way to distinguish between substances, events, and processes. Substances such as dogs, trees, and cars exist throughout extended periods of time and change their properties and mereological configuration while they exist. Events and processes, in contrast, sometimes exist for not more than a moment (think, for instance, of an explosion or the reaching of a mount summit) and their static nature makes them unfit to count as proper subjects of change. However, such a preliminary result has been contested at different levels. Some have argued that it is obvious why processes should not be counted amongst continuant entities (Stout 1997, 2015), or at least be thought of as belonging to a category of their own. Others (Steward 2013, 2015) have argued that processes display certain structural properties that make them similar to substances, although strictly speaking they should be regarded as a peculiar kind of occurrent. And then there are those who question not only that processes are continuants but also whether processes should be regarded as particulars at all (Crowther 2011, 2018; Seibt 1997, 2010, 2018). Their arguments attempt to show that processes have a distinctive way of recurring in time and that they are not countable entities. In fact, their view would turn processes into something similar to universal properties, for they would not be particulars given their non-countability and they would be repeatable or multi-located across space (for more on universals and location, see Chapter 13, this volume). I will examine these arguments in more detail in this and the coming sections. But for now, I want to emphasize that in each of them, properties play a crucial role in articulating our understanding of the categories of event and process. Let us look at the arguments that support the view that processes, unlike events, share some attributes with properties and continuants. The first sort of argument, already mentioned in the Introduction, is put forward by Mourelatos (1978) and later by Rowland Stout (1997, 2015), and it draws on the linguistic properties of sentences that report the occurrence of events and properties. Roughly speaking, Mourelatos’s argument proceeds from a categorization of different types of predication to a categorization of the referents that we get from nominalization transcriptions. A nominalization transcription allows one 285

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to reformulate a certain predication to explicitly quantify over its verbal expression, now transformed into a kind of noun. In other words, nominalizations make explicit the hidden quantificational commitments behind the structure of sentences that apparently do not have a quantificational form. The crucial matter is that the different predicative character of a certain type of sentence might give rise to nominal expressions that quantify over different types of entity. Take the examples below to illustrate the point (Mourelatos 1978, Steward 2013). The nominalization of the sentence (1) ‘Jones pushed the cart to the top of the hill’ gives us (2) ‘There was a pushing of the cart to the top of the hill by Jones’, while the nominalization of the sentences (3) ‘Jones pushed the cart for hours’ and (4) ‘Jones was painting the Nativity’ give us respectively (5) ‘There was pushing of the cart for hours’ and (6) ‘There was painting of the Nativity by Jones’. Sentences (2), (5), and (6) offer us nominalization examples that refer to events and processes. In the case of such nominalizations, differences seem to be grounded on an aspectual matter, since it is the aspectual character of predications that determines the categories of the nominals that we obtain. Aspect expresses how an occurrence takes place. We use the progressive aspect if we want to describe an occurrence as ongoing or repetitively, whereas we use the perfective aspect if we want to describe an occurrence as completed and bounded. Typically, the former is used to describe processes and the latter to describe events. Given that the activity described in (1) does have a clear end, this implies for Mourelatos that the nominal we find in (2) refers to an event. Sentence (3), in contrast, is determined by the imperfective aspect of the verbal expression it contains (‘pushed for hours’) and (4) is a sentence constructed with a progressive tense, so Mourelatos argues that the nominals found in (5) and (6) refer to processes. Furthermore, Mourletatos points out that the activities described by (3) and (4) do not have a terminus or a closure, which he thinks does not allow us to talk about a pushing or painting, just like we can talk about a pushing of the cart in (2). That conclusion differs from the one drawn by Stout from similar examples (1997: 19), for Stout holds the view that we can infer from sentences like (5) and (6) that there is a particular that we may identify with a certain process. But that inference is contested by other supporters of the ontological distinction between processes and events. For the time being, I will only flag the source of this disagreement, although I will return to it in Section 25.5 to explore its implications for the categories of event, process, and property. 286

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One last point that Mourelatos draws from these examples – and which will be important for our discussion later – is that the parallel of (5) and (6) with simple nouns must not be thought of in terms of sentences such as ‘There is at least one F’, that is, quantificational count-noun sentences, but rather sentences such as ‘There is snow on the roof’, or ‘There is gold in this mountain’, which quantify over mass-nouns. This caveat again eventually pinpoints an important ontological difference between the categories of process and event, highlighting the massy nature of the former and the countable nature of the latter.

25.4 The Modal Profile of Events and Processes The second sort of argument draws a distinction between events and processes appealing in a more straightforward metaphysical manner to the properties that constitute each of these ontological categories. The first case is the argument from the interruption of processes (Stout 1997, 2015). This argument can be understood by analogy with the argument offered in the spatial coincidence debate to account for the non-identity of a material substance and its matter. Usually, those who deny that a substance is identical to the material components that constitute it at a given time would justify such a distinction by appealing to the differences we find in their respective modal profile. It is often argued that substances can survive certain changes that material components cannot and vice versa. Thus, a clay statue can survive the gain or loss of minor bits of matter but the lump of clay that constitutes it cannot remain identical if it gains or loses parts. Conversely, the lump of clay can change its shape – for instance, it could be squashed – and still survive through change, whereas a statue cannot survive after being squashed. In a similar fashion, proponents of the argument from the interruption of processes argue that for any pair of events and processes that temporally coincide, it is possible that the process could still remain identical even if some of its parts are subtracted or some further parts are added to it, whereas in the case of the event that does not seem to be possible. Stout provides here the example of the process of the decaying of an apple (1997: 21). Such a process may have a temporal duration in the actual world that entirely coincides with the decay of the apple. Yet, it is possible that the process of the decaying of the apple might have stopped by freezing the apple for a period of time, and then the very same process resumed after unfreezing the apple. That does not seem to be possible in the case of events, for events that do not possess the same temporal parts cannot be identical. That property of processes would account for the fact that processes, unlike events, go on and cease or fail to cease, or can be intermitted. Some have even referred in this regard to a certain flow-like character that processes have (Steward 2013: 809), which allows us to make sense of these temporal verbs and phrases. The second case is the argument from the persistence of processes (Steward 2013; Stout 2015). According to this argument, if a process is indeed something that is/was/ will be happening and not something that has occurred, then it seems that what goes on at any moment during which a process lasts is the whole process, not a part or a stage of it. So, to pick up an example from Stout, the hurtling of a comet is present at each point of its temporal trajectory and it would not make sense, according to the argument, to claim that it is only partly present at each of those times. On the other hand, the event of the comet hurtling into the sun persists only in virtue of the temporal parts that it possesses at every time at which it is located, but none of those parts are identical to each 287

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other. In other words, events are never wholly present (at most, they are so in the totality of their temporal path), whereas processes are wholly present at each moment of their existence. Now, it could be argued that the conclusion of both arguments can also be explained in a unifying manner by the obtaining of the property that Helen Steward (2013: 807) calls Modal Robustness in Virtue of Form (hereafter, MRVF). MRVF is a property not possessed by events, but only by processes and substances, and in the case of the former, it would account for the priority of a processual whole over its temporal parts. Properties play a crucial role, therefore, in developing Steward’s theory of events and processes. According to Steward, processes have ‘a certain distinctive form by means of which they are singled out in thought and which underwrites their relative independence from the actual parts of which they consist in any particular’ (2013: 807). The notion of form can be understood here not necessarily as an Aristotelian form. While it is true that MRVF seems congenial to hylomorphic accounts of substances and processes,1 one need not be committed to such a metaphysics of properties and particulars to ascribe MRVF to them. Rather, I propose we understand MRVF as a structural property possessed by entities that fall under such categories. In Steward’s words, MRVF implies that both substances and processes are independent of the actual parts that compose them (2013: 807). Hence, the claim that an entity that possesses MRVF is not individuated or singled out by the parts – either spatial or temporal – that compose such an entity in a given world, but by something that is prior to those parts (2013: 808). That something prior would be its form, but such a property does not need to be an Aristotelian form or, in general, a property that inheres in the whole of which it is a form. In a further effort to clarify the view, Steward claims that ‘there are entities which are non-identical with the sums of their parts, entities concerning which form predominates over matter in the account we are to give of what it is that they essentially are’ (2013: 810–811). Thus, saying that an entity has the property of being modally robust amounts to saying that an entity in virtue of the form it possesses takes precedence over its parts. Accepting that processes exemplify MRVF implies thinking of processes as a type of cross-world identifiable entity that, for instance, could be made larger or shorter by adding or subtracting parts, or that they could display different properties than the ones they actually do. This is permitted because, on this view, processes are only contingently composed of the temporal stretches they possess. In contrast, given the dependence of events on their temporal parts, they cannot display this mereological and modal flexibility. Events could not have begun to exist earlier or cease to exist later than they actually do: their spatiotemporal boundaries fix their identity. There are two crucial points, nonetheless, that we need to bring up at this stage. The first one is that accepting that processes exemplify MRVF gives us the following taxonomy for the categories of process, event, and substance: on the one hand, processes and events share the property of being extended over time; on the other, processes and substances possess a certain form or structure that makes them prior to their component parts in virtue of exemplifying the property of being MRVF. The second is that Steward’s argument in support of processes exemplifying MRVF entails treating processes as countable particulars. I noted in Section 25.3 that that was already a conclusion drawn by Stout from the line of argument presented by Mourelatos. But, at the very least, that constitutes a controversial move, since the properties that processes possess by exemplifying MRVF are ultimately explained in virtue of them having the same properties as mass-quantifiable 288

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entities. In the last section of the chapter, I will examine recent arguments in the literature that in some way or other exploit this tension.

25.5 Occurrents, Properties, and Particularity Not everyone agrees with the way in which one could articulate the difference between the category of event and process in terms of the property of being MRVF. In this final Section, I will discuss two different antagonistic takes on the matter. These rival takes stress that processes cannot share structural properties with substances given that they are not particulars. If anything, it is events that come out closer to substances, whereas processes resemble in some important respects to universal properties. The first of the two takes comes from Thomas Crowther (2011, 2018). Crowther explicitly aims at reversing the approach from Stout and Steward regarding substances and processes. In particular, he argues that the mode of existence in time of processes is that of unfolding over periods of time, whereas the one of substances is simply to exist over periods of time. This unfolding of processes might be captured if we treat processes as timeoccupying stuff governed by the conceptual resources of temporal mass quantification. Crowther’s move, then, is a plausible extension of Mourelatos’s argument from Section 25.3. Let us take an example from Crowther to that effect (2018: 79). If there is some running that goes from time t1 to t10, that means that progressively there would be more running from t1 to t10. In other words, the unfolding of said process over a stretch of time entails that we have more and more of the process as we progress over that temporal stretch. Following Brian O’Shaughnessy (2000: 42), Crowther calls this persistence phenomenon ‘occurrent renewal’, which is distinctively different from the simple occurrence of events in time. The occurrent renewal contrasts with the way substances persist over periods of times. It seems odd to say of the person who runs t1 to t10 that we have more of her as running incrementally occurs over that temporal period. A person simply continues to exist over such a period, hence we regard her as a continuant. Events, on the other hand, can be count-quantified. There could be two, three, or more 400-meter runs, but not more or less of a 400-meter run. Thus, according to Crowther, events are picked out by terms that refer to quantities of space-filling stuff with limited boundaries. Mass quantification, in contrast, seems not to imply the existence of such boundaries. Therefore, the countability of events on Crowther’s account makes them more similar to substances than processes, which are picked out by mass-quantificational expressions. Drawing on that analogy, Crowther further understands the relation between events and processes in terms of the relation between countable material objects and spacefilling stuff (2018: 80). The example below illustrates this: If an event, say, the complete temporal particular which was the sinking of the Titanic, occurred from t1 to t10, then the occurrence of that event consisted, over that time, in an iceberg tearing a hole in the bow of the boat, water flooding into the hull and across the top of bulkheads, and so on. But it is the tearing and flooding—the processive constituents, or the ‘temporal stuff’ of the event—of which there can be more and more, and which exist by being occurrently renewed, the complete sinking. (Crowther 2018: 80)

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Pursuing an even more critical line than Crowther, Johanna Seibt advances an objection from an unresolved tension in the picture presented in Section 25.4. The tension, claims Seibt (2018: 135–137), comes from their particularity and claiming that processes have MRVF. Put in more perspicuous terms, her criticism is that one cannot have temporal entities that both extend through the temporal dimension and possess MRVF, as it allegedly would be the case for processes. Seibt defends the view that particularity amounts to non-repeatability in space. A particular, for Seibt, is something that necessarily exists in a single spatial location at any time at which it exists. There cannot be a particular located at two or more distinct spatial regions at the same time. As I noted in Section 25.3, we get a useful contrast with the spatiotemporal profile of universal properties. Typically, a universal property is located at several spatial regions at the same time,2 thus contrasted with substances, which are only located at one spatial location at a time. In the case of particulars with temporal extension, Seibt holds that they necessarily have a single spatial and temporal location. They are nonrepeatable entities in space and time. Yet, supporters of the view that processes exemplify MRVF are forced to accept that processes have a recurrent existence at least in time. They cannot accept that, as a particular in time, a process is non-repeatable, that is, it has a determinate unique temporal extent and therefore can only perdure in time. Now, Seibt further develops her objection claiming that an entity can be modally robust regarding its spatial extension iff it is the sort of entity that has a unique determinate spatial extent in the actual world (2018: 135). Given that biconditional, it would make perfect sense for Seibt to say that material objects such as the Taj Mahal could have been bigger or had a different spatial location, whereas it would sound odd to say the same about mass entities such as gold or water. At most, Seibt concedes that it is permissible to claim that there are possible worlds where the scattered spatial region occupied by mass entities in the actual world is larger or smaller, something weaker than claiming that such entities are modally robust regarding their spatial extension. Given that the same holds for temporal extension, namely, that a temporally extended entity can be modally robust with respect to its temporal extension iff it has determinate duration in the actual world, processes must be treated as particulars in time. But such particularity, according to Seibt, does not allow for recurrence in time. What recurs, as in the earlier example, between t1 and t10 is the running, but to ask whether the running could have lasted longer is as meaningless as asking whether gold or water could have been bigger. The upshot of this is that for anything that is extended and exists in time as an enduring continuant, we must either reject that it is a particular or that it exemplifies MRVF. One way out Seibt devises for particularists about processes such as Stout and Steward is to introduce a further notion of particularity: particularity1 is a predicate that stands for non-repeatability in space and it belongs to the categories of substance and process; particularity2 belongs to the category of event and it stands for non-repeatability in space and time. Take this example from Stout to illustrate the latter point: A fight between two men may have very stable boundaries distinguishing it from any other fighting that is going on. There is no difficulty in counting instances of such fighting. Other fighting pairs may arrive on the scene, but we can still individuate the original fighting from everything else that is going on. (Stout 2015: 55)

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Using Seibt’s distinction, Stout resists the idea that processes are ultimately of a masslike nature because the fighting between two men persists over time by enduring – it is the same fighting that we are able to identify at earlier or later times – and it seems perfectly distinguishable from other instances of fighting that may be taking place in its vicinity. But at most, the example only supports the view that processes exemplify particularity1 in virtue of their temporal recurring, which somehow makes processes similar to substances. In fact, Seibt presents two further problems to Stout’s rejoinder. The first problem is that it is debatable that all processes can be classified even as displaying particularity1, that is, as non-repeatable in space. To stick to Stout’s example, one could retort that it seems correct to affirm that fighting occurs in many locations throughout a street at the same time. If that is so, processes cannot be particulars1, for particulars1 are only located at one spatial location at each time of their existence. Moreover, it seems that from their pattern of temporal occurrence, processes are closer to universal properties than to substances. The second problem is that one might dispute the move from the possibility of counting processes to the fact that processes are particulars. Processes, according to Seibt, might be enumerable and individuated under certain identity conditions, but that does not necessarily imply that they are particulars as she describes above. The move is somehow analogous to what Gareth Evans (1985: 257) and Steward (2013: 793) note regarding the reidentification of processes. While it is true that there is a sense in which a process can be reidentified over time, that does not imply that it is exactly the same sense in which we say a substance can be reidentified. Now, in the case of Seibt, this compels us to engage in a larger revision of the category of particular, which for independent reasons has proven to be a problematic ontological category to characterize (for more on the universal/particular distinction, see Chapter 5, this volume).

25.6 Concluding Remarks Kim’s well-known account of events is a clear example of how properties play a central role in a theory of events and other occurrents. However, Kim’s account has problems that prompted a discussion about other work on theories of events and processes. One key debate in this literature is the question of how to distinguish between events and processes. How do properties figure in this debate? We found that the path opened up by the argument from nominalizations from Mourelatos offered us a more fruitful starting point to inquire about the interplay between the category of property and the categories of event and process. Yet, this framework is not free from trouble. Even though processes having the property of being MRVF allow us to draw a sharp metaphysical difference with events, it is not clear that processes possessing MRVF are compatible with their mass-like nature or that processes can both exemplify MRVF and display features of non-particular entities such as universal properties. All things considered, this debate remains open on an important number of fronts.

Notes 1 For an example of this, particularly in the case of substances and their parts, see Fine (1999), Schaffer (2009), Marmodoro (2013), and Inman (2018), among others. 2 By location, I mean to imply that universal properties are exactly located at multiple spatial regions at the same time. Although some have rejected this assumption ( Effingham 2015; Gilmore 2003), it

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References Bennett, J. (1984) Events and Their Names. Indianapolis, IN: Hackett. Crowther, T. (2011) The Matter of Events. Review of Metaphysics 65(1): 3–39. Crowther, T. (2018) Processes as Continuants and Process as Stuff. In Stout, R. (ed.) Process, Action, and Experience. Oxford: Oxford University Press: 59–81. Dodd, J. (2009) Events, Facts, and States of Affairs. In Le Poidevin, R. et al. (eds.) The Routledge Companion to Metaphysics. London: Routledge: 322–334. Effingham, N. (2015) The Location of Properties. Noûs 49(4): 846–866. Evans, G. (1985) Things without the Mind. In Evans, G. (ed.) Collected Papers. Oxford: Oxford University Press: 249–290. Fine, K. (1999) Things and Their Parts. Midwest Studies in Philosophy 23(1): 61–74. Galton, A. and Mizoguchi, R. (2009) The Water Falls But the Waterfall Does Not Fall: New Perspectives on Objects, Processes and Events. Applied Ontology 4(2): 71–107. Gilmore, C. (2003) In Defence of Spatially Related Universals. Australasian Journal of Philosophy 81(3): 420–428. Inman, R. (2018) Substance and the Fundamentality of the Familiar. London: Routledge. Johnson, W.E. (1924) Logic. Cambridge: Cambridge University Press. Kim, J. (1966) On the Psycho-Physical Identity Theory. American Philosophical Quarterly 3(3): 227–235. Kim, J. (1969). Events and Their Descriptions: Some Considerations. In Rescher, N. (ed.), Essays in Honor of Carl G. Hempel. Dordrecht: Reidel: 198–215. Kim, J. (1973) Causation, Nomic Subsumption, and the Concept of Event. Journal of Philosophy 70(8): 217–236. Kim, J. (1976) Events as Property Exemplifications. In Brand, M. and Walton, D. (eds.), Action Theory. Dordrecht: Reidel: 159–177. Marmodoro, A. (2013) Aristotle’s Hylomorphism without Reconditioning. Philosophical Inquiry 37(1): 5–22. Mourelatos, A. (1978) Events, Processes, and States. Linguistics and Philosophy 2(3): 415–434. O’Shaughnessy, B. (2000) Consciousness and the World. Oxford. Oxford University Press. Schaffer, J. (2009) On What Grounds What. In Chalmers, D.J. et al. (eds.) Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Oxford University Press: 347–383. Seibt, J. (1997) Existence in Time: From Substance to Process. In Faye, J., Scheffler, U., and Urs, M. (eds.) Perspectives on Time. Dordrecht: Kluwer: 143–182. Seibt, J. (2010) Particulars. In Poli, R. and Seibt, J. (eds.) Theory and Applications of Ontology: Philosophical Perspectives. New York: Springer: 23–55. Seibt, J. (2018) What Is a Process? Modes of Occurrence and Forms of Dynamicity in General Process Theory. In Stout, R. (ed.) Process, Action, and Experience. Oxford: Oxford University Press: 121–148. Steward, H. (1997) The Ontology of Mind. Oxford: Clarendon Press. Steward, H. (2013) Processes, Continuants, and Individuals. Mind 122(487): 781–810. Steward, H. (2015) Substances, Agents and Processes. Philosophy 95(1): 41–61. Stout, R. (1997) Processes. Philosophy 72(279): 19–27. Stout, R. (2015) The Category of Occurrent Continuants. Mind 125(497): 41–62.

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26 TEMPORAL PROPERTIES Katarina Perović

26.1

Introduction

This chapter discusses different ways in which philosophers have considered properties’ relation to time. I start with the famous problem of temporary intrinsics as it was presented by David Lewis (1986). Given that Lewis’s formulation of the problem set the parameters of the debate about persistence for decades to come, I spend some time uncovering and analyzing the assumptions of the problem. I suggest a more neutral and less skewed formulation of the problem which leaves open different avenues for approaching it, including an appeal to different conceptions of temporal properties. I present some of the familiar strategies that philosophers have employed in responding to the problem of change, and I conclude with a discussion of some recent dynamic approaches.

26.2 The Problem of Temporary Intrinsics Lewis (1986) presents the problem of temporary intrinsics within the context of his discussion of two theories of persistence – perdurance and endurance – which he characterizes as follows: Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time. Something endures iff it persists by being wholly present at more than one time. (Lewis 1986: 202) Lewis then compares perdurance to the way a road extends in space, by having a part here and a part there, whereas endurance is more like a universal, thought of as being wholly present in each of its instances. Without a concept of a temporal part, the distinction between perdurance and endurance is impossible to grasp, stresses Lewis; it is a required part of the conceptual apparatus for anyone who wishes to engage in this debate.

DOI: 10.4324/9781003246077-33

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Lewis then quickly moves on to provide what he takes to be “a decisive objection” against endurance: Persisting things change their intrinsic properties. For instance shape: when I sit, I have a bent shape; when I stand, I have a straightened shape. Both shapes are temporary intrinsic properties; I have them only some of the time. How is such change possible? (Lewis 1986: 204) The problem of temporary intrinsics thus asks us to explain a change in intrinsic properties of an object through time. A persisting entity has one intrinsic property at one time and a different intrinsic property at a subsequent time. When Lewis asks “how such change is possible”, he is after a metaphysical account of the pervasive phenomenon of apparent change in intrinsic properties. Lewis believes that an endurantist has a particularly difficult time providing such an account. Endurantists, according to him, would have to argue that intrinsic properties such as shape are not intrinsic after all; by making such properties relative to times, they turn out to be relational, and thus extrinsic: I have a bent-at-t1 shape property and then I have a straight-at-t2 shape property. This, claims Lewis, is “simply incredible”, since “if we know what shape is, we know that it is a property, not a relation” (1986: 204). In addition to this surprising result, an endurantist must contend with another oddity – the bearer of temporary intrinsic properties, when considered on its own, appears to be “something with an absolutely unchanging intrinsic nature” (1986: 204). The presentist solution to the problem is no better, claims Lewis; the only intrinsic properties a thing has are those it has at a present moment. Other times do not exist, they are merely representations, and thus in no sense can an object be said to have properties at those other times. Indeed, not only is the presentist not successful in accounting for change in intrinsic properties, but due to their commitment to the nonexistence of future and past times, the presentist’s objects do not endure past the present moment, and so they do not appear to persist at all. The remaining solution, and the only reasonable one in the face of the above difficulties, according to Lewis, is to reject endurance and embrace perdurance. He writes: “the different shapes, and the different temporary intrinsics generally, belong to different things. […] We perdure; we are made up of temporal parts, and our temporary intrinsics are properties of these parts, wherein they differ one from another. There is no problem at all about how different things can differ in their intrinsic properties” (1986: 204). Lewis’s appeal to temporal parts solves the problem of temporary intrinsics by ascribing distinct temporary intrinsics to distinct property-bearers. It is a temporal part of me, k1-att1 that is bent, and a different temporal part of me k2-at-t2 that is straight. The whole of me, K, does not endure and does not have any of these properties; K is simply a cross-temporal sum of the distinct temporal parts with their distinct properties.

26.3

Assumptions of the Problem

Given the extraordinary influence that the Lewisian formulation of the problem has had on the subsequent debate, it’s important to look more closely at the assumptions that it makes. It assumes: (i) that ordinary things such as tables, trees, persons, etc. frequently undergo a 294

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change in intrinsic properties; (ii) that there needs to be an account of such change; (iii) that there are indeed genuine temporary intrinsic properties and that any explanation of change that denies this is stating something implausible; (iv) that the distinction between an endurantist and a perdurantist approach to persistence is to be made by reference to the existence (or lack thereof) of temporal parts; and (v) that properties are had at times. A few words about each assumption. Assumption (i) seems to be obvious and unproblematic; it is what philosophers like to call a “Moorean fact”, the type of fact that no one should deny. One could, nonetheless, try denying (i) by granting the appearance of change, but claiming that in reality there is no such thing. Parmenidean denial of change took this form. The burden for such a view is then to provide an error theory of how such a pervasive illusion has come about, and what purpose it might serve. Assumption (ii) is present in the demand for a metaphysical explanation of the phenomenon of change. Change strikes us as puzzling because it brings out the difficulty of identity through change. On the one hand, according to Leibniz’s Law, two objects x and y are identical only if they share all the same properties. On the other hand, most things that are subject to change do not seem to become a different thing altogether with each small change. That is, we are not surprised to find out that a table, even after a scratch, is still the same table, or that we are the same people, even after various physical and mental changes. Lewis takes this traditional puzzle of change and sharpens its focus onto intrinsic properties. Why focus on intrinsic properties in particular? Well, the change in extrinsic properties does not seem to puzzle us as much; an object has extrinsic properties relationally. Change in relational properties, such as its spatial and temporal ones, does not appear to alter the object itself and thus the puzzle about how the object remains the same through that change does not arise. Change in essential properties is also not in focus here, but for a different reason. Essential properties of an object are those intrinsic features that it cannot be without; for instance, a ball that changes its color from blue to red is still a ball; but a ball that loses its essential feature of sphericality is no longer a ball. In other words, we expect a change in an essential property of an object to result in an object of a different kind, so there is no genuine puzzle of how an object remains the same through such change – it simply does not. Within this context, it comes as no surprise that Lewis assumes (iii) – that is, that there are indeed genuine intrinsic properties and that accounts that deny this are implausible. But despite Lewis’s best efforts to make the commitment to genuine intrinsic properties look like the most intuitive one, such intuition needs further support. After all, in philosophy, we are used to engaging in frequent re-evaluation of our intuitions and having to give up some intuitions in favor of preserving others. As we will see below, the distinction between what Lewis refers to as “intrinsic” and “extrinsic” properties might be recast as a distinction between two types of “extrinsic” properties. More needs to be said as to why such reframing is undesirable. Assumption (iv) takes it that the distinction between an endurantist and a perdurantist approach to persistence is to be made by reference to temporal parts – perdurantists embrace their existence and claim that objects persist by having distinct temporal parts at different times, whereas endurantists deny their existence and claim that objects persist by being wholly present at each time. But beyond the analogy with spatial parts, such as parts of a road, or river, temporal parts get no further treatment. This is because, from the perdurantist’s perspective, there is nothing more to be said. By embracing the fourdimensionalist approach to space-time, the perdurantist views the temporal dimension as 295

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analogous to the three spatial dimensions; thus, ordinary objects’ extension in space and time amounts simply to their having spatiotemporal parts. Endurantists are, in contrast, committed to the disanalogy between time and space, and though they take ordinary objects to have spatial parts, they do not take them to have temporal parts; this is why Lewis states the endurantist position in terms of objects being wholly present at a time – it is all of the objects’ spatial parts that are present at a single time. One could, of course, dispute this characterization of the two main approaches to persistence. Some might object that the notion of a temporal part is too obscure and that it needs further characterization before it can play such a decisive conceptual role.1 Others might further object that the Lewisian characterization leaves no room for entities that appear to take up time, such as thoughts, perceptions, persons, and so on, but that may not be adequately captured by appeal to temporal parts, instantaneous properties of such parts, and their mereological sums. Finally, assumption (v) takes it as a given that it makes sense to talk of properties being had at times. We are bent at t1 and then straight at t2; we are rested at t1 and tired at t2, and so on. But rather than assuming that these properties are had at times, one can question whether it might be more appropriate to describe them as being had through time or through a temporal interval. The intuition here is that momentary temporal parts or stages are simply too short to be adequate bearers of many non-instantaneous properties. To sum up, I have suggested that assumptions (i) and (ii) seem largely unproblematic, but that assumptions (iii), (iv), and (v) need further defense. They risk skewing the debate too much in the perdurantist direction and closing off certain viable approaches to temporal properties.

26.4

A More Neutral Formulation and Different at-t Replies

So how should the problem of temporary intrinsics be formulated in a more neutral and less restrictive way? If we don’t follow Lewis in assuming that there must be intrinsic properties in his sense (iii), and we don’t take for granted that the only two approaches to persistence are perdurantism and endurantism defined by reference to temporal parts (iv), and we don’t assume that properties are only had at times (v), the problem we are left with is one of providing a metaphysical explanation of change through time. An object o has a certain nonessential property P, and then it has a different nonessential property Q: how is such a change in properties through time to be analyzed? Or, put slightly differently: in what way does time enter the analysis of change in objects’ nonessential properties? Assuming that change is a temporal phenomenon, in what way does time enter the metaphysical analysis of change? This formulation of the problem is more neutral than Lewis’s, but it is not a completely neutral formulation either. It takes for granted that change is a real occurrence and not an illusion; it takes change, rather than the identity of an object, to be in need of an explanation; and it assumes that there cannot be change without time. Given all this, the issue becomes to explain how time enters the metaphysical analysis of change. The following possibilities have already received some attention in the literature: 1 o is P-at-t1 and then o is Q-at-t2 (properties at times) 2 o is P at t1, and there are no other times (properties at the present moment) 3 o-at-t1 is P and then o-at-t2 is Q (temporal parts/stages with instantaneous properties) 296

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4 o is-at-t1 P and then o is-at-t2 Q (instantiation relations at times) 5 [o is P] at t1 and then [o is Q] at t2 (states of affairs at times) We have already seen Lewis consider the first three possibilities, quickly dismissing 1) and 2) in favor of 3). But each of these possibilities deserves more detailed consideration in its own right.

26.4.1

Properties at Times

Lewis rejected 1) as a credible candidate for analysis of change in intrinsic properties because he found that it turned the apparent intrinsic properties into relations. Intuitively, he thought, properties should not be attached to times: this does not honor the intuition that intrinsic properties capture the way the object is by itself, independently of its relations to other entities; but furthermore, according to him, it treats the bearer of properties as a propertyless unchanging and unstructured blob.2 These Lewisian intuitions need further support if they are to be compelling. First, it is not obvious that there are irreducibly intrinsic properties to be had. Lewis insisted on the importance of there being non-relational properties that objects have simpliciter3 but offered nothing to support it. His chosen example of shape is not as straightforward as he takes it to be – the shape of a body might vary depending on its relation to other objects and points of reference; thus, some might find shape to be more of a relational property than an intrinsic one. On the other hand, if one tried to reduce the shape of a given body to the shape and position of its constitutive parts, one could then be off to a regress of smaller and smaller parts with their relative shapes and positions, with no genuinely intrinsic property in sight. This concern was brought up by E.J. Lowe (1988), and briefly discussed by Lewis (1988), but it led them to very different conclusions. Lowe thought that ultimate intrinsic properties will likely end up being the essential intrinsic properties of fundamental particles – properties such as mass, charge, spin, etc. But even these examples of intrinsic properties such as mass have already been challenged by those like W.A. Bauer (2011) who makes a strong case for mass actually being a dispositional extrinsic property grounded in the Higgs field. Lewis too seemed concerned that a focus on fundamental particles and their intrinsic properties leaves one open to “scientific surprises”, i.e., discoveries of variations in the very properties one initially took to be intrinsic and essential. To counter such surprises, Lewis thought that one should simply stick with intrinsic properties of macroobjects in solving the problem. But this way of settling the issue might strike some as ad hoc. Second, even if it is granted that there are some genuine intrinsic properties, it is far from clear that an endurantist is unable to capture the distinction between temporary intrinsic properties and temporary extrinsic properties. A temporary extrinsic property such as being taller than Lulu is a relational property I have relative to Lulu’s height and a time of comparison, so relative to two relata. On the other hand, a temporary intrinsic property such as being bent at t1 is, on the face of it, a property I have in relation to only one relatum – a specific time. Thus, an endurantist could, in principle, be able to preserve the distinction between intrinsic and extrinsic properties by appeal to the number of relata that the property stands in relation to – intrinsic properties would turn out to be relative only to times, whereas ordinary examples of extrinsic properties would be relative to times and another one, two, or more relata. 297

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Of course, those sharing Lewisian strong intuitions about intrinsicality would probably not be pleased with the above. They will likely still worry that the intrinsic property that gets this relational treatment will turn out to be too external to the thing that it ought to be characterizing “from within”, so to speak; and they will also share Lewis’s concern that the bearer of properties will turn out to be a propertyless substance or bare particular, the sort of entity that many find unappealing. It is outside of the scope of this chapter to evaluate whether one should indeed fear, as Lewis did, a commitment to a bare substratum (or bare particular)4; the point worth making here is that such a commitment is not inevitable. One might, for example, hold a view that takes essential properties as constitutive of the particular, making it so that the substratum is never actually completely bare. Lewisian worry about bare substratum was clearly fueled by a substance-attribute approach to objects and their properties, but a number of property theorists will simply disagree with this approach. Take, for instance, one-category trope theorists; they might not subscribe to the substance or anything like it; such theorists will have in their ontology trope bundles held together by different relationships of mutual co-dependence. The tropes within a bundle might be constituted by some essential intrinsic tropes that remain the same through time, and some intrinsic momentary tropes which change reasonably frequently. In addition to these tropes, there might be purely extrinsic relational tropes that hold between various trope bundles. And so on and so forth.5 The point of this example is just to show how this kind of trope theorist would not be stranded with a substratum-like blob that Lewis finds so undesirable. Other property theorists will approach the issue in their own ways. Even Lewis’s own commitment to class nominalism seems at odds with his insistence on intrinsic properties simpliciter. On his view, an object’s having of a given property boils down to its membership in a class of actual and possible particulars. But class-membership is external to the particular, and properties understood as classes of particulars do not, on the face of it, have what it takes to do the intrinsic characterizing and structuring that Lewis requires of them. Finally, it is worth noting that one might question the plausibility of a properties-attimes endurantist account from a different perspective entirely. As we will see in more detail in Section 26.5, there are those who argue that a great many properties, if not all, appear to be temporally extended – that they are had through a temporal interval, rather than at an instant. Thus, an adequate endurantist account should make room for such properties and not solely engage with properties at times.

26.4.2

Properties at the Present Moment

Lewis’s quick dismissal of 2) above was based on the thought that presentists must deny persistence altogether when they deny the existence of other times. For them, he notes, a thing can only have the intrinsic properties it has at a present moment; the puzzle about change in intrinsic properties does not then arise for a presentist because there are no other times at which the thing can exist and have different intrinsics. There is only the present moment.6 First, it is important to note that the presentist denial of other times need not mean that only present moments exist, one at a time, succeeding one another. One could conceivably hold a version of presentism which takes the present to be an extended short-lived interval. Such an extended present could perhaps even allow for some very quick changes in Lewisian intrinsic properties. If a presentist were to go down this road, they would then face the very same challenge about the change in nonessential properties that Lewis initially outlined. 298

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Most presentists, however, would likely prefer to stick to momentary stages and their inhabitants. Such presentists face Lewis’s accusation that they deny persistence altogether. To this, they could reply that they merely re-describe persistence and that perdurantists risk begging the question when they demand that persistence must presuppose two temporally distinct existents with distinct nonessential properties.7 Then, a presentist might suggest that rather than think of persistence in strictly perdurantist terms, as the tenseless existence of distinct temporal parts of a fourdimensional object, one might conceive of a present moment as a single short-lived instantaneous temporal part which comes into existence and then dies out, as the new relevantly causally related instantaneous temporal part comes into existence, and so on. This sort of view was defended by Berit Brogaard (2000) and she termed it “fourdimensional presentism”. The change in Lewisian intrinsic properties is described on this account as a coming into existence of a new stage with a distinct intrinsic property from the previous stage, which is now gone and no longer existent. Brogaard adds an interesting comment to this description: “The mere coming into existence of a temporal stage is not sufficient for a change to have taken place: it must involve further the coming into or going out of existence of a nonrelational property” (Brogaard 2000: 348). She doesn’t further elaborate on the way we should think about the properties’ coming into and out of existence with every instant, as something that is additional to the coming in and out of existence of the stages that have such properties. But this is certainly an interesting and important issue, worth exploring further for this sort of account to be fully fleshed out. Other ways that presentists can describe persistence through change in nonessential properties can draw on Ned Markosian’s (2004) discussion. He described a number of strategies available to presentists when talking about past and future objects and events, and relationships with them. Some of these strategies could be applied to the case of persistence: perhaps some might appeal to nonexistent object k having a property of being bent, and then an existent object k having a property of being straight. This proposal is problematic insofar as it appeals to nonexistent objects as existing in some sense, something most philosophers would rather avoid. Others will prefer to talk about the current existents such as k having a past-oriented property of having been bent-at-t as well as having the property of being straight simpliciter (at a present moment). And there are further possibilities still which will take a different shape depending on the theory of properties one holds.

26.4.3

Temporal parts/stages with Instantaneous Properties

Option 3) is, of course, the one that perdurantists favor and the one that Lewis and other fourdimensionalists take to be supported by the problem of temporary intrinsics in its original formulation. Time enters the analysis of change in a way that modifies the bearer of properties, not the property, and not the having of it. It is distinct temporal parts of a larger fourdimensional entity that have distinct intrinsic properties: o-at-t1 is P and then o-at-t2 is Q. The fourdimensional aggregate O is a sum of all its temporal parts o1+o2+o3+ … +on and as such, as a whole, it does not have any of the temporary intrinsic properties; that is, it has them only by proxy, by having a temporal part that has the intrinsic property. The temporal part approach thus preserves nicely the Lewisian intuition that there are such things as intrinsic properties that objects can have at different times. Preserving this intuition, however, comes at the cost of introducing temporal parts, which many do not 299

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find easy to accept. In addition to this, the common-sense understanding of change undergoes a deep revision: change is no longer thought of as something that happens to one and the same thing, through time; on the temporal parts approach, there is no one thing that survives change; change becomes simply a dissimilarity in properties belonging to distinct entities (temporal parts). With the common-sense understanding of change gone, the common-sense understanding of an ordinary object goes too. It is not one’s body that has different shapes of being bent and then being straight. Rather, it is temporal parts of The Body (aggregate) that have those shapes. As to The Body-aggregate, it is unclear what properties it itself has – it doesn’t have shape ordinarily conceived, but it also doesn’t have a sum of shape properties, whatever that might be; similar remarks apply to other properties we’d ordinarily apply to bodies – weight, height, blood counts, cholesterol levels, and so on and so forth. None of these can be thought of as properties of The Body-aggregate. Katherine Hawley (2001) and Theodore Sider (2001) latched on to this last concern and offered a stage-theoretic amendment to perdurantism. To circumvent the oddity of identifying ordinary objects with aggregates of temporal parts, they found it more intuitively plausible to identify them with the instantaneous temporal parts. Thus, it is one instantaneous temporal stage that is bent and another instantaneous temporal stage that is straight. There is no me that is an aggregate of parts and that has properties by having temporal parts that have them; rather I am to be identified with my current instantaneous temporal stage. This approach raises a host of additional concerns, however. The most obvious one is that a number of properties that we would ordinarily ascribe to objects just do not appear to be the sorts of properties that instantaneous objects can have. Hawley (2001) noted this difficulty in her discussion of ascriptions of sortal properties such as being a banana, lingering predicates such as “travelling across the court” and historical predicates such as “is six months old”. It seems decidedly wrong to say that an instantaneous banana stage is the adequate bearer of a sortal being a banana, or that it is an instantaneous tennis ball stage that travels across the court, or that an instantaneous baby-stage is six months old. Hawley’s response to this difficulty is twofold: on the one hand, she argues that these predicates do not pick out genuine properties; but the predicates do apply to the instantaneous stages in virtue of the relationships that such stages have to other nearby stages and their instantaneous properties. She writes: “Roughly speaking, the stage satisfies ‘is travelling across the court’ if and only if it is embedded in a series of stages which are appropriately located at points across the court. And the stage satisfies ‘is six months old’ if and only if it is preceded by an appropriate sequence of stages which stretches back over six months” (Hawley 2001: 54). So not only are there no temporally extended properties, but the apparent reference to such properties can be reduced to the properties of instantaneous stages with their instantaneous properties. This is quite a strong form of reductivism and, as we will see in the final section, it might just not be as easily generalizable to all of the cases of apparently temporally extended properties, as the stage theorists might have hoped.

26.4.4

Instantiations at Times

Rather than making the object relative to a time, or the property relative to a time, some have suggested that it is the having of a property that should be thought of as relative to a time. This is often referred to as “an adverbial” solution to the problem of intrinsic change 300

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and it has been discussed by Mark Johnston (1987), and endorsed by Lowe (1988) and Sally Haslanger (1989). This is option 4). Lewis (1988) immediately criticized this view for turning instantiation into a three-place relation with an object, a property, and a time as its relata, while treating the apparently intrinsic properties such as being bent and being straight as external to the object. In other words, there was no clear benefit to the adverbial analysis, according to him, as it could not capture his all-important intuition of having an intrinsic property simpliciter. Lewis later put this concern vividly in terms of alienation of the property from its bearer: “it is one thing to have a property, it is something else to bear some relation to it. If a relation stands between you and your properties, you are alienated from them” (Lewis 2002: 5). This is then related to a more general concern about Bradley’s regress which many believe is triggered when one treats instantiation as a genuine external relation. Lewis (2002) certainly took the Bradleyan worry seriously in this context, but not all would agree that it needs to be taken that way,8 or that making instantiation relative to a time would aggravate the issue. On their end, Lowe and Haslanger took care to distinguish between two ways one might understand instantiation of a property at a time. These ways can be represented schematically as follows: (a) o is-at-t1 P and then o is-at-t2 Q (b) [o is P] at t1 and then [o is Q] at t2 Lowe and Haslanger9 distanced themselves from interpretation a) and instead advocated for interpretation b) as the more plausible one, because this interpretation takes an object’s having a property, as a whole, to obtain at a time. The change through time in nonessential properties of an object should thus simply be seen as distinct states of affairs such as o being P and o being Q obtaining at different times. This way, time is not meant to modify the object, the property, or the instantiation relation; time only enters the picture as an external temporal anchor for states of affairs. Lewis (2002) tried to reintroduce the worry that obtaining of a state of affairs at a time is actually a relational property in disguise and that such an endurantist analysis of change in intrinsic properties fails. But his criticisms were quick and uncharitable, and I will not spend more time on them here. This is option 5). As we have already seen, many of the Lewisian objections to the endurantist approaches repeat themselves and these have been already addressed in detail previously. The more interesting, and more constructive challenge for the adverbialist approaches à la Lowe and Haslanger is to explain further if states of affairs at times are to be thought of as events, and if so, what such event ontology should look like. Furthermore, it seems odd to think of an event as an instantaneous occurrence – events such as wars, tsunamis, birthday parties, etc. are not, on the face of it, at times, but occur through time. How then the relationship between states of affairs at times and events through time is to be thought of requires further work.

26.5

Properties through Time

In conclusion, it is important to mention some recent developments in the literature on temporal properties, which begin by questioning and rejecting some of the critical 301

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assumptions – assumptions (iv) and (v) – of the Lewisian approach to the problem of temporary intrinsics we have seen above. For instance, Anne Sophie Meincke (2019) has recently argued that both the perdurantist and the endurantist approaches, as these are set out by Lewis, end up getting rid of change and persistence, as we ordinarily understand it. She diagnoses the problem as originating from a tacit commitment to the priority of static discrete things from which both groups of theorists vainly attempt to produce change. She suggests that instead of taking for granted static “thing ontology” or immutable “substance ontology”, and then building change somehow from these starting points, we ought to start from processes.10 Processes are seen as fundamentally dynamic, changing entities, while things, if there are any, are stabilized processes. This approach is very similar to A.N. Whitehead’s early temporal ontology of events and objects. Whitehead (1920) took passage and change to be irreducible features of reality, and he understood events to have passage “within them”, as somehow derived from nature, which he believed to be in perpetual flux. Objects, in contrast, are constituents of events which appear to be the same through time. Meincke points out that such fundamentally dynamic ontologies call for a change of perspective; as she puts it: “rather than asking how change is possible, we have to ask how identity is possible” (Meincke 2019: 25). Reflecting a similar shift in perspective, Katarina Perović (2019) has recently argued that fourdimensionalists struggle to account for temporally extended properties (TEPs). Examples of prima facie TEPs are various cognitive properties such as understanding and thinking, as well as various biological, chemical, and microphysical properties such as absorbing, freezing, radiating, and so on. Perović argues that candidates for temporally extended properties abound, and yet these properties have not received an adequate treatment within the current dominant approaches to persistence. In particular, fourdimensionalists’ exclusive focus on instantaneous temporal parts/stages with their instantaneous properties (IPs) does not offer a clear path for how the fundamentally dynamic aspect of TEPs can be adequately explained and/or reduced. Perović considers four proposals on behalf of fourdimensionalists: (1) the temporal chunk proposal; (2) the temporal series proposal; (3) TEPs as genuinely temporally extended; and (4) exemplification relation as temporally extended. The temporal chunks proposal takes the bearer of properties to be an aggregate of temporal parts, so that it turns out that it is not an instantaneous part or stage of an atom that has the apparent TEP of decaying, but a certain sum of temporal parts of an atom. Some of the greater difficulties for this proposal have to do with the bearer of properties – with defining clear boundaries of the aggregate chunk that is meant to instantiate the TEP, and some difficulties have to do with the property itself – with showing how the apparent TEP might be reduced to or eliminated in favor of IPs. The temporal series proposal draws on Hawley’s stage view and it explicitly treats TEPs as linguistic predicates that do not have genuine properties corresponding to them. For Hawley, predicates such as “travelling across the field” or “being six months old” or “decaying” only apply to a series of instantaneous fourdimensional stages that are causally related in the right way, with each of the stages instantiating its own IP. Of course, this proposal, just like the first one, takes for granted that the apparent temporal extendedness of properties mentioned above can indeed be reduced to instantaneous stages and their IPs, which is a philosophical thesis that cannot just be assumed, but needs to be argued for and defended. 302

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Proposals that take TEPs as genuinely extended will look different in the hands of different property theorists. Many realists about universals might not find it appealing to think of property universals as being in time in their own right. On the other hand, perhaps some trope theorists might find the idea of having temporally extended tropes, in addition to momentary ones, appealing.11 In any case, the takeaway from considering these kinds of proposals should not be that only fourdimensionalists face problems in trying to find room for TEPs. The challenge is worth exploring within a threedimensionalist framework as well. The outcome of such explorations, from the perspective of apparently dynamic properties, might just be a deeper re-evaluation of the way that we have approached the problem of persistence. This chapter opened with the discussion of Lewis’s framing of the problem of temporary intrinsics: how is change in intrinsic properties of an object possible? This question received a more neutral reformulation as the problem of explaining how time enters the analysis of change of objects’ nonessential properties. If one is to take dynamic proposals as the correct default view, Meincke might just be correct to claim that the problem would have to receive yet another reformulation. For time, in such ontologies, is not an add-on, and passage is not built out of constituent parts. There are no properties at an instant; change is pervasive, and the new problem becomes: how might one describe what is constant and identical in that flux?

Notes 1 See, for instance, Lowe (1988) and van Inwagen (2000) for concerns about the very intelligibility of the notion of temporal part, and see Hawley (2020) for a thorough overview of approaches to temporal parts in the literature. 2 This type of concern is made quite explicit in Lewis’s (1988) reply to Lowe (1988). 3 See in particular Lewis (1986: 52–54) and Lewis (1988: 65–66). 4 For a detailed treatment of different conceptions of bare particulars, see Perović (2016). 5 For more on trope bundle theories, see Chapter 21, this volume. 6 See Hinchliff (1996) for a thorough presentist defense of this approach. 7 Zimmerman (1996) makes this point and questions the intuitiveness of Lewis’s understanding of persistence. 8 See Perović (2014) and ( 2016) for a thorough re-evaluation of the impact of the famous regress arguments. 9 See also Haslanger (2003). 10 For a discussion of process philosophies, see Seibt (2022). 11 See also Mumford (2009) for his discussion of dispositional properties and perdurantism. He argues that dispositional properties cannot be appropriately accounted for within the static perdurantist framework, and he believes that a process approach that takes dispositions to be intrinsically dynamic is a more promising way forward.

References Bauer, W.A. (2011) An Argument for the Extrinsic Grounding of Mass. Erkenntnis 74(1): 81–99. Brogaard, B. (2000) Presentist Four-Dimensionalism. The Monist 83(3): 341–356. Haslanger, S. (1989) Endurance and Temporary Intrinsics. Analysis 49(3): 119–125. Haslanger, S. (2003) Persistence through Time. In Loux, M. and Zimmerman, D. (eds.) The Oxford Handbook of Metaphysics. Oxford: Oxford University Press: 315–354. Hawley, K. (2001) How Things Persist. Oxford: Oxford University Press. Hawley, K. (2020) Temporal Parts. In Zalta, E. (ed). Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/temporal-parts/>

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Katarina Perović Hinchliff, M. (1996) The Puzzle of Change. Philosophical Perspectives 10: 119–136. Johnston, M. (1987) Is There a Problem about Persistence? Proceedings of the Aristotelian Society supp. 61: 107–135. Lewis, D. (1986) On the Plurality of Worlds. Oxford: Blackwell. Lewis, D. (1988) Rearrangement of Particles: Reply to Lowe. Analysis 48(2): 65–72. Lewis, D. (2002) Tensing the Copula. Mind 111(441): 1–14. Lowe, E.J. (1988) The Problems of Intrinsic Change: Rejoinder to Lewis. Analysis 48(2): 72–77. Markosian, N. (2004) A Defense of Presentism. Oxford Studies in Metaphysics 1(3): 47–82. Meincke, A.S. (2019) The Disappearance of Change: Towards a Process Account of Persistence. International Journal of Philosophical Studies 27(1): 12–30. Mumford, S. (2009) Powers and Persistence. In Honnefelder, L., Runggaldier, E., and Schick, B. (eds.) Unity and Time in Metaphysics. Berlin: De Gruyter: 223–236. Perović, K. (2014) The Import of the Original Bradley’s Regress(es). Axiomathes 24(3): 375–394. Perović, K. (2016) A Neo-Armstrongian Defense of States of Affairs: A Reply to Vallicella. Metaphysica 17(2): 143–161. Perović, K. (2019) What Is a Fourdimensionalist to do about Temporally Extended Properties? European Journal of Philosophy 27(2): 441–452. Seibt, J. (2022) Process Philosophy. In Zalta, E. (ed.) Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/process-philosophy/> Sider, T. (2001) Four Dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press. van Inwagen, P. (2000) Temporal Parts and Identity across Time. The Monist 83(3): 437–459. Whitehead, A.N. (1920) The Concept of Nature. Cambridge: Cambridge University Press. Zimmerman, D.W. (1996) Persistence and Presentism. Philosophical Papers 25(2): 115–126.

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27 POSSIBLE WORLDS AS PROPERTIES Peter Forrest

27.1

Introduction

The Worlds are Structural Properties thesis, WASP, states that possible worlds either are or correspond to complex structural properties, and that world Wx is actual if and only if Wx but no proper conjunction of Wx, has an instance.1 WASP derives from Robert Stalnaker’s (1976) proposal that possible worlds are properties, and from their treatment as structural universals (Forrest 1986), a thesis criticised by David Lewis (1986a). Although not widely defended, WASP is acknowledged as one competing theory of possible worlds (e.g., Longenecker 2022: 17; McDaniel 2006: 320–321). I have provided two slightly different versions of the theory relying on Operator Theory (Forrest 2006, 2018). Unfortunately, these do not solve the problem of Infinite Worlds (see Section 27.7). With a problem like this left unresolved WASP is in need of further development. After various preliminaries, I present two versions, Uni-WASP and Trope-WASP, in which properties are respectively universals and particulars. Next, I state some metaphysical theses to which WASPers might find themselves committed. After that I consider some problems with WASP, notably that of Infinite Worlds and, building on Lewis’ “Magic or Mereology”, that of Structural Properties (Lewis 1986a). Finally, I appraise the Ockhamist case against Strong Platonism, exploring the doctrines that the Strong Platonist should hold in order to deal with Ockhamist considerations. In the conclusion, I list the problematic theses on which WASPers might have to rely, leaving readers to judge whether that amounts to a refutation of WASP. My judgement is that the problems are less severe, if we take properties to be particulars, and therefore uphold some version of Trope-WASP.

27.2 Motivations In this section, I present some motivations for WASP. The first motivation stems from actualism. Actualism, the thesis that to exist is to be actual, excludes Lewis’ Modal Realism, and is also often taken to exclude properties or relations that lack instances. For this reason, D.M. Armstrong proposes a fictionalist theory of worlds corresponding to combinations of instantiated universals (Armstrong 1989).2 Nonetheless, a metaphysician

DOI: 10.4324/9781003246077-34

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sympathetic to actualism might permit WASP by granting the existence of universals that have no instances, provided they depend for their existence on ones that do have. (I call this position Weak Platonism. More on Weak Platonism below.) WASP is further motivated by the way mathematics provides many impossible but conceivable fictional worlds, contrary to the analysis of necessity as truth at all worlds.3 This would be acceptable if there was a primitive metaphysical modality of necessity, but that hypothesis is itself problematic. For we do not begin our enquiry with a fairly clear idea of metaphysical, as distinct from nomic, necessity. One of the tasks of a theory of modality is, then, to help us understand what we are talking about. For instance, Lewis’ Modal Realism tells us that a universal generalisation is necessary if it is universal without qualification, which we may think of as a realist but somewhat deflationary theory. We require, then, some theory of what metaphysical necessity amounts to. There is a straightforward realist solution to this excess of fictional worlds: follow Lewis in supposing all and only the possible ones exist. But that cannot be combined with the straightforward realist theory of actuality, namely that all and only the actual worlds exist. And there are well-known problems with Lewis’ alternative theory of actuality, as token-reflexive, notably the “incredulous stare”, that is, the counter-intuitive commitment to the existence of talking donkeys, flying pigs, etc. (For additional objections, see the supplement to Menzel 2021.) To sum up, the above motivates a research programme. Instead of supposing some theory of necessity and then asserting the necessity of the ontology, we say that necessity is derived from the ontology using the heuristic that a non-actual ontology is impossible. Thus, if we have an ontology of substances (or states of affairs), properties, and relations, then we would claim that necessities derive from truths about properties. Call this the Ontological Necessity Programme.

27.3

Preliminaries

In this section, I clarify my terminology, including my use of the phrase “structural property”. First, I shall use the term “proplation” to include both properties and relations considered either as universals or particulars. Next, I follow Armstrong (1978b: ch. 13) in being a sparse realist about proplations (for more on sparse and abundant properties, see Chapter 4, this volume). Consider, for instance, the putative property of being electrically charged but not a proton. As a sparse realist, I say that this is a fiction. The alternative is to grant that such unnatural proplations exist but systematically to ignore all but the natural ones. It makes little difference what we do, but it avoids confusion to be explicit. There are three grades of structural property. In Section 27.8, I explain why I prefer the weak grade. Weak: Having parts with such and such properties and related in such and such ways.4 Intermediate: Being the sum of parts with such and such properties and related in such and such ways. Strong: Being the sum of parts with such and such properties, and related in such and such ways, but not in other ways, and which have no further properties and relations except those following of metaphysical necessity.

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The proplations in question will be referred to as the constituents of the structural property, not parts. This is to avoid the suggestion that anything like classical mereology holds for them. For consider the properties: (1) x’s having as parts an F and a G where the F is related by R to the G, and (2) x’s having as parts an F and a G where the G is related by R to the F. As Lewis points out, these are two different properties if Fx and Gy differ and if Rxy is asymmetric. Yet they have the same constituents (Lewis 1986a). Classical mereology does not recognise distinct entities that are composed of the same constituents. World-structures are highly complicated structural properties. Although an infinite degree of complexity is problematic, I acknowledge that structural properties as such are compatible with Sparse Realism. Lewis did not accept the idea that some categories depend on others that are more fundamental or basic (Lewis 1983: 358). Nonetheless, there are two dependence principles that may be extracted from his criticism of structural properties (Lewis 1986b). I add a third, inspired by Armstrong’s idea that supervenient entities are a “Free Lunch” (Armstrong 1997: 12). These principles are intended to hold with complete generality, but their relevance to this chapter is that structural proplations depend on their constituents. Assume that Ys exist and depend for their existence on, and wholly on, the Xs, which are said to be fundamental (or basic) if they depend on nothing else. Here are the three principles. 1 Parity Suppose the Zs would depend on the same Xs as the Ys do, should the Zs exist. Then if the Ys exist so do the Zs. 2 No Magic We cannot explain the Ys in terms of the Xs merely by hypothesising that the Ys depend on the Xs. To explain, we must understand why necessarily if there are Xs there are Ys. 3 The Free Lunch The Ys may be as complicated as we please, although the fundamental Xs are subject to Ockhamist/Parsimony considerations, both in ontology and ideology. The first principle is justified by reflecting on examples, such as Lewis’ favourite chemical compound. Suppose being methane (CH4) depended only on its constituents, being carbon, being hydrogen, and being bonded, and that these are universals. Then the universal being CH5, in which one extra hydrogen is bonded to the carbon, must also exist, even though its instantiation is, I am supposing, ruled out by the laws of nature. The principle that magic is not to be multiplied is an instance of the general principle that, in a hypothetical explanation, the explanans is hypothesised, not its capacity to explain the explanandum. We also need a theory of truth at a world. The following suffices: Instances at a world: A property Fy is instantiated at the (fictitious) world (with structure) Wx just in case Fy is a constituent of Wx.

27.4

Uni-WASP and Trope-WASP

If we treat the world-structures as universals, then we obtain Uni-WASP. The alternative is the Lockean theory, according to which properties are particulars. Following Robert Garcia’s distinction between modifier tropes and modules tropes (see Chapter 20, this 307

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volume), I call these modifier tropes. They are to be contrasted with the module tropes of Donald C. Williams (1953), Keith Campbell (1990), and others.5 On module trope theory, proplations are replaced by suitably abstract or “thin” substances that we would otherwise describe as instances of proplations. Ordinary objects are then suitably united sums of tropes. A possible world is a giant object. Hence, on this view, a possible world is a highly complicated united sum of tropes. This is problematic because there are no uninstantiated module tropes.6 On the modifier trope theory, proplations are taken to be genuine properties and relations, but particulars rather than universals. I shall consider a variant in which a given particular proplation has either no instance or just one.7 In that case, even uninstantiated universals may be identified with mereological sums of exactly resembling particular proplations. We have, then, a version of WASP that I shall call Trope-WASP.

27.5

Some Relevant Theses

This chapter is about problems with WASP. These do not, however, provide a conclusive refutation. Instead, each problem can be solved at some metaphysical cost. Readers should assess whether the cost is too high. Here are the various theses that WASPers might have to accept. Some are more, some less, plausible. Conjunction as Summation. This is the thesis that the mereological sum of some properties is their conjunction. From this thesis, it follows that Gx is a proper part of Fx if and only if Fx & Gx = Fx. There are two reasons for taking the conjunction of properties to be the sum. The first is the idea that the sum of things of an ontological category should be of the same category. Yet the only plausible candidate for the sum of two properties Ux and Vy – other than Ux & Vx – is the dyadic Ux & Vy, which is, arguably, not natural enough to be considered a non-fictional proplation. The second is that because I am critical of WASP I should concede any fairly plausible theses that help its defence. That will be aided by treating the sum as a conjunction, explaining why the conjunction depends on its conjuncts. If all proplations were monadic, this principle would not be controversial. The sum of a property and an asymmetric dyadic relation cannot, however, be any conjunction because there are three candidates for that conjunction. One of the advantages of Operator Theory, described below, is that it motivates a unique candidate. Impurity. This is the thesis that if Rab … is an instance of the relation Rxy … then there is a proplation Ray … . For ease of exposition, suppose Rxy is dyadic and Ruv is an instance. Then Impurity (applied to the converse of Rxy) implies that there is an impure property Rya, y’s standing in R to a. Now, Armstrong denies this, rejecting the putative property of being descended from Charlemagne (Armstrong 1978b: ch. 14). His case against them is that universals are respects of resemblance and confer causal powers, but impure universals do neither. There are, however, more plausible examples of impure universals, such as x being below y, which should be analysed as x being between the centre of the Earth and y. I conclude that although we might be selective about which relations generate impure proplations, it would not be a serious defect if a theory requires Impurity, provided Armstrong’s objection can be undercut. Operator theory. Armstrong’s objection is undercut by his ontology of states of affairs that consist of universals fully saturated by particulars. For then we are already committed to the process of saturation, and should not object to partial saturation. Formally, we may treat proplations as operators on particulars, where if R is n-adic and if a is a particular 308

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then R[a] is (n − 1)-adic, and where something 0-adic is a state of affairs (Forrest 2006). I adopt the convention that the operand is in the first place of the relation. Another advantage of Operator Theory is that it provides a way of treating the conjunction as a sum, without arbitrariness. For, if R[x] and S[y] are m-adic and n-adic operators, we may take the sum to be the (m + n − 1)adic operator R[x] & S[x]. Weak and Strong Platonism.8 By Weak Platonism I mean the thesis that there are proplations without instances. Now, an uninstantiated proplation may depend on instantiated ones. It might, for instance, be a conjunction such as being a planet made of plutonium. By Strong Platonism I mean the thesis that there are proplations independent of any instantiated ones. Directionalism. This thesis states that if the relation Rxy is non-symmetric, Rxy and its converse Rcxy are different relations. Note: Rxy is said to be symmetric if, of metaphysical necessity, for all u and v, Ruv if and only if Rvu. In that case, I assume, Rxy is identical to its converse. This generalises to any permutation of the places of an n-adic relation. Directionalism likewise generalises. Directionalism is contrasted with Kit Fine’s Neutral Relations thesis that states that any relation Rxy is the same as its converse Rcxy (Fine 2000). The Neutral Relations versus Directionalism debate is beyond the scope of this chapter (see Fine 2000, 2007; MacBride 2007, Chapter 7, this volume). I merely note that, for the case of simple relations, Directionalism seems plausible only in cases where there is a non-symmetric relation on which we may reasonably say the converse depends. An example where there does not seem any such dependence, and hence one in which Directionalism is problematic, is provided by the triadic relation that holds for three directions in three-dimensional space, or more generally a n-adic relation in n dimensions. If the three directions, x, y, and z, do not all fall in a plane, then either they are oriented in a right-hand way or they are oriented in a left-hand way. Neither the righthand nor the left-hand orientation is more fundamental than the other. Finitism. This is the controversial thesis that even if infinite complexity is conceivable it is metaphysically impossible. There would then be no structural properties with an infinity of constituents. Infinitary Simple Relations. One measure of the complexity of a theory is the largest integer n for which we require simple n-adic relations. I take an infinite n to be a serious defect. Infinite Ideology. Following W.V. Quine, I aim for a description of things in a regimented language – call it Q – consisting of the predicate calculus, with identity and with a list of predicates, the ideology (Quine 1951). The names correspond to the items in the ontology (Quine 2011[1948]).9 An infinite ideology is not plausible. There must be at least some subset of primitive terms of the regimented language. Absolute Infinite Duplication. To say there are absolutely infinitely many Ks is to say that for any infinite cardinal, however large, some of the Ks are of that cardinal. Alternatively, the Ks form a proper class, not a set. Absolutely Infinite Duplication is the thesis that there is some entity with absolutely infinitely many exact duplicates. The case of interest will be exactly resembling uninstantiated tropes. I appeal to readers to judge that this is “ridiculous excess”.

27.6

Transworld Identity

The first problem with WASP concerns transworld identity. It is metaphysically possible that Lewis had an illustrious career in chemistry, not philosophy. He says that would not 309

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be him just a counterpart. Not only is this counter-intuitive, but raises problems with personal responsibility. Suppose instead, therefore, that two possible worlds can overlap up to a certain time, both containing Lewis up to his choice of intellectual career. The corresponding world-structures would be impure properties, sharing as a constituent the region of space-time prior to the choice. This solves the problem of Transworld Identity, at the cost of Impurity, which is most plausible given Operator Theory.

27.7

The Problem of Infinite Worlds 10

This is a problem for Uni-WASP, not Trope-WASP. A drastic solution is to accept Finitism. Ignoring that, first consider a debate over whether the actual world has an infinity of substances, or, alternatively, of states of affairs. Why not reject such an infinity as contraOckham? The answer is that the concrete actual world, whether finite or infinite, may be specified as the mereological sum of overlapping finitely complex substances, or states of affairs, and it is their complexity that should be assessed using Ockham’s Razor, not the complexity of the world that depends on them. This follows from the Free Lunch Principle for dependence. And the same goes for one of Lewis’ concrete worlds. The Ockhamist assessment is clearest if we adopt an ontology of states of affairs (which I denote using square brackets). Then there are monadic states of affairs of the form [Pu], dyadic ones of the form [Ruv], and triadic of the form [Suvw]. I doubt we need the tetradic [Tuvwx]. The relevant measure of complexity is then 3 or 4. We obtain the same measure if we adopt an ontology of module tropes, in which the state of affairs [Pu], [Ruv], etc. are replaced by isomorphic module tropes, this P, this and that being in R, etc. Hence, by Conjunction as Summation, infinite conjunction is also acceptable. In this way, we may analyse the infinitely complex structural property as the infinite conjunction of finitely complex ones. But Uni-WASP then requires infinitely many identifications of various places xj. For, although an infinitely complex world would instantiate some infinite conjunction of finitely complex structural properties with only finitely many identifications, that conjunction would not be the strongest property it instantiated. The one with the infinity of identifications would be stronger. Hence the problem of infinite complexity is not solved by appealing to infinite conjunction. This problem does not arise on Trope-WASP. We may conjoin structural properties corresponding to a sequence of parts each included in the next in the sequence. Because the properties are particulars, there is no need to specify the identity of the bearers of the properties. For without identification, the one trope would have two instances, contrary to their definition. The complexity of the world-structure on Trope-WASP may be measured in terms of the modifier tropes, Px, Rxy, and Sxyz. These are isomorphic to the module tropes and the states of affairs. Unless we accept Finitism, the infinite complexity of the world-structure is, then, a serious objection to Uni-WASP.

27.8

Are Structural Properties Magic?

Lewis (1986a) complains that the purported dependence of structural properties on their constituents is “magic”. I interpret this as a demand to show rather than just hypothesise this dependence. Now, instantiated structural proplations might be taken to depend on their instances, which may, in turn, depend on parts of the instances. To illustrate this and, 310

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more importantly, to contrast it with the uninstantiated case, consider a lichen. The property of having a lichen part may be analysed as having parts x and y, such that Ax, Fy, and Exy. Here, Ax is the property of being an alga, or more accurately being either a singlecelled alga or a cyanobacterium; Fy the property of being a fungus; and Exy the antisymmetric relation of x being embedded in y. We may suppose the structure depends for its existence on any lichen.11 Now consider a kind of organism that I assume is possible but not actual, the henlic. Its nature is to be a fungus embedded in algae. Having a henlic as a part is an uninstantiated structural property, so it does not depend on instances. And it is not merely the mereological sum of the three proplations Ax, Fy, and Ewz. For in that case, henlics would be the same as lichens. The difference is that to obtain the property of having a henlic as a part we must identify places: x = z and y = w, whereas for a lichen we identify places x = w and y = z. There is a trilemma with this identification: (1) treat it as a brute fact; (2) treat it as a dyadic relation; or (3) derive it from conjunction. The first horn multiplies magic. The second leads to a regress, for the analysis of a structural property of which identity is a constituent will require the further identification of places. This leaves conjunction. Having a lichen part and having a henlic part are both conjunctions of Ax, Fy, and Euv. To avoid magic we should say that the conjunction of a property and a relation, not merely the unique conjunction of two properties, depends on the conjuncts. But we may appeal to Conjunction as Summation and hence avoid magical conjunctions only if there is a unique sum. The solution to this problem requires both Operator Theory and Directionalism. The former enables us to privilege one place in a relation, that of the operand, which by convention we can take to be the first. Then we may take the conjunction (and sum) of operators to identify their first places. So, for instance, the conjunction of Rxy and Sxy is the triadic Rxy & Sxz, which is the same as Sxy & Rxz. Directionalism is then required to ensure, for example, that we can distinguish having a lichen as a part from having a henlich as a part. The magician’s spell was just broken using Operator Theory and Directionalism. I now argue that it cannot be broken, if we take world-structures to be structural properties in the strong or intermediate senses. Porky the Pig concludes each episode of Looney Tunes by saying “That’s all folks!”. The problem with structural properties in the strong sense is the Porky clause that further proplations are absent. Suppose we say that such putative structural properties depend on the various uninstantiated proplations such as being of spin 1/3. Then it is not these properties that explain the absence but their lack of instantiation. Hence the proposed dependence is magical. The same charge of magic holds for intermediate structural properties, provided we reject Finitism. For in that case, they require the relation of infinite summation as a constituent. To avoid Infinitary Simple Relations, we must analyse it. In classical mereology the sum of some things, the xx, is treated as their fusion, namely the z such that for all y, z overlaps y if and only if y overlaps one or more of the xx (cf. Lewis 1991: 73). Hence the infinite sum depends partly on the absence of further overlappers. To say it depends only on its summands is therefore magical. To be sure, the sum supervenes on the summands but Porky’s magic is a confusion of supervenience with dependence.

27.9

Strong Platonism

If they are not to multiply fundamental categories, WASPers should suppose either: (1) that there are no substances (and hence no material objects); (2) that substances are not a 311

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fundamental category; or (3) that Strong Platonism is false because all proplations, including the uninstantiated ones, depend on substances. The denial that there are substances is a sceptical view I ignore. The denial that substances are fundamental is a central tenet of module trope theory, in which they are identified with bundles of tropes. It is more problematic, however, for realists about either modifier tropes or universals. Bertrand Russell at one stage took substances to depend on proplations by being bundles of properties (1940: ch. 6). Those that form a bundle are said to be compresent. It is not clear how asserting compresence differs from saying the conjunction has an instance. Moreover, as Armstrong points out, the Bundle theory implies the strong version of the Identity of Indiscernibles that no two objects share the same nonrelational properties (Armstrong 1978a: 91–97). The only plausible alternative to the Bundle Theory is for Strong Platonists to take the fundamental language Q to have no names and to have atomic predicates corresponding to fundamental universals. Then we may interpret the existential quantifier as instantiation and say that the substances depend for their existence on various properties and relations being instantiated. This may be used to defend Strong Platonism about universals, but Ockhamists cannot use it to defend Strong Platonism about modifier tropes. For it would require the ideology to have infinitely many predicates, because there are infinitely many simple tropes. This leaves the third Ockhamist response, the idea that uninstantiated structural properties depend for their existence on actual substances, and hence, although Weak Platonism is true, Strong Platonism is false. If the only uninstantiated proplations were conjunctions of instantiated ones, then this would be straightforward. But there is a serious problem due to structural properties whose constituents have instances but are not itself instantiated, such as being CH5. Because the composition is not mereological, the structural property does not depend wholly on its constituents, and because it is not instantiated it does not depend on an instance. In addition, it requires the thesis that simple uninstantiated modifier tropes can only depend on substances via the instantiated ones that exactly resemble them. I leave readers to decide whether that thesis is magic, but note the consequence that it leads to Absolute Infinite Duplication. For if there are only some cardinal number of them, then, by Parity, some larger cardinal of them should exist, because if they did exist, then they would likewise be necessitated by the instantiated tropes. Hence, like the second response, the third one fails to defend Trope-WASP from Ockham’s Razor. At this stage, we might conclude that Trope-WASPers should settle for there being two fundamental categories. So, I now consider alien proplations, which might force all WASPers and many other realists about proplations to accept Strong Platonism, and hence infer that Trope-WASP requires two fundamental categories. By an alien proplation I mean one that is neither instantiated nor analysable in terms of instantiated ones.12 (Hence, even if uninstantiated structural properties fail to depend on their constituents, they are not alien unless they have an alien constituent.) Plausible examples of alien proplations are those emergent properties that depend on a combination of structural properties with non-actual laws of nature. Consider, for instance, alien thermodynamic properties. The temperature of a well-mixed gas depends both on the kinetic energy per degree of freedom and the actual laws of nature. The kinetic energy depends not just on the velocity but on the mass, and there is no (natural) thermodynamic property that depends in much the same way on the mean velocity of molecules independently of their mass. But given different laws there 312

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might well be. Call it thermocrasia. Now, we might attempt to analyse both temperature and thermocrasia in terms of the properties of, and relations between, molecules, together with the laws of nature. Such analyses fail because in both cases there is a range of laws that could be considered, some classical, some quantum. Since the laws on which thermocrasia depends are non-actual, thermocrasia is alien. Alien properties seem to establish Strong Platonism and hence defeat Trope-WASP. Their existence follows from the thesis that proplations are non-contingent and hence, by the principle that the possibly necessarily true is true, the possibility of these alien properties implies their existence. This argument could be rebutted either by insisting that many modifier tropes are contingent or by adherence to Modal Realism – or at least to realism about enough worlds to ensure there are no alien properties (see Miller 2001; see also Wilson 2020).

27.10

Conclusions

WASP comes in two versions, Uni-WASP and Trope-WASP. I have argued that: 1 2 3 4

WASP combined with Transworld identity requires Impurity. WASP requires not only Operator Theory but also Directionalism. Uni-WASP requires Finitism. Trope-WASP is open to Ockhamist objections. At best, it requires two fundamental categories. 5 Alien possibilities show that WASPers should accept Strong Platonism, and hence reject Trope-WASP as contra-Ockham.

Notes 1 Wx & Ux is a proper conjunction unless Wx & Ux is the same property as Wx itself. 2 See also Rosen (1990). See Nolan (2022) for some problems. 3 We can coherently rely on the Axiom of Choice or, alternatively, coherently suppose Solovay’s Axiom that all sets are measurable. If we assume that mathematical truths are non-contingent, then either the Axiom of Choice worlds or the Solovay worlds are impossible fictions. 4 In the case of a world that is the sum of island universes, there are parts whose only relation is disjunction. 5 For the history of this position, see Maurin (2023). 6 If we held that ordinary objects had thisnesses (haecceities) which were themselves module tropes, then the analogue of an uninstantiated trope would be a trope that was not united with a thisness. This would result in a module trope variant of WASP. The problems with the modifier-trope version of WASP would still occur, so I shall not discuss it separately. 7 I understand this to be Kris McDaniel’s thesis MRO2 ( 2006: 319–321). McDaniel treats this as a version of Modal Realism, which I find perplexing. Unfortunately, space does not permit further engagement with McDaniel (2006). 8 Chad Carmichael argues that some universals are Platonic by which he means capable of existing without having any spatiotemporal location (see Chapter 11, this volume). Pure uninstantiated universals would be Platonic in this sense. 9 This is a minor departure from Quine, who considers the ontology to be what we quantify over in Q. 10 Lewis (1986a: 30) raises the problem of infinite complexity on the assumption that there might be no simple particulars. My version does not require this.

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Peter Forrest 11 Lewis criticises Armstrong’s idea that universals are abstracted from particulars (1986a: 35–36). No doubt abstraction implies dependence, but here I am considering dependence more widely. 12 The term “alien” in this context is due to Lewis, but my usage is slightly different ( Lewis 1986b: 91–92).

References Armstrong, D.M. (1978a) Universals and Scientific Realism I: Nominalism and Realism. Cambridge: Cambridge University Press. Armstrong, D.M. (1978b) Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press. Armstrong, D.M. (1989) A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press. Armstrong, D.M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Campbell, K. (1990) Abstract Particulars. Oxford: Basil Blackwell. Fine, K. (2000) Neutral Relations. Philosophical Review 109(1): 1–33. Fine, K. (2007) Response to MacBride. Dialectica 61(1): 57–62. Forrest, P. (1986) Ways Worlds Could Be. Australasian Journal of Philosophy 64(1): 15–24. Forrest, P. (2006) The Operator Theory of Instantiation. Australasian Journal of Philosophy 84(2): 213–228. Forrest, P. (2018) A Speculative Solution to the Instantiation and Structure Problems for Universals. American Philosophical Quarterly 55(2): 141–152. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986a) Against Structural Universals. Australasian Journal of Philosophy 64(1): 25–46. Lewis, D. (1986b) On the Plurality of Worlds. Oxford: Basil Blackwell. Lewis, D. (1991) Parts of Classes. Oxford: Basil Blackwell. Longenecker M. (2022) Dualism about Possible Worlds. Erkenntnis 87(1): 17–33. MacBride, F. (2007) Neutral Relations Revisited. Dialectica 61(1): 25–56. Maurin, A.-S. (2023) Tropes. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/archives/spr2023/entries/tropes/>. McDaniel, K. (2006) Modal Realisms. Philosophical Perspectives 20: 303–330. Menzel, C. (2021) Possible Worlds. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/archives/fall2021/entries/possible-worlds/> Miller, R.B. (2001) Moderate Modal Realism. Philosophia 28(1-4): 3–38. Nolan, D. (2022) Modal Fictionalism. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/archives/spr2022/entries/fictionalism-modal/> Quine, W.V. (1951) Ontology and Ideology. Philosophical Studies 2(1): 11–13. Quine, W.V. (2011[1948]) On What There Is. In Talisse, R.B. and Aikin, S.F. (eds.) The Pragmatist Reader: From Peirce Though the Present. Princeton, NJ: Princeton University Press: 221–233. Rosen, G. (1990) Modal Fictionalism. Mind 99(395): 327–354. Russell, B. (1940) An Inquiry into Meaning and Truth. London: Allen and Unwin. Stalnaker, R. (1976) Possible Worlds. Noûs 10(1): 65–75. Williams, D.C. (1953) On the Elements of Being: II. Review of Metaphysics 7(2): 171–192. Reprinted in (2018) A.R.J. Fisher (ed.) The Elements and Patterns of Being: Essays in Metaphysics. Oxford: Oxford University Press: 24–50. Wilson, A. (2020) The Nature of Contingency: Quantum Physics as Modal Realism. Oxford: Oxford University Press.

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28 POWERS, POTENTIALITY, AND MODALITY Barbara Vetter

28.1

Introduction

According to David Lewis, we can understand properties (at least in some sense of ‘property’) in terms of possibilities, more precisely, as sets of possible individuals (Lewis 1986a: 50–69, see also Lewis 1983). On a different approach, we can understand modality (possibility and necessity) in terms of properties. This chapter is dedicated to the latter kind of project, which shares with the Lewisian approach merely the persuasion that there is some intimate connection between properties and modality, but reverses the order of explanation. (See Allen 2017 for a detailed comparison between the two projects.) While there are different ways of accounting for modality in terms of properties (see, e.g., Chapter 27, this volume), my focus here will be on dispositionalist theories, which account for modality in terms of dispositional properties or powers (I use the two terms interchangeably here; for more on dispositions, see Chapter 24, this volume). Motivations for such views come from two sides. On the property side, dispositionalists have argued that our scientific understanding of the world gives us reasons to adopt the view that many or all of the properties that play a role in science are powers (see Bird 2007; Ellis and Lierse 1994; Ellis 2001; Shoemaker 1980; Shoemaker 1998); and once this explanatory resource is at our disposal, we might as well make use of it in a theory of modality. On the modality side, dispositionalism provides an account of modality that is hardcore actualist (Contessa 2009; see also Vetter 2011): it locates the grounds of modal facts entirely in the actual world and has no need to appeal to merely possible worlds. Much of contemporary metaphysics has been shaped by Lewis’s credo of ‘Humean supervenience’. In negative terms, Humean supervenience is the denial of necessary connections between distinct existences (see Wilson 2010 for a detailed discussion); positively put, it is the thesis that the world consists of ‘a vast mosaic of local matters of particular fact, just one little thing and then another. … All else supervenes on that’ (Lewis 1986b: ix f.). Dispositionalism, on a contrary, is a species of anti-Humean metaphysics, which holds that our world is a deeply connected place, and locates these connections in properties. Dispositionalist views come in many varieties. In Section 28.2, I outline a set of questions whose answers determine the shape of a dispositionalist theory. Section 28.3

DOI: 10.4324/9781003246077-35

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introduces, as representative examples, two versions of dispositionalism that give different answers to those questions. In the remaining two Sections, 28.4 and 28.5, I discuss problems that are shared by dispositionalist theories regardless of these differences.

28.2 Questions If we want to account for modality in terms of properties, there are three groups of questions: (1) which modality do we account for; (2) in terms of what kinds of properties; and (3) what form is the ‘account’ to take?

28.2.1

Which Modality?

It will be helpful to use a distinction from the semantics of modal terms, between the force and flavor of modals. Modality comes in different forces, the weaker force being that of possibility (what can happen) and the stronger that of necessity (what must happen); some more complicated cases such as the counterfactual conditional (what would happen if …) may or may not be subsumed under them. Modality also comes in different flavors (see Kratzer 1977). Epistemic modality concerns what must or can be the case given what is known; deontic modality concerns what must or can happen given certain rules and norms. The flavor of interest to us here is objective, sometimes also called dynamic or circumstantial, modality: what must or can be the case given how things are. Objective modality appears to allow for further differentiation, such as practical, nomological, or metaphysical. The kinds of modality philosophers have been trying to account for in terms of properties are nomological and metaphysical modality. Nomological modality is the kind of modality associated with laws of nature, such as the necessity that objects with like charges repel each other. Metaphysical modality is the modality typically at stake in philosophical debates and is often characterized as the ‘broadest’ or ‘absolute’ type of modality. Among the dispostiionalist accounts of modality, some start with possibility (Borghini and Williams 2008; Vetter 2015), some with necessity (Bird 2007; Ellis and Lierse 1994; Ellis 2001), and some with counterfactuals (Bird 2007 again and Jacobs 2010). These different starting points, however, do not indicate a difference in scope: necessity and possibility are interdefinable, so giving an account of one automatically yields an account of the other, and counterfactuals too are systematically related to possibility and necessity. But accounts also differ in terms of the flavor of modality that they aim to account for: metaphysical (Borghini and Williams 2008; Jacobs 2010; Vetter 2015), nomological (Bird 2007; Ellis and Lierse 1994; Ellis 2001), or a specific flavor called ‘dispositional’ (Anjum and Mumford 2018).

28.2.2

Which Properties?

We are focusing on accounts that begin with powers in the widest sense: properties that can manifest; that are imbued with an irreducibly modal character; that concern what their bearers can, must, or would do. This leaves open a great deal of detail. First, how are we to understand the modal character of powers or dispositions? According to orthodoxy, they come with a pair of individuating conditions, a stimulus and a manifestation, such that bearers of the disposition would exhibit the manifestation when subject to the stimulus if nothing interferes. Thus fragility is the disposition to break (manifestation) when struck (stimulus), and fragile things would break when struck and 316

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nothing interferes. (Some expressions of the orthodox view can be found in Bird 2007; Martin 1994; and Molnar 2003.) Alternatively (see Aimar 2019; Vetter 2014), dispositions or powers have been conceived as potentialities, individuated only by a manifestation (and the strength of the disposition), such that bearers of the disposition can exhibit that manifestation (more or less easily). Thus fragility is the disposition to break, and fragile things are those that can break (sufficiently easily). Second, what is the ontology of powers? They have been taken to be Platonic universals, existing independently of their instances (Bird 2007: 15–18; Tugby 2013); roughly Aristotelian universals whose existence depends on their (at least potential) instantiation (Vetter 2015: 269–273); tropes (Heil 2012; Molnar 2003; see Chapter 19, this volume); or even no reified properties at all, yielding a nominalist version of dispositionalism (Vogt 2022; Whittle 2009). Another issue of ontology concerns the status of the properties that are invoked in an account of modality. Some appeal only to sparse, natural, and even fundamental properties in their account of modality (see especially Bird 2007); some allow for less-than-fundamental, but not gerrymandered, properties (Anjum and Mumford 2018; Bird 2018); and maximally liberal views allow abundant properties into their account (see Vetter 2015, Vetter 2020).

28.2.3

What Form of Account?

In accounting for modality in terms of properties, we can formulate a reductive definition of the form: ‘it is metaphysically/nomologically possible/necessary that p iff … ’. This is perhaps the most straightforward approach, and we will see it at work in Section 28.3. A different approach in metaphysics has been to identify, not reductive definitions of phenomena to be accounted for, but truthmakers for the sentences expressing them. On this approach, we are looking not primarily for necessary and sufficient conditions, but for the kinds of entities that make true modal statements; and we can find those truthmakers, in every case, in powers (Borghini and Williams 2008; Jacobs 2010). A third approach that has recently gained some currency takes modal facts to be distinct from but grounded in properties. We will return to issues about grounding in Section 28.4. Dispositionalist theories, then, account for metaphysical or nomological modality; starting with possibility, necessity, or counterfactual conditionals; in terms of properties that are characterized in terms of stimulus and manifestation or manifestation alone; Platonist or Aristotelian universals, tropes, or even nominalistically construed, and more or less sparse or abundant; by either reducing the former to the latter, providing truthmakers for the corresponding statements, or making grounding claims. In the next section, we will look at two accounts from the dispositionalist literature that take different choices on most of the questions that have been listed here. We will see how those different answers are connected to each other, and how they lead to some issues that are specific to these combinations of answers.

28.3

Two Theories

In this section, I outline two different dispositionalist views. The first accounts for nomological modality, starting with counterfactuals and necessity, in terms of sparse, stimulus-manifestation dispositions tentatively taken to be Platonic universals. The second accounts for metaphysical modality, starting with possibility, in terms of abundant 317

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potentialities tentatively taken to be Aristotelian universals. Both views proceed by reductive definition.

28.3.1 Dispositional Essentialism Dispositional essentialism (DE) begins with the claim that ‘[a]t least some sparse, fundamental properties have dispositional essences’ (Bird 2007: 45). Electric charge (a popular toy example), for instance, is associated with certain dispositions: the disposition to attract positively charged objects, and to repel negatively charged ones, in ways that correspond precisely to the other object’s charge and distance, as formulated in Coulomb’s Law. According to DE, this is more than association: electric charge, by its very nature, is the disposition to attract positively charged objects and repel negatively charged objects, in this particular way. The second core claim of DE is that these dispositional essences are the source of nomological necessity: the laws are ‘those regularities whose truth is guaranteed by the essentially dispositional nature of one or more of the constituent properties’ (Bird 2007: 47). Thus, to stick with our example, Coulomb’s Law is a law because its truth is guaranteed by the essence of charge. DE accounts for nomological necessity, the modality associated with laws of nature. Given that it derives this necessity from the essences of properties, it yields the result that the laws are indeed not only nomologically, but metaphysically necessary, and in this sense collapses the nomological necessities into (a subset of) the metaphysical necessities. Nevertheless, what it is an account of is the modality associated with laws, and so we will continue to treat it as an account of nomological necessity. It is part of the dispositional essentialist project to rehabilitate the ‘necessary connections’ in nature that have been shunned by Humeans (see Section 28.1). According to DE, our world abounds in nomologically necessary connections, and it is essentially dispositional properties that give rise to them. It is important for the dispositional essentialist project, then, that those properties really do the connecting work needed for non-Humean laws. So it is unsurprising that DE starts with a conception of dispositions that conforms to the standard model where a disposition links a stimulus condition (being struck, or being in the vicinity of a negative charge) to a manifestation (breaking, or exerting a repulsive force). Given its focus on laws of nature more generally, DE naturally focusses on those properties that play a role in those laws. In Alexander Bird (2007), the focus is on the fundamental properties (of physics) alone. Others (Bird 2018; Ellis 2001) apply DE to sparse or natural properties as we find them in biology, chemistry, and so on. Still, there is no room for mere abundant properties that have no scientific role to play. In fact, DE does best to exclude that there are abundant properties with dispositional essences, for else it would be difficult to tell the difference between the laws of nature and the more accidental generalizations that those dispositions would give rise to. Finally, dispositional essentialism makes a crucial appeal to the essences of properties. Prima facie, this commits it to some form of realism about the bearers of those essences. Dispositional essentialists have indeed tended to prefer an ontology of Platonist universals or tropes, though Lisa Vogt (2022) has recently argued that DE is compatible even with a nominalist approach, as long as it makes use of some resources of recent debates on grounding and essence. DE is an attractive and explanatorily powerful account of the laws of nature; but it is not, of course, without its problems. Some have argued that it collapses into one or another 318

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of its competitors (Barker 2013; see also Barker and Smart 2012; Tugby 2012). Others object to its assimilation of nomological to metaphysical necessities (Lange 2009), or argue that DE has problems accounting for certain types of laws, such as functional laws (French 2014; Vetter 2012). But we will set these worries aside for now, and turn to another dispositionalist theory.

28.3.2 Potentialism Potentialism accounts for metaphysical possibility in terms of potentialities: it is metaphysically possible that p just in case ‘something has, had, or will have an iterated potentiality for it to be the case that p’ (Vetter 2015: 199; for a historical predecessor, see Fisher 2022). Generalization over times is needed since potentialities, being properties, are possessed at times and can be lost or gained (a child, when growing up, loses the potentiality to fit through some small openings, but gains many others), while metaphysical modality is insensitive to changes over time. Iterated potentialities are potentialities whose manifestation consists in something having a potentiality; thus liquid water, while lacking the potentiality to break, can be frozen to acquire that potentiality, and accordingly has an iterated potentiality to break. Iterated potentiality helps account for some more remote possibilities, such as the possibility that my granddaughter (who, as yet, does not exist) be a painter (Vetter 2015: 201). Necessity can be defined as the dual of possibility: it is metaphysically necessary that p iff nothing has, had, or will have a potentiality for it to be the case that not-p. For potentialism, powers are potentialities, individuated only by their manifestation. This is not strictly necessary for the account of modality, but it is a natural fit with the focus on possibility as the modality to be accounted for. If we thought of powers along stimulus-manifestation lines, it might seem more promising to start with an account of counterfactual conditionals and derive other modal claims from them (as in Jacobs 2010). Metaphysical necessity does not appear to be a suitable starting point for a powers theorist: powers just don’t yield enough necessities (see Schrenk 2010). Since potentialism is phrased as a reductive definition, it requires that for every possibility, there is a corresponding potentiality. (It does not require that distinct possibilities always correspond to distinct potentialities. One potentiality may give rise to many possibilities.) This makes an abundant view of properties a natural fit for potentialism. Consider the possibility that I am in Berlin or I am in Gothenburg. By potentialism, this entails that something – presumably I – have an iterated potentiality with a disjunctive manifestation condition: the potentiality to be-in-Berlin-or-be-in-Gothenburg. Perhaps that potentiality can be identified with something a little less strange-looking. But the easiest route for the potentialist is to embrace a liberal view of potentiality and be done with it. (Alternatively, the potentialist can turn to truthmaking instead of reductive definition and claim merely that for every true possibility claim there is some combination of potentialities that makes it true.) Finally, note that potentialism as formulated above accounts for possibilities in terms of instantiated properties. Objects are as central as properties – in fact, potentialism is intended to also work in nominalist terms (Vetter 2015: 29; but see Giannini and Tugby 2020). However, there are alternative versions of potentialism that define possibility in terms not of instantiation, but the existence of properties (Borghini and Williams 2008; Yates 2015), leading to a dialectic similar to what we saw for DE above. Potentialism provides an attractively actualist and down-to-earth view of metaphysical modality, but of course it, too, is not without its problems. Being focussed on de re 319

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possibility, it has been argued to have problems with both necessity (Yates 2015; Yates 2020; see also Vetter 2018) and with de dicto modality (Wang 2015); and since it bases all modality on the potentialities of actually existing objects, its account of possibilities for the non-existence of those very objects has been put into question (Leech 2017; see also Giannini 2020; Kimpton-Nye 2018). In what follows, however, we will focus on concerns that are shared by any dispositional theory of (any) modality.

28.4 Problems of Circularity On the views discussed here, powers are the metaphysical underpinning of modal facts; and powers are properties that are imbued with an irreducibly modal character. In short, modal properties give rise to modality. This has a ring of circularity to it; let us spell it out in some more detail. (The problem was, to my knowledge, first raised against DE by Jaag 2014, whose presentation I roughly follow. It is further discussed in Coates 2020; Kimpton-Nye 2021; Tugby 2021.) Both DE and potentialism account for modal facts in terms of properties. According to DE, what makes a regularity a law, what endows it with nomological necessity, is the dispositional nature of the properties involved; according to potentialism, metaphysical possibilities are nothing but a certain generalization over the potentialities of objects, and in this way derived from potentialities. Either way, we have an ordering of priority: properties are prior, in the order of explanation, to modality. Now let us look at powers. On both views, powers are essentially modal: a power’s modal profile – what an object would or can do in virtue of having the property – is essential to the power. Essentiality, too, imposes an order of priority: if A is essential to B, then B essentially depends on A, for B could not be what it is without A (see Fine 1995). Since (the relevant kind of) modality is essential to powers, powers essentially depend on (this kind of) modality. So in at least one sense, the essential-dependence sense, the modal facts are prior to the properties. Now we have what looks like a circle: properties are prior to modality (because modality derives from them), but modality is prior to properties (because properties essentially depend on modality). Cutting out the middleman, properties, we seem to have accounted for modality in terms of modality. There are a number of strategies for responding to this circularity worry. One strategy is to simply revise the theory: if properties are prior to modality, then it cannot be that modality is also prior to properties. And if the claim that properties are essentially modal entails that modality is prior to properties, then that claim must be rejected. This leads us into grounding theories of powers, which have become increasingly popular in the recent literature (see Kimpton-Nye 2021; Tugby 2021, 2022): the view that properties, while not themselves essentially modal, ground and thereby necessitate modal facts. How do they do that? They just do: this is a primitive fact, one which we are entitled to stipulate because of its explanatory powers. In this way, problems of circularity lead powers theorists to adopt a view of properties that is closest to (a grounding-based version of) the powerful qualities view. Another strategy tries to uphold both of the claims that seemed to lead into a circle, but disambiguate them so as to avoid circularity. One target for disambiguation is the two uses of ‘modality’ in the problematic statements.1 We saw above that distinguishing different 320

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flavors of modality is not a promising strategy. But the powers theorist has other distinctions at her disposal (see Vetter 2015: 5). In particular, she can distinguish between the localized modality of a power, a property that depends on how things stand with one particular object, and the non-localized modalities that philosophers have often focused on: possibility and necessity. The dispositionalist’s claim, then, is not that modality quite generally reduces to properties which are not themselves modal. It is rather that nonlocalized modalities, possibility and necessity, reduce to the localized modality of potentiality. Thus the circle is avoided: non-localized modality derives from properties; properties essentially involve localized modality. Circularity, then, can be avoided, but avoiding it comes at a price. Grounding dispositionalism has the price of giving up the idea of full-fledged powers and having to stipulate a primitive grounding link between non-modal properties and modal facts. Localization avoids it by stipulating a special kind of modality, localized modality, and giving up the idea of reducing the modal to the non-modal. Either price may well be worth paying, and each provides an interesting new way of looking at powers.

28.5

Problems of Locality

The localization strategy in the previous section appealed to an important feature of powers: as modal properties, they come with a localized kind of modality, in the sense that they depend, typically, on how things stand with a given object, not on how things stand with the world in general.2 The modal facts that are to be accounted for appear to lack that kind of localization. The nomological necessity of a law concerns how things must be anywhere in the world; metaphysical possibilities concern not just how this or that thing, but how things generally could have turned out. The dispositionalist claim is precisely that the non-localized modalities are to be accounted for in terms of localized ones. However, there are some problems in getting from the localized to the non-localized. One worry concerns modal facts that are so global that it seems difficult to find a localized basis for them in powers of objects. For DE, the objection concerns conservation laws and symmetries (see Livanios 2010), which seem to have a more general status, governing not this property or that but how the world develops quite generally. For potentialism, an analogous worry concerns how it might account for such global possibilities as the possibility that the laws of nature should have been different, or that there should always have been different objects than there actually are. It seems that no properties of any actual objects give rise to such possibilities. The dispositionalist has two general strategies for responding to such worries. One strategy is to argue that there are after all powers of the right kind to give rise to such global modal facts. In both cases, it will be tempting to think of them as powers of the world, as opposed to any particular objects in it (see Bigelow et al. 1992; Vetter 2015: 257–267). A second strategy is to deny the alleged modal fact (suggested in Bird 2007: 214). For potentialism, this may mean that the scope of metaphysical possibilities is narrower than philosophers have been prone to think; for DE, it may involve some revisionism with respect to scientific practice, making symmetry principles mere ‘pseudo-laws’ (Bird 2007: 214; see also Livanios 2010: 304). A second type of worry can be described, with an apt phrase of Neil Williams (2010), as ‘problems of fit’. We assume that there is a coherent set of possibilities and necessities, be they nomological or metaphysical; how is that coherent set produced by the many different 321

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and intrinsic powers that objects have? Why should we expect that the essences of the various sparse properties (on DE) combine into a coherent set of laws; or that the various potentialities (on potentialism) combine into a coherent set of metaphysical possibilities? Let me spell out the problem for each view in turn. Given DE, the essences of properties give rise to nomological necessities. Nomological necessities generally concern more than one property, but each property has its own essence. How can it be that the different essences – say, that of mass and that of gravitational force – happen to fit together so as to produce a coherent set of laws? DE solves this problem by way of adopting a view of properties that connects their essences from the start: a form of structuralism (Hawthorne 2001; Shoemaker 1980) or ‘holism’ (Williams 2010). On this view, a power is no longer characterized just by its manifestation(s) or a set of stimulus and manifestation condition(s). Instead, there is a network of properties, each of which is individuated by its place within the network as a whole. If we think of properties in this structuralist or holist way, then it is no wonder they fit together: each property’s nature is, as it were, given by how it fits with the others. The nomological necessities are best thought of as derived not from the nature of this or that property, but from some portion of the overall network of powers. Some have objected that this leads into a regress, but defenders of DE have developed sophisticated ways of responding to that objection (see Bird 2007; Lowe 2010: ch. 6). According to potentialism, each potentiality that an object has gives rise to a possibility. Even so, potentialities of different objects ought to be coordinated to provide a coherent picture. If I had a potentiality to sing a duet with you, but you had no potentiality to sing a duet with me, what should we say about the possibility of our singing a duet together? In such cases, potentialism does provide some coordination (Vetter 2015: ch. 4). My potentiality to sing a duet with you, as well as your potentiality to sing a duet with me, are extrinsic: they depend on how things stand not just with the one object that has the potentiality (say, you), but also with other portions of the world (me). We can think of such extrinsic potentialities as arising from potentialities that are intrinsic to a collection of individuals (in this case, our shared potential to sing a duet together); and it is through this shared basis that our potentialities are coordinated. However, there is still a problem. For all that potentialism says, an object might have an intrinsic potentiality (say, to sing) and yet be necessarily prevented from manifesting it (say, by a necessarily existing and necessarily benign and omnipotent deity who cannot but recognize how much worse the world would be if I ever sang). Given the localized, intrinsic nature of the potentiality, such necessary prevention should not remove my potentiality to sing. And given the intrinsic potentiality, potentialism yields the possibility that I sing. But given the necessary prevention (which, we assume, nothing has any potentiality to remove), it should be impossible that I sing. (See Spencer 2017; Vetter and Busse 2022; Werner 2021; Werner 2022) Again, we are facing a problem of fit: how do individual, localized potentialities fit with each other and into the more general structure of the world, so as to provide a coherent set of possibilities? Potentialism may need to adjust its account of metaphysical modality to accommodate the latter’s more holistic nature (Werner 2022 makes one suggestion for how to do so). In general, the tension between the localized nature of powers, and the more global, holistic nature of the modalities to be accounted for may require some adjustments in a theory of dispositions. But there is hope that such adjustments are available.3

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Notes 1 Alternatively, we might disambiguate ‘priority’: perhaps essential dependence and explanatory priority may go in different directions without circularity (thanks to Alex Skiles and Lisa Vogt). 2 I am assuming, for simplicity, that powers are typically intrinsic properties of individual objects (see Chapter 8, this volume). In fact, there are powers possessed jointly by multiple objects, as well as extrinsic powers. See Contessa (2012); McKitrick (2003); Vetter (2015: ch. 4). 3 For helpful feedback and conversation, I thank Anna-Sofia Maurin, Anthony Fisher, and the participants of the Online Properties Workshop 16–18 May 2022, Lisa Vogt, and Lea Würtenberger. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Centre for Advanced Studies in the Humanities ‘Human Abilities’ (grant number 409272951).

References Aimar, S. (2019) Disposition Ascriptions. Philosophical Studies 176(7): 1667–1692. Allen, S. (2017) From Possibility to Properties? Or from Properties to Possibility? Philosophy 92(1): 21–49. Anjum, R.L. and Mumford, S. (2018) What Tends to Be: The Philosophy of Dispositional Modality. London/New York: Routledge. Barker, S. (2013) The Emperor’s New Metaphysics of Powers. Mind 122(487): 605–653. Barker, S. and Smart, B. (2012) The Ultimate Argument against Dispositional Monist Accounts of Laws. Analysis 72(4): 714–722. Bigelow, J., Ellis, B., and Lierse, C. (1992) The World as One of a Kind: Natural Necessity and Laws of Nature. British Journal for the Philosophy of Science 43(3): 371–388. Bird, A. (2007) Nature’s Metaphysics. Oxford: Oxford University Press. Bird, A. (2018) Fundamental Powers, Evolved Powers, and Mental Powers. Aristotelian Society Supplementary 92(1): 247–275. Borghini, A. and Williams, N.E. (2008) A Dispositional Theory of Possibility. Dialectica 62(1): 21–41. Coates, A. (2020) Tropes, Unmanifested Dispositions and Powerful Qualifies. Erkenntnis 87(5): 2143–2160. Contessa, G. (2009) Modal Truthmakers and Two Varieties of Actualism. Synthese 174(3): 341–353. Contessa, G. (2012) Do Extrinsic Dispositions Need Extrinsic Causal Bases? Philosophy and Phenomenological Research 84(3): 622–638. Ellis, B. (2001) Scientific Essentialism. Cambridge: Cambridge University Press. Ellis, B. and Lierse, C. (1994) Dispositional Essentialism. Australasian Journal of Philosophy 72(1): 27–45. Fine, K. (1995) Ontological Dependence. Proceedings of the Aristotelian Society 95: 269–289. Fisher, A.R.J. (2022) Grace A. de Laguna’s Theory of Universals: A Powers Ontology of Properties and Modality. Australasian Philosophical Review 6(1). French, S. (2014) The Structure of the World: Metaphysics and Representation. Oxford: Oxford University Press. Giannini, G. (2020) New Powers for Dispositionalism. Synthese 200(384): 1–30. Giannini, G. and Tugby, M. (2020) Potentiality: Actualism Minus Naturalism Equals Platonism. Philosophical Inquiries 1(8): 117–140. Hawthorne, J. (2001) Causal Structuralism. Philosophical Perspectives 15: 361–378. Heil, J. (2012) The Universe as We Find It. Oxford: Oxford University Press. Jaag, S. (2014) Dispositional Essentialism and the Grounding of Natural Modality. Philosophers’ Imprint 14(34): 1–21. Jacobs, J.D. (2010) A Powers Theory of Modality: Or, How I Learned to Stop Worrying and Reject Possible Worlds. Philosophical Studies 151(2): 227–248. Kimpton-Nye, S. (2018) Hardcore Actualism and Possible Non-Existence. Thought 7(2): 122–131. Kimpton-Nye, S. (2021) Reconsidering the Dispositional Essentialist Canon. Philosophical Studies 178(10): 3421–3441.

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Barbara Vetter Kratzer, A. (1977). What ‘Must’ and ‘Can’ Must and Can Mean. Linguistics and Philosophy 1(3): 337–355. Lange, M. (2009) Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature. Oxford: Oxford University Press. Leech, J. (2017) Review of Barbara Vetter, Potentiality. Analysis 77(2): 457–467. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986a). On the Plurality of Worlds. Oxford: Blackwell. Lewis, D. (1986b). Philosophical Papers, Volume II. Oxford: Oxford University Press. Livanios, V. (2010) Symmetries, Dispositions and Essences. Philosophical Studies 148(2): 295–305. Lowe, E.J. (2010) On the Individuation of Powers. In Marmodoro, A. (ed.) The Metaphysics of Powers: Their Grounding and Their Manifestation. London: Routledge: 8–26. Martin, C.B. (1994) Dispositions and Conditionals. Philosophical Quarterly 44(174): 1–8. McKitrick, J. (2003) A Case for Extrinsic Dispositions. Australasian Journal of Philosophy 81(2): 155–174. Molnar, G. (2003) Powers. A Study in Metaphysics. Oxford: Oxford University Press. Schrenk, M. (2010) The Powerlessness of Necessity. Noûs 44(4): 725–739. Shoemaker, S. (1980) Causality and Properties. In van Inwagen, P. (ed.) Time and Cause. Dordrecht: Reidel: 109–135. Shoemaker, S. (1998) Causal and Metaphysical Necessity. Pacific Philosophical Quarterly 79(1): 59–77. Spencer, J. (2017) Able to Do the Impossible. Mind 126(502): 466–497. Tugby, M. (2012) Rescuing Dispositionalism from the Ultimate Argument: Reply to Barker and Smart. Analysis 72(4): 723–731. Tugby, M. (2013) Platonic Dispositionalism. Mind 122(486): 451–480. Tugby, M. (2021) Grounding Theories of Powers. Synthese 198(12): 11187–11216. Tugby, M. (2022) Putting Properties First: A Platonic Metaphysics of Natural Modality. Oxford: Oxford University Press. Vetter, B. (2011) Recent Work: Modality without Possible Worlds. Analysis 71(4): 742–754. Vetter, B. (2012) Dispositional Essentialism and the Laws of Nature. In Bird, A., Ellis, B., and Sankey, H. (eds.) Properties, Powers and Structures: Issues in the Metaphysics of Realism. London: Routledge: 201–215. Vetter, B. (2014) Dispositions without Conditionals. Mind 123(489): 129–156. Vetter, B. (2015) Potentiality: From Dispositions to Modality. Oxford: Oxford University Press. Vetter, B. (2018) A Plenitude of Powers. Synthese 198(Suppl 6): 1365–1385. Vetter, B. (2020) Explanatory Dispositionalism: What the Anti-Humean Should Say. Synthese 199(1-2): 2051–2075. Vetter, B. and Busse, R. (2022) Modal Dispositionalism and Necessary Perfect Masks. Analysis 82(1): 84–94. Vogt, L. (2022) Nominalist Dispositional Essentialism. Synthese 200(2): 1–29. Wang, J. (2015) The Modal Limits of Dispositionalism. Noûs 49(3): 454–469. Werner, J. (2021) Plenitude and Necessarily Unmanifested Dispositions. Thought: A Journal of Philosophy 10(3): 169–177. Werner, J. (2022) Extended Dispositionalism and Determinism. Ergo 9: 623–644. Whittle, A. (2009) Causal Nominalism. In Handfield, T. (ed.) Dispositions and Causes. Oxford: Oxford University Press: 242–285. Williams, N.E. (2010) Puzzling Powers: The Problem of Fit. In Marmodoro, A. (ed.) The Metaphysics of Powers: Their Grounding and Their Manifestation. London: Routledge: 84–105. Wilson, J. (2010) What Hume’s Dictum, and Why Believe It? Philosophy and Phenomenological Research 80(3): 595–637. Yates, D. (2015) Dispositionalism and the Modal Operators. Philosophy and Phenomenological Research 91(2): 411–424. Yates, D. (2020) A Strange Kind of Power: Vetter on the Formal Adequacy of Dispositionalism. Philosophical Inquiries 8(1): 97–116.

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PART 7

Properties in Science

29 PROPERTIES AND NATURAL KINDS Alexander Bird

29.1

Introduction

Natural kinds and natural properties are intimately related. First, it is plausible that there is a natural property corresponding to each natural kind. Copper is a natural kind and there is a corresponding natural property: being (a sample of, composed of) copper. The red squirrel is a natural kind and it seems that there is a corresponding natural property that some animals possess: being a red squirrel. Let us call each such property the ‘corresponding property’ for a natural kind. Second, the possession of a natural kind seems to imply the possession of yet other properties. Things that are copper have the properties of being metallic and being able to conduct electricity. Red squirrels are mammals and eat nuts. Note that sometimes these implied properties are necessarily implied (necessarily copper items are also metallic), sometimes they are contingently and universally implied (all copper items conduct electricity, all red squirrels are less than five kilograms in weight) and sometimes they are probabilistically implied (a red squirrel probably inhabits a nest in a tree, and probably weighs less than one kilogram). Let us call these the ‘implied properties’ for a natural kind. Desiderata for a good theory of the metaphysics of natural kinds therefore include the following: (i) The theory should explain the relationship between a natural kind and its corresponding natural property (e.g., the relationship between the kind copper and the property being composed of copper). (ii) It should explain the relationship between a natural kind and its implied properties (e.g., the relationship between the kind copper and the property being metallic). (iii) It should shed light on the relationship between natural kinds and other elements of a general metaphysics of science, such as the laws of nature (e.g., the relationship between the kind copper and the law that copper conducts electricity). In this chapter, I look at two theories that aim to meet these desiderata. The first is E.J. Lowe’s theory (Lowe 2006), based on his four-category ontology, in which natural kinds

DOI: 10.4324/9781003246077-37

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form a fundamental category of entities. The second theory is that proposed by Katherine Hawley and me (Hawley and Bird 2011), in which natural kinds are a subset of the natural properties – they are non-accidental mereological complexes of properties.

29.2

E.J. Lowe’s Theory of Kinds and Attributes

In this section, we look at the place of natural kinds in E. J. Lowe’s (2006) ‘four-category ontology’. The latter is interesting because in aiming to meet the desiderata outlined above it takes natural kinds to form a fundamental category of entity that is distinct from the category of natural properties. The objections to this view will help motivate the contrasting view that natural kinds are a type of natural property, which I consider in the following section. Lowe’s ontology has four fundamental categories: (i) individual substances (things, objects), (ii) property relation‐instances (modes, tropes), (iii) substantial universals (kinds), and (iv) non‐substantial universals (attributes: properties and relations) (see Figure 29.1). Our interest is primarily in the third and fourth categories. Note that kinds and attributes/ properties form distinct fundamental categories, although both are universals. So kinds themselves are not any type of property. Kinds and attributes stand in the following relationship: kinds are characterized by attributes. ‘Copper conducts electricity’ is an example of this, since the kind, copper, is characterized by the attribute, conducting electricity. Furthermore, this relationship is the basic form of a law of nature. According to Lowe, laws of nature are the characterizations of kinds by attributes: copper conducts electricity. Individual objects instantiate kinds, while modes instantiate attributes. The relationship between kinds and attributes – the latter characterizes the former – is mirrored by the relationship between objects and modes. In a standard two-category ontology of particulars (objects, things) and universals (attributes: properties, relations) there is one key relationship, usually called ‘instantiation’, but which Lowe calls ‘exemplification’. For Lowe, exemplification is not a fundamental relationship between the fundamental categories. Consider a red squirrel named Cyril. According to Lowe, the squirrel exemplifies the attribute of redness. This comes about in two ways. First way: there is a particular mode or trope of redness, the redness of this squirrel Cyril. Cyril’s redness mode is an instance of

kinds

characterized by

attributes

instantiated by

exemplified by

instantiated by

objects

characterized by

modes

Figure 29.1 Lowe’s Ontological Square with four categories.

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redness the attribute, and Cyril is characterized by his redness mode. So this manner of Cyril’s being red involves the bottom and right-hand connections in the ontological square. Second way: Cyril belongs to the kind Sciurus vulgaris. Since it is in the nature of the kind to be red, we can say that S. vulgaris is characterized by the attribute redness. (This is parallel to the fact that individual Cyril is characterized by his redness mode, but at the level of universals.) The kind (substantial universal) S. vulgaris is instantiated by the individual Cyril. (This is parallel to the fact that the attribute of redness is instantiated by the mode that is Cyril’s redness.) This account of Cyril’s redness involves the left and top sides of the square (see Schneider 2009 for a detailed and careful articulation of the Ontological Square). Lowe’s Ontological Square fulfils some of the desiderata we stated in the Introduction, by which an account of kinds and their relationship to properties should be judged. It articulates an account of the second of our two relations, the relation between a kind and its implied properties. The implied properties are attributes (non‐substantial universals, in Lowe’s terminology) and characterize the kinds. And we are thereby also given an account of the basic form of a law of nature, satisfying the third desideratum. The Ontological Square is less helpful when it comes to understanding the first desideratum, concerning the relationship between kinds and their corresponding properties: copper and being (a sample of, composed of) copper. One might suppose that the relationship is also the relationship of characterization between kind and attribute, hence: copper things are composed of copper. Or: copper is copper. On Lowe’s account that ought to be a law, but is in fact clearly a tautology. More of a problem is the concern that we have ontological redundancy. We have both a kind and the corresponding property: both belong to fundamental categories; neither is reducible to the other. Surely we do not need both the kind copper and the property of being copper to be fundamental. (Of course, scientifically neither is fundamental. But the problem is the same for scientifically fundamental kinds.) To avoid this redundancy, we can either (i) reduce the kind to the corresponding property (attribute) or (ii) reduce the corresponding property to the kind. To take the first of these options would be to eliminate the kind category from the Ontological Square – we would be halfway to returning to the traditional two-category ontology (represented by the diagonal of the Ontological Square). To implement the second option, we can make use of David Lewis’s (1983) distinction between sparse and abundant properties (see Chapter 4, this volume). The latter are defined by almost any predicate. If there are any entities that are abundant properties, they are sets, and so are found at the bottom left of the Ontological Square. Whereas sparse properties are that class of properties that contains the natural properties (or perhaps just the fundamental natural properties). Sparse properties seem to demand special ontological treatment – it is these that are the attributes (non‐substantial universals) in the Ontological Square. The proposal is, then, that being composed of copper is not a sparse property but an abundant one. There is therefore no attribute of being composed of copper. This would appear to resolve both the aforementioned problems. Since there is no attribute of being composed of copper, there is no worry about ‘copper things are composed of copper’ being a law of nature. And we do not have any redundancy, since the kind copper can do all the work. This, however, will not do, because we need some corresponding properties to be attributes, and so to be sparse. Take the kind mammal. There is a corresponding property, being a mammal (or: being mammalian). According to the proposal of the last paragraph, 329

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this is not a sparse property. However, consider: red squirrels are mammals (or: the red squirrel is a mammal). We already saw that this is an example of the top line of the Ontological Square, the characterization of a kind by an attribute. So for this law, or law‐like truth, we do need the property being a mammal to be an attribute and so sparse, not abundant. So the problem of redundancy returns – Lowe’s system seems to require us, at least in some cases, to have both the kind and its corresponding property as distinct and equally fundamental entities. There are also further problems with Lowe’s account of the laws of nature. While it seems to work for laws and lawlike statements such as ‘copper conducts electricity’ and ‘red squirrels are mammals’, it has difficulty with laws, such as the many laws of physics, that relate quantities, which are best understood as attributes, not as kinds (Bird 2011).

29.3

Kinds as Properties

I propose that the relationship between kinds and properties should not be seen as a relationship between entities of distinct categories. In at least some cases the properties corresponding to a kind must be sparse, natural properties. To avoid one or other of the kind and the corresponding kind property being a redundant entity, we should therefore get rid of the kind as a distinct and independent entity. This need not be eliminativism about kinds (especially as eliminativism does not sit well with essentialism about kinds). Rather kinds just are properties. So, for example, we do not need both the kind copper and the property being copper as distinct and independent entities; there is just the property being copper. Now we have an answer to the question posed in the first desideratum, about the relationship between kinds and properties, that concerning the corresponding kind properties. Kinds just are their corresponding kind properties. But we now do not have an answer (yet) to the question in the second desideratum, about the relationship between a kind and its implied properties. One might simply say that these are laws or lawlike relationships and therefore that the question should be answered by our best account of laws and lawlikeness. I think, however, that we can do better. We should first note that while mereology is typically applied to objects, there is no prima facie reason why it should not be applied also to properties, if those properties are genuine entities (Armstrong 1978: 33). Let us take it as given that natural properties are universals. Then given two universals, A and B, we can consider their sum or fusion, A+B. Let us say that there is such an entity and that it too is a universal. When it is present in some instance it is wholly present (that is the nature of universals) and so both A and B are present in that instance. So anything that instantiates the universal A+B also instantiates A and instantiates B. The fusion of two universals thus corresponds to the logical conjunction of the predicates denoting the universals (Hawley and Bird 2011). If we reject both nihilism and universalism but accept restricted composition regarding sums of universals, then in some possible cases of sums there really are entities that are the fusions of the constituent universals. These are genuine, complex universals that have simpler universals as parts. Peter van Inwagen’s (1990) special composition question asks those who advocate restricted composition regarding material objects, what is it that distinguishes cases where certain objects form some further object of which they are the parts from those cases where a collection of objects does not form such a whole. Similarly, 330

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for universals, we would like to have a principle of restricted composition that tells us when certain universals do form a complex universal. Quite what we should expect of a principle of restricted composition is controversial. Nonetheless, it is plausible that a principle of composition should reflect coherence among the parts of an object. That is, facts about one part should have implications regarding facts about some other parts. In a simple physical object, such as a pebble, facts about the location of one part have implications for the locations of other parts of the pebble. Whereas the sum of the pebble and the Eiffel Tower lacks such coherence since facts about the pebble and its parts have no implications for the Eiffel Tower or its parts. This, I think, is the appeal of the ‘fastenation’ view of the composition of physical objects (Markosian 1998: 223–227; van Inwagen 1990: 56–58). In the case of universals, I propose that coherence is a matter of correlations among them. For example, the possession of one universal by some object might imply the possession of some other universal, including the possession of a universal by some part of the particular. Or a set of universals might together imply the possession of several others. The implication might be probabilistic, so the possession of some universals makes the possession of other universals probable. So we can say that a set of universals is highly coherent when there are many highly probable implications among subsets of the set. According to this proposal, highly coherent sets of universals fuse to form an entity, one that is itself a universal.

29.3.1

Fundamental Kinds

Let us consider an example. The electron is a fundamental particle. Three properties are necessary and jointly sufficient to characterize the electron: unit negative elementary charge (qe = −1.6 × 10–19C), mass of 1/1,823 daltons (me = 9.11 × 10–31kg), and spin 1/2 (s = 1/2). There is a universal that is the fusion of the universals that are these three properties. We do not need a fourth property, being an electron, distinct from these. The property, being an electron, just is the fusion of these three properties. This fusion is instantiated in every electron, and so every electron also instantiates the parts of that fusion, viz. the universals of having unit negative elementary charge, having mass of 1/1823 daltons, and having spin 1/2. Given restricted composition, why should we think that there is such a universal as this fusion? But not, say, a fusion of the universals unit negative elementary charge, mass of 1/1,957 daltons, and spin 1/2 – that is, a fusion of the same charge and spin universals but a different mass universal? (Having mass of 1/1,957 daltons is a genuine mass universal – it is the mass of the charm quark.) For a start, there are lots of things instantiating the first combination of universals (all the electrons) but none instantiating the second combination. We can say more. Consider the determinable property, having negative charge, and let us assume that it is a universal. That something has this property raises the probability that it is an electron, but not by a great deal, since many things other than electrons are negatively charged. That is, having the negative charge universal does not raise the probability of having the mass of 1/1,823 daltons universal or the spin 1/2 universal to a significant value. On the other hand, that something has unit negative elementary charge makes it quite likely that it is an electron, since four kinds of entity – the three leptons (electron, muon, and tau), and the W− boson – have unit negative elementary charge. These particles have different masses, but the three leptons do all have spin 1/2. So the fact that something instantiates the unit negative elementary charge universal raises the probability that it instantiates the mass of 1/1,823 331

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daltons universal to quite a high value and raises the probability that it instantiates the spin 1/2 universal to a higher value still. If something instantiates both the unit negative elementary charge universal and the mass of 1/1,823 daltons universal, then it is certain that it also instantiates the spin 1/2 universal. Likewise, instantiating the mass of 1/1,823 daltons universal and the spin 1/2 universal raises to close to 1 the probability that it instantiates the unit negative elementary charge universal. The probability is close to 1 because positrons also have mass of 1/1,823 daltons and spin 1/2 but have positive elementary charge. As far as we are aware they are much rarer than electrons. I will discuss these probabilities in more detail later. While qe, me, and s are essential properties of the electron, in general, the properties fusing to form the property complex that is a natural kind may include accidental and contingent properties. One should not subscribe to mereological essentialism – a complex entity may have different parts in a different possible world, and this goes for complex universals as well as complex particulars. (This is potentially problematic if, like Lewis, one is a modal realist and allows the same universal to exist in more than one world. But see McDaniel (2004) and Hawley (2010) for responses.) In the case of the electron, it is unclear whether it possesses any sparse properties other than those essential ones just mentioned. For example, the magnetic moment of an electron is an important quantity. But its value is determined exactly by the essential properties plus the laws of nature. One might not regard it then as an additional property, especially if one thinks that the laws of nature are metaphysically necessary. On the other hand, if one thinks that the laws are contingent, then one might be inclined to regard the magnetic moment as an additional sparse property. In which case, it is a further, contingent part of the complex universal that is the electron kind. We can understand any natural kind as a complex that has sparse properties, universals, as its parts, including chemical and biological kinds (Hawley and Bird 2011). In such cases, those properties are not fundamental properties. That, however, is not inconsistent with their existence. For, as we have seen, there are non‐fundamental sparse properties that are universals – the electron kind is an example. That example is a case of a complex nonfundamental sparse property. Are there simple non‐fundamental sparse properties? That is unclear, but if there are emergent properties, they might be candidates.

29.3.2

Biological Kinds

Now let us now consider the kind, the red squirrel, S. vulgaris. This has many implied properties: the red squirrel is a mammal, it has a red coat with a cream or white underside. The red squirrel eats seeds and nuts, which it will also bury in caches. Red squirrels inhabit dreys and are non‐territorial. If we were to assume that these properties are sparse properties and so universals, then one might take the kind, S. vulgaris, to be the fusion of these (and other) properties. That, however, would not be quite right. For not all red squirrels have red coats – some will have grey coats in winter. Clearly, they are not always eating nuts and seeds. And so on. So the properties in question are typically dispositional properties. A red squirrel is disposed to have a red coat in certain conditions and is disposed to eat seeds and nuts, and so on. All squirrels are actually mammalian, not just dispositionally so. If we understand ‘mammalian’ as ‘belonging to the class Mammalia’, then this property, though essential to the kind S. vulgaris, is an extrinsic property of the squirrel. Biological taxa, for sexually 332

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reproducing organisms, are understood as clades, that is as kinds based on shared lineage. And so the complex universal (the kind S. vulgaris) has a part that is an extrinsic property/ universal (belonging to the class Mammalia).

29.3.3

Structural Kinds

I now consider a third kind of case, concerning those kinds where the structural relations among the parts are essential. On the view being discussed here, such kinds are universals. Universals whose nature concerns structural relations among the parts of their instances are structural universals (for discussion, see Armstrong 1978; Bigelow and Pargetter 1989; Fisher 2018; Hawley 2010; Lewis 1986). Methane is (essentially) the compound CH4 – that is, a sample of methane is made up of molecules of four hydrogen atoms bonded to a single carbon atom. It is natural then to think that the kind methane – the methane universal – is related somehow to the (probably complex) universals being a carbon atom and being a hydrogen atom. Could this relation also be parthood, as in the previous cases? If so, that would explain, as before, why wherever being a methane molecule is instantiated, so are being a carbon atom and being a hydrogen atom. (Note that in this case the latter universals are not instantiated in the whole of the object that instantiates being a methane molecule; rather they are instantiated in proper parts of that object.) Lewis (1986), however, rejects this idea on the ground that the combination of these universals does not uniquely determine the complex universal to be methane. Lewis subscribes to the principle of the uniqueness of composition: for any set of entities there is at most one complex entity whose parts are exactly those entities (van Inwagen 1990). The problem presented by methane is that exactly the same universals being a carbon atom and being a hydrogen atom that are supposed to be the parts of methane will be present in other hydrocarbon kinds – ethane, propane, butane, pentane, and so on. One might therefore add a further universal having parts arranged tetrahedrally. But even this will not be enough. Consider the compounds, chloromethane, dichloromethane, and trichloromethane. These all contain carbon, hydrogen, and chlorine arranged tetrahedrally, but are different kinds. Nonetheless, one does not have to subscribe to uniqueness of composition (Hawley 2010; Hawley and Bird 2011). After all, the same lump of clay and the statue it forms may be held to be distinct objects while having exactly the same proper parts. Likewise, there could be distinct complex universals composed of the same simple universals. If one were to demand uniqueness of composition, this is available anyway. The view I propose will include the implied natural properties in the complex universal, such as boiling points, density, characteristic chemical reactions, and such like. And these will distinguish between the different compounds with the same chemical constituents.

29.3.4 The Coherence of Universals Above I said that entities, including universals, might fuse when they have what I called ‘coherence’. Coherence enables one to make inferences about the parts from the whole and about the whole from the parts, and hence from some parts to other parts. In the case of a physical object, knowing where one part is located, for example, enables one to infer, at least roughly, where the other parts of the object are. This idea needs some fleshing out, in particular as it applies to universals. 333

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First, this coherence should be non‐accidental. Two properties might in fact be perfectly correlated in the actual world, but this is a mere coincidence. While one is in fact able to infer the presence of the one from the other, these inferences have no modal robustness. In very nearby worlds this correlation breaks down. In such a case there is no complex universal with these as parts. The rejection of such a complex universal is analogous to rejecting the claims of the contact view of composition for physical objects (van Inwagen 1990: 33–37). Fastenation, the view that the parts of a physical object are fastened together, provides some degree of modal robustness – if two things are fastened together, then changes in location of one part will typically mean changes in location of the other part. So, for two universals to fuse to form a conjunctive universal, their correlation, which need not be perfect, must nonetheless be non‐accidental. For example, in the case of the electron, that something possesses one of the essential properties raises the probability that it possesses the others. This is non‐accidental and is a consequence of the laws of quantum mechanics that underlie the standard model of particle physics. Second, the complex universals that are kinds should have boundaries. By a boundary, I mean that there should be (relatively) many things that possess the properties in the complex but fewer things possessing a set of nearby properties (in the actual and nearby possible worlds). For example, we can plot a histogram of the masses of the nuclei of atoms. These will fall into neat columns separated by a gap, each column corresponding to an isotope. While some theorists claim that natural kinds require sharp boundaries like this (Ellis 2001), that does not seem necessary. There can be intermediate cases between kinds, so long as these tend to be fewer in number than exemplary members of the kinds. There are gaps between kinds, but these are not empty. In our histogram, they are troughs. This is what we will find if we plot a histogram for properties of members of the squirrel genus Sciurus against properties such as body mass, coat colouring, and so on. Putting these two together, we can expect universals to cohere when, for non‐accidental reasons, objects will tend to instantiate those universals rather than nearby sets of similar properties. The instantiation of some subset of these cohering universals will make it likely that an object instantiates all the cohering universals, and rather more likely than that the object instantiates some similar but non‐cohering set of universals. This cohering of universals I take to be the correlate of Richard Boyd’s clustering of properties (Boyd 1999). The homeostatic processes underlying the clustering of properties in biological kinds I take to be one of the non‐accidental reasons why we find that the individuals in a domain distribute across the range of properties in the uneven way described (some combinations are highly populated, others less so). Such non-accidental reasons thereby explain why it is that some sets of properties cohere, but others do not. Just as the homeostatic property cluster view of kinds is consistent with both essentialism and its negation, this view of kinds as complex universals allows for essentialism but does not require it. It does not require it because the same complex universal may be made up of an entirely distinct (though typically very similar) set of universals in another possible world. We should reject mereological essentialism for universals as well as for particulars. Nonetheless, it could be that some members of the compounded set of universals are essential to the compound, just as having a part that is a cutting blade is essential to a penknife, even though it may or may not have parts that are other tools (bottle opener, hoof pick, etc.). Such properties will be those that are responsible for the cohesion of the universals. That a copper atom has 29 protons in its nucleus explains why copper has the other properties it does have. Without that universal, having atomic 334

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number 29, the other universals in the complex universal that is copper would not cohere.

29.4 Conclusion Natural kinds and natural properties are indeed intimately related: natural kinds are natural properties. They are complex natural properties (universals) composed of simpler properties, just as familiar physical objects are composed of simpler physical objects. Because universals are fully present wherever they are instantiated, whenever a natural kind is present, so are all its component properties, some of which may be dispositional, and some of which may be extrinsic. All things instantiating the kind copper thereby instantiate its component properties, such as being metallic, conducting electricity, being red in colour, and so on. When do simpler universals combine to form a natural kind? When they have sufficient coherence, which is to say that the presence of some of the properties implies or makes probable the presence of others. Coherence is vague, so it can be indeterminate whether a set of properties composes a natural kind. But physical objects are vague in this respect also. This account of natural kinds satisfies the desiderata set out at the beginning of this chapter. (i) It explains how a natural kind relates to its corresponding natural property. The relationship is identity: the kind copper is the property being copper. (ii) It explains how a natural kind relates to its implied properties. The latter are parts of the former: conducting electricity is a property that is part of the complex property (natural kind) copper. (iii) It sheds light on the relationship between natural kinds and other elements of a general metaphysics of science. Natural kinds do not underpin the laws of nature. Rather the relationship is the other way around. Laws and causal mechanisms explain why certain properties cohere (as in the homeostatic property cluster account of biological natural kinds) and so fuse to form natural kinds. It can also accommodate but does not require essentialism about natural kinds.

References Armstrong, D.M. (1978) Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press. Bigelow, J. and Pargetter, R. (1989) A Theory of Structural Universals. Australasian Journal of Philosophy 67(1): 1–11. Bird, A. (2011) Are Any Kinds Ontologically Fundamental? In Tahko, T. (ed.) Contemporary Aristotelian Metaphysics. Cambridge: Cambridge University Press: 94–104. Boyd, R.N. (1999) Homeostasis, Species, and Higher Taxa. In Wilson, R.A. (ed.) Species: New Interdisciplinary Essays. Cambridge, MA: MIT Press: 141–185. Ellis, B. (2001) Scientific Essentialism. Cambridge: Cambridge University Press. Fisher, A.R.J. (2018) Structural Universals. Philosophy Compass 13(10): e12518. Hawley, K. (2010) Mereology, Modality and Magic. Australasian Journal of Philosophy 88(1): 117–133. Hawley, K. and Bird, A. (2011) What Are Natural Kinds? Philosophical Perspectives 25: 205–221. Lewis, D.K. (1983) New Work for the Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. Lewis, D.K. (1986) Against Structural Universals. Australasian Journal of Philosophy 64(1): 25–46.

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Alexander Bird Lowe, E.J. (2006) The Four‐Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Oxford University Press. Markosian, N. (1998) Brutal Composition. Philosophical Studies 92(3): 211–249. McDaniel, K. (2004) Modal Realism with Overlap. Australasian Journal of Philosophy 82(1): 137–152. Schneider, L. (2009) The Logic of the Ontological Square. Studia Logica 91(1): 25–51. van Inwagen, P. (1990) Material Beings. Ithaca, NY: Cornell University Press.

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30 LAWS OF NATURE Tuomas E. Tahko

30.1

What are Laws of Nature?

Properties have an important role in specifying different views on laws of nature: virtually any position on laws will make some reference to properties, and some of the leading views even reduce laws to properties. This chapter will first outline what laws of nature are typically taken to be and then specify their connection to properties in more detail. We then move on to consider three different accounts of properties: natural, essential, and dispositional properties, and we shall see that different conceptions of properties also result in different views of the modal status of laws, such as the question of whether laws are metaphysically necessary or contingent. Finally, there are also important links specifically between properties, natural kinds, and laws of nature that deserve our attention. In scientific language, we continuously speak about laws of nature, but it is not immediately obvious what makes something a law. Some typical examples of laws of nature include Newton’s laws, Coulomb’s law, the ideal gas law (equation), and so on. At the highest level of generality, we could say that laws concern regularities, but it’s important to see that not all regularities are lawful or ‘law-like’. To see this, consider the following classic example: 1 All gold spheres are less than a mile in diameter. 2 All uranium spheres are less than a mile in diameter. In the case of (1), the regularity being expressed seems to be a mere contingent fact, whereas (2) could be considered to express or be based on a law of nature. So, what is the difference between genuine laws and mere contingent regularities? A possible starting point is that we can make predictions about the future based on laws, but that does not in itself provide a systematic way to distinguish between cases like (1) from cases like (2) because we often make predictions based on (rough) generalisations as well. For instance, the fact that I have had sandwiches for breakfast every day this week might lead one to predict (accurately) that I will have a sandwich for breakfast tomorrow, but this is hardly a lawlike regularity, even if I do have sandwiches for breakfast most mornings.

DOI: 10.4324/9781003246077-38

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A more promising starting point would be to find some way to connect laws with necessity. Indeed, nomological, natural, or physical necessity (all of these modal notions have been used synonymously) is generally defined in terms of laws of nature, so the connection between laws and modality is intimate. However, the basic question still remains unanswered: what is it to be a law? Here are some general approaches: 1 Dretske-Tooley-Armstrong (DTA) account based on relations between universals. 2 Mill-Ramsey-Lewis or ‘best systems’: the Humean approach. 3 Scientific/dispositional essentialism (e.g., Brian Ellis and Caroline Lierse, Alexander Bird, Anjan Chakravartty). 4 A powers or potentiality-based view (e.g., Heather Demarest, Samuel Kimpton-Nye, cf. also Barbara Vetter). 5 Anti-realism (e.g., Bas van Fraassen, Stephen Mumford). 6 Anti-reductionism/primitivism (e.g., Marc Lange, Tim Maudlin, cf. also ontic structural realism as developed by Steven French and James Ladyman). It will not be possible to do justice to all these views – and their treatment of properties – in this chapter, so I will mainly concentrate on the first three of these general approaches, with some reference to the fourth.1

30.2

All Fs are G

When thinking about the relationship between laws and properties, the Dretske-TooleyArmstrong (DTA) account is a very natural starting point, given that it is based on the idea that laws express relations between universal properties. I will illustrate the account through Fred Dretske’s classic paper ‘Laws of Nature’ (1977; see also Niiniluoto’s 1978 response to Dretske). Dretske starts by criticising the thought according to which laws are simply a set of universal generalisations. Formally, we may express this as follows: ∀x (Fx ⊃ Gx). In other words: all Fs are G. We may replace F and G with predicates like the ones in the following examples: • All metals conduct electricity. • All diamonds are hard. • All electrons attract positively charged particles. The thought is that if these generalisations are true, then they express laws. So, laws are generalisations from empirical data. We observe that this F is G, that F is G, and indeed that all examined Fs are G, which leads to the generalisation expressed above formally with the universal quantifier ‘∀’. The idea that Dretske questions is that we do not have to postulate a physical necessity between F and G – all we need is the fact that all Fs just are G. Compare: we do not confirm the analytically true statement ‘All bachelors are unmarried’ by investigating individual cases of the marital status of bachelors. This would of course support the truth of the claim, but not its modal status as necessary. So, the line of thought that this might be considered to support is that since we do examine individual cases of laws in order to confirm them, this suggests that there is no special modal force involved in laws.

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However, as should be clear from my naïve example featuring sandwiches, just the fact that all of my breakfasts consist of sandwiches does not make it a law. There is a broad consensus according to which laws cannot just be universal generalisations (for a more striking example, recall the gold vs. uranium sphere case). Compare: let us assume that ∀x (Fx ⊃ Gx). If we now substitute ‘F’ with some predicate ‘K’ that happens to be coextensive with ‘F’, we have ∀x (Kx ⊃ Gx). What does this entail? Well, according to Dretske, genuine laws are simply not compatible with these types of substitutions. The example he provides can be reconstructed as follow: 1 Diamonds have a refractive index of 2.419 (law). 2 ‘To be a diamond’ is coextensive with ‘is mined in kimberlite (a dark basic rock)’. 3 By substitution, it would follow that ‘things mined in kimberlite have a refractive index of 2.419’. We now see that the result in (3) cannot be a law since there are plenty of other things besides diamonds that we can mine in kimberlite. Accordingly, replacing the predicate with a coextensive one like in this example may lead to a change in the law status! It should now be clear that in order for the connection between two predicates to be a genuine law, something more is needed. This is exactly what Dretske proposes. He puts it famously: ‘F-ness ⟶ G-ness’, where he describes ‘⟶’ to be an extensional relation between the terms ‘F-ness’ and ‘G-ness’ (which we may understand as referring to properties). On this view, laws concern properties like length, mass, charge, spin, etc., and more precisely, they express relations between these properties. Dretske considers it an advantage that, on his formulation, we can replace the predicate ‘F’ with any term that refers to the same property. So, unlike with the earlier issue regarding coextensive predicates, we can safely substitute F and G with any term as long as they pick up the same property. Moreover, we can now explain the modal force of laws: the contingent relation between F and G produces the necessity of the phenomenon captured by the law. This F must be a G. Why? Because F-ness is linked to G-ness. One property ‘produces’ the other one. It’s worth noting here that, in Dretske’s picture, the modality in question is nomological or physical but not metaphysical necessity. Dretske compares laws of nature to the relationship between the President and the Congress: these relations are not necessary in a strong sense, but they nevertheless have modal strength. This is similar to David Armstrong’s (1983) view, who talks about nomic necessitation as opposed to metaphysical necessitation – in other words, the DTA account retains a level of (metaphysical) contingency regarding laws. Dretske concludes with the following famous passage, which nicely summarises the relevant view about the connection between properties and laws: I expect to hear charges of Platonism. They would be premature. I have not argued that there are universal properties. I have been concerned to establish something weaker, something conditional in nature: viz., universal properties exist, and there exists a definite relationship between these universal properties, if there are any laws of nature. If one prefers desert landscapes, prefers to keep one’s ontology respectably nominalistic, I can and do sympathize. I would merely point out that in such barren terrain there are no laws, nor is there anything that can be dressed up to look like a law. These are inflationary times, and the cost of nominalism has just gone up. (Dretske 1977: 267–268) 339

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Dretske is of course referring to the debate between Platonism and nominalism (about universal properties in particular).2 His conclusion is that in order to have laws we need universal properties and the relations between them – and these are not available to the nominalist. We should however acknowledge that one does not need to be a Platonist in order to believe in universal properties, as on certain Aristotelian views universal properties can be regarded as existing only when they are instantiated – this idea is also familiar from Armstrong’s (1989a: 75) famous principle of instantiation, which requires that any universal must be instantiated by some particular.3

30.3

Laws of Nature and Natural Properties

The approach to the relationship between laws and properties to be outlined in this section is best known from David Lewis’s work, but the ‘Humean’ approach that he advocated is now very popular. The central thought of this approach is that laws are a part of those true deductive systems which have the best combination of strength/simplicity/explanatory power.4 This view can quite easily accommodate the distinction between the generalisation that all gold spheres are less than a mile in diameter and the law-like nature of all uranium spheres being less than a mile in diameter. The thought here is that the latter fact would follow deductively from the axioms that are constitutive of the best system, but the former fact would not be among these axioms, nor entailed by them. So, the ‘law’ concerning gold spheres does not add any strength or explanatory power to our system, and instead only makes it more complicated. Hence, it should not be included (and so isn’t really a law). The theory has certain advantages, and variations of the Humean approach have been discussed extensively. A central motivation is that we might be able to explain everything based on ‘local matters of particular fact’, i.e., point-like facts in spacetime. The world is a Humean mosaic of such facts. The Humean mosaic may be considered to consist of fundamental, (perfectly) natural properties. Accordingly, the mentioned notion of simplicity when it comes to best systems can be understood in terms of relative naturalness: the more natural the relevant properties are, the simpler the resulting system. The reasoning here is as follows.5 Simplicity is a feature of the relevant theories and the system as a whole, but even when combined with strength, there is a risk of triviality. The risk can be illuminated by considering a maximally strong and simple system, which just consists of one allencompassing predicate, ‘W’, that describes or applies to the whole universe and captures its goings-on with a single high-level law. This system may be strong and simple, but it would lack in explanatory power. In order to avoid this type of result, we may introduce the requirement that the predicates in our best system must refer to (perfectly) natural properties, which helps to restrict the system and ensure that we have at least some objective measure for what is ‘best’. Given this line of thought, it is clearly the notion of natural vs. abundant properties that does a lot of work in this theory, and natural properties have an especially important role in the account of laws of nature (on sparse/abundant properties, see Chapter 4, this volume).6 There are various approaches to natural properties and one central issue concerns the question of whether naturalness comes in degrees or whether the only genuinely natural properties are the perfectly natural properties. Following Jonathan Schaffer (2004: 94), we can distinguish the following broad qualifications for being a natural or sparse property (the notions are often used synonymously): 340

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1 Similarity: sparse properties ground objective similarities; 2 Causality: sparse properties carve out causal powers; and 3 Minimality: sparse properties serve as a minimal ontological base. Conversely, non-natural or abundant properties could be picked out by any meaningful predicates that we might imagine, such as ‘being my favourite breakfast food’ (i.e., a sandwich!). The three listed criteria for naturalness or sparsity can of course be questioned. Schaffer himself drops (3) and distinguishes the scientific vs. fundamental conception of sparsity, where the first suggests that sparse properties are those invoked in the ‘scientific’ understanding of the world. However, we might reasonably ask: what counts as ‘scientific’? For instance, are psychological or social properties included?7 But if one favours the fundamental conception, whereby only fundamental or perfectly natural properties should be included, then one faces some difficult questions about what counts as the minimal ontological base. If a ‘gunky’ world is possible, i.e., a world where everything is a proper part and there are no simples, and hence no true mereologically fundamental level, then it might appear that nothing counts as natural according to (3) and we can’t get the account off the ground, as it were.8 Still, there are many ways to specify naturalness (albeit one can also take it to be a primitive notion like Lewis himself probably did), and it’s clear that this approach provides one popular and promising route to connect laws of nature and properties.

30.4 Laws of Nature and Essential Properties Essential properties concern the individual or general natures of entities and have been historically closely connected to laws of nature, although not always explicitly (such as in Aristotle’s work, since the contemporary notion of a ‘law of nature’ had not yet been invented). The basic connection between essential properties and laws of nature is that laws may be thought to ‘flow’ from these properties in some manner (see, e.g., Bird 2007; Kimpton-Nye 2021; Oderberg 2011). However, we should start from the distinction between individual vs. general essences (cf. Lowe 2008: 35). We may ask: is it essential to an individual x to be of kind K? This would be a question concerning the individual essence of x. But we may further ask: what is it that each member of kind K shares that makes it a member of the kind? This would be a question concerning the general essence of the members of K, and the answer could be that they share a given essential property or properties. Every entity will have a general essence in the sense that it is a member of a given ontological category or kind, but it may or may not be essential to the individual that it is a member of that kind. Moreover, not everyone accepts individual essences at all. We can set this complication aside though, since for the purposes of connecting essential properties and laws, it is the general essence that would seem to do the work, as I hope to make clear in what follows. A key question regarding the understanding of essence is the relationship with the essence of an entity and its essential properties, i.e., whether the essence is something over and above the ‘bundle’ of the essential properties. David Oderberg calls this the ‘unity problem’: ‘if the essence is a group (set, bundle) of properties, what holds those properties together?’ (Oderberg 2011: 90ff).9 Now, the connection to laws becomes evident when we consider one possible answer to the unity problem, namely, that a law of nature holds the essential properties together (or that it is a law of nature that they always come together). Analysing 341

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this suggestion will also help to illustrate how an account of laws based on essential properties differs from the DTA-style nomic necessitation account considered in Section 30.2. We can start by assuming that it is part of the essence of electrons, i.e., the general essence of the natural kind electron, that they possess unit negative charge. So, electrons have the property of unit negative charge essentially. This fact by itself does not appear to be law-like in the sense that we have been discussing earlier in connection to the DTA account, because there is no relation between the universal properties at hand – we just have the fact that electrons have a certain property essentially. Oderberg summarises the core issue succinctly (building on Bird 2007): We might think of the property being an electron as a complex property whose parts are, at least, the properties being an elementary particle and carrying unit negative electrical charge. Call these properties E and U, and represent the property being an electron as [E, U]. On the necessitation theory, then, there is a higher-order relation of necessitation between [E, U] and U. Such a relation exists, to be sure, but it is nothing other than necessary inclusion. Since, by definition, we already know that being an electron consists in part of carrying unit negative electrical charge, to assert that it does so in the form of a purported law statement is to add no new fact to the simple fact that electrons exist. In other words, the appeal to law as an explanation of why electrons carry unit negative electrical charge is an illusion. (Oderberg 2011: 91) The ‘necessitation theory’ that Oderberg refers to is the DTA-style account. The upshot for our discussion is that if there is a connection between laws and general essences or essential properties, it looks unlikely to be of the form where the laws explain features of essence. But could it be the other way around? Indeed, perhaps the most interesting connection to laws when it comes to essential properties is that if the modal force of laws somehow ‘flows’ directly from essential properties, then laws may appear to be metaphysically necessary rather than just nomologically or physically necessary – that is, laws of nature could not vary across possible worlds.10 This type of view is most familiar from the framework of scientific or dispositional essentialism, to which we now turn.

30.5

Laws of Nature and Dispositional Properties

Glass has the disposition to break; it’s fragile. Electrons have the disposition to attract positively charged particles, poison has the disposition to kill, water has the disposition to dissolve salt and so on The historical background of dispositional properties can be traced to Aristotle’s dunamis, i.e., potentiality or Locke’s powers (developed in contemporary metaphysics, e.g., by Vetter 2015; see also Chapters 24 and 28, this volume). Dispositional properties are sometimes analysed as possibilities, but they might not or don’t have to manifest. Alternatively, dispositions are often analysed in terms of counterfactuals: ‘if we were to put this salt into some water, it would dissolve’. The relevant that endorses properties with dispositional essences is usually known either as scientific essentialism or dispositional essentialism (e.g., Bird 2007; Ellis and Lierse 1994; Ellis 2001; the roots of the view are already in Kripke 1980 and Putnam 1975). Views falling under these labels generally share an opposition to the Humean position about categorical properties which do not link to any manifestation, i.e., they do not do anything (so have no causal powers). 342

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Categorical properties tell us how something is in itself, not how it behaves. On this view about properties, a property’s ‘essence’, if it can be thought to have one at all, is something non-dispositional and intrinsic, a ‘quiddity’ (as labelled by Armstrong 1989b).11 Resisting this line, the dispositional or scientific essentialists hold that the essence of object O consists in its entirety of the causal roles of O, and there is generally a necessary connection between the behaviour of a property and its causal or dispositional profile. The view regarding laws that emerges from all this is that we can explain all law-like behaviour strictly in terms of the dispositional essences of properties. Electrons essentially have a unit negative charge, and it’s essential to the property of a unit negative charge that it attracts positively charged particles. The upshot is that any relevant laws, such as those governing electrostatic interaction (van der Waals interaction), i.e., the attractive or repulsive interaction between objects having electric charges, can ultimately be explained in terms of the relevant dispositional essence of charge (possibly together with any other relevant dispositional essences).12 Moreover, if essences are understood as being metaphysically necessary to these dispositional properties, then we can trust that the relevant laws hold in all possible worlds, rendering them metaphysically necessary. The picture is very neat and has enjoyed wide support and various modifications.13 However, there are well-known problems with this approach as well. These concern laws that are not easily understood in terms of dispositional properties, such as conservation laws and symmetry principles (for discussion, see Bigelow et al. 1992; Bird 2007: 211–214; Jaag 2014; Vetter 2012).

30.6

Laws, Kinds, and Properties

I will conclude with a brief discussion of the connection between laws of nature, natural kinds, and the properties that members of natural kinds share. Natural kinds themselves may be conceived in many ways, e.g., as bundles of properties, substantial universals, sui generis entities, and so on.14 This in itself may have implications regarding their connection to laws of nature, and the relevant modal status of the laws. For instance, one may regard laws to be metaphysically necessary because they feature natural kinds, as E. J. Lowe (2006) has argued. We need to understand the relationship between natural kinds and the properties that their members have in order to clarify the role of laws. More specifically, we can distinguish three main questions about the relationship between kinds and properties (following Tahko 2022): 1 What are natural kinds, that is, what sort of entity (e.g., universals, bundles of properties … )? 2 Why are properties systematically clustered together in members of natural kinds? 3 How are the clustered properties unified in instances of kinds? One possible line of reasoning to answer (1)–(3) (modelled after Lowe 2006) would be to say that: 1* Natural kinds are substantial (Aristotelian) universals; 2* which are characterised by attributes (property universals) and instantiated by individual substances (instances of kinds); 3* and the clustering of the properties is governed (at least partially) by laws of nature featuring the relevant kind of universals.

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From (1)–(3), we see that the connection between laws, properties, and kinds will, unsurprisingly, depend on one’s views regarding the underlying ontology. The view outlined here, roughly in the spirit of Lowe’s proposal, is also close to my own view: laws may play a role in unifying the properties that members of natural kinds have. Interestingly, this brings us back to the problem of unity, which we briefly examined in Section 30.4. We might compare this to Oderberg’s account, whereby the properties that ‘flow’ from the essence of a particular object belonging to a given kind are caused by and originate in the form of that kind (Oderberg 2011: 99–103). But, as we saw earlier, we need to ask the further question of how the relevant properties are unified. We have no obvious evidence that there are any causal connections between the essential properties of fundamental natural kinds such as, say, electron – or between the kind itself and its properties. In fact, fundamental kinds are an especially problematic case and some (e.g., Chakravartty 2007: 171) have suggested that at least fundamental natural kinds unify their properties as a matter of brute fact. On this view, fundamental natural kinds, such as (supposedly) electrons, have their core properties (mass, charge, spin) as a matter of brute fact. However, it is problematic to conclude that there is no further explanation to the unity problem just because some cases of unification look to us like brute facts. It is another matter whether or not we are ever in a position to know how unification works in such cases. These subtle questions regarding the interplay between properties, natural kinds, and laws of nature are clearly at the core of many approaches to laws and properties, and we can expect the debate to continue.15

Notes 1 Sometimes theories of laws of nature (or natural necessity) are broadly classified as Humean or non-Humean, where at least (1), (3), (4), and (6) would count as non-Humean; (5) is somewhat more difficult to classify. For a survey of the non-Humean approaches, see Hildebrand (2020). For a survey of the Humean approaches, see Bhogal (2020). 2 On the universal/particular distinction, see Chapter 5, this volume, on Platonic universals, see Chapter 11, this volume, and on nominalism more generally, see Part 4, this volume. 3 See Chapter 12, this volume, for further discussion of Aristotelian views and Tugby (2022) for a comprehensive defence of Platonism. 4 See Lewis (1983, 1986) for the classic presentation of his system, and, e.g., Friend 2022; Hicks 2018; Jaag and Loew 2020; Loewer 2007; Schrenk 2014, for some recent discussion. There are also views that combine a non-Humean approach to ontology with a Humean approach to laws, such as Demarest 2017; Kimpton-Nye 2017. 5 Thanks to Samuel Kimpton-Nye for helping to spell this out as clearly as possible. 6 For a recent account developing a ‘package deal’ of laws and properties inspired by the Lewisian best systems account, see Loewer (2021). 7 In fact, we may ask this question about any of the various types of properties discussed in Parts 8 and 9, this volume. 8 For an overview of different conceptions of fundamentality, see Tahko (2018). 9 See also Dumsday (2010) on ‘complex essences’, Keinänen and Tahko (2019) on a bundle theoretic approach, and Hommen (2021) more generally on kinds as universals. 10 But see Tahko (2015b), where the question of contingent laws in an essentialist framework is examined, and Oderberg 2018; Hireche et al. 2021 for critical discussion. 11 For some good discussion of intrinsic properties, see Sider 1996; Whittle 2006, and on quidditism, see Hildebrand 2016; Smith 2016; Wang 2016.

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References Armstrong, D.M. (1983) What Is a Law of Nature? Cambridge: Cambridge University Press. Armstrong, D.M. (1989a) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Armstrong, D.M. (1989b) A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press. Bhogal, H. (2020) Humeanism about Laws of Nature. Philosophy Compass 15(8): 1–10. Bigelow, J., Ellis, B., and Lierse, C. (1992) The World as One of a Kind: Natural Necessity and Laws of Nature. British Journal for the Philosophy of Science 43(3): 371–388. Bird, A. (2007) Nature’s Metaphysics: Laws and Properties. Oxford: Clarendon Press. Chakravartty, A. (2007) A Metaphysics for Scientific Realism: Knowing the Unobservable. Cambridge: Cambridge University Press. Demarest, H. (2017) Powerful Properties, Powerless Laws. In Jacobs, J.D. (ed.) Causal Powers. Oxford: Oxford University Press: 38–53. Dretske, F. (1977) Laws of Nature. Philosophy of Science 44(2): 248–268. Dumsday, T. (2010) Natural Kinds and the Problem of Complex Essences. Australasian Journal of Philosophy 88(4): 619–634. Ellis, B. and Lierse, C. (1994) Dispositional Essentialism. Australasian Journal of Philosophy 72(1): 27–45. Ellis, B. (2001) Scientific Essentialism. Cambridge: Cambridge University Press. Friend, T. (2022) The Humean Pragmatic Turn and the Case for Revisionary Best Systems Accounts. European Journal for Philosophy of Science 12(11): 1–26. Groff, R.P. (2021) Conceptualizing Causal Powers: Activity, Capacity, Essence, Necessitation. Synthese 199(3–4): 9881–9896. Hicks, M.T. (2018) Dynamic Humeanism. British Journal of Philosophy of Science 69(4): 983–1007. Hildebrand, T. (2016) Two Types of Quidditism. Australasian Journal of Philosophy 94(3): 516–532. Hildebrand, T. (2020) Non-Humean Theories of Natural Necessity. Philosophy Compass 15(5): 1–14. Hireche, S., Linnemann, N., Michels, R., and Vogt, L. (2021) The Modal Status of the Laws of Nature: Tahko’s Hybrid View and the Kinematical/dynamical Distinction. European Journal for Philosophy of Science 11(1): 1–15. Hommen, D. (2021) Kinds as Universals: A Neo-Aristotelian Approach. Erkenntnis 86(2): 295–323. Ingthorsson, R. (2013) Properties: Qualities, Powers, or Both? Dialectica 67(1): 55–80. Jaag, S. (2014) Dispositional Essentialism and the Grounding of Natural Modality. Philosophers’ Imprint 14(34): 1–21. Jaag, S. and Loew, C. (2020) Making Best Systems Best for Us. Synthese 197(6): 2525–2550. Keinänen, M. and Tahko, T.E. (2019) Bundle Theory with Kinds. Philosophical Quarterly 69(277): 838–857. Kimpton-Nye, S. (2017) Humean Laws in an UnHumean World. Journal of the American Philosophical Association 3(2): 129–147. Kimpton-Nye, S. (2021) Reconsidering the Dispositional Essentialist Canon. Philosophical Studies 178(10): 3421–3441. Kistler, M. (2020) Powers, Dispositions and Laws of Nature. In Meincke, A.S. (ed.) Dispositionalism: Perspectives from Metaphysics and the Philosophy of Science. Dordrecht: Springer: 171–188. Kripke, S. (1980) Naming and Necessity. Cambridge, MA: Harvard University Press. Lewis, D. (1983) New Work for a Theory of Universals. Australian Journal of Philosophy 61(4): 343–377.

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Tuomas E. Tahko Lewis, D. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Loewer, B. (2007) Laws and Natural Properties. Philosophical Topics 35(1/2): 313–328. Loewer, B. (2021) The Package Deal Account of Laws and Properties (PDA). Synthese 199(1-2): 1065–1089. Lowe, E.J. (2006) The Four-Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Oxford University Press. Lowe, E.J. (2008) Two Notions of Being: Entity and Essence. Royal Institute of Philosophy Supplements 83(62): 23–48. McKitrick, J. (2018) Dispositional Pluralism. Oxford: Oxford University Press. Niiniluoto, I. (1978) Dretske on Laws of Nature. Philosophy of Science 45(3): 431–439. Mumford, S. (1998) Dispositions. Oxford: Clarendon Press. Oderberg, D. (2011) Essence and Properties. Erkenntnis 75(1): 85–111. Oderberg, D. (2018) The Impossibility of Natural Necessity. In Carruth, A., Gibb, S., and Heil, J. (eds.) Ontology, Modality, and Mind: Themes from the Metaphysics of E.J. Lowe. Oxford: Oxford University Press: 73–92. Putnam, H. (1975) The Meaning of ‘Meaning’. Minnesota Studies in the Philosophy of Science 7: 131–193. Schaffer, J. (2004) Two Conceptions of Sparse Properties. Pacific Philosophical Quarterly 85(1): 92–102. Schrenk, M. (2014) Better Best Systems and the Issue of CP-Laws. Erkenntnis 79(S10): 1787–1799. Sider, T. (1996) Intrinsic Properties. Philosophical Studies 83(1): 1–27. Smith, D. (2016) Quid Quidditism Est? Erkenntnis 81(2): 237–257. Tahko, T.E. (2015a) Natural Kind Essentialism Revisited. Mind 124(495): 795–822. Tahko, T.E. (2015b) The Modal Status of Laws: In Defence of a Hybrid View. Philosophical Quarterly 65(260): 509–528. Tahko, T.E. (2018) Fundamentality. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2018 Edition). URL = < https://plato.stanford.edu/archives/fall2018/entries/fundamentality/>. Tahko, T.E. (2022) Natural Kinds, Mind-Independence, and Unification Principles. Synthese 200(2): 1–23. Tahko, T.E. (forthcoming) Natural Kinds. In Koslicki, K. and Raven, M. (eds.) The Routledge Handbook of Essence. Abingdon and New York: Routledge. Tugby, M. (2022) Putting Properties First: A Platonic Metaphysics for Natural Modality. Oxford: Oxford University Press. Vetter, B. (2012) Dispositional Essentialism and the Laws of Nature. In Bird, A., Ellis, B., and Sankey, H. (eds.) Properties, Powers, and Structures: Issues in the Metaphysics of Realism. London: Routledge: 201–216. Vetter, B. (2015) Potentiality: From Dispositions to Modality. Oxford: Oxford University Press. Wang, J. (2016) The Nature of Properties: Causal Essentialism and Quidditism. Philosophy Compass 11(3): 168–176. Whittle, A. (2006) On an Argument for Humility. Philosophical Studies 130(3): 461–497. Yates, D. (2015) Dispositionalism and the Modal Operators. Philosophy and Phenomenological Research 91(2): 411–424.

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31 EMERGENT PROPERTIES Anne Sophie Meincke

31.1

Introduction

Emergent properties are understood to be higher-level properties instantiated by some entity S that are distinct from, yet dependent on, certain lower-level properties instantiated by S. Distinctness, sometimes also referred to as autonomy, denotes the assumption that emergent properties are novel relative to the relevant base properties and, accordingly, invoke their own characteristic type of explanation, distinct from the type of explanation pertaining to the base properties. Dependence, on the other hand, expresses the idea that emergent properties are not free-floating but systematically related, in some sense or another, to their base properties. An entity S would not have the higher-level properties it has, had these not emerged from S’s lower-level properties. Although the concept of emergence was introduced into scientific and philosophical debates already about two hundred years ago by the so-called British Emergentists, most notably G. H. Lewes, J. S. Mill, Samuel Alexander, C. Lloyd Morgan and C. D. Broad, it has only recently attracted wider attention (Campbell 2015; Corradini and O’Connor 2015; Gibb et al. 2019; Gillett 2016; Humphreys 2016; Kauffman 2019; MacDonald and MacDonald 2010; Wilson 2021). A prominent reason for the current surge of interest is an increasing frustration with physical reductionism (also known as physicalism). Even if the most fundamental level of reality is indeed the one described by physics, this need not be taken to imply that reality is sufficiently described in terms of physical properties. In that vein, friends of emergence typically emphasise the existence of higher-order phenomena involving mental properties, such as life, mind, agency or free will, and call for appreciating these phenomena in their own terms. At the same time, the emergentists share with their reductionist opponents a resistance against supranatural explanations as provided, for instance, by dualist views. Importantly, therefore, accounts of mental properties as higherlevel properties emerging from lower-level physical properties are intended to constitute a type of naturalist explanation, though not a reductionist one. Whether or not the concept of emergence facilitates a philosophically and scientifically viable agenda is highly controversial. The present chapter aims to shed light on this issue by revealing the broader metaphysical commitments involved in the assumption of emergent

DOI: 10.4324/9781003246077-39

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properties. To this end, we shall first look into the history of the concept of emergence and find that the concept of emergence is younger than often assumed. Understanding the intellectual situation in which the need for the concept of emergence arose – the repudiation of Cartesian psychophysical dualism in favour of physical reductionism – helps us see, in a second step, why contemporary debates on emergence tend to run into a characteristic dilemma that makes the concept of emergence seem either vacuous or mysterious. However, a possible way out of this appears once we come to appreciate the dynamic or processual constitution of emergent phenomena in nature, which I shall explore towards the end of this chapter.

31.2

The History of the Concept of Emergence: Playing “Two Truths and a Lie”

It is often assumed that, although the British Emergentists were the first to actually use the term “emergence”, “the basic notion has quite a long history stretching back at least to Aristotle (384–322 BC)” (O’Connor 2021: §1). Three features of Aristotle’s metaphysics are commonly cited as indicative of its commitment to emergence: (i) the generation of objects – so-called substances – from certain arrangements of matter; (ii) the distinctness of mental powers from, and their downward-causal efficacy upon, non-mental, i.e., physical, powers; (iii) the rejection of both substance dualism and reductionism (Caston 1997; O’Connor 2021). Was Aristotle the first emergentist on record? No, he wasn’t. It’s the “lie” in this case. Substances, according to Aristotle, are generated not from matter alone (see (i)). What needs to be added is the “causal agency” of form (Furth 2010: 164), which actualises certain of the matter’s inherent potentials. Form, as a distinct and ontologically fundamental principle that defines a substance’s essence, structures matter from the top down into a particular hylomorphic whole, the substance. This entails that forms are as little emergent as substances are. Forms, in fact, are not themselves generated at all but instead realised in something else (Metaphysics VII. 8. 1033b5–8).1 And because all essential information is present in a substance’s form, the coming-to-be of any given substance never involves the occurrence of any genuinely novel properties or powers, whether these be physical or mental (see (ii)). A rather striking case of this is the coming-to-be of living substances, which Aristotle regarded as a mere unfolding or unrolling of speciescharacteristic potentials pre-fixed by the living form or soul, with a few accidental particularities being added in the process.2 Which mental powers a given living substance has is just a question of what kind of living substance it is, i.e., what kind of soul it has – as opposed to a view where mental powers emerge from physical powers. Rejecting both substance dualism and reductionism thus does not necessarily make one an emergentist (see (iii)) – one could also be a hylomorphist as Aristotle was. The history of emergentism did not start with Aristotle because he did not have the need for the concept of emergence. Emergentism is wedded, both historically and conceptually, to the – originally physicalist – idea that the physical is the fundamental level of reality from which everything else is to be understood. This idea is foreign to Aristotle’s metaphysics. Aristotle does not even possess the concept of “the physical”. There is no matter without form for Aristotle; and the paradigmatic substances in the Aristotelian universe are living substances, hylomorphic unities with a living form or soul. The need for the concept of emergence only arose after Descartes tore apart what was united in Aristotle’s concept of living substance and of nature (φύσις) more generally: mind and matter. Only after Descartes did so, because Descartes did not have a need for emergence either. 348

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Descartes was convinced that any complexity to be found in matter (res extensa) could be fully accounted for in purely material terms, whereas mental properties belong to a distinct type of substance that is immaterial and intellectual (res cogitans) and that requires its own type of explanation. Deciphering the workings of the mind, therefore, cannot help us understand how material bodies work, not even if these bodies are alive, as we take those of plants, animals and humans to be. Bodies, whether alive or not, are machines operating by mechanical principles according to the laws of nature described by physics. Conversely, physics cannot contribute anything to understanding the mind, possessed, according to Descartes, exclusively by humans. But physics also needed not to make such contribution because the mind was taken care of separately within the framework of psychophysical dualism. Rather than having emerged from matter, the mind, Descartes believed, was created by God and is continuously kept in existence by God. The conditions for the concept of emergence to emerge were present only at that particular moment in the history of Western thought when reductionist mechanists had got rid of Descartes’s res cogitans while vitalists were rebelling against reductionism by reviving Aristotle’s view of nature. The bone of contention was whether or not physics was up to the task of explaining chemical bonding, life and, ultimately, the mind, i.e., whether or not the special sciences, chemistry, biology and psychology could be reduced to physics. The reductionists said yes, the vitalists said no. According to vitalists such as Justus Liebig, Louis Pasteur and Hans Driesch, life in particular resists reduction. The behaviour of chemical components in organisms and the development of organisms, they thought, are guided by an immaterial vital force or entelechy as an additional component, implying a sharp ontological distinction between inorganic and organic matter. A living being, they hence insisted, is a whole that is greater than the sum of its parts,3 as opposed to the mechanist view that a complete description of the behaviour of a system’s parts yields a complete explanation of that system’s behaviour as a whole – for living and non-living systems alike. For the mechanists, the difference between living and non-living systems was not a difference in kind but a matter of degrees of complexity.4 So-called British Emergentism (McLaughlin 1992), an intellectual movement lasting from the second half of the nineteenth century until the beginning of the twentieth century, must truthfully be remembered as an attempt to bring about a compromise between vitalism and mechanism. With the vitalists and against the mechanists, philosophers such as Lewes, Mill, Alexander, Lloyd Morgan and Broad,5 held that living beings possess novel properties not possessed by their parts; however, against the vitalists and with the mechanists, they denied the involvement of any supranatural powers in this. Instead, the idea was that those novel properties “emerged”, in a non-additive way, from matter itself, that is, from the arrangement of a living being’s material parts. The British Emergentists were, to speak in modern terms, both materialist substance monists and property dualists. Along with this combination comes a strong commitment to a hierarchical structure of material reality: while emerging from certain local arrangements of matter, emergent properties are thought to be possessed not by these local arrangements but by a higher-level material entity arising from them. The phenomenon of emergence itself, as a “brute empirical fact” (Alexander 1920: 46), is what structures matter into lower and higher levels of organisation6 such that each level has its own distinctive causally efficacious qualities which cannot be derived from the bottom up7 even though they are brought forth with necessity by certain lower-level arrangements of matter.8 This irreducible hierarchy of organisational levels of matter is reflected in an irreducible hierarchy of the special sciences – physics, 349

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chemistry, biology and psychology. If there are any (as Broad calls them) “trans-ordinal laws” linking adjacent orders, these are emergent themselves, which means that they cannot be predicted from the lower order’s distinctive “intra-ordinal laws” (Broad 1925: 79). In this sense, emergence “admits no explanation” (Alexander 1920: 47). It is a historical truth – the second truth of the game in this section’s title – that the British Emergentist project was superseded by reductionism, prompted, in particular, by newly available quantum mechanical explanations of chemical bonding and successes in molecular biology and genetics. I emphasise the historical nature of this break-down because the reappearance of emergentist theories in contemporary debates may well point towards persisting and promising prospects of the overall theoretical approach first launched by the British Emergentists.9

31.3

Contemporary Debates: The Dilemma of Emergence and its Processual Dissolution

Emergent properties first regained prominence in the context of debates on mental causation in analytic philosophy of mind. The multiple realisability of the mental and its phenomenal qualities led many scholars to turn their backs on the then predominant Mind-Brain Type Identity Theory and to argue instead that the mental cause of a given behaviour is distinct from, yet dependent on, that behaviour’s physical cause. Causally efficacious mental states thus came to be conceptualised as higher-order properties that supervene on physical properties, such as brain states. As Jaegwon Kim (e.g., 2006) pointed out, it is natural to conceive of these supervenient properties as emergent properties of the physical system on whose physical states they supervene, i.e., as emergent properties of a brain. Yet, appeals to emergence in the philosophy of mind appear to remain largely committed to a variety of physicalism, i.e., of “the view that bits of matter and their aggregates in space-time exhaust the contents of the world” (Kim 2005: 71). What is denied is that mental properties, albeit token-identical to or constituted of physical properties, can be reduced to the latter. In line with this so-called nonreductive physicalism, the emergence of novel properties, according to Kim’s reconstruction of contemporary emergentism, is considered a question of the structural organisation of bits of matter.10 Whether or not nonreductive physicalism and emergentism are in fact the same position is subject to ongoing debate (see Crane 2010 and O’Connor and Churchill 2010 for different stances on this). The question of their relationship is linked to the question of what notion of emergence is invoked. Theories of weak emergence are commonly contrasted with theories of strong emergence. According to Timothy O’Connor (2021), the former are consistent with physicalism (by embracing a nonreductive variant of physicalism) while the latter are not. Here the assumption is that both theory types intend to make ontological claims about emergent properties, as opposed to merely epistemological claims. The kind of emergentism that lends itself to nonreductive physicalism is one that deploys a notion of weak emergence. More specifically, this position endorses the following five claims: (1) emergent properties, such as mental states, supervene on base physical properties; (2) emergent properties are real; (3) emergent properties are causally efficacious; (4) emergent properties are distinct from their base properties; (5) all physical states have pure physical causes (physical causal closure) (O’Connor 2021). However, Kim (e.g., 2006: 557ff.) has famously argued that this combination of commitments makes nonreductive physicalism/ weak emergentism an inherently unstable position. Any emergent mental state M* supposedly caused by another mental state M can only be thus caused via its physical base P* being 350

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downwardly caused by same mental state M; however, physical base P* is already same-level caused by another physical state P. Hence if we do not want to assume that emergent states are systematically overdetermined, we must conclude that the supposed causal efficacy of M (as stated by premise (3)) is illusory; the causal work is done by its physical realisation base P alone. Nonreductive physicalism/weak emergentism collapses into reductive physicalism. One reaction to Kim’s so-called causal exclusion argument is to admit that emergent properties do not possess a special ontological but only a special epistemological status, by being unexpected from the perspective of a particular observer yet in principle deducible from sufficient knowledge of the system’s base properties (Chalmers 2006). Indeed, this is how weak emergence is often understood – as a reflection of our limited capacities of understanding a system’s complexity, be this limitation contingent and, hence, transitory or constitutional. Weak emergence accounts of this kind are popular in scientific discourses. Thus, Massimo Pigliucci (2014: 265) argues that “even if emergence is only an epistemic phenomenon, there are good reasons to take it seriously, for instance, because it points towards current methodological or theoretical deficiencies that make straightforward reductionist accounts unfeasible in practice, if not in principle”. Weakly emergentist explanations are, as it were, the progenitor of reductionist explanations.11 Another option is to deny premise (5) that all physical states have pure physical causes and to embrace strong emergence. If one considers physical causal closure an integral part of physicalism, this move amounts to rejecting physicalism, as opposed to endorsing a nonreductive variety of physicalism. O’Connor (1994: 98) defines emergence, within the framework of strong emergence, as follows: Property P is an emergent property of a (mereologically-complex) object O iff: 1 2 3 4

P supervenes on properties of the parts of O; P is not had by any of the object’s parts; P is distinct from any structural property of O; and P has direct (“downward”) determinative influence on the pattern of behaviour involving O’s parts. (O’Connor 1994: 98)

(1) asserts complete synchronic ontological dependence for emergent properties on their bearer’s microstructure; (2) refers to the higher-level status of emergent properties; (3) points to the requirement of radical novelty: an emergent property needs to be different in kind from its bearer’s structural properties which are constituted by the properties of the object’s parts (see also Anjum and Mumford 2017: 97 f.); and (4) appeals to the very strong sense in which an emergent’s causal influence is irreducible to that of the micro-properties on which it supervenes: it bears its influence in a direct, “downward” fashion, in contrast to the operation of a simple structural macro-property, whose causal influence occurs via the activity of the micro-properties that constitute it. (O’Connor 1994: 97f) Given that it is no longer assumed that for every physical state there must be a pure physical cause, no problems of overdetermination arise. 351

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Strong emergence is controversial. Besides general worries as to how downward causation and eschewing physicalism fit with a scientific worldview, there are also concerns about the coherence of the concept of strong emergence, one of these being the so-called collapse problem. Briefly put, the objection is that as supervenient on, and thus (nomologically or metaphysically) necessitated by, a certain set of base properties, a supposedly strongly emergent property cannot be novel after all; it rather amounts to no more than a manifestation of the base properties’ inherent potentialities and, thus, “collapses” into its base (O’Connor 1994: 98; Taylor 2022). O’Connor (1994: 98) responds to this by insisting that an emergent property’s causal power is irreducible (at least) “to the immediate causal potentialities of the subvening properties”; the “potentialities of an emergent property ‘go beyond’ those of the base properties” in the sense that any explanation of the corresponding object’s behaviour, including the formulation of laws, would need to invoke said emergent property. However, this invites the rejoinder that strong emergence, as Mark Bedau (1997: 377) puts it, “is uncomfortably like magic”, which resuscitates “the traditional worry that emergence entails illegitimately getting something from nothing”. According to a widely held view, emergence is what needs explaining rather than what does the explaining. Therefore, it seems unsatisfactory to appeal to strongly emergent properties as brute facts, something British Emergentism did and has been criticised for up until today (see, e.g., Kim 2006).12 It thus appears that strong emergentism is faced with a dilemma. Positing emergent properties is either vacuous because the purportedly strongly emergent properties are already contained in the base properties via the latter’s potentialities or dispositions, or it is mysterious because one does not see where these strongly emergent properties should come from if they are not contained in the base properties. There is a deeper dimension to this dilemma. On the one hand, the idea of potentialities for higher-order properties in base properties, if taken seriously, opens up a route back towards an Aristotelian metaphysics, one of whose key ideas, as we found, is that matter provides potentialities to be actualised and channelled into unified hylomorphic objects (“substances”) by form as a distinct principle. Genuine novelty, as you will recall, is ruled out within an Aristotelian framework for principal reasons, and so is emergence. On the other hand, the difficulty that, without the assumption of certain inherent potentialities, matter seems to lack any resources to account for the possibility of strongly emergent properties, especially of a mental kind, is a vestige of the Cartesian concept of matter as res extensa, which is no longer complemented with a mental counterpart. British Emergentism, we saw, arose as an attempt to account, in a purely naturalist or materialist way, for what seem to be genuinely novel qualities compared to the basic qualities of matter described by physics. But this means to ask things of matter that both Cartesian substance dualism and reductionism had denied it, as astutely noted by German philosopher Hans Jonas: One point easily overlooked is that a ‘matter’ called upon to account for spirit is no longer the same matter that science took over in the dualistic expurgation. Materialism inherited the estate of dualism without being fully aware that the left-over to which it succeeded carried an obligation to support theoretically those phenomena too that had formerly been taken care of by the vanished half of dualism’s estate. […] [D]eprived of the dualistic shelter, lonesome ‘matter’ must now account for mind and thereby loses the unambiguous nature of ‘mere matter’ once conceived. […] [I]ts concept is, by this very demand upon it, already reabsorbed into a concept of substance that transcends 352

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the aspect which materialism isolated under the name of matter; and this in effect reopens the issue of ontology which materialism claims to have settled. (Jonas 1966: 129) We may conclude from this that in order to overcome reductionism without relapsing either into substance dualism or into an Aristotelian or vitalist metaphysics, strong emergentism must rethink its basic metaphysical commitments. What is this matter that is capable of organising itself such that novel qualities and novel kinds of entity come about? Surely, if this capability is not the work of Aristotelian forms or of some supranatural entelechy acting upon matter, we ought to incorporate it in our concept of matter, thus moving away from a Cartesian mechanist concept of matter as a passive substrate towards an understanding that recognises matter’s active and creative powers. This will impact our understanding of nature more broadly. An inherently active matter makes the presence of life much less of a surprise than it must seem for reductionist mechanism, “whose model entity is pure matter, stripped of all features of life” (Jonas 1966: 9). Life, then, instead of being a puzzling deviation from “the natural”, becomes an integral part of nature, and so does mind, which, as empirical evidence tells us, has evolved biologically or even is an essential feature of life as such (Ginsburg and Jablonka 2019; Jonas 1966; Thompson 2007). With both mind and living body being encompassed by a comprehensive notion of nature, the traditional mind-body problem that permeates debates on emergence loses much of its force (Meincke 2022a). As it happens, dynamic conceptions of life are on the rise. In the light of recent developments in biology, especially in systems biology and evolutionary biology, a growing number of philosophers of biology are calling for a processual turn. Living systems, they argue, are better understood as processes than as substances (Dupré 2021; Meincke 2019; Nicholson and Dupré 2018). The philosophy of chemistry, too, is seeing a surge of processual approaches to understanding the nature of molecules and chemical reactions (Alassia 2022; Guttinger 2021; Stein 2004). A processual perspective can be expected not only to constructively inform studies of strong emergence in biology (Juarrero 2009; Noble 2006; Reid 2007; Thompson 2007) and chemistry (Hendry 2017) but also to prompt a radical change in the basic metaphysical understanding of strong emergence which so far has been strikingly static. The supervenience of emergent properties on their base properties, we have seen, is commonly thought to be a synchronic dependence relation, with both types of properties being simultaneously present as clearly individuated and re-identifiable things. However, as rightly pointed out by Richard Campbell and Mark Bickhard (2011), all thermodynamically open systems lack a stable base on which emergent properties could supervene. Such systems – whether living, such as organisms, or non-living, such as candle flames – maintain their stability through exchanging matter and energy with their environment, as a result of which any emergent properties cannot be mapped onto base properties in the way traditional models of emergence in metaphysics suggest. The point is not only that there are no sufficiently stable lower-level components that could serve as the ontological base for emergent higher-level properties, but also that those unstable lower-level components are themselves for their existence dependent on the higher-level, supposedly emergent features of the process as a whole. This is particularly true for living systems which, unlike candle flames, actively maintain the conditions for their interactive self-constitution or “autopoiesis” (Maturana and Varela 1980). Autopoietic (or autonomous) systems are characterised by a dynamic part-whole interdependence that 353

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cannot be cashed out in static terms (Meincke 2019). Evan Thompson, accordingly, speaks of “dynamical co-emergence”: In an autonomous system, the whole not only arises from the (organizational closure of) the parts, but the parts also arise from the whole. The whole is constituted by the relations of the parts, and the parts are constituted by the relations they bear to one another in the whole. Hence, the parts do not exist in advance, prior to the whole, as independent entities that retain their identity in the whole. Rather, part and whole coemerge and mutually specify each other. (Thompson 2007: 65) Along similar lines, Rani Anjum and Stephen Mumford (2017: 98) put forward a “causal-transformative model of emergence” according to which strongly emergent powers are those that emerge “from the powers of the components interacting and being changed by their causal participation in the whole”. This causal-transformative change undergone by the parts confers novel emergent powers not only to the whole, known as “emergence”, but also to the parts themselves, a process the authors dub “demergence” (2017: 102). Emergence is (a special form of) bottom-up causation whereas demergence is top-down causation. Causal transformation leads to supervenience failure,13 enforcing identification of the transformed emergence base with the whole (2017: 101). In effect, this is to say that whenever we have strongly emergent properties, we have new kinds of entities as well, and these new higher-level entities take the place of the lower-level entities from which they emerged. This idea, whose origins can be traced back to the British Emergentists, removes the ground from the collapse problem. Very bluntly put: if there is no independent and stable emergence base, emergent properties also cannot collapse into that base.14 Less bluntly put: if an emergent quality, as Alexander (1920: 46) phrases it, “constitutes its possessor a new order of existent with its special laws of behaviour”, we precisely cannot hope to explain this new behaviour in terms of the lower-level of existence from which it has emerged, whatever the latter’s potentialities were while it existed. A processual perspective provides a scientifically informed naturalist explanation as to why this is the case.

31.4 Conclusion Emergentism is a unique endeavour to steer a middle course between substance dualism and vitalism on the one hand and physical reductionism on the other that must be distinguished carefully from other positions, such as Aristotelian hylomorphism. In contrast to the latter’s top-down approach to explaining higher-level phenomena, i.e., composite objects (“substances”) and their properties, which is facilitated by the concept of a form, emergentism proceeds from the bottom up, claiming that novel qualities emerge from a respective base level, the most basal one being the one described by physics. The historically first form of emergentism was British Emergentism, which took reality to be structured into different levels of organisation of matter thanks to the emergence of novel qualities. Contemporary theories of emergence fall into theories of weak and theories of strong emergence, the former constituting a variety of nonreductive physicalism, the latter renouncing physicalism while still aiming at a naturalist explanation. Weak emergence is challenged by problems of overdetermination, strong emergence by the dilemma that the assumption of strongly emergent properties seems either vacuous because such properties 354

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are already inherent in their base properties or, else, mysterious. Taking seriously the dynamic, processual nature of emergence may dissolve these problems, thus opening up new avenues for understanding life, agency and free will.15

Notes 1 … Namely realised in something else either from without, as when a sculptor gives a lump of bronze the shape of Hermes, or from within, as when the form, which Aristotle believed to be contained in the male semen, orchestrates the developmental changes required for turning an embryo into a recognisable member of its species. In both cases, Aristotle insists, it is the formed thing, not the form, that is brought about; see Metaphysics VII. 8. 1033a31ff. This is consistent with understanding Aristotle’s notion of form as running together the aspects of individuality and of species-essence, as convincingly argued by Furth (2010) against the recent rise of interpretations that ascribe to Aristotle the adoption of particular forms (in addition to universal forms). Each hylomorphic living substance realises the same universal species-form transmitted via the male semen from one generation to the next, and by so realising the universal species-form, the living substance is individuated. 2 According to Aristotle, the form provided by the father via his semen holds all essential information required for development, whereas the pregnant female merely supplies matter and warmth ( Meincke 2022b). 3 This slogan is commonly associated with Aristotle’s dictum that a whole is distinguished from a mere heap (σωρός) by being something besides the parts (παρα τα μόρια), see Metaphysics VIII. 6. 1045a 8–12. 4 For detailed historical reconstructions of the vitalism-mechanism controversies in the nineteenth and twentieth century, see, e.g., Bechtel and Richardson (1998), McLaughlin (2008) and Normandin and Wolfe (2013). 5 See McLaughlin (1992) for an in-depth discussion of these philosophers’ works. A helpful overview is provided by Vintiadis (2022) and O’Connor (2021). 6 “The higher-quality emerges from the lower level of existence and has its roots therein, but it emerges therefrom, and it does not belong to that lower level, but constitutes its possessor a new order of existent with its special laws of behaviour” ( Alexander 1920: 46). 7 “[I]n no case could the behaviour of a whole composed of certain constituents be predicted merely from a knowledge of the properties of these constituents, taken separately, and of their proportions and arrangements in the particular complex under consideration” ( Broad 1925: 63). 8 “No doubt the properties of silver-chloride are completely determined by those of silver and of chlorine; in the sense that whenever you have a whole composed of these two elements in certain proportions and relations you have something with the characteristic properties of silver-chloride, and that nothing has these properties except a whole composed in this way” ( Broad 1925: 64). 9 This contra McLaughlin (1992) who takes British Emergentism to be irrevocably refuted on empirical grounds. 10 “[T]he intuitive idea of an emergent property stems from the thought that a purely physical system, composed exclusively of bits of matter, when it reaches a certain degree of complexity in its structural organization, can begin to exhibit genuinely novel properties not possessed by its simpler constituents” ( Kim 2006: 458). 11 See, however, Bedau (2008) for a critical discussion of epistemological accounts of weak emergence. 12 For two different but related defences of British Emergentism against this charge, see Crane (2010) and Vintiadis (2018). 13 “[O]nce composed into a whole, the parts no longer exist as they did prior to that composition; so you cannot say that the whole depends on those original parts, or that same parts = same whole, when the parts are not the same as before” ( Anjum and Mumford 2017: 101). Unlike Thompson, Anjum and Mumford do assume an existence of the parts prior to the whole. 14 Note the difference of this view from assumptions of “strongly emergent objects” existing in the literature and meant to tackle the collapse problem by assuming that “the emergent property is borne by an entirely different object from the object that bears the nonemergent properties”

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Anne Sophie Meincke ( Taylor 2022: 313). According to the process view of emergence sketched above, there are no such two co-existing objects but only one: the emergent object or rather process. 15 I gratefully acknowledge funding from the Austrian Science Fund (FWF) via its “Elise Richter” funding scheme for my research project “Bio-Agency and Natural Freedom”, grant agreement number V 714-G30. I also would like to thank Anthony Fisher and Anna-Sofia Maurin for helpful comments on an earlier version of this chapter.

References Alassia, F. (2022) A Process Ontology Approach in Biochemistry: The Case of GPCRs and Biosignaling. Foundations of Chemistry 24: 405–422. Alexander, S. (1920) Space, Time, and Deity, 2 vols. London: Macmillan. Anjum, R.L. and Mumford, S. (2017) Emergence and Demergence. In Paolini Paoletti, M. and Orilia, F. (eds.) Philosophical and Scientific Perspectives on Downward Causation. London: Routledge: 92–109. Bechtel, W. and Richardson, R.C. (1998) Vitalism. In Craig, E. (ed.) Routledge Encyclopedia of Philosophy. London: Routledge: 639–643. Bedau, M. (1997) Weak Emergence. Philosophical Perspectives 11: 375–399. Bedau, M. (2008) Is Weak Emergence Just in the Mind? Mind and Machines 18(4): 443–459. Broad, C.D. (1925) The Mind and Its Place in Nature. London: Routledge and Kegan Paul. Campbell, R. (2015) The Metaphysics of Emergence. London: Palgrave Macmillan. Campbell, R. and Bickhard, M. (2011) Physicalism, Emergence and Downward Causation. Axiomathes 21(1): 33–56. Caston, V. (1997) Epiphenomenalisms, Ancient and Modern. Philosophical Review 106(3): 309–363. Chalmers, D. (2006). Strong and Weak Emergence. In Clayton, P. and Davies, P. (eds.). The ReEmergence of Emergence. Oxford: Oxford University Press: 244–254. Corradini, A. and O’Connor, T. (eds.) (2015) Emergence in Science and Philosophy. London: Routledge. Crane, T. (2010) The Significance of Emergence. In Loewer, B. and Gillet, G. (eds.) Physicalism and Its Discontents. Cambridge: Cambridge University Press: 207–224. Dupré, J. (2021) The Metaphysics of Biology. Cambridge: Cambridge University Press. Furth, M. (2010) Substance, Form, and Psyche: An Aristotelean Metaphysics. Cambridge: Cambridge University Press. Gibb, S., Hendry, R. and Lancaster, T. (eds.) (2019) The Routledge Handbook of Emergence. London: Routledge. Gillett, C. (2016) Reduction and Emergence in Science and Philosophy. New York, NY: Cambridge University Press. Ginsburg, S. and Jablonka, E. (2019) The Evolution of the Sensitive Soul. Learning and the Origins of Consciousness. Cambridge, MA: MIT Press. Guttinger, S. (2021) Process and Practice: Understanding the Nature of Molecules. Hyle – International Journal for Philosophy of Chemistry 27(1): 47–66. Hendry, R.F. (2017) Prospects for Strong Emergence in Chemistry. In Paolini Paoletti, M. and Orilia, F. (eds.) Philosophical and Scientific Perspectives on Downward Causation. London: Routledge: 146–163. Humphreys, P. (2016) Emergence: A Philosophical Account. Oxford: Oxford University Press. Jonas, H. (1966) The Phenomenon of Life: Toward a Philosophical Biology. Evanston, IL: Northwestern University Press. Juarrero, A. (2009) Top-Down Causation and Autonomy in Complex Systems. In Murphy, N., Ellis, G. and O’Connor, T. (eds.) Downward Causation and the Neurobiology of Free Will. Berlin: Springer: 83–102. Kauffman, S. (2019) A World beyond Physics: The Emergence and Evolution of Life. Oxford: Oxford University Press. Kim, J. (2005) Physicalism or Something Near Enough. Princeton, NJ: Princeton University Press. Kim, J. (2006) Emergence: Core Ideas and Issues. Synthese 151(3): 547–559.

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Emergent Properties MacDonald, C. and MacDonald, G. (eds.) (2010) Emergence in Mind. Oxford: Oxford University Press. Maturana, H.R. and Varela, F.J. (1980) Autopoiesis and Cognition: The Realization of the Living. Dordrecht: Reidel. McLaughlin, B. (1992) The Rise and Fall of British Emergentism. In Beckermann, A., Flohr, H. and Kim, J. (eds.) Emergence or Reduction? Essays on the Prospects of Nonreductive Physicalism. Berlin: de Gruyter: 49–93. McLaughlin, B. (2008) Vitalism and Emergence. In Baldwin, T. (ed.) The Cambridge History of Philosophy. Cambridge: Cambridge University Press: 631–639. Meincke, A.S. (2019) Autopoiesis, Biological Autonomy and the Process View of Life. European Journal for Philosophy of Science 9: 5, 10.1007/s13194-018-0288-2. Meincke, A.S. (2022a) Biological Subjectivity: Processual Animalism as a Unified Account of Personal Identity. In Noller, J. (ed.) The Unity of a Person: Philosophical Perspectives. London: Routledge: 100–126. Meincke, A.S. (2022b) One or Two? A Process View of Pregnancy. Philosophical Studies 179(5): 1495–1521. Nicholson, D. and Dupré, J. (eds.) (2018) Everything Flows: Towards a Processual Philosophy of Biology. Oxford: Oxford University Press. Noble, D. (2006) The Music of Life: Biology beyond Genes. Oxford: Oxford University Press. Normandin, S. and Wolfe, C.T. (eds.) (2013) Vitalism and the Scientific Imagine in PostEnlightenment Life Science, 1800–2010. Dordrecht: Springer. O’Connor, T. (1994) Emergent Properties. American Philosophical Quarterly 31(2): 91–104. O’Connor, T. and Churchill, J.R. (2010) Nonreductive Physicalism or Emergent Dualism? The Argument from Mental Causation. In Koons, R.C. and Bealer, G. (eds.) The Waning of Materialism. Oxford: Oxford University Press: 261–280. O’Connor, T. (2021) Emergent Properties. In Zalta, E. (ed.) Stanford Encyclopedia of Philosophy, Winter 2021 Edition, URL = < https://plato.stanford.edu/archives/win2021/entries/propertiesemergent/>. Pigliucci, M. (2014) Between Holism and Reductionism: A Philosophical Primer on Emergence. Biological Journal of the Linnean Society 112(2): 261–267. Reid, R.G.B. (2007) Biological Emergences: Evolution by Natural Experiment. Cambridge, MA: MIT Press. Stein, R.L. (2004) Towards a Process Philosophy of Chemistry. Hyle – International Journal for the Philosophy of Chemistry 10(1): 5–22. Taylor, E. (2022) Power Emergentism and the Collapse Problem. Philosophy of Science 89(2): 302–318. Thompson, E. (2007) Mind in Life: Biology, Phenomenology, and the Sciences of the Mind. Cambridge, MA: Harvard University Press. Vintiadis, E. (2018) There Is Nothing (Really) Wrong with Emergent Brute Facts. In Vintiadis, E. and Mekios, C. (eds.) Brute Facts. Oxford: Oxford University Press: 197–212. Vintiadis, E. (2022) Emergence. The Internet Encyclopedia of Philosophy, ISSN 2161-0002, https:// iep.utm.edu/, accessed on 1 October 2022. Wilson, J. (2021) Metaphysical Emergence. Oxford: Oxford University Press.

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32 QUANTITATIVE PROPERTIES J.E. Wolff

32.1

Introduction

Many of the most important properties in the physical sciences are quantitative properties: think of mass, charge, temperature, or length. In virtue of their central role in physical theories, they look like they might have a claim to being fundamental properties. But what are quantitative properties, and in particular: what makes such properties quantitative? When we talk about quantitative properties, we might be talking about specific quantities, like 4 kg, or the mass of Jupiter,1 or we might be talking about general quantities, such as mass or temperature. Specific quantities are sometimes called ‘magnitudes’ (Mundy 1987; Swoyer 1987) and general quantities are sometimes called ‘general quantity types’ (Tal 2019). Calling specific quantities ‘magnitudes’ typically suggests that they are universals, whereas nominalists try to avoid talk of magnitudes. To remain neutral between these ontological options, this chapter will use the slightly clumsy, but neutral expressions ‘specific quantity’ and ‘general quantity’ to capture the distinction between a specific mass and mass in general. Both of these terms pick out properties, but this leaves open, how we should understand these properties, i.e., whether we should think of them as universals, or more nominalistically as tropes or as classes of objects. To understand quantitative properties, we need to understand the relationship between general and specific quantitative properties, as well as the relationships among specific quantitative properties. Nor are quantitative properties restricted to monadic properties. There also seem to be quantitative relations, like twice as massive as, or 4 kg heavier than. Ontologically, one might wonder whether we need to include both of these separately, or whether we could get away with only including quantitative monadic properties or only quantitative relations. Shamik Dasgupta (2013) calls the views that take the monadic properties to be primary absolutism, and views that take quantitative relations to be primary comparativism. Finally, quantitative properties in physics are not limited to scalar quantities, like mass and temperature, but also include more complicated quantities like vectors and tensors. Since the bulk of the philosophical literature has focussed on scalar quantities,2 this chapter will address the problem of quantitativeness as it applies to scalars.

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This chapter will focus on the question of quantitativeness – of identifying the feature(s) that makes quantitative properties quantitative, and mention specific ontological models of quantitative properties only in passing. The chapter begins with two traditional attempts at capturing what makes a property quantitative – being determinable and being numerical – and argues that neither is satisfactory. The chapter then turns to influential proposals which, inspired by the Representational Theory of Measurement, attempt to identify particular relations as characteristic of quantitative properties. These attempts fare better than the traditional ones, but have their own limitations. It concludes with a discussion of a very recent criterion for quantitativeness, which builds on a more abstract understanding of the representational theory of measurement.

32.2

Quantitative Properties as Determinable Properties

The first influential approach to the question of what makes quantitative properties quantitative is the determinable/determinate model (Armstrong 1978; Bigelow and Pargetter 1988, 1990; Johansson 2000). According to this model, a determinable like colour stands in a determination relationship to its determinates like blue or red, which in turn are determined further by navy or sky, or crimson and scarlet respectively. Determinates of the same determinable exclude one another: an object that is crimson all over is not also scarlet all over at the same time (Funkhouser 2006, 2014), see also Chapter 10, this volume. Applying this model to quantities is motivated by the observation that we have, on the one hand, general quantities, like mass, length, or temperature, and on the other hand specific quantities, like the mass of Jupiter, the diameter of Earth, or the temperature of melting ice. According to the determinable/determinate model, a general quantity, like mass, is a determinable, and specific quantities, like the mass of Jupiter, the mass of Mars, or the mass of Venus, are determinates of this determinable. Prima facie, this model fits quite well, because at least for quantities of classical physics, the determination relation as characterised by the model seems to hold for the relationship between specific and general quantities, and specific quantities seem to exclude one another: if an object has a mass of 4 kg, it does not also have a mass of 10 kg. Detailed ontological models of quantities using the determinable/determinate model are developed by D.M. Armstrong (Armstrong 1978, 1988) focussing on quantitative monadic properties, and John Bigelow and Robert Pargetter, who provide an account of quantitative properties in terms of determinate relations of proportion (Bigelow and Pargetter 1988, 1990). Armstrong’s application of the determinable/determinate model is relatively straightforward: mass is a determinable, specific masses are its determinates. Bigelow and Pargetter, by contrast, take determinate relations, e.g., being twice as massive as, to be a central ingredient in their theory. Despite this focus on relations, their theory shares much with Armstrong’s outlook: it is based on universals, seeks to offer an explanation of quantitativeness in non-quantitative terms, and takes the central problem of quantities to be how massive objects are both the same and different in seemingly the same respect: they are all massy, yet differ in mass. For a critical discussion of both views see (Eddon 2013b) and (Eddon 2006) for criticism of Armstrong’s view. How successful is the determinable/determinate model in capturing quantitativeness? J.E. Wolff (2020: ch. 2) has argued that despite initial appearances, the model does not seem to capture the structure of quantitative properties particularly well. Quantitative 359

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properties lack a nested hierarchy characteristic of paradigmatic examples of the determinable/determinate model, like colour. Where in the case of colour we find several intermediary levels between the superdeterminable and the superdeterminates, in the case of quantitative properties, we seem to proceed directly from superdeterminable (mass) to a superdeterminate (e.g., 8.33 kg). More importantly, the determinable/determinate model applies to many properties, including some that are not quantitative: colour, hardness, shapes, determinable kinds (e.g., different isotopes of iron, see (Tobin 2012)). Even if some of these turn out to be candidates for being quantitative properties, this wide applicability of the determinable/determinate model undermines the claim that this model captures what is distinctive about quantitative properties. Finally, and perhaps most problematically, the determinable/determinate model places its emphasis on the vertical relation between the general property – the determinable – and the specific properties – the determinates. But it is not clear that what is distinctive about quantitative properties can be found in this vertical relation. Instead, it seems what is distinctive about quantitative properties, in contrast to other determinable properties, are the relations among the determinate properties. It is widely acknowledged that the determinates of a determinable admit of a special kind of comparison to one another, because they stand in a similarity relation to one another (Funkhouser 2006). We can compare three shades of blue to one another and might conclude that indigo and navy are more similar to one another than either is to sky blue. The same is true in the case of quantities, where masses of 2 kg and 3 kg are more similar to each other than either is to a mass of 60 kg. But in the case of quantities, we can say a lot more than that: masses of 2 kg and 3 kg are much closer in mass than either is to 60 kg, and we can even quantify, how much closer they are to each other than either is to 60 kg. Masses stand in relations of proportion to one another, and they can be concatenated in such a way that their concatenate is the sum of the two masses. It is these latter features that seem characteristic of quantitative properties. The determinable/determinate model does not capture these well, because of its focus on the determination relation instead of on the relations between the determinates. The problem with the determinable/determinate model is not such much that it does not fit, but rather, that its fit is too generic.

32.3 Quantitative Properties as Numerical Properties A main alternative to the idea that quantitative properties are captured by the determinable/ determinate model is the idea that quantitative properties involve numbers in some way: quantitative properties are numerical properties.3 This approach gains plausibility on the one hand from the use of numbers in representing quantitative properties – we represent specific quantities using a number and a unit – and on the other hand from the quasi-mathematical relations that hold among specific quantities: ordering, ratios, addition. The problem of quantitativeness from this perspective is to articulate the sense in which numbers – abstract entities – can be ‘involved in’ physical properties, like mass or temperature. A popular answer to this question is to think of the involvement as a function from either an object to a number (Weatherson 2006), or a pair of objects to a number (Mundy 1988). For the former, we can imagine a quantity as a function from, say, Jupiter, to the number 1.898 × 1027. The advantage of this picture is its simplicity: a quantitative property is a function from an object to a number. Moreover, it seems to capture many of the features that make a quantity quantitative, because these features apply to numbers.4 The 360

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main drawback of this view, however, is that it seems to be committed to a preferred unit; in the example above: kilogram. There are functions from Jupiter to other numbers, for example, 4.1847 × 1027, if we prefer to measure the mass in pounds. This means we either choose a preferred unit as the ontologically fundamental one, which would seem arbitrary, or else we have to accept that a quantitative property involves not just one, but many functions to numbers, leading to a proliferation of fundamental functions. Mundy’s proposal avoids this particular concern, by taking the function to be from two objects to a number, which is to be interpreted as a ratio. For example, we might take a function from the Sun and Jupiter to 1047, where 1047 is the ratio between the mass of the sun and the mass of Jupiter. This proposal avoids committing to a preferred unit, at least for properties like mass, because mass ratios are preserved under changes of unit. Ontologically, both proposals will be unattractive to nominalists, as they involve ontological commitments to numbers, and even non-nominalists might worry that numbers on these proposals must be taken as fundamental (Eddon 2013a). But are quantitative properties really numerical properties? While quantitative properties are often represented numerically, so are other properties and objects. A postcode does not denote a quantitative property, even though it is a number used to represent a location. More tellingly, numbers can be used to represent straightforwardly nonquantitative properties, like categorical kinds. We can represent the property of being a cat using ‘1’ and the property of being a dog using ‘2’, but this does not mean either of these properties is quantitative. Of course, defenders of the numerical view of quantitative properties will insist that it takes more than our representing properties a certain way to establish the existence of the function in question. But it is not clear why we should accept the stipulation that some quantities simply stand in a fundamental relationship to numbers, especially when an alternative is available. This alternative holds that numbers are merely used to represent quantities.

32.4 Quantitative Properties as Relational Structures This brings us to the third, and most popular family of accounts of quantitative properties. These views hold that quantitative properties are structures, characterised by pairs of relations (Arntzenius and Dorr 2012; Field 1980; Mundy 1987; Sider 2020). These views take as their starting point the representational theory of measurement. The best-known version of axiomatic measurement theory is the Representation Theory of Measurement (RTM) (Krantz et al. 2007; Luce et al. 2007; Suppes et al. 2007). This formal theory shows how axiomatically characterised ‘empirical relational structures’ can be represented using specific numerical relational structures by constructing a homomorphism (a structure preserving map) from the empirical to the numerical structure. To take a classic example: a collection of rigid rods of different lengths can be described as set with an ordering relation (‘longer or equal’), and a concatenation operation (‘place rods end to end in a straight line’). This structure can be axiomatized as an additive extensive structure, and it can be shown that there is a homomorphism from such an additive extensive structure to the positive real numbers under ordering and addition. Moreover, proving a uniqueness theorem, it can be shown that this homomorphism is unique up to multiplication by a positive constant. A typical example of this is a change of unit, for example from centimetres to inches in the case of length. Not all quantitative properties form additive extensive structures. Specific temperatures, notoriously, cannot be concatenated, so a better 361

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structure for temperature will be a difference structure, where the axiomatized relations are betweenness and congruence. RTM provides a wide range of axiomatizations for different types of empirical relational structures, and proofs of representation theorems and uniqueness theorems. While representation theorems establish that there is a structure preserving map from a given relational structure to a numerical structure, the accompanying uniqueness theorem shows, how unique the resulting representation is. Here’s an intuitive example: in the case of mass, we can switch from kilogram to pounds by multiplying the original numerical assignments by 2.2. The resulting numerical representation preserves ordering, ratios, and sums. Preserving all of these relations is characteristic of ratio scale representations. Interval scale representations are slightly less unique, since they do not preserve ratios between elements. A typical example are the Celsius and Fahrenheit scales for temperature: a temperature of 20 degrees Celsius is not twice as hot as a temperature of 10 degrees Celsius, even though 20 is two times 10. When expressed in Fahrenheit, these temperatures would be 50 and 68 degrees respectively, and the numerical ratio is different. Other relations, like ordering and differences are preserved, however. The difference between 30 degrees Celsius and 20 degrees Celsius is the same as the difference between 20 degrees Celsius and 10 degrees Celsius, and the same is true on the Fahrenheit scale: the difference between 86 degrees Fahrenheit (30 degrees Celsius) and 68 degrees Fahrenheit is the same as the difference between 68 degrees Fahrenheit and 50 degrees Fahrenheit. Ordinal scales, by contrast, do not even preserve this. A 5-star restaurant is not obviously as much better than a 4-star restaurant, as the latter is to a 3-star restaurant. Paradigmatic quantitative attributes like mass and temperature are representable on ratio or interval scales. Philosophers have accordingly focused their efforts on describing relations that permit a representation on either interval or ratio scale, like betweenness and congruence, or ordering and concatenation. RTM’s own aim is to provide a formal characterisation for the conditions of numerical representability of empirical structures. Philosophers, however, have seen RTM’s potential for a theory of quantities early on (Field 1980; Mundy 1987), although the focus is not always on making quantitativeness explicit. Hartry Field’s influential work aims to provide a nominalistic treatment of quantities to resist indispensability arguments regarding numbers in science. The basic ingredients of his ontology are spacetime points, on which betweenness and congruence relations are defined for each general quantity. For instance, three space-time points a,b,c, might be such that a is Temp-Bet b,c, which is to be read as: a is a spacetime point at which the temperature is in between that of spacetime points b and c. Temp-Cong is a four-place relation, with ab Temp-Cong cd being interpreted as: the absolute temperature difference between a and b is congruent to that between c and d (Field 1980: 56). Brent Mundy (1987), by contrast, aims to show that an ontology of magnitudes, understood as universals, together with second-order relations on them can be formally as rigorous as the formally first-order framework deployed by RTM. In particular, he takes the relational structure to be represented numerically to be a structure of magnitudes with LESS THAN and SUM OF as second-order relations, which function like ordering and concatenation among magnitudes. Common to both Field’s and Mundy’s proposals (and others like theirs) is that quantitative properties are understood as sets with relations on them, and hence, as structures. The key ontological question for this approach to quantitativeness then becomes: what entities should be the members of the set, and which relations should be the ones that make 362

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for quantitativeness? Since the intended numerical representation is usually the reals or the positive reals, the set has to be infinite, but beyond that, the formalism does not impose restrictions on the entities involved. The entities are not what makes for quantitativeness; it’s the relations that hold between them. This relational approach to quantitative properties has several clear advantages. First, it seems to capture what is distinctive about quantities. While many properties might seem to fit the determinable/determinate model, requiring either ordering and concatenation or betweenness and congruence rules out determinable kinds, hardness, and (perhaps) colour, while applying to paradigmatic cases of quantitative properties, like mass, length and temperature. Second, it explains why numbers are so useful in the representation of quantitative properties, while firmly relegating numbers to a purely representational role. Numbers are useful for representing quantitative properties, because the relations that make for quantitativeness can be characterised axiomatically in such a way that the same axioms apply to relations that hold among numbers, like less than and addition. Finally, the approach is ontologically flexible: the relations can be thought to hold among concrete objects (suggested by RTM’s characterisation of empirical relational structures), spacetime points (Field 1980), platonic universals (Mundy 1987), or locations in quality spaces (Arntzenius and Dorr 2012). There are, however, some drawbacks. One is that this way of understanding quantitativeness seems to entail that there are fundamental relations, as the pairs of relations chosen are typically understood to be external relations. This is unattractive for certain metaphysical pictures, like Lewisian Supervenience (Eddon 2013a). More importantly, if our aim is to give necessary and sufficient conditions for quantitativeness in terms of relations, it seems odd that we seem to have a choice of relations. There are two senses in which we have a choice of relations. The first is that we choose, which kind of relational structure, in RTM’s sense, we take to be characteristic of quantities. That is, we have a choice whether we think quantitative properties are best characterised by difference structures or additive extensive structures, for example. The former corresponds to choosing betweenness and congruence as the defining relations for quantitative properties, the latter to choosing ordering and concatenation. This looks like a substantive disagreement over what makes for quantitativeness, with consequences for which properties will count as quantitative. The latter proposal works well for properties like mass, which can be concatenated, whereas the former works better for properties like temperature, where such concatenation is lacking. Length will do well on either proposal. The choice of relational structure is related to the scale at which the property is represented: ordinal, interval, or ratio. Additive extensive structures allow ratio scale representation, whereas difference structures typically only allow for interval scale representations. The second sense in which there is a choice of relations is less obviously a substantive one, which makes the existence of the choice all the more puzzling. The best way to introduce this problem comes from Brian Ellis (1966). Ellis observes that lengths can be concatenated either by placing rods end to end in a straight line, or alternatively, by placing them at right angles. Either way of concatenating the rods will satisfy the axioms for additive extensive structures, yet the numbers assigned to the concatenated lengths will differ. Using end-to-end concatenation in a straight line, the lengths of rods a and b will form the sum of length (a) and length (b): c = a + b. Using right angle concatenation, we instead get c2 = a2 + b2. In RTM, this problem is known as the problem of alternative numerical representations (Krantz et al. 2007: 99ff). The difficulty is that axiomatic 363

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characterisations of relational structures admit of a variety of interpretations, both empirical and mathematical. The axioms on their own hence do not select a particular pair of relations as characteristic even for the axiomatic structure in question. Metaphysical approaches to quantitativeness that rely on quantitativeness being a matter of particular pairs of relations being instantiated face a problem of underdetermination (for further discussion, see (Eddon 2014; Wolff 2020: ch. 9).

32.5

Quantitative Properties as Rich Structures

Wolff (2020) has recently proposed a somewhat more abstract criterion for quantitativeness based on RTM. The key idea is that quantitative properties are representable by numerical structures to a high degree of uniqueness. As we have seen, paradigmatic examples of quantitative properties, like mass and temperature, can be represented on either interval scales or ratio scales. An intuitive idea, then, is to say that quantitative properties are those that can be represented at interval or ratio scale level, but not those that are representable only at ordinal scale. This intuitive idea needs two pieces of support to be plausible. First, we need a good reason for drawing a sharp line between interval and ordinal scales, and second, we need to say something about what makes a property representable at these scales. Wolff argues that RTM in fact provides the ingredients to both steps (Wolff 2020: ch. 6). First, the Alper-Narens theorem shows that, formally speaking, interval and ratio scales are much closer in their uniqueness properties than either is to ordinal scales.5 This suggests that there is, in fact, a sharp distinction between interval and ordinal scale types. Second, R.D. Luce has shown that structures with particular kinds of automorphisms satisfy the conditions for representability on interval or ratio scale types as laid out by the Alper-Narens theorem.6 Specifically, they have translations as non-trivial automorphisms, and these translations form an Archimedian ordered group. An automorphism is an isomorphism that maps a set to itself. A trivial automorphism is simply the identity: a map that maps each element of the set to itself. A non-trivial automorphism is one that maps at least one element of the set to a different element of that set. For automorphisms to form an ordered group is to say that for the automorphisms of the structure, a relation ‘. Rayo, A. and Yablo, S. (2001) Nominalism through Denominalization. Noûs 35(1): 74–92. Schiffer, S. (1996) Language-Created, Language-Independent Entities. Philosophical Topics 24(1): 149–167. Strawson, P. F. (1959) Individuals: An Essay in Descriptive Metaphysics. London: Methuen. Skiba, L. (2021) Higher-Order Metaphysics. Philosophy Compass 16(10): 1–11. Wright, C. (2007) On Quantifying into Predicate Position. In Potter, M. (ed.) Mathematical Knowledge. Oxford: Oxford University Press: 150–174.

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34 MENTAL CAUSATION AND HIGHER-ORDER PROPERTIES David Robb

34.1

Introduction

Let us assume that all mental particulars – every mental state and event as well as minds themselves – are physical. Such a particular has many properties, some of which are mental. When a mental particular causes something, does it do so qua mental, that is, in virtue of its mental properties? The answer may seem to be clearly Yes. When a pain causes me to wince, it does so in virtue of how it feels, that qualitative property. When a belief causes me to walk to lunch, it does so in virtue of what it means, that content property. But matters are not so straightforward. It is often thought that mental properties are higher-order properties not reducible to physical properties. And it’s plausible to think that when a pain or a belief causes a bit of behavior, it does so in virtue of its first-order physical properties. Thus, there is no additional work for higher-order mental properties to do: they are epiphenomenal. In this chapter I examine this reasoning in some detail. I begin with some of the relevant metaphysical background in Sections 34.2–34.4, returning to mental causation in Sections 34.5–34.6. In Section 34.7, I conclude by sketching an alternative ontology in which there are no higher-order properties.

34.2

What are Higher-Order Properties?

It will be simplest to define only a certain kind of higher-order property, namely a secondorder property. Some mental properties are third- or fourth-order, but these need not concern us in this chapter. Similar issues will arise for these other higher-order properties. A first-order property is a maximally determinate property of an object. The mass of the Earth and a specific shade of red (such as crimson) are first-order properties. For an object to have a second-order property is for it to have some first-order property that meets a certain condition. The condition is typically causal. For example, a vase has the secondorder property of being fragile just in case it has some first-order property (a molecular structure) in virtue of which it would break when subjected to a strong force. For a liquid to be poisonous is for it to have some first-order property (a chemical composition) in virtue of which it causes death when ingested. Sometimes the defining condition is

DOI: 10.4324/9781003246077-43

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qualitative rather than causal. For an apple to be red is for it to have some first-order property, some determinate shade, that meets a certain qualitative condition, one that’s difficult to describe, but that we associate with the color red. For a paperweight to be rectangular is for it to have some first-order property, some determinate shape such as squareness, that meets the qualifications for rectangularity: closed plane figure with four straight sides and four right angles (for more on the determinate/determinable distinction, see Chapter 10, this volume). The first-order/second-order distinction is not the same as the micro/macro distinction. Both red (a second-order property) and scarlet (a determinate, first-order shade of red) are macroscopic, observable properties. That said, sometimes a first-order property is best described in micro-physical terms. This is the case for the first-order properties realizing fragility and poisonousness. The first/second order distinction is also not the same as the distinction between properties of objects and properties of properties. Being a shade of red characterizes crimson, as do, say, being a property and being an entity. But if these are properties at all, they are properties of a property. They are not second-order properties which are possessed, not by crimson, but by objects – an apple in this case. Finally, the firstorder/second-order distinction is not the same as the physical/non-physical distinction. While it is difficult to define what makes a property physical (Stoljar 2010), many secondorder properties are physical in a broad sense. For example, fragility and redness are plausibly physical, as are many mental properties. Furthermore, it’s possible that some first-order properties are non-physical. If there are souls, and if they are made of a certain kind of stuff, then it could turn out that among the first-order properties of a soul are the various spiritual configurations of its stuff, configurations that realize that soul’s secondorder mental properties. Or suppose that numbers are abstract objects and have properties. The number 3’s magnitude will be a non-physical first-order property, while its being odd will be a second-order (also non-physical) property, that of having some magnitude that is not divisible without remainder by 2.

34.3

Are There Second-Order Properties?

To define second-order properties is one thing; to show that they exist is another. There’s no doubt that there are second-order predicates; these can be defined in a way that closely mirrors the definition of second-order properties. But it’s controversial whether such predicates apply in virtue of second-order properties. To examine this issue, we must consider some of the criteria to be used when deciding when a predicate applies in virtue of a distinctive property. As an aside, I note that whether a predicate applies in virtue of a distinctive or unique property should be distinguished from whether it applies on any given occasion in virtue of some property or other. Consider the predicate “is red”, and for a moment deny that it picks out a distinctive property. That is, deny that red is a property. Still, one may hold that whenever “is red” applies to an object, it does so in virtue of some property or other of that object, presumably some particular shade: scarlet, crimson, or the like. These shades are distinct but resembling first-order properties making true “That is red” for each red object. That said, in the remainder of this section I shall consider the stronger thesis that the same property, red, answers to this predicate for all red things: apples, stop signs, and fire engines. Let us return then to the conditions under which second-order predicates pick out a unique property. According to one criterion, a predicate qualifies when it corresponds to a 384

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respect of objective resemblance (Armstrong 1989). Thus, “is red” seems to pick out a respect of resemblance, while “is a game” apparently does not. But this is not an especially useful test. We can account for the resemblance of objects falling under “is red” without appealing to the second-order property of red. We can instead appeal to the (primitive) resemblance among the first-order shades of red. The weaker thesis mentioned above will do: when “is red” applies to an object, it does so in virtue of that object’s having a firstorder property meeting the right qualitative condition. Another test for whether a predicate picks out a distinctive property asks whether that predicate plays an indispensable role in explanation, whether in science or ordinary life. Thus, “is fragile”, “is red”, and the like appear in successful explanations. Stephen Yablo’s (1992) pigeon Sophie is trained to peck at red things. Some super-cooled objects shatter when struck because they are fragile. An organism may survive a predator’s attack because it has a high degree of fitness. Removing the second-order predicates would make these explanations less informative. These predicates have, then, the explanatory credentials needed to pick out second-order properties. I consider the explanatory argument to be more promising than the resemblancebased argument. Nevertheless, there are ways to resist. Is Sophie trained to peck at red or shades of red? If the latter, then only these first-order shades are needed to explain her pecking behavior. Granted, they must be shades of red, but this can be spelled out in terms of the resemblance among the shades (as above). No second-order property is required. However, this modified explanation of Sophie’s behavior may seem to be less unified than one that appeals to the second-order property. Unity is a virtue of explanation (Kitcher 1989): when we bring diverse phenomena under a single property, the world becomes more intelligible as these phenomena are seen to be instances of the same feature. So while appeals to red and some shade of red may equally explain Sophie’s pecking behavior, the former achieves more unity, and thus should be favored. This is evidence for a second-order property at work. The strength of this reply, however, turns on the nature of unity as an explanatory virtue. When we explain Sophie’s pecking by appealing to shades of red, we do allude to a kind of unity, namely the relation of resemblance among these shades. This would seem to deliver at least as much intelligibility to our understanding of Sophie’s behavior as the relation of identity that holds between red across its various instantiations. A third test for whether a predicate picks out a distinctive property asks whether the alleged property has (or bestows) causal powers. Here we rely on the “Eleatic” principle: to exist is to have causal powers (Oddie 1982). If second-order properties do not bring with them their own causal powers, this is grounds for ontological elimination. We would retain the corresponding second-order predicates, but there would be no second-order properties, as there would be nothing for such properties to do. This particular criterion will be examined in Section 34.5, when we look at the exclusion argument. For now, I just note that this argument should be carefully distinguished from the explanatory argument sketched above. Whether second-order predicates appear in good explanations is one thing; whether second-order properties have causal powers is another. Explanation is an epistemic activity; causation and causal powers are metaphysical entities. While there are important connections between the two (Kim 1988), they should be disentangled in this context. I’ve considered a few reasons to think that there are second-order properties. Each has limitations, but for the time being I will assume that at least some properties are secondorder. I now turn to a more specific question: are mental properties among them? 385

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34.4 Second-Order Mental Properties One of the lessons of functionalism (Levin 2018) is that mental properties are secondorder. To be in pain is to have some first-order (neurological or micro-physical) property that plays a certain causal role: it is caused by tissue damage, it causes wincing, it causes the belief that one is in pain, etc. Functionalism says there is a distinctive causal role essential to every mental property. The first-order properties playing these roles are the various “realizers” of the mental property. Another lesson of functionalism is that a variety of firstorder properties can realize any given mental property (Fodor 1974). This is the “multiple realizability” of the mental, a doctrine driving much of the contemporary discussion of mental causation. One may object that qualitative mental properties, those characterized by a certain kind of feel, do not introspectively seem to be second-order properties. The hurt of pain, for example, or the taste of a strawberry, seem clearly to be first-order properties, as determinate as any shade of red. But I consider this appeal to introspection to be weak. Do qualitative properties seem to be first-order? What would they seem like if they seemed to be second-order? Introspection is neutral on such metaphysical issues. The order of mental properties must be settled on philosophical or scientific grounds, not on the basis of introspection. I should note that not all versions of functionalism say mental properties are secondorder. Some early versions of the view (Armstrong 1993[1968]; Lewis 1994) say that mental properties are first-order physical properties picked out by second-order predicates. “Is in pain”, for example, when it applies to a creature, applies in virtue of that creature’s first-order physical properties, which can vary depending on the type of creature in question. But in what follows, I will assume (until the final section) that this is not the brand of functionalism in play in this chapter. I will, that is, adopt a more orthodox version according to which mental properties are second-order. Another reason to think mental properties are second-order is also emphasized by orthodox functionalists: mental properties enter into psychological laws. Let us suppose that a law is a relation among properties (Dretske 1977; Armstrong 1983). Thus, Newton’s gravitational law relates mass and distance as well as other quantities. Voltage and resistance appear in Ohm’s Law. The genetic variation within a population appears in the Hardy-Weinberg principle. In psychology, laws tend to be “hedged”, holding only ceteris paribus, but they are for all that still laws. Intolerance for uncertainty tends to be correlated with anxiety. Depression is anger turned inward. We strive to reduce cognitive dissonance. The italicized terms appear to refer to psychological properties. If these are genuine laws, and if laws relate properties, then there are psychological properties. But, the argument continues, it’s implausible to think that these laws relate first-order properties (Fodor 1974). It’s not any determinate voltage or resistance that appear in Ohm’s Law, but the determinable, second-order properties of voltage and resistance. While for a given person a determinate kind of anger will result in a determinate kind of depression, the law itself abstracts away from these differences, relating only the second-order mental properties. This appeal to psychological laws can combine forces with the earlier explanatory argument. On the Deductive-Nomological view (Hempel 1965), laws are essential to scientific explanation. To explain a phenomenon is to deduce it from a covering law plus particular conditions. If successful psychological explanations appeal to laws, this is good

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reason to think that the properties appearing in such laws exist. And if psychological laws relate second-order properties, then these explanations thereby give us reason to think that mental properties are second-order.

34.5

Are Second-Order Mental Properties Causally Efficacious?

Let us assume, then, that mental properties are second-order. So conceived, are they causally efficacious in the production of behavior (as well as the production of other mental states)? The exclusion argument says No: the only causally efficacious properties are firstorder. Second-order properties don’t do any causal work. At best, appeal to second-order predicates is explanatorily useful, but this shouldn’t be taken to indicate the efficacy of the corresponding properties. This conclusion is clearly in tension with the Eleatic principle mentioned earlier. We must then either give up our working assumption that mental properties are second-order properties, abandon the Eleatic principle, or find something wrong with the exclusion argument. I now consider this latter argument in more detail. There are different versions of the exclusion argument (for samples, see Block 1990; Kim 2005; Malcolm 1968). Here I abstract from the details of any particular version. Let us consider a mental particular m (say, a mental event) with second-order mental property M, a property m has by virtue of some physical property P’s meeting a certain condition. (“P” is meant to suggest “physical”, but strictly speaking the first-order realizer of M could be a non-physical property, as noted earlier. Functionalism permits non-physical realizers of mental properties, even if most functionalists tend to reject these on empirical grounds.) Suppose m produces a bit of intentional behavior, such as walking to lunch or asking a question. It is plausible to assume that when m does this, its first-order property P is, relative to a causal background, efficacious in producing that effect. Let this be our first premise: (i) Whenever m causes a behavioral effect b, m’s first-order property P is efficacious in producing that effect. The case for this premise is most straightforward given functionalism, on which P counts as M’s realization by virtue of P’s causal role. That is, part of what it is for P to be a first-order realizer of M is that P is, in these circumstances, efficacious in producing b. On the other hand, what if M is defined in terms of P’s meeting some qualitative condition? It’s not immediately obvious in this case that P would do any causal work. Here we must rely on a certain kind of correlation between the qualitativeness of a property and the powers it bestows. In particular, as we move down the hierarchy from higher-order properties to their first-order realizers, increasing qualitative richness is matched by broadening causal powers, so that any powers found at any qualitative level must ultimately be found in the base first-order properties as well (cf. Wilson 2011). In the present case, this is enough to ensure that the qualitatively determinate P has all of the resources to produce m’s effect. Let us now add a second premise: (ii) Whenever a property is efficacious in producing an effect, no other property is efficacious in producing that effect, unless this is a case of overdetermination. Overdetermined effects are “overproduced”: they are produced by distinct properties. My engine may stop because it simultaneously overheats and runs out of gas. I may walk to the 387

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cafeteria both because I am hungry and because I want to meet a friend. If m’s production of b is similar to such cases, then we may say that M and P are both efficacious. But our last premise says that this is not the case: (iii) Whenever m causes a behavioral effect b, m’s first-order property P and its secondorder property M do not overdetermine that effect. This gets us to our conclusion: (iv) Therefore, whenever m causes a behavioral effect b, m’s second-order property M is not efficacious in producing that effect. Note that this conclusion does not deny the importance of second-order predicates in psychological explanation. It does deny, however, that such predicates pick out efficacious properties. Second-order mental properties may nevertheless retain a kind of explanatory relevance (see, e.g., Jackson and Pettit 1990). For example, as noted earlier, they may deliver the kind of unity we desire in good explanations. But if we are to keep our working assumption that such properties exist, we must abandon the Eleatic principle (or modify it to say that having either causal power or explanatory relevance is the mark of being). In any case, let us now look more closely at the argument’s third premise.

34.6

Against Overdetermination

Overdetermination does happen, but it is rare. This is an empirical claim. It could have turned out that many or even all effects in our world are overdetermined. (This seems to have been Spinoza’s view: every event is determined both by prior events and by God.) But we’ve discovered that this is not the case. It would thus be surprising if in the mental realm overdetermination were rampant, if every bit of intentional behavior were produced by both a mental and physical property. That said, the world is sometimes surprising, and there can be redundancy in nature. Moreover, there are reasons independent of the present issue to think that the mental realm is special. Nevertheless, I think we should deny that mental causation always involves the overproduction of the behavioral effect. Suppose first that causal production involves the transference of energy from efficacious property to effect (cf. Fair 1979). If M and P overdetermined the behavioral effect b, this would require two simultaneous energy transfers from m to b, two parallel causal processes. And while I cannot rule this out a priori, it strikes me as empirically unlikely. At the very least, we can say that the overdetermination hypothesis, so-construed, makes a risky empirical prediction. Whenever we discover a first-order neural process in the brain, a process that realizes the beginning of an intentional action, we should also discover a parallel energy process producing the same (immediate) effects. While one can imagine such redundancy in some cases, it seems implausible that it would hold in every case of intentional action. There is an alternative picture of M’s relevance to b that may avoid such problems. Suppose M helps to produce b, not by transferring energy to it, but by “structuring” the brain so that P can produce this effect. (Such a view is developed in different ways by Dretske 1988, Gibb 2015, and Lowe 2003.) By digging a ditch, I divert a stream so that the 388

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water in it drives a wheel. What energy I add to the system is not directly transferred to the wheel: the water does that. My role is to shape the ground in such a way that the water can accomplish this task. If this is overdetermination of the wheel’s turning, it is of an innocuous sort, and does not require two parallel processes overproducing the effect. Similarly, the role of M may be to structure the brain so that P can produce the effect. This kind of overdetermination would not be problematic. But whatever its virtues, this model of mental causation cannot work if M is conceived as a second-order property defined in terms of P’s meeting a certain condition. (And so it’s not surprising that none of the authors just cited thinks of M in this way.) After all, any efficacy attributed to M must also be attributed to P, so that if M structures parts of the brain, P must do so as well. This is just to reassert the first premise of the exclusion argument. And then the same empirical risk will arise, for any energy transfer involved in P’s structuring activities must be found in parallel for M. A second problem with the overdetermination hypothesis is also empirical. In cases of overdetermination, either property by itself would have produced the effect. To imagine M without P, we imagine M with a different first-order realizing property. To imagine P without M we must consider a counterpossible, for P is normally thought to necessitate M. But let us grant that this is an intelligible counterfactual (see Bennett 2003 for some of the subtleties here). In any case, P without M or M without P would produce the effect if the overdetermination hypothesis is true. However, and this is the empirical claim, overdetermined effects always leave a mark of their origin. That is, the effect b, while it occurs when produced by P and M together, would have slightly different properties if produced by just P or M alone. My engine would stop if it runs out of gas, and it would also stop if it overheats. But if it stops for both reasons, it will stop in a slightly different way: with more noise, say, or more vibration. Similarly, we should expect b to show signs of being overdetermined, but I suspect that neuroscience will reveal no such signs. Given that we never find P without M (and we never find M without some first-order realizer or other, even if it’s not P), one might wonder how we could detect b’s distinctive marks of overdetermination. After all, on the overdetermination hypothesis, behavioral effects are always overdetermined, so we never find them with just one cause. One solution is to study first-order properties similar to P, but different enough so that they do not realize a mental property. If the marks P leaves on b are discontinuous enough from those that P’s similar (but non-mental) properties leave on their behavioral effects, this will be evidence that b is overdetermined, that there is a second efficacious property at work (for another suggestion, see Robb 2018). My brief case against overdetermination has rested on a robust, “non-Humean” conception of causality. The first argument explicitly assumes the transference theory of causality. And the second, while it doesn’t mention any particular causal theory, does seem to depend on a “productive” notion of efficacy on which overdetermined effects bear a distinctive mark of their origin. But, one may object, there are other conceptions of causation on which these worries are not as pressing. Consider, for example, variations of the counterfactual theory, on which causally efficacious properties are counterfactually necessary (or on some versions, sufficient) for their effects (see, e.g., LePore and Loewer 1987, and for criticism Braun 1995). A substantial portion of the literature on the exclusion problem is devoted to working out the details of a counterfactual theory. If some version turns out to be correct, overdetermination may not be such a difficult problem, and we can safely reject the third premise of the exclusion argument. 389

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I cannot here take on the counterfactual theory (for critiques, see Dowe 2000 and, in the context of the mental causation debate, Kim 1998). I will instead flag a couple of problems with it: counterfactuals are superficial and subjective. Superficial: when a counterfactual holds, it rarely indicates on its surface the source of the counterfactual dependence. There is often a deeper story to be told about why the counterfactual holds. Supposing, for example, that if M hadn’t been instantiated, b wouldn’t have occurred, why is this the case? It is this underlying truthmaker for the counterfactual claim that reveals the causal story, and I suspect that in the case of second-order mental properties, the counterfactual will hold only in virtue of the efficacy of M’s first-order realizer P (as well as such realizers in nearby worlds). Subjective: It is well-known that evaluating counterfactual requires holding fixed certain factors and letting others vary. And it is difficult to see how the world could determine what to fix and what to vary. Such decisions seem to depend on, among other things, what is salient, the explanatory context, and even one’s willingness to allow small, local violations of natural law. But if causal efficacy is an objective relation, it’s difficult to see how it could turn on such subjective decisions.

34.7

Mental Causation in a World of First-Order Properties

For most of this chapter I have operated with the working assumption that there are second-order properties, and that among these are mental properties. I conclude by supposing that there are no second-order properties (a fortiori, mental properties are not second-order). What does mental causation look like in a world of first-order properties? I have argued elsewhere (e.g., Robb 2013) that this question is best answered by conceiving of first-order properties as tropes, i.e., properties that are particulars, not universals. The question is what mental causation looks like within a trope ontology, one that recognizes only tropes (as well as classes and bundles of tropes). In this final section, however, I relax this requirement and allow that first-order properties may either be tropes or universals of the sort defended by D.M. Armstrong (1989; see Maurin 2008 for discussion). Tropes and Armstrong-style universals have much in common: they exist in the objects that have them; they are sparse; and, most important for present purposes, they are first-order. If ours is a world of first-order properties, whether they be tropes or Armstrong-style universals, then something will need to be said about the arguments for second-order properties broached earlier. (Second-order predicates are not in question here; I consider their existence to be uncontroversial.) I have already sketched my reply to these arguments: we can account for the objective resemblance among objects picked out by a second-order predicate by appealing to the primitive resemblance among first-order properties. Along the same lines, the unity achieved by the use of second-order predicates can be found in those same relations of resemblance. As for the causal powers allegedly bestowed by secondorder properties, this has been rejected on the grounds of the exclusion argument. The Eleatic principle, which I can now reintroduce with full endorsement, adds to the reasons to reject second-order properties. Power, the mark of being, is possessed by, and only by, first-order properties. A primary reason for saying that mental properties are second-order was that this is an immediate consequence of orthodox functionalism. It’s clear, then, that functionalism in this version will need to be rejected. Yet because second-order predicates are still permitted, a kind of functionalist theory can be advanced, just one that claims to define mental 390

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predicates in in terms of causal roles. The properties that make such predicates true on a given occasion will need to be first-order. What results is a functionalism much closer to the version defended by David Lewis and Armstrong. Indeed, the theory of mind that results from this is the identity theory (cf. Horgan 1997). Every mental property is physical. (Of course, this does not entail that every physical property is mental.) When a mental predicate applies to a person or an event, it does so in virtue of that particular’s physical properties, all of which are first-order. There is no threat, then, that the efficacy of mental properties will be excluded by that of their first-order “realizers”, for every mental property just is what orthodox functionalists would call its realizer. There is just one property, not two, so there is no causal competition. What about psychological laws? Earlier these were taken to show that mental properties are second-order, for it is implausible to think that such laws relate first-order properties. One option here is to say there are no such laws. Granted, there are abstract generalizations that use second-order predicates, but if there are (governing) laws to make such generalizations true, they are clusters of laws relating first-order psychological properties. An alternative view, one I favor, rejects laws altogether. The idea is that first-order properties bestow powers on the object that have them, and these powers are enough to account for the regularity and modal structure of the world: laws aren’t needed (see Mumford 2004). This move would not be permitted by Armstrong, but one can imagine a view similar to his on which first-order universals are powers. The no-laws view also fits well with trope theory. None of this is to say that mental causation is unproblematic on the identity theory. One worry is that every mental property, being physical, will fall under two sorts of predicate, one mental and one physical. And one may argue that the exclusion problem comes up all over again, for our one property will itself have a mental property and a distinct physical property. (Neither will be second-order: as noted earlier, a property of a property isn’t second-order.) Let us call our single property F and its two alleged properties P* and M*. When F is efficacious in producing a bit of behavior, does it do its causing in virtue of P* or M*? This is not exactly the exclusion problem as presented above, but it is very close to it. And the worry is that it’s P*, not M*, that’s doing the real work here. I believe this objection is based on a mistaken view of properties (Robb 2017). Properties, I maintain, do not have properties (for discussion, see Grossmann 1983: 82–84). When F falls under two predicates, one mental and one physical, this should not be taken as indicating that F has two kinds of property. Rather, F itself is the truthmaker for both of these predications. The property has no internal subject-attribute complexity, but is rather a simple entity. There are thus no distinct natures in F for which the exclusion problem could arise.

References Armstrong, D.M. (1993[1968]) A Materialist Theory of the Mind, Revised Edition. London: Routledge. Armstrong, D.M. (1983) What Is a Law of Nature? Cambridge: Cambridge University Press. Armstrong, D.M. (1989) Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Bennett, K. (2003) Why the Exclusion Problem Seems Intractable, and How, Just Maybe, to Tract It. Noûs 37(3): 471–497. Block, N. (1990) Can the Mind Change the World? In Boolos, G. (ed.) Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge: Cambridge University Press: 137–170. Braun, D. (1995) Causally Relevant Properties. Philosophical Perspectives 9: 447–475.

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David Robb Dowe, P. (2000) Physical Causation. New York: Cambridge University Press. Dretske, F. (1977) Laws of Nature. Philosophy of Science 44(2): 248–268. Dretske, F. (1988) Explaining Behavior: Reasons in a World of Causes. Cambridge, MA: MIT Press. Fair, D. (1979) Causation and the Flow of Energy. Erkenntnis 14(3): 219–250. Fodor, J. (1974) Special Sciences (Or: The Disunity of Science as a Working Hypothesis). Synthese 28(2): 97–115. Gibb, S. (2015) The Causal Closure Principle. Philosophical Quarterly 65(261): 626–647. Grossmann, R. (1983) The Categorial Structure of the World. Bloomington, IN: Indiana University Press. Hempel, C.G. (1965) Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press. Horgan, T. (1997) Kim on Mental Causation and Causal Exclusion. Noûs 31(s11): 164–184. Jackson, F. and Pettit, P. (1990) Program Explanation: A General Perspective. Analysis 50(2): 107–117. Kim, J. (1988) Explanatory Realism, Causal Realism, and Explanatory Exclusion. Midwest Studies in Philosophy 12: 225–239. Kim, J. (1998) Mind in a Physical World. Cambridge, MA: MIT Press. Kim, J. (2005) Physicalism, or Something Near Enough. Princeton: Princeton University Press. Kitcher, P. (1989) Explanatory Unification and the Causal Structure of the World. In Kitcher, P. and Salmon, W. (eds.) Scientific Explanation. Minneapolis, MN: University of Minnesota Press: 410–505. LePore, E., and Loewer, B. (1987) Mind Matters. Journal of Philosophy 84(11): 630–642. Levin, J. (2018) Functionalism. In Zalta, E. (ed.), The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/functionalism/>. Lewis, D. (1994) Reduction of Mind. In Guttenplan, S. (ed.) A Companion to the Philosophy of Mind. Oxford: Blackwell: 412–431. Lowe, E.J. (2003) Physical Causal Closure and the Invisibility of Mental Causation. In Walter, S. and Heckmann, H. (eds.) Physicalism and Mental Causation: The Metaphysics of Mind and Action. Exeter: Imprint Academic: 137–154. Malcolm, N. (1968) The Conceivability of Mechanism. Philosophical Review 77(1): 45–72. Maurin, A-S. (2008) Does Ontology Matter? In Gozzano, S. and Orilia, F. (eds.) Tropes, Universals and the Philosophy of Mind. Frankfurt: Ontos Verlag: 31–56. Mumford, S. (2004) Laws in Nature. London: Routledge. Oddie, G. (1982) Armstrong on the Eleatic Principle and Abstract Entities. Philosophical Studies 41(2): 285–295. Robb, D. (2013) The Identity Theory as a Solution to the Exclusion Problem. In Gibb, S.C., Lowe, E.J., and Ingthorsson, V. (eds.) Mental Causation and Ontology. Oxford: Oxford University Press: 215–232. Robb, D. (2017) Power for the Mental as Such. In Jacobs, J.D. (ed.) Causal Powers. Oxford: Oxford University Press: 205–215. Robb, D. (2018) Could Mental Causation Be Invisible? In Carruth, A., Gibb, S.C., and Heil, J., (eds.) Ontology, Modality, and Mind: Themes from the Metaphysics of E.J. Lowe. Oxford: Oxford University Press: 165–175. Stoljar, D. (2010) Physicalism. London: Routledge. Wilson, J. (2011) Non-reductive Realization and the Powers-based Subset Strategy. The Monist 94(1): 121–154. Yablo, S. (1992) Mental Causation. Philosophical Review 101(2): 245–280.

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35 QUALIA AS PROPERTIES OF EXPERIENCES Umut Baysan

35.1

Introduction

Some of our mental states are such that there is something it’s like to have them. There is something it’s like to have a visual experience of a predominantly red and orange scene, and that is different from what it’s like to have a visual experience of a predominantly black and blue scene. Presumably, this talk of ‘something it’s like’ generalises from visual experiences to experiences in all sensory modalities and to bodily sensations. There is something it’s like to smell freshly brewed coffee, and that is different from what it’s like to smell expired milk. There is something it’s like to have a painful bodily sensation, and that is typically different from what it’s like to have a pleasant bodily sensation. The jury is out on whether other sorts of mental states, such as propositional attitudes like beliefs also have this feature (see essays in Bayne and Montague 2011), but this debate shall not concern us in what follows. Let’s say that a mental state is phenomenally conscious just in case there is something it’s like to have that mental state. So, the mental states we have considered above are all examples of phenomenally conscious mental states. ‘Qualia’ (‘quale’ for the singular form) is a term that is often used to refer to the properties that give such mental states this feature.1 The nature and the very existence of qualia have long been debated. While some philosophers draw anti-physicalist conclusions from considerations based on qualia and phenomenal consciousness (e.g., Chalmers 1996; Goff 2017; Jackson 1982), others find qualia too problematic to reify (e.g., Dennett 1988; Frankish 2012). My aim in this chapter is to clarify what it is to be minimally ontologically committed to qualia as properties. This is how the chapter proceeds: In Section 35.2, I will introduce what I shall call the spooky conception of qualia, according to which, qualia, if there are any, are properties of such a kind that their existence entails a ‘spooky’ metaphysics (to be explained shortly). Anti-realists and eliminativists about qualia typically reject the existence of qualia by invoking the spooky conception. In Section 35.3, I will contrast the spooky conception with what I shall call the neutral conception of qualia. On the neutral conception, qualia are simply understood as properties of experiences in virtue of which there is something it’s like to have those experiences, where such properties may or may not be spooky. By

DOI: 10.4324/9781003246077-44

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appealing to the neutral conception, I will illustrate what it is to be minimally ontologically committed to qualia. In Section 35.4, I will discuss the argument that qualia realism faces a problem of causation. The worry is that, in a causally closed physical world, qualia cannot be causally efficacious without entailing systematic causal overdetermination, which is found objectionable. I will conclude by illustrating some of the ways qualia realists can respond to this objection.

35.2

Qualia: The Spooky Conception

It is tempting to think that there are qualia. We are conscious creatures, so there is something it’s like to be us. As conscious creatures, we have conscious experiences, and there is something it’s like to have these conscious experiences. So, presumably, there are properties of our experiences that confer on them this feature. Although this line of reasoning is tempting, realism about qualia is often associated with views which are found objectionable and which I shall collectively refer to as ‘spooky’ views. The spooky views in question include: (a) Mental properties and physical properties are fundamentally different kinds of properties. (Dualism) (b) The mental is something ‘over and above’ the physical. (Anti-physicalism) (c) Consciousness is not a natural phenomenon. (Non-naturalism)2 These views are deemed spooky because they allegedly posit mysterious entities that are not in the purview of the physical sciences – things on a par with ghosts, ectoplasm, and other mysterious and blatantly unscientific entities. Let’s say that a property is spooky just in case its existence entails a spooky view (in the sense of ‘spooky’ as specified above). Thus, qualia are spooky properties insofar as only spooky views can accommodate them. But why think that qualia must be spooky? Why might qualia realism be associated with spookiness? One explanation might be that we are primed to think of qualia in association with what David Chalmers (1995) calls ‘the hard problem of consciousness’, which is the difficulty – and the alleged impossibility – of explaining the subjective and phenomenal aspects of our conscious experiences (i.e., ‘what it’s like to have them’) from a purely objective and physical point of view. Three influential accounts are often employed to illustrate this problem. First, Thomas Nagel (1974) makes the very striking observation that no knowledge of the physical make-up of a bat – a creature whose sensory organs work in radically different ways from ours – can give us the knowledge of ‘what it’s like to be a bat’ (i.e., what it’s like to experience the world through echolocation), suggesting that even a complete physical knowledge of all there is to know about a bat’s physiology will leave out the knowledge of qualia. Second, Frank Jackson (1982) provides the case of Mary, a brilliant colour scientist who has spent her life in a black and white room, having never experienced any colour other than black, white, and shades of grey. Mary is presumed to know all physical facts about colour perception, but when she is released from the black and white room for the first time to see a red tomato, she learns something new, i.e., what it’s like to see red, entailing, according to Jackson’s knowledge argument, that there are non-physical facts, and qualia must be non-physical properties. Third, Chalmers (1996) asks us to imagine zombies, creatures that are exact physical duplicates of phenomenally conscious creatures (like us) but nevertheless lack phenomenally conscious 394

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mental states. So, my ‘zombie twin’ is an exact physical duplicate of me, but there is nothing it’s like to be him. Since zombies in this sense are conceivable, Chalmers argues, they are also metaphysically possible. This is interpreted to entail that qualia are not duplicated when physical properties are duplicated, meaning qualia must be non-physical properties. The arguments and the thought experiments in these three seminal discussions may be – and have been – questioned. But their influence and the controversies they have generated work towards implicitly supporting the idea that one must be committed to a spooky view in order to make sense of qualia. That is, inspired by these influential accounts of qualia and phenomenal consciousness, it is tempting to work with a conception of qualia according to which if there are qualia, then there are spooky properties. Hence, we have the spooky conception of qualia. According to the spooky conception, spookiness is a ‘non-negotiable’ feature of qualia: if some properties are known to be non-spooky (e.g., unquestionably physical or naturalistically acceptable), then qualia cannot be identified with those properties. Once the spooky conception is in place, it is very easy to derive an argument for eliminativism about qualia. The argument would be: 1 If there are qualia, then there are spooky properties. (Conceptual claim) 2 As a matter of fact, there are no spooky properties. (Empirical claim) 3 Therefore, there are no qualia. There are variations on this argument. For example, Daniel Dennett (1988) argues that qualia are presumed to be ineffable, intrinsic, private properties that are directly or immediately apprehensible in experience (conceptual claim), but as a matter of fact, there isn’t anything in the world that can play the role of being an ineffable, intrinsic, private property that is directly or immediately apprehensible in experience (empirical claim), hence there are no qualia. Another example (which I shall discuss in Section 35.4) might be: if there are qualia, some of our behaviours must be caused by non-physical properties (conceptual claim), but as a matter of fact, there are no non-physical causes in the physical world (empirical claim), therefore, there are no qualia. I have chosen the pejorative label ‘spooky’ deliberately to emphasise the negative attitude that eliminativists have towards qualia (and towards views that qualia realism is thought to imply). The pejorative nature of the label can be helpful for illustrating two general strategies qualia realists have in responding to the sort of argument that I have sketched above. On the one hand, qualia realists can endorse the dualist, anti-physicalist (and perhaps non-naturalist) views that they take to be entailed by their position, but reject the pejorative label. Accordingly, qualia realists may argue that there is nothing wrong with any of these views. On the other hand, qualia realists may accept that these views are indeed undesirable (hence the ‘spooky’ label may be accepted for such views) but reject that qualia realism entails any of them. In other words, they can reject the spooky conception of qualia. In the remainder of this chapter, I will explore the prospects of this latter strategy.

35.3 Qualia: The Neutral Conception Here is one reason why the spooky conception may be rejected. Working with the spooky conception leads to very uncharitable readings of some arguments for dualism or 395

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anti-physicalism. To illustrate, recall Jackson’s (1982) knowledge argument I summarised above. That there are non-physical properties is meant to be the conclusion in that argument, whereas that there are properties of Mary’s experiences in virtue of which there is something it’s like for her to have those experiences is a premise, or at least a reasonable background assumption. The idea that qualia, as a matter of conceptual necessity, must be spooky properties leads to an interpretation of the knowledge argument as a blatantly question-begging one. After all, one might agree with Jackson that there are properties of Mary’s experiences in virtue of which there is something it’s like for her to have those experiences, but reject the conclusion Jackson draws from this claim and the thought experiment. So, whether qualia are spooky or not should not be built into the very concept of qualia. This kind of consideration suggests that a more neutral conception of qualia can serve our purposes better in debating the nature (and the very existence) of qualia. Thus, consider the neutral conception of qualia: qualia are properties of experiences in virtue of which there is something it’s like to have those experiences. Let me unpack this claim. There are mental states which are experiences, and as such, there is something it’s like to have them. These mental states have a range of properties, and some of these properties are responsible for the fact that there is something it’s like to have them. And qualia are these properties. Of course, as we have seen in the opening paragraph of this chapter, experiences differ from one another in terms of what it’s like to have them. Since qualia are the properties that are responsible for what it’s like to have these experiences, the differences in what it’s like to have different experiences will be partially explained by the fact that different experiences will typically have different qualia. This is compatible with what Chalmers seems to have in mind when he suggests that qualia are ‘properties of mental states that type those states by what it’s like to have them’ (1996: 359) and what Sydney Shoemaker thinks when he defines qualia as ‘features of sense experiences, in virtue of having which they resemble and differ from each other, qualitatively, in the ways they do’ (1982: 367) or (similarly) as ‘properties of perceptual and sensory states that give them their phenomenal character’ (2007: 115). More explicitly: A property will be a quale if it belongs to a family of properties such that, if the same properties in this family are instantiated in two or more experiences, then those experiences will be qualitatively identical. Experiences that differ in which properties in this family they instantiate will be qualitatively different, and all of the similarity and difference relations amongst experiences are determined by what properties in this family they instantiate. (Shoemaker 2007: 121–122.) This neutral conception says nothing about whether qualia are spooky or not. As it happens, while Chalmers thinks that qualia are spooky properties (as we have seen above in my summary of the zombie argument), Shoemaker thinks that they are not. According to Shoemaker, qualia are properties ‘realized in microphysical states of affairs’ (2007: 115), purely because all properties (other than the microphysical properties themselves) are realized in microphysical states of affairs. This is a reason to prefer the neutral conception to the spooky conception. While the spooky conception entails that qualia must be spooky properties, the neutral conception leaves it open that they may or may not be spooky properties. 396

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Now, although the neutral conception is indeed neutral when it comes to the spookiness of qualia (because, for example, it is compatible with both physicalist and anti-physicalist views about the mind-body problem), it doesn’t make the existence of qualia a trivial matter, for at least two reasons. First, note that there cannot be qualia if there are no properties. Qualia are meant to be properties after all. Though, this talk of qualia being properties should not necessarily commit the qualia realist to any particular theory of properties. If properties are universals, qualia will be universals, though of course their instances (e.g., a particular quale of a given experience) will be particulars. If properties are not universals but tropes, then qualia will be particulars, but qualia types will be whatever trope theorists identify trope types with (e.g., classes of tropes). My reading of Shoemaker is that he would have to take qualia to be universals (2007: 115–116). For an example of an account that rejects the idea that properties are universals but is happy to talk about qualia, see Heil and Robb (2003). What should we think about qualia if nominalism is true? While a nominalist about properties may legitimately engage in ‘qualia’ talk and find things other than properties as truthmakers for such ‘qualia’ talk, I am inclined to think that a nominalist cannot be a realist about qualia given that, strictly speaking, she thinks that there are no properties.3 Second, the neutral conception is ideologically committed to making sense of an ‘in virtue of’ claim. Recall that, on this conception, the quale of a given experience is in virtue of what there is something it’s like to have that experience. One way of making sense of this ‘in virtue of’ claim is by means of appealing to a grounding relation. On this understanding, we might say that the fact that there is something it’s like to have a given mental state is grounded in the fact that the mental state in question instantiates a quale. Alternatively, we might understand the ‘in virtue of’ claim to be a truthmaking claim. Accordingly, truths of the sort ‘There is something it’s like to experience X’ would have instantiations of qualia as their truthmakers. By now, it should be clear that, on the neutral conception, the ontology of qualia realism is as follows. Experiences are (token) mental states, and as such they are instantiations of mental properties (types). What marks the difference between a mental state that is an experience and a mental state that is not an experience (if there are such mental states) is that while the former is phenomenally conscious, the latter is not. The role of qualia in this picture is that a mental state’s instantiation of a quale is what explains this difference. Mental states that instantiate qualia are experiences, and mental states that do not instantiate qualia are not. Related to this last point, it is worth clarifying that the bearers of qualia are not conscious creatures. The bearers of qualia are experiences, which are instantiations of mental properties by conscious creatures. So, in this sense, qualia are properties of instances of properties. Shoemaker is explicit on this: ‘If experiences are events or states, and events and states are property instances or complexes of property instances, then qualia, understood as properties of experiences, will be properties of property instances or of complexes of properties instances’ (2007: 116).4 Endorsing the neutral conception, let me now explicitly state what it takes to be minimally ontologically committed to qualia. I shall illustrate this in six steps, but I don’t intend this to be an argument consisting of five premises and a conclusion. (i) Some sentences of the form ‘There is something it’s like to experience X’ are true.

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According to the claim that is expressed in (i), sentences like the ones I opened this chapter with are true. Let’s say that sentences of this sort are experience sentences. So, (i) states that some experience sentences are true. (ii) Some true experience sentences have truthmakers. This second step is a minimal ideological commitment to the idea of truthmaking, and as such, it is not a full-blown commitment to ‘truthmaker maximalism’, i.e., the principle that for every truth, there is something in the world that makes it true.5 (iii) A truthmaker of a true sentence S is the thing in virtue of which S is true. This step is one way we can make sense of the connection between truthmaking and the ‘in virtue of’ locution. (iv) Qualia are properties of experiences in virtue of which there is something it’s like to have those experiences. This step is merely a restatement of the neutral conception of qualia. When combined with (i), (ii) and (iii), it suggests that: (v) Qualia (or instantiations thereof) are truthmakers of true experience sentences. And, all this goes to show that: (vi) Ontological commitment to qualia is nothing over and above ontological commitment to truthmakers of true experience sentences. Insofar as we think that examples of the sort that I have opened this chapter with are true sentences with truthmakers, and qualia are properties of experiences the instantiations of which can make such sentences true, we can be realists about qualia. It should now be clear that ontological commitment to qualia is not necessarily an ideological commitment to a spooky view. If physicalism is true, then there are only physical and physically acceptable properties, so, if there are qualia, qualia will be physical or physically acceptable properties. One possible way this could go is as follows. Assuming physicalism, mental states can be token-identical with brain states: instantiations of mental properties are realized in instantiations of neural properties. Qualia, recall, are properties of experiences. Given that experiences are mental states and (on the physicalist assumption) mental states are brain states, then qualia will be physically realized properties of brain states. Alternatively, if physicalism is false for the reasons that Jackson (1982) and Chalmers (1996) have given, then qualia will not be physical or physically realized properties. An alternative to physicalism and anti-physicalism is what Nathan Wildman and I call the ‘disjunctive view’ (Baysan and Wildman 2022). On the disjunctive view, phenomenal consciousness is disjunctive in the sense that it has both physical and non-physical possible instances. More specifically, qualia are disjunctive properties with physical and non-physical disjuncts. One way of making sense of this idea is as follows. In some worlds qualia are instantiated in virtue of their physical disjuncts being instantiated. In some 398

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worlds, they are instantiated in virtue of their non-physical disjuncts being instantiated. And in ‘mixed’ worlds, they are instantiated in virtue of both physical and non-physical disjuncts being instantiated. On a view like this, there are qualia but neither physicalism nor anti-physicalism is true.

35.4

Qualia and Mental Causation

In the previous section, we have seen that ontological commitment to qualia is nothing over and above an ontological commitment to truthmakers for some experience sentences. But such a relatively minimalist ontology (and ideology) could still face objections. In this final section, I shall consider one such objection, namely the objection that qualia realists cannot find room for qualia in causation. Essentially, the problem is the alleged difficulty of squaring qualia realism with what is known as the causal closure of the physical: If a physical event has a cause at a time, it has a sufficient physical cause at that time. Proponents of the causal closure of the physical think that this is a principle that is inductively well supported by physics and other physical sciences (Papineau 2001). Next, it is commonly assumed that if there are qualia, they must have physical effects. We can call this idea the physical efficacy of qualia. One consideration in support of the physical efficacy of qualia is the general metaphysical principle that any real property must have real causal powers. Now, this general metaphysical principle does not quite say that any real property must have physical causal powers (which must be manifested in physical effects), but it is plausible to think that if qualia have causal powers, they should ultimately be manifested in physical effects, at least on some occasions. In fact, it is not uncommon to find discussions of Jackson’s thought experiment about Mary where it is suggested that Mary’s new knowledge of what it’s like to see red is caused by the qualia of this experience, and such knowledge, of course, must have physical effects in Mary’s behaviour (see Campbell 2003). Now, if qualia have physical effects and all physical effects must have sufficient physical causes, it follows that unless qualia are strictly identifiable with physical properties as parts of sufficient causes of physical effects of qualia, qualia realism entails causal overdetermination. This is because proponents of this objection typically assume, implicitly or explicitly, what is known as the causal exclusion principle: no effect has more than one (simultaneous) sufficient cause unless it is a case of causal overdetermination (e.g., Kim 2005). Those who accept the causal exclusion principle are in general happy to accept that there can be exceptional, rare instances of causal overdetermination, for example when two distinct bullets simultaneously (but independently) hit a porcelain vase and cause the vase to shatter. But, if causation by qualia entails causal overdetermination, then on any occasion whereby a quale is causally efficacious, we must have a case of causal overdetermination. This would entail systematic causal overdetermination, which is found implausible by the proponents of the causal exclusion principle. So, the worry for qualia realists is that if qualia are real, they must have real causal powers, but such causal powers cannot be manifested in the physical world without entailing a problematic sort of causal overdetermination. So, qualia realism seems to be in trouble. But this is too quick, as there are several ways out of this problem. In the remainder of this section, I will briefly survey some of these options, but leave a defence of these options for another occasion.6 399

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First, recall that, on the neutral conception, qualia may or may not be physical properties. Therefore, one immediate option is that this is not a problem for qualia realists that are physicalists, as physicalists can in principle accept all of the principles that are used in the articulation of this problem. In fact, the considerations that support these three claims can easily be seen as an argument for the conclusion that qualia are physical properties.7 Next, given that the causal argument that is raised against qualia realism rests on three principles, there should be at least three more responses to the argument, each consisting in rejecting one of these three assumptions. Many have explored ways to resist arguments of this sort by rejecting either the causal closure of the physical or the causal exclusion principle, but these responses don’t really say anything about qualia, so I shall omit them here because they are less directly relevant to the topic of this chapter. However, the response to this argument that rejects the physical efficacy of qualia explicitly focuses on the nature of qualia. This response is an endorsement of qualia epiphenomenalism, which I shall briefly discuss in concluding this section. Qualia epiphenomenalists hold that while qualia may be physically caused (to be instantiated), they don’t have any physical effects. In his presentation of the thought experiment about Mary and the knowledge argument, Jackson (1982) explicitly endorses qualia epiphenomenalism, hence the title of his paper: ‘Epiphenomenal Qualia’. In Jackson’s case, qualia epiphenomenalism is indeed supported by his reliance on the causal closure of the physical and implicit endorsement of something along the lines of the causal exclusion principle. Given that he thinks that qualia are non-physical properties, qualia can’t have any physical effects in a causally closed world. Jackson, at least at the time of writing ‘Epiphenomenal Qualia’, was content with this conclusion. The neutral conception of qualia may be helpful in making sense of qualia epiphenomenalism. Recall that on the neutral conception, qualia are properties of experiences in virtue of which there is something it’s like to have them. The neutral conception is not in any way committed to the claim that qualia are properties of experiences in virtue of which experiences have physical effects. One philosopher who takes epiphenomenalism seriously makes this very explicit in his characterisation of qualia epiphenomenalism: ‘the properties in virtue of which we are conscious are not properties in virtue of which events causally contribute to our behaviour’ (Robinson 2020: 27). An immediate reaction to qualia epiphenomenalism is that it makes the knowledge of qualia mysterious, if not outright impossible (Campbell 2003; Moore 2012). If qualia don’t have physical effects, they can’t be seen as causing our knowledge of them, which itself causes certain kinds of physical behaviour. Presumably, if they cause our knowledge of them, such knowledge should manifest itself in our behaviour. When Mary says: ‘A-ha! This is what it’s like to see something red!’, the qualia that Mary’s experience instantiates must play some causal role. In response to this powerful objection, one thing that qualia epiphenomenalists can do is to reject the presumed causal link that explains the knowledge of qualia. As Chalmers notes, a property dualist should argue that a causal theory of knowledge is not appropriate for our knowledge of consciousness … Our knowledge of conscious experience does not consist in a causal relationship to experience, but in another sort of relationship entirely. (Chalmers 1996: 193)

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As Chalmers elaborates on this point elsewhere, the objection against qualia epiphenomenalism assumes that a causal connection between experience and phenomenal belief [i.e., belief that one has an experience of some sort] is required for the latter to count as knowledge. But … the connection between experience and phenomenal belief is tighter than any causal connection: it is constitution. (Chalmers 2003: 255–256, emphasis added) Similarly, Yujin Nagasawa (2010) argues that one’s knowledge of one’s own qualia is partially constituted by the qualia in question (i.e., not caused by them). He holds that ‘since there is an intimate constitutive relationship between phenomenal knowledge and its object, there is no causal gap between them’ (2010: 52). (See Baysan 2021: 2782–2785 for further discussion of qualia epiphenomenalism in relation to knowledge of qualia.) So, whatever the merits of qualia epiphenomenalism, it is possible to defend it from the objection that it makes the knowledge of qualia impossible. The availability of responses of this kind lend further support for qualia realism.

35.5 Conclusion This chapter focussed on the neutral conception of qualia on which qualia are properties of experiences in virtue of which there is something it’s like to have those experiences. Qualia realism is often challenged on the basis that qualia, if there are any, must be spooky properties, and moreover, the existence of qualia cannot be made compatible with the causal closure of the physical. We have seen that understanding qualia along the lines of the neutral conception enables qualia realists to respond to these challenges.8

Notes 1 In this chapter, I focus on the conception of qualia according to which qualia are properties of experiences (hence the title). Like many other philosophical terms of art, the word ‘qualia’ is used in different ways, and sometimes it is used with the intention to refer to things that cannot be properties of experiences. See Tye (2021) for a discussion of different uses of ‘qualia’. 2 These three views are not equivalent. One can be an anti-physicalist without being a dualist (e.g., Goff 2017) and one can be a dualist without being a non-naturalist (e.g., Chalmers 1996). 3 It is important to reiterate here that these points hold only insofar as we take qualia to be properties. If, for example, one thinks that a quale is a certain kind of event (not property), and then give an account of events that is compatible with nominalism about properties, then nominalism can of course be made compatible with qualia realism. Thanks to Anthony Fisher for this observation. 4 See also Baysan (2019: 468). 5 Truthmaker maximalism faces well-known difficulties, as it is not clear if negative existentials, universal generalisations, and modal truths can have things in the world that make them true. But clearly, someone who accepts (ii) isn’t committed to truthmaker maximalism, and importantly, she need not worry about the problem cases for maximalism. Experience sentences are not negative existentials or universals generalisations, and they do not make modal claims 6 My own view, which I won’t argue for here, is that the causal exclusion principle is false ( Baysan 2018; 2021), the physical efficacy of qualia is not an obvious truth ( Baysan 2019; 2021), and some qualia realists are entitled to reject the causal closure of the physical ( Baysan 2021).

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Umut Baysan 7 Although he doesn’t use these premises explicitly, David Papineau’s (2002) case for physicalism about consciousness can be interpreted along these lines. Curiously, Jaegwon Kim (2005), who runs an analogue of this argument for physicalism about mental properties more generally, thinks that the case of qualia is an exception, hence the title of his book Physicalism or Something Near Enough (2005). 8 I thank the editors of this volume and the participants of the Online Properties Workshop 16–18 May 2022 for comments on a version of this chapter.

References Bayne, T., and Montague, M. (eds.) (2011) Cognitive Phenomenology. Oxford: Oxford University Press. Baysan, U. (2018) Epiphenomenal Properties. Australasian Journal of Philosophy 96(3): 419–431. Baysan, U. (2019) Mad Qualia. Philosophical Quarterly 69(276): 467–485. Baysan, U. (2021) Rejecting Epiphobia. Synthese 199(1–2): 2773–2791 Baysan, U. and Wildman, N. (2022) Physicalism or Anti-physicalism: A Disjunctive Account. Erkenntnis, doi: 10.1007/s10670-022-00530-0. Campbell, N. (2003) An Inconsistency in the Knowledge Argument. Erkenntnis 58(2): 261–266. Chalmers, D. (1995) Facing Up to the Problem of Consciousness. Journal of Consciousness Studies 2(3): 200–219. Chalmers, D. (1996) The Conscious Mind. Oxford: Oxford University Press. Chalmers, D. (2003) The Content and Epistemology of Phenomenal Belief. In Smith, Q. and Jokic, A. (eds.) Consciousness: New Philosophical Perspectives. Oxford: Oxford University Press: 220–272. Dennett, D. (1988) Quining Qualia. In Marcel, A.J. and Bisiach, E. (eds.) Consciousness in Contemporary Science. Oxford: Oxford University Press: 42–77. Frankish, K. (2012) Quining Diet Qualia. Consciousness and Cognition 21(2): 667–676. Goff, P. (2017) Consciousness and Fundamental Reality. New York: Oxford University Press. Heil, J. and Robb, D. (2003) Mental Properties. American Philosophical Quarterly 40(3): 175–196. Jackson, F. (1982) Epiphenomenal Qualia. Philosophical Quarterly 32(127): 127–136. Kim, J. (2005) Physicalism or Something Near Enough. Princeton, NJ: Princeton University Press. Moore, D. (2012). On Robinson’s Response to the Self-stultifying Objection. Review of Philosophy and Psychology 3: 627–641. Nagasawa, Y. (2010) The Knowledge Argument and Epiphenomenalism. Erkenntnis 72(1): 37–56. Nagel, T. (1974) What is it Like to Be a Bat? Philosophical Review 83(4): 435–451. Papineau, D. (2001) The Rise of Physicalism. In Gillett, C. and Loewer, B. (eds.) Physicalism and its Discontents. Cambridge: Cambridge University Press: 207–224. Papineau, D. (2002) Thinking about Consciousness. Oxford: Oxford University Press. Robinson, W. (2020) Thick NCCs Yield Physicalist Epiphenomenalism. Journal of Consciousness Studies 27(7–8): 77–94. Shoemaker, S. (1982) The Inverted Spectrum. Journal of Philosophy 79(7): 357–381. Shoemaker, S. (2007) Physical Realization. Oxford: Oxford University Press. Tye, M. (2021). Qualia. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/archives/fall2021/entries/qualia/>.

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36 PROPERTIES IN PERCEPTION Bence Nanay

When you look at an apple, you see it as having various properties, say, the property of being red, the property of being in front of you, the property of being round, and so on. Perception represents properties. A number of questions arise: 1 2 3 4

What is the range of perceptually represented properties? Does perception represent tropes or universals? Does perception represent determinate or determinable properties? What are the properties represented in perception attributed to?

I will address these questions in turn and then in the conclusion ask how these debates connect up with one another. One brief warning before we start: I will assume that perceptual states are representations. So perceptual states represent properties. Not everybody is comfortable with such representational talk (Brewer 2011; Martin 2004). But the very same questions arise for those who prefer talking about perception in terms of presenting properties or acquainting us with properties.

36.1 What Is the Range of Perceptually Represented Properties? You are looking at an apple. What is the range of properties that you attribute to it perceptually? You see it as red. But do you see it as an apple? Do you see it as a Granny Smith apple? Do you see it as a Granny Smith apple from Oregon, picked by Mr. Taylor? The range of properties that can be attributed by a belief is unlimited. I can have a belief that x is F for any value of F. But the range of properties that can be attributed by a perceptual state is limited. Just how limited is subject to debate. One of the most important debates in recent philosophy of perception is about the range of properties that is represented in perception (Nanay 2011a, 2011b; Siegel 2006, 2009). Some of the candidates I gave are obviously perceptually represented properties, like color, shape or spatial location. These are often called low-level properties. Some others are obviously not perceptually represented properties, like the property of being a Granny Smith apple from Oregon picked by Mr. Taylor. We can represent the apple as having this DOI: 10.4324/9781003246077-45

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property, but we don’t do so perceptually. The interesting question concerns the cases in between. Are sortal properties represented in perception? How about dispositional properties? Action properties? Aesthetic properties? Valences? And so on. Instead of going through the debates concerning whether these specific kinds of properties are perceptually represented, I want to distinguish two very different questions that are often lumped together as well as consider what kinds of methodology have been used to answer these questions. We are considering a question about the range of properties we perceive. But this question is ambiguous between at least two interpretations (Nanay 2012a). It could be understood as a question about perceptual representation. Or it could be understood as a question about perceptual experience. To see how different these two are, it is important to note that not all perceptual representations are conscious (for example, the perception of stimulus presented for less than 100 milliseconds or of masked stimulus would be unconscious), so many perceptual representations will not count as perceptual experience. Hence, the question about the range of perceived properties will get very different answers depending on whether we take this question to be about content or about consciousness. And the methodology used to address these questions will also be somewhat different. When it comes to addressing the question about what properties we experience perceptually, one tempting route to take would be to just use our introspection. And this is, presumably, what you did when you read the introductory paragraph of this section about apples and their properties. It just doesn’t seem like the property of being a granny smith apple picked by Mr. Taylor is a property that would show up in our perceptual experience. Given the welldocumented unreliability of introspection (see Schwitzgebel 2008 for a summary), this is a fairly dubious method to use in philosophy in general and in philosophy of perception in particular. Another often used methodology is called the phenomenal contrast argument. The general idea is to contrast two cases that differ only in their phenomenology and find that this difference in phenomenology can be best explained in terms of a difference in a represented property, which gives us reasons to posit that the property in question is perceptually attributed. One oft-cited example: you’re listening to someone speaking the very same Arabic sentences before and after having learned Arabic. If we contrast these two auditory experiences, they will have very different phenomenology. And, so the argument goes, the only difference between these two experiences lies in that the latter, but not the former attributes some kind of semantic properties. Thus, these semantic properties are perceptually represented. Without either endorsing or rejecting this specific argument, it is important to point out that any phenomenal contrast argument relies heavily on (unreliable) introspection. The starting assumption of any phenomenal contrast argument is that the two experiences in question differ only in their perceptual phenomenology. They feel different. But this claim is made on the basis of introspection (see e.g., Siegel 2006 for a salient example). And it is not obvious how we can keep apart the claim that two experiences differ only in their perceptual phenomenology from one another from a very different claim, namely, that two experiences differ only in their non-perceptual phenomenology from one another. Is the difference between the two auditory experiences in the previous paragraph a difference in perceptual phenomenology? Does it literally feel different? Or is it a difference in nonperceptual phenomenology? The point is that as long as we don’t have a principled way of 404

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keeping apart perceptual and non-perceptual phenomenology, phenomenal contrast arguments do not have a solid foundation (Nanay 2013). How can we address then the question about the range of perceived properties? Another influential methodology here is to focus on empirical findings, rather than on introspection (see, e.g., Bayne 2009). If, for example, we find some subjects who – maybe as a result of some form of brain injury – (a) consciously see object x, (b) experience property P of x, but (c) do not experience any lower-level properties of x, such as shape, size, or color, then we have good reason to conclude that property P is part of our perceptual phenomenology. Consider, for example, unilateral neglect patients who (a) consciously see object x, (b) experience the action-property of x (the property of what it can be used for, see Nanay 2021), but (c) do not experience any lower-level properties of x, such as shape, size, or color (Nanay 2012b). We have then good reason to conclude that action-properties are part of our perceptual phenomenology not only of these patients but also of people without any brain lesions. The skeleton of the argument is the following: Suppose, for reductio, that action-properties are part of the patients’ non-perceptual phenomenology. What about their perceptual phenomenology? We are forced to conclude that these patients lack any perceptual phenomenology while they are performing this visual search task. The only properties they are aware of are action-properties, but these properties are, by the supposition for reductio, not part of their perceptual phenomenology. This is an extremely problematic conclusion, as these people are staring at objects, performing visual tasks with what they see, talking about what they see, manipulating what they see, and, importantly, claim to consciously experience what they see. If we want to avoid the conclusion that they lack perceptual phenomenology altogether (that there is nothing it is like for them to see these objects), we need to deny the supposition for reductio – we need to say that actionproperties are perceptually experienced not just by these subjects, but by all of us. This way of determining the range of perceived properties does not rely on introspection. It needs to be emphasized that this is one possible methodology for determining what properties are perceived. But any account of perception would need to specify what is the set of properties that we perceive and what is the set of properties that we do not perceive, but represent post-perceptually.

36.2

Does Perception Represent Tropes or Universals?

When we say that perception represents properties, this claim is underspecified in a number of respects. One important question we need to ask is whether the properties represented in perception are tropes or universals. The term ‘property’ is ambiguous. It can mean universals: properties that can be wholly present in two (or more) distinct individuals at the same time. But it can also mean tropes: abstract particulars that are logically incapable of being wholly present in two (or more) distinct individuals at the same time (Almäng 2013; Bacon 1995; Campbell 1990; Lowe 2008; Schaffer 2001; Williams 1953; maybe even Broad 1933, see Fisher 2022). Suppose that the color of my neighbor’s black car and my black car are indistinguishable. They still have different tropes. The blackness trope of my car is different from the blackness trope of my neighbor’s car. These two tropes are exactly similar but numerically distinct. Thus, the blackness of my car and the blackness of my neighbor’s car are different tropes.

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If, in contrast, we interpret properties as universals, or, as I will refer to them, propertytypes, then the two cars instantiate the same property-type: blackness. Thus, depending on which notion of property we talk about, we have to give different answers to the question about whether the color-property of the two cars is the same or different. If by ‘property’ we mean ‘trope’, then my car has a different (but similar) color-property, that is, colortrope, from my neighbor’s. If, however, by ‘property’ we mean ‘property-type’, then my car has the very same property, that is, property-type, as my neighbor’s (Ehring 1997; Maurin 2016, see also Daly 1997; Robb 1997; Nanay 2009). The mainstream view in philosophy of perception a couple of decades ago was that perception attributes property-types (see, e.g., Jackson 1977). The thought was that we should model the way perception represent after the way beliefs, desires and other propositional attitudes represent. And since propositional attitudes attribute property-types, perception also attributes property-types. There are a number of problems with this line of thinking. First, assuming that the basic building blocks of the mind are propositional attitudes is deeply problematic (see, e.g., Stich 1983). But even so, just because beliefs represent the world one way, it does not follow that perception must represent it the same way. In fact, an important theme in the last decades of philosophy of perception has been to contrast the way perception represents with the way beliefs do (with the help of distinctions like analog vs. digital, imagistic vs. propositional, vertically articulate vs. not vertically articulate, and so on; see Dretske 1981; Evans 1982; Goodman 1968; Haugeland 1981; Kulvicki 2007, 2014, 2015; Lewis 1971; Matthen 2005; Peacocke 1986, 1989 for various versions of this distinction). Within metaphysics, however, the mainstream view has long been that perception attributes tropes. In fact, it was one of the reasons why tropes were postulated to begin with (Campbell 1981: 481; see also Campbell 1990 – although the core idea of perceiving tropes may go back to Husserl, see Mulligan 1995; see also Kriegel 2004 for a related but somewhat different claim as well as Mulligan et al. 1984; Mulligan 1999 for a detailed argument, and Rodriguez-Pereyra 2002: 93–95 for a rebuttal). But there are some reasons very much internal to philosophy of perception that could give us some reasons to hold that perception attributes tropes. They have to do with one of the grand questions in philosophy of perception, namely, the particularity of perception (Nanay 2012c). Here is the puzzle about the particularity of perception. If the content of a perceptual state is taken to be the conditions under which this perceptual state is correct (Peacocke 1989, 1992), then how can this content specify a token object? It specifies only the conditions a token object needs to satisfy. And then any token object that satisfies these conditions would equally qualify as the object of this perceptual state. Suppose that I am looking at a pillow. Replacing this pillow with another, indistinguishable, pillow would not make a difference in the content of my perceptual state. On these two occasions the content of my perceptual state is identical (and the phenomenal character of my perceptual experience is also identical – the two pillows are indistinguishable, after all). Thus, in terms of perceptual content, we cannot distinguish between these two experiences. But their objects are very different: the pillows are numerically distinct (see Soteriou 2000 and Montague 2011 for good summaries on the particularity of perception from two very different theoretical perspectives). One way out of this conundrum (not the only one, see Tye 2007 and Schellenberg 2010 for alternatives) is to take perception to represent tropes. If our perceptual experience 406

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always represents tropes, that is, particulars, then the particularity of perception is easy to account for. To see this, let us return to the example of the two indistinguishable pillows. Contrast the following two scenarios. In the first one, I am looking at a pillow, x, and, unbeknownst to me, it gets replaced with another, indistinguishable pillow, y. I do not notice that the two pillows are different: I have no idea that the first pillow, x, was replaced by the second pillow, y. In the second scenario, I am looking at pillow x all along – it does not get replaced with a different pillow. Any account of the particularity of perception needs to have a story about how to distinguish between these two experiences. If we accept that the properties we perceptually represent are tropes, then we have an easy answer to this question. I attribute the very same tropes to the pillow in the two perceptual experiences in both scenarios. Importantly, I attribute the trope of being the very same particular token object as the one I saw a moment ago. But the attribution of this trope is incorrect in the first case, it is correct in the second case. In the first case, after the switching of the pillows, this attributed trope (of being the very same token object as the one I was looking at a moment ago) does not match the propertyinstance of the pillow itself (which has the property of being a distinct token object from the one I was looking at a moment ago). In the second scenario, in contrast, the attribution of this trope is veridical. Thus, if we accept trope representationalism, there is a simple and principled way of differentiating the two experiences: the experience is veridical in the second scenario and it is nonveridical in the first. In short, taking perception to represent tropes can make us account for the particularity of perception while holding on to the assumption that perception represents the world. It is important to emphasize that these are arguments concerning what properties perception attributes – not arguments about what properties there are out there in the world. So it would be a dubious move to draw inferences about the metaphysics of properties from any of these arguments. It may be that nominalism is correct: there are only particulars out there. Nonetheless perception may represent property-types, not tropes (Nanay 2011d). Or the other way round.

36.3

Does Perception Represent Determinate or Determinable Properties?

Saying that perception represents properties is underspecified in another respect as well. This concerns the determinable/determinate distinction. One way of characterising the relation between properties is the determinabledeterminate relation (Funkhouser 2006; Johnston 1921; see also Chapter 10, this volume). To use a classic example, being scarlet is determinate of being red. There are many ways of being red and being scarlet is one of these: for something to be scarlet is for it to be red, in a specific way. If something is red, it also has to be of a certain specific shade of red: there is no such thing as being red simpliciter. The determinable-determinate relation is a relative one: the same property, for example, of being red, can be the determinate of the determinable being colored, but the determinable of the determinate being scarlet. Thus, the determinable-determinate relation gives us hierarchical ordering of properties in a given property-space. Properties with no further determinates, if there are any, are known as super-determinates. So does perception represent determinables or determinates? One consideration in favor of the view that perception represents determinates comes from David Hume, who contrasts perception and imagination in terms that could be interpreted to be about their 407

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determinacy: perception is more determinate than imagination (see Kind 2017 for some nuances and the ways in which Hume’s concept of vividness relates to determinacy). On the other hand, what we now know about the perceptual system paints a very different picture. We know that our peripheral vision is only capable of attributing extremely determinable properties. But even some of the properties we perceptually attribute to the objects that are in our fovea can be determinable. While this may seem to flatly contradict the Humean picture, understanding the perceptual representation of determinable and determinate properties can, in fact, shed light on some basic issues about perception. To put it simply, some of the properties we perceptually attribute to the perceived scene are determinates. Some others, on the other hand, are determinable properties. And whether determinable and determinate properties are perceptually represented depends on the allocation of attention. Attention increases (or at least tries to increase) the determinacy of the perceptually represented properties (Nanay 2010, 2011c, 2015; Stazicker 2011). So those features that you are attending to will be more determinate than the rest. And there is plenty of empirical evidence in support of this claim. A typical experimental task in the covert shift of attention paradigm is to fixate on a cross at the middle of the screen and while keeping your eyes there in the middle, shift your attention to the left or to the right (where there are some other visual displays). And the main finding is that those visual displays that are attended to are represented in a higher degree of determinacy (Yeshurun and Carrasco 1998). According to this picture, perceptual representation is constituted by the attributed properties and just what kind of properties (determinables or determinates) are attributed depends on attention. Perceptual content very much depends on the allocation of attention. I framed the discussion above as a question about whether perception represents determinables or determinates. But, as we have seen, determinables and determinates form a hierarchy that could go all the way down to super-determinates, that is, determinates without any further determinates. In fact, a big question in metaphysics is about whether there are super-determinates or determination occurs all the way down so that all determinates have further determinates (see Nanay 2014). It is important to note that whichever of these views is the correct one will be irrelevant from the point of view of perceptual representation. Even the most determinate of perceptually represented properties will be much less determinate than any property that could help us decide whether there are super-determinates. Perception is only capable of representing a very limited range of the outside world. And our perceptual system just does not have the resolution that would allow it to represent super-determinates.

36.4 What Are the Properties Represented in Perception Attributed To? If perception represents properties, this means that it represents something as having properties. Perception attributes properties to something. But what is this something? What does perception represent as having properties? We have seen at the beginning of this chapter that not all properties that we represent objects as having are perceptually represented. I may represent an apple as having the property of being a granny smith apple picked by Mr. Taylor in Oregon in 2022, but this is not a property that is likely to be perceptually represented. A structurally similar problem arises when we try to understand what entities these properties are perceptually attributed to. We may attribute properties non-perceptually to everyday objects, like the apple or the cedar 408

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tree in front of my window, but the question is what we perceptually attribute properties to. As the range of properties attributed perceptually and non-perceptually are often not the same, the entities these properties are attributed to may not be the same either. To avoid confusion, I call the entities our perceptual system attributes properties to ‘sensory individuals’ (Cohen 2004). Sensory individuals are not necessarily what we take ourselves to be perceiving (as perceptual content is not directly introspectable). Nor are they necessarily conscious. Whenever we have a perceptual representation, conscious or unconscious, this perceptual representation attributes properties to ‘sensory individuals’. Why should we posit sensory individuals at all? The widely cited reason is that properties need to be bound to particulars in perception. To use the classic example (Jackson 1977), if I see a red triangle and a blue square, the property of being red and of being a triangle are bound to one individual, whereas the property of being blue and the property of being a square are bound to the other. If they were not bound, then this perceptual state would be indistinguishable from seeing a red square and a blue triangle. Note that this consideration only specifies that the perceptually attributed properties need to be bound to an individual but there is more than one candidate for what this individual may be. The plausibility of an account of sensory individuals depends on which sense modality we talk about. The mainstream view of the sensory individuals of vision is that they are ordinary objects like an apple or a cedar tree (see Shoemaker 1990: 97 and Brewer 2007: 88 to mention just a few examples). Just what would count as an ordinary object is debated, but the most empirically plausible view seems to be that an ordinary object is a ‘spatio-temporally confined and continuous entity that can move and take its features with it’ (Matthen 2005: 281; see also Cohen 2004; Matthen 2004, 2010, 2023 for similar views). There are some dissenting voices, who argue that sensory individuals of vision are spatiotemporal regions (Clark 2000, 2004, 2011; Nanay 2022). The debate about the sensory individuals of audition is very different from the ‘ordinary object’ versus ‘spatiotemporal region’ debate concerning the visual sense modality (Matthen 2010; O’Callaghan 2008a). The main candidate for the sensory individuals of audition are sounds in contrast to ordinary objects, both historically (with support from Aristotle, Berkeley, Strawson, and Warnock) and in the contemporary literature (Bregman 1990; Martin 1997; O’Callaghan 2008b: 318, 2009: 609; Nudds 2010; Matthen 2010: 78, see also Cohen 2010; Young and Nanay 2023). This, of course, leaves open questions about the metaphysics of sound: whether they are sound waves, stable dispositional properties of objects or maybe events close to the sound source. One way in which this debate about audition is very different from the one about vision is that here the main question is not what we perceive, but rather, what we perceive directly or, as O’Callaghan says, what we perceive ‘in the first instance’ (O’Callaghan 2009: 609). Do we perceive ordinary objects ‘in the first instance’, or do we perceive ordinary objects in virtue of perceiving sounds (that is, we perceive sounds ‘in the first instance’)? In the case of the olfactory sense modality, we get a similar picture. The mainstream view here is that we smell odors – a claim that would be equivalent to saying that we hear sounds: ‘smells […] represent the environmental entities by representing odors’ (Lycan 1996: 148, see also Lycan 2000, see also Batty 2010, 2011, on this debate). As the quotation by Lycan shows, here, like in the case of the auditory sense modality, the main question is whether we perceive ordinary objects ‘in the first instance’ or we perceive ordinary objects in virtue of perceiving odors. Again, this leaves open questions about the metaphysics of odors. 409

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The diversity of sensory individuals across sense modalities is especially important (and also potentially problematic) when we consider the multimodality of perception. Different sense modalities all attribute very different properties to the same perceived scene. But all this information from all these different sense modalities would need to be united somehow. They need to be bound in the same framework. The perceptual system binds together a flash in the top left corner of my visual field and a chirping sound from somewhere above towards the left. But how does the perceptual system know that these two pieces of input belong together? These two properties would need to be bound to the same sensory individual. But if the sensory individuals of vision are of a different category from the sensory individuals of audition, then the perceptual system has an extra task, namely, to map out some correspondence between the sensory individuals of vision and the sensory individuals of audition (Matthen 2012). That is not, in itself, a knock-down argument in favor of having a single category of sensory individuals, but the opposing view needs to offer some further explanation here.

36.5 Conclusion: How Do These Debates Connect Up with One Another? I outlined four questions about perceived properties: about their range, about whether they are tropes or universals, about whether they are determinables or determinates, and about what they are attributed to. These questions are not independent from one another. For example, questions (1) and (4) are obviously related: depending on our account of sensory individuals, a very different range of perceptually represented properties will be plausible. And questions (2) and (3) are also intertwined as the determinable-determinate relation is one between property-types. So, if one takes perception to attribute tropes, this would need to be supplemented with an account of how we get property-types from tropes (maybe a version of trope resemblance nominalism). While these questions have been talked about very much independently from one another both in philosophy of perception and in metaphysics, finding connections between these isolated debates could help uss to make progress in each of them.1

Note 1 This work was supported by the ERC Consolidator grant [726251], the FWF-FWO grant [G0E0218N], the FWO research grant [G0C7416N] and the FWO-SNF research grant G025222N. I’m grateful to Anthony Fisher and Anna-Sofia Maurin for very helpful comments.

References Almäng, J. (2013) The Causal Self-Referential Theory of Perception Revisited. Dialectica 67(1): 29–53. Bacon, J. (1995) Universals and Property Instances. Oxford: Blackwell. Batty, C. (2010) Scents and Sensibilia. American Philosophical Quarterly 47(2): 103–118. Batty, C. (2011) Smelling Lessons. Philosophical Studies 153(1): 161–174. Bayne, T. (2009) Perception and the Reach of Phenomenal Content. The Philosophical Quarterly 59: 385–404. Bregman, A. S. (1990) Auditory Scene Analysis: The Perceptual Organization of Sound. Cambridge: BradfordBooks, MIT. Brewer, B. (2007) Perception and Its Objects. Philosophical Studies 132(1): 87–97. Brewer, B. (2011) Perception and Its Objects. Oxford: Oxford University Press.

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Properties in Perception Broad, C.D. (1933) Examination of McTaggart’s Philosophy. Vol. 1. Cambridge: Cambridge University Press. Campbell, K. (1981) The Metaphysic of Abstract Particulars. Midwest Studies in Philosophy 6: 477–488. Reprinted in Mellor, D.H. and Oliver, A. (eds.) (1997) Properties. Oxford: Oxford University Press: 125–139. Campbell, K. (1990) Abstract Particulars. Oxford: Blackwell. Clark, A. (2004) Sensing, Objects, and Awareness: Reply to Commentators. Philosophical Psychology 17(4): 563–589. Clark, A. (2011) Vicissitudes of Non-visual Objects. Philosophical Studies 153(1): 175–181. Clark, A. (2000) A Theory of Sentience. Oxford: Clarendon Press. Cohen, J. (2004) Objects, Places, and Perception. Philosophical Psychology 17(4): 471–495. Cohen, J. (2010) Sounds and Temporality. Oxford Studies in Metaphysics 5: 303–320. Daly, C. (1997) Tropes. In Mellor, D.H. and Oliver, A. (eds.) (1997) Properties. Oxford: Oxford University Press: 140–159. Dretske, F. (1981) Knowledge and the Flow of Information. Cambridge, MA: MIT Press. Ehring, D. (1997) Causation and Persistence: A Theory of Causation. Oxford: Oxford University Press. Evans, G. (1982) The Varieties of Reference. Oxford: Oxford University Press. Fisher, A.R.J. (2022) C.D. Broad on Things and Processes: A Process Ontology of Tropes. History of Philosophy Quarterly 39(4): 385–403. Funkhouser, E. (2006) The Determinable-Determinate Relation. Noûs 40(3): 548–569. Goodman, N. (1968) The Languages of Art. Indianapolis, IN: Hackett. Haugeland, J. (1981) Analog and Analog. In Biro, J. and Shahan, R. (eds.) Mind, Brain and Function. Norman, OK: University of Oklahoma Press: 213–225. Jackson, F. (1977) Perception: A Representative Theory. Cambridge: Cambridge University Press. Johnston, W.E. (1921) Logic. Part I. Cambridge: Cambridge University Press. Kind, A. (2017) Imaginative Vividness. Journal of the American Philosophical Association 3(1): 32–50. Kriegel, U. (2004). Trope theory and the Metaphysics of Appearances. American Philosophical Quarterly 41(1): 5–20. Kulvicki, J.V. (2007) Perceptual Content is Vertically Articulate. American Philosophical Quarterly 44(4): 357–369. Kulvicki, J.V. (2014) Images. London: Routledge. Kulvicki, J.V. (2015) Analog Representation and the Parts Principle. Review of Philosophy and Psychology 6(1): 165–180. Lewis, D. (1971) Analog and Digital. Noûs 5(3): 321–327. Lowe, E.J. (2008) Tropes and Perception. In Gozzano, S. and Orilia, F. (eds.) Tropes, Universals, and the Philosophy of Mind: Essays at the Boundary of Ontology and Philosophical Psychology. Heustenstamm: Ontos Verlag: 175–192. Lycan, W. (1996) Consciousness and Experience. Cambridge, MA: MIT Press. Lycan, W. (2000) The Slighting of Smell. In Bhushan, N. and Rosenfeld, S. (eds.) Of Minds and Molecules: New Philosophical Perspectives on Chemistry. Oxford: Oxford University Press: 273–289. Martin, M.G.F. (1997) The Shallows of the Mind. Proceedings of the Aristotelian Society 71: 75–98. Martin, M.G.F. (2004) The Limits of Self-awareness. Philosophical Studies 120(1–3): 37–89. Matthen, M. (2004) Features, Places and Things. Philosophical Psychology 17(4): 497–519. Matthen, M. (2005) Seeing, Doing, and Knowing: A Philosophical Theory of Sense-Perception. Oxford: Clarendon Press. Matthen, M. (2010) On the Diversity of Auditory Objects. Review of Philosophy and Psychology 1(1): 63–89. Matthen, M. (2012) Visual Demonstratives. In Raftopoulos, A. and Machamer, P. (eds.) Perception, Realism, and the Problem of Reference. Cambridge: Cambridge University Press: 43–67. Matthen, M. (2023) Material Object as the (only) Subject of Multimodal Perception. In MroczkoWąsowicz, A. and Grush, R. (eds.) Sensory Individuals: Contemporary Perspectives on Modalityspecific and Multimodal Perceptual Objects. Oxford: Oxford University Press: 261–276.

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Bence Nanay Maurin, A-S. (2016) Tropes: For and Against. In Calemi, F.F. (ed.) Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. Berlin: De Gruyter: 85–103. Montague, M. (2011) The Phenomenology of Particularity. In Montague, M. and Bayne, T. (eds.) Cognitive Phenomenology. Oxford: Oxford University Press: 121–140. Mulligan, K. (1995) Perception. In Smith, B. and Smith, D. (eds.) The Cambridge Companion to Husserl. Cambridge: Cambridge University Press: 168–238. Mulligan, K. (1999) Perception, Particulars and Predicates. In Fisette, D. (ed.) Consciousness and Intentionality: Models and Modalities of Attribution. Dordrecht: Kluwer: 163–194. Mulligan, K., Smith, B., and Simons, P. (1984). Truth-makers. Philosophy and Phenomenological Research 44(3): 278–321. Nanay, B. (2009) The Properties of Singular Causation. The Monist 92(1): 113–135. Nanay, B. (2010) Attention and Perceptual Content. Analysis 70(2): 263–270. Nanay, B. (2011a) Do We See Apples as Edible? Pacific Philosophical Quarterly 92(3): 305–322. Nanay, B. (2011b) Do We Sense Modalities with our Sense Modalities? Ratio 24(3): 299–310. Nanay, B. (2011c) Ambiguous Pictures, Attention and Perceptual Content. Phenomenology and the Cognitive Sciences 10(4): 557–561. Nanay, B. (2011d) What If Reality has no Architecture? The Monist 94(2): 181–197. Nanay, B. (2012a) Action-oriented Perception. European Journal of Philosophy 20(3): 430–446. Nanay, B. (2012b) Perceptual Phenomenology. Philosophical Perspectives 26(1): 235–246. Nanay, B. (2012c) Perceiving Tropes. Erkenntnis 77(1): 1–14. Nanay, B. (2013) Between Perception and Action. Oxford: Oxford University Press. Nanay, B. (2014) Natural Properties and Bottomless Determination. American Philosophical Quarterly 51(3): 215–226. Nanay, B. (2015) Perceptual Content and the Content of Mental Imagery. Philosophical Studies 172(7): 1723–1736. Nanay, B. (2021) Perception is not All-purpose. Synthese 198(Suppl 17): 4069–4080. Nanay, B. (2022) What Do We See in Pictures? The Sensory Individuals of Picture Perception. Philosophical Studies 179(12): 3729–3746. Nudds, M. (2010) What are Auditory Objects? Review of Philosophy and Psychology 1(1): 105–122. O’Callaghan, C. (2008a) Object Perception: Vision and Audition. Philosophy Compass 3(4): 803–829. O’Callaghan, C. (2008b) Seeing What You Hear: Cross-Modal Illusions and Perception. Philosophical Issues 18(1): 316–338. O’Callaghan, C. (2009). Sounds. In Bayne, T., Cleermans, A., and Wilken, P. (eds.) The Oxford Companion to Consciousness. Oxford: Oxford University Press. 609-611. Peacocke, C. (1986) Analogue Content. Proceedings of the Aristotelian Society Supplementary 60: 1–17. Peacocke, C. (1989) Perceptual Content. In Almog, J., Perry, J. and Wettstein, H. (eds.) Themes from Kaplan. Oxford: Oxford University Press: 297–329. Peacocke, C. (1992) A Study of Concepts. Cambridge, MA: MIT Press. Robb, D. (1997) The Properties of Mental Causation. Philosophical Quarterly 47(187): 178–194. Rodriguez-Pereyra, G. (2002) Resemblance Nominalism. Oxford: Clarendon Press. Schaffer, J. (2001) The Individuation of Tropes. Australasian Journal of Philosophy 79(2): 247–257. Schellenberg, S. (2010) Particularity and Phenomenology of Perceptual Experience. Philosophical Studies 149(1): 19–48. Schwitzgebel, E. (2008) The Unreliability of Naive Introspection. Philosophical Review 117(2): 245–273. Siegel, S. (2006) Which Properties are Represented in Perception? In Gendler, T. and Hawthorne, J. (eds.) Perceptual Experience. Oxford: Oxford University Press: 481–503. Siegel, S. (2009) The Visual Experience of Causation. Philosophical Quarterly 59(236): 519–540. Shoemaker, S. (1990). Qualities and Qualia: What’s in the Mind? Philosophy and Phenomenological Research 50:109. Soteriou, M. (2000) The Particularity of Visual Perception. European Journal of Philosophy 8(2): 173–189. Stazicker, J. (2011) Attention, Visual Consciousness and Indeterminacy. Mind and Language 26(2): 156–184.

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Properties in Perception Stich, S.P. (1983) From Folk Psychology to Cognitive Science: The Case Against Belief. Oxford: Oxford University Press. Tye, M. (2007) Intentionalism and the Problem of no Common Content. Philosophical Perspectives 21: 495–541. Williams, D.C. (1953) On The Elements of Being. Review of Metaphysics 7: 3–18, 171–192. Reprinted in (2018) A.R.J. Fisher (ed.) The Elements and Patterns of Being: Essays in Metaphysics. Oxford: Oxford University Press: 24–50. Yeshurun, Y. and Carrasco, M. (1998) Attention Improves or Impairs Visual Performance by Enhancing Spatial Resolution. Nature 396: 72–75. Young, N. and Nanay, B. (2023) Audition and Composite Sensory Individuals. In MroczkoWąsowicz, A. and Grush, R. (eds.) Sensory Individuals: Contemporary Perspectives on Modalityspecific and Multimodal Perceptual Objects. Oxford: Oxford University Press: 179–192.

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PART 9

Properties in the Normative Realm, the Social World, and Aesthetics

37 NORMATIVE PROPERTIES Matti Eklund

37.1

Introduction

My topic here is normative properties. What characterizes a property as normative? And are there any? As we will see, there are many ways of understanding these questions. Before proceeding, some preliminaries about “normative” and about “property”. Use of the label “normative” has become increasingly common in recent philosophy. The normative includes the moral but is a broader category. Some normative properties (assuming there are normative properties at all) are moral properties. But there is also, arguably, for example, prudential normativity, epistemic normativity and aesthetic normativity. And in much of the literature on normativity, focus is on presumed general or all-purpose normativity, such as expressed by the presumed all-things-considered ought (or “practical ought”, “deliberative ought”, or “ought of deliberation” – many different labels are used). I say “presumed”, for there is some skepticism about whether the notion makes proper sense.1 Turning to “property”, the most important thing to stress is that there is a seemingly crucial distinction between properties and concepts. Properties are had by entities; concepts are true of or apply to entities. Concepts, like for example linguistic expressions, are representations; properties are what some concepts represent.

37.2

Realism and Antirealism

I suspect that for many theorists the main inroad to the issue of normative properties is through the discussion of realist and antirealist theories in metaethics. Let me start by recounting some relevant aspects of that discussion. Note that what I here bring up as theories regarding normativity traditionally have more often been discussed as theories specifically regarding morality (compare Chapter 38, this volume). One question, given the way the debate is often set up, is whether there are normative properties at all. Maybe normative predicates like “good” and “right” are like expressions like “Zeus” and “phlogiston” and fail to pick out anything. This is what the so-called error theorist thinks. Assuming there are normative properties, then the question arises whether they are “natural” or “non-natural”. The naturalist thinks they are natural, the non-naturalist

DOI: 10.4324/9781003246077-47

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thinks they are non-natural. As is well-known, it is hard to characterize the natural/nonnatural distinction in a satisfactory way. But very roughly, natural properties are supposed to be those of the same general kind as the properties countenanced in the sciences; non-natural properties are supposed to be of a different kind. Naturalists and non-naturalists alike tend to be realists: they hold that there are normative properties and normative truths, and that these truths obtain independently of our judgments about the matter. A different view still is the traditional broadly non-cognitivist view which holds that despite superficial similarities between indicative sentences with normative vocabulary and other kinds of indicative sentence, indicative sentences with normative vocabulary have a different kind of meaning and normative predicates do not even purport to ascribe properties. Instead a sentence of the form “x is right” expresses a non-cognitive attitude. An error theorist and a non-cognitivist of the kind indicated agree that there are no normative properties, but they have importantly different views on why. The error theorist thinks that normative predicates are in the business of ascribing properties but fail; the traditional noncognitivist thinks normative predicates have a different function altogether and are not even in the business of ascribing properties. The non-cognitivism I have described is a simple form of non-cognitivism. Contemporary non-cognitivists differ from traditional ones and typically hold that while normative sentences express attitudes, normative predicates still do stand for properties, at least in a “minimal” or “deflationary” sense of property (for an overview, see van Roojen (2018)). Whether the properties are normative is a separate question. As already indicated, the question of what “natural” means in debates over naturalism and non-naturalism is difficult. Sometimes in the literature, theorists instead speak of normative contra descriptive properties (see, e.g., Jackson (1998)). It is typically not in doubt that normative predicates ascribe normative properties (though see below for criticism of this assumption), but it is an open question whether the properties ascribed are (also) descriptive. “Descriptive” may sound better than “natural”: it does not give rise to questions of what is of the same kind as properties countenanced in the sciences. But the label “descriptive” has other problems. Recall the distinction between properties on the one hand and representations such as concepts and linguistic expressions on the other. It is in the first instance items on the representational side that are properly called descriptive. It is representations, not properties, that describe. This does not have to mean that it is incorrect to label properties “descriptive”. But we must be careful in what we mean when so labeling them, and we must take care not to confuse properties and concepts.2 Perhaps one can understand “descriptive property” as follows: a property is descriptive if and only if it can be ascribed by a descriptive predicate. In one sense of “descriptive”, normative predicates are of course descriptive on any broadly realist view: they ascribe properties just as paradigmatic predicates do. But the idea is that in some narrower sense of “descriptive”, they fail to be descriptive because of their normativity. Given the proposed understanding of “descriptive property”, theorists who deny that normative properties are descriptive are saying that normative properties cannot be ascribed by descriptive predicates. I find such a claim odd, and I do not see why non-naturalists would want to subscribe to such a claim. Whatever property our “right” ascribes, it seems that a descriptive predicate could ascribe it. Another community can introduce a new predicate, call it “thgir”, by the stipulation that it is to ascribe the same property as our predicate “right” does, and then go on to use the predicate in such a way that “thgir” seems not to be normative – they do not use it in such a way that it has any direct connection to action-guiding or to 418

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motivation, or to any kind of evaluative assessment. If so, then “thgir” ascribes a normative property but it still is not a normative predicate. An underlying point is this. We characterize both representations (e.g., concepts) and the worldly items represented (e.g., properties) as normative. We should be careful about assuming that a representation is normative just in case the worldly item it represents is normative.

37.3

Kinds of Normative Properties

I introduced the notion of being normative just by appeal to some purported paradigm examples – “good” and “right” and what they ascribe. Before continuing I should say more about how I use the label “normative”. First, I am using it broadly in that it covers both the evaluative (paradigmatically “good” and the like) and the deontic (paradigmatically “ought” and the like). Second, I am using it broadly in that it covers both the so-called robustly normative and the so-called merely formally normative. The distinction between the robust and the formal is itself hard to characterize in non-impressionistic terms. But a paradigm example of robust normativity is found in the all-things-considered ought, what Gibbard colorfully describes as the “last ought before action”: all considerations are in, and I ask myself, what ought I to do? (Gibbard 2003: ch. 1). Among paradigmatic examples of formal normativity are the normativity of etiquette and of chess – one can, the idea is, say things about which fork one “ought” to eat with and how white “ought” to move without thereby saying anything about how the eater or the chess player ought to act in any normatively more significant sense. How to classify specifically moral properties in these terms is a difficult issue. Of course, it is a substantive theoretical claim that there is a significant distinction between formal and robust normativity. And applying this to properties and saying that some properties are robustly normative and some are formally normative is a separate substantive claim: it is possible to accept a robust/formal distinction but say that this applies only to how we represent the world and not to the properties represented. Maybe formally normative concepts ascribe properties that are not normative at all. Another prominent distinction in the realm of the normative is between the thin and the thick. As usually drawn, this is a distinction between types of normative concepts. Intuitively more general, all-purpose normative concepts like OUGHT, REASON, GOOD and RIGHT are regarded as paradigmatic examples of thin concepts and intuitively more specific or descriptive normative concepts like RUDE, LEWD, BRUTAL, COURAGEOUS, etc., are regarded as paradigmatic examples of thick concepts. Again it is a substantive theoretical claim that there is a significant distinction of the kind at issue. And again it is a substantive theoretical claim that there is a significant distinction between properties corresponding to the supposed distinction between thin and thick concepts.

37.4 Nominalism As normally conducted, the debate over normative realism presupposes that, generally speaking, there are properties. This underlying view can be questioned. Consider, for example, the perspective of a nominalist who rejects the existence of properties: she thinks there are no worldly correlates of predicates and who thinks, moreover, that predicate nominalizations like “redness”, “wisdom”, … generally fail to refer, and for this general reason, “goodness” and “rightness” fail to refer. Consistently with her nominalism she can 419

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think that all sorts of sentences of the form “a is F” are true, including sentences about what is good and what is right (she just that needs a story about what makes these sentences true that is compatible with her rejection of properties). Yet she would be an error theorist, given how that view was characterized above. This is of course easily remedied. Normative error theory can instead be described as the view that there are no true atomic sentences of the relevant kind. Error theory is, then, not primarily a view on normative properties. Only against the backdrop of a view according to which there generally speaking are properties for predicates to ascribe does it make sense to characterize error theory as being about the existence of normative properties. Nominalism has consequences also for other debates concerning normative properties. For example, the difference between naturalism and non-naturalism is naturally characterized as being over the nature of normative properties. If this is unavoidable, then the debate between naturalism and non-naturalism cannot be carried out against the backdrop of the nominalism under consideration. But it certainly seems that a nominalist can say that different sentences are true by virtue of different kinds of ways the world is, even if we should not think there are entities, “properties”, corresponding to those ways. Whether the sentence “a is suffering” is true depends on how the world is psychologically, whereas whether “a is metallic” is true depends on how the world is physically. Similarly, one can raise the question of what the truth of “a is right” depends on.3 Nominalism might matter for how the debate should be conducted. Consider for example the following well-known argument against non-naturalism, originally due to Frank Jackson (1998).4 First, even the non-naturalist should agree that normative properties strongly or globally supervene on naturalistic properties. Second, if they do, then if there is no naturalistic difference between two states there is no metaphysically possible normative difference between them. But then, third, given a suitable abundant ontology of property types this entails that for every normative property there is a naturalistic property necessarily coextensive with it. This is not by itself immediately a problem for the non-naturalist: she might hold that despite such necessary coextensiveness, normative properties are still importantly different from naturalistic properties. But Jackson goes on to argue that necessary coextensiveness of properties is sufficient for identity, and the non-naturalist can hardly accept that normative properties are identical to naturalistic properties. As stated, Jackson’s argument obviously relies on specific assumptions concerning the metaphysics of properties. If one rejects the assumption that there are properties, the argument must be transposed. For example, where Jackson asks whether certain entities, properties F and G, are identical given that they are necessarily coextensive, one must instead consider whether, given that it is necessarily the case that something is F if and only if it is G, what it is for something to be F is the same as what it is for something to be G. There is the metaquestion: are there reasons in favor of an affirmative or negative answer that carry more or less weight depending on whether the issue is couched in terms of properties? I myself do not see such reasons, but the issue may depend on one’s view on properties.

37.5

Concepts versus Properties

As discussed, we tend to characterize both representational items and worldly items as normative. But what is the relationship between the normativity of concepts and the 420

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normativity of properties? One might perhaps be inclined to believe one of the following kinds of views: Concepts First. For P to be a normative property is just for P to bear relation R to some actual or possible normative concept or concepts. Properties First. For C to be a normative concept is just for C to bear relation R* to some actual or possible normative property or properties.5 More specifically, one may be attracted to one of the following simple views of these respective kinds: Simple Concepts First. For property P to be normative is for P to be ascribed by a normative concept. Simple Properties First. For concept C to be normative is for C to be ascribed by a normative property. But both these simple views should be rejected. Start with Simple Concepts First. Consider objectionable thick concepts: thick concepts that in some way presuppose untrue normative claims. Certain thick concepts pertaining to sexual morality are arguably examples. Concepts like LEWD, CHASTE and PROMISCUOUS seem to ascribe properties. The properties they ascribe are instantiated: some behaviors are lewd, some people are chaste, and some people are promiscuous. But one should not think that whatever is lewd and promiscuous is on that account to be condemned or that whatever is chaste is on that account to be commended: that is just the view of conservative morality. The properties that these concepts ascribe are not normative in the way the concepts present them as being, and arguably they are not normative at all. Simple Properties First, in turn, is refuted by the “thgir” example introduced earlier. Simple Properties first is not itself a thesis about what distinguishes a property as normative. But there are views on what normative properties are that are problematic for the same reason that Simple Properties First is. Chris Heathwood defends a view according to which “normative properties are those such that, to attribute one to something is, in virtue of the nature of the property attributed, necessarily to commend or condemn that thing” (Heathwood 2015: 216).6 But a community that uses “thgir”, and in this way attributes rightness, does not thereby seem to commend or condemn that to which they attribute rightness. Of course, the mere fact that the simple views fail does not mean that more sophisticated versions of Concepts First and Properties First might not succeed. It might even be that even the simple views are more plausible if restricted to specific subclasses of normative concepts and properties. For example, consider the following claim: Thin Concepts First. For a property to be thinly normative is for it to be ascribed by a thin normative concept. Whatever in the end its fate, this claim is immune to the counterexample against Simple Concepts First, which appealed specifically to the possibility of thick concepts ascribing non-normative properties. But of course the friend of Thin Concepts First would need to tell a separate story about thick concepts and properties if she seeks a full characterization 421

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of the realm of the normative, and she would presumably need to tell a story about how her stories about the thick and the thin relate. Later, Section 37.7, I will also raise a problem for Thin Concepts First. One alternative to Concepts First and Properties First is a no-priority view. One may think that the “normativity” of concepts somehow has to do with something like commending and condemning, that the “normativity” of properties has to do with, e.g., what obligations we have, and that while there are connections and a resemblance between these ways in which something can be “normative” there is no relation of priority and there are no interesting constitutive or necessary connections between the normativity of concepts and the normativity of properties. Another kind of possibility is that only concepts, or only properties, are properly classified as normative. Maybe normativity should be seen as just a feature of representations, and we should abandon the idea that properties are normative, even if normative representations sometimes ascribe properties. Or maybe normativity should be seen as a feature only of the world represented, and we should refrain from seeing representations such as concepts as normative. Or maybe the normative-ish features of representations are so different from the normative-ish features of the worldly features represented that we simply should use different labels for these two different kinds of features, without there being any deep issue concerning how to use the label “normative”.

37.6

The Normativity of Properties

Assuming that we can and should speak of normative properties, what characterizes a property as normative? Accounting for what it is for a property to be normative is different from giving theories of the specific properties that typically would be identified as normative, such as the property of being good and the property of being right. Even given successful accounts of what specific properties are like, the question still remains of what it is for a property to be normative. The question of what it is for a property to be normative has a somewhat technical flavor: the notion of a normative property is hardly found in ordinary parlance. In part this is due to the use of the technical word “normative”. But even if the question concerned “moral” properties, the issue would remain. We hardly speak of “moral properties” in ordinary parlance. This means that we need to be especially careful about relying on intuitive judgments about what is a normative property and not. It is at least reasonable to suspect that the proper way to approach the issue is by considering how best to stipulate a meaning for the expression “normative property”. One view is that a property is normative just in case it is ascribed by some possible normative concept or other. (Of course, one cannot then in turn explain a concept’s being normative in terms of it referring to a normative property.) This is Simple Concepts First from earlier. We have already seen problems with this view. Another possibility is that a property is normative just in case it has the right sort of connection to some other given property or relation, which is presumed to be normative. For example, it could be that a property is normative just in case it has the right sort of connection to what one has reason to do, or what one ought to do.7 There are questions about the nature of the connection. I think many theorists would hold that even if, metaphysically necessarily, whatever action has the property of maximizing happiness also has the property of being right, the property of maximizing happiness is not a normative property – so given the way 422

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they reason, metaphysical necessity is not a strong enough relation. A stronger condition might be: a property is normative if and only if it is part of the essence or nature of this property that, necessarily, it is right to promote(/dispromote) it (Eklund 2017: 97). A concern regarding this general kind of suggestion is that it has the consequence that whichever property or relation P is such that the normativity of a property is a matter of its relation to P, the fact that P itself is normative risks ending up being trivial (Eklund 2017: 97; compare Horwich 2018: 1129). Yet another suggestion is that a property is normative just in case it has the right connection to motivation. The connection between normativity and motivation can be spelled out in different ways. A simple idea is that a property P is (positively) normative just in case: if a thinker knows that x is P then the thinker is thereby motivated to promote x. This simple account is on the face of it implausible. It seems that, e.g., the property of being right is a normative property, but sometimes an agent’s de re knowledge, of the property ascribed by “right”, that something has this property does not motivate her. (Note: it is more plausible that knowledge de dicto that something is right does motivate. Consider how knowledge that something is thgir might fail to motivate.) A somewhat more sophisticated version would be that a property P is (positively) normative just in case: if a rational thinker knows that x is P then the thinker is thereby motivated to promote x. A nearby suggestion is that a property P is (positively) normative just in case an agent’s knowing that x is P ought to motivate the agent to promote x. An obvious concern, whether in the end justified or not, concerns the use of normative vocabulary in the statement of the condition. In the next section I will bring up issues that dramatize this. One view on the issue of normativity of properties is a primitivist view according to which the normativity of a property is a primitive feature of this property. I suspect many may find such primitivism attractive. But even if this primitivism is accepted, one can still significantly ask what generalizations, of the kind discussed, necessarily hold of normative properties. So the primitivist does not avoid the issues discussed.

37.7

Other Normative Properties

For natural reasons, the normative properties that tend to be in focus in theoretical discussions are the properties that our most central normative concepts ascribe. But especially from a realist perspective, given which normative properties are independent of us and how we think of them, it should be natural to think that there are other normative properties too. Compare physics: it would be silly to think that what physical properties there are perfectly mirrors what we use concepts for at any given point in time. In my own work, issues in this vicinity have come up in the following specific form.8 Could it not be that while there are truths about what ought to be done, what is right to do, etc., there are also truths about what ought* to be done, what is right* to do, etc. – where the alternative concepts OUGHT*, RIGHT*, etc., have the same normative roles as OUGHT, RIGHT, etc., but stand for different properties? The normative role of a normative concept is here the aspects of its use, however they are best characterized, by virtue of which the concept counts as normative. A possible gloss is: the normative role of a normative concept has to do with its distinctive role in guiding action. Intuitively speaking, the alternative concepts recommend different actions from those recommended by our actual concepts. Of course, whether the scenario described is possible is something that can be debated. If concepts having the same normative role must stand for the same property, then the 423

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scenario is not possible. In my work, e.g., Eklund (2017), I have used discussion of the kind of scenario described in order to problematize normative realism. What tends to underlie normative realism is the sense that, intuitively speaking, some actions are to be preferred from the point of view of reality. My label for this is ardent realism. One might have thought that ardent realism is vindicated so long as there are mind-independent truths about what ought to be done, what it is right to do, etc. But if there are different facts about what ought* to be done, etc., then that doesn’t seem to be so. To relate back to the intuitive thought: does the world prefer us to do what we ought to do or what we ought* to do? A problem that the scenario described presents for ardent realism is: what, at bottom, is at issue when we try to choose between OUGHT and OUGHT*? One may think that the question is whether we ought to be guided by what we ought to do or by what we ought* to do. But the problem with seeing the question that way is that even if we ought to be guided by what we ought to do, maybe we ought* to be guided by what ought* to do – and then we are back at square one. I believe the questions just described are very important and go to the heart of issues about normative realism. But back to normative properties. How, if at all, do these questions relate to the issues about normative properties brought up earlier in this chapter? So let me turn to this. To begin with, recall the suggestion, from the last section, that a property P is (positively) normative just in case an agent’s knowing that x is P ought to motivate the agent to promote x. What if there is an alternative to OUGHT, OUGHT* – and a property P* is such that the agent’s knowing that x is P* ought* to motivate the agent to promote x – even if it is not the case that the agent’s knowing that x is P* ought to motivate the agent to promote x. Should we then classify P* as normative? Not according to the proposal at issue. But what warrants privileging OUGHT over OUGHT* in that way? One way to deal with this complication is to say that P* is indeed not normative but normative*. But this just invites new questions. Don’t normative and normative* properties belong to the same general category? And if so, how does one characterize that general category in turn? A different reaction goes back to the issues regarding ardent realism that I briefly brought up. One may think that our concepts and what they ascribe are normatively better than the *-variants from the point of view of reality, and therefore the properties that our concepts ascribe are normative and the properties the *-variants ascribe are not (or, of course, vice versa!). This stance has two notable consequences. First, since both our concepts and the *-concepts undeniably are normative, this has the consequence that many normative concepts fail to ascribe normative properties. Second, to stress, this way of characterizing what it is for a property to be normative relies on there being a satisfactory way of resolving the issues regarding ardent realism that I mentioned above. It may be thought that if some properties are in themselves more metaphysically jointcarving than others (Lewis 1983; Sider 2011), then the more natural properties among the candidates are the normative ones. But why think there is a close connection between being joint-carving and being normative? (Eklund 2017: 29ff). Recall too Thin Concepts First from earlier: Thin Concepts First. What it is for a property to be thinly normative is for it to be ascribed by a thin normative concept.

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If one is happy to say that both properties ascribed by our thin concepts and the properties ascribed by the *-concepts are (thinly) normative, then one can hold on to Thin Concepts First. A natural thought is that these properties should all be counted as normative only if normativity of properties is a relatively cheap feature, easily had. If not all these properties are normative, then Thin Concepts First must be rejected. As already mentioned, one can hope to avoid the issues I raise regarding alternative concepts by saying that the scenario mentioned is impossible. If OUGHT and OUGHT* have the same normative role, they must ascribe the same property. If in this way there are properties such that some concepts are guaranteed to ascribe them simply by virtue of their normative roles, then these properties seem to be normatively distinguished. There is something about them such that they are apt to be picked out by concepts with the normative roles in question. This suggests a different view on the conditions under which a property is normative. In my (2017) I defended the idea that a property is normative just in case it is the referent of a possible concept whose reference is determined by normative role alone. (It is not plausible to make the stronger claim that a property is normative by virtue of being the referent of such a concept, but already the (necessary) biconditional is significant.) Intuitively, the idea is that if (and only if) a property is normative, it is apt to be picked out by a normative role. “Thgir” from above refers to a property, rightness, that is normative, and the fact that rightness is normative is shown by it being the referent of a concept whose reference is determined by normative role alone. An intuitively normative concept may fail to refer to a normative property: this is so if the reference of this concept is not determined by normative role alone, and no other concept referring to that property has its reference determined that way. I believe these consequences are reasonable. Of course, in order to assess this idea properly one would, among other things, need to attempt to be precise about what counts as part of normative role and what does not. Among recent discussions getting into some more detail regarding normative role are Dunaway (2020) and Plunkett (2020).

37.8 Concluding Remarks Several of the questions about normative properties that I have discussed are not very much studied in the literature. What characterizes a property as normative? What is the relationship between the normativity of properties and the normativity of concepts? What kinds of other normative properties are there, besides the ones we tend to focus on? There is more work to be done.

Notes 1 For discussion, see, e.g., Baker (2018), Copp (1997), Dorsey (2013), Gibbard (2003: ch.1), McLeod (2001), McPherson (2018), Risberg (2023), Tiffany (2007), and Wedgwood (2007: 24 f). While Philippa Foot does not put the point in these terms, the main argument in her classic ( 1972) is naturally seen as an argument against the possibility of an ought simpliciter. 2 In an effort to avoid “descriptive” one might attempt to use “non-normative” instead. But a straight swap leads to problems: the naturalist’s view becomes the absurd view that normative properties are also non-normative. 3 Clarke-Doane (2020: 25f) makes the point I am pressing in the main text about nominalism and the metaethical debate. 4 My presentation of the argument follows McPherson (2019: sec. 3.2). Jackson talks about the “moral” but the moral/normative distinction does not matter for the argument.

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Matti Eklund 5 Adapted from McPherson (2020: 520). McPherson focuses on “authoritative” – robust – normativity. 6 Heathwood goes on to refine this formulation but the refinements do not affect the points I make in the main text. 7 For an overview of the debate over which property is fundamental, and critical discussion, see Wodak (2020). 8 See primarily ( Eklund 2017). Similar issues have been brought up in, e.g., Clarke-Doane (2020) and Dasgupta (2017).

References Baker, D. (2018) Skepticism About Ought Simpliciter. Oxford Studies in Metaethics 13: 230–252. Clarke-Doane, J. (2020) Morality and Mathematics. Oxford: Oxford University Press. Copp, D. (1997) The Ring of Gyges: Overridingness and the Unity of Reason. Social Philosophy and Policy 14(1): 86–101. Dasgupta, S. (2017) Normative Non-Naturalism and the Problem of Authority. Proceedings of the Aristotelian Society 117: 297–319. Dorsey, D. (2013) Two Dualisms of Practical Reason. Oxford Studies in Metaethics 8: 114–139. Dunaway, B. (2020) Reality and Morality. Oxford: Oxford University Press. Eklund, M. (2017) Choosing Normative Concepts. Oxford: Oxford University Press. Foot, P. (1972) Morality as a System of Hypothetical Imperatives. Philosophical Review 81(3): 305–316. Gibbard, A. (2003) Thinking How to Live. Cambridge, MA: Harvard University Press. Heathwood, C. (2015) Irreducibly Normative Properties. Oxford Studies in Metaethics 10: 216–244. Horwich, P. (2018) Is Truth a Normative Concept? Synthese 195(3): 1127–1138. Jackson, F. (1998) From Metaphysics to Ethics. Oxford: Clarendon Press. Lewis, D. (1983) New Work for a Theory of Universals. Australasian Journal of Philosophy 61(4): 343–377. McLeod, O. (2001) Just Plain ‘Ought’. The Journal of Ethics 5(4): 269–291. McPherson, T. (2018) Authoritatively Normative Concepts. Oxford Studies in Metaethics 13: 253–277. McPherson, T. (2019) Supervenience in Ethics. In Zalta, E. (ed.) Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/supervenience-ethics/>. McPherson, T. (2020) Ardent Realism Without Referential Normativity. Inquiry 63(5): 489–508. Plunkett, D. (2020) Normative Roles, Conceptual Variance, and Ardent Realism about Normativity. Inquiry 63(5): 509–534. Risberg, O. (2023) Ethics and the Question of What to Do. Journal of Ethics and Social Philosophy 25(2): 376–412. Sider, T. (2011) Writing the Book of the World. Oxford: Oxford University Press. Tiffany, E. (2007) Deflationary Normative Pluralism. Canadian Journal of Philosophy 37(5): 231–262. van Roojen, M. (2018) Moral Cognitivism vs. Non-Cognitivism. In Zalta, E. (ed.) Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/moral-cognitivism/>. Wedgwood, R. (2007) The Nature of Normativity. Oxford: Oxford University Press. Wodak, D. (2020) Who’s on First. Oxford Studies in Metaethics 15: 48–70.

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38 MORAL PROPERTIES Caj Strandberg

38.1

Introduction

Metaethics is concerned with fundamental semantical, metaphysical, and epistemological issues with respect to morality. One important part of metaethics explores the nature of moral properties: How should moral properties be characterized? Are they like some other properties with which we are familiar? If so, which type of properties? Or are they quite different from other properties? The relation between metaethical theories of moral properties and metaphysical studies of properties is multifaceted. On the one hand, metaethical theories normally stay neutral as regards general metaphysical issues about properties, such as the debate between realism, nominalism, and trope theory. On the other hand, metaphysical studies of properties are essential to metaethical theories and arguments in at least two ways, as we shall see. First, particular metaphysical theories of properties sometimes function as models for metaethical theories of moral properties. Second, metaphysical considerations are often crucial for the plausibility of metaethical claims about moral properties. In this chapter, I provide a critical overview of different theories on moral properties. I am concerned with theories about ‘thin’ moral properties (such as ‘morally right’, ‘morally wrong’, and ‘morally good’) rather than ‘thick’ moral properties (such as ‘generous’, ‘cruel’, and ‘selfish’) (for the distinction, see Chapter 37, this volume). Throughout the text, I will use ‘morally right’ (henceforth ‘right’) as illustration when discussing theories of moral properties. The focus is on positive accounts of the nature of moral properties rather than theories that deny their existence.

38.2

Realism and Anti-realism

Theories of moral properties are concerned with three basic claims: (i) Cognitivism: Moral sentences of the type ‘x is right’ express a proposition or belief that ascribes a moral property to x, where x is an action. (ii) There are moral properties which make some moral sentences true. (iii) Moral properties are objective. A theory that accepts all three claims is known as ‘realism’, while a view that denies at least one of them is known as ‘anti-realism’.

DOI: 10.4324/9781003246077-48

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There are consequently three types of anti-realism. Non-cognitivism denies (i) and maintains that moral sentences express non-cognitive attitudes. Error-theory denies (ii) and maintains that all sentences ascribing moral properties are false. Other anti-realist theories deny (iii) and maintain that moral properties are subjective or relative. There are debates about how (i)–(ii) should be understood. However, the most central issue with relevance for the nature of moral properties concerns (iii) and how ‘objective’ is to be characterized. The most influential way to understand objectivity is in terms of ‘mind-independence’. The basic intuition that motivates the claim that morality is mind-independent can be expressed by the slogan ‘Morality isn’t Arbitrary’: What is right is not an arbitrary matter in the sense that it is not counterfactually dependent on subjective mental states. For example, whether an action is right does not depend merely on whether an agent happens to approve of it or not. Similarly, whether an action is right does not vary depending on what some agents happen to believe is right. According to the standard notion of mind-independence, it amounts to independence of mental states in general: General Mind-Independence: It is not the case that the nature of moral properties is counterfactually dependent on agents’ actual or idealized mental states. An advantage of this notion is that it classifies theories as anti-realists that widely are understood as such. Thus, it entails that subjectivism, which states that an action is right insofar as an agent approves of it, is anti-realist. Similarly, it entails that relativism, which states that an action is right insofar as it is believed to be right in a certain society, is antirealist. However, this notion tends to classify too many views as anti-realist. It seems evident that what actions are right might in some way depend on people’s mental states, for example, how they affect people’s actual or idealized happiness or desire satisfaction, or with which intention they are performed. Thus, theories that are considered as realist generally agree with this fundamental assumption, but would be classified as anti-realist on General Mind-Independence. To make progress, I think we should return to the intuition motivating the claim that moral properties are mind-independent: ‘Morality isn’t Arbitrary’. We might try to understand mind-independence in terms of independence of individual agents’ mental states: Specific Mind-Independence: It is not the case that the nature of moral properties is counterfactually dependent merely on individual agents’ actual or idealized mental states. Gloss: The nature of moral properties is not counterfactually dependent on the mental states of an individual agent or individual agents S if there are some other agent or agents S* that have the same type of mental states which satisfy the same idealizing conditions. According to this notion, what actions are right is generally allowed to be counterfactually dependent on mental states of agents. For example, whether x is right might depend on whether it maximizes idealized desire satisfaction, or in some other way takes into consideration the mental states of all individuals involved. However, whether x is right is not allowed to be counterfactually dependent on the mental states of an individual agent 428

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or group of agents S if there is another individual agent or group of agents S* that have the same type of mental states that satisfy the same idealizing conditions. For example, x cannot be right merely because an individual agent or group of agents desire that x is performed, if there is another agent or group of agents that have the same type of desire in relation to x, for example a desire that x is not performed. However, whether x is right might be counterfactually dependent on mental states of an individual agent or group of agents S, if there is no individual agent or group of agents S* that have the same type of mental state which satisfies the same idealizing condition. There are particularly two cases that are relevant. First, when S has a type of mental state that is unique by satisfying an idealizing condition such that there is no other individual agent or group of agents S* that have the same mental state which satisfies it. In this case, what is right might depend on S’s mental state in virtue of it fulfilling a particularly qualified condition. Second, when S has a type of mental state that is unique by satisfying a moral condition such that there is no other individual agent or group of individuals S* that have the same mental state satisfying it. In this case, what is right might depend on S’s mental state in virtue of it being morally significant. It is plausible to think that Specific Mind-Independence accounts for the intuition ‘Morality isn’t Arbitrary’, since it entails that what is right is not an arbitrary matter by depending on individual agents’ mental states without taking into consideration mental states of other agents. Insofar as what is right depends on mental states, it is an ‘objective’ matter by taking all agents’ mental states into account that satisfy the same idealizing condition. Thus, in contrast to General Mind-Independence, it entails that what is right might depend on agents’ actual or idealized mental states, as long as it is not arbitrary in being dependent merely on the mental states of individual agents in the specific sense explained above.

38.3 Naturalism vs. Non-naturalism and Reductionism vs. Non-reductionism Theories that accept (i) and (ii) are thus divided between those that accept (iii), ‘realism’, and those that deny it, ‘anti-realism’. There are, however, two other distinctions that divide these theories and cut through the distinction between realism and anti-realism. According to naturalism, moral properties consist in ‘natural properties’. The basic idea is that moral properties are not different from other properties we are familiar with in the natural world. Natural properties have been understood as properties that (a) are the subject matter of science; (b) are part of nature by being involved in causal explanations, or (c) can be known empirically. According to non-naturalism, moral properties consist in ‘non-natural properties’, which means that they are different from ‘ordinary’ properties in nature and might be understood in terms of negations of (a)–(c). The distinction between naturalism and non-naturalism is sometimes conflated with another distinction: that between reductionism and non-reductionism. According to reductionism, moral properties are reducible to ‘non-moral properties’, understood as properties that can be fully defined without employing moral terms. According to nonreductionism, moral properties constitute a separate class of properties in that they consist in properties that can be fully defined only by using moral vocabulary. Thus, theories of moral properties vary on three dimensions: realist and anti-realist, naturalist and non-naturalist, reductionist and non-reductionist.

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38.4

The Practicality of Morality

There are certain core features of morality for which a comprehensive metaethical theory should be able to account. How a theory accounts for these features to a large extent determines whether it provides a plausible characterization of moral properties. The most important feature concerns the practicality of morality: the action-guiding function of morality. This feature can in turn be divided into two parts. First, the normative function of morality: morality provides us with reasons to act. A simple version of this function: Necessarily, if x is right, there is a normative reason to perform x. Moral reasons are usually thought to be categorical in the basic sense that an agent’s moral reasons are not contingent on her actual desires. For example, an agent has moral reason to help another person in need irrespective of whether she desires to or not. To complicate matters, normative reasons are often thought to have a necessary connection to practical rationality: If an agent has a normative reason to perform x, she would desire to perform x if she were fully rational and informed. There are in turn different views about rationality. According to one view, rationality consists in having a coherent set of desires that would be the result of a process of rational deliberation which takes its starting point in her actual desires (Williams 1981). However, on this view it is difficult to maintain that an agent’s moral reasons are not contingent on her actual desires, since what is rational for an agent to desire might vary with the ‘input’ of the deliberative process in the form of her actual desires. According to an alternative view that recently has become influential, rationality consists in responding to normative reasons of which one is aware (Parfit 2011: Part One). Second, the motivational function of morality: morality motivates us to act. For example, if an agent says that an action is right, we immediately presume that she is to some extent motivated to perform it. Motivational internalism is a strong and contested view about this connection: Necessarily, if an agent judges that x is right, she is at least to some extent motivated to perform x. There are different versions of internalism that vary in strength. The denial of internalism is known as ‘externalism’.

38.5 Varieties of Naturalism The general motivation for naturalism is the contention that if moral properties do not differ in any principled manner from other properties in the natural world, they are metaphysically and epistemologically unproblematic. Thus, naturalists maintain that we do not have more reason to question their existence than the existence of other natural properties. According to reductionist versions of naturalism, moral properties consist in natural properties that can be fully defined without employing moral terms. Analytic reductionism claims that a moral term, like ‘right’, has the same semantic meaning as a natural term, i.e., a term referring to a natural property. Many versions of this view characterize moral properties as instantiating a response-dependence scheme: x is right = x is such that S would have a motivating attitude A towards x in condition C. It might be hoped that such theories can account for the practicality of morality in virtue of referring to a motivating attitude. However, they do so in widely different manners and thereby suggest alternative explanations of this feature of morality.

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Most versions of the response-dependence scheme refer to idealized conditions of some sort. Idealized observer theories employ idealized responses of an observer: x is right = x is such that an observer who is fully informed, impartial, and consistent would approve of x. (Firth 1952) What might be called rational agent theories employ idealized responses of an agent: x is right = x is such that an agent who is fully informed and practically rational would desire that x is performed. One instance of this type of theory is noteworthy by providing a systematic account of the practicality of morality (Smith 1994: chs. 5–6). According to this view, if x is right, there is a normative reason to perform x, where such reasons are analysed in terms of rationality, which is understood as having a coherent set of desires. It is further hypothesized that fully informed and rational agents would ‘converge’ in their desires in a way securing that an agent’s moral reasons are categorical in not being contingent on her actual desires. Moreover, the view entails a moderate form of motivational internalism: Necessarily, if an agent judges that x is right, she desires to perform x given that she is rational in the specified sense. There are versions of analytic reductionism that are not instances of the responsedependence scheme. Moral functionalism is inspired by ‘network analyses’ of theoretical terms (Lewis 1970). The view takes its starting point in ‘folk moral theory’ understood as dispositions of competent language that display the complex connections between moral concepts and other concepts. For example, it displays that rightness has various conceptual connections to normative reasons, motivation, outcome of actions, etc. In a series of steps, rightness is then identified with the natural property that fulfils the same role as rightness in this network of conceptual connections. Formulated very simply: x is right = x has the natural property that fulfils the role of rightness in the network of conceptual connections in folk moral theory. (Jackson 1998: ch. 6) Moral functionalism promises to account for the practicality of morality in the form that turns out to be part of folk moral theory. However, it has been doubted whether it suffices to specify a unique natural property corresponding to each moral property (Smith 1994: 44–56). The most influential argument against naturalism is G.E. Moore’s open question argument (Moore 1993[1903]: ch. 1). The argument is basically that all questions of the form ‘Is an action that is N right?’, where ‘N’ refers to a natural property, are open, which is taken to entail that ‘right’ does not have the same meaning as any natural term. Moore took this to be an argument against naturalism in general, but it is better seen as an argument against analytic reductionism. Analytic reductionists respond in different ways to the argument, for example by maintaining that the meaning of a term need not be transparent to competent language users (Smith 1994: 35–39).

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Synthetic naturalism maintains that a moral term, like ‘right’, does not have the same conventional semantic meaning as any natural term. However, it is argued that ‘right’ refers to the same property as a certain natural term. The view is inspired by a causal reference theory of natural kind terms such as ‘water’ (Putnam 1975). The basic idea is that ‘right’ refers to the natural property that is causally responsible for our use of the term. One way it may do so is by causing the features that we use to identify actions to which we apply the term, such as ‘being approved of’, ‘motivating to action’, etc. Again simplifying immensely: x is right = x has a natural property that causally regulates our use of ‘right’. There are both reductionist and non-reductionist versions of synthetic naturalism. On synthetic reductionism, rightness consists in a natural property that can be fully defined without employing moral terms (Boyd 1988; Railton 1989; Sayre-McCord 1997). On synthetic non-reductionism, rightness consists in a natural property that cannot be fully defined without using such vocabulary (Brink 1989: chs. 6-7; Sturgeon 1984). However, on this view, rightness supervenes on natural properties that can be thus defined. In this way, rightness is claimed to be ‘multiply realizable’ in a manner analogous to mental properties and properties in special sciences. In consideration of their semantic claim, synthetic naturalists have developed alternative ways to account for the practicality of morality. According to one version, if x is right, there is a reason to perform x, where moral reasons are understood in terms of what would maximize idealized desire satisfaction (Railton 1989). In this way, an agent’s moral reasons are categorical in the basic sense that they are not contingent on her actual desires. However, it is maintained that an agent’s moral reasons do not have any necessary connection to her rationality. Moreover, most synthetic naturalists maintain motivational externalism and reject that there is any necessary connection between moral judgments and motivation. Externalism is often supported by appealing to the conceivability of an amoralist, someone who judges that an action is right but remains completely unmotivated to perform it (Brink 1989: ch. 3). According to one suggestion, the connection between moral judgments and motivation can be accounted for by employing a pragmatic concept of implicature (Copp 2001; Finlay 2014: ch. 5; Strandberg 2012). Synthetic naturalism has the advantage of avoiding the open question argument, since it denies that moral terms have the same meaning as natural terms. However, it faces a similar challenge known as ‘Moral Twin Earth’. The argument applies Hilary Putnam’s original thought experiment in support of a causal reference theory to moral terms and concludes that they do not refer like natural kind terms (Horgan and Timmons 1992). The theories mentioned above are merely some instances of naturalism. For other important contributions, see e.g., (Finlay 2014; Foot 2002; Schroeder 2007). For a view that maintains the connection between categorical moral reasons and rationality understood as coherence, see (Strandberg 2018). It can now be seen that Specific Mind-Independence provides intuitively plausible classifications of naturalist theories as realist or anti-realist. Subjectivism is an anti-realist view, since it entails that whether an action is right depends on whether an individual agent would approve of it, quite irrespective of the approval of other agents. A similar consideration applies to relativism. Other naturalist theories might qualify as realist. On ideal observer theories, what is right depends on the approval of an ideal observer but in virtue 432

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of this state being unique and qualified in the sense explained earlier. On the abovementioned instance of rational agent theories, what is right does not depend merely on mental states of individual agents, since their desires are hypothesized to ‘converge’ in virtue of satisfying a certain idealized condition. Moreover, versions of reductionist and non-reductionist synthetic naturalism are sometimes conjoined with the view that what is right depends on maximizing idealized desire satisfaction of all individuals affected, which means that they qualify as realist. Naturalist theories raise metaphysical issues that are relevant for the plausibility of these views. Let me briefly mention some of them. First, naturalist theories in general raise issues about supervenience and how the modality of such claims should be understood. It is generally thought that in order to account for the notion that moral properties depend on other properties the following claim needs to be adopted: Strong Supervenience: It is necessary that, for any object x, and for any moral property M, if x is M, then there is some set of natural non-moral properties G (G1, G2, G3, …) such that (a) x has G, and (b) it is necessary that, for any object y, if y has G, then y is M. A plausible requirement on linguistic competence with moral terms is to acknowledge that moral properties depend on other properties, which suggests that the outer ‘necessary’ amounts to analytical necessity. Reductionist versions of naturalism maintain that M is reducible to G, whereas non-reductionist versions deny this. Analytic reductionism is committed to reading both occurrences of ‘necessary’ as analytical necessity. Synthetic naturalism is presumably best advised to read the outer ‘necessary’ as analytical necessity and the inner ‘necessary’ as metaphysical necessity. It has been argued, however, that accounting for the modality of moral supervenience constitutes a problem for realist theories in general (Blackburn 1993). Second, many versions of naturalism raise issues about supervenience and identity conditions of properties. Moral functionalism maintains that M is identical with the possibly disjunctive property G. It thus seems committed to the claim that necessary coextension is sufficient for property identity, and that properties can be formed both by conjunction and disjunction. Non-reductionist synthetic naturalism maintains that M is not reducible to G in spite of the former strongly supervening on the latter. Thus, it appears that this view needs to deny some of these assumptions about property identity. Third, synthetic naturalism raises issues about the causal powers of properties. It has been argued against non-reductionist naturalism that the best causal explanations of moral observations do not refer to moral properties as conceived by this view. This is taken as an argument for doubting that there are moral properties thus understood (Harman 1977: ch. 1). The argument thus seems to presume that to be ‘real’ properties need to be involved in causal explanations.

38.6

Varieties of Non-naturalism

As indicated, non-naturalism exists in reductionist as well as non-reductionist forms. However, the latter is overwhelmingly dominant and will be in focus in what follows.

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The general motivation for non-naturalism is the contention that moral properties are too different from natural properties to be reducible to them. As noticed, naturalists might argue that there is a necessary connection between rightness and reasons, and then understand reasons in terms of what agents would desire in some idealized condition. Nonnaturalists argue, however, that this would mean that moral reasons are a function of desires in a way incompatible with the normativity of morality. It is maintained that moral properties need to consist in non-natural properties in order to have the required connection to normative reasons, which also need to be understood in non-natural terms. A parallel argument can be made regarding the motivational function of morality, although most non-naturalists embrace motivational externalism. One version of non-naturalism is moral sensitivity theories that instantiate the responsedependence scheme: x is right = x is such that an agent with moral sensitivity would approve of x. (McDowell 1979) In similarity with other instances of the response-dependence scheme, it might be hoped that this view can account for the practicality of morality by referring to a motivational attitude. However, on this alternative, moral properties are non-natural and irreducible, since moral sensitivity cannot be spelled out in other terms. In this way, it is argued, they are analogous to secondary properties that also eschew reductive analyses. According to reason-based theories, moral properties can be characterized in terms of normative reasons (Parfit 2011: Part One; Scanlon 1998: chs. 1, 5). One version can be summarized thus: x is right = x is allowed by any set of principles that could not be reasonably rejected as a general basis of behaviour. (Scanlon 1998: ch. 5) That a principle ‘could not be reasonably rejected’ in turn entails that the principle is supported by normative reasons. Reason-based theories seem suited to account for the practicality of morality, although they do so in widely different manners. It is maintained that if x is right, there is a normative reason to perform x that is not a function of desires in any way threatening the categoricity of morality. Moreover, the view is combined with the claim that rationality consists in responding to reasons, meaning that moral reasons have a necessary connection to rationality. It might also be argued that there is a necessary connection between moral judgments and motivation by exploiting the connection between judgments about normative reasons and motivation. According to robust theories, moral properties are simple, irreducible properties, indicating that it might be more difficult to say anything informative about them. They can be summarized thus: x is right = x has the simple irreducible and non-natural property of being right. (Enoch 2011: ch. 1)

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Notwithstanding its claim that moral properties are simple, it might be argued that this view is able to account for the practicality of morality. Accordingly, it has been maintained that reference to irreducible and non-natural moral properties is needed to explain the normative function of morality and to account for moral deliberation (Enoch 2011: chs. 2–3). There are also other significant versions of non-naturalism but that have not been mentioned above; see e.g., (Shafer-Landau 2003; Wedgwood 2009). It is generally thought that non-naturalist theories entail realism. However, there are grounds to question this assumption. Specific Mind-Independence provides intuitively plausible classifications of recognized versions of non-naturalism as realist. On moral sensitivity theories, what is right depends on the approval of a morally sensitive agent but in virtue of this state being unique and morally significant in the sense explained above. Reason-based theories and other versions of non-naturalism entail that what is right depends on considerations that in different manners take into account the mental states of all individuals involved. However, the mere claim that moral properties consist in nonnatural properties does not secure realism. After all, it seems possible to imagine anti-realist versions of non-naturalism according to which rightness is a non-natural property but what actions have this property is counterfactually dependent on mental states of individual agents. It might be wondered why it is thought to be so important that moral properties consist in non-natural properties. It was found above that (a) there are theories on which moral properties are natural that qualify as realist, and (b) there might be theories on which moral properties are non-natural that are anti-realist. Moreover, we have seen that (c) there are theories on which moral properties are natural that claim to account for the normative function of morality, and (d) theories that seem most suitable to account for the normative function of morality do so by exploiting the connection between moral properties and reasons rather than claiming that moral properties are non-natural. In light of (a)–(d), it might be wondered why the claim that moral properties consist in non-natural properties as such is relevant for maintaining realism or explaining the normative function of morality. Like naturalism, non-naturalist theories bring to the fore metaphysical issues that are essential for their plausibility. First, non-naturalist theories in general raise issues about supervenience and modality. Many versions of non-naturalism maintain strong supervenience as described above. The aforementioned considerations as regards how the two occurrences of ‘necessary’ should be interpreted apply also to these views. Second, non-naturalism raises specific concerns about supervenience and identity conditions of properties. According to most versions of this view, M supervenes on G although M is not reducible to G. Insofar as a non-naturalist theory maintains strong supervenience, it then seems that it needs to deny that necessary coextension is sufficient for property identity or that properties can be formed both by conjunction and disjunction. This is more important than in the case with non-reductionist naturalism, since non-naturalism denies that moral properties consist in natural properties. Moreover, non-naturalism is subject to a particular supervenience challenge (McPherson 2012; Väyrynen 2019): Non-naturalism maintains that moral properties consist in non-natural properties that are entirely distinct from natural properties. At the same time, it is plausible to assume that moral properties strongly supervene on natural properties where the inner ‘necessary’ is read as metaphysical necessity. However, what is known as ‘Hume’s Dictum’ entails that there are no 435

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necessary metaphysical connections between ‘distinct existences’. One response to this challenge is to provide an explanation of the metaphysically necessary connection between moral properties and natural properties. Another response is to deny strong supervenience by exchanging ‘metaphysical necessary’ for ‘normative necessary’, which is modally weaker than the former. Recently, non-naturalists have employed the notion of grounding (Rosen 2012). Grounding refers to an asymmetric metaphysical relation that is assumed to explain the fact that x is M because, or in virtue of, x having G. It has been argued that M is grounded in G in combination with a separate normative principle. In this way, nonnaturalists can maintain that M is not reducible to G. Moreover, it might provide them with a response to the supervenience challenge by providing the requested explanation. Third, non-naturalism also raises issues about the causal powers of properties. If it is a condition for a property to be ‘real’ that it figures in causal explanations, and moral properties fail to do so because they are non-natural, this can be taken as an argument against this view. There is also a related type of argument that affects non-naturalism but to which realism in general might be vulnerable. According to evolutionary debunking arguments, fundamental moral judgments can be fully explained as a result of natural selection. It is argued that it is not part of the evolutionary explanation that these judgments in addition track moral properties in the form of non-natural properties (Street 2006). The argument is understood to put doubt on the existence of such properties.

38.7 Concluding Remarks To end, I would like to make three interrelated observations. First, the influence on metaethics often comes from philosophy of language rather than from metaphysics directly. Second, it is crucial that metaethical theories account for the practicality of morality. The two observations are connected: The practicality of morality concerns how we think and talk about morality, which means that considerations about moral language are fundamental. However, as semantic claims are considered to have metaphysical implications, metaphysical considerations become essential to metaethical theories. Indeed, on many metaethical theories moral properties exemplify a type of property as described by metaphysical theories. Third, which theories that dominate metaethics vary depending on what features of morality are considered most central. Non-naturalism has recently received much attention due to the focus on the normative function and the alleged incapability of naturalism to account for it. However, notwithstanding such variations the fruitful exchange between metaphysics and metaethics will persist.

References Blackburn, S. (1993) Supervenience Revisited. In Blackburn, S. (ed.) Essays in Quasi-Realism. Oxford: Oxford University Press: 130–148. Boyd, R. (1988) How to Be a Moral Realist. In Sayre-McCord, G. (ed.) Essays on Moral Realism. Ithaca, NY: Cornell University Press: 181–228. Brink, D. (1989) Moral Realism and the Foundations of Ethics. Cambridge: Cambridge University Press. Copp, D. (2001) Realist-Expressivism: A Neglected Option for Moral Realism. Social Philosophy and Policy 18(2): 1–43. Enoch, D. (2011) Taking Morality Seriously. Oxford: Oxford University Press.

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Moral Properties Finlay, S. (2014) Confusion of Tongues: A Theory of Normative Language. Oxford: Oxford University Press. Firth, R. (1952) Ethical Absolutism and the Ideal Observer. Philosophy and Phenomenological Research 12(3): 317–345. Foot, P. (2002) Natural Goodness. Oxford: Clarendon Press. Harman, G. (1977) The Nature of Morality. Oxford: Oxford University Press. Horgan, T. and Timmons, M. (1992) Troubles for New Wave Moral Semantics: The ‘Open Question Argument’ Revived. Philosophical Papers 21(3): 153–175. Jackson, F. (1998) From Metaphysics to Ethics. Oxford: Oxford University Press. Lewis, D. (1970) How to Define Theoretical Terms. Journal of Philosophy 67(13): 427–446. McDowell, J. (1979) Virtue and Reason. The Monist 62(3): 331–350. McPherson, T. (2012) Ethical Non-Naturalism and the Metaphysics of Supervenience. In ShaferLandau, R. (ed.) Oxford Studies in Metaethics, vol. 7. Oxford: Oxford University Press: 205–234. Moore, G.E. (1993[1903]) Principia Ethica. Cambridge: Cambridge University Press. Parfit, D. (2011) On What Matters. Volume One and Two. Oxford: Oxford University Press. Putnam, H. (1975) The Meaning of “Meaning”. In Putnam, H. (ed.) Mind, Language and Reality, vol. 2. Cambridge: Cambridge University Press: 215–271. Railton, P. (1989) Naturalism and Prescriptivity. Social Philosophy and Policy 7(1): 151–174. Rosen, G. (2012) What is a Moral Law? In Shafer-Landau, R. (ed.) Oxford Studies in Metaethics, vol. 12. Oxford: Oxford University Press: 135–159. Sayre-McCord, G. (1997) ‘Good’ on Twin Earth. Philosophical Issues 8: 267–292. Scanlon, T.M. (1998) What We Owe to Each Other. Cambridge, MA: Harvard University Press. Schroeder, M. (2007) Slaves of the Passions. Oxford: Oxford University Press. Shafer-Landau, R. (2003) Moral Realism: A Defence. Oxford: Clarendon Press. Smith, M. (1994) The Moral Problem. Oxford: Blackwell. Strandberg, C. (2012) A Dual Aspect Account of Moral Language. Philosophy and Phenomenological Research 84(1): 87–122. Strandberg, C. (2018) Towards an Ecumenical Theory of Normative Reasons. Dialectica 72(1): 69–100. Street, S. (2006) A Darwinian Dilemma for Realist Theories of Value. Philosophical Studies 127(1): 109–166. Sturgeon, N. (1984) Moral Explanations. In Copp, D. and Zimmerman, D. (eds.) Morality, Reason and Truth: New Essays on the Foundations of Ethics. Totowa, NJ: Rowman and Allanheld: 49–78. Väyrynen, P. (2019) The Supervenience Challenge to Non-Naturalism. In McPherson, T. and Plunkett, D. (eds.) The Routledge Handbook of Metaethics. New York: Routledge: 170–184. Wedgwood, R. (2009) The Nature of Normativity. Oxford: Oxford University Press. Williams, B. (1981) Internal and External Reasons. In Williams, B. (ed.) Moral Luck. Cambridge: Cambridge University Press: 101–113.

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39 SOCIAL PROPERTIES Dee Payton

39.1

Introduction

Consider the property of being a US one dollar bill. What does it take for a particular piece of paper to have that property? The answer here will likely have something to do with being printed by the US Bureau of Engraving and Printing, but of course (and perhaps more centrally) it will have something to do with being treated by people in certain ways, as when the paper is traded in exchange for goods and services. And of course, in order for exchanges like that to happen, the relevant parties have to represent the piece of paper in certain ways – in particular, they have to think about it, communicate about it, and understand it as currency. And this sort of representation is facilitated by the fact that these kinds of exchanges almost always happen within particular environments, structured by economic institutions, markets, and ideologies, as well as facts about how similar pieces of paper have been (and are currently being) treated in similar contexts. Other things will likely matter here too, but this is just to sketch out a rough explanation for why a particular piece of paper might have the property of being a US one dollar bill.1 Notice that here we’re not asking why a particular piece of paper is called a dollar bill, or is correctly categorized under the label “dollar bill”. That is a question about language. We are asking a metaphysical question about a property, and what might explain why a certain thing has that property. As such, we’re looking for a particular type of explanation, namely, a metaphysical explanation. In the paragraph above, I listed several things which might metaphysically explain why a particular piece of paper has the property of being a dollar bill, and interestingly, all of these things seem to be social. In other words, this is a situation in which the fact that a particular piece of paper has the property being a dollar bill is metaphysically explained by social things. This is the basic recipe for social properties. Very generally, we can say that a property, F, is social when, for any x, Fx is metaphysically explained by social things. There are, of course, many different ways to fill in the details of this general recipe, and some of those ways will be discussed in this chapter. First though, it’s important to note that in the metaphysics literature on social properties, the question of what it takes for a property to be social is often treated as a question about the

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social construction of properties, and so most of the discussion about social properties happens in the language of social construction. I will do the same in this chapter. And this social construction debate is, very generally, a debate about the nature of the explanatory connection between x’s being a dollar bill and things like the US Bureau of Engraving and Printing.2 In the pages below, I will focus on the question of what it takes for a property to be social, how that question has been asked, and how it has been answered in social metaphysics. I will begin in Sections 39.2 and 39.3 with a survey of some of the general theoretical constraints at play in the literature on social properties, and a brief discussion of the property/kind distinction. Then in Sections 39.4–39.7 I will present what I take to be the four main views currently on offer in this literature. These are: the view that social properties are causally constructed, the view that social properties are constitutively constructed, the view that social properties are constructed via grounding relations, and the view that social properties have social essences.

39.2

Social Characteristics

The literature on social properties operates with several theoretical constraints. To start, note that the social domain is characteristically contingent (Epstein 2015, 2021; Hacking 1999; Haslanger 2012). For example, it is contingently true that a particular piece of paper is a dollar bill, and it’s also contingent whether anything at all is a dollar bill. The social domain is also characteristically non-fundamental; on a familiar “levels” picture of metaphysical reality, the social domain sits at a higher level than, say, the domain of quantum physics (Barnes 2014, 2017; Schaffer 2009, 2017; Sider 2011, 2017). So, for example, the fact that a particular piece of paper is a dollar bill is not a fundamental fact; it is explained by more fundamental things. We also tend to think that this relationship is one of dependence: that a particular piece of paper is a dollar bill depends upon the existence of e.g., certain economic institutions and markets (Ásta 2018; Mason 2021; Searle 1995). Moreover, these things make it true that a particular piece of paper is a dollar bill – they generate that fact, in some sense (Haslanger 2012; Schaffer 2017). So in summary: socially constructed things are contingent and non-fundamental, and they are generally taken to be explained by, generated by, and dependent upon the things that construct them. These features of social construction form a minimal baseline for any view of social properties. My aim is to present the views in this chapter in a way which is neutral with respect to what properties are (e.g., whether they are tropes, universals, sets). Notably, properties themselves aren’t always treated as relata for each of the relations discussed below. For example, we don’t usually say things like “being a dollar bill is grounded in social factors”; instead, we say things like “the fact that X is a dollar bill is grounded in social factors”, or alternatively, “X’s being a dollar bill is grounded in social factors”. I will do my best to adjust the discussion below accordingly. Before moving on to the views about what it takes for a property to be social, I’d like to briefly address the idea that social properties are not biological properties. This view sometimes appears in discussions about the social construction of gender, for example, where it is argued that gender is social as opposed to biological. This suggests that part of the reason gender is social is that it is not biological, and so perhaps not being biological is a necessary condition on being social. However, there are good reasons to think that properties can be both biological and social. For example, biologists will describe the 439

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behaviors of many non-human animals as social in a way which is consistent with those behaviors being, in some sense, biological as well (consider: being an ant colony and being the waggle dance of a honey bee). In addition, feminist scholars have argued that sex and sexuality are socially constructed in ways which leave these properties both social and biological (Ásta 2018: 70–92; Butler 1980; Fausto-Sterling 1993, 2003). As such, it is implausible that not being biological is a necessary condition on being social. The view that social properties are not biological is sometimes generalized into the proposal that social properties are not natural properties. This proposal is more difficult to discuss because “natural” can mean so many things (for more on natural properties, see Chapter 4, this volume). However, on most popular interpretations, the natural/nonnatural distinction does not map directly onto the social/non-social distinction, and so it is implausible that the social properties are simply the non-natural properties. To be fair, offering a non-circular definition of sociality is notoriously difficult, and as we’ll see, much of the literature on social properties presupposes a basic, intuitive notion of what it takes to be social. For much of this literature is concerned with the question of how social properties are constructed by other social factors, factors which work to infuse the properties they construct with sociality. In other words, this literature has largely been concerned with capturing how social properties are built by other social factors (Bennett 2017).3

39.3

How to be Social: Properties and Kinds

In the next four sections, I will present what I take to be the four main views currently on offer in the literature on social properties. Each of these views uses a different type of metaphysical explanation (causation, constitution, grounding, essence) and so, to the extent that there is a debate here about which view is correct, it is a debate over which type of metaphysical explanation holds between social properties and the things that construct them. Before moving on to these views however, it will be good to observe that many things are social, not just properties. There are social institutions, facts, individuals, artifacts, relations, and representations, likely among a great many others. And there are also social kinds. Much of the literature on social construction is concerned with the construction of kinds (Ásta 2013, 2018; Haslanger 2012; Mallon 2016) and this literature significantly overlaps with the literature on social properties. This is because, very generally speaking, in this literature kinds are treated as collections or categories of individuals which share one or more properties in common (Ásta 2013, 2018). And when it comes to social kinds, these properties are social properties. In addition, the question of what makes a kind social is often answered in terms of an explanation for how the individuals in the kind came to have the properties which purchase their kind membership. And where those properties are social, that explanation references social things. It is my sense that the social literatures on properties and kinds are close enough to where, in many places, there isn’t a clear line between them, and most of what has been said about social properties has been said in discussions about social kinds. For example, some of the views described below treat properties as though they are kinds, and vice versa. I don’t know that a rigorous treatment of this distinction exists within social ontology and so for my part I will follow the literature in switching between the two, although I will acknowledge when a particular author takes care to separate them. 440

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39.4 Causal Views According to causal views, social properties have social causes. So, for example, being a dollar bill is social because, for all x, if x has the property of being a US dollar bill, then social factors are among the causes for x’s being a dollar bill. Ian Hacking’s (1999) view on the construction of interactive kinds is a prominent early example of a causal view. Hacking argues that certain kinds are caused to exist through the introduction of certain tools to represent certain populations (e.g., labels, taxonomies, often introduced by relative authorities on the populations being represented, like social scientists). The introduction of these representational tools then causes the relevant populations to respond and adjust to being represented in those ways, which in turn causes changes in the representations, and so on. These interactions form causal cycles, or what Hacking famously calls looping effects. The general idea is that interactive kinds are social because they come about through these causal exchanges between representations and worldly phenomena, where those worldly phenomena are often intuitively social (e.g., human behavioral patterns). Other examples of prominent causal views include Sally Haslanger’s (1995, 2012) view of causal social construction, according to which “something is causally constructed iff social factors play a causal role in bringing it into existence, or to some substantial extent, in its being the way it is” (Haslanger 1995: 98).4 Ron Mallon (2016) argues for a view according to which some social kinds are homeostatic property clusters, or clusters of properties which are regularly gathered together by an underlying causal mechanism. On Mallon’s view, these mechanisms are usually social norms or conventions, and that is what makes these kinds social. Mallon’s is a causal view because these underlying norms and conventions cause the existence of the social kinds in question.5 On causal views, social properties have social causes. But in addition to this, causal constructionists are also often interested in the causal consequences of the construct, and that a particular construct has social consequences is sometimes taken to be part of the reason why the construct itself is social, in the first place (Ásta 2015; Wendell 1990). Hacking’s looping effects present one example of this: interactive kinds have social causes, but they also have social effects, e.g., changes to the ways in which the kind is represented, and subsequent changes to the members of the kind. Haslanger discusses something similar in the form of discursive social construction (Haslanger 1995, 2012) and Mallon argues that causally constructed human kinds have causal powers (Mallon 2003, 2016). Whether properties themselves can serve as causes is a matter of debate (see Chapter 23, this volume), but if they can, then this is yet another characteristic of social properties on the causal view: they have social effects.

39.5

Constitution Views

According to constitution views, social properties are constituted by social factors. So for example, the property of being a dollar bill is a social property just in case it is constituted by social factors. The central challenge facing constitution views is one of specifying how, exactly, this sort of constitution works. It is implausible that the sort of constitution at work here is material constitution, for example, as this is typically understood as a one-to-one relation which obtains between spatially and materially coincident things (Wasserman 2021). Many social properties and the factors which construct them do not comfortably fit into

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this equation however, so it will be good to have something different to say about the constitution relation in this context. John Searle’s (1995) view of constitutive rules is a prominent early example of constitutive construction. On Searle’s view, a particular piece of paper, x, is a member of the kind dollar bill in a context C just in case x counts as a dollar bill in C. This is an example of what Searle calls a constitutive rule, the more general formulation of which is: x counts as a y in C. This “counts as” relation is to be understood as a constitution relation, which is here analyzed in terms of a status function: a particular piece of paper constitutes a dollar bill in context iff it counts as a dollar bill in that context iff it functions as a dollar bill in that context. Social kinds, on Searle’s view, are constructed in contexts where individuals collectively endorse rules with this general shape. These collective endorsements are facilitated by the existence and activities of institutions, like the US Bureau of Engraving and Printing (among many, many others). Importantly, kinds are centrally dependent upon social institutions and collective representations in a way that facts about individual kind membership are not. This is to ensure that e.g., particular pieces of paper can be dollar bills even when no one ever directly represents them as such (say, because they have been lost under someone’s bed, or something like that). This means that facts like [the kind dollar bill exists in C] and [x is a dollar bill in C] are made true in different, but importantly related ways: the kind dollar bill exists in C because individuals in C collectively endorse rules like “green pieces of paper count as dollar bills in C”, rules which lay down the conditions for membership in the kind dollar bill. The fact that x is a dollar bill in C is true, then, because x satisfies these membership conditions, and so functions as a dollar bill in C. Other prominent examples of constitutive views include Haslanger’s (1995, 2012) view of constitutive social construction, according to which “something is constitutively socially constructed just in case in defining it we must make reference to social factors” (Haslanger 2012: 87). I list this view here because it has been understood as a constitution view at times (Ásta 2015), but in her more recent work, Haslanger (2014) has clarified that here she has in mind real definitions, or essences, and so this is perhaps best characterized as an essence view of social properties (more on this in Section 39.7). In more “mainstream” metaphysics literatures, it has become popular to analyze constitution in terms of grounding (Audi 2012; Bennett 2011, 2017) and this option is available to constitution theorists working in the social metaphysics of properties, as well. I will turn to grounding views next.

39.6 Grounding Views According to grounding views, things with social properties are grounded in social factors. So, for example, the property of being a dollar bill is social because entities with this property are grounded in social factors (or alternatively, for fact-grounding views: facts about entities with this property are grounded in social factors). Grounding is typically characterized as a relation which holds between facts (Fine 2012; Rosen 2010), although there are some views according to which entities can ground, as well (Schaffer 2009, 2016). Grounding is an explanatory relation, such that where x grounds y, x explains y. This relation is largely taken to be asymmetric, irreflexive, and transitive, and it is often taken to be one of dependence as well: y depends in some crucial sense upon x. 442

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And, for at least those reasons, in most cases x can be understood as being metaphysically prior to, or more fundamental than, y. The distinction between full ground and partial ground also matters here: roughly, x fully grounds y when x alone is sufficient to explain y, and x partially grounds y when x together with some other things is sufficient to explain y. This distinction matters because, oftentimes, social factors make up only a partial ground for (a fact about/entity with) a social property, as there may be elements of a full ground for the property which are not social. Jonathan Schaffer (2017) has defended a grounding view of social construction, according to which “to be socially constructed is to be grounded in distinctive social patterns” (Schaffer 2017: 2454). Aaron Griffith (2018a, 2018b) has also argued for a grounding approach to social construction, according to which “for something to be socially constructed is for it to be (at least partly) grounded in social reality” (Griffith 2018a: 3). Notably, on both views, when x grounds y, x doesn’t need to be absolutely fundamental (that is, x itself may be grounded in other things). This allows for grounding relations to obtain between facts and entities in the social domain, which is characteristically non-fundamental. Brian Epstein (2015) defends a view according to which social facts are constructed via grounding relations, in addition to what he calls anchoring relations. Very generally, on Epstein’s view, there is a grounding relation which holds between the fact that paper1 is a dollar bill and e.g., the Bureau of Engraving and Printing, and there is a grounding relation which holds between the fact that paper2 is a dollar bill and the Bureau of Engraving and Printing … and so on. We can then ask: why do all of these individual grounding instances obtain? The answer is that they are all anchored by a general rule of the following form: for all x, the fact that x is printed by the Bureau of Engraving and Printing grounds the fact that x is a dollar bill (Epstein 2015: 77).6 Notably, Schaffer, Griffith, and Epstein propose general grounding construction frameworks which might then be applied to social properties, but they are not concerned with the social construction of properties in particular. There are grounding views specifically oriented toward properties, however. For example, Ásta (2015, 2018) argues that social properties are the social significance of underlying base properties. On Ásta’s view, social properties are conferred onto their bearers in particular contexts by other individuals and institutions in those contexts. I list this view among grounding views here because Ásta analyzes these conferrals in terms of grounding relations. For example, let’s say that, in Ásta’s terms, there is a gender property, being a woman, which is the social significance of some further property, being taken to be feminine. Then if someone (Suzy, say) has this gender property in context C, it is because other people and/or institutions operative in C take Suzy to be feminine, and by taking Suzy to be feminine, those people and institutions confer unto her the property of being a woman. Importantly, for Ásta, that other people/ institutions in C treat Suzy in this way grounds Suzy’s being a woman in C. In other words, on Ásta’s view, the fact that Suzy is a woman in C is grounded in facts about how other people/institutions in C treat Suzy (Ásta 2018: 7–33). The last collection of views to be considered here are essence views. It’s worth noting that grounding views and essence views often overlap, in part because, on some of these views, essences are analyzed in terms of grounding (Rosen 2015) and generally, grounding and essence have been described as closely related (Correia and Skiles 2019).

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39.7

Essence Views

According to essence views, a property is social just in case it has an essence which includes social factors. So for example, the property of being a dollar bill is social because it has social factors in its essence. Sally Haslanger’s notion of constitutive social construction is perhaps best understood as an essence view like this (Haslanger 2012, 2014). For Haslanger, something is constitutively constructed just in case it has a real definition which includes social factors (Haslanger 2012: 87; Haslanger 2014: 29). Real definitions can be contrasted against nominal definitions: when I ask after the meaning of a term, e.g., “dollar bill”, I’m asking about the nominal definition of “dollar bill”; on the other hand, when I ask after the real definition of the property of being a dollar bill, I’m asking about the essence of the thing the term “dollar bill” picks out (in this case, the property being a dollar bill). Here, Haslanger is working with an analysis of real definitions developed by Gideon Rosen (2015), an analysis which incorporates a Finean notion of constitutive essence. Generally speaking, the constitutive essence of an entity x is a set of propositions which together define what it is to be x (Fine 1994). So, on Haslanger’s view, for a constitutively constructed entity x to be defined by social factors is for x to have a constitutive essence, (at least some of) the propositions of which have social factors as elements. Asya Passinsky (2021) also argues that Fine’s notion of essence can be fruitfully employed to analyze social construction. Passinsky argues that essence views of social construction have certain advantages over grounding views in the context of feminist metaphysics, where many of the important questions center around the nature of e.g., gender (as opposed to being solely questions about what grounds facts about gender). Other examples of essence views include Rebecca Mason’s (2021) view that social kinds are essentially mind-dependent. On Mason’s view, “a kind, K, is mind dependent =df it is essential to being K that if an entity, x, is K, then x is K (partially) because certain mental states exist” (Mason 2021: 3981). I have defended an essence view of properties which employs a Finean notion of essence as well, together with partial grounding (Payton 2022). This view builds on the consequences of two observations: first, that a huge number of social properties are constructed, at least in part, by facts about how language is used. And second, that on several popular semantic externalist views, facts about language use play a role in explaining why particular words take particular meanings. So, in both cases, facts about language use are playing a central explanatory role, and I argue that this overlap tells us something interesting about the nature of social properties. Very generally, the view is that a special relationship holds between social properties and the devices we use to represent them (e.g., predicates, concepts). This relationship can be generally stated as follows: there are representational facts which explain both (i) why someone/something has a particular social property F, and (ii) why a particular representational device (e.g., a particular predicate) picks out F. So for example: plausibly, there is a fact about language which explains both (i) why a particular piece of paper has the property being a dollar bill, and (ii) why “dollar bill” picks out being a dollar bill. The grounds here overlap in a unique way, and that, I argue, is a distinctive mark of sociality.

39.8 Conclusion In this chapter I’ve covered four general views about social properties currently available in the social metaphysics literature. I have not, generally, taken the time to evaluate these

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views here, or attempted to argue for the advantages of one view over the rest. However, an evaluative project like that might begin with the theoretical constraints presented in Section 39.2. For example, we might ask: how well does each particular view account for the relations of dependency, generation, and explanation that we observe in the social world? In addition, I have said that the constraints sketched in Section 39.2 form a kind of minimal baseline for a view of social properties, but there are often additional desiderata at play in these debates. For example, much of the social metaphysics literature on properties overlaps with the philosophy of gender (Barnes 2020; Haslanger 2000; Jenkins 2016; Witt 2011), the philosophy of race (Glasgow et al. 2019), the philosophy of disability (Barnes 2016), and the philosophy of sexuality (Andler 2021; Dembroff 2016), and other similar social literatures. And importantly, discussions in these literatures are often informed by political and pragmatic considerations, considerations which then bear on the utility of particular views about the metaphysics of social properties in these contexts. As just one example of this, consider the general argument that, necessarily, if we were to stop engaging in certain patterns of behavior, then this would result in changes to, or else the elimination of, certain oppressive social structures (Haslanger 2012). Note that arguments like this build in a dependence claim: y depends on x in such a way that, necessarily, if notx then not-y. Some but not all of the views surveyed in this chapter can support claims like that. This is just one example of how arguments in socially and politically engaged literatures can generate additional constraints and desiderata for views about social properties.

Notes 1 Hereafter “being a dollar bill”. 2 Importantly, we should distinguish this general question of what it takes for any property to be social from more specific questions about e.g., which particular things actually explain why x has the property of being a dollar bill. Debates over whether and why particular properties like this are social tend to be debates over (i) what actually explains why people/things have the property in question, and (ii) whether those really are social explicantia. I won’t engage those sorts of debates here. 3 Of course, this leaves open the question of what makes those factors social in the first place, and whether there are any social properties which are constructed purely by non-social factors. Unfortunately, I lack the space to address these issues here, but Sally Haslanger’s recent work on the materiality of social structures is a good place to begin to explore this topic ( Haslanger 2020). 4 More recently, Riin Kõiv (2019) has defended a view of causal construction which centrally employs a contrastive notion of causation. On this view, “x is socially causally constructed iff, if [social factors*] rather than [social factors] obtained, then x* rather than x would obtain” ( Kõiv 2019: 86). Kõiv argues that this characterization of causal construction avoids some of the issues for common interpretations of Haslanger’s original definition (see Díaz-León (2015) and Marques (2017) for additional evaluations of causal construction). 5 On Mallon’s view, kinds are clusters of properties, but kinds are also properties themselves. That is, kinds are “categories that are or could be relevant or important or significant enough to figure in our successful theories” and the relevant categories, for Mallon, are “properties or kinds instantiated by humans” ( 2016: 6–7). So kinds, properties, and categories strongly overlap on this view. Given this, note that on Mallon’s view, it makes sense to talk about social factors directly causing properties/kinds to exist (in addition, perhaps, to generating facts about things with the properties). 6 There is some debate over whether anchoring is a type of grounding (specifically, whether anchoring relations are best understood as grounding laws). See Epstein (2019) and Schaffer (2019) for discussion.

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References Andler, M. (2021) The Sexual Orientation/Identity Distinction. Hypatia 36(2): 259–275. Ásta (2013) The Social Construction of Human Kinds. Hypatia 28(4): 716–732. Ásta (2015) Social Construction. Philosophy Compass 10: 884–892. Ásta (2018) Categories We Live By. Oxford: Oxford University Press. Audi, P. (2012) A Clarification and Defense of the Notion of Grounding. In Correia, F. and Schnieder, B. (eds.) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press: 101–121. Barnes, E. (2014) Going Beyond the Fundamental: Feminism in Contemporary Metaphysics. Proceedings of the Aristotelian Society 114: 335–351. Barnes, E. (2016) The Minority Body: A Theory of Disability. Oxford: Oxford University Press. Barnes, E. (2017) Realism and Social Structure. Philosophical Studies 174(10): 2417–2433. Barnes, E. (2020) Gender and Gender Terms. Noûs 54(3): 704–730. Bennett, K. (2011) Construction Area (no hardhat required). Philosophical Studies 154(1): 79–104. Bennett, K. (2017) Making Things Up. Oxford: Oxford University Press. Butler, J. (1980) Gender Trouble: Feminism and the Subversion of Identity. New York: Routledge. Correia, F. and Skiles, A. (2019) Grounding, Essence, and Identity. Philosophy and Phenomenological Research 98(3): 642–670. Dembroff, R. (2016) What Is Sexual Orientation? Philosophers’ Imprint 16: 1–27. Díaz-León, E. (2015) What is Social Construction? European Journal of Philosophy 23(4):1137–1152. Epstein, B. (2015) The Ant Trap: Rebuilding the Foundations of the Social Sciences. Oxford: Oxford University Press. Epstein, B. (2019) Anchoring versus Grounding: Reply to Schaffer. Philosophy and Phenomenological Research 99(3): 768–781. Epstein, B. (2021) Social Ontology. In Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 Edition). URL = < https://plato.stanford.edu/archives/win2021/entries/social-ontology/> Fausto-Sterling, A. (1993) The Five Sexes: Why Male and Female are Not Enough. The Sciences 33: 20–24. Fausto-Sterling, A. (2003) The Problem with Sex/Gender and Nature/Nurture. In Williams, S.J., Birke, L., and Bendelow, G.A. (eds.) Debating Biology: Sociological Reflections on Health, Medicine and Society. London and New York: Routledge: 133–142. Fine, K. (1994) Senses of Essence. In Sinnott-Armstrong, W., Raffman, D., and Asher, N. (eds.), Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus. Cambridge: Cambridge University Press: 53–73. Fine, K. (2012) Guide to Ground. In Correia, F. and Schnieder, B. (eds.) Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press: 37–80. Glasgow, J., Haslanger, S., Jeffers, C., and Spencer, Q. (2019) What is Race? Four Philosophical Views. Oxford: Oxford University Press. Griffith, A. (2018a) Social Construction and Grounding. Philosophy and Phenomenological Research 97(2): 393–409. Griffith, A. (2018b) Social construction: big-G grounding, small-g realization. Philosophical Studies 175(1): 241–260. Hacking, I. (1999) The Social Construction of What? Harvard: Harvard University Press. Haslanger, S. (1995) Ontology and Social Construction. Philosophical Topics 23(2): 95–125. Haslanger, S. (2000) Gender and Race: (What) are they? (What) do we want them to be? Noûs 34(1): 31–55. Haslanger, S. (2012) Resisting Reality: Social Construction and Social Critique. Oxford: Oxford University Press. Haslanger, S. (2014) Individualism, Interpretation and Injustice: A Reply to Stahl, Betti, and Mikkola. Krisis 1: 24–38. Haslanger, S. (2020) Failures of Methodological Individualism: The Materiality of Social Systems. Journal of Social Philosophy 53(4): 512–534. Jenkins, K. (2016) Amelioration and Inclusion: Gender Identity and the Concept of Woman. Ethics 126(2): 394–421.

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40 AESTHETIC PROPERTIES Sonia Sedivy

40.1

Introduction

Aesthetic properties figure prominently in our daily lives, our conversations and actions. I notice the blazing fall leaves outside my window. Later at the gallery, you point out the delicacy of the cherry blossoms on Sakai Hoitsu’s Blossoming Cherry Trees. We talk about the jarring hand-held camera running scene as we watch the latest episode of Stranger Things. Most mornings, I notice the sleek curve of my tea kettle’s spout. On summer evening, I often close my windows to the pungent smell of an upset skunk. Two friends, one a fan of rap, the other not so much, clash over the powerful urgency or droning monotony of rap, in particular Tupac’s So Many Tears. Later at a concert, they both revel in the cacophony of Shostakovich’s War Symphony. Even later, they play Dead Cells which recreates video games from decades ago to enjoy its retro feel and look. These examples give a small indication of the wide variety of aesthetic properties. Theoretical disagreement prevails concerning their nature, their epistemic and metaphysical status. Nevertheless, it is fair to say that there are two points of consensus (which is not to say that even these have gone unchallenged) (see Goldman 2009; Kelly 2014; Levinson 2005b). 1 Many if not all aesthetic properties are immediately perceptible or observable, or a matter of immediate apprehension (in cases of literary works and poems, mathematical or geometrical equations or proofs, scientific theorems, laws or models, etc.). 2 Aesthetic properties are relevant to the aesthetic value of the things, scenes or events that possesses them. Beyond these two hallmarks, theorists disagree about whether aesthetic properties require exercises of imagination or metaphoric thought, or whether they evoke emotions and feelings. Do aesthetic properties occasion a distinctively aesthetic pleasure, perhaps one that is independent of practical concerns, a pleasure of “mere contemplation” rather than desire? And do all aesthetic properties require trained appreciative and evaluative capacities or “taste” to be discerned?

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Insofar as aesthetic properties are linked to our pleasures or tastes, they are open to skeptical challenge. The charge is that attributions of aesthetic properties are subjective and lacking in truth value. A variety of responses are on offer. Some propose that aesthetic properties are dispositional or response-dependent. Another approach is that insofar as aesthetic properties systematically depend on non-aesthetic properties – for example, the aesthetic properties of musical works depend on non-aesthetic properties of sounds such as tones and temporal relationships – this raises the possibility that aesthetic properties supervene on non-aesthetic properties. But do aesthetic properties depend only on a thing’s “narrow” or formal properties – such as colours or contours; or are they gestalt in character, dependent on relational features of the larger whole of which they are a part, be that an object, scene, event, etc.; or are they “broad” dependent also on facts of the broader context in which they figure? Last but not least, insofar as aesthetic properties are immediately perceivable and contribute to aesthetic value, this raises issues about the nature of the judgements and claims in which they are predicated. For example, are such judgements and claims only singular, or can we formulate general aesthetic principles concerning aesthetic properties? In what follows, the second section introduces the heterogeneity and historical dependence of aesthetic properties. I will propose that we add both heterogeneity and historical dependence to the above consensus about aesthetic properties. The third section examines the repercussions of recognizing heterogeneity and historical specificity for explaining aesthetic properties. Can we reasonably expect to demarcate aesthetic properties solely in terms of non-aesthetic properties? If not, this suggests that explanations of aesthetic properties need to draw on other aesthetic notions. The fourth section examines several accounts of aesthetic value to show how they extend to aesthetic properties. Although our aesthetic responses – such as experiences, attitudes, attention, or judgements – might also provide a way to demarcate and explain aesthetic properties, this large set of topics lies outside our scope. The fifth section outlines some of the metaphysical debate between realists and non-realists about aesthetic properties.

40.2

Heterogeneity and Historicism

I suggest that aesthetic properties are heterogenous in that they are made up of sub-kinds of aesthetic properties or individuals that retain their identity – for example, as olfactory or visual; natural, artefactual or artistic. The notion of heterogeneity is common in dealing with mixtures – such as substances, chemical solutions or populations. Smoke is a heterogenous mixture of gas and solid, which retain their identity while mixing together; salad dressing is a heterogenous mixture of two liquids, typically oil and vinegar which retain their identity rather than dissolving in one another to make up a uniform or equal distribution. Though the heterogeneity of aesthetic properties is implicit in typical lists of aesthetic properties, I am suggesting that it is important to make it explicit as a hallmark feature as it plays a role with respect to explanation (as I will show). In the examples above, aesthetic properties such as cacophony and pungency are specific to things we hear or smell and retain their identity as such. They provide the clearest examples of the heterogeneity of aesthetic properties. But aesthetic properties that can be features of artefacts, artworks and natural beings, which are readily identifiable as such, retain their identity as artefactual, artistic or natural. That is, the identity conditions of artefacts, natural or artistic things are part of the identity conditions of the respective 449

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aesthetic properties. If we turn to the arts, we find further heterogeneity. Aesthetic properties such as dissonance are specific to certain art forms such as music. And the openendedness of artistic media underscores the open-endedness of aesthetic properties. A whole range of aesthetic properties specific to moving pictures become available that would not have been possible to encounter before the advent of movies, for example. Insofar as some measure of historicism has become broadly accepted about the arts, it carries over to at least some aesthetic properties of works. Two landmark arguments for the historical nature of visual art by Arthur C. Danto (1981) and Kendall L. Walton (1970) illustrate this point. Analogous considerations hold for other arts such as dance or music. Danto (1981) offers a relational and historical definition of art according to which artworks embody meanings and extends this view to aesthetic properties. The key is that embodiment of meaning is historical. Danto argues that works like Andy Warhol’s Brillo Box or Marcel Duchamp’s Fountain illustrate that the identity conditions of an artwork must distinguish it from potential lookalikes in any category. Warhol’s Brillo Box is distinguished from a lookalike carton at least partly by its content. And crucially, the content of Brillo Box is determined or fixed by (among other things) the historical and theoretical contexts in which the work is situated. Some contents can only be entertained and embodied in certain historical contexts. A century or two earlier nothing could have meant what Brillo Box means. To illustrate that the aesthetic properties of artworks are bound up with the meaning a work embodies, Danto asks us to imagine a Gallery of Indiscernibles with distinct works of the same size, shape and colour, identified by different titles such as The Israelites Crossing the Red Sea, Kierkegaard’s Mood, Red Square and Nirvana. These works are made by distinct artist of different eras. The gallery also contains two artefacts of the same size and colour, a mere red canvas and a canvas that is a prepared ground for a work by an artist of historical consequence. Danto’s point is that the aesthetic impact of each would be different. The aesthetic properties of Red Square are integral to the way it embodies its content, whereas the aesthetic properties of the painted canvas are the experiential impact of its specific colour, sheen, texture, etc. Each work has a different aesthetic impact with different aesthetic properties that are integral to the content each embodies – even though each work uses the same red colour as well as same shape and size canvas. Insofar as there are no bounds on how an artwork may look – consider Brillo Box or Fountain – aesthetic properties are correlatively unconstrained, just about “any” property may be aesthetic depending on the content being embodied by the work and the context. Aesthetic properties are not restricted to oft cited examples such as elegance or harmony. Walton (1970) focuses on a specific range of categories of art to show that some aesthetic properties of individual works depend on such categories. His argument does not rely on a theory of the nature of art and does not tie aesthetic properties to the meanings of artworks. Crucially, Walton delineates categories of art that are both historical and perceptually distinguishable. Discernible media like painting or bas relief, genres such as fantasy, or styles such as Cubist or Brahmsian are historical in that they are “well established in and recognized by the society in which [the work] was produced” (Walton 1970: 357), and the artist could expect their work to be “perceived” in the specific category or could have “thought of it” as being in that category. Walton’s point is that some aesthetic properties depend on the conditions or properties that are standard, contra-standard or variable for such historical categories, and such normative conditions are specific to societal contexts and practices. 450

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To illustrate, Walton’s best known example situates a particular work, Picasso’s Guernica, in two different societies where it belongs to different art categories. In our world, Guernica is a painting, whereas in the hypothetical scenario it is a guernica. This is a category of works that have the three-dimensionality of bas-reliefs but whose raised surfaces have the same arrangement of surface colours and shapes – those of Guernica – but in different moldings. Different parts of the surfaces of guernicas “are molded to protrude from the wall like relief maps of different kinds of terrain” (Walton 1970: 347). There are no paintings in the hypothetical context, only guernicas. The key is that changing the social context, and thereby the category to which the work belongs, changes some of its aesthetic properties. In our context, the flatness that is standard for paintings makes the markings of the surface which are variable for painting – in this case Guernica’s sharp angles, edges, shapes and black and white colours – stand out, or to be dynamic or vital or violent. In the hypothetical context, bas-relief molding of figures or markings are standard, so that the flatness of Guernica would stand out, making the work boring or bland or serene. Because only the social context and art categories change, it is not (only) properties such as colours or contours that determine aesthetic impact but rather “which are ‘standard,’ which ‘variable,’ and which ‘contra-standard,’” (Walton 1970: 338). Some aesthetic properties depend on the normative roles that properties such as colour or flatness have for specific categories. Moreover, in the example, vividness or vitality are properties that the painting Guernica has and is correctly perceivable to have. This does not suggest that Guernica might not have other aesthetic properties, perhaps purely subjective ones. Rather, the point is to zero in on often discussed perceptible aesthetic properties and show their historical nature. Walton and Danto’s views illustrate at least four important consequences of historicist arguments. First, aesthetic properties can depend on historical context. Second, historical aesthetic properties are objective and correct to perceive or apprehend in a work. This blocks a thorough subjectivism about aesthetic properties. Third, establishing that at least some aesthetic properties are historical blocks a thorough formalism or aesthetic empiricism that holds that all aesthetic properties depend on low-level sensory properties such as colours, contours, sounds, etc. Insofar as some aesthetic properties depend on facts of their historical contexts – so that our experience of them requires some grasp of those facts or conditions – they do not depend only on sensory properties of works and our grasp of such properties. A fourth result that has not been noted is that, according to Danto and Walton’s arguments, at least some aesthetic properties do not depend on what we might call nonaesthetic properties simpliciter such as colours or sounds, etc., but on conditions specific to artworks. According to Walton, at least some aesthetic properties depend on the normative conditions for the perceptually distinguishable medium, genre or style of an individual work. Similarly, according to Danto, the aesthetic properties of artworks depend on properties that implicate the identity conditions of works of art as opposed to artefacts (or natural objects) since all these might share sensory properties simpliciter.

40.3 Demarcation and Explanation Since Frank Sibley’s “Aesthetic Concepts” (1959) and “Aesthetic and Non-Aesthetic” (1965), it has been standard to draw a distinction between aesthetic and non-aesthetic 451

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properties that corresponds to Sibley’s distinction between aesthetic and non-aesthetic terms. (But see Cohen 1973; Kivy 1973.) The distinction implies that aesthetic properties can be demarcated in a principled way. This is important because it suggests that we might be able to explain aesthetic properties in terms of non-aesthetic properties. But I argue that historical dependence and open-ended heterogeneity make it difficult to demarcate or distinguish aesthetic properties from non-aesthetic ones. Sibley was concerned with the use of aesthetic terms in critical discourse about the arts and he offered a principle for demarcation for these cases: aesthetic terms require taste, whereas ordinary perception is sufficient for the use or application of non-aesthetic terms. His view is that aesthetic terms are not condition governed: no conditions can be stated in non-aesthetic terms for the application of aesthetic terms (or for aesthetic properties). But Sibley’s appeal to taste does not demarcate all aesthetic properties since it does not work well for our appreciation of nature and the use of aesthetic terms to characterize natural objects or scenes. One does not need well-trained critical capacities to appreciate the beauty of the sky one day or its gloominess the next (though beautiful nature might be the subject of pure judgements of taste in the Kantian sense). The considerations in the previous section about the historical dependence and openended heterogeneity of some aesthetic properties suggest that just about any property (or term or use) may be aesthetic depending on context. Criticizing Sibley’s view, Ted Cohen (1973) points out that many non-aesthetic terms or uses of terms can be aesthetic and provides over fifty examples. Here are just a few: linear, murky, sentimental, suspenseful. (See Eaton 1994.) Moreover, modern and contemporary art show that properties such as being discordant, disunified or heavyset might be aesthetic no less than properties such as being harmonious, unified or delicate. It no longer seems apt to say that there are paradigmatic aesthetic properties. In view of these difficulties, one might argue that aesthetic properties can at least be distinguished from “low-level” perceptible properties such as colours, shapes, sounds, etc. But artworks in various media illustrate that such “low-level properties” may be aesthetic depending on context. Even a particular stretch of silence may be aesthetic in a specific context as in the case of John Cage’s 4′33". Immersive installations that consist in nothing but colour such as James Turrell’s The Substance of Light and Carlos Cruz Diez’ Chromosaturation challenge excluding colours as only non-aesthetic properties. Turrell places us in a foggy light filled space that obliterates all contours and continually melds from one colour to another. Cruz Diez allows us to walk through colourfully illuminated spaces that retain some wall-like spatial contours. In each case, experiences of the specific colours are intensely aesthetic – it is the colours that are aesthetically valuable, each is appreciated for its experiential character. These considerations against drawing a systematic distinction between aesthetic and non-aesthetic groups or families of properties do not tell against distinguishing between such properties in a case by case way. In particular cases, if something has some aesthetic properties we can distinguish these from its non-aesthetic ones. This is integral to much critical and ordinary appreciative discussion. My point is that we do not have a principled distinction that can be used to frame explanations. The alternative is to explain aesthetic properties by appeal to other aesthetic phenomena such as aesthetic value or different kinds of aesthetic responses, for example aesthetic pleasure, aesthetic experience or aesthetic judgement. Explaining aesthetic properties in connection with other aesthetic matters would be neither viciously circular nor trivial. If there are good reasons for denying that 452

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aesthetic properties can be demarcated from non-aesthetic properties, it is appropriate to consider more complex ways of picking them out.

40.4

Aesthetic Properties and Aesthetic Value

Let’s focus on the consensus view that aesthetic properties contribute to aesthetic value. The challenge is to articulate just what aesthetic value is, and to do so in a way that explains the diversity of aesthetic properties explicitly or implicitly, showing how the account can be extended. Mary Mothersill (1984), Walton (2008) and Alan H. Goldman (1995) illustrate some key strategies. Mothersill (1984) shows how focusing on beauty can be used for an account of aesthetic properties. Beauty figures on all lists of aesthetic properties, and of course being beautiful is a property. But beauty has played the role of the highest or generic aesthetic value – beauty has been the value and aim of art in many historical eras, just as it has been a core aesthetic value for persons and nature. Mothersill’s approach treats beauty as our generic term for aesthetic value. She focuses on the singularity of our experiences of beauty to argue that aesthetic properties cause the pleasure we find in beautiful individuals. She takes Thomas Aquinas’s view as her point of departure: “Let us call that beautiful of which the apprehension in itself pleases” (Mothersill 1984: 323). Because she approaches aesthetic properties by thinking about the beautiful she can use the hallmark particularity of beauty and the singularity of our experiences of it to propose that aesthetic properties cause the pleasure we find in beautiful individuals. (i) Beauty is grasped in singular experiences or judgements, which are conveyed through success verbs such as apprehends, sees and knows. (ii) Beauty belongs uniquely to an individual so that beauty is not capturable through general principles. (iii) If there are no general principles for beauties, then this holds for the properties of beautiful things as well. Carrying these points about beauty over to aesthetic properties suggests that they are apprehended in singular experiences and unique to the individual one finds beautiful or of aesthetic value. But this raises an instructive problem. If we want to say that it is in virtue of a thing’s aesthetic properties that we find it beautiful or of aesthetic value and that these properties are unique to the beautiful individual, then we need to be able to explain their repeatability or generality. Mothersill offers an unpublished definition of aesthetic properties from Sue Larson (Mothersill 1984: 343). “q is an aesthetic property” means that for any x, if q of x, then for any y, q of y, IFF y is indistinguishable from x. (See Nehamas 2007 for recent discussion.) This definition states that an aesthetic property is a property common and peculiar to individuals that are indistinguishable from one another (where indistinguishability is relativized to the individual person). This may seem uninteresting because if two individuals are indistinguishable then they will have all the same properties – so of course they will 453

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have the same aesthetic properties. But Mothersill’s point is that the converse is important: no two distinguishable items can have the same aesthetic properties. On this view, aesthetic properties are unique but also repeatable: they are features of indistinguishable individuals that have the same beauty or aesthetic value. For example, if she finds this pottery mug beautiful, its aesthetic properties are those it would share with all mugs indistinguishable from this one. Mothersill’s final point is that beauty is a disposition and aesthetic properties play a causal role with respect to the pleasure we feel: Any individual is beautiful IFF it is such as to be a cause of pleasure in virtue of its aesthetic properties. (Mothersill 1984: 347) (For recent accounts designed to explain the diversity of beauty, see Lopes 2018; Nehamas 2007; Sedivy 2016. For examples of recent work on aesthetic value, see Gorodeisky 2021; Shelley 2010.) Walton’s (2008) approach explains aesthetic value as a second order value for which diverse first order values are primary. We might summarize his view as follows. Something has aesthetic value IFF we take pleasure in admiring an individual for having a first order value and the pleasure is properly taken with respect to that individual. Aesthetic pleasure involves taking pleasure in our own attitude. Walton’s point is that although we might take pleasure in a hot shower, that pleasure is not aesthetic, unless we take pleasure in our own admiration for the hot shower. The notion of aesthetic value is of valuing something not just for the way it is or the pleasure it gives but also for the attitude one takes to it, for “… one’s experience of admiring it, … one’s judging it to be good” (Walton 2008: 14). “One does not merely enjoy it, one takes pleasure or delight in judging it to be good” (Walton 2008: 12). Like Mothersill, Walton highlights that “Aesthetic pleasure is not just pleasure taken in my admiration of something, but in its getting me to admire it” (2008: 14). But instead of focusing on causality, he emphasizes normative conditions: “there must be a certain propriety in taking aesthetic pleasure in it; it must be reasonable or apt or make sense to do so” (2008: 14). Aesthetic properties are the properties of an individual that get me to admire it with propriety – they explain not simply pleasure in an object, but the pleasure of admiration. Walton is explicit that his account is designed to secure the diversity of the things that are aesthetically valuable. “Understanding aesthetic value in this way enables us to accommodate its diversity while locating a common thread. The thread is the pleasure taken in admiring things. The diversity lies in what we admire things for” (2008: 15). Since there are many different values for which we may admire an object, his account has the breadth that aesthetic properties require. Goldman (1995) offers a two-pronged approach. He explains aesthetic properties in terms of their contribution to aesthetic value while also invoking a Humean analogy between aesthetic properties and secondary qualities. He restricts his focus to artworks to argue that “our basic criterion for identifying aesthetic properties [is] that they are those 454

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that ground or instantiate in their relations to us or other properties those values of artworks that make them worth contemplating” (1995: 20). That is, artworks have a broad overarching aesthetic value: they engage all of our capacities – perceptual, cognitive and affective – by providing an alternative world or whole “to which we must fully attend” (Goldman 1995: 20). More specific values such as being expressive, representational, symbolic or formally interesting contribute to make a work fully engaging and challenging. Aesthetic properties ground or instantiate the more specific values. Goldman explains aesthetic properties as analogous to secondary ones. He proposes that: Object O has aesthetic property P = O is such as to elicit response of kind R in ideal viewers of kind V in virtue of its more basic properties B. (Goldman 1995: 21) On a Humean approach, ideal viewers or critics play an analogous role to normal perceivers. Whether aesthetic properties can be construed as objective comes down to how we can explain the fact of widespread aesthetic disagreement, which renders aesthetic properties disanalogous from perceptible properties like colours. Goldman’s discussion provides a bridge to our next section concerning the metaphysics of aesthetic properties. Realism about aesthetic properties has to confront the problem that when two viewers disagree, they might attribute different and arguably contradictory aesthetic properties to an object. Goldman argues that this problem saddles realists with the notion of ideal viewers whose judgements are largely free of individual bias (though not entirely free from historical or cultural preferences or outlooks) to explain that (i) there are observers “to whom aesthetic properties appear as they are” (1995: 27); (ii) there can be correct judgements about aesthetic properties; and that (iii) some of our ordinary conflicting aesthetic judgements are not simply different but erroneous. However, non-realists can argue that their approach to the problem of disagreement is simpler and more preferable. Non-realism appeals to ordinary individuals’ experience, training and historical situation to explain differences in attribution of aesthetic properties. Since non-realists are not trying to explain real properties, or the possibility of correct and erroneous judgements, they do not need to appeal to ideal critics. Non-realists charge that intractable disagreement is always possible even when it comes to ideal observers, which undermines a realist construal of the Humean definition. Goldman’s view is that “realism comes in degrees” (1995: 38). We need to recognize both that the aesthetic properties of a work are independent of a person’s “particular responses to them” and that the truth of individual judgements are “not independent of ways they appear to ideal critics, of all evaluative responses to them, or of other aesthetic judgements and beliefs that constitute different tastes” (1995: 38).

40.5

Metaphysical Debates

The metaphysics of aesthetic properties is subject to intense dispute. Should we be objectivists or subjectivists, realists or non-realists about aesthetic properties? Are such properties suited to explanation in terms of response-dependence or supervenience? In outline, here is what subjectivists or non-realists have going in their favour and what non-subjectivists or realists can claim for their side. 455

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Subjectivists or non-realists suggest that aesthetic properties are not qualities of objects, they are not part of the fabric of the world. They may appeal to: (i) faultless disagreement among appreciators; (ii) subjectivist accounts of aesthetic value and aesthetic judgements, etc. (Goldman 1995; Wiggins 1998); (iii) objections to aesthetic supervenience; (iv) the difficulty of drawing the distinction between the aesthetic and non-aesthetic; (v) the heterogeneity of aesthetic terms or properties. A core motivation for subjectivism is the claim that aesthetic properties are open to “faultless disagreement” among appreciators, as we saw above. Well situated experienced perceivers or critics – even ideal critics – may have irreconcilable disputes over aesthetic properties (Bender 1996, 2005). According to John Bender, “It seems manifest that individuals with the same taste can faultlessly disagree over the aesthetic properties of the same work” (2005: 92). But this is puzzling. If sameness of taste allows for faultless disagreement among ideal critics, it is hard to understand what it is to have the same taste – surely sameness of taste is sameness in our aesthetic preferences and evaluations? If faultless disagreement pertains to ineliminable individual differences, then what is it to have the same taste in such cases? We seem to have lost the notion of sameness of taste, especially in the case of ideal critics. Aside from the dispute over aesthetic disagreement, non-realists may charge that realists have not given compelling arguments for aesthetic realism, especially if they can show that explanations of aesthetic properties in terms of aesthetic value, response-dependence or supervenience run into trouble. Non-realists argue that the burden of proof is on realists who need to explain why we should favour positing aesthetic properties over more parsimonious approaches that do without them (Matravers 2005). On the other hand, to show that aesthetic properties are part of the fabric of the world, realists or non-subjectivists can argue that: (i) response-dependent properties are properties of objects that involve our responses; (ii) historicist arguments provide empirical conditions for at least some aesthetic properties; (iii) arguments concerning intractable disagreement fail to show that aesthetic properties are subjective; (iv) realist arguments for aesthetic value can extend to aesthetic properties (e.g., Mothersill 1984; Walton 2008); (v) aesthetic properties supervene on non-aesthetic or physical properties. Let’s focus on response-dependence and supervenience. Though realists need to explain aesthetic disagreement, they can avoid being saddled with the notion of “ideal critics” by arguing that aesthetic properties are response-dependent (Jackson and Pettit 2002; Johnston 1989, 1998; Pettit 1983, 1991). If aesthetic properties are response-dependent, it is a priori that they involve responses on the part of subjects. To put it differently, the concept of an aesthetic property involves the idea that subjects have certain distinctive responses. These may differ to some extent. Importantly, a response-dependent property is no less real by involving subjects’ responses so long as a case can also be made that the property is one that the object possesses. 456

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This brings us to the debate over aesthetic supervenience. Some realists point out that aesthetic properties satisfy the core idea of supervenience: that there is no aesthetic difference without a non-aesthetic difference (Currie 1990; Levinson 1990). They propose that aesthetic properties supervene on a subvenience base of non-aesthetic properties which are hypothesized to be some sort of structural properties – like colours or sounds – or appearance properties. (See also Levinson 2005a.) This metaphysical picture is consistent with the widely accepted view that there are no aesthetic principles, that sufficient conditions for an aesthetic property cannot be stated in non-aesthetic terms. But it is arguable that aesthetic properties fail to meet the conditions for supervenience. Supervening as well as base properties need to be demarcated or distinguished from one another. The considerations I raised above undermine the idea of a principled distinction between non-aesthetic and aesthetic properties. In contrast, Nick Zangwill (2023) expresses a widely assumed confidence that “The controversial questions are about the extent of the dependence base of aesthetic properties, not whether aesthetic properties have some nonaesthetic dependence base” (Zangwill 2023: sec. 2.3). In other words, though arguments for the historical nature of some aesthetic properties suggest that aesthetic supervenience is global and this is problematic for the specific explanatory needs of aesthetics, we can nevertheless be confident that there is some subvenience base for aesthetic properties. The proposal that mental predicates and properties supervene on physical ones provides instructive contrast. Unlike mental supervenience, aestheticians do not argue that aesthetic properties supervene on physical properties, which can be clearly demarcated from mental and other properties, including aesthetic ones. (For example, see Davidson 1980.) Perhaps aesthetics could argue that aesthetic properties – like many others – supervene on physical ones, but aestheticians strive to find an “in-between” kind of property on which aesthetic properties depend. This would serve a dual explanatory aim: to establish the metaphysical credentials of aesthetic properties while also providing specific explanations of them in particular cases. But this is where problems about demarcating aesthetic and non-aesthetic properties come in. In short, realists may also place the burden of proof on their opponents: given how entrenched aesthetic attributions are in human life, it is the non-realist who needs to show that an explanation that does not countenance aesthetic properties is best.

40.6 Conclusion To summarize, I have presented some of the main contemporary trends concerning aesthetic properties in the following way. Greater attention to global aesthetics and historical context, as well as to environmental aesthetics and the aesthetics of the everyday increase our appreciation of the variety and heterogeneity of historical properties. The openendedness of art forms or media brings open-endedness in their aesthetic properties. We might say that it is open-ended which properties may be aesthetic depending on broad historical context or situation. Yet aesthetic realism is just as thriving – or just as troubled – as nonrealism about aesthetic value and properties.

References Bender, J.W. (1996) Realism, Supervenience, and Irresolvable Aesthetic Disputes. Journal of Aesthetics and Art Criticism 54(4): 371–381.

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Sonia Sedivy Bender, J.W. (2005) Aesthetic Realism 2. In Levinson, J. (ed.) The Oxford Handbook of Aesthetics. Oxford: Oxford University Press: 81–98. Cohen, T. (1973) Aesthetic/Non-aesthetic and the Concept of Taste: A Critique of Sibley’s Position. Theoria 39(1–3): 113–152. Currie, G. (1990) Supervenience, Essentialism and Aesthetic Properties. Philosophical Studies 58(3): 243–257. Danto, A.C. (1981) The Transfiguration of the Commonplace. Cambridge, MA: Harvard University Press. Davidson, D. (1980) Mental Events. In Davidson, D. (ed.) Essays on Actions and Events. Oxford: Clarendon Press: 207–228. Eaton, M.M. (1994) The Intrinsic, Non-Supervenient Nature of Aesthetic Properties. Journal of Aesthetics and Art Criticism 52(4): 383–397. Goldman, A.H. (1995) Aesthetic Value. Boulder, CO: Westview Press. Goldman, A.H. (2009) Aesthetic Properties. In Davies, S. et al. (eds.) A Companion to Aesthetics, 2nd edition. Malden, MA: Wiley-Blackwell: 124–128. Gorodeisky, K. (2021) On Liking Aesthetic Value. Philosophy and Phenomenological Research 102(2): 261–280. Jackson, F. and Pettit, P. (2002) Response-Dependence without Tears. Philosophical Issues 12(1): 97–117. Johnston, M. (1989) Dispositional Theories of Value. Proceedings of the Aristotelian Society 63: 139–174. Johnston, M. (1998) Are Manifest Qualities Response-Dependent? The Monist 81(1): 3–43. Kelly, M. (ed.) (2014) Encyclopedia of Aesthetics 2nd Edition. Oxford: Oxford University Press. Kivy, P. (1973) Speaking of Art. The Hague: M. Nijhoff. Levinson, J. (1990) Aesthetic Supervenience. In Levinson, J. (ed.) Music, Art, and Metaphysics. Ithaca, NY: Cornell University Press: 134–158. Levinson, J. (2005a) Aesthetic Properties. Aristotelian Society, Supplementary Volume 79(1): 211–227. Levinson, J. (2005b) Philosophical Aesthetics: An Overview. In Levinson, J. (ed.) The Oxford Handbook of Aesthetics. Oxford: Oxford University Press: 4–24. Lopes, D. (2018) Being for Beauty: Aesthetic Agency and Value. Oxford: Oxford University Press. Matravers, D. (2005) Aesthetic Properties. Aristotelian Society, Supplementary Volume 79(1): 191–210. Mothersill, M. (1984) Beauty Restored. Oxford: Clarendon Press. Nehamas, A. (2007) Only a Promise of Happiness: The Place of Beauty in a World of Art. Princeton, NJ: Princeton University Press. Pettit, P. (1983) The Possibility of Aesthetic Realism. In Schaper, E. (ed.), Pleasure, Preference and Value. Cambridge: Cambridge University Press: 17–38. Pettit, P. (1991) Realism and Response-Dependence. Mind 100(4): 587–626. Sibley, F. (1959) Aesthetic Concepts. Philosophical Review 68(4): 421–450. Sibley, F. (1965) Aesthetic and Non-Aesthetic. Philosophical Review 74(2): 135–159. Shelley, J. (2010) Against Value Empiricism in Aesthetics. Australasian Journal of Philosophy 88(4): 707–720. Sedivy, S. 2016. Beauty and the End of Art: Wittgenstein, Plurality and Perception. New York: Bloomsbury. Walton, K.L. (1970) Categories of Art. Philosophical Review 79(3): 334–367. Walton, K.L. (2008) How Marvelous: Toward a Theory of Aesthetic Value. In Walton, K. (ed.) Marvelous Images: On the Values and the Arts. Oxford: Oxford University Press: 3–22. Wiggins, D. (1998) A Sensible Subjectivism. In Wiggins, D. (ed.) Needs, Values, Truth: Essays in the Philosophy of Value. Oxford: Clarendon Press: 185–214. Zangwill, N. (2023) Aesthetic Judgment. In Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. URL = < https://plato.stanford.edu/entries/aesthetic-judgment/>

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INDEX

Note: Page numbers followed by ‘n’ refer to notes. abstract-concrete distinction 73–76; uses and abuses of 78–80 abstract entities 29, 34, 72–80, 284, 285 abstractness 67, 73–79, 139; of properties 74, 76, 77 abstract objects 6, 8, 40, 128, 134, 185, 189, 191, 371–373 abundant conception, properties 48–57 abundant properties 48, 129, 130, 184, 317, 318, 329, 340, 341, 374, 375 accidental properties 4, 103–105, 107, 109, 111 A-essence/A-essentiality/A-essential/A-essential properties 4, 104–112; non-modal accounts of 108–110; sophisticated modal accounts of 107–108 aesthetic properties 9, 10, 448–457; and aesthetic value 453–455; attributions of 10, 449, 455; demarcation and explanation 451–453; heterogeneity and historicism 449–451; metaphysical debates 455–457 Alexander, S. 354 Almog, J. 107 Alston, W. 32 Anjum, R.L. 354 anti-realism 28, 112, 277, 338, 427–429 apparent property-referring terms 370–373 Aristotle 1, 67, 104, 115, 250, 348, 409 Armstrong, D.M. 3, 39–41, 44, 66, 135, 136n1, 136n4, 141, 143, 146n10, 162, 171, 173, 175, 176, 181n12, 196, 207, 250, 251, 306, 339, 340, 375, 390 atomic sentences 42, 43, 86

Barker-Dowe problem 152 base properties 347, 350, 352–354, 443, 457 Bealer, G. 136n1, 375 bearer of properties 165, 297–299, 302 Bedau, M. 352 Beebee, H. 179 Benacerraf, P. 80n4 Bender, J.W. 456 Bergmann, G. 141, 142 Best System Account of laws (BSA) 54 Bickhard, M. 353 Bird, A. 318 Black, M. 159, 165 blackness tropes 64, 65, 405 Blumson, B. 187 Bowers, J. 157n4 Bradley, F.H. 1, 87, 255 Brogaard, B. 108, 299 bundle theory 156, 159–167, 219, 221, 234, 237, 312; objections and replies 162–165; substratum theory versus 160–162; universals 1–2, 159–167 Busse, R. 186, 189 Butchard, W. 101n3 Calemi, F.F. 181n7 Callender, Craig 54 Cameron, R. 39 Campbell, K. 66, 181n5, 240, 241, 243, 308 Campbell, R. 353 Carlson, G.N. 371 Carmichael, C. 136n1, 137n12 Carnap, R. 78, 185

459

Index causal exclusion principle 399, 400 causal overdetermination 235, 236, 399 causation 7, 74, 75, 232, 251, 263–271, 399; accommodate properties 266–268; hasteners and delayers 269–270; motivations 263–266; role of properties 263–266; switches 270–271; transitivity of 263, 265, 268–269 Chalmers, D. 394, 398 circularity, problems of 320–321 Clarke-Doane, J. 425n3 classical mereology 307, 311 class nominalism 3, 4, 6, 40–41, 184–193, 200, 298; advantages of 187–188; coextension difficulty 188–193; problems for 186–187 coextension difficulty 188–190, 192, 193 coextensive properties 185, 188–191 Cohen, Jonathan 54 Cohen, T. 452 compresence relations 161, 162, 166, 221, 241, 243, 244 compresent tropes 243, 244, 252 concrete objects 35, 77, 160, 201, 219, 251, 363 concrete particulars 139–141, 188, 219–222, 258, 266, 267 concrete universals 139, 140, 160 contemporary metaphysics 196, 315, 342 Correia, F. 108–112 Cowling, S. 112n3 Crowther, T. 289 Danto, A.C. 450 Dasgupta, S. 358 Davidson, D. 375 Declos, A. 202 Denkel, A. 240, 245 dependence theories 240, 244, 245 descriptive metaphysics 8, 369, 370 determinate/determinable properties 115–124, 232, 359–360, 383, 403, 407–408; comparison 117–118; exclusion 118–119; grand metaphysical projects 123; metaphysical and epistemic indeterminacy 123; models and theories 119–123; ontological reduction and causation 123; specification 115–116 Devitt, M. 129, 196, 200 dispositional essences 318, 342, 343 dispositional essentialism 318–319, 342 dispositional monism 275, 279 dispositional properties 273–281, 315, 318, 332, 337, 342, 343; categorical properties 274–275; irreducible 279–280; powerful

qualities 276; property dualism 275; pure dispositions 275; reducible 276–278, 280 Ditter, A. 112 Dodd, J. 179 Dorr, C. 24n2, 29 Dretske, F. 338 Dunaway, B. 425 duplication accounts 95–100 efficacious properties 387–389 Ehring, D. 65, 121, 122, 153, 241, 243 E.J. Lowe’s problem 155 The Elements of Being (2018a) 239 Ellis, B.D. 363 emergentism 348, 350, 354 emergent properties 8, 312, 332, 347–355; contemporary debates 350–354; history of concept 348–350; processual dissolution and 350–354 endurantism 7, 152, 153, 163, 164, 247, 296 epistemic modality 316 Epstein, B. 443 essentialism 52, 330, 334, 335 essential properties 38, 104, 111, 266, 267, 295, 298, 332, 334, 341, 342, 344; versus accidental properties 103–112; Aristotelian and modal notion 104–105 Evans, G. 291 events 283–292; modal profile of 287–289; occurrence, aspect, and nominalizations 285–287; occurrents, properties, and particularity 289–291; as property exemplifications 284–285 existential metaontology 18 existential propositional commitment 18 existential sentential commitment 18–19 explicit property-referring terms 375–380 extrinsic properties 92–94, 96–100, 295, 297, 332, 333 Figdor, Carrie 95 Fine, K. 107, 111, 203n3, 370, 380n1 first-order metaontology 21 first-order ontology 22 first-order propositional commitment 22 first-order quantification 21 first-order sentential commitment 22 first-order state of affairs 145n1 Forbes, G. 112n3 formal ontological relations 240, 245, 246 Forrest, P. 75, 196 fragility 72, 231, 274, 277, 279, 316, 317, 384 functionalism 9, 121, 386, 387, 390, 391 fundamental commitment 20

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Index fundamental metaontology 19–20 fundamental ontological categories 5, 207, 239, 240, 242 fundamental truths 180, 199, 200 Furth, M. 355n1 generic essence 111–112 Gilmore, C. 153 Goldman, A.H. 453–455 Goodman, N. 185 Gorman, M. 108, 110 Griffith, A. 443 Grossmann, R. 139, 141, 142, 152 grounding nominalism 6, 195, 197, 199, 201–202; first-order facts, fundamentality 197–198; universals and one over many, existence 198–200 Guigon, G. 186, 189 Guillon, J.-B. 181n11 Hacking, I. 441 Hale, B. 108 Hall, N. 271 Haslanger, S. 301, 442 Hawley, K. 35n1, 300, 332 higher-order properties 350, 352, 383–391 higher-order quantification 21–24 Hochberg, H. 41, 253 Hornsby, J. 181n9 Husserl, E. 42 immanent realism 5, 135, 138–146, 202; abstract versus concrete universals 139–141; non-relational realism 143–144 immanent universals 67, 138–141, 145, 151, 156, 159–162 individual agents 428, 429, 432, 433, 435 individual essences 110 individual tropes 239, 242, 244, 246 infinitival and gerundive clauses 374–375 instantaneous properties 296, 299, 300, 302 instantiations 43, 65, 94–98, 115, 138–140, 142, 160, 301, 398; approach 65; of universals 43, 197 internal relations 41, 86, 89, 220, 222, 251–256, 258 intrinsicality 93, 95, 96, 98–100, 298 intrinsic/extrinsic distinction 92–101; applications 93–94; combinatorial accounts 97–99; duplication accounts 95–97; future research 100–101; general features of 99–100; grounding-based approaches 97–99; hyperintensionality and vagueness 99–100

intrinsic properties 85, 86, 92, 93, 95–97, 99, 108, 294, 295, 297–299, 301 Jackson, F. 394, 396, 398, 400, 420 Johnson, W.E. 115, 117, 285 Johnston, M. 301 Jones, N.K. 19 Kim, J. 70n4, 379, 402n7 Kment, B. 108 Knight, Helen 2 Kõiv, R. 445n4 Koslicki, K. 108 Kripke, S. 21 laws of nature 1, 2, 8, 50, 51, 278, 318, 328, 329, 332, 337–345; and dispositional properties 342–343; and essential properties 341–342; F and G 338–340; laws, kinds, and properties 343–344; and natural properties 340–341 Leech, J. 107, 110 Leibniz, G.W. 110 Lewis, D. 2, 35n1, 66, 74, 75, 80n2, 106, 112, 129, 130, 135, 136n1, 136n2, 179, 203n7, 251, 293, 297, 301, 303n2, 305, 310, 313n10, 314n11, 315, 329, 333, 374, 375 Linsky, B. 106 locality: problems of 321–322 locationism 77, 78 locations 63, 65, 72, 74–78, 128, 135, 136, 140, 148–157, 240, 246, 247, 331, 334; chorology 148; ‘eliminativist’ bundle theory 157n1; multiple location 151–155; naturalism and causation 149; properties, constituents 150; self-instantiation 151; singularly located properties 156; spacetime 149; trope individuation 150; of tropes 148–149, 156; of universals 148–149, 151 Lowe, E.J. 108, 139, 140, 251, 297, 301, 303n2, 328, 343 Mackie, P. 107, 110 Mahlan, J. 155 Maienborn, C. 376, 378 Mallon, R. 441, 445n5 Mantegani. N. 175–176 Markosian, N. 299 Martin, C.B. 177 Maurin, A.-S. 242, 243 McDaniel, K. 313n7, 332 McKitrick, J. 94

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Index McLaughlin, B. 355n9 McPherson, T. 425n4 Meincke, A.S. 302 Melia, J. 181n9, 181n10, 196 mental causation 383–391; in world of firstorder properties 390–391 mereological nominalism 77 M-essentiality/M-essential properties 105–107, 110–112; variations 105–106 metaphysical explanation 77, 78, 178, 295, 296, 438, 440 metaphysical modality 112, 316, 317, 319, 322 metaphysical necessity 21, 105, 111, 306, 309, 318, 319, 339, 423, 433, 435 metaphysical theories 76, 79, 80, 187, 188, 436 Millikan, R.G. 118 mind-independence 131, 428, 432, 435 mind-independent predicables 128 modality 7, 8, 112, 134, 224, 315–323, 409, 410, 433; accounting for 317; account of 315, 317, 319; two theories 317–318 Modal Realism 74, 223, 224, 313 modifier trope theory 232–235, 308 module tropes/module trope theory 6, 7, 229–237, 307–308, 310, 312 Moltmann, F. 372, 373, 380n7 Montague, W.P. 2 Moore, G.E. 250 morality 9, 427–432, 434–436 moral properties 9, 417, 419, 422, 427–436; naturalism vs. non-naturalism 429; practicality of 430; realism and antirealism 427–429; reductionism vs. nonreductionism 429; varieties of naturalism 430–433; varieties of non-naturalism 433–436 More-Ehring problem 153 Morganti, M. 245 Mothersill, M. 453 Mourelatos, A. 283, 285 Mulligan, K. 42, 181n8, 223 Mumford, S. 354 Mundy, B. 362

natural kinds 327–335; biological kinds 332–333; coherence of universals 333–335; E. J. Lowe’s theory of 328–330; fundamental kinds 331–332; as properties 330–331; structural kinds 333 natural language 8, 15, 16, 133, 369–373, 375, 377, 379, 380 natural language ontology 369–370, 372, 380; learnability and the core- periphery distinction in 380 naturalness 19, 48–57, 96, 340, 341 necessary truths 5, 39, 130–134 neutral conception 128, 393–397, 400, 401 nominalism 5, 6, 18, 27, 28, 30, 34, 35, 40, 41, 185, 202, 207, 212, 419, 420 nominalism, Mathematics 206–214; field’s program 213–214; metaphysical and epistemological characterizations 207–209; nominalists and platonists, objects 207–209; reference programs 211–213; referential thesis and Quine’s criterion 209–211 Nominalism and Realism (1978) 171 nominalizations 42, 283, 285, 286, 291 nomological modality 316, 317 nomological necessities 318, 320–322 non-aesthetic properties 10, 449, 452, 453, 457 nonessential properties 296, 298, 299, 301, 303 non-naturalism 9, 394, 418, 420, 429, 433–436 non-natural properties 4, 95, 375, 418, 429, 434–436, 440 non-physical properties 387, 394–396, 400 non-relational realism 142–145, 174 non-relational tropes 240, 243, 244 normative concepts 9, 419, 421, 423–425 normative properties 417–426; concepts versus properties 420–422; kinds of 419; nominalism 419–420; normativity 422–423; other normative properties 423–425; realism and antirealism 417–419 normativity 417–419, 422, 423, 434 Nyāya school of Hindu philosophy 1

Nagasawa, Y. 401 Nagel, T. 394 Narens, L. 365n5 natural classes 184, 185, 188, 220, 221, 223, 226 natural class trope nominalism (NCTN) 220, 221; objections 223–226; trope individuation, primitivist view of 221–223 naturalism 9, 138, 139, 141, 149, 208, 418, 420, 429–433, 435, 436

objectivity 50, 53–55, 428 objectual essence 111, 112 O’Connor, T. 350–352 O’Leary-Hawthorne, J. 166 Oliver, A. 172, 181n4 One over Many (OoM) problem 171–174, 176 ontological commitment 13–25; fundamentality 19–21; Quinean paradigm 15–17 ontological commitments 3, 13–18, 20, 22, 23, 27, 172, 178, 212, 398, 399 ontological economy 187, 240, 242

462

Index O’Shaughnessy, B. 289 Ostrich Nominalism 3, 5, 6, 171–181; Armstrong’s caricature 173; Imaguire’s “Priority Nominalism” 180–181; metaphysical request, truthmaker 177–180; OoM of Lewis and Van Cleve 174; Peacock’s problem 174–175; Pickel and Mantegani, ontological parsimony 175–176; truthmaking, interpreting 176–177 overdetermination 351, 354, 387–390

Priest, G. 18 priority nominalism 196–197 Problem of Universals (PU) 195, 197, 201 processes 283–292; modal profile of 287–289 projects objection: conflicting 34 property space 5, 121–123 propositional identity 16, 17, 22 psychological laws 386, 387, 391 Putnam, H. 36n5, 121

Papineau, D. 402n7 paradigmatic trope theories 240–244 paraphrase method 26–36; Quinean argument 27–28; reconciling 29–30, 32–34; revising 29–32; types of 28–30 Parsons, J. 44 particularity 61–70; first-order criteria 63–67; pre-philosophical distinctions, neighborhood 62–63; second-order criteria 67–70 Passinsky, A. 444 Paul, L.A. 161, 162 Peacock, H. 155, 172, 174, 175, 203n1 Peirce, C.S. 2 perception, properties 403–410; determinate or determinable properties 407–408; range of 403–405; tropes or universals 405–407 philosophy of mind 8, 93, 350 philosophy of perception 404, 406, 410 philosophy of science 2, 3, 8, 53, 54 physicalism 347, 350, 351, 398, 399 physical objects 100, 116, 208, 213, 266, 331, 333–335 Pickel, B. 175–176 Pigliucci, M. 351 Plantinga, A. 112n3 Platonic properties 128 Platonic realism 127–139; Benacerraf-field argument 134–135; Lewis’s argument 130; modal argument 130–131, 134; necessary truths and logical form 133–134; “one over many” argument 128–130; parsimony arguments 135; second-order quantification 131–133; truth 131; weak Platonism 135–136 Plunkett, D. 425 potentialism 319–320 potentiality 315–323 Potochnik, Angela 54 powerful qualities 274, 276, 279, 320 powers 7, 8, 229, 231, 315–323, 348, 387, 390, 391 predicates and special quantifiers 373–374

qualia, properties of experiences 394–395; and mental causation 399–401; neutral conception 395–399 qualia realism 394, 395, 397, 399–401 quantification 13–25; existence, notion of 17–19; higher-order quantification 21–24 quantitative properties 358–365; as determinable properties 359–360; as numerical properties 360–361; open questions 365; as relational structures 361–364; as rich structures 364–365 Quine, W.V. 14, 16, 129, 181n3, 185, 196, 200, 210 Quinean argument: paraphrase method 27–28 Quinean metaontology 15 Quinean paradigm 14, 15, 17–19, 21–23 Quinean Propositional Commitment 16–17 Quinean Sentential Commitment 15–16 rationality 115, 430–432, 434 Raven, M. 203n3 Rayo, A. 109 reality 19 red tropes/redness tropes 6, 63, 156, 222–224, 230, 328 Reinach, A. 141 relatedness 83–89 relational realism 142, 144, 145 relational truths 241, 251, 253 relations 82–91; believing in 86–87; general design brief 83–84; internal and external 88–89; ontology-ideology framework 90; specialized design briefs 85–86 repetition approach 63 resemblance classes 184, 185, 254, 255 resemblance nominalism 2, 6, 41, 184–193; advantages of 187–188; coextension difficulty 188–193; problems for 186–187 resemblance trope nominalism (RTN) 220, 221 response-dependence scheme 430, 431, 434 Restall, G. 39 Rodriguez-Pereyra, G. 130, 179, 180, 185, 186, 203n1, 233, 258n2 Rosen, G. 70n4, 111, 203n3, 444 Russell, B. 136n1, 136n4, 141, 253, 254, 312

463

Index Salerno, J. 108 Schaffer, J. 66, 133, 137n12, 196, 202, 203n3, 203n10, 203n13, 237, 340, 443 Schiffer, S. 372 Schulte, P. 196, 202 scientific evidence objection: lack of 33 scientific theories 52, 208, 210 Searle, J. 120, 442 second-order mental properties 384, 386–388, 390; causally efficacious 387–388 second-order metaontology 21 second-order ontological commitment 23 second-order ontology 22 second-order properties 384–385 second-order propositional commitment 22 second-order states of affairs 145n1 Seibt, Johanna 290 Shoemaker, S. 122, 397 Sibley, F. 451 Sider, T. 43, 44, 79, 108, 163, 300 Simons, P. 245, 246 Skiles, A. 101n2, 109, 110, 112 Smith, Edith May 1 social properties 438–445; causal views 441; constitution views 441–442; essence views 444; grounding views 442–443; properties and kinds 440; social characteristics 439–440 Socrates 61, 103–111, 139, 154, 178, 196, 197 Socratic essentiality 112n2 spacetime 74, 77, 78, 148, 149, 239, 251, 252, 340 sparseness 48; abundance, problems of 49–50; challenges 52–53; motivating 49–50; philosophy of science 53–55; related notions 52; responses 56; roles and features 50–52; social inquiry 55 sparse properties 48–57, 184, 185, 192, 329, 330, 332, 340, 341 Speaks, J. 137n9 sphericity trope 229–231, 234–236 Stalnaker, R. 305 standard trope nominalism (STN) 220, 221 states of affairs 5, 43–45, 138–146, 149, 284, 301, 310; relational realism 144–145 Steward, H. 288, 291 Stout, G.F. 2 Stout, R. 285 Strawson, P.F. 370 substance dualism 348, 353, 354 Summerford, J. 196 Supervenience-Truthmaking 38, 39 symmetry objection 32

of problem 293–296; instantiations at times 300–301; neutral formulation and different at-t replies 296–297; properties at present moment 298–299; properties at times 297–298; properties through time 301–303; temporal parts/stages, instantaneous properties 299–300 temporary intrinsic properties 294, 297, 299 temporary intrinsics 7, 163, 164, 293, 294, 296, 299, 302, 303; problem of 293–294 Thomasson, A. 26 transcendent universals 63, 74, 138, 139, 141 transworld identity 309, 310, 313 Trogdon, K. 101n3 trope bundle theories 7, 234, 239, 240, 243, 244; dependence theories 244–247; independence theories 243–244; paradigmatic trope theories 240–243; of substance 239–248 trope individuation 150, 220, 221 trope nominalisms 219–227; three forms 220–221 trope-relations 7, 250–258; existence of 250–258 tropes, types 229; fundamental determinables 232; modifier tropes, character-grounders 233–234; modifier tropes versus module tropes 229–231; module tropes, character-grounders 234–237; perception and causation 232–233; powers, objects 231; thin and thick character 233 truthmaker maximalism 40, 398, 401n5 truthmaker necessitarianism 39–40, 43, 46, 192; revisiting 45–46 truthmaker principle 3, 38, 40, 41, 44–45, 176, 177 truthmakers 3, 38–46, 145, 176–178, 184, 185, 192, 317, 398 truthmaking argument 40, 44 truth values 116, 117, 210, 372, 449

Taylor, A.E. 5 temporal properties 269, 293–303; assumptions

Vallicella, W.F. 142, 145, 166 Van Cleve, J. 174, 196

universality/universals/universal properties 61–70, 103, 206, 284, 285, 289–291, 338–340, 342; bundle theory with 159–167; existence of 1, 5, 198, 199, 201, 202, 306; first-order criteria 63–67; objections and replies 162–165; Platonic versus immanent 159–160; prephilosophical distinctions, neighborhood 62–63; principle of identity of indiscernibles, objection 165–167; second-order criteria 67–70

464

Index duplication 309; conjunction as summation 308; directionalism 309; finitism 309; impurity 308; infinite ideology 309; infinite worlds, problem of 310; motivations 305–306; operator theory 308–309; preliminaries 306–307; strong Platonism 311–313; structural properties 310–311; transworld identity 309–310; uni-WASP and trope-WASP 307–308; weak and strong Platonism 309

van Inwagen, P. 136n1, 136n4, 330 Vogt, L. 318 Walton, K.L. 450, 453, 454 Way of Causation 74, 75 Weatherson, Brian 365n4 Whitehead, A.N. 302 Williams, D.C. 2, 65, 239–241, 308 Williams, N.E. 321 Williamson, T. 106 Wilson, J. 115, 122 Wisdom, J. 65 Witmer, D.G. 101n3 Wittgenstein, L. 118, 141 Wolff, J.E. 359, 364 Worlds are Structural Properties thesis (WASP) 305–306, 308, 309, 313; absolute infinite

Yablo, S. 120, 385 Zalta, E.N. 18, 106, 112n4 Zangwill, N. 457

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