Worldviews, Science And Us: Studies Of Analyticalmetaphysics: A Selection Of Topics From A Methodological Perspective 9789814295819, 9814295817

Table of contents :
CONTENTS......Page 6
1. Introduction......Page 8
2. Contributions......Page 9
Acknowledgments......Page 10
1. Analytic Metaphysics Today......Page 11
2. Caveats......Page 12
2.1. Methodological Illusion?......Page 13
2.2. Fragmentation and Constriction......Page 14
References......Page 16
1. Structural Realism as a Metaphysical Position......Page 17
2. The Argument from Quantum Entanglement......Page 27
3. The Argument from Space–Time......Page 30
4. Conclusion and Open Issues......Page 34
References......Page 36
1. Methodologies......Page 39
2. McTaggart's Argument......Page 41
3. Theories of Time......Page 42
4. Closed Time-like Curves in the General Theory of Relativity......Page 44
5. Is Dynamism Coherent?......Page 45
6. Loops......Page 46
References......Page 49
1. Dispositional Essentialism and Categoricalism......Page 51
2. Dispositions All the Way Round?......Page 53
3. The Problem of Random Coincidence......Page 57
5. A Concluding Remark......Page 60
References......Page 69
1. Introduction......Page 71
2. The Problems with the Kripke–Putnam Account of Natural Kinds......Page 76
3. Taking Stock......Page 87
4. Natural Kinds — What are they?......Page 88
References......Page 91
1. Introduction......Page 94
2. Personal Identity and Conceptual Analysis......Page 97
3. Conceptual Analysis and The Soul......Page 99
4. Error Theory or Conceptual Revision?......Page 100
5. Faultless Disagreement......Page 102
6. Beyond Mere Semantics......Page 107
References......Page 111
1. Introduction......Page 114
2. Truthmaker Theory......Page 118
3. How Does Truthmaker Theory Regiment?......Page 121
4. Tropes as Truthmakers......Page 127
5. Why Should One Hold That the World Is a World of Tropes?......Page 133
References......Page 135
1. Introduction......Page 138
2. The Straightjacket View......Page 140
3. The Functional View......Page 142
4. The Two-Concept View......Page 144
5. Varieties of Pluralism......Page 146
5.1. The Symptoms of Causation......Page 148
6. Wittgensteinian Pluralism......Page 151
7. Three Objections......Page 156
Acknowledgments......Page 157
References......Page 158
Introduction......Page 159
1. Philosophy of Mind and Social Theory......Page 160
2. Keith Sawyer's Nonreductive Individualism......Page 161
3. The Introduction of Emergence and Its Use(fullness) in Social Theory......Page 163
4. How to Evaluate Sawyer's Metaphysics? Questioning Social Emergence......Page 167
5. Conclusion: If At All .........Page 169
Acknowledgments......Page 171
References......Page 172
Counterfactuals, Causation and Humean Supervenience Paul Noordhof......Page 174
1. Counterfactuals and Humean Supervenience......Page 180
2. Counterfactuals, the Future Similarity Objection and Chance......Page 186
2.1. Isolating the Cause......Page 187
2.2. Indeterminism and Lewis's Similarity Weighting......Page 191
3. Causal Asymmetry......Page 201
3.1. Microphysical Causal Asymmetry?......Page 203
3.2. Tooley's Inverted Universes......Page 206
4. Concluding Remarks: Methodological Implications......Page 208
References......Page 211
1. Introduction......Page 214
2. Conceptual Causal Pluralism......Page 215
3.1. Causation as a Realistic Notion Versus a Mental Construct......Page 218
3.2. Causation as a Single Versus a Plural Empirical Relation......Page 221
3.3. Causation as a Relation Between Elements at the Fundamental Versus at All Levels of Reality......Page 222
4. The Relations Between Metaphysical and Conceptual Positions......Page 225
6. Conclusion......Page 228
Bibliography......Page 229
1. No Mathematical Entity With Identity......Page 231
2. The Size of Plato's Heaven......Page 235
3. Fear of the Abstract......Page 239
4. The Social Construction of Mathematical Entities......Page 242
5. Metaphysical Methodology......Page 244
References......Page 247

Citation preview

Worldviews, Science and Us

Studies of Analytical Metaphysics A Selection of Topics from a Methodological Perspective

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editors

Robrecht Vanderbeeken Ghent University, Belgium

Bart D’Hooghe Vrije Universiteit Brussel, Belgium

Ghent, Belgium, 2 – 3 June 2005

Worldviews, Science and Us

Studies of Analytical Metaphysics A Selection of Topics from a Methodological Perspective

World Scientific NEW JERSEY

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

WORLDVIEWS, SCIENCE AND US: STUDIES OF ANALYTICAL METAPHYSICS A Selection of Topics from a Methodological Perspective Copyright © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN-13 978-981-4295-81-9 ISBN-10 981-4295-81-7

Printed in Singapore.

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CONTENTS

Worldviews, Science and Us: Studies of Analytical Metaphysics. A Selection of Topics from a Methodological Perspective Robrecht Vanderbeeken and Bart D’Hooghe

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Introduction: Contemporary Analytic Metaphysics, its Crisis and Challenge Robrecht Vanderbeeken

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Holism and Structural Realism Michael Esfeld and Vincent Lam

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Common Sense, Relativity and Theories of Time Phil Dowe

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Purely Dispositional Worlds Sungho Choi

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Natural Kinds — What Are They? Joanna Odrow¸az˙ –Sypniewska

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Personal Identity, Conceptual Analysis and No-Fault Disagreement Caroline West

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A World of Tropes? Anna-Sofia Maurin

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Causal Pluralism Stathis Psillos

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Why Social Emergence? Discussing the Use of Analytical Metaphysics in Social Theory Jeroen Van Bouwel Counterfactuals, Causation and Humean Supervenience Paul Noordhof

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Disentangling Causal Pluralism Leen de Vreese

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Mathematical Entities Lieven Decock

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WORLDVIEWS, SCIENCE AND US: STUDIES OF ANALYTICAL METAPHYSICS. A SELECTION OF TOPICS FROM A METHODOLOGICAL PERSPECTIVE

ROBRECHT VANDERBEEKEN Centre for Logic and Philosophy of Science Ghent University, Belgium E-mail: [email protected] BART D’HOOGHE Leo Apostel Centre for Interdisciplinary Studies Vrije Universiteit Brussel (VUB), Belgium E-mail: [email protected]

1. Introduction A general practical tendency of contemporary analytical metaphysics goes as follows. Research focuses on certain largely isolated topics e.g. the nature of properties, (mental) causation, actions, perception, colours, qualia, the self etc. In such a discussion, different possible ontological positions are traced and mapped in function of the capability to individuate and define the subject-matter. A wide range of methodological instruments is used in order to support or either criticise them. Such instruments are conceptual analysis, generalisations based on paradigmatic examples, a strategy of counter examples, intuitive constructs, scientific findings and thought experiments. At the same time, several criteria of legitimacy are considered in order to evaluate and defend ontological positions. Common criteria are thriftiness, simplicity, robustness, compatibility with sciences, completeness and plausibility. Judging on the number of publications, analytical metaphysics is clearly a booming business. But does the level of the debate follow this positive slope? A focal point in analytical metaphysics is 1

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a strong emphasis on methodology. However, a diversity of methodological tools is circulating which often leads to sheer methodological chaos. This diversity is not in se a problem. Rather, the problem is that there is no consensus on which methods are (contextually) appropriate. Metaphysicians often criticize their opponents on methodological grounds. But while doing so, they often only discuss those criteria which are in their own advantage, using different standards depending on the topic at hand. The aim of this volume is twofold. First, a selection of ongoing discussions on a central topic is included. Several authors are asked to bring a pr´ecis, i.e. to point down the contesting views, to mention the main arguments pro and contra, and to describe the origin, the evolution and the eventual offspring of a respective discussion. Second, the methodological question is addressed; What can be learned if we compare these discussions from a methodological perspective? What are the red harrings and shortcomings? Is an integrated methodology possible? Does each discussion finally awaits a pluralism of plausible positions or is an overall convincing account to be expected? And finally, can analytical metaphysics methodologically assert and investigate their basic assumptions, if not from a common sense stance?

2. Contributions (1) Preface Robrecht Vanderbeeken and Bart Dhooghe, Ghent University & Free University Brussels, Belgium (2) Introduction: Contemporary Analytic Metaphysics, its Crisis and Challenge Robrecht Vanderbeeken, Ghent University, Belgium (3) Holism and Structural Realism Michael Esfeld and Vincent Lam, Universit´e de Lausanne, Switzerland (4) Common Sense, Relativity and Theories of Time Phil Dowe, University of Queensland, Australia (5) Purely Dispositional Worlds Sungho Choi, Seoul National University, Korea (6) Natural Kinds — What are they? Joanna Odrow¸az˙ –Sypniewska, University of Warsaw, Poland (7) Personal Identity, Conceptual Analysis and No-Fault Disagreement Caroline West, University of Sydney, Australia

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(8) A World of Tropes? Anna-Sofia Maurin, Lund University, Sweden (9) Causal Pluralism Stathis Psillos, University of Athens, Greece (10) Why Social Emergence? Discussing the Use of Analytical Metaphysics in Social Theory Jeroen Van Bouwel, Ghent University, Belgium (11) Counterfactuals, Causation and Humean Supervenience Paul Noordhof, University of York, UK (12) Disentangling Causal Pluralism Leen de Vreese, Ghent University, Belgium (13) Mathematical Entities Lieven Decock, Free University Amsterdam, The Netherlands Acknowledgments The material of this book initially refers to lectures presented at the 5th Metaphysics of Science Workshop, June 2–3, 2005, Ghent, Belgium. For all information see the website of the Metaphysics of Science Group: http://logica.ugent.be/MSG/. This workshop was funded by a British Academy International Networks grant (thanks to Helen Beebee) and the Scientific Research Network ‘De constructie van integrerende wereldbeelden’ [The construction of integrating worldviews] of the Research Foundation–Flanders (FWO). We thank the authors and the anonymous referees for their persistent efforts. We also thank Diederik Aerts from the Free University Brussels and Erik Weber of Ghent University for their support in the process of publishing. Please address all correspondence to: [email protected] or [email protected]

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INTRODUCTION: CONTEMPORARY ANALYTIC METAPHYSICS, ITS CRISIS AND CHALLENGE

ROBRECHT VANDERBEEKEN Centre for Logic and Philosophy of Science Ghent University, Belgium E-mail: [email protected]

1. Analytic Metaphysics Today Judging by the number of publications, analytic metaphysics is an intensive and illustrious scholarship nowadays. Recent discussions even give the impression to be supported by a long tradition. Nonetheless, analytic metaphysics is a relative recent phenomenon. When analytic philosophy arose at the end of the 19th century, based on the doctrine of the linguistic turn, it regrouped academic intellectual powers, while initiating a break with history of Modern philosophy and its metaphysics. After all, analytic philosophy wanted to recommence and write its own history. This intention coincided with an explicit anti-metaphysical attitude that was evoked by three dominant trends: logical positivism, a formalistic hyper-empiricism, and the rhetoric of orthodox adherents of the linguistic doctrine, stating that all philosophical problems are merely problems of language, especially ordinary language. Eventually, mid 20th century, the underlying metaphysical questions of analytic philosophical discussions could no longer be ignored. Analytic metaphysics originated within, and gradually emancipated from these discussions. A new kind of metaphysical inquiry emerged, based on logic, philosophy of science and philosophy of language. It readdresses some classical metaphysical topics in an Anglo-Saxon manner, mainly relying on conceptual analysis and common-sense argumentation. If we observe contemporary analytic metaphysics in general, we can pinpoint the following two overall characteristics. 4

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(1) Those who practice analytic metaphysics form a group of academic specialists that claim to produce reliable research since they cherish the sincere intention to get things right and carry trough their investigations with analytic rigor. The initial linguistic doctrine is replaced by a methodological doctrine: points of view should not only be argued for but should also comply with certain epistemological criteria. (2) Several divergent discussions popped up, each revolving around a different topic like e.g. causation, mental causation, colours, actions, identity, perception, laws of nature, the nature of properties, dispositions, consciousness, free will, the self, etc. Due to the atomistic inclination of analytic inquiry, these discussions got more and more elaborated and specialized. Different possible points of view are scrutinized, concepts are parcelled out and new ramifications are inserted. In order to obtain a representative sample of contemporary analytic metaphysics, this book takes both characteristics as a starting point. Firstly, we selected articles dealing with different discussions of analytic metaphysics like Causation (Psillos, De Vreese), Tropes (Maurin), Theories of Time (Dowe), Personal Identity (West), Natural kinds (Odrowaz Sypniewska), Structural Realism (Esfeld & Lam) Mathematical Entities (Decock), Dispositions (Choi), Counterfactuals (Noordhof) and Social Emergence (Van Bouwel). The authors are asked to bring a pr´ecis, i.e. to indicate the contesting views, to mention the main arguments pro and contra, and to describe the origin, the evolution and the eventual offspring of a respective discussion. Secondly, methodological issues are addressed: What are the red herrings and shortcomings?; Is an integrated methodology available? Does each discussion finally awaits a pluralism of plausible positions or is an overall convincing account to be expected? And finally, can analytical metaphysics actually assert and investigate its basic assumptions from a common sense stance? The selected contributions confront the reader with some of these focal questions. Abstracts of the contributions are included at the beginning of each chapter. 2. Caveats In the remainder of this introduction, we take the occasion to probe both overall characteristics from a meta-philosophical stance in order to obtain

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a critical evaluation of analytic metaphysics in general. Each of these characteristics encompasses a problem that jeopardizes the future of analytic metaphysics. Firstly, the preference for methodological rigor is meant to be the distinguishing trait of analytic metaphysics (which is sometimes used to exclude or repudiate other kinds of metaphysical inquiries) but at the same time, a conclusive methodology is missing, which often leaves us with a methodological chaos. Secondly, the analytic stance produced specialized discussions that focus on largely isolated topics. This results in a fragmented and constricted metaphysical picture. In what follows, both problems are discussed separately. In order to get a grip on their implications, we consider two opposite conclusions: a pessimistic (or cynical) and an optimistic (or constructive) one. The pessimistic conclusions are meant to outrun critics of analytic metaphysics. Exaggerating a crisis often is the best steppingstone to a remedy. The optimistic conclusions are meant to emphasize that the soundness of analytic metaphysical inquiry largely depends on the way we assess this knowledge epistemologically. Although most adherents of analytic metaphysics claim to endorse a subtle and reasonable attitude, it is no doubt not redundant to recall the enticement of denying theoretical weaknesses. Evidentially, such denial is dangerous since it leads to excessive and hence dogmatic opinions. The optimistic conclusions, on the contrary, regard limitations as conditions of possibility and defy us to take them up as a challenge.

2.1. Methodological Illusion? Since methodology is the backbone of analytic metaphysics, a multitude of methodological tools is at ones disposal. For instance, there are different criteria of legitimacy (e.g. thriftiness, simplicity, robustness, compatibility with the sciences, consistency, completeness, soundness). These criteria determine the plausibility and validity of a theory. We also have a plurality with respect to instruments for argumentation (e.g. sorts of conceptual analysis, generalizations based on paradigmatic examples and counterexamples, reference to supporting scientific findings, thought experiments). This diversity is of course not in se a problem. However, problems arise since there is no consensus on which methods are (contextually) appropriate. Analytic metaphysicians constantly criticize their opponents on methodological grounds. But while doing so, they often only discuss those criteria which are in their own advantage. Sometimes they also argue for different standards depending on the topic at hand, and at the same time they often do not meet the demands they put forward to others.

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Frustration with this methodological chaos could provoke the following pessimistic conclusion. Analytic metaphysics distinguishes itself with its self-attributed analytic rigor which gets its justification from the methodological doctrine. However, if we take a closer look at the methodological deontology, analytic metaphysics clearly faces a crisis. The impact of this crisis is reinforced by the fact that this methodological impasse is largely ignored. If this crisis does not become a point of interest but instead keeps on being denied, the following imputation is not so overly impertinent: analytic metaphysics, and a fortiori analytic philosophy, has become an academic orthodoxy based on a chimera. Its methodological doctrine partly functions as window-dressing. Hence, analytic metaphysics constantly produces a dominant rhetoric that is meant to consolidate its privileged position.1 We can also opt for an optimistic conclusion. The methodological limitations invite us to bring back analytic metaphysics to its proper proportions, to reflect on its finitude and to rate the status of its theoretical findings. Conceptual analysis and common sense argumentation, so it seems, allows for making different metaphysical intuitions explicit. Once a discussion faces methodological uncertainties concerning the mentioned criteria of legitimacy, this discussion enters a final, maximal stadium. Depending on the subject-matter at hand and the hedging of research interests, we likely end up with a plausible and worked-out pluralism of views, each with their own advantages and disadvantages. This conclusion implies a scientific mentality that renounces an epistemic imperialism and instead assesses the modesty of its philosophical methods. Analytic metaphysics begets a clear and distinct plurality of conceptual assemblages. This no doubt is a merit. Most of these assemblages are valuable in their own respect, due to their particular, conceptual compatibility or practical applicability.

2.2. Fragmentation and Constriction Due to the analytical stance, analytical metaphysics concerns specific and isolated topics like causation, colours, actions, universals, etc. The adversity of the atomistic inclination is that the bigger picture remains absent. For instance, how do the respective positions of the pluralisms in each of these debates relate? What are the consequences of such a position in one discussion with respect to other discussions? With the enhancement of specialization, fragmentation seems to increase. Therefore, it is important to address the question how a global perspective is possible. How can we avoid this ongoing heterogeneity? Of course, analytical metaphysicians are

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not against unification. They normally subscribe to the claim that we first have to get things right in each separate discussion before we can start assembling theories. However, this plausible reply does reveal the belief that a unified worldview will be possible one day. Here, two skeptical remarks are appropriate. Firstly, if we take into account that the different discussions in analytic metaphysics tend to develop a pluralist status quo, then how can we acquire this integrated view? Does pluralism not impede unification? Secondly, even if we can obtain a synthesized metaphysics, then what guarantees that it is a relevant presentation that sufficiently includes different aspects of the subject matters involved? For instance, does the enforcement of conceptual analysis not also imply the insertion of certain restrictions? Put differently, does an analytical elaboration on the identification and individuation of a subject-matter not presuppose that we make an abstraction and hence dispense with certain diverse aspects? This, I believe, is the very reason why a pluralism of views surfaces in several analytical discussions in the first place. The assumption that analytic metaphysical inquiry is liable to a constriction as regards content is also reinforced if we take into account that there is a plenitude of non-analytic metaphysical research that scrutinizes subjects and aspects of subjects that are not (yet) considered within an analytic metaphysical framework. Because of its allegiance to its particular philosophical methods, it is reasonable to doubt that, in its turn, analytic metaphysics will ever be able to cope with these topics in a sufficient degree. This problem of fragmentation and constriction, again, can provoke a pessimistic conclusion: analytic metaphysics is a victim of self-deception since its preoccupation with its methodological doctrine evokes a false comfort. The virtuous intention to get things right functions as a blinker because, due to the desire to obtain univocal, clear and certain insights, important aspects are left aside. After all, it is quite plausible that reality is a messy place. Objects can be vague, elusive, diffuse, hybrid or in a permanent transformation. Trying to grasp them in simple and coherent descriptions could just increase the mess. If concepts change with changes in culture, for instance, there is no getting things right in conceptual analysis. If this is true, analytic metaphysical discussions are, in a way, arcane, contingent and scholastic practices. They are also prone to revert to an old-European notion of reality, persisting in the belief that its stable and unambiguous truth is out there somewhere waiting to be discovered. When analytic metaphysicians hold on to this out-thereness, they keep on chasing a truth, a mysterious X, that always seems to break away.2

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We can again also opt for an optimistic conclusion. The problem of fragmentation and constriction could reveal that analytic metaphysics is not so much in the business of describing and representing (parts of) reality. Rather, it is performative. It crafts unique concepts and generates new dimensions concerning its subject-matters. Conceived in this way, the methodological doctrine helps to produce reality, extends it. Note that this view, compared to the pessimistic conclusion, implies that we take an opposite starting point: the assumption of an ultimate and stable out-thereness is replaced by the assumption of ongoing creation. This also implies that analytic metaphysics has a responsibility to the world: we have to avoid that analytical rigor overturns in rigidity. That is to say, that it collapses into a methodism that eclipses the possibility of, or even worse, that imposes a prohibition to other kinds of research that are less strict or certain but nonetheless contain an innovative or useful contribution. Both optimistic conclusions, being the mentality change with respect to the modesty of its philosophical method and the acceptance of its constricted but creative responsibility, will no doubt encourage the development of a promising future of analytic metaphysics. Both conclusions also entail a generous and open mentality that allows for new challenges. For instance, why should analytic metaphysicians not try to link up to metaphysical inquiries which analytic philosophy wanted to escape from in the first place, like transcendental philosophy, phenomenology, immanent metaphysics, etc.? Compared to the beginning of the 20th Century, the situation has obviously changed. For instance, an alternative analytical metaphysics has emerged. Now, then, the question is: What would such a post-analytic metaphysics consist of? References 1. A. Preston, Analytic Philosophy: The History of an Illusion. New York: Continuum (2007). 2. S. Zizek, For They Know Not What They Do. London and New York: Verso (1991).

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HOLISM AND STRUCTURAL REALISM

MICHAEL ESFELD AND VINCENT LAM University of Lausanne, Department of Philosophy CH–1015 Lausanne, Switzerland E-mail: [email protected], [email protected] We first introduce structural realism as a position in the metaphysics of science, pointing out the way in which this position replaces intrinsic properties with relations so that it amounts to a holistic in contrast to an atomistic metaphysics. We argue in favour of a moderate version of structural realism that puts objects and relations on the same ontological footing and assess the general philosophical arguments for this position. The second section shows how structural realism gains support from quantum physics. The third section explains how structural realism can be applied to the metaphysics of space–time.

1. Structural Realism as a Metaphysical Position Structural realism in the metaphysics of science is a sort of a holism in contrast to an atomism. To bring out that contrast, consider David Lewis’ thesis of Humean supervenience; one can regard that thesis as the paradigmatic conception of a philosophical atomism in current mainstream analytical metaphysics: “Humean supervenience is named in honor of the greater denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. (. . . ) We have geometry: a system of external relations of spatio–temporal distance between points. Maybe points of spacetime itself, maybe point-sized bits of matter or aether or fields, maybe both. And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all” (Ref. 1, p. ix–x). According to Lewis, thus, the only irreducible relations are the ones of spatio–temporal distance between points. The fundamental physical 10

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properties are instantiated at those points. One may think of mass, energy, momentum, charge, spin among others as candidates for fundamental physical properties. It is of no importance for this position whether (a) the space–time points themselves instantiate the fundamental physical properties, or whether (b) there are material objects located at the space–time points that instantiate these properties, or whether (c) there are no space– time points at all, the spatial–temporal relations being relations among material point particles that instantiate the fundamental physical properties. What is crucial for this position is that the fundamental physical properties are intrinsic properties. According to the standard view developed by Lewis himself, intrinsic are all and only those properties that an object has irrespective of whether or not there are other contingent objects; in brief, having or lacking an intrinsic property is independent of accompaniment or loneliness (see Ref. 2 and for a refinement Ref. 3). All other properties are extrinsic or relational, consisting in the object bearing certain relations to other objects. The view hence is that the world is the distribution of fundamental physical intrinsic properties at points that are connected by spatio–temporal relations. This view is an atomism. The world consists of atoms in a philosophical sense, namely a plurality of objects that are characterized by certain intrinsic properties each and that are linked only by spatio–temporal relations. There is an obvious epistemological problem for this position that is acknowledged by Lewis himself:4 if the fundamental physical properties are intrinsic ones, how can we get knowledge of them? Frank Jackson brings out this problem in the following passage: “When physicists tell us about the properties they take to be fundamental, they tell us what these properties do. This is no accident. We know about what things are like essentially through the way they impinge on us and our measuring instruments. It does not follow from this that the fundamental properties of current physics, or of ‘completed’ physics, are causal cum relational ones. It may be that our terms for the fundamental properties pick out the properties they do via the causal relations the properties enter into, but that at least some of the properties so picked out are intrinsic. They have, as we might put it, relational names but intrinsic essences. However, it does suggest . . . the uncomfortable idea that we may know next to nothing about the intrinsic nature of the world. We know only its causal cum relational nature” (Ref. 5, p. 23–24).

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The core of this argument can be reconstructed as follows: (1) We gain empirical knowledge owing to the causal relations that obtain between physical objects and our senses. (2) Knowledge thus gained may refer to intrinsic properties of physical objects. (3) But the way in which that knowledge is caused imposes a constraint on its content: physical properties can be identified only through the relations in which they enter. If we explain the meaning of the propositions that refer to the fundamental physical properties, it turns out that these propositions describe these properties as relational. (4) Identity of relations, however, does not imply identity of intrinsic properties. (5) We therefore do not know the properties of physical objects insofar as they are intrinsic. The argument is not that since we gain knowledge through the way in which physical objects impinge on our senses, we know only the way in which they are related to us. The argument is one about the content of empirical predicates, namely that they reveal only relations among objects. The argument applies to all relations; the relations in which physical objects stand to us do not have any special status as far as the content of empirical knowledge is concerned. The laws of physics, in short, describe relations among physical objects, and only relations, but without relations of measurement having a special status. If it is true that our basic physical theories give us knowledge only of the relations in which physical objects stand, the metaphysics of intrinsic properties is in trouble: metaphysics has it that the world consists of objects that are characterized by intrinsic properties each. On epistemological reflection, however, we have to concede that we do not have access to these properties insofar as they are intrinsic. A gap between metaphysics and epistemology thus arises. This problem for the metaphysics of intrinsic properties is a purely philosophical motivation to go for structural realism. One can reformulate the problem that Jackson among others raises in such a way that its conclusion is a position known as epistemic structural realism, namely the view that structure in the sense of relations among physical objects and as captured by the mathematical equations of a physical theory is all that we can know. Epistemic structural realism in the current discussion goes back to a paper that John Worrall published in 1989 (see Ref. 6, in particular p. 117–123). Worrall’s aim is to employ epistemic structural realism as an argument to establish a mitigated version of scientific realism. According to him, there is continuity in our views about structure despite theory change in the history of science: the views about structure of a predecessor theory

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can be construed as an approximation of the views about structure of the successor theory. Therefore, following Worrall, our views about structure do not fall victim to the arguments against scientific realism from theory change. That claim is in dispute (see Ref. 7, chapter 7, against Worrall). Be that as it may, our concern in this paper is with the metaphysics of science. We shall therefore not employ structural realism as an argument for scientific realism, but simply presuppose that a version of scientific realism can be established that is strong enough to warrant the project of proposing metaphysical claims based on scientific theories. Of course, these claims then are subject to change in the same way as are our scientific theories. Structural realism as a metaphysical position is the claim that there are no fundamental intrinsic properties underlying the relations that we can know. That is to say, all there is to the fundamental physical objects are the relations in which they stand. By structure, we mean concrete physical relations. Structural realism as a stance in the metaphysics of science is therefore not subject to what is known as the Newman objection against structuralism (see Ref. 8; see Ref. 9, section 3 as regards the point that concrete relations are not subject to this objection). As a first approximation, one can conceive structural realism as not touching the objects, but as replacing what is considered as intrinsic properties of objects in atomism with relations among the objects. However, this is only a first approximation, for it presupposes that there first are objects as something ontologically primitive and that these objects then are put into relations with each other (‘first’ and ‘then’ in a logical sense, not a temporal one). The structural realist, by contrast, maintains that objects and relations are on the same ontological footing. Neither objects nor relations (structure) have an ontological priority with respect to the physical world: they both belong to the ontological ground floor. It makes no sense to assign an ontological priority to objects, because instead of having fundamental intrinsic properties, there are only the relations in which they stand. In other words, an object as such is nothing but that what bears the relations. As regards the relations, it makes no sense to attribute an ontological priority to them, for at least insofar as they are instantiated in the physical world instead of being abstract entities, they exist as relations between objects. Thus, as far as the physical world is concerned, there is a mutual ontological as well as conceptual dependence between objects and structure (relations): objects can neither exist nor be conceived without relations in which they stand, and relations can neither exist in the physical world nor

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be conceived as the structure of the physical world without objects that stand in the relations. Structural realism is a holism in contrast to an atomism. In atomism, one considers the world as being composed of atoms in the sense of objects that exist independently of one another because they are characterized by intrinsic properties each (“local matters of particular fact, just one little thing and then another”, in the words of David Lewis in the citation above). Holism, by contrast, can be conceived as regarding the whole world — or the domain of the world that one considers — as just one object in the last resort. ‘Object’ here has the same meaning as in atomism, namely ‘being that exists independently of other beings’ (this is one sense of the traditional term ‘substance’). All the properties of that one object trivially are intrinsic properties, for there is nothing outside that object. Structural realism rejects only the view of intrinsic properties underlying the relations, not intrinsic properties of a whole that is the only object in the last resort. It is trivial that any relations among the parts of a whole can be represented as intrinsic properties of the whole (although the converse is not the case). However, holism would collapse into atomism if the one whole did not have an internal structure. The claim would then simply be that there is just one atom. The notion of an internal structure of the whole is therefore central to holism.10 The idea is that there is an internal differentiation within the whole such that there are parts of the whole, and these parts have relational properties, that is, they stand in certain relations to one another. The parts are objects in a weaker sense than the whole — or an atom — is: they do not exist independently of one another, but they are subjects of the predication of properties, namely relational properties, standing in relations. In the following, we shall talk about the parts of the whole as objects. When we talk about the whole, we explicitly mention this. The idea hence is that the objects that are parts of the whole have only relational properties and no intrinsic ones. In other words, they are nothing but that what stands in the relations. This idea may seem incoherent. There is a master argument for intrinsic properties that can be put in this way: (1) Relations require relata, that is, objects that stand in the relations. (2) These objects have to be something in themselves, that is, they necessarily have some intrinsic properties over and above the relations that they bear to one another — even if the relations do not

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supervene on the intrinsic properties and even if we cannot know the intrinsic properties (see, for instance, Ref. 11, chapter 2, in particular p. 22, who attributes that argument to Kant). Structural realism rejects that argument. More precisely, the position that we shall put forward under the name of moderate structural realism accepts the first claim of this argument, but refuses to endorse the second one (see Ref. 12, section 3, and Ref. 13, section 1). Whereas the first claim of this argument can be considered as a conceptual truth (‘no relations without relata’), the second claim is clearly not a conceptual truth. It is rather a prejudice based on simply presupposing atomism. There are strong empirical arguments stemming from quantum physics and general relativity against that claim. We shall present these arguments in the second and the third section of this paper. However, one may wonder whether relations are capable of individuating objects. If there are objects, don’t they require intrinsic properties as identity condition? Recall that, according to structural realism as a metaphysical position, (1) objects are not atoms that exist independently of each other and that (2) structure always consists in certain specific, concrete relations, these relations being as determinate as intrinsic properties are supposed to be. Consequently, relations are exactly on the same footing as intrinsic properties as far as identity conditions are concerned: insofar as intrinsic properties account for identity conditions, relations can perform that task as well. For instance, if A is bigger than B, heavier than C, etc., these relations individuate A and distinguish A from B and C. It goes without saying that there is in structural realism no question of identity conditions for an object independently of other objects. But this does not mean that relations cannot provide identity conditions. Which relations make up for identity conditions for which types of objects depends obviously on the case under consideration. Consider an analogy: since Quine’s seminal paper on ‘Two dogmas of empiricism’14 and the subsequent development of semantic holism (inferential role semantics), we are familiar with the notion of a web of beliefs. We are used to thinking of beliefs as points in a web that are individuated by their position in the web, that is, their relations to other beliefs. Content (meaning) is not an intrinsic property of a belief, but consists in inferential relations to other beliefs (the same goes for other properties of beliefs such as confirmation or justification). Semantic holism has no problem in individuating beliefs on that basis: each belief is defined by its position in

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the web, being distinguished from all the other beliefs in the web, for no two beliefs stand in exactly the same relations to all the other beliefs in the web. The problem is that we do not want any old change of relations in the system to amount to a change in the content of all the beliefs in the system. Some inferential relations thus have to be distinguished as being more important than others. But this problem does not touch the central issue that it is relations that provide the identity conditions for the members of the system. Structural realism can be received as proposing to transfer this idea from semantics to metaphysics, the objects being now physical entities instead of beliefs. If this idea is intelligible in semantics, then so it is in metaphysics. Hence, insofar as intrinsic properties can provide identity conditions, so can relations. However, there are cases in physics where neither relations nor intrinsic properties are able to establish identity conditions. Quantum systems of the same kind whose states are entangled are indistinguishable,15 although in the common cases there is a definite number of them that is greater than one. These systems do not have an identity in time. An analogous consideration applies to space–time points on certain symmetry assumptions about space–time: space–time points can stand in exactly the same spatio–temporal relations and, yet, be of course numerically distinct (see below section 3). One may receive these cases as speaking against a bundle theory of objects: quantum systems and space–time points can neither be bundles of intrinsic properties nor can they be bundles of relational properties; for the intrinsic or relational properties may be as concrete as is physically possible and, nevertheless, fail to establish a distinction between quantum systems or space–time points. A bundle theory of objects accords ontological priority to intrinsic properties or relations over objects: objects are constituted by intrinsic properties or relations on that theory. The other big position in the metaphysics of objects apart from the bundle theory is the view that objects are bare particulars: each object has a primitive thisness (haecceity). It is that primitive thisness which individuates the object and provides its identity conditions (see Ref. 16). Primitive thisness is not a property. It functions rather like a proper name. If there are one hundred entries under the name ‘Jones’ in a telephone directory, this does not mean that there are one hundred instantiations of the property of being Jones in the space–time region to which the telephone directory applies. However, as far as quantum systems are concerned, one can complain that primitive thisness is a purely metaphysical position for which

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there cannot be any empirical argument stemming from science. More importantly, as far as space–time points are concerned, there is a strong argument against primitive thisness on which we shall elaborate in section 3, namely the hole argument. The view of each object having a primitive thisness accords ontological priority to objects over intrinsic properties or relations: objects are first constituted by a primitive thisness that provides for their identity and then equipped with intrinsic properties or put into relations (‘first’ and ‘then’ in a logical sense, not a temporal one). The view of objects being constituted by a primitive thisness stands in opposition to the spirit of structural realism. The bundle theory and the view of objects as bare particulars are not the only options in the metaphysics of objects. In the cases where neither intrinsic properties nor relations provide for identity conditions one can simply accept a numerical distinction (diversity) — among quantum systems or space–time points — as primitive (a similar view is held by Pooley, see Ref. 17, section 4). A numerical distinction tells us that there is a number of objects that is greater than one — in many cases of quantum entanglement even a definite, finite natural number of objects —, and that is all that it tells us. A numerical distinction is not a primitive thisness, for it does not establish an identity in time — or any other sort of an identity — that is not empirically accessible. Accepting a numerical distinction as primitive is motivated by the physical cases — quantum entanglement, space–time points — in which there is a plurality of objects without these objects being distinguished from one another by any intrinsic properties or relations in which they stand and without primitive thisness being an open way out, since there are strong physical arguments against primitive thisness. This empirical situation — and thus the motivation for acknowledging numerical distinction as a primitive — is independent of structural realism. Any position in the metaphysics of science has to come to terms with this empirical situation. Nonetheless, recognizing numerical distinction as a primitive is the reason why we are committed to the view that objects and relations are interdependent, being on the same ontological footing: we get the relata and the relations at once as the internal structure of a whole, neither of them being eliminable or reducible to the other one. Hence, in short, insofar as there are factors that individuate objects over and above numerical distinction, intrinsic properties and relations are on a par. If there are no such factors, we either have to accept a numerical distinction as primitive or we have to go for primitive thisness. Moderate structural realism is committed to the former view.

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As the characterization as moderate suggests, there is a more radical version of structural realism. The view that Steven French and James Ladyman put forward under the name ‘ontic structural realism’ is a radical metaphysics of structural realism in contrast to the more moderate position proposed by us, because it rejects both claims of the above mentioned master arguments for intrinsic properties. According to French and Ladyman, the fact that quantum systems of the same kind in entangled states are indistinguishable is a good reason to drop the commitment to objects in metaphysics. They maintain a metaphysics of structural realism according to which there is only structure in the sense of concrete, physical relations, but no objects standing in the relations, the objects being dissolved into structure. Their view, however, has become less radical recently, since they seem to be prepared now to admit objects as a secondary category, being derived from relations (see Refs. 18, 19 for the original view and Ref. 20, chapter 3, in particular the opening paragraph, as well as Ref. 21, section 3, in particular first paragraph on p. 6 for more recent, less radical statements. For another version of a radical structural realism independent of the one of French and Ladyman see Ref. 22). Be that as it may, if objects are conceived as being derived from relations, one would like to see how this can be so, given that relations fail to distinguish between objects in the cases of quantum entanglement and space–time points. And if there are no objects at all, the complaint is that structural realism runs into absurdity: for the relations to be instantiated in the physical world, there has to be something that instantiates them, that is, something that stands in the relations. That is why the first claim of the master argument for intrinsic properties is a conceptual truth if anything is (as to this objection against the position of French and Ladyman, see Refs. 23; 24, p. 871–872; 25; 26, section 2). And that is why the version of structural realism that we endorse puts objects on the same ontological footing as relations. The difference between the radical structural realism of French and Ladyman and our more moderate version is, however, a difference in detail within a common position. The central element of structural realism as a position in the metaphysics of science is the commitment to relations instead of intrinsic properties and the rejection of an atomistic in favour of a holistic metaphysics consequent upon that commitment. One can put forward three types of arguments for structural realism as a stance in the metaphysics of science:

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• the argument from coherence: Our metaphysics should be coherent with our epistemology. Postulating intrinsic properties that are unknowable leads to a gap between metaphysics and epistemology as explained above. Structural realism makes metaphysics coherent with epistemology: all there is can in principle be known; for all there is are relations among objects. There is no principled obstacle to the knowledge of relations, whereas there is a principled obstacle to the knowledge of intrinsic properties (although all our physical theories are, of course, at best approximately true). • the argument from parsimony: We have to recognize relations (structure) in our metaphysics anyway. It is not possible to reduce all relations to intrinsic properties. Even if, as according to atomism, the world consists of objects whose fundamental properties are intrinsic ones, there have to be some relations: at least spatio– temporal relations are not supervenient on — and consequently not reducible to — intrinsic properties (that much is conceded even by David Lewis in his thesis of Humean supervenience; see the quotation at the beginning of the paper). On the other hand, it is questionable whether we have to recognize both relations and intrinsic properties in our metaphysics. Parsimony (Occam’s razor) tells us that we shall not admit entities beyond necessity. Thus, the claim is that the metaphysics of structural realism is parsimonious, because it does not recognize more than is necessary anyway, namely relations (structure). • the empirical arguments from quantum entanglement and space– time: The argument from coherence is a general argument that applies to all our knowledge of the physical world, physics be as it may, saying that there is no reason to suppose that there are fundamental intrinsic properties. There are two concrete arguments based on our current two fundamental physical theories that establish a stronger conclusion: the assumption that there are fundamental intrinsic properties underlying the relations leads to a conflict with what these theories tell us about the physical world. Before turning to these arguments and to conclude this section, let us come back to the contrast between structural realism and David Lewis’ thesis of Humean metaphysics quoted at the beginning of the paper. A world to which the metaphysics of structural realism applies is a world of holism, being tied together by relations that do not supervene on intrinsic

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properties — by contrast to a world of atomism that is composed of objects that exist independently of one another, being characterized by intrinsic properties each. However, holism is not committed to the anti-Humean thesis that there are necessary connections among distinct entities in the world. The distribution of relations in a world of structural realism can be contingent in the same way as the distribution of intrinsic properties in David Lewis’ Hume world. More precisely, the relations that there are in one part of the world do not have to necessitate the relations that there are beyond the part of the world considered. To illustrate this claim by means of an example from non-relativistic quantum mechanics, assume that there is a state of the world which is an entangled state and that this state develops in time. Structural realism is compatible with the view that the state of the world at a given time does not necessitate the state of the world at other times. Thus, structural realism is compatible with the view that there are no necessary connections among the state of the world at different times. The dynamics of the development of the state of the world in time may of course be deterministic (such as the Schr¨ odinger equation). But a Hume world can be deterministic too. Physical determinism does not imply the view that there are metaphysically necessary connections in the world. Consequently, in structural realism as in a Hume world, the laws of nature can be contingent instead of being metaphysically necessary. The issue of contingency vs. metaphysical necessity is independent of the issue of intrinsic properties vs. relations. Structural realism and holism can go with both of these views — in the same way as one can combine a metaphysics of intrinsic properties with a Humean world view as well as with the view that there are metaphysically necessary connections in the world (for instance, by conceiving the fundamental intrinsic properties as powers).

2. The Argument from Quantum Entanglement If we try to translate David Lewis’ thesis of Humean supervenience into physics, we can make use of the principle of separability. Einstein based his criticism of quantum mechanics on this principle (see Refs. 27, 28). One can characterize separability in this way: Physical systems have a state each in the sense that (1) this state completely encompasses the state-dependent properties of the system and (2) the joint state of two or more systems supervenes on the states which each of these systems has. Physical systems may be particles, field modes, space–time points, etc. In non-relativistic

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quantum mechanics, the state of a system at a time can be conceived as containing the complete information about the properties of the system at that time, the properties being limited to those properties whose value can change in time. These are known as state-dependent properties. Properties such as rest mass and charge, by contrast, are state-independent, since their value always remains constant. The principle of separability thus conceives the world as being built up of single systems each of which has a state independently of all the other systems, and the joint state of two or more systems — or, in the last resort, the whole world — supervenes on the states that these systems have independently of each other. In other words, the relations among the systems supervene on the states that the systems have independently of each other; consequently, the state-dependent properties are conceived as intrinsic properties. Quantum entanglement violates separability. If the states of two or more quantum systems are entangled, only the joint state of the whole is a pure state. The parts, the single systems whose states are entangled, do not have a state each that completely encompasses their state-dependent properties. Instead of the parts fixing the state of the whole, it is only the joint state of the whole that completely determines the state-dependent properties of the parts in the form of certain correlations among these properties, entanglement signifying that there is a superposition of all the possible correlations. This way of determining the properties of the parts in the form of correlations among them makes it superfluous to call for intrinsic properties underlying the correlations. Claiming that there are intrinsic and thus local properties of the parts that serve as a supervenience base for the correlations would come into conflict with the fact that the correlations of quantum entanglement violate the theorem of Bell29 (as regards the philosophical importance of that theorem, see e.g., the papers in Ref. 30). Quantum mechanics hence is not silent on the issue of whether or not there may be intrinsic properties underlying the correlations, but contains a strong argument against any such view. Quantum non-separability fits into structural realism as sketched out in the first section of this paper (for a detailed argument in this sense, see Ref. 12; see furthermore Refs. 31– 33 on the link with holism and Refs. 18, 19 on the link with structural realism). The way in which the joint state of the whole determines the state-dependent properties of the parts in the form of certain correlations confirms the claim of a mutual ontological dependence between objects and relations: the objects (single quantum systems — ‘particles’ in the framework of non-relativistic quantum mechanics) cannot

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be presupposed as simply being there and then entering into correlations (for instance, through interaction). Quantum entanglement is generic and fundamental. We cannot but take as fundamental the joint state of the whole, in the last resort the joint state of the whole world. That state is such that it permits and calls for an internal differentiation in the form of correlations and thus correlata — although the correlata are nothing but that what stands in the correlations. We thus get correlations and correlata as internal differentiation of the world, these two being on the same ontological footing. The interpretation of quantum entanglement in terms of holism and structural realism is independent of the stance that one takes on the measurement problem. If one follows Everett in holding that the Schr¨ odinger 34 equation is the complete dynamics of quantum systems, there only is quantum entanglement. If one modifies the Schr¨ odinger dynamics — as, for instance, along the lines of the proposal of Ghirardi, Rimini and Weber in Ref. 35 — to allow for state reductions and thus processes of the dissolution of quantum entanglement, nonetheless, quantum entanglement is fundamental. To the extent that there are pure states of single quantum systems, they are derived from entanglement. The argument from quantum entanglement in favour of structural realism can be considered in a general framework: it takes the physical relation of quantum entanglement as a fundamental feature of the world — whatever the fundamental objects standing in the relation are. In particular, the argument is not restricted to non-relativistic quantum theory. It applies in the framework of (relativistic) quantum field theory (QFT) as well, according to which entanglement is a fundamental feature of nature too (see Ref. 36). In other words, the structural realist interpretation is not tied to any particular ontology of basic entities; as regards QFT, quantum field systems can play the role of objects among which the relations of quantum entanglement obtain (where a quantum field system can be understood basically as a specified bounded open region of space–time in which some field properties are instantiated). Therefore, the argument from quantum entanglement for structural realism is independent of the ‘particle ontology vs. field ontology’ debate in the philosophy of quantum field theory (in favour of a field ontology, see Refs. 37, 38 for instance; for a more cautious stance based on some physical considerations, see Ref. 39, sections 4 and 6). The important point is that the relation of quantum entanglement is fundamental within quantum theory, for both relativistic and non-relativistic cases — fundamental in the sense of being non-supervenient upon intrinsic

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properties and of involving non-separability. To the extent that quantum theory is our best physical theory about matter, this constitutes a strong empirical argument against the traditional atomist metaphysics of intrinsic properties and in favour of the structural realist account proposed in this paper, at least as far as matter is concerned. However, one may still wonder whether such a structural realist account provides a coherent metaphysics of space–time that accords with our contemporary fundamental physical description of it. Therefore, we now turn to the case of space–time as described by the theory of general relativity (GR).

3. The Argument from Space–Time At first sight and in a realist (substantivalist) move, it seems that the standard mathematical representation of space–time within contemporary physics in terms of a set of points endowed with certain topological, smooth differential and metric properties — the standard manifold description of space–time — constitutes a straightforward implementation of atomistic metaphysics such as David Lewis’ thesis of Humean supervenience. Indeed, such representation of space–time seems to fit well into the conception of the world as a distribution of fundamental intrinsic properties (together with space–time relations) instantiated at space–time points or events, which then play the role of atoms in the philosophical sense. Whereas such a conception fares well with the non-general-relativistic representation of space–time as a fixed background, it, however, faces some serious difficulties within GR. In this framework and in the standard formulation of the theory, space– time is represented by a four-dimensional smooth differentiable manifold — the above mentioned set of points with topological and smooth differential properties — together with a Lorentz metric tensor field, or metric for short, defined on it. This latter geometric object encodes the fundamental space–time relations, like the chronogeometrical relations (space–time intervals), the inertio-gravitational relations (describing the behaviour of freely falling test particles in a gravitational field — the metric field and the gravitational field being one and the same field within GR) and the causal relations (defining a light cone at each space–time point and providing a distinction between spatial and temporal directions). One of the major novelties of GR is that the metric, incorporating the fundamental relations of the space–time structure, is fundamentally dynamical: it is related to the behaviour of the (non-gravitational) energy–matter (‘ordinary’

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energy–matter), represented by the stress–energy tensor field, through the (non-linear) dynamical equations — the Einstein field equations — it satisfies. In this section, we mainly consider the pure gravitational cases, that is, the physical solutions of the Einstein field equations with vanishing nongravitational stress–energy tensor (roughly, they are descriptions of space– time without ‘ordinary’ energy–matter). This does not alter the main argument in favour of the metaphysical thesis of structural realism, nor does it make this argument dependent on a specific position with respect to the ontological status of space–time. We briefly discuss at the end of this section the link with this long-standing debate. The important feature of GR for our considerations is the principle of active general covariance. This principle tells us that if we have a space– time model of GR, that is, a solution of the Einstein field equations, then any active diffeomorphism applied on this model will generate a space– time model of GR. An active diffeomorphism is a differentiable, one-to-one and onto mapping (with differentiable inverse) acting on the Lorentz metric and stress–energy tensor fields defined on the manifold. Such diffeomorphic models are observationally indistinguishable. However, in a substantivalist move and according to the traditional metaphysics of individuals applied to space–time, these diffeomorphic models have to be interpreted as describing distinct physical situations, since any given space–time point or event (merely represented by a manifold point from this perspective) is individuated by some intrinsic properties independently of the space–time relations represented by the metric. It will therefore be ‘coloured’ by different metrical properties in the different diffeomorphic models. For instance, the question whether the metric (or gravitational) field is flat around some specific space–time point may receive different answers in the different diffeomorphic models. The famous hole argument, originally due to Einstein, shows that such an attitude towards diffeomorphic models leads to a kind of indeterminism (see Ref. 40): we consider a hole in the space–time manifold, that is, an open subset of the manifold where all non-gravitational fields vanish. We furthermore consider a non-trivial active diffeomorphism on the hole that smoothly reduces to the trivial diffeomorphism, that is, the identity, on the boundary and outside the hole. A complete physical model outside the hole is then insufficient to determine a unique physical solution inside the hole, since, within the substantivalist and atomistic metaphysical framework, diffeomorphic models represent distinct situations. More

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precisely, considering a space–time manifold that can be foliated, the ‘hole’ can be chosen to be the portion of the manifold after a certain time t in the considered foliation. But then, two physically possible models, which are related by a ‘hole diffeomorphism’ and in which we consider the same foliation, may agree till a time t and then disagree for any time t0 > t in the foliation. This constitutes a breakdown of common determinism, and no unique evolution can be determined from a set of initial data (in the initial value formulation of the theory). Since diffeomorphic models are observationally indistinguishable, it is then generally argued that such indeterminism is not an empirically supported feature of the physical theory, but rather an artifact of the (metaphysical) conception of space–time that implies the physical nonequivalence of diffeomorphic models. Indeed, a wide range of philosophers of physics and physicists agree on the fact that this non-equivalence and the hole argument itself are a consequence of the non-physical primary individuation of space–time points independently of the metric (see for instance Refs. 17, 41–44). In other words, space–time points are not individuals independently of the space–time relations they enter into, which are represented by the metric; they do not possess any primitive thisness (haecceity) or intrinsic properties that would turn them into individuals over and above bearing the space–time relations. Therefore, with respect to space–time, the fundamental GR-principle of active general covariance, which underlies the hole argument, constitutes a strong empirical argument against the traditional atomistic metaphysics of individuals. On the contrary, the (holistic) metaphysical framework of structural realism provides a convincing and coherent account of the physical description of space–time provided by GR. Indeed, with respect to active general covariance and the GR-representation of space–time in terms of a manifold with a dynamical metric that encodes all the fundamental space–time relations, space–time can be naturally understood as a purely relational physical structure, that is, a network of space–time relations among space–time points that do not possess any intrinsic properties. Moreover, the space–time structure described by GR is such that the space–time relations and the objects that stand in the relations (the space– time points or events) are on the same (fundamental) ontological footing. On the one hand and in an analogous way to the general case discussed in the first section, it makes no sense to consider an actual (that is, instantiated in the physical world) space–time relation without relata standing in the relation — space–time points or events in the pure gravitational cases. On

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the other hand, the physical description of space–time within GR (and in particular the principle of active general covariance) makes meaningless any individuation of space–time points (with the help of intrinsic properties or of primitive thisness for instance) independently of the space–time relations they inter into or independently of the space–time structure they are part of — both being represented by the metric. Space–time points do not possess any independent existence (they are not atoms in the philosophical sense), but only exist in virtue of their standing in relation to other space–time points. There is no ontological priority, but rather a mutual ontological dependence between space–time relations and space–time points. As regards individuation and identity conditions for space–time points, we argue, as explained in the first section, that space–time relations, which are concrete and determinate relations, are on a par with intrinsic properties. In a space–time with no symmetries, a space–time point can be individuated, at least in principle, through the unique way it stands in (space–time) relations to other space–time points. A concrete physical implementation of such individuation within GR is the Bergmann–Komar assignment to space–time points of four scalar polynomials of the curvature, where the curvature can be understood as a functional of the metric (for recent developments, see Ref. 45). What about the cases with symmetries, like for instance the homogeneous and isotropic Friedman–Lemaˆıtre– Robertson–Walker solutions, which constitute the ‘standard model’ of contemporary cosmology? In these cases, the above mentioned individuation procedure becomes degenerated and, in general, no properties — intrinsic or relational — seem to be able to provide well-defined identity conditions for space–time points. However, this is not a difficulty for the structural conception of space–time points (and of objects in general, see section 1) proposed here, since in this metaphysical framework, space–time points and space–time relations are on the same ontological footing: numerical distinction of space–time points is neither reduced to space–time relations nor grounded independently of them (by some intrinsic properties or primitive thisness). Therefore, numerical distinction of space–time points can be accepted as primitive in the same way as space–time points and space–time relations — the whole space–time structure indeed — can. Thus, within the structural realist interpretation of space–time, even in the cases with symmetries, there is a metaphysically coherent notion of numerical distinction for space–time points. As a physical consequence of this kind of ‘structural individuality’ implied by the theory, the space–time location of any physical entity (like ‘being localized at a space–time point or in a space–time

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region’) makes only sense within GR with respect to the dynamical space– time structure, that is, with respect to the metric (or gravitational) field (see Ref. 46, chapter 2). The main claim of this section is that there are strong empirical arguments from contemporary space–time physics against the traditional atomistic understanding of space–time in terms of a set of individuals possessing intrinsic properties (together with some space–time relations). We have seen that the holistic metaphysics of structural realism provides a convincing and coherent account of space–time as described by GR. According to this view, space–time is rather a network of space–time relations among constituents (space–time points) that do not possess intrinsic properties. However, this metaphysical claim about space–time does not constitute a clear-cut position in the debates about the ontological status of space–time and about the relationship between space–time and (non-gravitational) energy–matter. In particular, the structural realist conception of space– time is open with respect to whether or not the space–time structure and (non-gravitational) energy–matter are distinct ontological beings. If the space–time structure can be ontologically dependent on there being some non-gravitational energy–matter, we want to stress that structural realism about space–time has nothing to do with any kind of relationalism about space–time understood in the reductive sense, since the space–time structure is not reduced to something non-spatio–temporal. On the contrary, the structural realist thesis about space–time, claiming the existence of the space–time structure, seems to be committed to some kind of substantivalism with respect to space–time. But it leaves the question of the relationship between space–time and non-gravitational energy–matter open — substantivalism a ` la Newton (matter ontologically distinct from space– time) or substantivalism a ` la Spinoza (matter identical with space–time).

4. Conclusion and Open Issues In the first section of this paper, we have set out structural realism as an ontological thesis about the world. The main claim of this postion is that the physical world is at the fundamental level a purely relational structure, that is, a network of relations among objects that do not possess intrinsic properties. The version of structural realism that we propose is a moderate one, since it regards relations and objects as being mutually ontologically dependent. This position implies that there are no fundamental intrinsic propreties in nature. It thereby avoids a gap between what we can know about the world and what the world really consists of.

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We have argued that this structural realist position is coherent, answering the objections usually raised against structuralism. The Newman objection against formal structures has no force in the case of the actual concrete relations considered by moderate structural realism. Moreover, the metaphysics of objects provided by the moderate structural realist position rejects any commitment to haecceitism, but it does not amount to the bundle theory of objects. Since structure is conceived in such a way that objects and relations are ontologically on a par, a numerical distinction among the objects can be considered as primitive in the sense of being already incorporated into the notion of a concrete, physical structure. We have not only shown that the metaphysical thesis of moderate structural realism is coherent, we have also argued in section 2 and 3 that it is strongly supported by empirical arguments from our fundamental physical theories. Both GR and Q(F)T describe fundamental physical relations — namely, the quantm entanglement relations and the space–time relations — that are irreducible to and non-supervenient on intrinsic properties of the physical relata standing in the relations. These physical relations belong therefore to the most fundamental part of the physical descriptions of the world. In a scientific realist move, they have to be recognized in any metaphysical framework that pays heed to contemporary physics. Nonetheless, some work remains to be done to justify the conclusion that all the fundamental physical features of nature are best understood in this holistic metaphysical framework. For instance, state-independent fundamental features of quantum (field) systems, such as (rest) mass, charge, spin, etc. seem to be good candidates for intrinsic properties (they are, however, of no help in individuating entangled quantum (field) systems). A possible line of investigation for the structural realist is to look at the mathematical (namely, group-theoretic) structures in terms of which these properties are defined and which therefore may have some physical significance. The mutual ontological dependence between relations and objects proposed by moderate structural realism holds whatever the relations are (quantum, spatio–temporal) and whatever the objects are (single quantum systems, space–time points). However, it is committed to there being some fundamental objects standing in the relations — there is no infinite regress (no ‘structures all the way down’). Ultimately, the structural realist’s understanding of nature is therefore open with respect to what kind of fundamental objects and relations there are in the world, as long as their relationship is conceived as one of mutual ontological dependence. We therefore contend that this central idea of moderate structural realism

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will continue to prove sound even if current quantum field theory and general relativity will be replaced with a new fundamental physical theory that offers a unified view of matter and space–time.

Acknowledgments We are grateful to Rob Vanderbeeken and Erik Weber for the invitation to contribute to this volume. Vincent Lam thanks the Swiss National Science Foundation (100011–113688) for partial financial support.

References 1. D. Lewis, Philosophical papers. Volume 2. Oxford: Oxford University Press (1986). 2. R. Langton and D. Lewis, Defining ‘intrinsic’. Philosophy and Phenomenological Research 58, 333–345 (1998). 3. D. Lewis, Redefining ‘intrinsic’. Philosophy and Phenomenological Research 63, 381–398 (2001). 4. D. Lewis, Ramseyan humility. In: D. Braddon–Mitchell and R. Nola (Eds.), Conceptual analysis and philosophical naturalism. Cambridge (Massachusetts): MIT Press, 203–222 (2009). 5. F. Jackson, From metaphysics to ethics. A defence of conceptual analysis. Oxford: Oxford University Press (1998). 6. J. Worrall, Structural realism: the best of two worlds? Dialectica 43, 99–124 (1989). Reprinted in: D. Papineau (Ed.), The philosophy of science. Oxford: Oxford University Press, 139–165 (1996). 7. S. Psillos, Scientific realism. How science tracks truth. London: Routledge (1999). 8. W. Demopoulos and M. Friedman, Critical notice: Bertrand Russell’s The analysis of matter: its historical context and contemporary interest. Philosophy of Science 52, 621–639 (1985). 9. A. Chakravartty, Structuralism as a form of scientific realism. International Studies in the Philosophy of Science 18, 151–171 (2004). 10. M. Esfeld, Holism and analytic philosophy. Mind 107, 365–380 (1998). 11. R. Langton, Kantian humility. Our ignorance of things in themselves. Oxford: Oxford University Press (1998). 12. M. Esfeld, Quantum entanglement and a metaphysics of relations. Studies in History and Philosophy of Modern Physics 35B, 601–617 (2004). 13. M. Esfeld and V. Lam, Moderate structural realism about space–time. Synthese 160, 27–46 (2008). 14. W.V.O. Quine, Two dogmas of empiricism. Philosophical Review 60, 20–43 (1951). 15. S. French and M. L. G. Redhead, Quantum physics and the identity of indiscernibles. British Journal for the Philosophy of Science 39, 233–246 (1988).

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16. R. M. Adams, Primitive thisness and primitive identity. Journal of Philosophy 76, 5–26 (1979). 17. O. Pooley, Points, particles, and structural realism. In: S. French, D. Rickles and J. Saatsi (Eds.), Structural foundations of quantum gravity. Oxford: Oxford University Press, 83–120 (2006). 18. J. Ladyman, What is structural realism? Studies in History and Philosophy of Modern Science 29, 409–424 (1998). 19. S. French and J. Ladyman, Remodelling structural realism: quantum physics and the metaphysics of structure. Synthese 136, 31–56 (2003). 20. J. Ladyman, D. Ross, D. Spurrett and J. Collier, Every thing must go: Metaphysics naturalised. Oxford: Oxford University Press (2007). 21. S. French, Identity and individuality in quantum theory. In: E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (2006). http://plato. stanford.edu/archives/spr2006/entries/qt-idind/ 22. R. R. Dipert, The mathematical structure of the world: the world as a graph. Journal of Philosophy 94, 329–358 (1997). 23. T.-Y. Cao, Can we dissolve physical entities into mathematical structure? Synthese 136, 51–71 (2003). 24. A. Chakravartty, The structuralist conception of objects. Philosophy of Science 70, 867–878 (2003). 25. J. Busch, What structures could not be. International Studies in the Philosophy of Science 17, 211–223 (2003). 26. S. Psillos, The structure, the whole structure and nothing but the structure. Philosophy of Science 73 (Proceedings), 560–570 (2006). 27. A. Einstein, Quanten–Mechanik und Wirklichkeit. Dialectica 2, 320–324 (1948). 28. D. Howard, Einstein on locality and separability. Studies in History and Philosophy of Science 16, 171–201 (1985). 29. J. S. Bell, On the Einstein–Podolsky–Rosen-paradox. Physics 1, 195–200 (1964). 30. J. T. Cushing and E. McMullin (Eds.), Philosophical consequences of quantum theory. Reflections on Bell’s theorem. Notre Dame: University of Notre Dame Press (1989). 31. P. Teller, Relational holism and quantum mechanics. British Journal for the Philosophy of Science 37, 71–81 (1986). 32. D. Howard, Holism, separability, and the metaphysical implications of the Bell experiments. In: J. T. Cushing and E. McMullin (Eds.), Philosophical consequences of quantum theory. Reflections on Bell’s theorem. Notre Dame: University of Notre Dame Press, 224–253 (1989). 33. R. A. Healey, Holism and nonseparability. Journal of Philosophy 88, 393–421 (1991). 34. H. Everett, ‘Relative state’ formulation of quantum mechanics. Reviews of Modern Physics 29, 454–462 (1957). Reprinted in: B. S. DeWitt and N. Graham (Eds.), The many-worlds interpretation of quantum mechanics. Princeton: Princeton University Press, 141–149 (1973).

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35. G. Ghirardi, A. Rimini and T. Weber, Unified dynamics for microscopic and macroscopic systems. Physical Review D 34, 470–491 (1986). 36. R. Clifton and H. Halvorson, Entanglement and open systems in algebraic quantum field theory. Studies in History and Philosophy of Modern Physics 32, 1–31 (2001). 37. N. Huggett, Philosophical foundations of quantum field theory. British Journal for the Philosophy of Science 51, 617–637 (2000). 38. T.-Y. Cao, Structural realism and the interpretation of quantum field theory. Synthese 136, 3–24 (2003). 39. H. Halvorson, Algebraic quantum field theory. In: J. Butterfield and J. Earman (Eds.), Handbook for the Philosophy of Physics. Elsevier (2006). 40. J. Earman and J. Norton, What price spacetime substantivalism? The hole story. British Journal for the Philosophy of Science 38, 515–525 (1987). 41. J. Stachel, The meaning of general covariance. The hole story. In: J. Earman, I. Janis, G. J. Massey and N. Rescher (Eds.), Philosophical problems of the internal and external worlds. Essays on the philosophy of Adolf Gruenbaum. Pittsburgh: University of Pittsburgh Press, 129–160 (1993). 42. C. Brighouse, Spacetime and holes. In: D. Hull, M. Forbes and R.M. Burian (Eds.), Proceedings of the 1994 biennial meeting of the Philosophy of Science Association. Volume 1. East Lansing: Philosophy of Science Association, 117–125 (1994). 43. C. Hoefer, The metaphysics of space-time substantivalism. Journal of Philosophy 93, 5–27 (1996). 44. M. Dorato, Substantivalism, relationism, and structural spacetime realism. Foundations of Physics 30, 1605–1628 (2000). 45. L. Lusanna and M. Pauri, General covariance and the objectivity of spacetime point-events. Invited Contribution to the ESF 2004 Oxford Conference on Space–Time. arXiv:gr-qc/0503069 (2004). 46. C. Rovelli, Quantum gravity. Cambridge: Cambridge University Press (2004).

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COMMON SENSE, RELATIVITY AND THEORIES OF TIME

PHIL DOWE School of History, Philosophy, Religion and Classics University of Queensland, Australia E-mail: [email protected] A-theories of time claim to best respect common sense, whereas B-theories of time typically eschew common sense and instead draw their inspiration from science, in particular relativity theory. For 100 years the battle lines have tended to be drawn over the existence of a universal present. Less prominently, but nevertheless wellknown for the last 50 years, similar battle lines have been drawn over the possibility of closed time-like curves. In this battle A-theorists have argued that closed timelike curves are incompatible with common sense and hence are impossible. In this paper I show how A-theory can be reconciled with the existence of closed time-like curves, albeit with some theoretical loss. I argue, however, that given that Atheorists tend to also hold that time travel would entail restrictions on free will, they might actually welcome this particular theoretical loss.

1. Methodologies One conception of philosophy is that the aim of philosophy is to analyse a concept implicit in the way we talk and think. Evidence for such an analysis is the intuitions of any competent user of the language concerning the appropriate use of the term. The best analysis is one which captures as many as possible of such intuitions in a coherent, ‘powerful’ and illuminating fashion. Further, for reasons discussed below, conceptual analysis tends to respect the edicts of common sense. One influential proponent of this conception of philosophy has been David Lewis, whose functionalism and use of the so-called Ramsey–Lewis sentence has helped fashion a sophisticated brand of analysis. A second conception of philosophy to be found among ‘analytic’ philosophers eschews common sense in favour of science. On this view the aim of analysis is to capture something objective, independent of the way we talk or think, and science insofar as it goes is our best guide to matters objective.1 Time is a good case in point. According to the second conception 32

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relativity theory shows that a common sense notion of time involving, for example, a universal absolute ‘now’, is simply false, even though it may still be implicit in everyday folk concept.2 Proponents of the first conception have felt compelled to deny that relativity does indeed refute common sense.3 On this particular issue there are some who have sought a rapprochement of sorts.4,5 Interestingly, however, these philosophers have presented themselves as belonging to the second conception of philosophy, rather than as seeking a common ground between the two methodologies. However, conceptual analysts such as Lewis do want to incorporate scientific developments. For example, take functionalism in philosophy of mind. Before functionalism physicalist theories such as behaviourism and early mind-brain identity theories were objected to on the grounds that they were inadequate as a conceptual analysis of the mental. Cartesian dualism on the other hand was criticised as out of keeping with the direction of science. However functionalism says that mental states are whatever it is that causes a certain kind of behaviour and is caused by certain experiences (the causal theory). Then these are identified — contingently — with brain states (identity theory). The causal theory is conceptual analysis (an attempt to provide a coherent and illuminating account of the mental that respects folk intuitions) and the identity theory is empirical analysis, together in one account of the mental. Why should the developments of science be relevant to conceptual analysis? Perhaps it’s because conceptual analysis also tells us about what is out there, and it does so only if common sense is respected as a guide to what is out there. And conceptual analysis is construed as an attempt to respect common sense because the edicts of common sense will tend to correlate with folk intuitions about the appropriate uses of a concept. Thus there is a driving demand to reconcile common sense and science. Ironically, then, when it comes to the topic of time, Lewis jumps straight to a B-theory (see below) of time, and does so on the grounds of science. Further, he does so without any consideration of the claims of A-theorists that their view is a better account of common sense concept of time. It is as though on this topic Lewis has traded methodologies.6 In this paper I want to explore this relation between science and common sense, and in particular the compatibility of A-theories of time and relativity theory. I will grant for the sake of argument that the A-theorist is correct when she claims that common sense is best aligned with A-theory. I will leave aside the problem of absolute simultaneity, as that has been well covered, and focus instead on loops in time.

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2. McTaggart’s Argument Much of twentieth century thinking about time stemmed from McTaggart’s influential 1908 paper The Unreality of Time. McTaggart’s argument relies on a distinction between what he, famously, calls the ‘A-series’ and the ‘B-series’ (Ref. 7, p. 458). The B-series is the series of events temporally ranked according to the relation ‘earlier than’. For example, we can order the series of events {John graduates; John marries; John dies} simply in virtue of which occurs before which. The A-series is the temporal series of events ordered by the designations being past, present and future. The A-series changes, since what is now past used to be future, whereas the Bseries is true timelessly — it never changes. Although McTaggart doesn’t use the terms, it has become commonplace to describe theories of time which hold the B-series to be enough for time as ‘B-theories’ and those which in addition require A-series as ‘A-theories’. The first step in McTaggart’s argument is to show that the A-series is essential to our concept of time — i.e., that B-series concepts are not enough (Ref. 7, p. 459-461). His main argument here concerns the notion of change. It is “universally admitted” (Ref. 7, p. 459), he says, that change is essential for time. However, B-series concepts do not allow us to show how events can change. A world containing only B-series temporal concepts is a fixed, changeless static universe. On the other hand, the A-series does allow us to see how events can change. The event ‘John dies’ changes from being future, to then being present, to then being past. Therefore, since change is essential to our concept of time and the B-series does not explain change, it follows that the B-series is inadequate to explain our notion of time. For this we need A-series concepts. B-theorists do of course have a notion of change: something changes if it has different properties at different times. But this is not McTaggart’s idea of change, which involves a non-essential difference in an event. A world with change is not static, it is dynamic. We will call such a view ‘dynamism’: that an event which is future then becomes present then past, or alternatively, the present moves. The alternative B-theory is that the world is static, involving no such dynamism. McTaggart thus argues that a conceptual analysis of time cannot be given purely in terms of B-notions but must involve dynamism. The second step of his argument is to show that A-series notions are nonetheless ultimately incoherent, in that they lead to contradictions. To start with, McTaggart says that ‘being future’, ‘being present’ and ‘being

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past’ are incompatible determinations. That is to say, all three can’t be true of something. However, in the A-series, all three determinations are true of an event. There is a time where John’s wedding is future, a time when it is present, and a time when it is past. Therefore A-series leads immediately to a contradiction. There is an obvious comeback available to the defender of the A-series, McTaggart notes. It is never true that an event is future, is present, and is past. Rather, the options are: ‘John’s wedding is future, will be present, and will past’, or ‘John’s wedding has been future, is present, and will be past’, or ‘John’s wedding has been future, has been present, and is past’. In response to this McTaggart claims that this simply reintroduces further notion of time, and so begs the same question. We must then ask, what is meant by the ‘is’, ‘has been’ and ‘will be’ ? The answer can only be: ‘X has been Y’ = X is Y at a moment of past time; ‘X is Y’ = X is Y at a moment of present time; ‘X will Y’ = X is Y at a moment of future time. But now the same problem arises again: every moment is past, future, present. Again, we could answer as before, but this will simply raise the same further question, and so on ad infinitum. It never will be established that there really is no contradiction. So, if the A-series leads to a contradiction, then it cannot be true of anything in reality. But if, as shown earlier, A-series is essential to time, then time cannot be true of anything in reality. Therefore, McTaggart concludes, time is unreal. We will return to McTaggart’s argument that the A-series is incoherent. First, however, we need to distinguish various theories of time.

3. Theories of Time McTaggart’s distinction enables us to divide theories of time into two: those which hold that B-series is essentially all there is to time, and those which hold that the A-series is also part of time, over and above the B-series. The former kind is called the 4-dimensional, block, static, or B-theory. On this view time is quite analogous to space. Time is the fourth dimension of the universe after the three spatial dimensions. All events exist in an equal sense; there is for example no special metaphysical status associated with the present. On this view we should think of events as strung out through time like objects strung across space. ‘A-theories’ cover a bag of theses, which are best treated separately. First, ‘dynamism’ holds that time has a dynamic element over and above the static 4-dimensional universe envisaged by B-theorists. Time flows past

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us (the ‘passage’ of time) — or we move through it — in an irreducible way. In other words, the ‘now’ moves. If we think of the temporal dimension of the B-theorists, then according to dynamism the now moves along this dimension. First 2000 is now, then 2001 is now, then 2003 is now, etc. The moving now can be thought of as an absolute, single cross-section of the universe, or in versions intended to be more in line with Special Relativity, the moving now is really the moving ‘here–now’. As mentioned above, dynamism should be contrasted with the static B-theory, essentially the view that there is nothing literally dynamic about time. Second, McTaggart’s distinction also has a linguistic dimension: ‘tensed’ theories hold that tensed statements cannot (all) be reduced to tenseless ones. In particular, A-relations cannot be reduced to B-relations — there’s always a remainder. In contrast B-theory holds that all tensed statements can be reduced to tenseless statements; for example, ‘John’s death is future’ is equivalent to ‘John’s death is later than this utterance’. However, metaphysicians in the second half of the twentieth century tended to be less interested in this question of linguistic reductionism. There are other ‘A-theories’ which are not discussed by McTaggart. ‘Presentism’ holds that only the present exists, which implies that the past and the future do not. This implies, though is not implied by, dynamism, since on this view events become real when they become present. Presentism and sometimes dynamism thus also go by the name ‘becoming’. Then there is also the related view according to which only the past and present exit, which implies the future does not. Call this the ‘growing block’ theory. Presentism and the growing block theory should be contrasted with the B-theory known as ‘eternalism’ — all events exist in a timeless sense. And finally, there’s ‘indeterminacy’, the view that the only contingent statements that have truth values are those concerning the present and the past. This also entails dynamism, given only that what is present was future, but is not entailed by dynamism, presentism, or the growing block. So, to summarise the versions of the A-theory: (1) Dynamism: the present moves (discussed by McTaggart). (2) Irreducible tense: tensed statements are not reducible to tenseless statements (discussed by McTaggart). (3) Presentism: only the present exists.8 (4) Growing Block: only the present and the past exist.3 (5) Indeterminacy: only past and present tensed contingent statements have truth values.9

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4. Closed Time-like Curves in the General Theory of Relativity Einstein’s General Theory of Relativity allows closed timelike curves (CTC’s) in severely warped spacetimes. In this class of spacetimes future lightcones (the region in the future of a spacetime point into which something can travel without exceeding the speed of light) tilt in different directions in different regions. In the simplest case, a trajectory within the forward lightcone in one region can cross into another region, extend along the forward lightcone in that region, cross back into the first region, and arrive where and when it began without ever violating the requirement of special relativity that the trajectories of particles remain within the forward light cone. The original example discovered by Kurt G¨ odel in 1949 was a large, rotating disc-shaped universe.10 A related example of a CTC produced by rotation is the ‘Tipler cylinder’. Frank Tipler showed in 1974 that an infinitely long cylinder of very dense matter spinning very rapidly would tilt the light cones for very close spacetime.11 Yet another way to create CTC’s, suggested by Gott in 1991,12 involves two extremely thin and dense cosmic strings, stretching the width of the universe, and passing each other in opposite directions at speeds close to the speed of light. One further option from General Theory of Relativity has received a lot of attention as a serious option for what might occur in our universe. This involves travelling through a wormhole — an alternate route between two spacetime points. As shown by Kit Thorne (e.g., Ref. 13), it is possible to turn a wormhole into a time machine by setting up a temporal discrepancy between the two mouths of the wormhole. This could be done by dragging one mouth through space close to the speed of light, and then back again. Suppose it travelled for two weeks, but twenty years have passed back ‘at home’. Because of time dilation the time in the travelling mouth is earlier than the time at the stationary mouth, by twenty years. From that time onwards you could enter one mouth, traverse the wormhole, and emerge from the other mouth twenty years before you departed. This wormhole option for time travel is the one that has received the most attention (see for example Ref. 14). In this paper we will consider just the simplest case of a loop in time, or a closed timelike curve, i.e., circular time. Take a string of times of finite extent, and identify the first and last time. Call this circular time. This model is not so much a solution to Einstein’s field equations as a matter of topology.15 But so far as A-theory is concerned, if it can’t handle circular

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time it won’t handle the more complex cases (see my forthcoming for a discussion of the latter).

5. Is Dynamism Coherent? It is not my purpose in this paper to defend the coherence of the A-theory of time. If A-theory is incoherent in linear time then I suppose it is incoherent in circular time. I wish to show that if it’s coherent in linear time then it is also coherent in circular time. But to do so I need to need to indicate how to coherently represent dynamism and the other versions. If ultimately this doesn’t work, it needs to be for reasons that have nothing to do with the move to circular time. Dynamists believe in the moving now. Of course, the idea that the present ‘moves’ is an analogy, since motion literally means covering a certain distance in a certain time. Dynamism thinks of the present as analogous to a spot moving along a line. The line that the now moves along is in some sense an aspect of time itself, such that the now moves from earlier to later dates on that line. (Of course, it’s not a spot, it’s a three-dimensional time-slice of the world moving through the four-dimensional manifold, but for simplicity we will treat the three dimensions of space as one.) In fact dynamism faces a task analogous to normal motion. For example, how are we to characterise the motion of a spot along a line? Answer: place the line along an x-axis, take time as an orthogonal axis (t), and represent the motion of the spot as a line in this two-dimensional x-t plane. So how are we to characterise the motion of the now from, say, Monday to Friday? Answer: place the date-line along a t-axis, take time∗ (or ‘A-time’) as an orthogonal axis (t∗ ), and draw the ‘now’ as a line in this two dimensional t-t∗ plane. A point t∗1 on the t∗ axis will correspond a unique point t1 on the t-axis, meaning that the now passes t1 at t∗1 . Say t1 is Monday, then Monday is present at and only at t∗1 in A-time. For the dynamist, the line represents the present’s motion. For the presentist, the line also represents what exists. In the growing block, the line and all below it represents what exists; for indeterminacy the line and all below it represents what can be referred to in sentences which have truth values. I don’t know whether there are any actual A-theorists who understand dynamism in this way, but it appears to be a perfectly coherent way to do so. It seems to adequately capture the thesis that the now moves from Monday to Friday. For example, it answers McTaggart’s argument that

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A-time is incoherent because it involves attributing incompatible attributes — past, present and future — to the one event. There is a large literature on McTaggart’s argument, and it’s not the purpose of this paper to engage that literature, except to note that an answer here to McTaggart is that our representation of A-theory attributes these ‘incompatible attributes’ to events at different A-times (t∗ ). The McTaggart response to this is to claim that t∗ , for it to be time, must itself not be static. My reply is that t∗ is not in itself time, but that the t-t∗ diagram represents the motion of the now without either dimension needing to be dynamic. I’ll leave it to the A-theorist to decide whether this is satisfactory to them, or whether a McTaggart-style regress will ensue, and whether a regress would be fatal. If there is a regress, I simply note, it remains the case that I appear to have coherently represented the motion of the now, and that any putative implicit incoherence has not been introduced by the move (below) from linear to circular time.

6. Loops We can now consider circular time. The most natural way to represent the moving now in circular time is to depict the t-axis radially and the t∗ axis as linear, so that time is projected onto the surface of a cylinder. Then the ‘now’ follows a spiralling trajectory around the surface (just as we might represent a spot continually moving around a circle in terms of the angle T for a given radius r, taking a linear time axis orthogonal to the T-r plane and representing the motion of the spot as spiralling around the surface of a cylinder). The ‘now’ will never cross the same point in the T-t∗ space, although it periodically passes the same point on the T-axis. The upshot of the latter is that the ‘now’ hits every date along the T-axis very many times (how many depends on how long we allow ‘A-time’ to continue). Further, events are ordered in the A-series by their position along t∗ axis. We have, I claim, a coherent representation of all four A-theories. In the case of dynamism, the line represents the motion of the now. In the case of presentism — ‘only the present exists’ — this line represents what is real and all other points on the surface of the cylinder are not real. In the case of the growing block theory — ‘only the present and past exist’ — all points on the surface exist, at least in the case of t∗ extended indefinitely into the ‘past’. And for indeterminacy — ‘only sentences about the past and present have truth values’ — all points on the surface can be the reference of sentences which have truth values, again at least in the case of t∗ extended indefinitely into the past.

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All four versions of A-theory are thus represented coherently. However, two issues require discussion. (i) In circular time it is not the case that ‘being future’ entails ‘not being past’. It therefore is important that I formulated presentism, growing block and indeterminacy that way I did. It is common to characterise presentism as ‘the present exists but the past and future do not’. This would lead to an immediate contradiction, since in circular time any present event is also future and past. Thus I defined presentism as the view that only the present exists, which generates no contradiction. Then we can say that in linear time this entails that the past and future do not exist, but in circular time it does not. The same applies to growing block and indeterminacy: again it’s important that we formulate the theories carefully. This may seem like a sleight of hand. However a moment’s reflection shows that this is necessary if we are to take circular time seriously. Similar issues arise for B-theorists — ‘being earlier than’ excludes ‘being later than’ in linear time but not in circular time. So there is no absolute exclusive distinction between past and future. Does this mean there is no distinction at all between past and future? Fortunately not. In circular time an event which is both past and future will be closer in one direction than the other, with the exceptions of the present event and the event equidistant in both directions from the present. Let an event be ‘proximally future’ if it is closer to the present in the future direction, and ‘proximally past’ if it is closer in the past direction. This is an exclusive distinction (apart from the two exceptions just mentioned). This may help with the common sense distinction between past and future, although I will not argue for that here. It will however help with a theoretical problem. Dynamism, we saw earlier, derives from the idea that future events become present and present events become past. While it is true in circular time that a future event becomes present then past, the same fact could equally be described as ‘a past event becomes present then future’. But if we replace the unqualified future and past with proximally future and past, then we have the exclusive truth that a proximally future event becomes present then proximally past. This is sufficient to express the dynamic notion of becoming present. (ii) In circular time, for the growing block the future exists and for indeterminacy statements about the future have truth values. This holds if t∗ extends indefinitely into the ‘past’. Suppose then that there is a beginning to A-time, t∗ = 0. Then for the first circuit of the circle for the growing block the future does not exists and for indeterminacy statements

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about the future lack truth values. Thereafter for the growing block the future exists and for indeterminacy statements about the future have truth values. One possible response for these theories is to insist that only one circuit of A-time is possible. This does not have any consequences for the physics. However it runs into trouble for more complex loops in time such as wormholes (see Ref. 16), so we will not pursue that option here. The alternative is to admit that in circular time, for the growing block the future exists and for indeterminacy statements about the future have truth values. This amounts to an admission that the connection between becoming present and becoming real/determinate is not necessary but contingent. The connection holds in linear time but not in circular time. This is indeed a theoretical loss for these theories, if for example they seek to explain becoming present by becoming real. There is however a consideration which may mean such A-theorists would be quite willing to accept the contingency of the connection between becoming present and becoming real/determinate. It is well known that time travel appears to limit freewill. For example, after travelling back in time I am for no apparent immediate reason unable to kill my baby self, for that would engender a contradiction — the so-called grandfather paradox. There is a serious debate about whether this is indeed a limitation on freewill (see for example Refs. 6, 17 and 18) which I will not engage here. But at least some proponents of the growing block and indeterminacy base their case for those theories on the claim that they are required for free will (e.g., Ref. 9). Further, these theorists tend to be the ones who find a problem for free will in the grandfather paradox. An example is William Grey, who holds both the growing block and indeterminacy, says of the grandfather paradox: “Although this may not be self-contradictory it does lead to intolerable restrictions on the range of possibility, and the range of efficacious choice available to an agent” (Ref. 19, p. 70). So it may be that since circular time involves a limiting of the openness of the future, such A-theorists will find it appropriate that under such conditions the growing block collapses into eternalism and indeterminacy into determinacy. I have argued that the common sense notion — if such it be — that time flows survives the possibility of circular time that arises in the general theory of relativity. To do so I have shown how to coherently represent in circular time four A-theories of time that encapsulate a strong notion of the flow of time. I have assumed the flow of time is indeed implicit in the common sense notion of time, and that general relativity does indeed show

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that circular time is possible. Both issues could be debated. But if we do make these assumptions, then it is indeed curious that conceptual analysts should opt for a B-theory of time on the grounds of scientific developments. I have shown that at least for the case of circular time, they need not. Acknowledgments For comments I would like to thank Helen Beebee, Alex Bird, Sungho Choi, Paul Noordoff, and others in audiences in Ghent and at Washington University. References 1. P. Dowe, Physical Causation. New York: Cambridge University Press, ch. 1 (2000). 2. H. Putnam, Time and Physical Geometry. Journal of Philosophy 64, 240–247 (1967). 3. M. Tooley, Time, Tense, and Causation. Oxford: Oxford University Press (1997). 4. H. Stein, On Einstein–Minkowski Space–Time. The Journal of Philosophy 65, 5–23 (1968). 5. R. Clifton and M. Hogarth, The Definability of Objective Becoming in Minkowski Spacetime. Synthese 103, 355–387 (1995). 6. D. Lewis, The Paradoxes of Time Travel. In: Philosophical Papers Volume II. New York: Oxford University Press, 67–80 (1986). 7. J. McTaggart, The Unreality of Time. Mind 17, 457–74 (1908). 8. J. Bigelow, Time Travel Fiction. In: G. Preyer and F. Siebelt (Eds.), Reality and Humean Supervenience: Essays on the Philosophy of David Lewis. Lanham: Rowman & Littlefield, Chapter 3 (2001). 9. Aristotle, On Interpretation 9. In: J. H. Ackrill (Trans.), Categories and De Interpretatione. Oxford: Clarendon Press (1963). 10. K. G¨ odel, An Example of a New Type of Cosmological Solution to Einstein’s Field Equations of Gravitation. Reviews of Modern Physics 21, 447–450 (1949). 11. F. Tipler, Rotating Cylinders and the Possibility of Global Causality Violation. Physical Review D 9, 2203 (1974). 12. R. Gott, Closed Timelike Curves Produced by Pairs of Moving Cosmic Strings: Exact Solutions. Physical Review Letters 66, 1126 (1991). 13. K. Thorne, Black Holes and Time Warps. New York: Norton (1994). 14. P. Davies, How to Build a Time Machine. London: Penguin (2001). 15. D. Kutach, Time Travel and Consistency Constraints. Philosophy of Science 70, 1098–1113 (2003). 16. P. Dowe, Every Now and Then (forthcoming).

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17. B. Brown, Defending Backwards Causation. Canadian Journal of Philosophy 22, 429–44 (1992). 18. K. Vihvelin, What Time Travelers Cannot Do. Philosophical Studies 81, 315–30 (1996). 19. W. Grey, Troubles with Time Travel. Philosophy 74, 55–70 (1999).

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SUNGHO CHOI Centre for Time, Department of Philosophy University of Sydney, Australia & Department of Philosophy Kyunghee University, South Korea E-mail: [email protected]

In this paper I will discuss Richard Holton’s defence of dispositionalism that all properties are essentially dispositional. By way of countering the objection that dispositionalism generates an infinite regress, Holton attempts to advance a consistent model of possible worlds where all truths are dispositional truths. But I will argue that the simple conditional analysis of dispositions, on which Holton’s model is built, is so mistaken that Holton’s model fails to serve his goal. What is more, it is not likely that we can successfully materialize the driving idea of Holton’s model on an appropriately revised version of the conditional analysis of dispositions. Finally, I will discuss the lesson about the methodology of philosophy that we can learn from Holton’s failure.

1. Dispositional Essentialism and Categoricalism On dispositional essentialism, the essence of a property is identified by what causal or nomic powers it bestows on its instances. For instance, dispositional essentialists say that the property of being negatively charged essentially bestows on its instances the power to interact with other charged particles. But those powers are most effectively characterized in terms of disposition to exhibit a certain manifestation in response to a certain stimulus. For example, the power the property of being negatively charged bestows on its instances can be characterized in terms of the disposition to attract positively charged particles and repel negatively charged particles. Therefore, dispositional essentialism is acknowledged to entail that properties have dispositional essences, in other words, that properties are essentially dispositional. There are at least two distinct versions of dispositional essentialism one of which says that all properties, without exceptions, are dispositional, whilst the other says that most properties are dispositional but there are some properties, most notably, spatio-temporal 44

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properties that aren’t. The first and strong version is championed explicitly by Sydney Shoemaker,1 Popper (Ref. 2, p. 424), Alexander Bird,3 whilst the second and weak version by Chris Swoyer,4 George Molnar,5 Ellis and Lierse.6,a Dispositional essentialism has been advanced as an alternative view on properties to categoricalism that properties are essentially nondispositional. On categoricalism inexorably advocated by such authors as David Armstrong,7 – 9 the identity of a property doesn’t depend upon the causal or nomic powers it confers on its instances. Rather, the identity of a property is determined by its internal or self-contained nature that is only contingently related to the specific causal or nomic powers it confers on its instances. Obviously, there is a stark contrast between dispositional essentialism and categoricalism, which has inevitably given rise to an enduring debate between the two positions. It is remarkable that the foremost significance of this debate lies in the fact that categoricalism and dispositional essentialism necessitate diametrically opposing views of laws of nature. Because the property of being negatively charged has the essence characterized in terms of the disposition to attract positively charged particles and repel negatively charged particles, on dispositional essentialism, all actual or merely possible objects that are negatively charged are disposed to attract positively charged particles and repel negatively charged particles. If so, it is not metaphysically possible that a negatively charged particle isnt so disposed, entailing that Coulombs law, which describes how charged particles interact with one another, is metaphysically necessary. In general, dispositional essentialists maintain, laws of nature are just universal descriptions of dispositional essences of properties; and they are metaphysically necessary because the truth of them is ensured by the dispositional essences of relevant properties in all the possible worlds where those relevant properties exist. Conversely, on categoricalism, the property of being negatively charged has an internal or self-contained essence that doesn’t necessitate specific ways in which a negatively charged particle is disposed to interact with other particles. Therefore, it is metaphysically possible that a particle has the property of being negatively charged but is not disposed to attract positively charged particles and repel negatively charged particles, which means aI

believe that Ref. 4 can be best understood to promote the first and strong version of dispositional essentialism. But Armstrong points out that, in person communication, Swoyer has told that he doesn’t mean to buy into the strong version of dispositional essentialism that all properties are dispositional (Ref. 7, p. 76).

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that Coulomb’s law is metaphysically contingent. In general, on categoricalism, the identity of properties isn’t determined by how their instances are disposed to act or react, and hence it is perfectly possible that the same set of properties is subject to different laws of nature. It follows from this that, on categoricalism, laws of nature are metaphysically contingent. In view of the fact that the nature of natural laws is one of key issues in contemporary metaphysics, from what has been said, it is clear that the stake of the debate between dispositional essentialism and categoricalism couldn’t be higher. If so, it will be instructive to carefully appraise arguments and criticisms the two side have exchanged so far. Keeping this in mind, in this paper, I will call attention to one crucial criticism of the strong version of dispositional essentialism, i.e., the view that all properties are dispositional, with an eye on the connection between dispositional ascriptions and counterfactual conditionals.

2. Dispositions All the Way Round? To begin with, it will be useful to say a word about the conception of dispositional property at work in what follows. Approximately, something has a dispositional property insofar as it would exhibit a certain distinctive manifestation in response to an appropriate stimulus. For instance, salt is water-soluble insofar as it would dissolve in response to being submerged into water. Analogically, metal is electrically conductive insofar as electric current would flow in response to its being connected to an electrical source. But what does it mean to say that something would exhibit a certain distinctive manifestation in response to an appropriate stimulus? According to the simple conditional analysis of dispositions, its meaning can be cashed out in terms of the counterfactual conditional that if it were to undergo an appropriate stimulus, it would exhibit a certain distinctive manifestation. Here, as usual, I will assume the standard Lewis/Stalnaker possible worlds semantics for counterfactual conditionals according to which the truth condition of a counterfactual conditional is given in terms of possible worlds. So conceived, we seem to be able to say that dispositional ascriptions are made true by what is going on in other possible worlds. This observation has been utilized by some philosophers to make one important criticism against the strong version of dispositional essentialism that all properties are essentially dispositional properties — for short, let us call it ‘dispositionalism’. A simplified version of the criticism goes as follows: “Suppose that all properties are dispositional. Then all truths

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must be dispositional truths. According to the conditional analysis of dispositions, this means that all truths in the actual world are counterfactual truths, and therefore made true by what are true in other possible worlds. But all truths in those possible worlds are again dispositional. Therefore, assuming the conditional analysis of dispositions, they are counterfactual truths, which means that they are made true by what are true in still other possible worlds. This incurs an infinite regress. To avert such an infinite regress, we have to oppose the idea of purely dispositional worlds, namely, dispositionalism”. This criticism, however, is severely challenged by Richard Holton.10,b His basic idea is that if we can construct a finite, coherent model of purely dispositional worlds, this will establish that dispositionalism doesn’t necessarily give rise to an infinite regress, and thereby we will be able to rebut the criticism described above. To begin with, Holton observes that it is strictly false to say that, on dispositionalism, all truths in the actual world are made true by what is going on in other possible worlds: “It is only counterfactuals with unactualized antecedents — counterfactuals that really are counter to fact — that are made true by what happens at neighbouring worlds; or to put the point in terms of dispositions, it is only unmanifested dispositional properties that are made true in this way” (Ref. 10, p. 10). Dispositional properties are manifested or not manifested. But, in case of manifested dispositional properties, their stimulus and manifestation conditions are actually satisfied. Therefore, true ascriptions of manifested dispositional properties are analyzed by the simple conditional analysis of dispositions into counterfactual conditionals whose antecedents and consequents are actually true. But, on the standard Lewis/Stalnaker semantics, the truth of a counterfactual conditional is entailed by the truth of its antecedent and consequent. Therefore, on the standard Lewis/Stalnaker semantics, those counterfactual conditionals which are meant to analyze manifested dispositional ascriptions by the simple conditional analysis of dispositions are made true solely by what happens in the actual world. Hence, according to the simple conditional analysis of dispositions, manifested dispositional ascriptions are made true by what is true in the actual world (as opposed to what is true in neighbouring possible worlds).

b The

objection explicitly discussed by Holton is due to Ref. 11, p. 64. But similar objections have been advanced by other authors, most recently, by Armstrong (Refs. 7, p. 80; 8, p. 31–33).

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Based on this observation, Holton argues that we can provide a finite and coherent model of possible worlds where all contingent truths are dispositional truths. To be specific, Holton suggests that the following four sentences are dispositional sentences and that it is possible to provide a finite model of possible worlds which are entirely described in terms of them and, at the same time, consistent with their definitions. P =df (R♦ → S) Q =df (S♦ → R) R =df (P ♦ → Q) S =df (Q♦ → P )c Obviously, here Holton assumes the simple conditional analysis of dispositions and hence defines dispositional ascriptions in terms of simple counterfactual conditionals. As we will see, though, even Holton admits that the simple conditional analysis of dispositions, as it stands, is indefensible. Since Holton’s key claim is that there is a consistent model of possible worlds where all truths are dispositional truths, it will be convenient to have another set of symbols that primarily represent dispositional ascriptions. Let us suppose that ‘P *’ primarily represents a dispositional ascription whose characteristic stimulus and manifestation are R and S, respectively. That is, P * is that S is disposed to be the case in response to R’s being the case. By the same token, ‘Q*’primarily represents a dispositional ascription whose characteristic stimulus and manifestation are S and R, respectively. That is, Q* is that R is disposed to be the case in response to S’s being the case. The same goes for ‘R*’and ‘S*’. Thus understood, P , which is defined to be ‘R♦ → S’, is identified with the dispositional ascription P * by the simple conditional analysis of dispositions. Likewise, Q, which is defined to be ‘S♦ → R’, is identified with the dispositional ascription Q* by the simple conditional analysis of dispositions. The same can be said about R and S. Holton, in Ref. 10, p. 10, maintains that when we have similarity between possible worlds given by agreement over the four sentences — i.e., P , Q, R, S —, it can be proved that there are four possible worlds which can be entirely characterized by them and their negations and, at the same time, consistent with their definitions. The following diagram represents the four possible worlds and their relations. c It

is evident that these definitions are circular. For example, P is defined in terms of R which is in turn defined in terms of P . Holton though goes to great length to argue that this circularity doesn’t mar his defence of dispositionalism (Ref. 10, p. 12–13).

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P QRS • w1 ∼ P QR ∼ S

w2 •

• w3

P ∼ Q ∼ RS

• w4 ∼P ∼Q∼R∼S Holton’s Model Here the distance on the page between two points is meant to correspond to the similarity between possible worlds. It is easy to see that P , Q, R and S are true at w1; and that ∼ P , Q, R and ∼ S are true at w2, and so on. Thus, on the standard semantics for counterfactual conditionals, Holton’s four possible worlds are consistent with the definitions of the four sentences. Here it is to be noted that, in Holton’s model, some of the counterfactual conditionals and their negations are made true at a possible world solely by what happens at that world. For instance, P , which is defined to be ‘R♦ → S’, is true at w1 in virtue of the fact that R and S are true at w1. By the same token, P is false at w2 in virtue of the fact that R is true but S is false at w2. This reveals that the idea that some of counterfactual conditionals and their negations are true at a possible world solely in virtue of what is going on at that world is at work in Holton’s model. In Holton’s model, each of the four worlds is entirely specified by counterfactual conditionals and their negations. For instance, the possible world w2 is fully specified by the four sentences, ∼ P , Q, R and ∼ S. Therefore, Holton’s model can be said to offer a set of possible worlds where all truths are counterfactual truths. Moreover, on the assumption of the simple conditional analysis of dispositions, the simple counterfactual conditionals, P , Q, R and S are equivalent to dispositional ascriptions, P *, Q*, R* and S*. From this Holton concludes that his model serves to show that there is a finite, consistent model of possible worlds that are entirely characterized by dispositional ascriptions and their negations; and therefore that the idea that all truths are dispositional truths is not incoherent nor does it lead to an infinite regress.d But I will argue below that Holton’s conclusion is unjustified.

d Holton’s

argument has been explicitly endorsed by such philosophers as Alexander Bird (Refs. 12, p. 270, p. 506 n4; Refs. 13, 14).

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3. The Problem of Random Coincidence It is unquestionable that Holton’s four possible worlds are completely described by counterfactual conditionals and their negations. Does this entail that they are completely described by dispositional ascriptions and their negations? Yes if the simple conditional analysis of dispositions is accepted. For clarity, it will be useful to offer an exact formulation of the simple conditional analysis of dispositions: SCA Something x has the disposition at time t to exhibit manifestation m in response to stimulus s iff if x were to undergo s at t, it would exhibit m. According to SCA, from the fact that there is a consistent class of possible worlds completely characterized by Holton’s counterfactual conditionals, P , Q, R, S and their negations, it is deducible that there is a consistent class of possible worlds completely characterized by dispositional ascriptions, P *, Q*, R*, S*, and their negations. However, as already mentioned, Holton himself concedes that the simple conditional analysis of dispositions is not fully successful. Referring to Charlie Martin’s memorable examples of finkish dispositions,15 Holton says “any plausible counterfactual analysis of dispositions will have to be more sophisticated than this [SCA]. I hope that the central feature of the account sketched here will remain when we substitute the more sophisticated counterfactuals” (Ref. 10, p. 3 n.3). I agree with Holton that we can defend SCA against Martin’s examples in a way that doesn’t affect the central features of Holton’s argument, which I will not recount here. But I believe that SCA has quite a different kind of defect which can’t be repaired without impairing Holton’s argument. Indeed I take it that Holton’s argument takes advantage of this defect. One persistent criticism of the simple conditional analysis of dispositions is due to a feature of the standard Lewis/Stalnaker semantics for counterfactual conditionals which is that the truth of the counterfactual conditional that if it were to be the case that F then it would be the case that G is trivially derivable from the truth of F and G. Suppose that I actually twist my left foot and then scratch my right shoulder and that my twisting the left foot has nothing to do with my scratching the right shoulder. Then, according to the simple conditional analysis of dispositions, I am disposed to scratch the right shoulder in response to twisting the left foot because the counterfactual conditional that if I were to twist my left foot I

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would scratch my right shoulder is trivially true (Refs. 16, p. 393; 17, p. 10– 11; 12, p. 159). However, it is preposterous to say that I have the disposition to scratch the right shoulder in response to twisting the left foot. This is what I call ‘the problem of random coincidence’ for the simple conditional analysis of dispositions. Here it should be noted that it is also a true counterfactual conditional that if I were not to twist my left foot I would still scratch my right shoulder. Given that my twisting the left foot has nothing to do with my scratching the right shoulder, I would still scratch my right shoulder in the closest possible worlds where I don’t twist the left foot. According to the simple conditional analysis of dispositions, this entails that I am disposed to scratch the right shoulder in response to not twisting the left foot. As a consequence, I am both disposed to scratch the right shoulder in response to twisting the left foot and disposed to scratch the right shoulder in response to not twisting the left foot. In general, when it is supposed that F is actually true and utterly unrelated to G, according to the simple conditional analysis of dispositions, F is both disposed to be the case in response to G’s being the case and disposed to be the case in response to G’s not being the case. That being said, the two dispositions are manifested regardless of whether the corresponding stimuli obtain or not. But this is blatantly counterintuitive. Given that there is no connection whatsoever between F and G, what is more reasonable to say is that F is neither disposed to be the case in response to G’s being the case nor is it disposed to be the case in response to G’s not being the case. At this point it might be objected that the problem of random coincidence is not a real problem: “Admittedly we are reluctant to accept that I am disposed to scratch the right shoulder in response to twisting the left foot. But this is just because the dispositional ascription under consideration is not useful to us. Thus there is a pragmatic explanation of why we are inclined to deny the dispositional ascription in question. This means that we can keep the simple conditional analysis of dispositions safe by maintaining that I am indeed disposed to scratch the right shoulder in response to twisting the left foot but this dispositional ascription is not useful in our everyday life. The same can be said about my disposition to scratch the right shoulder in response to not twisting the left foot”. I take it, though, this objection is not acceptable. To be sure, there are some true dispositional ascriptions that are not useful to us. But in those cases we can offer an explanation of why this is so. For instance, a fragile glass is disposed to shatter in response to a far-off sneeze in a circumstance

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where via a butterfly effect the sneeze would bring about a major disturbance.e This, I think, is a true dispositional ascription that is not useful in our everyday life. For under normal circumstance a butterfly effect does not occur, and therefore the characteristic stimulus of the disposition in question does not occur often enough in our everyday life. But when the characteristic stimulus of a disposition D does not occur often enough in our everyday life, there is no pressing need to sort things in terms of D, and hence the true ascription of D is not useful to us. Supposing that, on Mars, butterfly effects frequently occur because of unstable atmosphere, however, it will be of great use to Martians to sort things in terms of the disposition to shatter in response to a far-off sneeze via a butterfly effect. f Thus we can offer an explanation of why it is not useful in our everyday life to say that a glass is disposed to shatter in response to a far-off sneeze via a butterfly effect although it is a true dispositional ascription. However, the same doesn’t apply to the cases that give rise to the problem of random coincidence. Should I be indeed disposed to scratch the right shoulder in response to twisting the left foot, there would be no reason why this dispositional ascription is not useful to us. In fact, even if it is supposed that I twist my left foot very often, we will still be loath to say that I am disposed to scratch the right shoulder in response to twisting the left foot. This indicates that the reason why we are inclined to deny the dispositional ascription at issue is not merely that it is not useful. Furthermore, we firmly believe that the stimulus of a disposition is essential to its manifestation. That is, the stimulus must be necessary to bring about the manifestation. Otherwise, there would be no point of associating dispositional properties with their characteristic stimuli. Therefore, as long as it is true that x is disposed to exhibit a manifestation m in response to undergoing a stimulus s, we are inclined to think that it is not disposed to exhibit m in response to not undergoing s. This is so regardless of whether the dispositional ascription is useful to us or not. For instance, it may be that the disposition to shatter in response to the presence of a far-off sneeze is not useful to us. Nonetheless, we are tempted to say that, if x is disposed to shatter in response to the presence of a far-off sneeze, it is not the case that x is disposed to shatter in response to the absence of a far-off sneeze. But this is not the case for the disposition to scratch the right shoulder in response to twisting the left foot. As already noted, e This f This

example is due to Alexander Bird (Ref. 18, p. 231). point is also made in (Ref. 19, p. 578).

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according to SCA, I have both the disposition to scratch the right shoulder in response to twisting the left foot and the disposition to scratch the right shoulder in response to not twisting the left foot. I hold that this should be taken to be a telltale sign betraying that there is something wrong with SCA. If so, it is not a profitable move to suggest that both of the dispositional ascriptions at issue are indeed true and that we can explain away our strong inclination to deny them by saying that they are not useful. In short, the problem of random coincidence is a real problem. When F and G both are true and utterly unrelated to one another, we have every reason to deny that F is disposed to be the case in response to G’s being the case. But, on the standard semantics for counterfactual conditionals, SCA says to the contrary, namely, that F is disposed to be the case in response to G’s being the case. Therefore, I conclude that SCA must go.g I urge, however, that this is exactly where Holton’s model goes wrong. 4. What is Wrong with Holton’s Model? As I said in Section 2, in Holton’s model, each of the four worlds is entirely described by counterfactual conditionals and their negations. And, on the basis of SCA, Holton identifies counterfactual conditionals, P , Q, R, and S with dispositional ascriptions, P *, Q*, R*, and S*, from which he derives that each of the four worlds is entirely described by dispositional ascriptions and their negations. Now that it proves that SCA is crippled by the problem of random coincidence, though, it is doubtful that Holton’s reasoning still remains valid. For example, let us examine what truth value P *, which is that S is disposed to be the case in response to R’s being the case, has at w1. Surely, the counterfactual conditional P is true at w1. But it has been revealed that the simple conditional analysis of dispositions is in real trouble, which suggests that the truth of a dispositional ascription is not immediately g Strictly

speaking, the problem of random coincidence arises from the standard Lewis/Stalnaker semantics for counterfactual conditionals and simple conditional analysis of dispositions combined. This might lead one to think that we shouldn’t blame the problem of random coincidence on the simple conditional analysis of dispositions but on the standard Lewis/Stalnaker semantics for counterfactual conditionals. Indeed, with a view to solving the problem of random coincidence, Gundersen gives up the standard Lewis/Stalnaker semantics for counterfactual conditionals, in particular, its thesis that the truth of a counterfactual conditional is implied by the truth of its antecedent and consequent and proposes a modified semantics for counterfactual conditionals. 16,17 But, as I’ve thrashed out,20 this is the right way of looking at the matter. I maintain that the blame must be laid squarely on the simple conditional analysis of dispositions.

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deducible from the truth of the corresponding simple counterfactual conditional. That is, P * is not immediately deducible from P . Here it may be pointed out that Holton, in Ref. 10, p. 11, claims that P , which is defined to be ‘R♦ → S’, is not just stipulated to be true at w1 but is ‘made true’ at w1 by the fact that both R and S are true at w1. But this makes no difference. P * is not deducible from the truth of R and S, either. Indeed, we have found above that SCA is inflicted with the problem of random coincidence precisely because SCA validates the inference of the truth of a dispositional ascription from the obtainings of its characteristic stimulus and manifestation. Having said that, we have no reason at all to think that P * is true at w1. Similarly, at w1, Q* is not immediately deducible from Q nor, as revealed by the problem of random coincidence, from the truth of R and S. Hence, we can’t justifiably suppose that Q* is true at w1. In general, once we repudiate SCA, we have no good reason to think that dispositional ascriptions are true in Holton’s possible worlds in a way that is intended by Holton. What is more, there is a clear analogy between Holton’s model and the case of random coincidence. It is to be observed that ‘∼ R♦ → S’ is true at w1: S would be true in the closest possible world to w1 where R is false, namely, at w3. If so, on the assumption of SCA, we are forced to say that it is true at w1 that S is disposed to be the case in response to R’s not being the case. Then it follows that, on the assumption of SCA, at w1, S is both disposed to be the case in response to R’s being the case and disposed to be the case in response to R’s not being the case. We can get the same result for other sentences at w1. For instance, ‘∼ S♦ → R’ is true at w1: R would be true in the closest possible world to w1 where S is false, namely, at w2. But Q, which is defined to be ‘S♦ → R’, is also true at w1. Therefore, assuming SCA, at w1, R is both disposed to be the case in response to S’s being the case and disposed to be the case in response to S’s not being the case. And much the same can be said about the sentences that are true in other possible worlds. For example, Q, which is ‘S♦ → R’, is true at w2. But ‘∼ S♦ → R’ is true at w2 as well: R would be true in the closest possible world to w2 where S is false, namely, at w2. Hence, given that SCA is accepted as an adequate analysis of dispositions, at w2, R is both disposed to be the case in response to S’s being the case and disposed to be the case in response to S’s not being the case. But this is precisely what happens in the case of random coincidence: on the simple conditional analysis of dispositions, I am both disposed to scratch the right shoulder in response to twisting the left foot and disposed

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to scratch the right shoulder in response to not twisting the left foot. And, as I have argued earlier, this is just an inauspicious consequence of the simple conditional analysis of dispositions which we should consider as a ground for reductio ad absurdum against the simple conditional analysis of dispositions. So much worse for Holton’s model as it crucially relies on the simple conditional analysis of dispositions. Note further that I’ve argued earlier that what is reasonable to say in the case of random coincidence is that I am neither disposed to scratch the right shoulder in response to twisting the left foot nor disposed to scratch the right shoulder in response to not twisting the left foot. In view of the parallelism between Holton’s model and the case of random coincidence, what is reasonable to say in Holton’s model is that, for example, at w1, S is neither disposed to be the case in response to R’s being the case nor disposed to be the case in response to R’s not being the case. As a consequence, we not only have no reason to think that P * is true at w1 but also we has a good reason to think that P * is false at w1. In general, whenever, in Holton’s model, the simple conditional analysis dispositions entails that A is both disposed to be the case in response to B’s being the case and disposed to be the case in response to B’s not being the case, what is more reasonable to say is that A is neither disposed to be the case in response to B’s being the case nor disposed to be the case in response to B’s not being the case. As a consequence, we may well maintain that none of P *, Q*, R* and S* is true at w1. But this is far from what Holton wants to say about his model. From this I come to the conclusion that, once the problem of random coincidence for SCA is recognized, Holton is not entitled to claim that his model exemplifies a consistent set of possible worlds that are entirely characterized by dispositional ascriptions and their negations in a way intended by him. What if we improve SCA in such a way that it gets around the problem of random coincidence? Recall that Holton’s reasoning is that P * is made true at w1 by the truth of P which is in turn made true at w1 by the truth of R and S. But this reasoning relies on the very feature of the simple conditional analysis of dispositions from which the problem of random coincidence arises. If so, there is no guarantee that, when we revise the conditional analysis of dispositions in a way that solves the problem of random coincidence, the central feature of Holton’s reasoning can be preserved. In fact, I suspect that such a revision will annul Holton’s reasoning not least because, in order to solve the problem of random coincidence, we need to modify the very feature of the simple conditional analysis of dispositions

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on which Holton’s model is built. To illustrate this point, it will be useful to consider one promising solution to the problem of random coincidence.h Very plausibly, it may be suggested that we can solve the problem of random coincidence by adding to the analysans of SCA the causal requirement that the stimulus would cause the manifestation. This idea has been flirted with by many philosophers of dispositions such as Molnar (Ref. 22, p. 2), Armstrong (Ref. 7, p. 72) and Bird (Ref. 18, p. 233). Indeed, Lewis has incorporated this idea into his analysis of dispositions — although he does so for other reasons than to solve the problems of random coincidence. 23 For the present purpose, it will be fine to discuss the simplest way of incorporating the causal requirement into the simple conditional analysis of dispositions: CCA Something x has the disposition at time t to exhibit manifestation m in response to stimulus s iff if x were to undergo s at t, s would cause x to exhibit m. Unlike SCA, CCA requires that the stimulus would cause the manifestation. It is easy to see that CCA has no troubles in handling the case of random coincidence. Let us consider the case of random coincidence where I actually twist my left foot and then scratch my right shoulder. In this case, my twisting the left foot doesn’t cause me to scratch my right shoulder. Then, according to CCA, I am not disposed to scratch the right shoulder in response to twisting the left foot. Also, I am not disposed to scratch the right shoulder in response to not twisting the left foot because if I were not to twist my left foot, this wouldn’t cause me to scratch my right shoulder albeit I would still scratch my right shoulder. What if we suppose that my twisting the left foot actually causes me to scratch my right shoulder? Then CCA delivers the verdict that I am disposed to scratch the right shoulder in response to twisting the left foot. But this result is not counterintuitive at all, as can be seen from the fact that, in this case, there is a strong inclination to say that I am indeed so disposed. As a result, I h Recently,

the problem of random coincidence has been attracting attentions from some philosophers of dispositions. For instance, Malzkorn, in Ref. 21, p. 463, claims that we can solve the problem of random coincidence by adding to the analysans of SCA the additional requirement that, to a first approximation, if x were not to exhibit manifestation m, it would not undergo the stimulus s. Meanwhile, Gundersen,16,17 as noted earlier, argues that we can solve the problem of random coincidence by modifying the standard Lewis/Stalnaker semantics for counterfactual conditionals. I think though that neither of Malzkorn’s and Gundersen’s attempts is successful. For my extended discussion on this issue, see Ref. 20.

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believe that CCA is not troubled by the problem of random coincidence. Of course, this doesn’t mean that CCA is a perfectly adequate account of dispositions.i Nonetheless, CCA is undoubtedly a good attempt to solve the problem of random coincidence. In Section 2, we have seen that, based on the idea that, according to SCA, dispositional ascriptions are made true at a possible world by what is going on in neighbouring possible worlds, some philosophers have presented the charge of infinite regress against dispositionalism that all properties are dispositional properties. It should be noted that, with CCA in place of SCA, much the same can be done. This is because, just like SCA, CCA analyzes dispositional ascriptions in terms of counterfactual conditionals. This means that, even if CCA is substituted for SCA, dispositionalism is still under the threat of infinite regress. If so, it will be an interesting question whether the central feature of Holton’s defence of dispositionalsim can be preserved under the substitution of CCA for SCA. On the assumption of CCA, we can define P , Q, R and S in a way that is analogous to Holton’s definitions: P =df (R♦ → (R causes S)) Q =df (S♦ → (S causes R)) R =df (P ♦ → (P causes Q)) S =df (Q♦ → (Q causes P )) As with Holton’s model, let us consider possible worlds specified by the four sentences P , Q, R, S and their negations. Some of the possible worlds are incompatible with the above definitions. First, the apparently possible worlds where one of the four sentences is false but the rest of them are true are inconsistent with their definitions. For example, let us consider the apparently possible world where P , Q and R are true but S is false. Given that R is true, P is true iff it is true that R causes S. But S is supposed to be false. And unless both A and B are true, it is not true that A causes B. That is, ‘A causes B’ is true only if both A and B are true. Since S is false, it is false that R causes S, which is inconsistent with the supposition that P is true. Therefore, there is no possible world where P , Q and R are true but S is false. Much the same reasoning applies to other apparently possible worlds where one of the four sentences is false but the rest of them are true. Second, not all but some apparently possible worlds where two of the four sentences are true but the rest of them are false are i In

fact, I think that CCA is not fully acceptable, which I have argued in Ref. 20.

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inconsistent with their definitions. For example, there is no possible world where P and R are true but Q and S are false. This is because, according to their definitions, if P and R are true, S must be true as well. The same can be said about the apparently possible world where Q and S are true but P and R are false. To sum up, there are ten possible worlds that are completely described by the four sentences and their negations and, at the same time, individually consistent with their definitions: w1 at which P , Q, R, S are true w2 at which ∼ P , ∼ Q, R, S are true w3 at which P , Q, ∼ R, ∼ S are true w4 at which P , ∼ Q, ∼ R, S are true w5 at which ∼ P , Q, R, ∼ S are true w6 at which P , ∼ Q, ∼ R, ∼ S are true w7 at which ∼ P , Q, ∼ R, ∼ S are true w8 at which ∼ P , ∼ Q, R, ∼ S are true w9 at which ∼ P , ∼ Q, ∼ R, S are true w10 at which ∼ P , ∼ Q, ∼ R, ∼ S are true Note that the truth of P and R necessitates that R causes S, the truth of Q and S necessitates that S causes R, and so on. If so, all of ‘P causes Q’, ‘Q causes P ’, ‘R causes S’, and ‘S causes R’ are true at w1. Conversely, all of ‘P causes Q’, ‘Q causes P ’, ‘R causes S’, and ‘S causes R’ are false at w2. ‘P causes Q’ is false at w2 since P and Q are false at w2. For the same reason, ‘Q causes P ’ is false at w2. And, according to the definition of P , ‘R causes S’ is false at w2 since R is true but P is false at w2. By the same token, according to the definition of Q, ‘S causes R’ is false at w2 since S is true but Q is false at w2. As a result of this, all of the four causal sentences are false at w2. By applying similar reasoning to other possible worlds, it can be demonstrated that, for each possible world except for w1, all of ‘P causes Q’, ‘Q causes P ’, ‘R causes S’, and ‘S causes R’ are false. Here again let us assume that similarity between possible worlds is determined by agreement over the four sentences. Then w10 is equally similar to w6, w7, w8, and w9; and w10 is more similar to w6 than to w2, and so on. It is easy to recognize that this time the model created by the ten possible worlds is not consistent on the standard Lewis/Stalnaker possible world semantics for counterfactual conditionals. Let us consider the possible world w2 where R, which is defined to be ‘P ♦ → (P causes Q)’, is true. There are two closest possible worlds to w2 where P is true. They are w1

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and w4. But ‘P causes Q’ is false at w4. Hence, it is not the case that ‘P causes Q’ is true in all closest possible worlds to w2 where P is true. Then it follows that, on the standard semantics for counterfactual conditionals, ‘P ♦ → (P causes Q)’ is false at w2, which contradicts the supposition that R is true at w2. What about the sentence S that is supposed to be true at w2? Recall that S is defined to be ‘Q♦ → (Q causes P )’. There are two closest possible worlds to w2 where Q is true. They are w1 and w5. But ‘Q causes P ’ is false at w5. If so, it is not the case that ‘Q causes P ’ is true in all closest possible worlds to w2 where Q is true. As a consequence, on the standard semantics for counterfactual conditionals, ‘Q♦ → (Q causes P )’ is false at w2, which doesn’t agree with the supposition that S is true at w2. We can get the same result for other possible worlds. For instance, consider the possible world w6 where P is true. Recall that P is defined to be ‘R♦ → (R causes S)’. Then what is the closest possible world to w6 where R is true? It is w8. But, ‘R causes S’ is false at w8, which is to say that, on the standard semantics for counterfactual conditionals, ‘R♦ → (R causes S)’ is false at w6. Again, this is at odds with the supposition that P is true at w6. As I said earlier, there are ten possible worlds which are entirely described in terms of the four sentences P , Q, R and S and individually consistent with their definitions. And, it has come to light that the model consisting of all of them isn’t consistent on the Lewis/Stalnaker semantics for counterfactual conditionals. It is to be recognized, though, that we don’t have to use all of the ten possible worlds to construct a candidate for finite and consistent models of purely dispositional worlds. That is, we can only use some of them with a view to constructing such a candidate. For example, one might consider the following selection of possible worlds: w1 at which P , Q, R, S are true w2 at which ∼ P , ∼ Q, R, S are true w5 at which ∼ P , Q, R, ∼ S are true w10 at which ∼ P , ∼ Q, ∼ R, ∼ S are true These four possible worlds form a model that is much more likely to be consistent on the Lewis/Stalnaker semantics than the one formed by all of the ten possible worlds. For example, unlike the second, the first has no problem with the truth of R at w2. R, which is defined to be ‘P ♦ → (P causes Q)’, is true at w2. This time there is only one closest possible world to w2 where P is true, which is w1. But ‘P causes Q’ is true at w1. Then it follows that, on the standard semantics for counterfactual conditionals,

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‘P ♦ → (P causes Q)’ is true at w2, which is in line with the supposition that R is true at w2. The same reasoning applies to the truth of R at w5. Also, we have satisfying results for w10. P , which is defined to be ‘R♦ → (R causes S)’, is false at w10. And w2 and w5 both are the closest possible worlds to w10 where R is true. But, in both worlds, ‘R causes S’ is false, which means that it is not the case that ‘R causes S’ is true in all closest possible worlds to w10 where R is true. If so, on the Lewis/Stalnaker semantics, ‘R♦ → (R causes S)’ is false at w10, which in agreement with the supposition that P is false at w10. Unfortunately, however, it doesn’t take much time to see that the model at issue eventually fails. S, which is defined to be ‘Q♦ → (Q causes P )’, is true at w2. There are two closest possible worlds to w2 where Q is true. They are w1 and w5. But ‘Q causes P ’ is false at w5. Then it follows that it is not the case that ‘Q causes P ’ is true in all closest possible worlds to w2 where Q is true. If so, on the Lewis/Stalnaker semantics, ‘Q♦ → (Q causes P )’ is false at w2, which clashes with the supposition that S is true at w2. We can have the same result for the truth of Q at w5. Then we are led to the conclusion that the four possible worlds, w1, w2, w5, and w10, fail to form a finite and consistent model of purely possible worlds on the Lewis/Stalnaker semantics for counterfactual conditionals. What about other selections from the ten possible worlds? A little thought reveals that the only consistent model is the one composed solely of w1. Note though that w1 is a possible world where all dispositional properties are manifested. But unmanifested dispositions are the main source of trouble for dispositionalism which most critics cast doubt on. Therefore, unless those critics are offered a finite model where truth values are consistently assigned to unmanifested dispositions, they won’t withdraw the charge of infinite regress described in Section 2. Once this is seen, we can justifiably say that the fact that w1, by itself, generates a finite and consistent model for dispositionalism doesn’t in the least suffice to expunge our misgiving that underlies the charge of infinite regress against dispositionalism. To recapitulate, I’ve argued that the problem of random coincidence is a real problem for SCA and tentatively proposed CCA as a revision on SCA. And, based on CCA, I have defined four dispositional ascriptions which are analogous to those discussed by Holton. But it has been brought to light that the model of possible worlds generated by these four dispositional ascriptions is not consistent on the standard Lewis/Stalnaker possible world semantics for counterfactual conditionals. This naturally leads to the

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conclusion that the central feature of Holton’s defence of dispositionalism can’t be upheld when the simple conditional analysis of dispositions is so improved as to overcome the problem of random coincidence.

5. A Concluding Remark Holton’s model successfully exemplifies a set of possible worlds each of which is completely described by simple counterfactual conditionals and their negations. But it fails to exemplify a set of possible worlds each of which is completely described by dispositional ascriptions and their negations as the simple conditional analysis of dispositions is mistaken. What is more, it is unlikely that we can materialize the driving idea of Holton’s model on a revised version of the conditional analysis of dispositions that would be free from the problem of random coincidence. This brings us to the conclusion that dispositionalism has yet to be cleared of the charge of infinite regress. Finally, it is remarkable that the failure of Holton’s defence of dispositionalism teaches us one important lesson about the methodology of philosophy. The key question is whether or not all properties are essentially dispositional. This is primarily an ontological question in that it concerns what exist in the world independently of our mind. As discussed earlier, some philosophers answer in the negative by arguing that the idea of purely dispositional worlds results in an infinite regress. Holton, though, counters this argument by claiming that it is possible to construct a finite, coherent model of purely dispositional worlds. Here it is important to realize that this ontological debate presupposes a rough and ready conceptual understanding of what we mean by saying that a property is dispositional. More specifically, both sides of the debate, explicitly or implicitly, seem to agree that, to a first approximation, when we are talking about dispositional properties, we mean simple counterfactual conditionals. Without such a conceptual understanding, it would be hard to make sense of what this ontological debate is all about. Indeed, I believe that, in most areas of philosophy, we need to address conceptual questions before being able to embark on ontological questions properly (Refs. 24, p. 415; 25, p. 758). What is suggested by this point is that, should our rough and ready conceptual understanding of dispositions prove to be mistaken, we couldn’t rule out the possibility that the entire debate has got lost. Unfortunately, I take it, this is the case for Holton’s defence of dispositionalism. In defending dispositionalism from the charge of infinite regress, Holton tentatively

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assumes the simple conditional analysis of dispositions for the purpose of making sense of what a dispositional property is. But, as it turns out, the simple conditional analysis of dispositions is mistaken in such a way that Holton’s defence of dispositionalism is completely misdirected. The methodological lesson to be drawn from this is that it is always hazardous to carry out ontological investigations in the absence of a proper understanding of relevant concepts; and therefore that it is vital to have a proper understanding of relevant concepts in order to keep ontological investigations on the right track. Acknowledgments I would like to thank Toby Handfield for bringing Holton’s article to my attention. And, I also thank Paul Dicken for useful discussions. Finally, I am grateful to Rob Vanderbeeken for constructive advice and encouragement. References 1. S. Shoemaker, Causality and Properties. In: S. Shoemaker, Identity, Cause, and Mind. Cambridge: Cambridge University Press (1980). 2. K. Popper, The Logic of Scientific Discovery. London: Hutchinson (1959). 3. A. Bird, Nature’s Metaphysics: Laws and Properties. Oxford: University Press (2007). 4. C. Swoyer, The Nature of Natural Laws. Australasian Journal of Philosophy 60, 203–223 (1982). 5. G. Molnar, Powers. Oxford: Oxford University Press (2003). 6. B. Ellis and C. Lierse, Dispositional Essentialism. Australasian Journal of Philosophy 72, 27–45 (1994). 7. D. M. Armstrong, A World of States of Affairs. Cambridge: Cambridge University Press (1997). 8. D. M. Armstrong, The Causal Theory of Properties: Properties according to Shoemaker, Ellis, and Others. Philosophical Topics 26, 25–37 (1999). 9. D. M. Armstrong, Four Disputes about Properties. Synthese 144, 309–320 (2005). 10. R. Holton, Dispositions All the Way Round. Analysis 59, 9–14 (1999). 11. S. Blackburn, Filling in Space. Analysis 50, 62–65 (1990). 12. A. Bird, Structural Properties. In: H. Lillehammer and G. Rodriguez– Pereyra (Eds.), Real Metaphysics: Essays in Honour of D.H. Mellor. London: Routledge, 154–168 (2003). 13. A. Bird, Strong Necessitarianism: the Nomological Identity of Possible Worlds. Ratio 17, 256–276 (2004). 14. A. Bird, Potency and Modality. Synthese 149, 491–508 (2006). 15. C. Martin, Dispositions and Conditionals. The Philosophical Quarterly 44, 1–8 (1994).

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16. L. Gundersen, In Defence of the Conditional Account of Dispositions. Synthese 130, 389–411 (2002). 17. L. Gundersen, Outline of a New Semantics for Counterfactuals. Pacific Philosophical Quarterly 85, 1–20 (2004). 18. A. Bird, Dispositions and Antidotes. The Philosophical Quarterly 48, 227–234 (1998). 19. S. Choi, Improving Bird’s Antidotes. Australasian Journal of Philosophy 81, 573–580 (2003). 20. S. Choi, Revising the Conditional Analysis of Dispositions (manuscript). 21. W. Malzkorn, Realism, Functionalism and the Conditional Analysis of Dispositions. The Philosophical Quarterly 50, 452–469 (2000). 22. G. Molnar, Are Dispositions Reducible? The Philosophical Quarterly 49, 1–17 (1999) 23. D. Lewis, Finkish Dispositions. The Philosophical Quarterly 47, 143–158 (1997). 24. D. Lewis, Reduction of Mind. In: S. Guttenplan (Ed.), A Companion to the Philosophy of Science. Oxford: Blackwell, 413–431 (1994). 25. H. Mellor, The Semantics and Ontology of Dispositions. Mind 109, 757–780 (2000).

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NATURAL KINDS — WHAT ARE THEY?

˙ JOANNA ODROWA ¸ Z–SYPNIEWSKA Institute of Philosophy University of Warsaw, Poland E-mail: [email protected] The main topic of this paper is Kripke’s and Putnam’s view of natural kinds. After briefly recounting the history of the concept of natural kinds in English-language philosophical literature of which Kripke and Putnam are descendants, I describe the main problems that the Kripke–Putnam conception is facing and present the solutions that have been offered to overcome those problems. Finally I advance a characteristics of natural kinds that is based on Kripke’s and Putnam’s conception but is modified so as to avoid the disadvantages of its predecessor. It is claimed that a kind will count as natural if it (i) is not human-made, (ii) has a complex stereotype and (iii) has an epistemologically hidden essence. In addition a kind that satisfies conditions (i)–(iii) has to comply with a version of Mill’s principle, which is to prevent counting kinds whose members differ only in very few properties, such as cat and white cat, as different natural kinds.

1. Introduction In this paper we will be concerned mainly with Kripke’s and Putnam’s view of natural kinds. Natural kinds, in their conception, are typically kinds of things. The representative examples are kinds of macroobjects from our everyday experience, such as cat, tiger, water, gold, lemon, liquid and acid. Two opposing views on natural kinds may be distinguished. Both can be traced back to John Locke. As is well known, Locke distinguished nominal essences and real essences. Nominal essence is comprised of the superficial properties of objects, whereas real essence pertains to structural, ‘hidden’ properties. For instance, the nominal essence of gold “is that complex idea the word gold stands for, let it be, for instance, a body yellow, of a certain weight, malleable, fusible, and fixed” (Ref. 1, § 2) whereas the real essence of gold is 64

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“the constitution of the insensible parts of that body, on which those qualities and all the other properties of gold depend” (Ref. 1, § 2). Natural kind realism is the essentialist view that says classifications aim to ‘carve nature at its joints’. According to this view classifications are made on the basis of real essences: kinds are real kinds determined by underlying structural properties that determine their distinguishing superficial characteristics. Natural kind nominalism is the view according to which kinds are delimited by their nominal essences. According to Locke, kinds like gold are nominal kinds: the name ‘gold’ is inseparably tied to the nominal essence of gold. Locke considers which of the essences is the basis of the classification of objects into species and claims that it is evident that it is the nominal essence: “the species of things to us are nothing but the ranking them under distinct names, according to the complex ideas in us, and not according to precise, distinct, real essences in them” (Ref. 1, § 8). The main contemporary proponent of this view is John Dupr´e, who writes: “deciding how to sort the phenomena within a domain into kinds is much the same thing as deciding what concepts are to be applied in classifying the relevant domain. This suggest (. . .) that we are dealing with kinds distinguished by a purely nominal essence: to be a member of the kind is just to satisfy the concept that was used in distinguishing the kind.”2 Dupr´e proposes methodological pluralism and promiscuous realism. Methodological pluralism is the view that there are many natural kinds, but these kinds do not have the properties traditionally ascribed to them and they are not metaphysically important. Their ‘essences’ are bare and therefore are not subject to investigation. Moreover ‘natural’ kinds are natural only relative to a specific enquiry. Hence promiscuous realism: “The realism derives from the fact that there are many sameness relations that serve to distinguish classes of organisms in ways that are relevant to various concerns; the promiscuity derives from the fact that none of these relations is privileged”.3

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Muhammad Khalidi defends a similar position and claims that scientists divide up the world relative to their particular interests and it is only to be expected that the kinds that the scientists of various scientific inclinations will come up with will be different and often crosscutting. According to Khalidi, the interest-relativity of kinds is inconsistent with the assumption of their mutual exclusivity. Such an assumption is necessary, however, if one wants to understand kinds metaphysically and investigate their essences. Therefore, the thesis that natural kinds form crosscutting categories is incompatible with essentialism. The fact that classifications depend on the interests of those who make these classifications contradicts the thesis that putting a given object into a given natural kind reveals the (metaphysical) essence of this object. In the dispute between natural-kind realism and natural-kind nominalism Kripke and Putnam side with realism. Ian Hacking gives an account of the tradition of natural kinds in the English-language philosophical literature of which Kripke and Putnam are descendants.4 According to him, the crucial role in the characterisation of natural kinds is played by the notion of induction: natural kinds are those kinds that help us to understand our ability to make inductions. To this natural-kind tradition belong, among others: J.S. Mill, Peirce, Russell and Quine. The most important principles to which they assent are the following: i) Objectivity 1a) Kinds of things, of substances, of organisms, etc. are independent of human beings. 1b) The differences which are the basis for classifications into kinds are made by nature, but the classifications themselves are made by men.a ii) Definability 2a) Natural kinds are definable. We do not have the adequate definition of natural kinds, but we can give its rough and ready characterisation. 2b) Natural kinds may be kinds of various types. iii) Utility 3a) Natural kinds play an important part in the development of a Nota

bene a similar view has been defended by Locke.

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science, but this part diminishes with technological and scientific advances. 3b) For various purposes and interests there are better and worse classifications of things, organisms and interests. There is also a fourth principle, which some of the philosophers in the tradition accepted, but which is rejected by Hacking: iv) Uniqueness There is a unique best taxonomy in terms of natural kinds that represents nature as it is, and reflects the network of causal laws. Out of Mill, Peirce, Russell and Quine, the least demanding as far as natural kinds are concerned is Quine. He has argued that kinds are groups of similar objects. The kind with paradigm a and foil b is the set of all the things to which a is more similar than it is to b. Hence, the class of white objects, the class of cats and the class of white cats will all count as natural kinds. Russell requires more of natural kinds for he writes: “The essence of a ‘natural kind’ is that it is a class of objects all of which possess a number of properties that are not known to be logically interconnected”.5 Hacking notices that, according to this characterisation, both the class of cats and the class of white cats will constitute natural kinds, but neither the class of white objects nor family resemblance classes will. Mill requires of his Real Kinds that they have a large and probably inexhaustible number of common properties. Mill introduces a principle to the effect that if K is a Real Kind and P is a property, and L is a non-empty subset of members of K that have P, then L is a Real Kind only if it has a large and probably inexhaustible set of properties not possessed by members of K that lack P.4 Therefore, cats will constitute a Real Kind, but white cats won’t, for white cats do not possess a large and probably inexhaustible number of properties not possessed by cats with different fur. Peirce proposes the following definition: “Any class which, in addition to its defining character, has another that is of permanent interest and is common and peculiar to its members, is destined to be conserved in that ultimate conception of the universe at which we aim, and is accordingly to be called ‘real’.”6 Peirce’s conception opposes that used by Mill, for it stresses that natural kinds are such that laws of nature account for their properties of permanent interest to people. Mill, on the other hand, regarded kinds whose

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properties “follow as a consequence under laws of nature, from a small number of primary differences” as finite (i.e., not real).7 The important thing that Hacking observes is that Russell’s, Mill’s and Peirce’s conceptions of kinds invite an epistemological distinction. Russell writes about properties which are not known to be connected, Peirce mentions properties that are of permanent interest, while Mill talks about discovering new properties not implied by those that we previously knew (Ref. 4, p. 118). The recent revival in interest in natural kinds has begun with Kripke and Putnam. Their notion of natural kind is akin to Peirce’s. Kripke and Putnam were interested mainly in natural kind terms. Neither of them has formulated a definition of natural kind, but they hinted several times what they mean by ‘natural kinds’ as well as by ‘natural kind terms’. Putnam writes, for example: “the extension of certain kinds of terms (later I was to speak of ‘natural kind words’, meaning names for such things as natural substances, species, and physical magnitudes) is not fixed by a set of criteria laid down in advance but is, in part, fixed by the world” (Ref. 8, p. 71); “it is tempting to say that a natural kind term is simply a term that plays a certain kind of role in scientific or pre-scientific theory: the role, roughly, of pointing to common ‘essential features’ or ‘mechanisms’ beyond and below the obvious distinguishing characteristics” (Ref. 9, p. 141). He also argues that “with any natural understanding of the term ‘property’, it is just false that to say that something belongs to a natural kind is just to ascribe to it a conjunction of properties” (Ref. 9, p. 140). What does the claim that something belongs to a natural kind amount to, then? According to Putnam, to be water is to bear the relation sameL to certain ostended paradigms, where x bears the relation sameL to y just in case (1) x and y are both liquids, and (2) x and y agree in important physical properties. Importance is an interest-relative notion, but usually the important properties of chemical substances are those that are structurally important, i.e., those “that specify what the liquid or solid, etc., is ultimately made out of — elementary particles, or hydrogen and oxygen, or earth, air, fire, water, or whatever — and how they are arranged or

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combined to produce the superficial characteristics” (Ref. 10, p. 238–239). The grounding of a natural kind term consists of two elements: ostension (i.e., pointing to certain samples) and stipulation that the newly introduced term is to refer to all and only objects that bear the same kind relation to the ostended samples. Being of the same kind is a theoretical relation and it is the appropriate scientists that have to establish what it consist in for every given case. However, Putnam frequently stresses the importance of structural properties and suggests that for chemical kinds (such as water) this relation consists in having the same chemical composition, and for biological kinds (such as lemon) it consists in having the same genome. 2. The Problems with the Kripke–Putnam Account of Natural Kinds The Kripke–Putnam conception has come in for a lot of criticism. The most important problems that arise for their account are the following: i) The qua problem and the problem of the hierarchical order of natural kinds ii) The problem of isotopes and allotropes iii) The problem of impurities iv) The problem of the underestimation of the role of decisions in fixing the reference of natural kind terms v) The problem with defining chemical structure vi) The problem of the underestimation of the role of superficial properties in delimiting natural kinds vii) The problem concerning the fact that essences of biological kinds are relational and historical in character viii) The problem of the alleged role of structural properties in explaining the superficial characteristics of natural kind members ix) The problem of defining objective laws spoken of by Putnam x) The problem of the tension between the postulated explanatory value of natural kinds and their supposed objectivity xi) The problem of the relation between manifest kinds and chemical kinds (i)–(iv) are problems for the Kripke–Putnam account of natural kind terms, while (v)–(xi) endanger mainly their conception of natural kinds. (i) The qua problem is probably the best known problem for any account of natural kinds and natural kind terms similar to Putnam’s. Already Locke

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argued that a given particular belongs to many different kinds and pointing to that particular does not determine which kind has been pointed to. Kripke writes: “The original concept of cat is: that kind of thing, where the kind can be identified by paradigmatic instances” (Ref. 11, p. 122). The problem is, however, that paradigmatic instances of the kind cat are also paradigmatic instances of the kinds animal, mammal, vertebrae, furry animal, domestic animal, source of food etc. The fixing of the reference of a term T by mere pointing to samples and declaring that T is to refer to all and only objects that are of the same kind as the majority of ostended samples leaves the reference indeterminate. The problem of the hierarchy of natural kinds is a special type of the qua problem. It arises because natural kinds are arranged in a hierarchy. For instance, in biology species are subsumed under genera, genera under families, families under orders, and so on. This problem shows that even if we were dealing with natural kinds only, the problem of the indeterminacy of reference would still arise. Supplying several paradigms instead of one may narrow the range of eligible kinds, but in general it is not sufficient to narrow the range down to one. Pointing to foils may help even further, but certain indeterminacy will still remain. (ii) A related problem is the problem of isotopes and allotropes. On Earth gold naturally occurs in the form of only one isotope. We use the term ‘gold’ to refer to the element with atomic number 79 and isotope number Au-197. Now, imagine that another isotope of the element with atomic number 79 is discovered. It seems that the rules governing our use of the term ‘gold’ are not specific enough to determine whether something that has the same atomic number as gold of our experience, but differs in isotope number should be called ‘gold’. A similar problem is caused by the fact that some elements occur in the form of various allotropes. Allotropes are different crystalline structures of pure elemental substances.b For instance, the element carbon has several different allotropes, the best known being diamond and graphite. If someone pointed to several samples of diamond and declared that the term ‘diamond’ is to refer to all and only objects bA

similar problem arises for compounds. Compounds can stand to one another as isomers — i.e., substances with the same composition but different chemical and physical properties. In general composition provides only a necessary condition for sameness of kind (substances of different composition cannot be the same substance, but substances of the same composition may be different substances (different isomers). (See Ref. 12, p. 212).

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that have the same chemical structure as the samples, then graphite would also be a diamond. If we want ‘gold’ to apply to all forms of the element with atomic number 79, and ‘diamond’ to refer only to the element with atomic number 6 and a particular form, then we have to assume that in case of diamond the grounders had a very particular structure in mind, whereas in case of gold the structure has been less particularly specified. The problem is, however, that the grounders of the terms ‘gold’ and ‘diamond’ knew nothing about chemical structures and, therefore, could not make the adequate stipulations. (iii) A separate problem is the problem of impurities. The problem arises from the fact that natural kinds usually occur on Earth in impure form. The samples of water contain not only H2 O but also D2 O, H2 O2 , salt and other minerals. Pointing to water samples and declaring that the term ‘water’ is to refer to all and only substances that are of the same kind as the samples leaves it indeterminate whether ‘water’ applies to pure H2 O or to H2 O with impurities. If we decide that ‘water’ should apply only to pure samples of H2 O, then it would be a predicate that has no naturally occurring samples in its extension. On the other hand, if we declare that it should apply to both pure and impure samples, then we will have trouble explaining why, for instance, tomatoes, tea and coffee are not water. Another problem arises for kinds that differ only by impurities. Ruby and sapphire are two varieties of the compound alumina. They differ in colour (rubies are red while sapphires are blue), which is due entirely to impurities. Someone who intended to name rubies and declared that the term ‘ruby’ is to refer to all and only solids that are of the same kind as the samples, would end up naming sapphires as well as rubies. (iv) Keith Donnellan constructs a thought experiment which is to demonstrate that — contrary to what Putnam has argued — “nature (. . .) does not fully determine the extension of vernacular natural kind terms, and science is not wholly responsible for discovering their true extensions” (Ref. 13, p. 104). He assumes that on Earth as well as on Twin Earth gold occurs in the form of a single isotope. Before the discovery of the atomic structure of gold, the reference of the term ‘gold’ was the same on each planet. It is possible however that after such a discovery, the extensions of ‘gold’ on Earth and on Twin Earth will cease to coincide. Twin-Earthlings may decide that isotope number is more important than atomic number and in consequence identify gold with a certain isotope having a certain isotope number. On the other hand, Earthlings may regard atomic number as more important and rule that gold is to be identified with the element

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having atomic number 79. Once such decisions are taken, the truth-value of certain statements will be different on Earth and on Twin Earth. For instance, statements ‘Some gold has isotope number x and some gold has isotope number y’ will be deemed true by Earthlings and false by TwinEarthlings. It seems that Putnam was wrong when he claimed that scientific discoveries concerning the important physical properties of members of natural kinds do not change the extension of natural kind terms. In the thought experiment described, after the isotopes of gold were discovered, scientists have had to make a decision which number is to be regarded as crucial for the definition of gold: the atomic number or the isotope number. If the scientists chose the latter, the extension of ‘gold’ would be modified. Chenyang Li, in similar spirit, notices that the process of naming is not finalised with pointing out the samples. The initial ostensive definition has to be supplemented by decisions that would further specify the kind named. Moreover, that process is never finalised. It is always possible that we encounter a specimen that forces us to further delimit the extension of a natural kind term (and hence the ‘borders’ of a relevant natural kind). (Ref. 14; cf. here also Ref. 15). (v) Putnam argues that being of the kind water consists in being H2 O. However, Jaap van Brakel and Paul Needham argue that it is unclear what ‘Water is H2 O’ means. Contrary to what Putnam suggests, ‘H2 O’ does not describe the microstructure of water. What it describes is (at best) the composition of water. Needham notices that we know only certain aspects of the microstructure of water and “whereas the composition of water was settled long ago, any talk of having discovered the microstructure of water would be premature” (Ref. 12, p. 207). Moreover, specification of the chemical composition does not suffice to determine the identity of a substance, for substances with the same composition may be different substances.c In philosophical texts it is often assumed that ‘Water is H2 O’ says something about the molecular structure of water. On this interpretation ‘H2 O’ refers to molecules consisting of two hydrogen and one oxygen atom, and ‘Water is H2 O’ means that water consists only of such molecules. Van Brakel points out, however, that on such a reading ‘Water is H2 O’ is simply false: liquid water contains not only H2 O molecules, but also H4 O6 and ions OH− and H3 O+ , while in ice it is not possible to identify individual H2 O molecules (Ref. 16, p. 299). c See

fn. b.

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If we assume that ‘Water is H2 O’ is false or only approximately true, then — according to van Brakel — we have two ways out. We can either modify (1) so that it becomes true, or we can reject (1) and substitute for it another statement that would determine what being water consists in. Putnam chooses the former and modifies (1) so that it becomes “Water is a quantum-mechanical superposition of H2 O, H4 O2 , H6 O3 . . . plus D2 O, D4 O2 . . .” or “Water is similar in composition to H2 O” (Ref. 17, p. 63). Van Brakel notices however, that it is difficult to claim that either of these statements gives the essence of water. He himself chooses the latter solution and replaces (1) with statements like ‘Water boils at 100◦ C’d or ‘Water has an index of refraction of 1.33299’. He argues that such statements are a posteriori, are used to fix the reference, and give operational meaning to such relations as ‘being the same liquid as’. In his view the explanation of the ‘being the same liquid as’ relation does not have to appeal to structural properties of water. On the contrary, this relation can be explained in terms of macroscopic properties such as density and boiling temperature. However, replacing (1) with any of the above statements leaves no trace of Putnam’s “‘intuitive’ idea that we should discover the ‘objective essence’, the ‘fundamental structure’, or the ‘underlying trait’ that yields the ‘ultimate explanation’ ” (Ref. 16, p. 304). (vi) According to D. H. Mellor, the source of the view that in all possible worlds water is H2 O, is the Quinian idea that only those objects exist to which our scientific theories refer. A way of eliminating macroobjects from our ontology is the microreduction — i.e., the reduction of the properties of macroobjects to the properties of their parts. The properties of water can then be reduced to the properties of H2 O. Mellor stresses, however, that such a reduction requires deducibility. If some properties of macroobjects are not deducible from the properties of molecules and relations among them, then reference to things of the kind is still needed. On the other hand, if all macroproperties are deducible, then in all possible worlds in which the macroproperties occur, the microstructure occurs as well. In such a case the macroproperties will be as essential as microproperties. Mellor concludes: “So-called ‘essential’ properties are thus no more essential than any other shared properties of a kind. They are just properties ascribed d Neither

Putnam nor Kripke would agree with such a replacement. According to Kripke statements ‘Water is H2 O’ and ‘Water boils at 100◦ C’ have a different status: the former is necessary a posteriori, while the latter is contingent a priori.

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by the primitive predicates in a comprehensive deductive theory of a kind” (Ref. 18, p. 311). and primitive predicates may cease to be primitive when the present theory is replaced by a more exact one. Also Needham argues that microproperties of water are no more essential than its other properties. If we assume that water is necessarily H2 O, then it will necessarily have its characteristic density, it will necessarily freeze at 0◦ C under normal atmospheric pressure, etc. Hence, Needham claims that “The distinction between macro- and microfeatures doesn’t coincide with accidental and necessary ones” (Ref. 19, p. 21). Thomas Kuhn also argues that superficial properties of water are as essential as the hidden ones: “The so-called superficial properties are no less necessary than their apparent essential successors. To say that water is liquid H2 O is to locate it within an elaborate lexical and theoretical system. Given that system, as one must be in order to use the label, one can in principle predict the superficial properties of water (. . .), compute its boiling and freezing points, the optical wavelengths that it will transmit, and so on. If water is liquid H2 O, then these properties are necessary to it. If they were not realised in practice, that would be a reason to doubt that water really was H2 O” (Ref. 20, p. 312–313). Alexander Bird points out, however, that the system which Kuhn is talking about need not be so complex and complicated. Berzelius announced at the beginning of the nineteenth century that water is H2 O, but he could not make most of the calculations mentioned by Kuhn. Moreover, Bird notices that the claim that superficial properties of water are necessary would be more plausible, if the relevant laws of nature, which are used in calculating water’s boiling and freezing points, were themselves necessary. Yet most philosophers of science think that these laws are contingent. It may be that contingent laws of nature support necessary properties, but such a possibility is highly contentious and has yet to be investigated.21 – 23 It should also be remembered that not all necessary properties are essential (See e.g., Ref. 24). Hence, even those philosophers who regard laws of nature as necessary may not equate superficial and hidden properties.

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They may treat the former as necessary but not essential, and the latter as both necessary and essential. It seems to me that even Kripke could agree with such a view, for he recognises that certain non-structural properties may be necessary properties of gold: “to the extent that such properties [as colour and metallic properties] follow from the atomic structure of gold, they are necessary properties of it” (Ref. 25, p. 104). Kripke would not agree, however, that these properties are equally important. According to him the property of having atomic number 79 differs from other necessary properties of gold in that it is fundamental to being gold (See Ref. 25, p. 104). McGinn argues that according to Kripke the structural properties of gold are its fundamental primary properties, which explain secondary properties such as malleability, conductivity, and so on.26 (vii) The importance of structural properties for natural kinds has been questioned also in case of biological kinds. Samir Okasha notices that the essence of biological natural kinds is relational — i.e., not intrinsic.e In current biology there is no unique agreed-upon definition of species, but on each of the viable conceptions the essence of species is either relational (e.g., interbreeding conception, ecological conception) or both relational and historical (phylogenetic conception). On neither of these conceptions are the structural properties decisive as far as species-membership is concerned. For instance, on the interbreeding concept of species the property in virtue of which a particular organism belongs to a particular species is ‘being able to reproduce successfully with one group of organisms and not another’ and on the phylogenetic conception the relevant property is ‘being a member of a particular segment of the genealogical nexus’ (Ref. 27, p. 201). The existence of sibling species (i.e., species that are morphologically indistinguishable but treated as distinct because they form separate reproductive communities) and polytipic species (i.e., species that contain phenotypically different organisms that interbreed freely), intra-specific genetic variation and inter-specific genetic similarity all show that neither on the interbreeding nor on the phylogenetic conception is the essence of species structural. Phenetic and ecological conceptions are even worse in this respect. e Thus,

someone who insists that essences can consist merely of intrinsic properties has to admit that species have no essences.

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A separate problem is that according to current biological conceptions of species, belonging to a particular species is not essential to its members. This constitutes a problem for Kripke, who argued that being a table is essential to any given table, so presumably he would also claim that being a tiger is essential to tigers. It is also troublesome for the proponents of the view according to which natural kind terms are rigid appliers (or essential predicates). On such a view a given natural kind term is a rigid applier iff it is such that if it applies to an object in any possible world, then it applies to that object in every possible world in which the object exists.28 If belonging to a particular species is not essential for organisms, then an organism x, which in the actual world w belongs to species S, in the world w1 may exist and belong to species S’. In such a case the predicate ‘S’ would not be rigid. If one thinks that being rigid is constitutive of natural kind terms, then names of biological kinds would not be natural kind terms and biological kinds themselves would not be natural kinds. Excluding biological kinds from among natural kinds is a considerable weakening of the natural kind theory, for kinds such as tiger and lemon are usually considered flagship natural kinds. The problem of kind essences that are not individual essences is not a problem for Putnam, since he does not ascribe to the rigid appliers view and he explicitly rejects claims about individual essences (Ref. 17, p. 64n). Hence, the claim that essences are relational is not devastating for Putnam and he can accommodate it within his theory, providing that he allows that relational properties may count as ‘important physical properties’. (viii) Putnam remarks that natural kinds are “classes of things that we regard as of explanatory importance; classes whose normal distinguishing characteristics are ‘held together’ or even explained by deep-lying mechanisms” (Ref. 9, p. 139). For such a view the fact that kind essences may not be individual essences is not a problem. What is problematic though, is that it is hard to imagine how historical and relational properties could explain the distinguishing superficial properties of typical members of natural kinds. For instance, being able to interbreed freely with tigers is hardly a reason why tigers are large, carnivorous, feline, brownish in colour, have a white belly and transverse black stripes. Okasha writes that Kripke and Putnam were half-right: relational properties that replace Putnamian ‘hidden structures’ are able to play the semantic role of fixing the reference of natural kind

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terms, but they are unable to play the causal/explanatory role of causally explaining the presence of superficial characteristics. Okasha does not regard this as a major blow for Putnam’s theory and claims that “there is no reason at all why the same thing should play both roles” (Ref. 27, p. 204). It seems to me that the problem is more severe than this, however. Putnam has argued that when we point to paradigmatic members of natural kinds we are in fact pointing to their hidden natures and it is those natures that determine the ‘borders’ of natural kinds. In using natural kind terms people are guided by distinguishing characteristics of typical members, but the crucial role in fixing the reference of those terms is played by “‘essential features’ or ‘mechanisms’ beyond and below” these characteristics (Ref. 9, p. 141). If we assume that the ‘mechanisms’ are causally responsible for the characteristics, then the view is quite plausible. If we argue, however, that the characteristics are due to certain features that particular organisms have and are not due to the ‘mechanisms’, then the view immediately looses its apparent plausibility. Someone who thinks that ‘hidden structures’ determine the reference of natural kind terms but does not think that they are casually responsible for the superficial properties, faces the following problem: if the distinguishing characteristics of individual tigers are not causally linked to tigers’ ‘hidden nature’ then it is hard to explain why superficial characteristics are — in most cases — reliable. If such characteristics are caused by individual natures, which have nothing to do with kind essences, then one has to explain the far reaching convergence. (ix) Putnam argues that “There are objective laws obeyed by multiple sclerosis, by gold, by horses, by electricity; and what is rational to include in these classes will depend on what those laws turn out to be” (Ref. 8, p. 71). Van Brakel and Igor Douven notice however that objective laws, to which Putnam appeals, are unable to determine the ‘borders’ of natural kinds. First of all, almost any class obeys a certain objective law. Van Brakel and Douven give the example of the kind vovetas recognised by Cheyenne. This kind comprise the kind vulture, some hawks, some types of insect swarms, and tornadoes. Such a kind may seem completely unnatural to us, but its members do obey the same objective law: every member of this class exhibits in normal circumstances a circular vortex-like motion (Ref. 29, p. 62). In order to avoid treating virtually any kind as natural, one would have to somehow restrict the laws that may count as objective.

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One way would be to require that objective laws are laws of nature. However, the problem is that the notion of a law of nature is almost as vague as the notion of a natural kind. Alternatively, one could restrict objective laws to the laws of physics. Van Brakel and Douven point out, however, that the laws of physics do not tell anything about multiple sclerosis and horses.f Moreover, they notice that Putnam himself argued that the laws of the special sciences could not be reduced to the laws of physics. Hence, objective laws that determine the extensions of natural kinds should include not only the laws of physics, but also the laws of chemistry, the laws of psychology, biology, etc. If one does not want to be forced to treat all kinds as natural, one would have to propose a criterion that would distinguish ‘good’ scientific laws from other laws. Such a criterion is missing and each attempt to find one will depend on the interests and values recognised by a particular scientist who is conducting the research. Paul Churchland proposes to treat as natural those kinds which obey genuine natural laws understood as purely logical consequences of basic laws of nature (Ref. 30, p. 9). As a result natural kinds will be very few and the kinds which traditionally are regarded as natural will loose their status. For Churchland natural kinds comprise mass, length, duration, charge, energy, momentum, and so on.g Van Brakel remarks that if one wants to apply scientific criteria only, one will be left with kinds such as quarks, whereas if one allows more classifications, then each of these classifications will bring its own ways of determining essences: Either we allow kinds like (. . .) vovetas to be natural kinds, having projectible properties, essences, or whatever else goes with being a natural kind. Or, if we want to deny (. . .) vovetas this status, we’re pushed all the way down the path to hard reductionism” (Ref. 32, p. 256). f Douven

and van Brakel remark: “Of course, the laws of physics do in some sense determine the behaviour of horses, diseases, etcetera — every horse ‘can be represented by a wave function and a Hamiltonian’ — but in that sense they determine the behaviour of absolutely anything, quite apart from how things are classified into natural and other kinds” (Ref. 29, p. 65). g Strictly speaking such kinds are natural provided that world is not an explanatory onion with an infinite number of concentric explanatory skins. If the world is like this, then there are no basic laws, and hence no natural kinds. All kinds are merely practical, distinguished mainly for practical reasons (Ref. 30, p. 14). Ronald De Sousa notices moreover that if we assume that natural kinds are kinds of molecules at the basic physical level, then we will have to admit that on this level everything can conceivably be transmuted into everything else.31 Such a conclusion contradict common (as well as Putnam’s) intuitions concerning natural kinds.

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(x) I have already mentioned that Putnam thinks that natural kinds are classes that we regard as of explanatory importance. Mark Platts also alludes to the explanatory value of natural kinds and writes that ‘important physical properties’ spoken of by Putnam are those important for explanatory purposes. According to him the initial idea of a natural kind is that “there be explanations, of law-based kind, which serve to account for the nature of each member of that [kind] but which do not so serve for any other object” (Ref. 33, p. 134). Natural kind classifications are closely connected to explanation. When we encounter members of natural kinds we assume that there is a law-based theory that explains why those members possess certain characteristic properties. We distinguish natural kinds of different taxonomic levels, because there is a tension between two explanatory desiderata: the maximisation of potential explanatory range and the maximisation of potential explanatory power. Distinguishing fruit as a natural kind has narrow potential explanatory power, but large potential explanatory range, whereas in distinguishing lemon as a natural kind the narrowing of potential explanatory range is accompanied by great potential explanatory power (Ref. 33, p. 137). Explanation is clearly an interestrelative notion. The worth of explanation depends in part on pragmatic considerations. Hence, natural kind classifications do not merely mirror the natural order of things. They reflect our interest in law-based explanation: “our natural kind classifications are as interestingly informative about ourselves as about the natural order of things” (Ref. 33, p. 148). The explanatory-value criterion makes ‘naturalness’ of kinds dependent on the current state of science. Changes of standards and changes of scientific explanations will have to be accompanied by changes in ‘natural’ kinds. ‘Natural’ kinds become scientific kinds, where ‘scientific’ means having scientific (i.e., explanatory) value. De Sousa writes: “Virtually any kind can be termed ‘natural’ relative to some set of interests and epistemic priorities. Science determines those priorities at any particular stage of its progress, and what kinds are most ‘natural’ in that sense is always a real and lively scientific question” (Ref. 31, p. 561). (xi) When Putnam argues that the ‘hidden essence’ of natural kinds is constituted by their microstructural properties, he seems to be suggesting that manifest kinds (such as water) are identical to chemical kinds (such as H2 O). This claim has been contested, e.g., by Avrum Stroll, Mark Johnston, Helen Steward and David Barnett.34 – 37 Both Stroll and Johnston

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point out that manifest kinds usually are — and chemical kinds usually are not — phase-sensitive. H2 O can be in liquid, solid or gaseous condition, whereas ‘water’ (as typically used) refers merely to liquid H2 O. If we assume that water is H2 O, then we will have to agree that ice/water vapour/snow is also H2 O, and next we will be forced to admit that water is ice/water vapour/snow.h Steward argues that while it is conceivable that H2 O constitutes pink solids, it is not conceivable that water does. Barnett has a similar argument to the effect that H2 O in principle could — while water could not — occur in the form of poisonous mushrooms. All of these arguments point out that there is more to a common natural kind than its chemical structure. 3. Taking Stock It has been argued that problems (i)–(iv) may be resolved by taking into account the role that identifying properties play in determining the reference of natural kind terms. Once we admit that distinguishing superficial characteristics play an important role in the process of reference-fixing, the problem of the indeterminacy of reference caused by the qua problem, the problem of isotopes and allotropes and the problem of impurities will become less serious. The trouble is how to do this without admitting that natural kinds are nominal kinds after all. Such an account has been offered, e.g., by Kim Sterelny, by Philip Kitcher and P. K. Stanford, and by Jessica Brown.38 – 40 Moreover, it might be argued that the recognition of the role played by identifying properties accords well with Putnam’s original view.i After all, he wrote that the important properties of kinds are those that list the ultimate elements and specify “how they are arranged or combined to produce the superficial characteristics” (Ref. 10, p. 239). In this quote it is clear that structural properties are important in so far as they explain the relevant superficial features. Unfortunately, the problems (i)–(iv) are the only problems that can be resolved. Other problems have to be acknowledged and the account of natural kinds has to be modified so as to accommodate their consequences. One has to admit that Donnellan and Li are right in claiming that natural hA

similar argument showing that manifest kinds are and chemical kinds are not allotrope-sensitive concerns carbon, diamond and graphite: if diamond = carbon and graphite = carbon, then we get the unwanted diamond = graphite. See Ref. 35, p. 565. i For the opposite view, see e.g., Ref. 41, p. 157.

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kind terms are indeterminate and in order to reduce this indeterminacy suitable decisions have to taken. One should not quarrel with van Brakel, Douven and Needham and ought to agree that the formula ‘H2 O’ does not specify the microstructure of water. One ought to recognise that it is not always the real essences that determine membership in natural kinds. If one wants to treat biological kinds as natural, one has to come to terms with the idea of relational essences of kinds that do not causally explain the distinguishing characteristics of the members of those kinds. One should also admit that natural kinds are not entirely objective in the sense that while natural kind classifications do reflect the natural order of things, they are still of our own making.j 4. Natural Kinds — What are they? In this section we will attempt to offer a characterisation of a natural kind. Our objective is to define natural kinds of the sort the Kripke–Putnam account was mainly concerned with. We will try, however, to take into account the observations made in previous sections. Khalidi notices that kinds may be natural and artificial in more than one way. Firstly, one may think that those categories are natural which are innate (up/down) and not acquired by learning (democracy/authoritarianism). Secondly, one may regard as natural those categories that are theoretically based (vertebrate/invertebrate) and not ad hoc (under 1 kg/over 1 kg). Thirdly, one may take natural categories to be those that pertain to natural phenomena (plant/animal) and not to social institutions (legal/illegal). Fourthly, one may take it into consideration whether a category is lexicalised in natural language (blue/red) or requires a compound linguistic expression (red-and-round/blue-and-square). Fifthly, one may consider as natural those categories that are projectible (green/blue) and treat such categories that are non-projectible (grue/bleen) as artificial. Finally, natural categories may be regarded as those that are not crosscutting, and crosscutting categories may be treated as unnatural.43 For us the important senses will be the second and the third. Furthermore, we may agree that not having a semantically simple name in natural language may be regarded as a (fallible) indication that the kind named is not natural. The distinction between categories that are innate and those that are acquired by learning is very unclear and moreover, all kinds in j Putnam

admitted this in his later paper, Ref. 42.

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which we are interested seem to be acquired by learning. We have already seen that projectibility is not a good criterion for being a natural kind. Since we assume that classifications are made by people (even though they are intended to mirror natural divisions) our natural kinds may crosscut. We assume that a necessary condition for a kind to be natural is that it is not human-made. It may have human-made members (cf. kind sponge, diamond or quartz), but the kind itself (i.e., its paradigmatic samples) must be made by nature. Moreover, following Mill, we will assume that typical (maturek ) members of a natural kind must have a great number of properties in common. The set of all shared properties of typical (mature) members of a kind may be called the ‘stereotype’.l The lesson we have learned from Putnam is that the stereotype does not determine the extension of the relevant natural kind term. One can say at most that if the property P belongs to the stereotype of T, then if x is a typical T, then x has P. In addition, following Peirce and Putnam, we take it that to be natural a kind must have a ‘hidden mechanism’ that decides the membership in this kind.m The claim that such ‘mechanism’ is hidden should be understood epistemologically. The fourth requirement is that a kind that 1) is not human-made, 2) has a complex stereotype and 3) has a ‘hidden essence’, has to comply with a version of Mill’s principle, according to which if K is a kind that fulfils conditions 1–3 and P is a property, and L is a non-empty subset of members of K that have P, then L is a natural kind only if it fulfils conditions 1–3 and has a large and probably inexhaustible set of properties not possessed by members of K that lack P. The most controversial is condition 3. If one wants — following Putnam — to treat acid, liquid and hypothetical water devoid of important structural properties as natural kinds, then one should reject this condition. However, if one wants — also following Putnam — to claim that the main function of natural kind terms is to point to “common ‘essential features’ or ‘mechanisms’ beyond and below the obvious distinguishing characteristics”, then condition 3 becomes crucial. For if it were not for this condition, jade would be counted as a natural kind. We do not agree with van Brakel’s conclusion that either ‘all kinds are natural’ or ‘only kinds of fundamental particles are natural’. We are k The

maturity of members is important only in case of biological kinds. our stereotype is different from Putnam’s in that it has to be adequate and it need not be a part of individual speaker’s competence. m Notice however that we do not require that ‘hidden’ properties explain the superficial characteristics. l However,

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particularly interested in those natural kind terms that have been a part of natural language long before modern science has been developed. Kinds such as tiger, gold or lemon are kinds whose members we encounter in our everyday life and whose superficial properties and behaviour we had known long before we learned about their criteria for kind-membership. Since it is probably the observation of typical examples that has been the reason for naming such natural kinds, making being a natural kind conditional upon the number of shared properties of typical (mature) members seems legitimate. The pre-scientific origin of the majority of natural kinds also justifies the assumption that a natural kind should possess hidden fundamental features which determine what is a member of that kind. The first condition says that kinds are not human-made. It follows from this that we do not originally know anything about such kinds and we have to gain knowledge by empirical means. In particular, the discovery which properties are essential to a given kind must be empirical. Therefore, the essence of natural kinds is hidden both from lay-people and from experts. It has to be discovered by empirical investigations. The claim that the essence is hidden does not amount to the claim that all essential features must be hidden. As a result of empirical discovery it may turn out that some superficial (or even relational) features are essential to the given kind. The question arises, however, whether a kind whose members have only distinguishing characteristics in common should be regarded as natural. In other words, the question is whether a kind which is made by nature, whose typical members have many properties in common, which complies to our version of Mill’s principle, but whose members share only distinguishing characteristics is a natural kind. It seems to me that the existence of such a kind is very unlikely, but if there were such a kind it should not be called ‘natural’. Putnam’s remark to the effect that natural kinds should share ‘important physical properties’ is very important. We should modify it slightly however: ignore the word ‘physical’ and replace it with ‘scientific’. I have already mentioned that importance is an interest-relative notion and depends on the interests of scientists, but we may assume that the important properties are properties that are important from the point of view of science. The shared essential properties should be scientifically important. What science regards as important, however, changes as science develops. Nevertheless, it seems that scientists would not now say that the objects that have only distinguishing characteristics in common share ‘important scientific properties’.

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The term ‘natural kind’ defined in points 1–4 is of course vague and admits of degrees. Especially condition 2, which mentions a very large number of shared properties blurs the borders of the extension of that term. However, with certain kinds there is no doubt that they are natural kinds (e.g., tiger, lemon, gold) and with certain other kinds it is obvious that they are not natural (e.g., green product of nature is not a natural kind, because its stereotype ‘is green and is produced by nature’ is not very complex). About other kinds we may say that they are more natural than others (the kind larch is more natural than the kind coniferous tree). It is obvious that natural kind classification is to some degree dependent on our interests. The external world plays a part in delimiting natural kinds, but humankind has much room for manoeuvre. Acknowledgments I’d like to thank the members of the Metaphysics of Science Group, especially Helen Beebee, Alexander Bird, Paul Noordhof and Samir Okasha for valuable comments and suggestions. References 1. J. Locke, An Essay Concerning Human Understanding, III, 6 (1690). 2. J. Dupr´e, Is ‘natural kind’ a natural kind term? The Monist 85, 45 (2002). 3. J. Dupr´e, Natural kinds and biological taxa. The Philosophical Review 90, 82 (1981). 4. I. Hacking, A tradition of natural kinds. Philosophical Studies 61, 109–126 (1991). 5. B. Russell, Human knowledge: its scope and limits. London: Allen and Unwin, 335 (1948). 6. C.S. Peirce, Kind. In: J. M. Baldwin (Ed.), Dictionary of philosophy and psychology. New York: Ginn, 601 (1911). 7. J.S. Mill, A System of Logic. In: J. M. Robson (Ed.), Collected Works of John Stuart Mill. Toronto: University of Toronto Press, 122 (1974). 8. H. Putnam, Reference and truth. In: H. Putnam, Realism and reason. Cambridge: Cambridge University Press (1983). 9. H. Putnam, Is semantics possible? In: H. Putnam, Mind, language and reality. Cambridge: Cambridge University Press (1975). 10. H. Putnam, The meaning of ‘meaning’. In: H. Putnam, Mind, language and reality. Cambridge: Cambridge University Press (1975). 11. S. Kripke, Naming and necessity. Oxford: Basil Blackwell, 125 (1980). 12. P. Needham, The discovery that water is H2 O. International Studies in the Philosophy of Science 16, 212 (2002).

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13. K. Donnellan, Kripke and Putnam on natural kinds. In: C. Ginet and S. Schoemaker (Eds.), Knowledge and mind. Philosophical essays. Oxford: Oxford University Press (1983). 14. C. Li, Natural kinds: direct reference, realism and the impossibility of necessary a posteriori truth. The Review of Metaphysics 47, 270 (1993). 15. F. Waismann, Verifiability. Aristotelian Society (supp. vol.) 19, 119–150 (1945). 16. J. Van Brakel, The chemistry of substances and the philosophy of mass terms, Synthese 69 (1986). 17. H. Putnam, Possibility and necessity. In: H. Putnam, Realism and reason. Cambridge: Cambridge University Press (1983). 18. D.H. Mellor, Natural kinds. British Journal for The Philosophy of Science 28 (1977). 19. P. Needham, What is water? Analysis 60 (2000). 20. T. Kuhn, Dubbing and redubbing: the vulnerability of rigid designation. In: C. Wade Savage (Ed.), Scientific theories, Minnesota Studies in the Philosophy of Science 14. Minneapolis (1990). 21. A. Bird, Kuhn on reference and essence. Philosophia Scientiae 8, 89 (2004). 22. A. Bird, Necessarily, salt dissolves in water. Analysis 61, 267–274 (2001). 23. A. Bird, On whether some laws are necessary. Analysis 62, 257–270 (2002). 24. K. Fine, Essence and modality. Philosophical Perspectives 8, 1–16 (1994). 25. A. Bird, Natural kinds. In: A. Bird, Philosophy of science. London: University College London Press (1998). 26. C. McGinn, A note on the essence of natural kinds. Analysis 35, 177–183 (1975). 27. S. Okasha, Darwinian metaphysics: species and the question of essentialism. Synthese 131 (2002). 28. M. Devitt, Rigid application. Philosophical Studies 125, 146 (2005). 29. I. Douven and J. van Brakel, Can the world help us in fixing the reference of natural kind terms. Journal for General Philosophy of Science 29, 62 (1998). 30. P. Churchland, Conceptual progress and word/world relations: in search of the essence of natural kind terms. Canadian Journal of Philosophy 15 (1985). 31. R. De Sousa, The natural shiftiness of natural kinds. The Canadian Journal of Philosophy 14, 572 (1984). 32. J. Van Brakel, Natural kinds and manifest forms of life. Dialectica 46, 256 (1992). 33. P. Platts, Explanatory kinds. British Journal for the Philosophy of Science 34 (1983). 34. A. Stroll, What water is or back to Tales. Midwest Studies in Philosophy 14, 258–274 (1989). 35. M. Johnston, Manifest kinds. Journal of Philosophy 94, 564–83 (1997). 36. H. Steward, Identity statements and the necessary a posteriori. Journal of Philosophy 87, 385–98 (1990). 37. D. Barnett, Is water necessarily identical to H2 O? Philosophical Studies 98, 99–112 (2000).

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38. K. Sterelny, Natural kind terms. Pacific Philosophical Quarterly 64, 110–125 (1983). 39. P. Kitcher and P.K. Stanford, Refining the causal theory of reference. Philosophical Studies 97, 99–129 (2000). 40. J. Brown, Natural kind terms and recognitional capacities. Mind 107, 275–303 (1998). 41. B.-Y. Hanoch, The semantics of kind terms. Philosophical Studies 102, 157 (2001). 42. H. Putnam, Is it necessary that water is H2 O? In: L.E. Hahn (Ed.), The philosophy of A. J. Ayer. Chicago, Illinois: Open Court Publishing Company, 429–454 (1992). 43. M. Khalidi, Natural kinds and crosscutting categories. Journal of Philosophy 95, 33 (1998).

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PERSONAL IDENTITY, CONCEPTUAL ANALYSIS AND NO-FAULT DISAGREEMENT

CAROLINE WEST Department of Philosophy University of Sydney, Australia E-mail: [email protected]

The personal identity debate seems to have reached an impasse. There appear to be (at least) two different families of candidate meanings for our person talk, corresponding to each of the main theories of personal identity; and it does not seem that either way of speaking is demonstrably mistaken, or irrational, or in clear violation of firm a priori constraints governing use of the term ‘person’ and its cognates. This threatens to make debate over the nature of personal identity look merely semantic — simply a dispute about how everyone should use the words. Yet this is very hard to believe. Making progress requires showing how what is at issue in the debate is more than merely terminological. I offer some suggestions as to where progress might lie.

1. Introduction For more than a century the personal identity debate has been dominated by a battle between various theories, typically presented as rival and mutually exclusive conceptual analyses. According to the psychological continuity theory, x at an earlier time, t, and y at a later time, t0 , are stages of the same person if and only if they stand to each other in certain psychological relations, such as those of memory, projects, values and character.a According to the bodily continuity theory, x at t and y at t0 are stages of the same person if and only if y stands to x in certain bodily relations — for example, if and only if y has the same functioning brain and/or body as x, or if and only if x and y are each stages of the same human animal.b While the duel between bodily and psychological continuity theories has a Prominent

defenders of a psychological continuity theory include Lewis,1 Noonan,2 Perry,4 Rovane5 and Shoemaker.6 b Well-known defenders of a bodily continuity theory include Wiggins, 7 Williams,8 Thomson,9 Olson,10 Snowdon11 and van Inwagen.12 Parfit,3

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dominated the contemporary debate, it is important to note that there are also significant in-house disagreements within each of these broad camps as to precisely which of the various kinds of psychological or bodily relations are most central.c In addition, various ‘mixed’ or hybrid theories have been proposed.d Mixed theories hold that both bodily and psychological continuity are necessary, and jointly sufficient, for a person’s continued existence over time. There are other views that do not fall into any of these three camps. While it has largely fallen out of favour among contemporary naturalistically inclined philosophers, some philosophers continue to defend the soul view, according to which different stages belong to the same person if and only if they each have the numerically same immaterial soul.16,17 There are also theorists who reject all such attempts to analyse personal identity, holding instead that personal identity is simple and unanalysable.18,19 How do we decide which, if any, of these theories is the right one? Ever since Locke,20 the dominant method has been to test the various theories against our intuitive judgements to cases in which the theories deliver different verdicts. These include actual cases involving amnesia, brainwashing, brain death, permanent coma and the like, and also possible cases, such as brain transplants, brain-state transfers and teleportation. The correct analysis, it is generally supposed, is the one that best predicts and explains our considered judgements about who is who across a range of these cases. Notoriously, however, people’s intuitive responses to these cases tend to vary considerably; and, after more than a century of pumping intuitions regarding many and varied such puzzle cases, we still seem no closer to reaching a consensus in favour of any one of the theories that have been proposed. The personal identity debate seems to have reached an impasse.

c In

what follows, I will speak of ‘being a persisting body-person’ and ‘being a persisting psychological-person’ as if they were ‘two’ different candidate conceptions of personal identity. But given the internal disputes within each of the bodily and psychological continuity camps over exactly which kinds of bodily or psychological relations are most central, it should be noted that this is a gross oversimplification for the sake of convenience. In fact, there are many different versions of each of these theories; and so there are not two but many different candidate conceptions of being a persisting body-person and being a persisting psychological-person, corresponding to each of these versions. This is worth noting, since it suggests that reaching a consensus in favour of one or other of these general approaches would still not be sufficient to settle the debate. We would still need to resolve the further in-house debates about precisely which version of the winning general approach is correct. For further discussion see Ref. 13. d See, for example, Refs. 14, 15.

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My main aim in this paper is to shed light on the nature and roots of this impasse, and to suggest what needs to be done if we are to make progress. The outline of the paper is as follows. In section 2, I suggest that soul theorists are right to think that a persisting strictly identical immaterial soul, if it existed, would be the best candidate for personal identity, in the sense of according most closely with our ordinary conception of what persons are.e Sadly, however, our best science tells us that souls do not actually exist; so soul theorists are mistaken to think that personal identity over time in fact consists in a persisting immaterial soul. The upshot is that it turns out that the best candidate for personal identity does not exist. This raises the disturbing spectre of an error theory regarding persons. In sections 3 and 4, I argue that an error theory can only be avoided if one of the remaining candidates that are instantiated — most obviously, being a bodily-continuer or else being a psychological-continuer, or both — is a good enough candidate for personal identity over time, and clearly better than any of the other existing candidates. However, the trouble is that it is not obvious that any one of these candidates is clearly (second-)best, as the entrenched and seemingly irresolvable disagreement that characterizes the personal identity debate testifies. It appears that some people use ‘person’ and its cognates to refer to bodily-continuants, while others use the words to refer to psychological-continuants; and it does not seem that either way of speaking is obviously mistaken. This threatens to make the dispute over whether persons are human animals or else psychological beings look merely semantic: simply a disagreement about how everyone should use the words ‘person’, ‘I’ and proper names.f Yet this is very hard to believe. Making progress in the personal identity debate requires showing how the debate is more than merely semantic. This is a difficult task. I conclude, in section 6, with some suggestions about where progress might lie.

e By

‘best candidate’ I mean the best deserver of the label ‘person’, in the sense to be discussed in section 2. A ‘best deserver’ theory is a meta-theory about what type of object best satisfies our ordinary conception of persons. It should be distinguished from what is sometimes called a ‘best candidate’ view, which is not a meta-theory, but rather a substantive object-level account of what personal identity consists in. f I focus on the word ‘person’ as the one word that comes closest to expressing the concept that concerns us here. But the linkage here noted between the use of ‘person’, ‘I’ and proper names reveals that the underlying concept cannot simply be identified with the meaning of a single word. It is the concept that we are fundamentally interested in, not the words. In what follows, I use the word ‘person’ as a philosophical term of art, stipulated to express the concept person.

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2. Personal Identity and Conceptual Analysis We can think of a conception, or ‘folk theory’, of some subject matter x as made up of a cluster of reasonably widespread and relatively entrenched beliefs about x.g In the case of personal identity, these include beliefs such as the following: • Normally, if someone today looks exactly the same as some earlier person, then they are the same person. • Usually, if someone has the same body as a person as some earlier person, they are the same person as the earlier person. • Normally, if someone has the same brain as an earlier person they are the same person as the earlier person. • Normally, if someone has the same fingerprints as an earlier person, they are the same person. • Normally, if someone remembers doing something in the past, they are the same person as the person who did it. • Normally, when a person acts freely, he or she is acting on his or her own previously formed intentions, and not on someone else’s. • Normally, if someone has the same values and character as an earlier person, then they are the same person. There are also beliefs about the connections between the concept of personal identity and a range of other practical and ethical concepts. For instance, the following statements seem to express conceptual truths: • It is fair to hold a person morally or legally accountable for a past action only when they are the same person who did the action. • While I can wish that other people had acted differently in the past, I can regret only my own past mistakes. • If someone else will be in pain, I may empathize with them; but I should fear only those painful events that will happen to me. • Only if someone is the same person as your spouse is it appropriate to treat them as your spouse. • Usually, someone is entitled to a particular piece of property only when they are the same person as the person who bought it. Collectively, these and other of our commonsense beliefs regarding persons form our ordinary conception of personal identity. To the extent that these g Here

and in what follows, I am indebted to the general approach to conceptual analysis defended in Ref. 21.

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beliefs are shared, they constitute our common conception or ‘folk theory’ of personal identity. However, not all of our commonsense beliefs about persons are equally central to our conception. For instance, it is part of our conception that persons have legs and that they can talk. But these beliefs are not especially central to our conception of what persons are. This is revealed by our judgements about certain cases: in particular, by the fact that we are willing to allow that a mute or a legless being can still be a person, providing other conditions are satisfied. (If, by contrast, we were not willing to allow that a legless being could be a person, then this would suggest that we employed a slightly different conception of persons, person*, in which the property of having legs occupied an extremely central place.) Judgements about actual and possible cases reveal our ordinary conception of persons and of being the same person over time by revealing what possibilities we are disposed to rule in, and what we are disposed to rule out, as falling under the extension of ‘person’ and of ‘same person’. There will also be properties that do not even get to count as candidates for personal identity in virtue of failing to satisfy enough of our ordinary conception: the property of a person’s having the same number of atoms in the left big toenail as an earlier person is perhaps an example. It is also worth noting that not all of our commonsense beliefs about persons are held with equal confidence. Speaking for myself, I am much more confident in the correctness of my belief that I have reason to fear my own future pain than I am in my belief that a future person will be me if they have my body. One important point to glean from this preliminary discussion is that whether something satisfies our ordinary conception of something need not be an all-or-nothing affair. A perfect deserver for our conception of personal identity would be a property or relation among ‘person-stages’ (i.e., how persons are at various times) that squares with all of our beliefs about personal identity, or at least with all of the relatively central ones. In the absence of such a perfect candidate, various candidates may be better or worse suited to falling under our concept, depending on the degree to which they satisfy greater or fewer of the beliefs about personal identity that we hold most dear. The best deserver of our ordinary conception of personal identity, or of the labels ‘person’ and ‘same person’, will be the kind of thing that satisfies a weighted most of our commonsense beliefs concerning persons. The traditional quest for an answer to the question of personal identity can be seen as the search to discover what this best deserver is.

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3. Conceptual Analysis and The Soul Of the different candidates for personal identity picked out by the various theories of personal identity, which is best placed to fall under our ordinary conception? Arguably, a stock-take of common intuitive reactions to actual and possible cases reveals that our ordinary conception of personal identity is Cartesian in character. For the hypothesis that seems best to explain many people’s pre-analytic intuitions to cases is the view that persons are essentially immaterial souls, for which the various observable bodily and psychological properties and relations are normally reliable but fallible evidence. While I cannot undertake a full survey of our intuitions regarding cases here, discussion of a few such cases should be sufficient to make a prima facie case for this claim. Some of the most striking evidence is provided by widespread intuitive responses to two famous cases due to Bernard Williams.8 Williams first asks us to imagine a case in which two persons, A and B, are to undergo a procedure in which a machine gradually transfers A’s psychological life to B’s body, while B’s mental life is in turn transferred to A’s body. We are told that, after the procedure is complete, one of the resulting persons will be tortured, while the other will get a large financial reward. We are to imagine that we are the A-body person about to undergo the procedure. While we cannot alter the fact that someone after the procedure will be tortured, we can choose which of the A-body person and the B-body person after the procedure receives the torture and which receives the reward. We are to make this choice on purely self-interested grounds. The dominant reaction to this case is that, if we were the A-body person before the procedure, we would choose that the A-body person after the procedure gets the torture, and that the B-body person gets the reward. On the natural assumption that a self-interested person would choose so as to avoid their being tortured in the future, this intuition seems to support the psychological continuity theory. It suggests that we believe that A would be the B-body person after the procedure; and so that we think that a person goes where their distinctive psychology — memories, intentions, values, projects and character, and so forth — goes, and not where their body goes, in cases where these relations come apart. Williams then asks us to consider the following case. You are told that you will be tortured tomorrow. There is nothing you can do to avoid the torture, but you are offered the following ‘consolations’. First, you will lose your memories. Then you will be given a set of new memory impressions.

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Following this, you will acquire a whole new set of character traits that happens resemble those previously associated with a different body. None of these changes, Williams thinks, would come as any relief; they would make no difference to the fear you feel at the prospect of the impending torture. On the reasonable assumption that you fear a future pain only when you believe it will happen to you, this suggests that you think that the person who will be tortured will be you, despite the complete lack of psychological continuity between you now and that future person. Williams takes this to support the bodily continuity theory. For it suggests that you think that the person with your body will be you, despite the absence of psychological continuity. But, as Williams notes, there is something very puzzling about our intuitive responses here. For the second case is the very same case as the first, simply differently described. We therefore seem to have contradictory intuitions about the very same case: tracking personal identity with psychological continuity, not bodily, continuity in the first case; and tracking it with bodily continuity, not psychological continuity, in the second. Taken together, our intuitive judgements about these cases seem to reveal that we take neither bodily continuity nor psychological continuity to be either necessary or sufficient for personal identity. The combination of these intuitions cannot readily be explained by either of the bodily or the psychological continuity theory.h They seem to make sense only on the supposition that we take a person to be a featureless ‘soul pellet’ — a ‘bare locus’ of mental life — an entity that can continue to exist over time despite any amount of bodily and psychological discontinuity.23 The hypothesis that we implicitly take ourselves to be soul pellets explains other features of our ordinary practice that would otherwise be puzzling, such as the widespread tendency to find coherent tales of reincarnation without accompanying bodily or psychological continuities. 4. Error Theory or Conceptual Revision? If this is right, we face a difficult choice. Our pre-analytic conception of personal identity presupposes the existence of persisting immaterial souls. But our best science tells us that in fact there are no such things.i So h Although

see Ref. 22 for an alternative explanation. as Locke noted,20 critical reflection on various possible cases in which the soul comes apart from bodily and psychological continuities seems to reveal that a featureless soul, even if it existed, would not be worth caring about in the way in which we ordinarily care about personal identity. i Moreover,

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descriptive conceptual analysis, combined with certain a posteriori information about the way the world actually is, reveals that the best candidate for personal identity does not exist. There exists nothing that answers fully to our current conception of what persons are and how they persist; nothing that is quite what we pre-analytically take personal identity to be. How should we respond? There seem to be two options. The first would be to accept an error theory of persons, holding that while we preanalytically believe that persons exist and persist, informed critical reflection on the commitments implicit in our ordinary conception of what persons are reveals that there is nothing that answers to our conception closely enough, so that these beliefs are in fact uniformly false. Alternatively, we might look to see if there is a ‘nearby’ conception that a) is instantiated, and b) satisfies enough of the things we currently take to be true of persons so as to deserve to count as a conception of personal identity — and then adopt it as our preferred conception. On occasions, we are willing to accept an error theory of some subject matter. For instance, at some point in our lives most of us come to accept an error theory concerning Santa Claus. We become error theories about Santa when we come to think that we were mistaken to believe that there in fact exists a jolly red-suited man who lives with elves in the North Pole and flies through the sky once a year on a sled pulled by reindeers to deliver presents to children who have been good. The discovery that there is no man who has (enough of) the properties we associate with Santa leads us to conclude that Santa does not exist. Note that we come to be error theorists about Santa despite the fact that there is in fact someone who has some of the properties we associate with Santa, such as leaving presents from ‘Santa’ under the tree on Christmas eve — namely, our parents. But when we catch our parents and not a jolly red suited man depositing presents from ‘Santa’ under the Christmas tree on Christmas Eve, we do not generally revise our view about Santa’s nature and conclude that Santa is our parents. Rather, we conclude that Santa does not exist. What our response here reveals is that our parents are not sufficiently good deservers for the label ‘Santa’. They do not satisfy enough of our ordinary conception of what Santa is to deserve to fall under the concept. Another example: some people become error theorists about God when they come to believe that there in fact exists no omnipotent, omni-benevolent, omniscient person who created the world.

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Neither of these discoveries are entirely without costs: the discovery that Santa does not exist can be greatly distressing, and giving up belief in God yet more so. But however difficult it is to live without Santa or God, it would be considerably more difficult to live without persons. Personal identity plays an absolutely central role in our everyday lives. Giving up on the belief that persons exist and persist through time would force changes to our existing ways of thinking, feeling and behaving on a scale that is difficult fully to imagine. Prudential concern, friendship and loving relations, ascriptions of moral and legal accountability and attributions of property entitlement are but a few of the many emotions and practices that would need to be abandoned or radically revised should we give up believing that persons exist and persist over time. While some seem prepared to toy with accepting an error theory of persons, it seems to me that because of these considerable costs this should be an option of last resort, to be accepted only if all of the nearby candidate conceptions — bodily-continuers, psychological-continuers, or the like — are patently undeserving of the label ‘person’.j We have, then, considerable incentive to look to see which (if any) of the actually available candidates is the (second-)best deserver for personal identity. 5. Faultless Disagreement Unfortunately, however, once we eliminate the soul from contention, none of the obvious remaining candidate conceptions — the conceptions corresponding to the various theories of personal identity that have been proposed, e.g., human animal or bodily continuer, psychological continuer, and the like — seems uncontroversially to stand out from all the others as clearly best. This is what I think we learn from the entrenched and ongoing disagreement over whether bodily continuity, or else psychological continuity, or else some or other conjunction or disjunction of these, provides the correct analysis of personal identity over time. One striking feature of the personal identity debate is that it is not unusual to find that people who agree about the non-personal facts of a case nonetheless continue systematically to disagree about whether or not the case is one in which personal identity is preserved. Consider, for instance, the much discussed possible case of Star Trek-style teleportation, in which a person’s original matter is destroyed while a machine constructs j In

places Jackson,21 for instance, seems to endorse this view.

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an exact duplicate from new matter at another location from a blueprint taken of the original. The person who emerges from the booth has all of the psychology of the original persons — memories, intentions, values and so forth — but realized in a new body that is qualitatively indistinguishable from the original. When presented with this case, some judge that a person determinately could not survive such a procedure; while others are equally firmly convinced that teleportation would constitute a perfectly fine way for a person to travel. The former judgement is taken to be evidence in favour of a bodily continuity theory, while the latter judgement is supposed to support a psychological continuity theory. It is worth noting that this kind of disagreement is not confined merely to possible cases, but arises equally when people consider certain actual cases in which bodily and psychological continuities come apart. Does a person’s life history include foetal stages? Can a person continue to exist in a permanent vegetative state? People’s opinions about whether it is correct to say that there is a continuing person in these cases differ, as the continuing debates surrounding abortion and euthanasia testify. Of course, people’s intuitive judgements about a case may sometimes be a less than fully reliable guide to their concept. For instance, if there was evidence that subjects on one side of the dispute were confused, or hadn’t understood the details of a case properly, or if their judgements about a case contradicted their judgements about other relevantly similar cases, we would be justified in discounting their judgements about this case as unreliable. While it is clearly sometimes right to discount a person’s judgements to cases on these grounds, it is implausible to suppose that all differences of opinion in the personal identity debate can be resolved by pointing to one of the disputing parties as uniformly demonstrably confused, irrational or linguistically incompetent. This is especially so given that there seems to be no non-question begging way of identifying the mistake that one (or other) side is making. For example, many bodily continuity theorists claim that the intuition that a person survives teleportation can be explained away by the presence of misleading features in how the case is usually presented: for instance, that the process is typically described as ‘teletransportation’, which primes subjects to view it as a form of travel, not suicide; or that it is the product of subjects confusing the intuition that teleportation preserves what is of practical significance in personal identity with the judgement that it preserves personal identity. Purged of these confounding factors, it is often suggested, it would

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become clear that our intuitions in fact go along with a bodily criterion.k But psychological continuity theorists might (and do) equally employ this strategy to explain away the contrary intuition that a person does not survive teletransportation. For instance, they may claim that those who have this intuition are failing properly to distinguish between personal identity (which is preserved in teletransportation) and animal identity (which is not). Once people grasp this distinction properly, it might be suggested, they will converge on the view that persons are essential psychological beings, which typically coincide with particular human animals in everyday life, but which need not do so. But, of course, whether the case is misdescribed, or whether failure to distinguish between persons and animals is evidence of conceptual confusion rather than clear-headed thinking, are precisely the kinds of questions that appeal to intuitions is supposed to help settle; and so not something to which either side can appeal in advance. Apparently informed, linguistically competent and otherwise seemingly rational people who have thought long and hard about a wide range of cases, genuinely seem to differ somewhat as to exactly what it takes for a person to persist. It is hard to see how these disagreements can be rationally resolved. Consider, for example, the debate about whether an early term foetus is a person. The majority of naturalistically inclined parties to this debate agree about the relevant (non-personal) facts. They agree, for instance, that an early term foetus is a human animal, but one that lacks the mental capacities and traits — consciousness, reasoning abilities, projects and so forth — possessed by typical adult members of our species. Moreover, they generally agree that these facts are the only facts that are relevant to deciding the question of whether or not an early term foetus is a person. What they seem to disagree about then is the semantic question of whether a being with these properties is correctly called a ‘person’. Some say an early-term foetus is determinately not a human person, for it lacks the psychological properties central to personhood; others say that it determinately is a human person, for it is a human being. Neither side, it seems, can be faulted for being mistaken about a matter of non-personal fact. And neither side seems in violation of firm a priori constraints governing use of the term ‘person’. We do not generally find either way of speaking literally unintelligible or incoherent. If it were clear that there was a particular privileged natural kind to be associated with the term ‘person’, then we might k See,

for instance, Refs. 10, 15, 24.

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be justified in viewing one way of speaking as correct and the other as deficient. But it is not obvious that either way of speaking better carves nature at its joints.l (I return to this issue briefly in section 6.) If so, the debate over whether a foetus is a person is simply a terminological disagreement; a dispute about whether the term ‘person’ is true of an early term foetus. Consider a different, more innocuous example. I once had a disagreement with a neighbour about whether Neil, the head chef at the local Thai restaurant, was a bachelor. I said he was; my neighbour disagreed. Looking for an explanation of our differences, we proceeded to confirm that we had the same person in mind, that he was indeed an unmarried man, that he was in fact of marriageable age, and so on. Granting that all this was so, my neighbour nonetheless insisted that Neil was not a bachelor since his apartment was always clean and he was a good cook. This, in her opinion, meant that he could not be a bachelor. In this case, we discover that our disagreement is merely terminological. For we agree about all the relevant facts described one way. What we disagree about is whether the term ‘bachelor’ correctly applies to describe those facts. By her lights, bachelors cannot be neat and good cooks, notwithstanding being male and unmarried; as I use the term, they can. Our differing judgements about Neil’s case reveal that we employ (somewhat) different conceptions of bachelor. There would be no point here arguing about which of us is right — unless she were to go on to claim that everyone uses the word ‘bachelor’ to mean what she does, in which case she would be mistaken about that. Strictly, we might say that my judgements are governed by my conception bachelor; while she employs a conception, bachelor*, which is different from, but overlaps with mine, in the sense of delivering the same verdict about many (but not all) actual cases. One last example, this time closer to the subject at hand. People who argue about whether teleportation is person-preserving agree about the non-personal facts of the case — that is, the facts about what occurs to the brain, body and psychology of a person who undergoes teleportation, as it is described. If we have understood the case properly, we know that teleportation will produce, by way of a reliable causal mechanism, a person who is in all physical and psychological respects indistinguishable from the original, but constructed from new matter. Suppose furthermore, we know that the process is regarded by the person’s community, and by the person

l For

a more detailed argument to this effect, see Ref. 25.

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themselves, as a form of travel.m The person who emerges from the booth at the receiving end will be regarded as entitled to the property of the person who entered the booth prior to being teleported, held accountable for their actions, and so forth. Then, on any of the naturalistically acceptable accounts of personal identity that have seriously been proposed, we know everything we need to know in order to decide the question of whether or not the person who emerges from the teleporter is the same person as the original. If, on reflection, some people then go on to say that teleportation is person-preserving while others say that it is not, this suggests that there is some variation in how the term ‘person’ is used by different sub-sections of the general population. Those who regard the statement ‘a person survives teleportation’ as being determinately false are presumably using the term ‘person’ to refer to a bodily-continuant or human animal. Their judgements about cases seemed to be governed by a conception of persons as human animals or personbody . Those who regard the claim that ‘a person survives teleportation’ as obviously true, on the other hand, are using the term ‘person’ to pick out a psychological continuant. Their judgements about who is who in the various cases seem to be governed by a conception of persons as psychological entities, i.e., personpsych . These concepts deliver the same verdict about most everyday cases in which bodily and psychological continuities are present together. The variation emerges in their respective judgements about the less common cases where bodily and psychological continuity come apart. Though they differ as to what kind of entity ‘person’ is true of, these concepts have something in common in virtue of which it seems plausible to regard each as a person concept. Parties who disagree about whether it is true to say that a person survives teleportation, nonetheless agree about the connections between personal identity and certain other evaluative and ethical concepts. They typically agree, for instance, that if a later person is the same person as an earlier person then inter alia it would be appropriate for the earlier person to extend prudential concern to the later person, and for the later person to be held accountable for the earlier person’s actions.n

m Stephen

White claims that facts about how a person or community view a processand, in particular, whether or not they treat the resulting person as the same as the originalis relevant to determining whether or not they survive it.26 n Although two recent defences of a bodily approach deny this, see Refs. 10, 24. To my mind, this raises the question of whether these analyses deserve to be thought of analyses of personal identity, rather than accounts of animal identity. For further discussion, see Ref. 27.

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What they differ about is what relation or properties these practices track. Given that the concepts play the same functional role in structuring the person-directed practical and ethical concerns of those who employ them, it may be more apt to say that the parties are employing different person ‘sub-concepts’, rather than different concepts simpliciter. However, it is very hard to believe that the dispute over whether a bodily or a psychological criterion is correct is merely semantic. It is counterintuitive to think that the difference between whether I will survive some upcoming process or event depends on something as ostensibly trivial as how I, or my community, use our words. Suppose I am wondering whether I will survive some upcoming event — teleportation, for instance. It is hard to believe that whether or not I will survive this event simply depends on whether I, or my community, use ‘person’ to refer to a human animal (which does not survive this process) or to a psychological continuer (which does). This is one important difference between the cases of ‘bachelor’ and ‘person’. It seems comparatively untroubling to concede that the answer to the question of whether Neil is a bachelor depends on which of a number of closely related conceptions of bachelorhood we choose to employ. Not so, in the case of personal identity. It seems to be part of our ordinary conception of personal identity that the difference between continuing to exist and ceasing to be does not simply depend on what conceptual scheme we happen to employ or how we use words, but is a substantive matter that is settled independently of our conceptual or linguistic practices. We tend to think that it is correct for me to call some future person ‘me’ because that future person will be me, not the other way around. It therefore seems to be part of our ordinary conception of personal identity that there is a single, clearly best deserver for the label ‘person’. The very fact that there appear to be a number of different but apparently equally good candidates for the label ‘person’ itself thereby seems to undermine the deservingness of each of the available candidates. The absence of an obvious single best candidate for personal identity seems to push us back in the direction of an error theory of personal identity.

6. Beyond Mere Semantics Making progress in the personal identity debate requires showing how what is at issue is more than merely semantic. There seem to me to be three main ways in which this might be so, and, consequently, that there are three main avenues along which we might hope to make progress.

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The first concerns underlying questions about fundamental ontology. There are certain views about the nature of persistence that, if correct, would rule out the existence of multiple candidates for personal identity. Suppose that there exists one and only one kind of persisting entity available to be associated with our person-talk. It would then turn out that there is at most one correct use of the term ‘person’ — namely, the use that corresponds to the only candidate in fact available. For instance, defenders of a bodily continuity might hold for general ontological reasons that only body-persons exist, while psychological-continuants do not. In this case, they will view the psychological continuity theory as mistaken for much the same reason that the soul view is generally thought to be mistaken, i.e., because it relies on a false view about what entities exist. Following Sider,25 call this view about the ontology of persistence, ‘chaste endurantism’. If chaste endurantism is correct, then disagreement about personal identity would be more than merely semantic. There would then be at most a single correct answer to the question of personal identity — the one that corresponds to the only actually existing candidate — even if we did not agree on what it was. However, the question of whether such a ‘chaste’ ontology is correct is itself a hotly contested issue in analytic metaphysics. Others (including myself) accept a different, four-dimensionalist account of the nature of persistence.o On this view, persisting objects (including persons) are collections or aggregates of numerically distinct time-slices. On unrestricted or ‘rich’ versions of four-dimensionalism, there exist many such aggregates: in particular, there exists an aggregate that corresponds to the bodily continuity theory and a (different) aggregate that corresponds to a psychological continuity theory, and aggregates that corresponds to each of the various mixed theories. If rich four-dimensionalism is true, no account of personal identity can be dismissed as factually mistaken on the grounds that there is in fact no entity that corresponds to the theory. There will exist multiple candidates for being the meaning of person talk. From the perspective of rich four-dimensionalism, the question of personal identity equates to the semantic question of which of the many existing space–time worms ‘person’ refers to. This itself may seem to make the question of personal identity for fourdimensionalists merely a semantic one.p But this is not so. While rich o For

a comprehensive recent discussion and defence of four-dimensionalism see Ref. 28. for example, makes this claim.10

p Olson,

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four-dimensionalists admit that there are many candidates available for being the referent of ‘person’, not all of these candidates need be equally good. If one candidate conception were in any way head and shoulders above the rest, this would settle the question of personal identity in favour of that candidate. As I see it, there are two ways in which a particular candidate might clearly beat the rest of the competition. It might be that one of the available candidate meanings is more intrinsically eligible to be meant than any other in virtue of carving nature at its joints. This is another way in which it might turn out that the debate over what persons are is more than merely semantic.q There is another way in which the question of personal identity might be more than merely semantic. As previously noted, personal identity plays an absolutely central role in our psychological and social lives. Facts about personal identity underpin prudential concern (the distinctive anticipatory concern that we ordinarily have only for our own future experiences, and connected emotions and motivations such as fear of future pain and the desire to take action to avoid it); attitudes to our past (such as the special kind of remorse that we feel for our own past mistakes); moral agency and ascriptions of responsibility (only I can be held responsible for my past actions); property entitlements (I own my car now because I am the person who bought it); how we treat others (whether as a colleague, a spouse, a friend or a stranger), and much else besides. Answers to the question of personal identity therefore have important practical and moral consequences: for whose actions we can be held accountable for, whose future experiences (if anyone’s) we can look forward to having and plan for, how we should feel about someone’s past actions or experiences, and for how we should treat and be treated by others. Determining whether or not a process is one that a person can survive therefore plausibly involves more than merely deciding how to use words, but is bound up with a range of central practical concerns. Whether it is true to say that a person survives teleportation is not then simply a decision about how to use the word ‘person’ or which of a number of available person concepts to employ, but is also a decision about whether it would be appropriate for the person who enters the teleporter to extend their prudential concern to the person who emerges at the other end, whether it would be reasonable to hold the q For

a persuasive argument that neither of the candidates better carves nature at its joints, see Ref. 25.

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resulting person morally and legally accountable for the original person’s actions, and so forth. Consider again the dispute over whether an early term foetus is a person. It seems that there is something more substantive at issue in this debate than simply whether we call such a being a ‘person’. One obvious suggestion is that the substantive matter is at issue in this debate is whether an early term foetus ought to be accorded the moral standing of a person — i.e., whether it has a serious claim or right to life, which makes abortion seriously immoral — which turns into a debate about whether it is a person via the common assumption that all and only persons have a serious right to life. This brings us to a third way that the personal identity debate might turn out to be more than merely semantic. As noted previously, the concept of personal identity is normally assigned a central quasi-theoretical role in structuring some important practical and ethical concerns. If there was a candidate that was uniquely intrinsically suited to be the reasonable object of our person-directed practices — prudential concern, ascription of moral and legal accountability, and the like — then this too might provide a substantive reason to favour that candidate over all the others. The answer to the question of personal identity might then be settled by the correct answer (if there is one) to certain ethical questions — for example, how earlier and later person-stages need to be related to each other in order for it to be legitimate to hold later stages morally and/or legally accountable for the actions of earlier stages. A consequence of this third approach is that it reverses a traditional way of thinking about the nature of the connection between questions of personal identity and ethical questions. It is commonly assumed that we settle the question of whether an early-term foetus has a serious right to life by first settling the question of whether it is a person. It is also generally supposed that the answer to the question of whether it is legitimate to hold a current person accountable for some past crime depends partly on whether they are the same person who committed that crime, where this question is supposed to be settled independently and antecedently of the question about responsibility. On the current suggestion, things go the other way round. Ethical considerations would partly decide the question of whether or not it an early term foetus is a person, perhaps by adjudicating whether it is a being that possesses properties that ground a claim to its possessing a serious right to life in virtue of possessing these properties. Ethical considerations become the arbiter of the question of personal identity, rather than the other way around. This goes contrary to ordinary thought, which

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plausibly takes facts about personal identity to be ‘independent justifiers’, in Mark Johnston’s phrase, of ethical and legal questions.29 If this is right, then at this point the question of personal identity becomes a question for ethicists, not metaphysicians; and questions of personal identity become hostage to the outcome of certain substantive ethical debates. 7. Conclusion The personal identity debate seems to have reached an impasse. There seem to be (at least) two equally good families of candidate meanings for our talk of persisting persons: being a persisting body-person and being a persisting psychological-person. The challenge confronting contemporary theorists of personal identity is how to make progress. If what I have said is right, progress may be made on one (or more) of three fronts. There may be ontological arguments that show that only one of these conceptions is in fact instantiated. That would resolve the debate. There might be metaphysical arguments to show that one of the available candidate conceptions is more intrinsically eligible to be meant by our person talk than others. This too might help settle the question in favour of a single candidate conception. Finally, there might be an ethical argument to show that one of these conceptions is the reasonable object of our person-directed ethical practices, while the others are not. That too would resolve the debate in favour of one of the conceptions. In the absence of a convincing argument along any of these three lines, we may be forced to accept a kind of relativism or pluralism about personal identity, and admit that the question of personal identity can legitimately be settled any one of a number of different ways. Whether we are obliged to accept relativism about personal identity — or whether it is even a genuine option in light of the links between personal identity and ethical questions which may themselves presuppose that there is a uniquely correct answer to the question of personal identity — awaits a resolution of some fundamental questions in ethics. Acknowledgments Thanks to Robert Bezimienny, David Braddon-Mitchell, Kristie Miller and Denis Robinson for helpful discussion and comments. References 1. D. Lewis, Survival and Identity. In: A. Rorty (Ed.), The Identities of Persons. Berkeley: California (1976). Reprinted in his Philosophical Papers vol. I. Oxford University Press (1983).

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2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19. 20.

21. 22. 23. 24. 25.

26.

H. Noonan, Personal Identity, Second edition. London: Routledge (2003). D. Parfit, Reasons and Persons. Oxford: Oxford University Press (1984). J. Perry, Can the Self Divide? Journal of Philosophy 69, 463–488 (1972). C. Rovane, The Bounds of Agency. Princeton University Press (1998). S. Shoemaker, Personal Identity: A Materialist’s Account. In: Shoemaker and Swinburne, Personal Identity. Oxford: Blackwell (1984). D. Wiggins, Sameness and Substance. Oxford: Blackwell (1980). B. Williams, The Self and the Future. Philosophical Review 59 (1970). Reprinted in his Problems of the Self. Cambridge University Press (1973). J. J. Thomson, People and Their Bodies. In: J. Dancy (Ed.), Reading Parfit. Oxford: Blackwell (1997). E. Olson, The Human Animal: Personal Identity Without Psychology. New York: Oxford University Press (1997). P. Snowdon, Persons, Animals, and Ourselves. In: C. Gill. (Ed.), The Person and the Human Mind. Oxford: Clarendon Press (1990). P. van Inwagen, Material Beings. Ithaca: Cornell University Press (1990). D. Robinson, Failing To Agree Or Failing To Disagree?: Personal Identity Quasi-Relativism. The Monist 87 (4), 512–536 (2004). T. Nagel, Brain Bisection and the Unity of Consciousness. Synth`ese 22, 396–413 (1971). Reprinted in Ref. 30 and in: Nagel, Mortal Questions. Cambridge University Press (1979). P. Unger, Identity, Consciousness, and Value. New York: Oxford University Press (1990). R. Swinburne, Personal Identity: The Dualist Theory. In: Shoemaker and Swinburne, Personal Identity. Oxford: Blackwell (1984). A. Quinton, The Soul. Journal of Philosophy 59, 393–403 (1962). Reprinted in Ref. 30. G. Maddell, The Identity of the Self. Edinburgh University Press (1981). T. Merricks, There Are No Criteria of Identity Over Time. Noˆ us 32, 106–124 (1998). J. Locke, An Essay Concerning Human Understanding. P. Nidditch (Ed.). Oxford: Clarendon Press (original work, 2nd ed., first published 1694); partly reprinted in Ref. 30. F. Jackson, From Metaphysics To Ethics. Oxford: Clarendon Press (1998). R. Nozick, Philosophical Explanations. Cambridge: Harvard University Press (1981). M. Johnston, Human Beings. Journal of Philosophy 84, 59–83 (1987). M. Schechtman, The Constitution of Selves. Ithaca: Cornell University Press (1996). T. Sider, Criteria of Personal Identity and the Limits of Conceptual Analysis. Philosophical Perspectives 15. Metaphysics, Cambridge, MA: Blackwell, 189–209 (2001). S. White, Metapsychological Relativism and the Self. The Journal of Philosophy 86 (6), 298–323 (1989).

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27. C. West, Personal Identity: Practical or Metaphysical? In: K. Atkins and C. Mackenzie (Eds.), Practical Identity and Narrative Agency. New York: Routledge, 54–78 (2008). 28. T. Sider, Four Dimensionalism. Oxford: Oxford University Press (2001). 29. M. Johnston, Relativism and the Self. In: M. Krausz (Ed.), Relativism: Interpretation and Confrontation. South Bend: University of Notre Dame Press, 441–472 (1989). 30. J. Perry (Ed.), Personal Identity. Berkeley: University of California Press (1975).

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A WORLD OF TROPES?

ANNA-SOFIA MAURIN Department of Philosophy Lund University E-mail: [email protected] Why should one hold that the world is a world of tropes? Or, more generally: How do we justify our ontological conclusions? It seems clear that the only evidence at our disposal must belong to appearances. For a realist, however, it is unreasonable to think that our conceptualisation of reality will reveal to us reality as it is independently of how it seems. You simply cannot ‘read off’ the structure of reality from the way we talk and think about it. To some, this has been considered a reductio against any metaphysics interested in unveiling the structural features of reality hidden behind a veil of appearances. In this paper it is argued that ontological conclusions can nevertheless be justified. A close study of reality as it appears to us may not be able to reveal to what categories the most fundamental constituents of reality as it is belong. It can, however, reveal the fundamental ‘truthmaking roles’ that whatever there is must be able to play. An ontological theory is hence justified precisely if its posits can fulfil their truthmaking function. We could justifiably hold that the world is a world of tropes if tropes (or structured complexes of tropes) are able to play the requisite truthmaking roles, and in this paper it is argued that they can. Whether we should hold that the world is a world of tropes is another matter. In ontology, our choice between otherwise equally truthmaker-apt theories can not be justified with reference to anything pertaining to appearances; only the theoretical virtues can serve as the arbitrator. It is concluded, therefore, that in ontology, theory choice is less exciting than one might think.

1. Introduction Trope theorists, not surprisingly, share the conviction that tropes (i.e., abstract particulars) belong to the ultimate furniture of reality. Besides being abstract and particular tropes are simple, but this (I believe essential characteristic) is not recognised by all trope theorists and has been attacked by several trope critics.a,b aI

defend the simplicity of tropes in Refs. 1, p. 11–15; 2, p. 137–145. Critics include Hochberg3 and Armstrong.4 b It might be objected that my list of trope-traits is incomplete as it fails to mention 107

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Their core conviction aside, trope theories may differ considerably. Radically different are theories set in different theoretical frameworks. To see this, we need only consider the history of the theory. Early trope theorists treated the abstract particular as (one of) the ultimate constituents of experience.c The majority of contemporary trope theorists, on the other hand, treat what may appear to be the very same thing as a constituent of reality as it is, independently of how it seems.d To borrow useful terminology introduced by Strawson (Ref. 16, p. 9), contemporary trope theorists do revisionary rather than descriptive metaphysics.e,f With trope theory set in a contemporary framework we can ask:g Why should one hold that the world is a world of tropes? It is impossible to assess an account of tropes without examining the theoretical framework within which that account was developed. Revisionary trope theory recognises a distinction (and hence the possibility of a difference) between appearance and reality. The goal of the revisionary trope theorist’s investigation, moreover, is an account of reality. The that tropes are dependent entities (cf. Ref. 5). As I am not convinced that tropes are essentially dependent entities, and as I do not believe that whether or not they are will make a difference here, I have opted to put dependence to one side. c Early trope theorists include Segelberg,6 Stout,7 and Husserl.8 Williams similarly set his theory in an empiricist, if not full-blown phenomenological, framework.9 Of these theorists, only Williams named his abstract particulars ‘tropes’ (it was in fact he who invented the name — presumably as a joke). d Contemporary trope theorists include Bacon,10 Campbell,11 Kein¨ anen,12 Martin,13 Maurin,1 Simons5 and Trettin.14 ,15 e Strawson’s original distinction will not do as it stands; I return to its modification below. See also Refs. 1, Ch. 3; 17, 18 and 12, Ch. 2. f Both early and contemporary trope theorists, moreover, have regarded their theories as ‘formal’ in character. All hold that we should expect it to provide information, not about the substance of reality, but rather about its form (i.e., about what categories there are, how distinct categories relate to one another, and so on). The claim that ontology, whether it is revisionary or descriptive, should be formal has been persuasively argued by Simons (Ref. 18, p. 38). See also Ref. 19, p. 156. g As this is the framework in which a majority of contemporary trope theories (along with quite a few other ontological theories) are set, the consequences of its adoption will be of interest independently of the reason one might have for choosing it in the first place. I will not, therefore, attempt to defend setting trope theory in a revisionary framework — something which has in any case been defended by, among others, Simons,18 Kein¨ anen12 and to some extent by myself.1 Lowe has even argued that ontology must be revisionary in this sense because “to attempt to recast all ontological questions as questions about our thoughts about what exists is to engender a regress which is clearly vicious”. 20

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revisionary metaphysician wants to carve reality at the joints; its aim is a theory about ‘the thing in itself’ and not only ‘the thing as it appears to us’. All of this brings with it well-known problems. Appearances, first of all, can be deceptive, and it is hard to determine to what extent they are misleading and in what circumstances. Experiential evidence, therefore, becomes difficult to evaluate. This becomes apparent when we consider the possibility of systematic perceptual error. Even more troubling, perhaps, is the fact that experiential evidence supplied by our unaided senses may differ very much from that obtained with the help of various types of machinery, such as a microscope or a telescope.h In a revisionary framework, therefore, any argument that takes us directly from observation to ontology must be supplemented with elaborate and assumption-laden arguments explaining why such a move is justified. Linguistic arguments — arguments from meaning — are also problematic, as it seems close to impossible to distinguish, in meaning, between what is ontologically relevant and what is not. Arguments from meaning are therefore shunned by almost all of today’s revisionary metaphysicians. Armstrong, for instance, rejects this type of argument when it is pressed into service to establish the existence of universals (Ref. 21, vol. 1: xiv): “This second argument moves from the existence of meaningful general words to the existence of universals which are the meanings of those words. Universals are postulated as the second term of the meaning relation . . . I regard this second line of argument as completely unsound. Furthermore, I believe that the identification of universals with meanings (connotations, intensions), which the argument presupposes, has been a disaster for the theory of universals”. Even arguments that take us from premises about (not meaning as such, but) the logical structure of our conceptualisations to conclusions about the hA

case in point is the conflict we find in Ref. 21. Here Armstrong claims that the main argument for the existence of universals is what he calls ‘the argument from the One over Many’ (which, very briefly, runs as follows: the world seems to include identity in distinction — this must be explained — it cannot be explained away — the world does include identity in distinction — there are universals). But Armstrong also adopts a form of scientific realism (which, I take it, implies a type of revisionary framework); and there seems to be no reason to believe that a commitment to the existence of (scientific) universals will follow from belief that ‘universal’ experiences exist. For a more detailed argument to this effect, see Ref. 22.

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ontological structure of reality draw criticism.i For why should we believe that, although reality is both distinct and probably also different from the way we represent it, it just so happens that the logical form of the latter mirrors or exactly resembles the ontological form of the former? Once again, a convincing explanation is lacking. But if neither experience, nor language, nor thought can straightforwardly vindicate ontological conclusions, what can? Logic and the ordinary theoretical virtues are still available, of course. However (and unfortunately), their regulatory impact is much too weak: an ontology regimented only by their means can hardly earn more than the status of being a ‘consistent but incredible fairy-tale’ (Ref. 18, p. 381). The revisionary metaphysician finds herself in a serious predicament — a predicament, moreover, considered by many to be a reductio of the revisionary framework itself. Her only option is to investigate once again if there is not, after all, something in appearance apt to inform her about the formal features of reality. She can defuse the reductio only if she can answer the following questions in a convincing way: What in reality as it seems can inform us about reality as it is? How can it so inform us? In this paper I will argue that reasonable answers to both these questions are available. I will suggest that the now much discussed truthmaker theory, together with a modified version of what Strawson called descriptive metaphysics, can regiment ontological conclusions drawn in a revisionary framework enough to make them justified. The world is a world of tropes if (minimally) tropes can play the requisite truthmaking roles. The claim that tropes can play these roles I have argued for elsewhere,1 and here those reasons can be rehearsed only cursorily. That they can does not mean that they do, however. That tropes can play the requisite truthmaking roles tells us merely that the world could be a world of tropes; it does not tell us why we should prefer a theory of tropes as truthmakers to a theory of, say, states of affairs. I end the paper with a discussion of the limits of theory comparison in revisionary ontology.

i Compare

below.

the logical atomism of Russell23 and Wittgenstein.24 I return to this issue

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2. Truthmaker Theory According to truthmaker theory, truth conforms to principle (T):j,k (T)

is true iff there exists at least one truthmaker T for

.l Whether or not (T) holds for all truths is disputed. Armstrong believes that it does (he calls this view ‘Truthmaker Maximalism’).m Others are convinced that it does not and suggest that (T) be reserved for true atomic propositions and their conjunctive compounds. In general, truths conform instead to the weaker principle (T’):n (T’) If there exists at least one truthmaker T for

then

is true. To be able to regiment, and hence to justify, revisionary trope theory, truthmaker theory must have independent support. Why should we believe that truths are made true? A first answer is this: it is reasonable to believe that truths are made true in the sense given by (T) and (T’) because this accords well with our intuitions about truth. What is true depends on what the world is like. Truth is ‘grounded’ in reality. However, as noticed by j (T)

is not a definition of truth, as the notion appears also in its explanans. It could be regarded as a necessary and sufficient condition for truth, however. As much is suggested by Armstrong (Ref. 4, p. 17). Armstrong does not think that the fact that no definition of truth seems forthcoming is surprising, as “a fundamental concept such as truth is likely to be so entwined with other fundamental notions that no total explication of it in terms of other concepts is possible”. For some good discussions of (T) and (T’), see Ref. 25. k

= whatever carries a truth-value. Here I will talk of propositions as the bearers of truth, but I shall regard the expression as a place-holder for whatever detailed investigation reveals as the most appropriate truth-bearer. A similar approach is taken by Simons,26 Rodriguez–Pereyra27 and Armstrong.4 l That ‘at least one truthmaker’ makes

true is consistent with there being one or many truthmakers (separately or jointly). The notion that a proposition is made true by several truthmakers jointly, moreover, does not entail that their union is anything ‘over and above’ their constituent truthmakers (Ref. 28, p. 313). m See Ref. 4, p. 5. Armstrong does not argue directly for Maximalism, but hopes that “philosophers of realist inclination will be immediately attracted by the idea that truth, any truth, should depend for its truth on something ‘outside’ it, in virtue of which it is true”. n Critics of Maximalism include Simons (Ref. 29, p. 254): “The most tendentious of Armstrong’s general truthmaking principles is Truthmaker Maximalism It results from extending the plausible and attractive idea that some basic contingent truths are in need of something to make them true to the whole gamut of truths. In particular necessary truths are not usually thought to stand in need of truthmakers, since they are true come (or exist) what may. /. . ./ It is Armstrong’s insistence on looking for truthmakers for every truth that gets him into unnecessarily tight corners”. See also Ref. 30, p. 284–285.

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Rodriguez–Pereyra: “The idea that truth is determined by reality sounds grand, but in itself it is a very minimal idea: it is simply the idea that the truth of a truthbearer is determined by its subject matter, or some feature of it — no matter what the nature of the subject matter may be” (Ref. 27, p. 21). We must add, therefore, that according to truthmaker theory, the reality in which truth is grounded is distinct from, and independent of, the truths it grounds. Truthmaker theory naturally belongs in a revisionary framework. The relationship between reality and what reality (or relevant portions of reality) grounds or makes true, furthermore, is importantly asymmetric. That truths are true in virtue of entities is the core idea of truthmaker theory (Refs. 31, p. 32; 4, p. 5).o To add that the reality in which truth is grounded is both distinct from, and independent of, the truths it grounds, and that it is portions of reality that determine truth but not the other way around, does not subtract from the intuitive attraction of truthmaker theory. Rather the opposite. However, these are substantive additions, and as such they give rise to some difficult questions. In particular, one may wonder at the nature of a truthmaking relation that is able to bridge the supposed gulf between reality in itself and reality for us. The claim that the nature of the truthmaking relation is primitive, although true, does nothing to dispel this mystery. Demystification is instead more effectively achieved if truthmaking is compared with another relation: entailment. According to the basic truthmaker principle, if there is a truthmaker some truth must be (made) true. Truthmakers necessitate truth. In other words, if T is a truthmaker for

then ( entails

). According to what is sometimes called the ‘entailment principle’, furthermore:p o Both

Rodriguez–Pereyra and Armstrong devote some time separating this core idea from another idea which in fact follows from it but should not be confused with it. This is the idea that truth supervenes on being.32 Supervenience, they point out, is a symmetrical relation, whereas the truthmaking relation is asymmetric. “Thus what is fundamental in the idea of truthmaking is not supervenience but the idea that truths are true in virtue of entities. That truth supervenes on being is a consequence of the fact that truths are true in virtue of entities, and this is why the supervenience of truth on being is important but the supervenience of being on truth is not” (Ref. 31, p. 32). p Armstrong points out that for (ET) to enjoy general applicability the entailment cannot be classical entailment, as that would make any contingent truth a truthmaker for any necessary truth — a consequence which “robs truthmaking theory of all interest for the

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(ET) If T makes true

and (

entails ) then T makes true

The truthmaking relation is not, nor can it be reduced to, the entailment relation. Entailment is a logical relation that relates propositions; truthmaking is an ontological cross-categorial relation connecting entities to propositions.q Hence, comparing the truthmaking relation with entailment can inform us only indirectly about one aspect of the former’s ontology. If there is a truthmaker T and a corresponding proposition

, the truthmaking relation must exist. Truthmaking supervenes on its relata. From an ontological perspective this means that truthmaking is an internal relation (Refs. 4, p. 9; 1, p. 87–91)). In ontology, furthermore, internal relations are often considered a bargain. For if the existence of the relata is enough to guarantee (to necessitate) that relating obtains, then, in the name of ontological parsimony, no more than the relata must, fundamentally, exist. The truthmaking relation is a ‘pseudo addition’; it is an ‘ontological free lunch’. Moreover, those who remain (I believe, plausibly) sceptical about the move here made from internality to ‘no addition’ can still agree that, although the truthmaking relation is no free lunch, its nature is not, after all, left entirely obscure. Truthmaker theory is not only supported by intuition. The following, further reason for its adoption is perhaps more surprising, as it may seem at first to count against it. Deflationary theories of truth, it appears, offer an alternative yet ontologically much less expensive theory of truth.r Like truthmaker theory (although in a much weaker sense) they ground truth in reality. Unlike truthmaker theory, they account for truth without truthmakers and without mysterious truthmaking relations. To see how the availability of a successful deflationary theory of truth can nevertheless be made to count in favour of truthmaker theory, consider the Tarskian schema (disquotationally interpreted):

is true iff p. It can be argued that this schema does not fully explicate truth — although it does of course case of necessary truths” (Ref. 4, p. 11). Suggestions on how to restrict entailment have been made by Restall,33 Read34 and Rodriguez–Pereyra,35 among others. q Propositions may also be part of reality. If that is so, I do not mean to deny that the truthmaking relation can hold between propositions; I only wish to deny that it is a ‘propositional’ relation. r Versions of the type of theory I have in mind have been defended by G. Frege; F. P. Ramsey; A. J. Ayer; W. V. O. Quine; H. Field and P. Horwich. Deflationary theories of truth, I imagine, minimally share the conviction that someone has the concept of truth only if he or she accepts all (non-paradoxical) instances of the schema (

is true iff p).

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explicate it just enough to meet the needs of a formal semantics. What is lacking, furthermore, is precisely what truthmaker theory is able to supply. As Niiniluoto says:s “Some philosophers suggest that everything relevant to this issue, as far as semantics is concerned, is expressed by Tarski’s Tequivalences /. . . / [This] may be right in the sense that T-sentences are sufficient for the purpose of stating and generating actual truthconditions for all sentences, and the set-theoretical approach as such is compatible with various philosophical and metaphysical accounts of the nature of reality. But many philosophers nevertheless find it frustrating if we cannot understand the nature of predication employed in simple atomic statements /. . . / To analyze these problems, set-theoretical semantics should be complemented by some ontological considerations” (Ref. 37, p. 66). Truthmaker theory is, for the reasons just given, a plausible theory possessing independent support from sources other than those having to do with its regimenting role. 3. How Does Truthmaker Theory Regiment? Truthmaker theory regiments, and hence justifies, revisionary theorising by explaining and making plausible the ‘leap’ from appearance to reality on which such theorising depends. It informs us, moreover, about what, in appearance, should concern the revisionary metaphysician: the true propositions. True propositions are importantly and relevantly concerned with reality as they are made true by it. But, what exactly can true propositions tell us about the fundamental structure of reality? In trying to answer this question, it is instructive to compare truthmaker theory with its near relative, correspondence theory.t s Lewis

similarly contests the view that deflationary theories of truth puncture “the big, interesting claims made by rival theories of truth such as correspondence theory, the coherence theory, the pragmatic theory, or what have you” (Ref. 36, p. 603). Substantial and deflationary theories not only can ‘co-exist peacefully’, but (and here Lewis has the company of Niiniluoto37 ) should. Similar arguments appear in Refs. 28, p. 288– 89; 26, p. 159 and 38, p. 25 ff. t By ‘correspondence theory’ I here intend the type of theory proposed in inter alia Russell23 and Wittgenstein.24 As both Russell and Wittgenstein later abandoned strong and simple correspondence theory (Wittgenstein completely, Russell less radically and variably over time), the correspondence theory here discussed should be cautiously described as ‘Russellian’ or ‘Wittgensteinian’.

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Correspondence theory, like truthmaker theory, ‘grounds’ truth in a distinct and independent reality; and according to both theories it is possible to identify a basic stock of ‘truth atoms’ by studying and logically analysing known truths (whether they are mathematical, scientific or everyday truths). Atomic truths are ontologically significant, since they are made true by, or correspond to, reality directly. Molecular propositions, by contrast, have a truth value that depends entirely on the truth value of their constituents, and on the manner in which these are (logically) combined. Molecular propositions consequently require no special truthmakers but can sponge off the truthmakers of their constituent atomic propositions. This ‘logical atomism’ regiments ontological theorising by once again restricting its relevant object of study. Reality minimally contains whatever is required for the truth of the logically atomic propositions. It is therefore only by studying these, and not molecular truths, that information about the fundamental structural features of reality can be procured.u What sets correspondence and truthmaker theory apart is that, according to the former, the logical analysis of known truths reveals much more than what are the ultimate truthbearing units. According to the correspondence theory’s ‘mirror thesis’, once the atomic propositions have been identified, their logical structure (which is hidden beneath their grammatical structure) will mirror the ontological structure of that portion of reality to which they correspond. “Propositions show the logical form of reality”, says Wittgenstein (Ref. 24, p. 4.121). Again: “The propositions of logic describe the scaffolding of the world, or rather, they represent it” (Ref. 24, p. 6.124). It is because correspondence theory assumes an isomorphism between the logical structure of propositions and the ontological structure of reality that its regimentation is both strong and transparent.v In the framework of the u Much

effort has been spent investigating, criticising or trying to save logical atomism in its most general form. Contemporary critics include Cox,39 Gregory40 and Milne.41 Logical atomism is defended by Simons,26,29 Smith42 and Rodriguez–Pereyra.31 It is especially the negative and universally quantified propositions that seem to resist the prescribed variety of logical analysis. The questions raised in this debate are both many and interesting, but I will, for the purposes of this paper, disregard them. If it turns out that not all molecular propositions can have their truth determined in the way prescribed by logical atomism, this will add to, and probably complicate, the explanatory task for a theory set in a truthmaker theoretical framework. Whatever the consequences for individual theories, however, finding out that logical atomism does not hold generally will make no difference to the regimenting capacity of truthmaker (or correspondence) theory. v Unveiling the correct logical form of propositions may, of course, be both complicated and highly controversial. Consider e.g., Ramsey’s argument against the distinction

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correspondence theory, it is precisely those categories disclosed by logical analysis that ought to be posited in ontology. Logical atomism can be portrayed as a ‘two-tiered system’ (Ref. 26, p. 158). Its first tier involves identification of the formally atomic propositions — the atoms of our conceptualisations — by means of logical, conceptual and linguistic analysis. To obtain the second tier, not only formally, but also substantially, atomic propositions must be identified. Substantially atomic propositions are those that are made true by entities that are likewise ‘atomic’. With the mirror thesis added to logical atomism, formally and substantially atomic propositions coincide. Adding the mirror thesis is equivalent to saying that “if a sentence has or could have more than one truth-maker, then it is logically complex” (Ref. 28, p. 298–99). It is this running together of formally and substantially atomic propositions that renders the correspondence theory less suitable for regimenting ontological theorising. It simply does not seem very plausible to suppose that, although they are distinct and possibly different, the structural features of reality and the structural features of atomic truths as represented in classical first-order predicate logic coincide.w With the mirror thesis in place, moreover, substantial ontological disagreement appears to be ruled out and replaced instead by disagreement over the proper analysis of the logical form of propositions. Luckily, the distinction between formally and substantially atomic propositions can be preserved; and if it is, the substantially atomic propositions will form only a privileged subset of the formally atomic propositions. To illustrate this, consider the (let us suppose) formally atomic proposition . Given the science of colour, it seems reasonable to suppose that although it is formally atomic, this proposition will nevertheless between universals and particulars.43 Ramsey, it seems to me, agreed with Russell on the fundamentals of logical atomism (at least, for the purposes of this argument). They disagreed, however, over the correct logical analysis of the atomic propositions. According to Russell, atomic propositions are constituted by terms of two types that are not only grammatically but also logically different. According to Ramsey, atomic propositions do consist of two sorts of term, yet anything there is can serve the function of either term. Consequently, the linguistic complexity in question is merely grammatical, not logical, and does not require a corresponding complexity in its truthmakers. Without the mirror thesis, the view that there is no distinction between particulars and universals could not earn support from the claim that there is no distinction between subject and predicate. See also Ref. 44. w Armstrong refers to the mirror thesis as the ‘bane of correspondence theory’ (Ref. 4, p. 16). Smith calls it ‘a dark force’ which “haunts much of what is most admirable in the philosophy of the last hundred years” (Ref. 19, p. 153).

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require complexity of its truthmakers. Formally atomic propositions, consequently, can turn out to be substantially complex; and whether or not they are cannot be decided with recourse only to logical analysis. To hold that formal and substantial atomicity come apart is to hold that logical and ontological form come apart, and hence to reject the mirror thesis. As this is the avenue chosen by the truthmaker theorist, she cannot, like the correspondence theorist, be accused of regimenting revisionary theorising too rigidly. As Mulligan et al. state: “Here, in contrast, we uphold the independence of ontological from logical complexity: Ontologically complex objects (those having proper parts) are not for that reason also in some way logically complex, any more than there is reason to suppose that to every logically complex (true) sentence there corresponds an ontologically complex entity which makes it true” (Ref. 28, p. 298). Unfortunately, rejection of the mirror thesis has left a hole, and unless this hole is somehow plugged it will be complained, rightly, that the theory is unable to regiment ontological theorising enough. There is no ‘royal road’ to truthmakers, and that is a good thing; but to be able to regiment, the truthmaker theory must offer us some road. What does the truthmaker theory offer in place of the correspondence-theoretical mirror thesis? This is the short answer: although there is no royal road from truths to truthmakers, studying the one will give us some information about the other. In particular, the atomic propositions inform us about the truthmaking roles that the entities posited in our favoured ontology should be able to play. As Read says: “Rather than enter into a detailed metaphysics of the nature of truthmakers, the theory of truthmaking works top-down by explicating the roles which truthmakers play — by formulating the postulates they must satisfy” (Ref. 34, p. 67). Ontological theorising in accordance with truthmaker theory, then, first involves the identification of the formally atomic propositions. Let us suppose that these include (at least) propositions of the following three forms: Subject–predicate propositions () Identity propositions () Singular existential propositions ().x xI

have argued elsewhere (See Ref. 1, p. 57–58) that the list of formally atomic proposition

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It next involves thinking about the roles that whatever there is must, minimally, be able to play for these types of proposition to be true. Role identification is sometimes relatively straightforward — as when singular existential propositions like are said to require for their truth something playing the roles normally associated with the concrete particular. Sometimes, however, it is more difficult. A case in point is the rudimentary subject–predicate proposition — propositions like . Here opinions are divided between those who believe that truthmaking requires us to posit truthmakers capable of playing the roles we associate with the abstract universal3 and those who argue instead that no more than the roles we associate with tropes is required.1 On reflection, moreover, it may turn out that the atomic propositions should be further subdivided in ways that relevantly reflect differences in the roles their truthmakers must be able to play. This appears to be true, for instance, of propositions of the subject–predicate form: Simple predicative propositions () Second order predicative propositions () Kind predicative propositions () Substantially predicative propositions () Truthmaker theory regiments by singling out propositions whose examination will reveal what roles the relevant truthmakers must be able to play if their inclusion in ontology is to be justified. But this is only to say that the regimenting burden has shifted from the meticulous unveiling of hidden logical structures to the proper identification of truthmaking roles. To say that the truthmaker for must be able to play the roles associated with concrete particulars is not to properly explain what its truth really requires. What roles are those? What does identifying them entail? How is their identification regimented? Together, these questions require a long answer; and only a small portion of that answer could refer to a study of the formal features of the atomic propositions. This portion would concern the role of entailment. For, given the entailment thesis, if a truthmaker makes true

, it also and necessarily, makes true all the propositions (relevantly) entailed by

. To should include what I have called ‘comparative’ propositions (‘a is the same F as b’). It could be argued (as well it has been) that comparative propositions are not atomic, but rather complex propositions (‘a is F’ and ‘b is F’). This is Rodriguez–Pereyra’s view (See Ref. 31, p. 39). I shall not pursue this matter here.

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understand and properly identify the roles our truthmakers must be able to play will involve understanding how complex roles break down into simpler ones, and how different roles relate to one another. Here, knowing what a proposition entails will, of course, be valuable. However, entailment is far from powerful enough to be our only source for such information. As pointed out by Armstrong, the truthmaking relation seems to hold in many cases where entailment is completely lacking: “Suppose that it is true that there exists a certain quantity of water in a certain place at a certain time. Will not a sufficiently dense conglomeration of H2 O molecules in that space at that time be a truthmaker for this truth? It seems to me that we ought to accept such truthmakers. But if we replace this truthmaker, as we can do easily enough, with a truth of existence, this truth does not entail the first truth” (Ref. 4, p. 6). If we wish to identify the relevant truthmaking roles, continued formal examination of the atomic propositions, however fastidious, will not do. Something else is needed, but what? Consider, again, the (true) atomic proposition . It requires for its truth the existence of something playing the roles normally associated with concrete particulars. To find out more about these roles, it seems that we must consult not only logic, or language, but also sources like common sense or mature science. y To be able to start doing revisionary metaphysics in a justified and well regimented way, it now seems that another philosophical investigation must already be finished — an investigation, that is to say, issuing in the formulation of a coherent account of what there seems to be according to our different and partly conflicting conceptions of reality. This is an enterprise very much like Strawson’s descriptive metaphysics: “How should [descriptive metaphysics] differ from what is called philosophical, or logical, or conceptual analysis? It does not differ in kind of intention, but only in scope and generality. Aiming to lay bare the most general features of our conceptual structure, it can take far less for granted than a more limited and partial conceptual inquiry. Hence, also, a certain difference in method. Up to a point, the reliance upon a close examination of the actual use of words is the best, and indeed the only sure, way in philosophy. y For

an interesting discussion of the relationship between metaphysics and science, see Ref. 45.

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But the discriminations we make, and the connexions we can establish in this way, are not general enough and not far-reaching enough to meet the full metaphysical demand for understanding” (Ref. 16, p. 9–10). To “meet the full metaphysical demand for understanding”, the descriptive enterprise is extended. This, I believe, is why Strawson’s own characterisation of the descriptive enterprise as “content to describe the structure of our actual thought about the world” (as opposed to the revisionary enterprise which is “concerned to produce a better structure”) is misleading. In trying to lay bare the core-structural features of appearance, and in attempting to harmonise and make consistent different ways in which the world appears to us, we shall probably find recourse to revision necessary. If, for instance, we find that the way our best science describes the world has earned it a special status among our many and various conceptual schemes, the result may be a descriptive metaphysics that is, according to (say) our everyday conception of the world, partly in conflict with appearances. It is the descriptive metaphysician’s job to identify and characterise the truthmaking roles and the revisionary metaphysician’s job to supply truthmakers able to play them (cf. Ref. 12, p. 74 ff). This occasions another modification of the Strawsonian distinction between the descriptive and the revisionary enterprise. Not only can descriptive metaphysics be revisionary, but it also seems that revisionary metaphysics in a certain sense cannot. The truthmaking roles identified in descriptive metaphysics regiment the revisionary enterprise. They constitute the starting point for revisionary theorising, as well as the background against which evaluation and justification proceeds. Truthmaker theory is able to justify revisionary theorising just enough because, when it is added to a descriptive metaphysics concerned with identifying truthmaking roles, it licenses our drawing conclusions from the results of the descriptive investigation to ontology. The fact that whatever we posit in our revisionary ontology must be able to play the truthmaking roles identified by descriptive metaphysics is what makes ontology relevantly concerned with reality as we know it. 4. Tropes as Truthmakers Revisionary trope theory holds that the world is a world of tropes. The theory is justified if tropes can play the truthmaking roles identified in descriptive metaphysics. That there is still controversy over exactly which

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roles to include in the revisionary ‘must-do’ list is not surprising. In fact, as much should be expected given the intricate and extensive investigation their identification entails. That there is no finalised list of truthmaking roles does not mean that we cannot propose or evaluate a revisionary ontology. To be able to do that, we need merely a provisional list of truthmaking roles. Such a list, I take it, will include some of the roles associated with two categories that are obviously implicated by the truth of some (perhaps all) of the atomic propositions: the category of concrete particulars and the category of abstract universals. To say that the world’s truthmakers should include concrete particulars, let us suppose, is to demand that the world’s truthmakers include entities capable of fulfilling (at least) the following truthmaking functions: (i) they should be able to change over time while retaining their identity; (ii) they should be able to monopolise their position in space–time (i.e., no other entity of the same kind should be able to occupy exactly the same position); and (iii) they should not be able to exist at more than one place in space at one moment in time. To say that the world’s categories should include abstract universals is to demand that the truthmakers of one’s choice simultaneously be capable of fulfilling (at least) the following functions: (i) they should not monopolise their place in space–time (i.e., more than one entity of the same kind should be able to occupy the same position in space–time); and (ii) they should be shareable (i.e., they should be able to characterise, or be true of, more than one entity at one time). These are highly provisional lists, but evaluation of the prospects for revisionary trope theory does not require much else. In fact, it is enough if the trope theorist concentrates on only two of these roles — roles that appear particularly problematic from a trope-theoretical perspective. Concrete objects are complex entities that monopolise their place in space and time. Tropes are not concrete in this sense, and an explanation of how a world of only tropes can nevertheless supply truthmakers that are able to play the concreteness role must be produced. Universals, furthermore, are shareable. If everything is particular, some elaborate story telling us how what is particular can nevertheless give rise to what is shareable must be supplied. That trope theory can provide a satisfactory explanation of the emergence of at least these roles I have argued in depth elsewhere.1 Here I can only indicate how the required explanations might look, and why I believe criticism of them can be handled in a satisfactory manner.

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The role associated with so-called abstract universals, first. From the perspective of a one-category trope theory, the question becomes: how can there be anything universal when all that exists is particular? If the world is a world of tropes, the shared nature of concrete objects boils down to the shared nature of the tropes that characterise them individually. From a trope-theoretical perspective, therefore, the fundamental question is this: what makes it true that two or more distinct tropes, each with their own particular qualitative character, can also be said to share this character? A reasonable trope-theoretical answer is that tropes share a nature by (exactly) resembling each other. Exact resemblance is an equivalence relation that will partition the entire field of tropes without residue or overlap. Equivalence classes play the role of the universal — they are ‘ersatz universals’.11 Resemblance, moreover, is an internal relation; and to some observers, as we have seen, this means that it can partition the field of tropes without being added to the ontology — it is a free lunch. But even if one is unwilling to agree that what is internal is a free lunch, resemblance manages to explain how what is particular can play the universality role. Adding resemblance while still respecting the basic theses of trope theory, it has been objected, forces the trope theorist to recognise the relation as yet another trope, a recognition that gives rise to the famous Russellian resemblance regress.23,z Now the type of theory against which this regress argument was originally formulated admitted only the existence of concrete particulars, and argued that to have a property was for a concrete particular to resemble an exemplar to a suitable degree, whilst for two objects to share a property was for them to resemble the same exemplar, once again to a suitable degree: “The general term ‘white’, in this view, is defined for a given person at a given moment by a particular patch of white which he sees or imagines; another patch is called white if it has exact likeness in colour to the standard patch. In order to avoid making the colour a universal, we have to suppose that ‘exact likeness’ is a simple relation, not analyzable into a community of predicates; moreover, it is not the general relation of likeness that we require, but a z Whether a regress is also generated if resemblance is regarded as a ‘free lunch’ is disputable. However, for present purposes it does not matter either way. If no regress is generated, there is no problem. If a regress is generated, it is virtuous — so, again, there is no problem.

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more special relation, that of colour-likeness, since two patches might be exactly alike in shape or size but different in colour” (Ref. 23, p. 111). It is to avoid making the relation of colour-likeness universal that the same analysis as was previously applied to the property shared by distinct objects must now be applied to it: “we may take a standard particular case of colour-likeness, and say that anything else is to be called a colour-likeness if it is exactly like our standard case” (ibid.). This leads to an infinite regress which, according to Russell, is ‘plainly vicious’. Trope theory can be the target of a similar argument. To illustrate, imagine three objects sharing the property of being red. Sharing a property, says the trope theorist, amounts to the exact resemblance of the three red-tropes characterising each of the three red objects individually. But if there are only tropes, exact resemblance is a trope. Consequently, for each class of exactly resembling tropes, there will be one resemblance-trope uniting its members. Moreover, all resemblance-tropes will be the same. As it has already been decided that to be the same is to be related by exact resemblance, the sameness of the exact resemblance-tropes will force into existence a second ‘level’ of exact resemblance tropes. Resemblance-tropes that hold between resemblances are (also) the same — they are resemblances. That is to say (as above) that there will be resemblance-tropes holding between the resemblance-tropes, and so at the next level, and at the next, ad infinitum. On the face of it, Russell’s original resemblance regress and its tropetheoretical counterpart look exactly the same. The trigger, in both cases, is the state of affairs that ‘a exactly resembles b’. One difference is, of course, that on the view criticised by Russell a and b are concrete objects, whereas the basic question for trope theory will concern the exact resemblance of tropes. The relevant difference is not this one, however. What is relevant is instead a difference in the direction of dependence that characterises each kind of regress. According to the view criticised by Russell, for an object to have a property is for it to be exactly like the object serving as a standard for that property. According to trope theory, on the other hand, for an object to have a property is for it to contain a trope. Tropes belong to classes of exactly similar tropes, and because objects contain tropes they, too, form classes based on their likeness in certain respects. However, and in contrast with the view criticised by Russell, these objects do not have properties because they belong to a particular similarity class. Instead, they

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belong to a particular similarity class because they have some properties — the tropes — which, as it were, ‘are’ their primitive nature. On the view criticised by Russell, it is a condition of the trigger — a exactly resembles b — existing, or obtaining, that the existence of the similarity class to which the exact similarity holding between a and b belongs also exists, and so on for each new level of exact similarity. In the trope theory case, however, the existence of the very same trigger requires no more than the existence of tropes a, b and their resemblance. The fact that the view criticised by Russell requires, for the existence of the trigger, that the next step of the regress should exist, and so on, ad infinitum makes this regress vicious. The trope-theoretical regress exhibits the opposite direction of dependence; and therefore the infinite regress does not prevent the trigger from existing. It is rather the existence of the trigger that sets into motion the infinite generation of exact resemblance tropes. The trope-theoretical resemblance regress is, therefore, infinite but virtuous. It is like the truth regress and other well known virtuous regresses. The roles associated with concrete particulars, next, seem problematic from the perspective of a one-category trope theory, because tropes are abstract entities that do not, for one thing, monopolise their place in space– time. Once again, relations come to the rescue here. It is possible for the world to contain concrete things that are apt to make propositions like true, says the trope theorist, because tropes in compresence give rise to concrete particulars. (If enough tropes are congregated, the result, it is supposed, will be what Husserl called a ‘pregnant whole’.) This suggestion struggles with a notorious problem: the Bradley regress. Suppose that something rather simpler than Mary exists — imagine, for example, that is true. Suppose, furthermore, that the ball is constituted by its roundness (r), its yellowness (y) and its weighing 0.5 kilos (w). According to the trope-theoretical suggestion, the roles we associate with whatever makes true cannot be played by r, y and w individually. They can, however, be played by the whole they form if they are related by compresence. Compresence, unlike resemblance, is an external relation: a world that containsr, y and w does not have to contain the ball. Adding compresence makes a difference.a If the world is a world of tropes, moreover, compresence must be yet another trope. But why, if a Notice

that to be able to generate this regress we must agree that the relation in question is external. I have argued that one should regard compresence as an external relation in Maurin (Ref. 1, p. 129–134). Not everyone agrees, however. (Most notably Simons does not.5 ) I will not argue for the externality of compresence here.

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the existence of our original tropes was not enough to account for their unity, should the addition of one more trope suddenly do the trick? Compresence, it seems, could exist without relating anything. Alternatively, if this possibility is denied — if one holds, plausibly it would seem, that relations must relate something — it will follow that compresence could exist and not relate r, y and w. To make sure, therefore, that the addition of compresence does the work for which it was intended, something must again be added. What unites r, y, and w with compresence? The answer seems as unavoidable as it is problematic: another trope of compresence — and so the regress is up and running.b The unity of r, y and w depends on their being compresent. What the Bradley regress shows is that adding relation does not result in the requisite unity; instead it just pushes us one step further up the regressive ladder, making each step depend on the next. The Bradley regress, consequently, exhibits a dependence pattern of the vicious kind. Although this situation is, admittedly, serious, all is not lost for the trope theorist. A way out is to affirm what Bradley denies: to insist, that is, that relations are different from their relata, and that they are different in precisely the sense that they relate whereas their relata do not. I have suggested in previous work (Ref. 1, p. 163–166) that this difference can be spelled out in terms of dependence. The difference between a monadic property and a relation, I suggest, is that a relation, although its existence is contingent (that is, it might or might not exist), must, if it exists, relate exactly the entities it in fact relates. In other words, every relation is specifically dependent on the entities it relates. This is true while, on the other hand, the related entities are not likewise dependent on the existence of the relation in question (unless, of course, the relation is internal); so the specific dependence is one way. To put the point another way, relations are external to the entities they relate, but at the same time the related entities are internal to the relation. This suggestion manages to both respect our intuitions about relations as something other than their b This is how Bradley originally put it: “The 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 to be the ascription of one to the other. If so, it would appear to be another relation, D, in which C, on the 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” (Ref. 46, p. 23).

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relata and provide an ontologically sound account of this difference. It is however a controversial suggestion that has generated some criticism.3,15 Fortunately, the success of trope theory does not necessarily depend on it, as alternative solutions have been devised, and, I am sure, others remain to be formulated.5,12 5. Why Should One Hold That the World Is a World of Tropes? Although some problems and many details remain to be worked out, it does not seem unreasonable to suppose that the entities posited in a one-category trope theory could play the requisite truthmaking roles. Suppose even that it had been firmly established that they could. Would it follow that one should hold that the world is a world of tropes? Unfortunately not. Noting that tropes can fulfil their truthmaking function does not discriminate trope theory from rival revisionary ontologies — unless, of course, and very implausibly, the posited entities of no other ontology were able, likewise, to fulfil this function. There is still room for wondering whether or not the world is a world of tropes rather than states of affairs, concrete objects, Platonic forms or whatever else is apt to play the truthmaking roles. That reasons traditionally cited for holding that the world is a world of tropes are inadequate should come as no surprise. Such reasons include arguments from experience (“What we primarily see of the moon, for example, is its shape and color and not at all its whole concrete bulk” (Ref. 9, p. 16)); from causality (“When you drop it, it is the weight of this particular brick, not bricks or weights in general, which breaks the bone in your particular left big toe” (Ref. 11, p. 113)); from evaluation (“Evaluation is similarly focussed on abstracta. What most men value the moon for is its brightness; what a child wants of a lollipop is a certain flavour and endurance” (Ref. 9, p. 16)); and from language:c “The clue that moments may serve as truth-makers comes initially from linguistic considerations. Most terms which describe moments, or under which moments fall, are in fact nouns formed by nominalisation of verbs and verb-phrases” (Ref. 28, p. 296). Some of these arguments cite perfectly respectable reasons for holding that the world is a world of tropes if trope theory is developed in a framework c What

Mulligan, Simons and Smith call ‘moments’ is what I here call ‘tropes’. See also Refs. 47, 48.

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other than the revisionary one. Regrettably, however, these reasons cannot be called upon to the same effect by the revisionary metaphysician.d We find ourselves at a crossroads very much like the one at which we first asked how conclusions in revisionary ontology can be justified if there is no substantial evidence on which they can rely. I have argued since then that there is some such evidence after all, and that justification is therefore forthcoming. We now ask the similar question: how can we justifiably decide between rival ontological theories if there is no substantial arbitrator available? We cannot, however, answer this question in the same vein as we answered our first question. The theories up for comparison have already made use of what evidence, derived from appearance, they are allowed. They are all ex hypothesi theories positing entities that are equally apt to fulfil their truthmaking function. This time, therefore, the ordinary theoretical virtues will provide the only basis on which we can make our decision, and even some of those are unavailable. The explanatory value of rival theories, for instance, must, again ex hypothesi, be the same. Simplicity, it seems, must play a decisive role and prima facie it appears to count in favour of a one-category theory of tropes. But simplicity is a complicated thing. We must ask ourselves what type of simplicity we should prefer and why.e The fact that we are obliged, when choosing between theories that are equally apt to provide truthmakers, to appeal merely to (some of) the theoretical virtues is not as bad as it would have been if we had been forced to appeal to these virtues alone when we faced our first predicament, however. The theories to be compared, we assume, are independently justified. They all feature entities that relevantly and adequately fulfil their truthmaker-theoretical function. They are not ‘consistent but incredible fairy-tales’. To sum up, revisionary theorising can be justified if one agrees that truths are made true by portions of reality, and that, by studying known truths in descriptive metaphysics, the roles we should expect our truthmakers to play can be identified. To justify revisionary theorising more d From

the quote above, it may appear that Mulligan, Simons and Smith argue inappropriately in this sense. However, after claiming that language is at least to some extent a reason to hold that the world is a world of tropes, they add: “This simplest possible version of the theory is inadequate as it stands, however . . . because the theory which claims that by nominalising a sentence we have thereby designated the relevant truthmaker can hardly count as a substantial elucidation of making true. It seems — like Tarski’s theory — to turn on a linguistic trick” (Ref. 28, p. 297). e Cf. Ref. 49, in which it is argued that trope theory is worse off than universal realism because it must (and universal realism need not) posit primitive axioms of resemblance.

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theory is consequently needed. The revisionary metaphysician asks about the fundamental constitution of reality as it is, independently of how it seems, but cannot, for obvious reasons, get beyond discoveries about the way the world seems to us, on our best evidence. There is no view from nowhere. This is why the revisionary enterprise is a hypothetical enterprise. If truth is determined by reality, and if descriptive metaphysics can uncover the requisite truthmaking roles, then. . . Revisionary ontology set in this type of framework, furthermore, is only concerned with truth and with coming up with entities fit to play the roles required by truth. This means that such ontology is relevantly concerned with reality as it seems to us, but also that it is concerned only with one aspect of this reality: truth. It is because revisionary ontology is, in this sense, underdetermined by appearance that the comparison of theories, once the otherwise equivalent revisionary ontologies have been formulated, becomes a less interesting affair. In a revisionary framework the interesting and difficult philosophical questions are intra- rather than inter-theoretical. If reality is constituted by tropes (or, by states of affairs, or universals, or particulars, or some such) what does this entail? What problems does the choice of this or that ontology engender, and how are these problems best solved? This is the ‘hypothetical stance’ which, from a revisionary point of view, is the only interesting stance to take. Acknowledgments I would like to thank Johan Br¨ annmark, Nils-Eric Sahlin and the participants at the Reading–Lund workshop in May 2006 for helpful comments and suggestions on earlier drafts of this paper. References 1. A.-S. Maurin, If Tropes. Dordrecht: Kluwer Academic Publishers (2002). 2. A.-S. Maurin, Same but Different. Metaphysica 1, 129–146 (2005). 3. H. Hochberg, Relations, Properties and Predicates. In: H. Hochberg and K. Mulligan (Eds.), Relations and Predicates. Heusenstamm: Ontos Verlag, 17–53 (2004). 4. D. M. Armstrong, Truth and Truthmakers. Cambridge: Cambridge University Press (2004). 5. P. Simons, Particulars in Particular Clothing: Three Trope Theories of Substance. Philosophy and Phenomenological Research 54 (3), 553–74 (1994). 6. I. Segelberg, Properties. In: S. Ringstr¨ om–Hochberg and H. Hochberg (Trans.), Three Essays in Phenomenology and Ontology. Stockholm: Thales, 133–233 (1999 [1947]).

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7. G. F. Stout, Are the Characteristics of Particular Things Universal or Particular? Proceedings of the Aristotelian Society (supp. vol.) 3. London: Williams and Norgate, 114–122 (1923). 8. E. Husserl, Logical Investigations. J. N. Findlay (Trans.). London: Routledge and Kegan Paul (1970 [1900]). 9. D. C. Williams, On the Element of Being. The Review of Metaphysics 7 (1–2); 3–18, 171–192 (1953). 10. J. Bacon, Universals and Property Instances — The Alphabet of Being. Aristotelian Society Series 15. Oxford: Blackwell (1995). 11. K. Campbell, Abstract Particulars. Oxford: Blackwell (1990). 12. M. Kein¨ anen, Trope Theories and the Problem of Universals. Helsinki: Department of Philosophy (2005). 13. C. B. Martin, Substance Substantiated. Australasian Journal of Philosophy 58 (1), 3–10 (1980). 14. K. Trettin, New Literature on Tropes. Metaphysica 1, 151–158 (2004). 15. K. Trettin, Tropes and Relations. In: H. Hochberg and K. Mulligan (Eds.), Relations and Predicates. Heusenstamm: Ontos Verlag, 203–218 (2004). 16. P. F. Strawson, Individuals. London and New York: Routledge and Kegan Paul (1959). 17. P. Simons, New Categories for Formal Ontology. In: R. Haller (Ed.), Investigating Hintikka. Grazer Philosophische Studien 49, Amsterdam: Rodopi, 77–99 (1995). 18. P. Simons, Metaphysical Systematics: A Lesson from Whitehead. Erkenntnis 48 (2–3), 377–393 (1998). 19. B. Smith, Against Fantology. In: M. E. Reicher and J. C. Marek (Eds.), Experience and Analysis. Vienna: o ¨bv&hpt, 153–170 (2005). 20. J. Lowe, Recent Advances in Metaphysics. Formal Ontology in Information Systems: Collected Papers from the Second International Conference, New York: ACM Press (abstract) (2001). 21. D. M. Armstrong, Universals and Scientific Realism vol. 1., Cambridge: Cambridge University Press (1978). 22. A.-S. Maurin, The One over Many. In: T. Mey and M. Kein¨ anen (Eds.), Problems from Armstrong. Acta Philosophica Fennica 84 (2008). 23. B. Russell, Logic and Knowledge. R. C. Marsh (Ed.). London: George, Allen & Unwin (1956). 24. L. Wittgenstein, Tractatus Logico–Philosophicus. D. F. Pears and B. F. McGuiness (Trans.). London: Routledge & Kegan Paul (1922). 25. H. Beebee and J. Dodd, Truthmakers — The Contemporary Debate. Oxford: Oxford University Press (2005). 26. P. Simons, Logical Atomism and its Ontological Refinements: A Defense. In: K. Mulligan (Ed.), Language, Truth and Ontology. Dordrecht: Kluwer Academic Publishers, 157–179 (1992). 27. G. Rodriguez–Pereyra, Why Truthmakers. In: H. Beebee and J. Dodd (Eds.), Truthmakers. Oxford: Oxford University Press (2005). 28. K. Mulligan, P. Simons and B. Smith, Truth-Makers. Philosophy and Phenomenological Research 44 (3), 287–321 (1984).

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29. P. Simons, Negatives, Numbers, and Necessity: Some Worries About Armstrong’s Version of Truthmaking. Australasian Journal of Philosophy 83 (2), 253–261 (2005). 30. B. Smith, Truthmaker Realism. Australasian Journal of Philosophy 77 (3), 274–291 (1999). 31. G. Rodriguez–Pereyra, Resemblance Nominalism: A Solution to the Problem of Universals. Oxford: Oxford University Press (2002). 32. J. Bigelow, The Reality of Numbers. Oxford: Clarendon Press (1988). 33. G. Restall, Truthmakers, Entailment and Necessity. Australasian Journal of Philosophy 74 (2), 331–340 (1996). 34. S. Read, Truthmakers and the Disjunction Thesis. Mind 109 (433), 67–79 (2000). 35. G. Rodriguez–Pereyra, Truthmaking and the Slingshot. In: Metaphysics in the Post-Metaphysical Age — Papers of the 22nd International Wittgenstein Symposium. Kirchberg am Wechsel: Austrian Ludwig Wittgenstein Society, vol. 2, 177–184 (2001). 36. D. Lewis, Truthmaking and Difference-Making, Noˆ us 35 (4), 602–615 (2001). 37. I. Niiniluoto, Tarski’s Definition and Truth-Makers. Annals of Pure and Applied Logic 126, 57–76 (2004). 38. H. Putnam, Meaning and the Moral Sciences. London: Routledge and Kegan Paul (1978). 39. D. Cox, The Trouble with Truth-Makers. Pacific Philosophical Quarterly 78, 45–62 (1997). 40. D. Gregory, Smith on Truthmakers. Australasian Journal of Philosophy 79 (3), 422–427 (2001). 41. P. Milne, Not Every Truth has a Truthmaker. Analysis 65 (3), 221–24 (2005). 42. B. Smith, Truthmaker Realism: A Response to Gregory. Australasian Journal of Philosophy 80 (2), 231–234 (2002). 43. F. P. Ramsey, Universals. Mind 34 (136), 401–417 (1925). 44. A.-S. Maurin and N.-E. Sahlin, Some Ontological Speculations: Ramsey on Universals, Particulars and Facts. Metaphysica special issue 3, 7–28 (2005). 45. K. Hawley, Science as a Guide to Metaphysics. Synthese 149, 451–470 (2006). 46. F. H. Bradley, Appearance and Reality. 2nd ed., London: The MacMillan Company (1908). 47. F. Moltmann, Properties and Kinds of Tropes: New Linguistic Facts and Old Philosophical Insights. Mind 123 (1), 1–41 (2004). 48. F. Moltmann, Events, Tropes and Truthmaking. Philosophical Studies 134 (3), 363–403 (2007). 49. D. M. Armstrong, Properties. In: H. Mellor and A. Oliver (Eds.), Properties. Oxford: Oxford University Press (1997).

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CAUSAL PLURALISM

STATHIS PSILLOS Department of Philosophy and History of Science University of Athens, Greece E-mail: [email protected] Most of the philosophical discussion about the metaphysics of causation has been dominated by what I call the ‘straightjacket’: the view that there is a single, unified and all-encompassing metaphysical story to be told as to what causation is. It has been presumed that the aim of philosophical inquiry is to tell this story. More specifically, it has been assumed that the aim of a philosophical theory of causation is to engage in conceptual analysis of the relation c causes e, where this analysis a) covers all and only cases in which intuitions determine that we correctly assert that c causes e; and b) is cast (preferably) in non-causal terms. This paper questions the plausibility and fruitfulness of the ‘straightjacket’ as a whole. It lays out a number of ways to deny the straightjacket, ranging from some mild ones to some genuinely pluralistic. It outlines and defends a version of causal pluralism according to which causation is very much like the common cold: a rather loose condition with no single underlying nature. What philosophers have taken to be the (competing) identifying characteristics of causation are, it is claimed, symptoms of causation. And though there is no unique nature of causation that these symptoms track, it can be traced reliably by its symptoms. Part of the argument for this causal pluralism will be what may be called Wittgensteinian pluralism, a view that can be traced back to G. E. M. Anscombe. The thrust of the argument is that explicit causal talk is dispensable, or almost dispensable, being useful for forming certain generalisations.

1. Introduction Most of the philosophical discussion about the metaphysics of causation has been dominated by what I shall call the ‘straightjacket’: the view that there is a single, unified and all-encompassing metaphysical story to be told as to what causation is.a It has been presumed that the aim of philosophical inquiry is to tell this story. More specifically, it has been assumed that the aim of a philosophical theory of causation is to engage in conceptual a If

this expression is taken to be too provocative, it may be replaced by the milder term ‘monism’. 131

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analysis of the relation c causes e, where this analysis a) covers all and only cases in which intuitions determine that we correctly assert that c causes e; and b) is cast (preferably) in non-causal terms. There has been no shortage of such conceptual analyses and no shortage of counterexamples to all of them. The counterexamples exploit, at least partly, situations in which we are presumed to have clear intuitions about what causes what, but which intuitions are not being respected by the suggested philosophical analysis. The counterexamples typically lead to a battery of sophisticated attempts to revise or amend the philosophical analysis so that it is saved from refutation. These attempts, typically, either deny the intuitions on which the counterexamples are based or accommodate the problematic cases within the theory by adding further clauses to the original philosophical analysis. The result of all this is that where the original philosophical theory rested on a simple, forceful and intuitively plausible idea (e.g., that causation consists in a relation of counterfactual dependence between discrete events), the modified philosophical theory becomes very convoluted, somewhat ad hoc and implausible. In this paper, my aim is not to review these theories. Anyone who has worked on the philosophy of causation is familiar with the problems they face.b My aim is to question the plausibility and fruitfulness of the ‘straightjacket’ as a whole. I will lay out a number of ways to deny the straightjacket, ranging from some mild ones to some genuinely pluralistic. I will outline and defend a version of causal pluralism according to which causation is very much like the common cold: a rather loose condition with no single underlying nature. What philosophers have taken to be the (competing) identifying characteristics of causation, viz., regularity, counterfactual dependence, probability raising, presence of a process, presence of a mechanism, are, I claim, symptoms of causation. And though there is no unique nature of causation that these symptoms track, though that is, causation (like the common cold) can be many things, it can be traced reliably by its symptoms. Part of the argument for this causal pluralism will be what may be called Wittgensteinian pluralism, a view that can be traced back to G. E. M. Anscombe.2 The thrust of the argument is that explicit causal talk is dispensable, or almost dispensable, being useful for forming certain generalisations. Causation comprises whatever conditions in fact exist in the general region corresponding to causal talk. But this talk is diverse and variegated and there is no conceptual or linguistic pressure to b Cf.

my Causation and Explanation.1

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have a theory of causation that ascribes to it a single and deep underlying nature. 2. The Straightjacket View The ‘straightjacket view’ of causation is the view that there are facts of the matter as to the whole bunch of issues that relate to the nature of causation (that is, that causation has a determinate nature), that a philosophical theory of causation should aim to reveal these facts and that a good philosophical theory of causation should tell a unified and complete story that covers each and every aspect of the nature of causation. In particular, the straightjacket view assumes that there are facts of the matter as to: • what kind of relation causation is. Here, the debate is about whether causation is ◦ singular or general ◦ extrinsic to its relata or intrinsic to them ◦ irreducible to anything else or reducible to (or supervenient upon) non-causal facts. If causation is taken to be irreducible, there is the further issue of whether it is a primitive relation or further analysable (though irreducibly so). If causation is taken to be further reducible, there is the issue of what the basis of reduction is:       

regularities necessary and/or sufficient conditions relations of counterfactual dependence probabilistic relations (e.g., contextual unanimity) the transference of some property, or trope, or . . . the possession of a conserved quantity the fact that some event was the last change in the environment of another event just before the latter happened  relations of invariance under interventions  . . . (fill in the dots with your preferred view, if it is none of the above).

Supposing that these issues have been settled, the straightjacket assumes that there are further facts as to • what formal properties the causal relation has • what the causal relata are.

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Here, the debate is about whether the causal relata are events or facts or properties or tropes or. . . or a combination thereof. Supposing that these issues have been settled, the straightjacket assumes that there are further facts as to • the number (adicity) of the relata • the proper form of causal statements Finally, supposing that these issues have been settled, the straightjacket assumes that there are further facts as to • what the direction of causation is. There is no point in putting flesh on the above philosophical skeleton by detailing well-known philosophical theories of causation. But there is a point in reminding the reader that there is no theory of causation that is counterexample-free. Nor is there any theory of causation that tallies best with all our intuitions about what causes what. Nor are these intuitions always clear-cut and forceful. Hence, the current-state of play in the philosophy of causation is something like this: ingenious additions of epicycles to intuitively plausible theories and inconclusive (though suggestive) intuition-based arguments. This point could be brought home by examining any theory, but to illustrate it one could just look at the counterfactual theory of causation and the massive literature concerning the problems of pre-emption, early pre-emption, late pre-emption, trumped pre-emption, double prevention, etc. The persistent failure to find an adequate philosophical theory of causation may well make us sceptical about the prospects of a theory that complies to the straightjacket: there is no single, unified and all-encompassing theory of causation. Perhaps, there is no metaphysical fact of the matter as to what causation is; no deep, simple and unified nature of causation. Obviously, this type of argument is not conclusive. But it is not meant to be so. Rather, it is meant to cast doubt on the plausibility and fruitfulness of the search for an adequate metaphysical account of causation. Why is there any hope that persistent failure will be, at some point, replaced by success? This kind of scepticism is not of the sort associated (perhaps, mistakenly) with Hume. It is not based on qualms about the unobservability of the supposed necessary connections in nature, nor on claims about the undefinability of causation. Nor is the kind of scepticism associated with Russell. It is not based on the claim that science does not search for causes,

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nor on the claim that the principle of causation is devoid of content. As will be explained later on, we can and do know a lot about what causes what. One need not be sceptical about causal knowledge, or indeed about causation, if one is sceptical about the possibility of a metaphysics of causation of the sort envisaged by the straightjacket. In the sequel, I will use this kind of scepticism as motivation for the development of causal pluralism. Then, in articulating and defending causal pluralism I will present an argument that aims to remove some of the rationale for trying to offer a metaphysical account of causation that reveals its deep and unique nature. Before we move on to this, let us in sections 3 and 4 examine some prima facie plausible ways to resist the straightjacket.

3. The Functional View A popular viewc has been that causation should best be understood in a functional way. State a number of propositions that our folk theory of causation consists in (or a number of platitudes that the concept of causation should satisfy) and use them to fix the reference of CAUSATION: causation is whatever satisfies this folk theory (or the set of platitudes). This move can be worked out more formally in terms of Ramsey-sentences: causation is whatever satisfies the Ramsey-sentence of our folk theory of causation (or the set of platitudes). Though compatible with the straightjacket, the functional view is a step forward since it is also compatible with a more neutral account of the metaphysics of causation. An advocate of the functional view does not have to accept that there is a deep metaphysical story to be told about the nature of causation. Nor does she have to accept that the folk theory of causation has something or other to say about all issues that the straightjacket says there is a fact of the matter. It is typical, however, of the advocates of the functional view to claim that there is a deep and unified metaphysical nature of causation that the functional approach identifies indirectly through the platitudes. Menzies, for instance, includes among the platitudes the claim that causation is a singular relation among events, thereby making it inevitable that only a certain metaphysical account of causation will be compatible with the functional approach. The problem with functionalism is that the folk theory of causation is not given in a forceful and intuitively compelling way. A lot of questions c Defended

by Peter Menzies in Refs. 3–4.

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will be begged if the platitudes are chosen one way instead of another. If, for instance, the claim that causation is a singular relation among events is taken as part of the folk theory, no regularity (or generalist) account of causation can satisfy the folk theory. But who’s to decide and how what the platitudes of causation are and in particular that the platitudes are such that some (but not others) metaphysical theories are excluded from being adequate for theories of causation? This issue is far from trivial. Drawing a distinction between intuitions and platitudes of causation,d we can assume that the folk theory of causation attributes some platitudinous features to causation. Here are four of them: ♦ The difference platitude: causes make a difference, viz., things would be different if the causes of some effects were absent. ♦ The recipe platitude: causes are recipes for producing or preventing their effects, viz., causes are the means to produce (or prevent) certain ends (effects). ♦ The explanation platitude: causes explain their effects, but not vice versa. ♦ The evidence platitude: causes are evidence for their effect, viz., knowing that c causes e, and knowing that c occurred, gives us (some) reason to expect that e will occur. Arguably, each and every philosophical theory of causation should accommodate these platitudes, that is, show how each of them is brought out by whatever constitutes, according to the theory, the relation of cause and effect. But we can also assume that there are two firm pre-philosophical views about what causation is — what I have called ‘intuitions’ about causation. ♦ The regularity intuition: whether or not a sequence of two distinct events c and e is causal depends on whether or not events like c are regularly followed by events like e. ♦ The intrinsic-relation intuition: whether or not a sequence of two distinct events c and e is causal depends wholly on the events c and e and their own properties and relations, that is, it depends wholly on the intrinsic and local features of the actual sequence of events.

d Cf.

Ref. 1, p. 6–7.

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The regularity intuition is mostly driven by folk epistemological considerations: how can causal relations be known or reliably manipulated unless they embody or instantiate regularities? This intuition is underpinned by the fact that we are unwilling to pronounce a sequence of events c and e causal unless there has been a regular association between events like c and events like e. If a causal relation were an one-off thing (this causing that here and now), causation would be of little usefulness and causal knowledge would require some kind of special non-inductive method. The intrinsicrelation intuition, on the other hand, is mostly driven by folk metaphysical considerations: causal relatedness is a matter of something in the cause bringing about the effect; it is a tie between cause and effect which is independent of things that happen at other places and other times. These intuitions are equally firm, I presume, but each of them is too controversial to be taken as a platitude of causation. Although a functional account can (and should) accommodate the platitudes of causation, no functional account can accommodate both intuitions. To be sure, there can be compatibilist accounts of causation. That is, there can be accounts based on the intrinsic-relation intuition that can accommodate the thought that, as a matter of fact, causal relations give rise to stable regularities (that is, that the world is essentially nomological). But such accounts depend on putting a premium on the folk metaphysical intuition of intrinsic relation; a move that is certainly question-begging, since it presupposes that one of the two intuitions is really more central to our folk theory, while the other is derivative. An egalitarian view that gives, as it were, equal footing to both intuitions is excluded by a functional account.

4. The Two-Concept View One way to deny the straightjacket view, as well as the functionalist presupposition that CAUSATION is a single and unitary concept, is to claim that there are more than one concepts of CAUSATION. The case for there being two concepts of CAUSATION has been made by Ned Hall.5 He distinguishes between causation as dependence and causation as production. Hall takes dependence to be simple counterfactual dependence, while he takes the concept of production (c produces e) as primitive. This view is plausible. In fact, I have argued that there have been (historically and conceptually) two broad approaches to the metaphysical issue of causation.6 On the dependence approach, to say that c causes e is to say that e suitably depends on c. On the production approach, to

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say that c causes e is to say that something in the cause produces (brings about) the effect or that there is something (e.g., a mechanism) that links the cause and the effect. There have been different ways to cash out the relation of dependence: nomological dependence (cause and effect fall under a law); counterfactual dependence (if the cause hadn’t happened, the effect wouldn’t have happened); probabilistic dependence (the cause raises the probability of the effect). Similarly, there have been different ways to cash out the concept of production, but the most prominent among them are cast in terms of something being transferred from the cause to the effect (e.g., a property, or some physical quantity — force, energy etc.). A key thought in the production approach is that cause and effect are connected by means of a local mechanism. Why take seriously the two-concept view? One reason is that the two concepts we are discussing align quite naturally with distinct intuitions about causation: the production view aligns with the intrinsic-relation intuition, while the dependence approach aligns with the intuition that causation is an extrinsic relation between events (a species of which is a regularity). Another reason is that the two views set conceptually distinct constraints on causal relatedness. On the production view causal connectedness amounts to the presence of some tie between cause and effect, while no such tie is required by the dependence approach — just a robust dependence. Finally, dependence theories and production theories are extensionally distinct. There can be cases of causation licensed by dependence theories without being licensed by production theories and conversely. Most typical cases, however, concern situations based on no clear-cut intuitions, such as causal overdetermination and causation by disconnection. If we take the two-concept view seriously, we have reason to be sceptical about the straightjacket view. If causation has a double nature, there is no single, unified and all-encompassing theory of causation to be had. Yet, ironically, the two-concept view ends up with two straightjackets. For each of the two concepts, there is supposed to be a metaphysical matter of fact as to what causation is and what features it has. For each of them, there is a single and unified story to be told. But now, each story is not comprehensive: it leaves out some facets of causation that the other account covers. Obviously, this kind of thought requires that we are clear on what the facets of causation are and that they are all facets of causation, even though they cannot be accommodated under a single and unitary concept. Our intuitions are still at play, but since these are not always forceful and clear-cut, we may be left wondering whether some of the features that one

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or the other concept of causation accommodates really are worth accommodating. In virtue of what is it the case that these two concepts are both concepts of CAUSATION? There may well be some interesting answer to this question. It may be argued that the two-concept view is genuinely egalitarian: since there is no way to privilege one set of intuitions concerning CAUSATION over the other, and since there is no other way to tie causation with either production or dependence, egalitarianism dictates that both approaches are equally acceptable accounts of causation. The difficulty with this answer is that though the two-concept view entails that there is a metaphysical fact of the matter as to what causation is (it is either production or dependence), there is no further way to tell when it is this rather than that. For we are not told when to apply the one concept and when the other. Here again, we have to rely on our intuitions. If there were no other way to deny the straightjacket I would go for the two-concept view. But the difficulties of this view highlight, to me at least, the claim that once the straightjacket view is denied, there is little gain by replacing it with watered down versions of it, even if the replacements are in the right direction. This thought might lead to a more radical denial of the straightjacket view: causal pluralism.

5. Varieties of Pluralism One way to be pluralist about causation has been explored recently by Christopher Hitchcock.7 He means to deny that there is a single thing that is the referent of the expression ‘the causal relation’. He motivates his pluralism by highlighting two distinct stages in causal analysis. In the first stage, some privileged class of entity is identified which pertains to causal relations, e.g., laws, relations of counterfactual dependence, probabilistic dependence, manipulability, causal processes. The thought here is that when it is the case that c causes e, some such entity is present. After this stage is completed (and in particular, after the privileged class of entity is discriminated from impostors — e.g., after genuine laws are distinguished from accidentally true generalisations, or genuine causal correlations are distinguished from spurious correlations), the second stage kicks in. This is an analysis of causation in terms of the privileged class of entity identified in stage one. For instance, causation consists in the ancestral of counterfactual dependence among events. Or causation consists in the exchange of a conserved quantity etc. Here, the point is that among the privileged classes

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of entity identified in the first stage, one is selected as being constitutive of the causal relation. Hitchcock’s suggestion is that we should embrace causal pluralism at stage two, viz., there is no unique way to analyse the causal relation; there is no single thing such that the causal relation consists in. His point, then, is that there are assorted causal relations and none of them should be identified as the causal relation: causal analysis should consist in identifying some causal relation that is present in a particular case of causation. Though suggestive, this idea needs further development. As it stands, it seems consistent with two opposing views: disjunctivism and the manyconcept view. The disjunctivist view: the causal relation is disjunctive. It is nomological dependence, or counterfactual dependence, or probabilistic dependence, or the presence of a causal process, or invariance-under-intervention, or . . . This line admits a unique but multiply realised causal relation. A problem with the disjunctive view is that it is not clear how causation is identified in the first place. There must be some independent grasp of CAUSATION, which is then identified with a certain disjunction. But it is not clear what this independent grasp consists in. Perhaps, causation is identified in the functional way noted above. Then CAUSATION is a second-order concept whose realisers are given by the disjunction. If this line is taken, disjunctive causal pluralism becomes a species of the functional view and inherits its problems concerning what exactly should be included in the folk theory of causation. Another problem with this view is that it is not clear how the context can specify which disjunct is realised in particular cases. To say the least, it is typically the case that more than one disjuncts are realised in cases of causings. How, on this view, would one of the disjuncts be picked out as the one in which a particular causal relation consists in (it is realised by)? The many-concept view: there are many concepts of CAUSATION each corresponding to a way of identifying the causal relation; none of them should be privileged in being the concept of CAUSATION. This line is a development of the two-concept view. As with the case of the two-concept view, the many-concept view allows for a number of straightjackets. For in each and every case, there should be a fact of the matter as to what concept of CAUSATION applies. Yet, it is not clear any more why and in virtue of what all these concepts are concepts of CAUSATION.

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Hitchcock’s pluralism seems to go beyond both of these two views in denying, or at least aiming to deny, that there is anything deeper that unites the many and varied causal relations. Still, he wants to argue that all these are causal relations; hence, though there is something in virtue of which they are all causal relations, it is not clear what this is. It seems that it’s left to our intuitions to play the role of classifying all these relations as causal. Different intuitions favour different relations as being causal and since there is no way in which we can privilege one set of intuitions over another we should be egalitarian, and hence pluralist, about causal relations. 5.1. The Symptoms of Causation Here is another way to develop the pluralist line. In most typical cases, where causal talk has a bite, there are many ways to identify the presence of a causal connection — that is to ascertain that c causes e. This is because, generally, when c causes e, it will be the case that ♦ ♦ ♦ ♦ ♦

there is a law (deterministic or statistical) that links c and e if c hadn’t happened, e wouldn’t have happened prob(e/c)>prob(e) in (all) relevant background contexts some causal process (mechanism) connects c and e something gets transferred from c to e.

This is obvious in many ordinary cases, e.g., when we say that the ball broke the window or that aspirin causes headache relief or that smoking causes lung cancer. But it is no less obvious when we turn to more ‘scientific’ cases, e.g., when we say that the tides are caused by the moon’s attraction or that increases of unemployment rates cause a rise of the crime rates. In most typical cases, these entities (regularity, counterfactual dependence, probability raising, presence of a process, presence of a mechanism etc.) are correlated. This correlation explains why there are many ways to identify a causal fact and why there is, typically, agreement about what causes what, even if there is (philosophical) disagreement about what causation consists in. Let us call the entities above ‘symptoms’ of causation. There are many and different symptoms of causation. It’s not necessary that all of them are present in order to claim that a certain relation is causal. Nor is any of them privileged in identifying the presence of a causal relation. The case here is similar with diseases. Think of either measles or common

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cold. In both cases, we have many symptoms of them. It is not necessary that all symptoms are present in order to claim that someone suffers from measles (or common cold). Sometimes, some typical symptom might be absent. On many occasions, it might be necessary to combine more than one symptom to assert that someone has measles (or common cold). Similarly, I’d claim, with causation and its symptoms. Yet, measles is a disease with a single underlying nature. It is a respiratory infection caused by the measles virus. With the common cold, however, things are more complicated (and more interesting). What we call ‘common cold’ is a rather loose condition with no single underlying nature. Several hundred cold-causing viruses have been found to cause the symptoms of the common cold (sneezing, sniffling, running/blocked nose, scratchy, sore, or phlegmy throat, coughing, headache, and a general feeling of unwellness). In light of this, there are two ways to develop causal pluralism, one along the lines of the measles analogy and the other along the lines of the common cold analogy. Agnostic causal pluralism: there might be a deep and unique nature to causation — and hence a metaphysical fact of the matter as to what causation is — though there are many symptoms of it and many ways (none of which is privileged) to identify its presence. Atheist causal pluralism: there is nothing single and deep that unites all the symptoms of causation and makes them track the unique nature of causation. Causation is a rather loose condition with no single underlying nature. Agnostic causal pluralism is consistent with the claim that causation has a metaphysical nature, but differs from the straightjacket in that it does not search for this nature — if indeed there is. Rather, it counsels the use of the symptoms of causation in identifying causal facts — without bothering about whether there is anything deeper that these causal facts share in common. Atheist causal pluralism is more radical. On this view, we can meaningfully talk of causation, as we can meaningfully talk of common colds. We can identify cases of causation and discriminate them from cases of non-causation, as we can do the same with cases of common cold. But atheist causal pluralism denies that all cases of causation share something deep in common — a single and determinate common nature. In what follows I will leave agnostic causal pluralism to one side and try to defend the more radical atheist position. The less radical agnostic view can always act as the pluralist’s fallback position. Part of the positive argument for atheist pluralism is the fact that the symptoms of causation, like the symptoms of common cold, are reliably

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co-related in most ordinary cases. This allows us to group them together and claim that they track the same condition (causation; common cold) though, as it turns out, there is no single thing they track. The failures of the straightjacket are part of the negative argument for atheist pluralism. These failures suggest that no symptom of causation should be taken to be constitutive of it. Against the two- or many-concept view, atheist pluralism claims that CAUSATION is a single concept. But one may wonder: what makes all these symptoms symptoms of causation? The atheist pluralist need not give a deep answer to this question. After all, what makes all the symptoms of common cold symptoms of common cold? As we have already noted, the atheist view is motivated by the fact that these symptoms are correlated in most typical cases in which we can ascertain causal facts. These correlations plus reasons of conceptual economy suggest that they are all symptoms of something, viz., causation. It turns out, however, that there is no single nature they track — this, if anything, is motivated by the failures we have had so far to identify it. Like the concept of common cold, the concept of causation has a history that goes back to antiquity. Tracing this history, thereby tracing the origins of the thought that causation (like common cold) is a single thing, would be a tall order. It might seem that atheist pluralism is defeated by the fact that there are cases of genuine causation that do not involve some characteristic symptom of it, e.g., counterfactual dependence or regularity or the presence of a process or what have you. Cases such as these have produced well-known counterexamples to philosophical theories of causation. They show, presumably, that causation should not be identified with X, where X is some suitable entity. However, the attraction of atheist pluralism is that it does not identify causation with anything. The absence of a symptom is no reason to think that causation is not present, provided other symptoms are present. Besides, since there is some vagueness to CAUSATION, extreme and atypical cases do not turn the balance in favour of one symptom being more privileged than others. In most typical cases, the advantage of atheist pluralism is that there is no reason to choose one among the many symptoms of causation as being privileged (or constitutive of causation). Indeed, a problem faced by Hitchcock’s pluralism, viz., that it cannot easily answer the question of how we choose among causal relations when more than one of them are present in a certain case, evaporates under the symptoms view. Atheist pluralism, then, is not pluralism in the sense of ‘two concepts or more’. It is not the view that there are two or more conditions called

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‘causation’ and hence two or more deep metaphysical natures of causation. It is pluralism at the level of symptoms. At the level of the metaphysics of causation it is simply atheistic: there is no deep metaphysical nature of causation; there is no single thing that these symptoms track. Atheist pluralism, no less than any other view on causation, presupposes that we know some causal truths. But where typical theories of causation rely on this knowledge to uncover the deep metaphysical nature of causation, atheist pluralism can take a more deflationary stance. Taking a cue from Arthur Fine’s Natural Ontological Attitude, we can claim that we can and do know a host of causal truths.8 That is, we do know what causes what. I will call the Natural Causal Attitude the stance that there is causal knowledge even if we do not know what causation is. According to it, in order to claim (correctly) that c causes e we don’t have to answer first some deep metaphysical questions about causation. In light of the above discussion, in order to know that c causes e we can appeal to some of the symptoms of causation and in particular to their correlation in most typical cases. The underlying idea is that causal truths are robust: they can be traced by means of regularities, relations of counterfactual dependence, relations of invariance under intervention, transference of energy-momentum etc. The Natural Causal Attitude shifts the issue from the metaphysics to the epistemology of causation. It deflates the debate over the metaphysical nature of causation and stresses that we can get along with finding causal truths without being committed to any particular metaphysical view. But as it stands, it does not particularly favour atheistic pluralism, viz., the claim that there is no deep metaphysical nature of causation. To this end, the natural causal attitude needs to be supplemented by a relevant argument. The argument I will put forward suggests that there is no need to assume a deep and unique metaphysical nature of causation. It will lead us to what may be called Wittgensteinian pluralism.

6. Wittgensteinian Pluralism It might be thought that the need for a deep metaphysical theory of causation, and in particular of a theory that reveals the single and determinate nature of causation, stems from the fact that there is a concept of CAUSATION and certain words in our languages (the verb ‘to cause’, the nouns ‘cause’ and ‘causation’) which aim to capture this concept. That is, it might be claimed that the very fact that there is explicit causal talk in our

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language, that explicitly causal expressions are used, that certain generalisations are formed using explicitly causal language, is best explained by the admission of a condition in the world — causation — that answers to this talk. This line of thought, however, can be defeated. There is a sense in which explicit causal talk is dispensable, or almost dispensable. It is nonetheless useful for forming certain generalisations. The relevant argument can be found in Anscombe’s pregnant quotation: “The truthful — though unhelpful — answer to the question: ‘How did we come by our primary knowledge of causality?’ is that in learning to speak we learned the linguistic representation and application of a host of causal concepts. Very many of them were represented by transitive and other verbs of action used in reporting what is observed. (. . . ) The word ‘cause’ itself is highly general. How does someone show that he has the concept cause? We may wish to say: only by having such a word in his vocabulary. If so, then the manifest possession of the concept presupposes the mastery of much else in language. I mean: the word ‘cause’ can be added to a language in which are already represented many causal concepts. A small selection: scrape, push, wet, carry, eat, burn, knock over, keep off, squash, make (e.g., noises, paper boats), hurt. But if we care to imagine languages in which no special causal concepts are represented, then no description of the use of a word in such languages will be able to present it as meaning cause” (Ref. 2, p. 93). Anscombe’s focus in this particular quotation was on the issue of the observability of causation. Yet it seems clear that what she has in mind is the thought that there is a sense in which explicit causal language has only (or mostly) an expressive role to play vis-` a-vis ordinary language: it expresses in a more abstract way facts that are already captured by causefree vocabulary. Of course, for Anscombe this vocabulary is only explicitly cause-free. It is equipped to capture causal concepts such as those expressed by the verbs cited in the quotation. But her point, I take it, is that there is no need to invoke explicit causal expressions to capture and come to know causal truths. Anscombe’s claim rests on an idealisation. Ordinary language does already contain explicit causal expressions. But let us think in terms of a metaphor. Let us envisage a fragment of natural language NLf which does not contain the word ‘cause’ (and relevant explicitly causal expressions).

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Then we can think of an extension NLf +c of this fragment which (explicitly) contains the word ‘cause’. What would the role of the word ‘cause’ be in NLf +c vis-` a-vis whatever can be expressed in NLf ? Would substantial new truths not already captured in NLf be expressed in NLf +c ? The answer I want to explore is that explicit causal expressions play a useful role in forming certain generalisations, but do not add new content to whatever can already be expressed within NLf . Suppose I say (truly) in NLf that the hitting with the hammer broke the vase. If I were to make, in NLf +c , the statement ‘The hitting with the hammer caused the vase to break’, I would not capture or prove any facts that were not already captured or proved by the cause-free formulation in NLf . Similarly, for all causal verbs of NLf . Are there contexts in which the content of expressions that use explicit causal language cannot be captured by cause-free expressions in the way indicated above? Since I have no general answer to offer to this question, let us proceed by considering three important cases. Case A: ‘x causes φ’, e.g., ‘Unemployment causes poverty’. Suggestion: It can be captured by claims of the form ‘x φ’s’. For instance, ‘Unemployment impoverishes (people)’. This kind of move is impeded by the fact that we lack stock of relevant verbs. But though true, this is a stylistic point. There is no neat way to paraphrase the statement ‘Smoking causes lung-cancer’ as suggested above. But if we leave ugliness aside, we can always introduce new verbs. So, we can claim ‘Smoking lungcancerises’. This would be on a par with perfectly acceptable causal statements such as ‘Smoking kills’ or ‘Aspirin relieves headaches’, which are true statements without explicitly causal expressions. The general idea, then, is that the expression ‘causes φ’ can always be paraphrased by means of a concrete (new or already existing) concrete verb. Case A suggests that we should think of the verb ‘to cause’ as a placeholder for more specific verbs — sometimes they are available, in others they are not, and in yet other cases it is a twist of language to introduce them. Case B: ‘the cause of e was φ’, e.g., ‘The cause of Peter’ s death was hypothermia’. Suggestion: Think of it intuitively. The content of the statement ‘The cause of Peter’ s death was hypothermia’ is fully captured by the statement ‘Peter died of hypothermia’. Statements such as ‘The cause of e was φ’ can be analysed as definite descriptions: there is an x (caused-e x) and for all y (if caused-e y) then x = y and (φ = x). For instance, There is an x (caused Peter’ s death x) and for all y (if caused Peter’ s death y) then

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x = y and (hypothermia = x). The paraphrased sentence does not contain any constituent ‘the cause of’ for which we could substitute ‘hypothermia’. Yet, something true is asserted, viz., that Peter died of hypothermia. In the end, Case B suggests that we should think of the noun ‘cause’ as a placeholder for more specific events. Case C: Consider the following claim: ‘John knocked the cup on the floor’. (i) This, according to the above, implies ‘John caused the cup to be on the floor’. (ii) The converse, of course, does not hold right away. John might have caused the cup to be on the floor in a different way. But statements such as (ii) do imply some kind of concrete statement like (i), e.g., ‘John dropped the cup on the floor’. (iii) So explicitly causal statements will always be made true by some concrete (implicitly) causal statement. The usefulness of (ii) consists in that it does not specify the way in which an effect was brought about and talks about it in an indefinite way. Case C highlights the fact that causal language is useful if we do not know how exactly an event was brought about, or if we do not want to be committed to any specific way. If what said above is broadly right, then explicit causal talk is useful not because it enables us to talk about facts that we cannot, in principle, capture in another way. Its usefulness consists in the contingent fact that our languages are not rich enough to capture all causal truths by means of more specific verbs or expressions. This, however, is more of a practical difficulty. Besides, explicit causal talk is useful for forming generalisations (e.g., there are unknown causes of some phenomena or all events have causes), and for talking in an indefinite manner about the results of an action or an event-type. The truth is that the verb ‘to cause’ is part of the language. Indeed, language has three general periphrastic causatives such as cause, enable and prevent. But note an interesting difference. Though we talk about enabling and prevention, there is no general theory of either enabling or prevention. Nor is there any presumption that enabling or prevention has a single and deep metaphysical nature; that all cases of enabling or prevention share something deep in common — a single and determinate common nature. Both ‘enable’ and ‘prevent’ play useful roles in language (and are

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used to report truths) without requiring or implying a deep theory of what enabling or preventing is. Given the similarity of these three general verbs, there is no reason to treat ‘to cause’ differently. We may well treat it as an ordinary periphrastic causative, with no implication that something (some deep metaphysical nature or a deep and unique relation or activity) underwrites all correct applications of it. We do exactly this with other periphrastic causatives, such as ‘to enable’, or with concrete causatives, such as ‘to break’. Why should we not do it for ‘to cause’ ? According, then, to this sort of Wittgensteinian pluralism, causation comprises whatever conditions in fact exist in the general region corresponding to causal talk — this talk being diverse and variegated. The linguistic expressions of causation are multiple and varied and do not require explicitly causal expressions, save for the need to form certain generalizations. e There is no conceptual or linguistic pressure to have a theory of causation that ascribes to it a single and deep underlying nature. There is no pressure to assume that causal talk (which is mostly carried by implicitly causal verbs and other expressions) captures one and the same deep thing. Breaking, pushing, creating, capsizing, dissolving, decompressing, bonding and attracting (to name by a few) are all causings. But there is no pressure to think that they also share something deep in common, viz., that they are all causings in virtue of the (supposed) fact that they are all instances of a single and deep condition. To be sure, there can be (and there are) deep theories of each of these causings — e.g., in terms of molecular structure. If this is what is we search when we look for a deep theory of causation, then well and good. But, apparently, it is not. Activities such as the above are all causings without the need to assume that they share some hidden causal essence. And yet, it is also true that each of them gives rise to the symptoms of causation noted in the previous section. For instance, where there is breaking or pushing or . . . there is transfer of energy, relations of counterfactual dependence, the presence of a law etc. This is reason enough to group them together as instances of e Language

already possesses a host of concrete (implicitly) causal expressions: causal conjunctions (e.g., because), prepositions (e.g., because of) and lexical causatives, that is verbs that encode causings (e.g., Peter broke the vase or Demetra tore the book). There are also the so-called periphrastic causative verbs (or auxiliary verbs such as make, force, get etc.). For a useful discussion of the linguistic representation of causation see Ref. 9. There are syntactic and semantic criteria to circumscribe the causal verbs. For instance, to beg is not a periphrastic causative, since I can meaningfully say: Mary begged John to leave, but he didn’t. But I cannot meaningfully say: Mary forced John to leave but he didn’t.

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causation, even if, as stressed above, they do not necessarily track one and the same condition. That is how atheist causal pluralism and Wittgensteinian pluralism support each other.f 7. Three Objections Let us consider three objections to what said above. First: Doesn’t talking of causal truths imply that a) all these truths share something in common and b) that this something is a substantive property? Reply: I agree with the first implication. As will be explained in the reply to the second objection, causal truths share some robustness which distinguishes them from another set of truths, viz., correlational truths. In this sense, they are substantive enough. What does not follow from this is that c) that there is a metaphysical fact of the matter as to what exactly causation is and that this fact underlies (and makes true) all causal truths. In other words, it does not follow that there is one single, unique, fully definite etc. truth-maker for all causal truths. But we need to be careful here. Atheist causal pluralism of the sort defended here is not causal anti-realism, tout court. It is anti-realist in so far as it denies that there is a single and deep truth-maker for all causal truths. But, in line with the natural causal attitude endorsed above, atheist causal pluralism admits that there are causal truths and that they can be (and are) known. Hence, it does not deny that causal truths have truth-makers. On the contrary, the thrust of atheist pluralism is that causal truths have a plurality of truth-makers that do not share anything deep in common. Second: What do scientists search when they search for causes? Reply: If answering this question presupposes an answer to the metaphysical question of what causation is (or a commitment to the view that causation has a deep and unique nature), clearly no progress has been made in finding out causes (since we don’t know what causation is). But since there has been such progress, the argument is a reductio of the basic presupposition. In any case, the simple answer to the foregoing question is that scientists search for causal truths. What are these? They are a) truths and b) more robust than mere co-relations. (Recall that the statement of causal truths does not presuppose explicitly causal language. Consider: drug X f Due

to lack of space I will not discuss here Nancy Cartwright’s relevant views. See her The Dappled World.10

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cures disease Y; drug Z relieves from pain; policy Q reduces urban crime etc; teaching method K improves the exam results of children; the earth attracts the moon.) But why do we need (b)? I think this is a broadly empirical issue. We are interested in a special kind of truth (causal truth) because we are not interested solely in predictions. Co-relations (that is, truths that are not causal, but may appear to be causal) serve well in prediction. But they don’t serve well in explanation; they break down upon manipulation; and they do not lead to effective strategies. So, we are interested in robust causal truths. No matter what the metaphysics of causation is (and no matter whether there is a fact-of-the-matter about this metaphysics), causal truths (should) satisfy a set of platitudes noted in section 3. Mere correlations do not satisfy these platitudes. Third: Famously, Anscombe took it that her argument from causal verbs implies that causings (and hence causation) are observable. Reply: Though I used to think differently, now Anscombe’s point seems to me compelling. Suppose one says that a particular tree branch bent after having had pressure exerted on it. Then, by the very use of the verb ‘to bend’, one makes a causal claim. If this claim is true, since one had directly perceived the bending of the tree branch, one has thereby directly perceived the tree being caused to bent. So one has directly observed the causing. Anscombe’s mistake, if I am allowed to talk in such terms, was the conclusion she wanted to draw from the observability of causings, viz., that some kind of non-Humean, that is singularist, (metaphysical) account of causation is true. This does not follow. The observability of causings is consistent with a number of metaphysical views about causation.g It is also consistent with the kind of pluralism defended above. Acknowledgments Earlier versions of this paper were presented in seminars at: the Centre for Logic and Philosophy of Science, University of Ghent; the University of Lund; Bogacisi University; the University of Cyprus; at: the Symposium Causal Inference and Probability in the Physical Sciences in the meeting of the Spanish Society for Logic, Methodology and Philosophy of Science, Valladolid, Spain, November 2004; the fifth workshop of the Metaphysics in Science Group, University of Ghent, May 2005; and as an invited talk at g This

point has been ably defended by Helen Beebee.11

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the Fifth European Congress for Analytic Philosophy, University of Lisbon, August 2005. I have benefited from comments by a number of people. They are too many to be thanked all personally, but here is a partial list: Helen Beebee, Alexander Bird, Phil Dowe, Pascal Engel, Bengt Hansson, Carl Hoefer, Gurol Irzik, Antonis Kakas, Igal Kvart, Joke Meheus, Anna-Sofia Maurin, Demetris Portides, Rebecca Schweder, Mauricio Suarez, Erik Weber and Stephen Voss. Research for this paper was funded by the framework EPEAEK II in the programme Pythagoras II. References 1. S. Psillos, Causation and Explanation. Acumen & McGill-Queens University Press (2002). 2. G. E. M. Anscombe, Causality and Determinism. Cambridge University Press (1971). Extracts reprinted as ‘Causality and Determination’. In: E. Sosa and M. Tooley (Eds.), Causation. Oxford: Oxford University Press, 88–104 (1993). 3. P. Menzies, Probabilistic Causation and the Pre-emption Problem. Mind 105, 85–117 (1996). 4. P. Menzies, Intrinsic Versus Extrinsic Conceptions of Causation. In: H. Sankey (Ed.), Causation and Laws of Nature. Dordrecht: Kluwer, 313–329 (1999). 5. N. Hall, Two Concepts of Causation. In: J. Collins, L. Paul and N. Hall (Eds.), Counterfactuals and Causation. MIT Press, 225–276 (2004). 6. S. Psillos, A Glimpse of the Secret Connexion: Harmonising Mechanisms with Counterfactuals. Perspectives on Science 12, 288–319 (2004). 7. C. Hitchcock, Of Humean Bondage. The British Journal for the Philosophy of Science 54, 1–25 (2003). 8. A. Fine, The Shaky Game: Einstein, Realism and the Quantum Theory. Chicago: University of Chicago Press (1986). 9. P. Wolff and G. Song, Models of Causation and the Semantics of Causal Verbs. Cognitive Psychology 47, 276–332 (2003). 10. N. Cartwright, The Dappled World. Cambridge: Cambridge University Press (1999). 11. H. Beebee, Seeing Causing. Proceedings of the Aristotelian Society 103, 257–280 (2003).

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WHY SOCIAL EMERGENCE? DISCUSSING THE USE OF ANALYTICAL METAPHYSICS IN SOCIAL THEORY

JEROEN VAN BOUWEL Centre for Logic and Philosophy of Science Ghent University, Belgium E-mail: [email protected] Recently the concept of emergence has been used in social theory to understand and defend social causation and nonreductive individualism (cf., Refs. 1, 2 and 3). In this paper, I want to analyse what the contribution of analytical metaphysics, and, in particular, the concept of emergence is, or might be, to the discussion in social theory. Especially Keith Sawyer’s use of emergence in his defence of social explanation will be scrutinized. Therefore, it will be important to distinguish ontological from epistemological emergence. Where Sawyer focuses on ontological emergence, I will argue that social explanation might better be defended by putting emphasis on pragmatic aspects of explanation and considering emergence as an epistemological category.

Introduction Recently, Keith Sawyer has put emergence high on the agenda in the philosophy of social science. Emergence would help to conceptualize the relation between individual and society and to defend social causation and social explanation (cf., Refs. 1, 2 and 3). In this paper, I want to analyse what the contribution of analytical metaphysics to the discussions in social theory is, or can be, by scrutinizing what the added value is of introducing emergence. Especially, the way Keith Sawyer is using emergence to conceptualize the individual–collective relation in social science, paying attention to the analogies with philosophy of mind, will be examined. In the first section, I will briefly discuss the relation between philosophy of mind and social theory. Secondly, I will introduce Keith Sawyer’s social translation of nonreductive materialism in section 2. The place of emergence in Sawyer’s framework and the use of emergence in social theory will be discussed in section 3. Subsequently, questions will be raised about Keith Sawyer’s use of emergence in his defence of social explanation in section 4. 152

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Therefore, it will be important to distinguish ontological from epistemological emergence. Where Sawyer focuses on ontological emergence, I will argue that social explanation might better be defended by putting emphasis on pragmatic aspects of explanation and considering emergence as an epistemological category. In section 5, conclusions will be drawn. 1. Philosophy of Mind and Social Theory Conceptualizing the relation between the individual and the collective has always been a central issue in social theory. In recent years, the concept of emergence has been used in order to illuminate the individual–collective relation in social theory, drawing attention to the analogies with philosophy of mind. The typical questions in philosophy of mind can easily be translated to social theory, e.g.: What is the relation between the lower-level physical entities, respectively individuals, and higher-level mental entities, resp. social entities? Can we assign causal efficaciousness to our mental states, resp. social entities or social properties? Are explanations invoking mental states, resp. social factors, good explanations? How can our mind, resp. the social, influence the physical world, resp. the individuals, granting that our intentional actions and our perceptions, resp. individual actions, seem to entail that mental events, resp. social events, can be, respectively, causes and effects of physical events, resp. individual actions? Etc. As the idea of nonreductive physicalism/materialism has been having a lot of supporters the last decade — Sawyer calls it the consensus position in philosophy of mind nowadays (Ref. 4, p. 539) — an interesting exercise would be to transfer this nonreductive physicalism to social theory and the debates on methodological individualism and holism in the philosophy of social science. Let us briefly sketch the contours of that exercise. Two characteristics of nonreductive physicalism are salient: a) dependence: mental properties are properties of physical objects b) distinctness: mental properties are distinct from physical properties The first claims that higher level entities are composed of and are nothing more than their lower level components. This is sometimes expressed as the supervenience claim.a In this sense, a position different from Cartesian dualism is defended. The second claim is a reaction against reductionism, aI

adopt the most common version of supervenience in the consensus position here. Some will object that the original definition of supervenience does not express dependence, but only determination, cf., Ref. 5.

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and type-identity theory (which denies distinctness as it asserts that mental properties are identical with physical properties). This is where emergentists usually enter; they reject a dualist ontology, but at the same time argue that higher-level phenomena do have causal power. Starting from the analogies between the philosophy of mind debate and the debate in social theory, we can articulate nonreductive physicalism/materialism in social theory. First, the rejection of dualism: the so-called collectivist sociologists and social theorists have been proposing theories in which social properties are causal antecedents. Often these properties were considered to have ontological autonomy, but how can they have causal power if they are ontologically autonomous? Do we have two distinct ontological orders, a dualist ontology, when ‘structural’ sociologists are claiming that social terms and concepts are real? This opens up the road to the criticism of hypostatizing the social group as an entity. To avoid dualism the social version of nonreductive physicalism should put emphasis on (a) the ontological dependence of the higher social level on the lower individual level. Secondly, many social theorists do not want to reduce the social to the individual, and will have to find an argument for (b) the distinctness of social causation, analyzing the ontological relation between the higher-level phenomena and individual actions.

2. Keith Sawyer’s Nonreductive Individualism Keith Sawyer has recently developed such a social version of nonreductive physicalism more thoroughly; one that “would be to hold that only individuals exist and that social entities do not have a distinct existence, yet there may be irreducible social properties and social laws” (Ref. 1, p. 559). He combines ontological individualism (dependence) with a rejection of methodological individualism and reduction (distinctness). Let us analyse the metaphysical concepts he is using in the elaboration of his nonreductive individualism (NRI). Sawyer considers himself to be an ontological individualist, even though he considers social properties, social structures and social mechanisms to be real. “NRI is compatible with the ontological assumption of individualism — social groups are composed of nothing other than individuals” (Ref. 4, p. 554). What is then the status of social entities and properties? “Ontological individualism accepts that collectives do not exist apart from their constituent individuals, and NRI accepts this ontological commitment of individualism” (Ref. 2, p. 219). This individualism does, however, not imply

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reduction: “there are strong grounds for believing that this reduction is not possible, even though there is nothing in the universe other than physical matter. The argument is based on supervenience, multiple realizability, and wild disjunction” (Ref. 1, p. 555). (a) Supervenience. Sawyer starts from ontological individualism and token identity (Ref. 4, p. 541) and in his words: “token event identity entails that emergent higher-level properties supervene on the system of lower-level components. Supervenience refers to a relation between two levels of analysis and states that if two events are identical with respect to their descriptions at the lower level, then they cannot differ at the higher level” (Ref. 1, p. 555–556). As supervenience does not suffice to substantiate irreducibility, Sawyer adds multiple realizability to his argument: “If supervenience is to be used to ground a nonreductive stance, one must develop a version of the supervenience thesis that argues that the reductionist approach of methodological individualism is not possible for some social properties, despite ontological individualism. I will argue that to reject methodological individualism one must show how type identity versions of supervenience might not obtain. . . . nonreduction due to multiple realizability is now the consensus position in the philosophy of mind” (Ref. 4, p. 544–545). (b) Multiple realizability. “The argument is based on the notion of multiple realizability: the observation that although each mental state must be supervenient on some physical state, each token instance of that mental state might be implemented, grounded, or realized by a different physical state” (Ref. 1, p. 556). (c) Wild disjunction. Multiple realizability alone does not necessarily imply irreducibility; if there are only a few realizing states, or if those states display some common features, the reduction may not be problematic. Therefore, Sawyer introduces the idea of wild disjunction: “reduction would be difficult if the neurobiological equivalent of a psychological term were an otherwise unrelated combination of many neurobiological concepts and terms . . .. Fodor termed such a realization wildly disjunctive. If a higher-level property is realized by a wildly disjunctive set of lower-level properties, then the

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physical equivalent of a psychological law must contain wildly disjunctive terms” (Ref. 1, p. 557). This can be used to show “how a higher-level property could be supervenient on and yet not reducible to its lower-level base” (Ref. 1, p. 575). Here the metaphysical battle can be declared open: what is the status of supervenience, is multiple realizability a good argument for the nonreducibility of the social level, and what about wild disjunction? Which arguments are decisive here? Let us hold our metaphysical horses — or should I say, unicorns — for now, and discuss the last metaphysical concept that is central in Saywer’s account: emergence. 3. The Introduction of Emergence and Its Use(fullness) in Social Theory Sawyer links his NRI and the existence of irreducible social properties to the idea of emergence: “Emergentism does not claim that all higher-level properties are irreducible; some of them are predictable and derivable from the system of lower-level components. Only in cases where the relation between higher-level and lower-level properties is wildly disjunctive beyond some threshold of complexity will the higher-level property not be lawfully reducible” (Ref. 1, p. 558). Emergence should be understood as follows, according to Sawyer: “when basic physical processes achieve a certain level of complexity of an appropriate kind, genuinely novel characteristics emerge; the emergent higher-level properties could not, even in theory, be predicted from a full and complete knowledge of the lower-level parts and their relations. Further, they could not be reduced to properties of the parts and their relations, even though those properties are supervenient on and thus determined by the system of parts” (Ref. 1, p. 554). How can this idea of emergence presented by Sawyer help us in developing social theory? Let me browse through some examples of the use of emergence in social theory, as I am interested in how analytical metaphysics could contribute to social theory (and analyze whether it actually does). Sawyer has enumerated some social theorists that apply emergence

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in their work, and distinguishes collectivist emergentists from individualist emergentists (Ref. 1, p. 552). Let us start with that distinction. The individualist emergentists in social theory believe that macro-social properties and laws can be explained in terms of properties and laws about individuals and their relations. The existence of emergent system properties that are not possessed by the parts does not entail irreducibility of those properties, according to them (which might be unexpected as emergence is traditionally interpreted as the contrary to reduction, cf., infra, footnote b). Examples of this individualist emergence can, for instance, be found in the work of James Coleman who adopts emergence in his Foundations of Social Theory,6 and in Thomas Schelling’s classic Dynamic Models of Segregation in which he uses a checkerboard simulation to explain the emergence of residential segregation.7 George Homans, elaborating behavioural sociology, defends in his book Social Behavior how emergent properties could be explained using psychological propositions:8 “new properties are always emerging . . . The question is how the emergence is to be explained. I say that the emergence, and the nature of the properties that emerge, are to be explained by psychological propositions” (Ref. 9, p. 229). Homans does not deny that something new can emerge out of the interactions between individuals. The explanation of these emergent properties can, however, be provided on the individual and psychological level: “The great example of a social fact is a social norm, and the norms of the groups to which they belong certainly constrain towards conformity the behavior of many individuals. The question is not that of the existence of constraint, but of its explanation . . .. The norm does not constrain automatically: individuals conform, when they do so, because they perceive it is to their net advantage to conform, and it is psychology that deals with the effect on behavior of perceived advantage” (Ref. 10, p. 60). Robert Axelrod, in Ref. 11, developed artificial society simulations which enable him to explore the emergence of new political actors: how do higher-level actors (i.e., supranational entities) emerge out of the interaction of lower-level actors (i.e., nation-states)? Understanding these mechanisms of emergence, aggregation and disaggregation helps us in the development of global policies, according to Axelrod, e.g., concerning the question of sustainability:

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“The emergence of new political actors is fundamental to the question of sustainability. One of the main problems of attaining sustainability is the tragedy of the commons. The tragedy of the commons arises when many independent actors (people, villages, states, or whatever) each ‘overgraze’ because there is no mechanism to enforce the collective interests of all against the private interests of each. This leads to resource depletion, elimination of bio-diversity, overpopulation, war, and other major social problems. A major route to the prevention of the tragedy of the commons is the emergence of a political actor based upon the organization of previously independent actors” (Ref. 11, p. 20). Axelrod’s simulation might be a bit simple in set-up, but it does reproduce historically observed patterns, e.g., imperial overstretch. Axelrod’s analysis of emergence aims at answering questions like: what are the minimal conditions necessary for a new actor to emerge? How is emergence affected or constituted by the basic actors? How can new actors emerge out of the existing ones? The simulation model of Axelrod that he presents to answers these questions, presupposes that the instances of emergence it describes do not preclude the formulation of reductive, individualistic explanations. If we evaluate the conceptualization of emergence in the work of Coleman, Schelling, Homans and Axelrod within the framework of Sawyer’s NRI (cf. section 2), we conclude it is consistent with token identity and supervenience, but not with multiple realizability and wild disjunction; the existence of emergent properties that are not possessed by the parts does not entail irreducibility of those properties. A second group of social theorists can be labelled collectivist emergentists. They believe that emergence is incompatible with reductionist individualism and explicitly draw on emergence to ground nonreductionist, nonindividualist social theories, e.g., Margaret Archer,12 Roy Bhaskar,13 and Peter Blau.14,15 Margaret Archer has elaborated the idea of morphogenetic dualism in her Realist Social Theory: The Morphogenetic Approach and works within the tradition of Critical Realism. The morphogenetic cycle consists of three phases: “prior structural conditioning → social interaction → structural elaboration” (Ref. 12, p. 328). Through this cycle new properties emerge. The result of this emergence is described by Archer as follows:

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“Once emergence has taken place the powers and properties defining and distinguishing strata have relative autonomy from one another; Such autonomous properties exert independent causal influences in their own right and it is the identification of these causal powers at work which validates their existence, for they may indeed be non-observables” (Ref. 12, p. 14). Hence, according to Archer, emergence leads to independent causal powers on the higher level, i.e., higher-level properties exert an autonomous causal influence. Archer endorses Roy Bhaskar’s realist conception of causal powers, but Bhaskar’s Transcendental Realism does not only talk of emergent properties, but also of emergent entities, ‘things’ (Ref. 16, p. 51), to which causal autonomy is ascribed. Finally, Peter Blau, does talk of emergent properties too in his work. Especially in his later work,14,15 he is emphasizing the inherent antireductionistic character of emergent properties (Ref. 15, p. 10). The social structure is not merely a conceptual representation of a sociologist, but it does exert causal influence on individuals (Ref. 15, p. 15–16 and Ref. 14). Several have criticized Blau for reifying social structure. Others reproach him that his ideas on emergence are not satisfactorily elaborated. Considering the work of Archer, Bhaskar and Blau, one can conclude that these collectivist emergentists — interpreting emergent properties as ontologically autonomous, exerting independent causal influences in their own right — go against the supervenience claim, present in Sawyer’s NRI. In general, reflecting on the use of emergence by these social theorists — both the individualist and collectivist emergentists — we can notice some conceptual overstretch. Sawyer draws the same conclusion and criticizes the way emergence is used by social theorists; he articulates how they deviate from his philosophical view of emergence, and he evaluates the use of emergence in social theory by applying his framework of NRI and emergence as the standard, defining the ‘correct’ interpretation of emergence. Individualist emergentists do not take MR and wild disjunction into account, according to Sawyer (Ref. 1, p. 564); they presume type-identity. The collective emergentists have a too autonomous view of emergent properties or reify social structure, such that society becomes ontologically autonomous from individuals. Sawyer’s strategy is one way of dealing with the conceptual overstretch of emergence in social theory, i.e., we need analytical metaphysics to assure

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some conceptual hygiene and decide on what emergence precisely is. This could mean, for instance, following Sawyer’s interpretation of emergence as the new standard. A second strategy would be that we should be aware of the poly-interpretable nature of emergence, and look for an alternative way to deal with emergence, for instance, by introducing the distinction between ontological and epistemological emergence. I will defend this second strategy, as the first strategy faces some problems which will be enumerated in the following section.

4. How to Evaluate Sawyer’s Metaphysics? Questioning Social Emergence Evaluating Sawyer’s social emergence, I first want to pay attention to the distinction between ontological and methodological issues in social theory. Discussing the debate between individualists and collectivists, Sawyer himself distinguishes two levels, namely: “an ontological level, concerning arguments about what entities and properties exist in the world, and a methodological or epistemological level, concerning the proper way to proceed in scientific practice” (Ref. 4, p. 537). Furthermore, he rightly points out that: “The logical error of making ontological arguments in support of methodological claims is quite common in the philosophy of social science” (Ref. 4, p. 538). I fully agree with these two remarks of Sawyer, i.e., ontological and methodological issues are often mixed up and we should try to clearly distinguish them. This does, of course, not imply that ontological issues are completely irrelevant for methodological issues or vice versa. Notwithstanding his own remarks, I do notice that Sawyer is mainly interested in getting the ontological arguments sound, “. . . to make an argument for social causation that is consistent with ontological individualism” (Ref. 4, p. 540), and he seems to presuppose that the ontological framework has to be fully elaborated or fixed, so we can stipulate methodological recommendations. Does Sawyer adopt a similar strategy as the one he just claimed to be erroneous, i.e., developing ontological arguments out of which methodological consequences seem to follow automatically? Why does he not make a clear distinction between ontological and epistemological versions of emergence — a distinction that has been made by scholars before, e.g., Ref. 17? Ontological emergence claims that novel, real and irreducible properties do exist (or come into existence) on the higher level. These emergent properties are just as real as physical properties. Sawyer seems to adhere to the ontological version of emergence as the following quote shows:

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“For the latter properties — real emergent social properties — explanation may of necessity involve irreducible social properties and laws. I will draw on analyses of complexity, self-organization, and emergence to explore these questions. I conclude that for certain social mechanisms, we may be required to pursue macrosociological explanation in terms of emergent social properties, not only because of epistemological limits to current science but because of the structure of reality” (Ref. 18, p. 270). The structure of reality (with its real emergent social properties) is the source of emergence, not merely our epistemological capacities, according to Sawyer. Following epistemological emergence, on the other hand, the concept of emergence is characterized in terms of possibilities and limitations of human knowledge of complex systems: it deals with the (in)adequacy of reducing theories and is based on the fact that it sometimes appears to be impossible to understand the global behavior of a complex system by analyzing the local behavior of the individual parts. Hence, epistemological emergence regards the ineliminability of some higher-level descriptions or explanations, and defends that in science some phenomena or questions can best be understood or answered by referring to properties on the higher level. This version of emergence has been argued for by, e.g., Andy Clark19 and Robert Batterman.20 It should be emphasised that subscribing to epistemological emergence does not imply any precipitant ontological statements, i.e., that there would exist a distinct class of real emergent properties. One can accept epistemological emergence without ontological emergence. Sawyer does not consider this possibility, and defends ontological emergence, a position which is (at least) problematic. Firstly, the ‘novel’ causal powers of emergent properties raise questions about downward causation and the causal completeness of the lower level. Secondly, Sawyer’s ontological emergence is embedded in his NRI argued for by referring to multiple realizability (MR) and wild disjunction (WD). MR and WD suffice to prove irreducibility and substantiate emergence, according to Sawyer, but for both MR (cf. Ref. 21) and WD (cf. Ref. 22) arguments have been formulated to question their incompatibility with reduction. Thirdly, by subscribing to ontological emergence in order to secure the necessity and indispensability of social, higher level explanations and social, higher level laws, Sawyer follows an old strategy

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in philosophy of the social sciences. This strategy overlooks pragmatics as it wants an a priori or a-contextual certainty, and presupposes an identity between causation and explanation, a move we have criticised before (cf. Refs. 23, 24). Sawyer will have to defend his ontological emergence against these three weaknesses. I want to propose to subscribe to the epistemological version of emergence. This version can support the program of social theory — invoking social factors in the explanation of phenomena — including a version of nonreductive individualism. Discussing the different levels of explanations, we have shown in earlier work that in some cases explanations on the social level are preferable because of the efficient way in which they provide us with the explanatory information required, even though an explanation on the individual level is possible in principle (cf., Ref. 25). A social-level explanation might be more efficient, and/or provide us with better explanatory information, and/or be easier to construct, and/or supply better understanding, because of the complexity or redundancy of the individuallevel explanation. Whether an individual-level or a social-level explanation is the best, depends on the explanatory request. Hence, instead of a priori discussing the possibility of reduction, the attention should rather go to the pragmatic surplus the higher-level explanations might have in the explanatory practice of the social sciences.

5. Conclusion: If At All . . . In discussing the contributions of some social theorists in section 3, we have noticed a manifest conceptual overstretch in the use of emergence. It is Sawyer’s merit to try to remedy this situation and to be more explicit about how to understand or conceptualize emergence. Therefore, he turns to philosophy of mind and analytical metaphysics which can provide some conceptual clarity. The development of a nonreductive individualism analogous to the nonreductive physicalism of the philosophy of mind literature is a constructive and valuable proposal to understand emergence in social theory, and causality in general. The concepts introduced, i.e., supervenience, multiple realizability and wild disjunction could help social theorists to sharpen their ideas on emergence. Denying the distinction between ontological and epistemological emergence, however, Sawyer does seem to want to convince us that subscribing to ontological emergence is indispensable in legitimizing social explanations

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(and — preferably — his particular version of emergenceb ), which is incorrect. Moreover the ontological version raises several problems (cf., supra) and risks turning into an unending battle of metaphysical intuitions, rather than contributing to the analysis of scientific practice. The metaphysical debates do help us to clarify concepts, but often open up the road to the imposition of the ‘correct’ ontology for all situations, as is done, for instance, by the ontological emergentist Sawyer postulating the existence of emergent properties in order to ‘prove’ the causal efficaciousness of the social level (putting the question what emergence would ‘prove’ and how to ‘prove’ emergence between brackets). Why can we not just start from the existing competing social explanations, and compare which of the ontological partitions of social reality — present in the different explanations — serves us the best explanatory information? In stead of getting paralysed by ontological or metaphysical debates in social theory, I want to suggest that more attention should be paid to methodology and explanatory practice, and the information we want, in order to maximize (our understanding of) good scientific practice (as done in Refs. 25, 27). Although we cannot deny the impact of metaphysical concepts and ontological issues in general — and, therefore, attention should be paid to those issues — I claim that our views on methodological and explanatory options in the social sciences have too long been dictated by our views on ontology and causation. Introducing epistemological emergence can help us in giving less weight to metaphysical and ontological debates, and more to methodological ones. Returning to the philosophy of mind, where we started our journey, we can find some scholars that warn us (just like I did) not to get paralysed by these ontological or metaphysical debates, but rather pay more attention to methodology and explanatory practice. E.g., Tyler Burge states the following about the worries that exist in philosophy of mind on mental causation: “But what interests me more is the very existence of the worries. I think that they are symptomatic of a mistaken set of philosophical priorities. Materialist metaphysics has been given more weight b Sawyer’s

interpretation of emergence is rather traditional and mainly used as the contrary to reduction, while recent contributions propose to review this opposition and explore a more nuanced conceptualisation of emergence which is independent from reduction (cf., Ref. 26).

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than it deserves. Reflection on explanatory practice has been given too little” (Ref. 28, p. 97). A similar idea has been defended by Lynne Rudder Baker: “Given standard metaphysical and methodological assumptions, not only has the problem of mental causation proved to be intractable but even worse: the same reasoning that leads to scepticism about mental causation also leads to scepticism about almost all supposed ‘upper-level’ causation, and hence to skepticism about explanations that mention ‘upper-level’ properties, including explanations offered by the special sciences and much of physics. Of course, pointing out such skeptical conclusions, even of this magnitude, is not a refutation of the metaphysical assumptions that generate them. But skeptical consequences may well be a motivation for taking a different philosophical tack. . . . My proposal is to perform a methodological about-face. Instead of beginning with a full-blown metaphysical picture, we should begin with a range of good explanations, scientific and commonsensical. . . . Although my proposal has a strong pragmatic cast, it is by no means an anti-realist suggestion. I am not equating what is real with what is needed for explanations and predictions. The point is, rather, that we have no better access to reality than what is required for cognitive success, construed broadly enough to include what is cognitively required for achieving goals in both science and everyday life” (Ref. 29, p. 94–95). Using the analogy between the discussion physical–mental and individual– collectivism/holism, we risk running into metaphysical debates and getting stuck (just like the philosophers of mind), presupposing these debates have to be resolved first or hoping that analytical metaphysics will provide us with some sound a priori worldview. Too much attention to ontological and metaphysical issues (as is done in the contributions of Sawyer), might lead to the neglect or obstruction of fruitful methodological issues in social theory. If at all we want analytical metaphysics to get involved, be aware of the hazards. Acknowledgments The author is a Postdoctoral Fellow of the Research Foundation–Flanders (FWO). He would like to thank Rob Vanderbeeken and an anonymous reviewer.

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References 1. R. K. Sawyer, Emergence in Sociology: Contemporary Philosophy of Mind and Some Implications for Sociological Theory. American Journal of Sociology 107 (3), 551–585 (2001). 2. R. K. Sawyer, Nonreductive Individualism: Part II — Social Causation. Philosophy of the Social Sciences 33 (2), 203–224 (2003). 3. R. K. Sawyer, Social Emergence: Societies as Complex Systems. Cambridge: Cambridge University Press (2005). 4. R. K. Sawyer, Nonreductive Individualism: Part I — Supervenience and Wild Disjunction. Philosophy of the Social Sciences 32 (4), 537–559 (2002). 5. T. Grimes, Supervenience, Determination and Dependence. Philosophical Studies 62, 81–92 (1991). 6. J. Coleman, Foundations of Social Theory. Cambridge, MA: Harvard University Press (1990). 7. T. Schelling, Dynamic Model of Segregation. Journal of Mathematical Sociology 1, 143–186 (1971). 8. G. Homans, Social Behavior: Its Elementary Forms. New York: Harcourt, Brace & World (1961). 9. G. Homans, Commentary. Sociological Inquiry 34, 221–231 (1964). 10. G. Homans, The Nature of Social Science. New York: Harcourt, Brace & World (1967). 11. R. Axelrod, A Model of the Emergence of New Political Actors. In: N. Gilbert and R. Conte (Eds.), Artificial Societies: The Computer Simulation of Social Life. London: University College London Press, 19–39 (1995). 12. M. Archer, Realist Social Theory: The Morphogenetic Approach. Cambridge: Cambridge University Press (1995). 13. R. Bhaskar, The Possibility of Naturalism. Brighton: Harvester Press (1979). 14. P. Blau, A Macrosociological Theory of Social Structure. American Journal of Sociology 83, 26–54 (1977). 15. P. Blau, Introduction: Diverse Views of Social Structure and Their Common Denominator. In: P. M. Blau and R. K. Merton (Eds.), Continuity in Structural Inquiry. Beverly Hills, California: Sage, 1–23 (1981). 16. R. Bhaskar, A Realist Theory of Science. New York: Verso Classics (1975). 17. M. Silberstein and J. McGeever, The Search for Ontological Emergence. The Philosophical Quarterly 195, 182–200 (1999). 18. R. K. Sawyer, The Mechanisms of Emergence. Philosophy of the Social Sciences 34 (2), 260–282 (2004). 19. A. Clark, Being There: Putting Brain, Body, and World Together Again. Cambridge, MA: The MIT Press (1996). 20. R. Batterman, The Devil in the Details. Oxford: Oxford University Press (1999). 21. J. Zahle, The Individualism–Holism Debate on Intertheoretic Reduction and the Argument from Multiple Realization. Philosophy of the Social Sciences 33 (1), 77–99 (2003).

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22. E. Sober, The Multiple Realizability Argument Against Reductionism. Philosophy of Science 66, 542–564 (1999). 23. J. Van Bouwel and E. Weber, The Living Apart Together Relationship of Causation and Explanation. Philosophy of the Social Sciences 32 (4), 560–569 (2002). 24. J. Van Bouwel, Individualism and Holism, Reduction and Pluralism. Philosophy of the Social Sciences 34 (4), 527–535 (2004). 25. E. Weber and J. Van Bouwel, Can we dispense with the structural explanation of social facts? Economics and Philosophy 18, 259–275 (2002). 26. M. Kistler, New perspectives on reduction and emergence in physics, biology and psychology. Synthese 151 (3), 311–312 (2006). 27. J. Van Bouwel and E. Weber, Remote Causes, Bad Explanations? Journal for the Theory of Social Behaviour 32 (4), 437–449 (2002). 28. T. Burge, Mind–Body Causation and Explanatory Practice. In: J. Heil and A. Mele (Eds.), Mental Causation. Oxford: Clarendon Press, 97–120 (1993). 29. L. Rudder Baker, Metaphysics and Mental Causation. In: Heil, John and Alfred Mele (Eds.), Mental Causation. Oxford: Clarendon Press, 75–95 (1993).

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COUNTERFACTUALS, CAUSATION AND HUMEAN SUPERVENIENCE

PAUL NOORDHOF Department of Philosophy University of York, UK E-mail: [email protected] Counterfactual theories of causation are standardly put forward by proponents of the doctrine of Humean Supervenience. Nevertheless, the plausibility of such counterfactual theories does not rely upon, nor does it entail, the truth of Humean Supervenience. To illustrate the significance of these points, I consider three problem areas for the counterfactual theory of causation arising from the key component in evaluating its success: the semantics of the counterfactuals constituting the analysis. The first is the future similarity objection. The second relates to the connection between counterfactuals and chance. The third concerns the relationship between counterfactual asymmetry and causal asymmetry. In response to the first two difficulties, I place a constraint upon Lewis’s perfect match condition for the similarity weighting for counterfactuals and recommend appealing, more generally, to the idea of failure of fit rather than law violation in formulating the conditions. I explain how the constraint is motivated, and distinguished from something stronger that applies in certain contexts, and not others, by considering the connection between chance and frequency. I argue that the combination of this solution to the first two problems and recognition of the, at best, contingent truth of the doctrine of Humean Supervenience provides a successful treatment of the third problem. I draw out the methodological implications of my approach both with regard to the traditional aims of analysis and, more particularly, with regard to the proper understanding of the aims of counterfactual analysis of causation in the final section of the chapter.

Introduction Striking a match causes it to burn. Kicking someone in the shins causes them pain. How are we to understand the occurrence of the word ‘causes’ in these two statements. Proponents of the counterfactual theory of causation claim that, at root, causation involves the truth of certain counterfactuals, specifically, (1) If I were to strike this match, it would burn. (2) If I had not struck this match, it would not have burnt. 167

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(3) If I were to kick you in the shins, you would feel pain. (4) If I had not kicked you in the shins, you would not have felt pain. ‘Counterfactual’ is a contraction of ‘contrary-to-fact’ conditional apparently first coined by Nelson Goodman.1 Counterfactuals are contrary-to-fact in the sense that the antecedent (in italics) is presumed to be false by the speaker or writer. This is compatible with the antecedent actually being true and also with the counterfactual overall being true, if the consequent is true. On this issue, the Routledge Encyclopaedia of Philosophy 2 is more reliable than, for example, either the Oxford Dictionary of Philosophy 3 or the Oxford Companion to Philosophy.4 The counterfactual theory of causation has its roots in the following passage of David Hume: “we may define a cause to be (i) an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second. Or in other words (ii) where, if the first object had not been, the second had never existed ” (Ref. 5, p. 76, (i) and (ii) my labelling). The ‘other words’ are clearly not obviously other words for the definition labelled (i). The definition makes an accidental invariable association sufficient for causation. Yet, plausibly, there are cases in which all objects of one kind are followed by objects of another kind, and yet the first doesn’t cause the second. It is either just a coincidence or the result of other regularities. As an example of the first, suppose that, as a matter of fact, whenever there has been an eclipse, someone somewhere has given birth. We wouldn’t want to claim, on that basis, that eclipses were causes of human pregnancy. As an example of the second, days are followed by nights and nights by days. Yet we don’t count the days as causes of nights. So the first definition seems too weak. We might say that this is because, even if all objects of the first kind are followed by objects of the second kind, it would not follow that, if an object of the first kind had not existed, the second would not have existed. If there hadn’t been an eclipse, the pregnancy would have come to term anyway. If there hadn’t been day, then there may still have been night with the Earth still on its axis. The counterfactual seems to add something which goes beyond mere regularity and the addition seems exactly what is needed for causation. The first definition is also apparently too strong in so far as it rules out the possibility of brute singular causation — that is, causation which

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there is not part of a regularity or supported by law — which a simple appeal to counterfactuals does not (Ref. 6, p. 169). Suppose I drop a vase to the ground and it breaks into a thousand pieces. It would be very puzzling if, were I to drop another vase exactly like it in exactly the same circumstances, it did not smash. Nevertheless, we would not want to deny, in those circumstances, that my dropping the vase was a cause of vase smashing. Although prima facie plausible, counterfactual theories of causation have come under sustained attack on a number of fronts. One source of attack stems from the possibility of redundant causation such as that involved in pre-emption and overdetermination. In such cases, there are two or more competing causal chains each of which is sufficient to cause an effect independent of the other. One chain is pre-empted if it is stopped by another chain from causing the effect. The effect is overdetermined if more than one of these chains manages to complete and end with the effect. Let c be an event on one of the causal chains and e be the effect. Then the counterfactual If c had not occurred, then e would not have occurred allegedly distinctive of causation would be false. If c hadn’t occurred, e would still have occurred as a result of events on one of the other causal chains. Counterfactual theories increase in complexity to deal with these types of cases but it is not at all obvious that they will provide to be decisive grounds for their rejection. One type of response draws upon the idea that, in the absence of the competitor process(es), if c hadn’t occurred, then e wouldn’t have occurred in exactly the same way, although different means are used to characterise this in an acceptable way to those who seek to provide an informative account of causation (e.g., Refs. 7, p. 193–212; 8–11). Where the first line of attack questioned whether counterfactuals such as (CS) If c were to occur, e would occur, (CN) If c were not to occur, e would not occur, are necessary for causation, a second line of attack questions whether they are sufficient. If two effects, e1 and e2 , are effects of a common cause, c, then, the objection goes, the following counterfactual may hold (CE) If e1 had not occurred, then e2 would not have occurred.

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yet here e1 is not a cause of e2 . This is known as the problem of epiphenomena and it was discussed (amongst other problems) in the paper which more or less launched modern interest in the counterfactual theory, David Lewis’s paper entitled ‘Causation’ published in the Journal of Philosophy in 1973. On the strength of that paper and subsequent discussion, David Lewis became the foremost proponent of counterfactual theory until his death in 2001. David Lewis’ famous answer to the problem of epiphenomena is to deny that (BT) If e1 had not occurred, then c would not have occurred is true. He calls this a backtracking counterfactual because it runs (backtracks) from effect to cause. If the backtracking counterfactual is false, then c may still have occurred (indeed Lewis says would still have occurred), and as a result e2 may or would have occurred anyway. (CE) is not true. Lewis’s solution to the problem of epiphenomena thus rests upon his solution to another way of challenging the sufficiency of (CS) and (CN) (hereafter the counterfactual dependence of e upon c), the problem of effects also discussed in the 1973 paper. Here the concern is whether counterfactual dependency can distinguish between cause and effect. May there not be cases in which both (CS) If c were to occur, e would occur, (CN) If c were not to occur, e would not occur, and also (ES) If e were to occur, c would occur, (EN) If e were not to occur, c would not occur hold? In particular, if a putative effect, e, had not occurred, would we be inclined to say that the cause wouldn’t have occurred either? Lewis argues not. His answer is based upon his semantics for counterfactuals. This brings us to the key question for the counterfactual theory of causation, namely ‘How are we to understand the counterfactuals themselves?’, and the subject matter of my discussion ahead. It is here that issues in the methodology of metaphysics receive their sharpest focus and we may have most to learn. The matters raised up to now concern the precise formulation of the counterfactual theory of causation. Those who are sceptical about its success view the counterexamples from redundant causation, for

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instance, as yet further indication that metaphysical analysis of fundamental features of reality is not possible. They often couch this as the claim that our concepts of these fundamental features are not to be understood in terms of necessary and sufficient conditions. I do not view the scepticism in this area to be warranted and consider the connection between the analysis of fundamental features of reality and the analysis of concepts to rest upon dubious claims about the means by which we obtain knowledge about reality and the conditions for the possession of our fundamental concepts concerning it. In brief, the requirements on what it is to possess the concept of causation are insufficiently rich to explain how conceptual analysis of this concept should provide us with knowledge about the fundamental nature of reality. But that just goes to show that successful analysis of causation is not conceptual analysis and its character need not reflect the nature of our concept of causation in this regard. By contrast, the issues which are raised by seeking to come to a proper understanding of the counterfactuals which constitute the counterfactual analysis of causation relate to the programme of Humean Supervenience, the related denial of necessary connections in nature, the extent to which an analysis can be illuminating if it involves features taken to be distinctive of the thing to be analysed and, finally, the significance of the conviction that proponents of the counterfactual analysis of causation leave out the very substance of causation, whatever ‘sophisticated’ manoeuvres they may make. In the first section of the paper, I will characterise the programme of Humean Supervenience and explain how the counterfactual analysis is supposed to play a role in its advancement. In the subsequent sections, I consider three problem areas for the counterfactual theory arising from the semantics of counterfactuals. It is here that the analytic claims of counterfactual theories of causation are most obviously under threat and their consideration provides us with the possibility of enriching our understanding of what an analysis needs to do. The first is the future similarity objection. The second relates to the connection between counterfactuals and chance. The third concerns the relationship between counterfactual asymmetry and causal asymmetry. I will use these problems to motivate my discussion of the aims and proper development of the counterfactual theory and its contribution to the programme of those who defend the doctrine of Humean Supervenience. The problems are connected. The future similarity objection arises because of Lewis’s attempt to relate counterfactual asymmetry to causal asymmetry. Similarly, if the world is indeterministic, a particularly poisonous version of the future similarity objection arises.

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In the second section of the paper, I turn to the first two of the three problems I have identified. I begin by sketching the future similarity objection and how it is strengthened in the indeterministic case. I then go on to present a solution to these difficulties in terms of placing a constraint upon Lewis’s perfect match condition for the similarity weighting for counterfactuals. I explain how this constraint is motivated, and distinguished from something stronger that applies in certain contexts and not others, by considering the connection between chance and frequency. The constraint I favour does not appeal to causation, something which would present a more immediate threat to the success of a counterfactual analysis of causation although, even here, the matter would turn upon whether the appeal could be cashed out in terms of a variety of sufficient conditions which, independently, did not need to be characterised in terms of causation. In the third section, I introduce David Lewis’s counterfactual account of causal asymmetry and consider two problems for it, one developed by Huw Price relating to microphysics, the other Tooley’s inverted universes case. I explain how the combination of my solution to the first two problems and recognition of the merely contingent truth of Humean Supervenience enables us to provide a successful treatment of these difficulties. In the fourth and final section, I draw out the methodological implications of my approach with regard to the traditional aims of analysis. My treatment of these problems involves two central ideas. The first is that counterfactual theories of causation have been primarily developed to show the compatibility of the doctrine of Humean Supervenience with causation. In a world in which Humean Supervenience is the case, there may be causation because certain counterfactuals are true. It is no part of the counterfactual theory of causation to claim that Humean Supervenience is a necessary truth. Thus there may be worlds in which we can recognise the existence of causation in certain kinds of situations that Humean Supervenience would not countenance and, so long as there is reason to suppose the relevant counterfactuals still hold, there is no threat to a counterfactual theory of causation. Second, and partly following on from this, the proper similarity weighting for the possible worlds approach to counterfactuals may appeal to elements which need not be realised in every possible world in a way which is compatible with Humean Supervenience. Some of these elements may, themselves, be characterised in counterfactual terms. This is no threat to the provision of a non-trivial similarity weighting for counterfactuals so long as the truth of these counterfactuals can be cashed out ontologically in a way which does not mention the counterfactuals. If

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this condition is met, counterfactuals will supply the means by which we may recognise the proper similarity weighting adjusted to different worldly conditions. The matter will be clearer when I come to discuss the relevant cases. 1. Counterfactuals and Humean Supervenience Lewis characterises the doctrine of Humean Supervenience as follows. “Humean supervenience is named in honour of the great denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing after another” (Ref. 7, p. xi). More formally, we may capture the doctrine of Humean Supervenience as follows. “Any world which is a minimal duplicate of our world in terms of the qualities instantiated and their spatiotemporal arrangement is a duplicate simpliciter of our world.” In other words, any world which is a duplicate of our world in terms of the spatiotemporal arrangement of qualities and stops right there — i.e., has no extraneous material — will be a duplicate simpliciter of our world. He takes the nature of the qualities in question to place no constraints upon their co-instantiation. For instance, suppose that, necessarily, if something were fragile, then it would break in certain circumstances. Then there would be a constraint on whether fragility could occur without breaking occurring in the circumstances in question. By Lewis’s lights, fragility could not be one of the qualities mentioned in his characterisation of Humean Supervenience. Interpretative work on David Hume’s writings has suggested, particularly in the Enquiry, that David Hume may not, in fact, be a denier of necessary connections, hence not a proponent of Humean Supervenience and not a Humean (Refs. 12; 13, p. 69–130; 14). However, the term has sufficient currency and this caution is sufficiently widely known that we may proceed without confusion in characterising the position as Humean (after some strains in Hume’s writing). There are also some who remain of the view that Hume is a Humean (e.g., Ref. 15, p. 110–111). At the beginning of this paper, we saw that appeal to counterfactuals in the characterisation of causation went beyond regularities to capture a dependency between the putative cause and effect. If the truth of a

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counterfactual depends upon more than the presence of an invariable association between kinds of particulars, it may seem as if it implies that there will be intra-world necessary connections between distinct existences of the very kind that Humeans deplore, namely, a metaphysically necessary connection, between intuitively distinct existences. The concern is not that there must be a necessary connection of the deplored kind between a putative cause, c, and a putative effect, e. Given the contingency of the laws of nature, it will not be the case that metaphysically necessarily, if c occurs, then e occurs even assuming the circumstances are otherwise unchanged. For instance, David Armstrong and Adrian Heathcote’s idea that singular causation involves the instantiation of a relation of nomic necessitation between universals characterising the cause and the effect respectively does not mean that there is a metaphysically necessary connection between the cause and effect.16 Nevertheless, it may seem that there will be an intraworld metaphysically necessary connection between c’s necessitating e and e. Suppose that an event of type C has the power to bring about an event type E. Putting aside complications which arise in special circumstances, that means that in certain triggering conditions, an event of type C would necessitate an occurrence of an event of type E. Let c’s necessitating e be what happens when c, an event of type C, occurs in the triggering conditions: a bringing about of e. Proponents of the counterfactual theory of causation don’t deny that events necessitate other events. Rather, their counterfactual theory of causation is an account of how events necessitate other events. The counterfactuals reflect a truth about this world and the truth they seem to reflect implies that there is a metaphysically necessary connection between two distinct existences of this world: c’s necessitating e and e and also, for that matter, between c’s power to bring about an event of type E and the triggering conditions on the one side, and e on the other. David Lewis’s semantics for counterfactuals shows why there need be no such implication. We may break his account down into three components: first, there is the analysis of counterfactuals; second, there is his similarity weighting; and third, there is his particular brand of realism about possible worlds. Lewis’s analysis of counterfactuals is as follows. “A counterfactual ‘If it were that A, then it would be that C’ is non-vacuously true if and only if some (accessible) world where both A and C are true is more similar to our actual world, over-all, than is any world where A is true but C is false” (Ref. 17, p. 41).

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Appeal to possible worlds is a way of formalising the intuitive idea that, when we evaluate a counterfactual, we consider circumstances very like the actual circumstances in which A holds and assess whether C also holds. The appeal to accessibility provides scope for a restriction on the worlds we need to consider in the evaluation of the counterfactual. It is standard to suppose that no restriction, in fact, needs to be placed. So I will say no more about this feature here. The analysis makes the truth of the counterfactual ‘If it were that A, then it would be that C’ depend upon whether A and C hold in certain worlds (the close-by ones determined by the similarity weighting). The similarity weighting for possible worlds serves to characterise which worlds are to count as most similar for the assessment of the counterfactual. I will outline in some detail Lewis’s proposal and the problems with it in the next section. For the moment, the issue is orthogonal to the question of whether the truth of counterfactuals reflects intra-world necessities. So I set this aside and move to the third component of Lewis’s position. If reference to possible worlds is simply taken to be a heuristic way of thinking about intra-world necessities in space–time, then obviously the possible worlds analysis of counterfactuals reflects intra-world necessities. The more interesting question is what follows if we take reference to possible worlds ontologically seriously. Lewis’s brand of realism about possible worlds has a role to play at this point. To see what it is, suppose, instead, that Actualism is true, that is, that all possible worlds actually exist. One of these is realised by the concrete world in which we inhabit. The others are unrealised but still exist as properties, sets of propositions, or what have you, in our world. To fix ideas, suppose that merely possible worlds are maximal consistent sets of propositions. In this case, at best the intra-world necessity reflected by the counterfactual is just relocated. It still must be present in the actual world. Suppose that A is ‘c occurs with the power to bring about an event of type E’ and C is ‘e occurs’. Suppose further that any conditions required for the manifestation of the power are realised and that, in all the closest A worlds (setting aside the actual world), C is the case and that in all the closest not-A worlds, C is not the case. These facts about the closest worlds, the truth of A in the actual world, and the conditions which hold in the actual world bracketing the occurrence of e, metaphysically necessitates that e occurs. If the character of close-by worlds did not have this implication, then they would not secure the truth of the relevant counterfactuals. In other words, close-by worlds are sensitive to what occurs in the

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actual world. Nevertheless, c’s occurrence with the power of bringing an event of type E together with the facts about the maximal consistent sets of propositions which comprise the close-by worlds are a distinct existence from e. So even if we suppose that a possible worlds analysis reveals the real character of intra-world necessities, the Actualist version of this analysis does not banish intra-world necessities between distinct existences from our world. Perhaps it will be argued on the Actualist’s behalf that, since the laws of the actual world partly determine what counts as the closest possible worlds, it is not correct to take the relevant facts about close-by worlds to be distinct existences from the occurrence of e. However, this seems to confuse a relational identification of the worlds in question with the facts to which we are appealing. I do not deny that the fact that a world is closeby is partly settled by the laws which hold in the actual world. However, enumerate the facts of these close-by worlds without mentioning that they are the close-by worlds. These facts together with the fact that c occurred in the circumstances it did in the actual world will still metaphysically necessitate that e occurred. Relevant similarities between worlds set up the relations of closeness and distance. However, it is the particular patterns of fact in what are, in fact, the close-by worlds which settle whether or not c is occurring in the actual world with the power to bring about an event of type E. If, furthermore, c occurs in triggering circumstances, then it is these facts which constitute the necessitation of e. Lewis’s own brand of modal realism denies that all the possible worlds actually exist. The other possible worlds are no part of the actual world. The consequence of this is that, while he does not deny the necessary connection between the character of the close-by worlds and the nature of the actual world, it is not an intra-world necessary connection. This enables him to retain the hypothesis that there are no necessary connections between distinct existences in the actual world while, at the same time, not denying that these modal facts in our world supervene upon non-modal facts. The supervenience of causal truths holds in virtue of what holds in the close-by worlds in addition to the actual world. It is less clear whether Lewis supposes that denial of intra-world necessary connections between distinct existences is a necessary or contingent truth. The matter turns on the connection between the denial and the doctrine of Humean Supervenience. In the passage with which I began this section, he clearly takes the doctrines to be closely related. Lewis’s commitment to taking the doctrine of Humean Supervenience to be contingent is clearly expressed in the following passage.

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“. . . I concede that Humean supervenience is at best a contingent truth. Two worlds might indeed differ only in unHumean ways, if one or both of them is a world where Humean Supervenience fails. Perhaps there might be extra, irreducible external relations, besides spatiotemporal ones; there might be emergent natural properties of more-than-point sized things; there might be things that endure identically through time or space, and trace out loci that cut across all lines of qualitative continuity. It is not, alas, unintelligible that there might be suchlike rubbish. Some worlds have it. And when they do, it can make a difference between worlds even if they match perfectly in their arrangements of qualities” (Ref. 7, p. x). If there were intra-world necessary connections between distinct existences, the doctrine of Humean Supervenience would be false. Nevertheless, that does not mean that he takes the denial of such necessary connections to be a contingent truth. There are other reasons why Humean Supervenience may fail, for instance, if there are external non-spatiotemporal relations or emergent properties from the arrangements of point qualities. Lewis may hope that the world does not contain such stuff but he does not think that no world could. Matters may be different for necessary connections between distinct existences. Indeed, perhaps the current orthodox interpretation of Lewis’s position is that he thinks that the denial of intra-world necessary connections between distinct existences is a necessary truth. There are at least two pieces of evidence to support this interpretation of Lewis’s position. The first is that when he considers the various ways in which Humean Supervenience might fail in the first passage I quoted, the possibility of intra-world necessary connections between distinct existences doesn’t figure among them. Second, in the On Plurality of Worlds, he appeals to a principle of recombination in order to specify all the possibilities in logical space. According to the principle of recombination, anything can coexist with anything (or, more precisely within his framework, a duplicate of anything can coexist with a duplicate of anything) provided they occupy distinct spatio-temporal positions (size and shape of world permitting) (Ref. 18, p. 87–89). He then goes on to write “It is no surprise that my principle prohibits strictly necessary connections between distinct existences” (Ref. 18, p. 91). If the principle of recombination fixes what possibilities there are and it rules out the possibility of necessary connections between distinct existences, then their denial seems to be a necessary truth.

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In his final work, though, his position seems to have softened to the possibility of necessary connections between distinct existences. When he considers what might occupy the ‘biff’ role — characterised in terms of being an intrinsic relation between distinct positive events associated with probabilistic counterfactual dependence (Ref. 19, p. 280) — he writes that in some worlds “It might be a Humean-supervenient relation. Or it might be a relation posited by some anti-Humean metaphysic of nomological necesssity . . . Myself, I’d like to think that the actual occupant of the biff-role is Humean supervenient, physical, and at least fairly natural” (Ref. 19, p. 283–284). An anti-Humean metaphysic of nomological necessity involves intraworld necessary connections between distinct existences as Lewis has, on more than one occasion, pointed out. For instance, according to David Armstrong whose work Lewis cites in illustration, Fa and N(F, G) may sometimes — when N(F, G) is not an oaken law — necessitate that Ga in the sense that it could not be the case that Fa and N(F, G) and yet not Ga (Ref. 20, p. 85–99, 147–150). Yet, the instantiation of G is a distinct existence from Fa and N(F, G). Of course it is possible to view these later remarks by Lewis as an aberration, or as showing a willingness to consider a possibility, for the sake of argument, which he did not really take seriously. Two considerations incline me to suppose that, in any event, the option that Lewis considers is worth taking seriously and that it is congenial with his overall aims. The first is that, since he allows for the existence of an apparently infinite number of alien properties, we are unable to specify all the entities which may be recombined and hence unable to characterise the range of possibilities in logical space via the principle of recombination.21 So Lewis’s reason for endorsing the principle of recombination — and hence denying that there may be necessary connections between distinct existences — falls away. Second, as we shall see, allowing for the possibility of necessary connections between distinct existences has some utility in the development of a response to certain difficulties afflicting a counterfactual theory of causation. This will become clear when I turn to the question of causal asymmetry. In this section, I have argued that Lewis’s denial of metaphysically necessary connections between distinct existences is a contingent truth. By providing a semantics for counterfactuals which does not require the presence of such intra-world necessary connections, he can explain how causation is

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compatible with Humean Supervenience without having to reject intuitive verdicts about causal relations in certain possible situations. In the subsequent sections, we shall see that his semantics for counterfactuals is in need of some adjustment but not so as to detract from this basic virtue.

2. Counterfactuals, the Future Similarity Objection and Chance As we have already seen, Lewis characterises closeness of possible worlds in terms of similarity. Some have taken the appeal to similarity to be an appeal to an atheoretical intuitive notion of similarity. This led Kit Fine and others to suppose that Lewis must get the wrong verdict regarding the truth or falsity of the following counterfactual. (5) If Nixon had pressed the button, then there would have been a nuclear holocaust. Given that we are in a non-holocaust world, then a world in which the holocaust failed to occur due to a small miracle resulting in the failure of the signal of the button to transfer down the wire to the rockets would be much more similar to the actual world than one in which, from Nixon’s time, there was nothing but devastation and death. Thus, counterintuitively, Lewis’s verdict on the counterfactual is that it is false (Ref. 22, p. 453). This has come to be known as the Future Similarity Objection to Lewis’s semantics for counterfactuals because it rests upon the idea that overall similarity is achieved by maximising the similarity in the future of the button pressing world with our future in which a holocaust did not occur. By 1979, Lewis makes clear that he is not appealing to a pre-theoretical and intuitive notion of similarity. Instead, his preliminary similarity weighting for possible worlds has the following four clauses. (A) It is of the first importance to avoid big, widespread, diverse violations of law. (B) It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails. (C) It is of the third importance to avoid even small, localized, simple violations of law. (D) It is of little or no importance to secure approximate similarity of particular fact, even in matters which concern us greatly (Ref. 17, p. 47–48).

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Lewis explains that when he talks of law violations he means violations of laws in our world so that, in the putative world in which the laws are violated, different laws hold. He does not mean that the laws of the lawviolating world are themselves violated (Ref. 17, p. 44–45). Many have claimed that Lewis was putting forward a new approach to similarity in his later work. I have never seen the basis of this charge. Right back in his 1973 book on Counterfactuals under review by Fine, he argued that laws should have particular weight and that what might make us discount future similarity to violation of laws is that many more violations of law would be required to achieve future similarity (Ref. 23, p. 75–76). In any event, Lewis argues that the counterfactual, ‘if Nixon had pressed the button, then there would have been a nuclear holocaust’ is true because to obtain future perfect match we would have to have many miracles to cover up all the traces of the button pressing. The similarity weighting proclaims such worlds further away than those in which there are no widespread violations of law. However, if we have less violations of law for simply approximate match in the future, then the third condition of the similarity weighting comes into effect. Better to have no law violations than those which yield only approximate match (Ref. 17, p. 43–48). The first two problems I consider deriving from the semantics of counterfactuals rest upon considering circumstances in which the facts to which Lewis appeals do not hold. 2.1. Isolating the Cause Since Lewis’s initial response to the Future Similarity Objection rested upon an apparently contingent fact about the world — namely that a cause has many consequences and so perfect match in the future is hard to obtain — a natural issue to raise is: what happens if this contingent fact does not hold. Some have explicitly written the possibility into the antecedent such as the following. (6) If Nixon had pressed the button and, by some miracle, all imminent traces of this action except for the signal travelling down the wire were eliminated, then there would have been a holocaust (Ref. 24, p. 30). I don’t believe that such cases force an adjustment to the similarity weighting Lewis recommends. It is within his rights to press the following dilemma in the assessment. Either it is assumed that ‘except for the signal travelling

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down the wire’ requires that the signal did travel down the wire to the rockets or this is left open. If the former, then fizzling out possibility is ruled out in the antecedent of the counterfactual in which case perfect match in the future cannot be secured. Alternatively, as seems much more likely, the possibility of fizzling out is intended to remain open. In which case, it is by no means clear that the counterfactual is true. The easiest way in which all traces of the button pressing except for the signal travelling down the wire might be covered up is to cover up the signal travelling down the wire too. So we might concur that it is by no means certain in the situation envisaged in the antecedent that it would be the case that there is a holocaust although indeed there might be one. Hence the counterfactual is false. Others have invited us to consider the counterfactuals we would be inclined to hold in other worlds in specifically tailor-made cases. Suppose that there is an indeterministic lottery draw which you set going by pressing a button. A signal travels into a box which, when it reaches point r1 , can go down either a path leading to randomising device r2 or randomising device r3 . Each gives the same chance to each possible outcome of the lottery. The paths reconverge and lead out of the box to a display. The box is totally impenetrable and isolates the processes going down the paths to either r2 or r3 from all other effects in the world. Suppose, in fact, the signal travelled down the path to r2 to generate and display the winning number 17.a Now consider the following counterfactual. (7) If the random process in r1 had turned out differently and the signal had travelled from r1 to r3 rather than to r2 , ticket number 17 would still have won. Intuitively, (7) is not true at the world described. Yet, one might secure perfect match with regard to that world if we retained the winning number to be 17 (Ref. 25, p. 275). Boris Kment suggests that the right moral to draw from this case is that only certain kinds of perfect match matters, namely perfect match for those items with the same causal history (or no causal history in the default case) (Ref. 25, p. 276, 282). It is clear how such a moral would be potentially damaging to the counterfactual theory of causation. The formulation of the constraint upon perfect match does not allow for the aI

have re-lettered Kment’s original example appealing to A, B and C, with r1 , r2 , r3 at the suggestion of an anonymous referee who feared confusion with my use of A, C to refer to the antecedent and consequent, and (A), (B), (C), and (D) to label the clauses of Lewis’s similarity weighting for counterfactuals.

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assessment of counterfactuals without appeal to causal conditions. Yet, according to the counterfactual theory, the counterfactuals are supposed to capture when the causal conditions hold. Although I think there is a bit of wriggle room if the counterfactuals to which the proponent of the counterfactual theory of causation appeals involve probabilities rather than events in the consequents, there is not much. As Stephen Barker has pointed out to me,b it is possible for Lewis to tough it out against Kment’s case and note that the future does not contain perfect match because of the differences that Kment acknowledges occur within the box (Ref. 25, p. 276). Indeed, on the assumption that a cause does not have consequences for every point in future space–time, it will always be possible to identify a patch of perfect match in the future if perfect match just requires that a portion of space–time matches perfectly with the actual world rather than that all of space–time after a certain time perfectly matches. There are a number of options which follow from this observation. Either (i) we should take cases like the one Kment offers to provide information as to how we should fill in the approximate match clause or (ii) some limitation should be placed upon just how extensive the consequences should be before we fail to have something we might allow as perfect match or (iii) we might adjust Kment’s case so that the box decomposes in exactly the same way whichever path the signal travels down shortly after the transmission of the signal so that there will be future perfect match. I shall assume, for the sake of argument, that either of (ii) or (iii) are viable and present Kment with a way to retain his counterexample to the perfect match clause. In fact, even with this assumption in place, the moral that Kment draws appears too strong. Suppose that the paths leading from randomising device r2 and r3 are unreliable and that sometimes the display displays a number simply as a result of its own spontaneous indeterministic processes. We could secure more perfect match of the right kind if we retained the fact that the winning number was 17 spontaneously generated. Yet, intuitively, the counterfactual seems false. We feel inclined to say, if the path had been via the other randomising device, who is to say what the winning number would be? We only know that the signal fizzled out on the r2 -path. Kment himself recognises that his proposal has difficulties of this kind. He notes that, first, certain differences in causal history do not undermine an event’s contribution to perfect match. Suppose that there are two b Stephen

Barker, personal communication.

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qualitatively identical cell phones, CP1 and CP2, varied day by day for the use of, Susie, the lottery administrator. The following counterfactual seems intuitively true without a special story. (8) If Susie had used CP2 rather than CP1 for that day, the outcome of the lottery draw would have been just the same.c Nevertheless, which phone is used does count as a difference to the causal history of a particular outcome (Ref. 25, p. 297–298). Second, although not just productive causes — such as a bus smashing into a car — but also preventative causes — such as the pedestrian failing to warn the bus driver about the car — count as a difference in causal history for the purposes of perfect match, they do not always count as a difference. Suppose a King is able to toss a coin as a result of the successful prevention of his assassination by a foiler F1 rather than another foiler F2. We still would not reject the following counterfactual (9) If a plot by the assassin had been prevented by F2 rather than by F1, the outcome of the toss would have been the same (Ref. 25, p. 299– 300). It should be emphasised that, in all of these cases, the difference in causal history does not make a difference regarding the outcome: intuitively, which cell phone is used does not make a difference to the outcome of the lottery nor does the activity of one foiler or another change the King’s toss. However, this is precisely Kment’s point. He argues that even differences in causal history which are not difference-makers would make it inappropriate to take across facts which would maximise perfect match. He takes this to be the lesson of the original lottery mechanism in a box case. It would not be appropriate to retain the outcome of 17 because of a difference in causal history even though this difference will not be a difference-maker in a world in which we get the same outcome via the r3 mechanism. That is why he is worried by the cases just mentioned.d cI

have re-lettered the cell phones, CP1 and CP2, rather than A and B as in Kment’s original article, because of an anonymous referee’s fear that this further use of A and B would add confusion in the reader’s mind. d An anonymous referee suggested that, in the cell phone and assassin cases, the differences in causal history had not been established as difference-makers and that this undermined the effectiveness of the cases against Kment’s position. This paragraph is addressed to that concern.

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I will argue that a certain kind of probabilistic relation between the events mentioned in the antecedent and the consequent is required to yield the appropriate verdicts. To get there, though, it pays to consider the second way in which the future similarity objection has been exacerbated, namely as a result of indeterminism. 2.2. Indeterminism and Lewis’s Similarity Weighting This problem does not rely upon consideration of exotic worlds with special circumstances. It is a straightforward consequence of certain reasonably well agreed facts about our own world. Consider once more the counterfactual (5) If Nixon had pressed the button, then there would have been a nuclear holocaust. As we have already seen, in the deterministic case, Lewis relied upon the need for a massive cover up which, thereby, involved many law violations — so placing clause (B) in conflict with clause (A). However, if, as we believe, the world is indeterministic, all the effects of Nixon pressing the button can be covered up without law violation. If it is a law, say, that for all x, if Fx then chance (Gx) = 0.9, then it is no violation of this law if Fa and not-Ga. Therefore, Lewis’s similarity weighting proclaims (5) false. By itself, that might not be too counterintuitive. Indeed, some say that strictly speaking (5) is false. Moreover, we can still say (5*) If Nixon had pressed the button, then a nuclear holocaust would have been very likely is true. The real problem is that Lewis’s similarity weighting proclaims (10) If Nixon had pressed the button, then there would not have been a nuclear holocaust true. The closest world to the actual world will be one in which there is a complete cover up since this will involve no law violation and secure the maximal amount of perfect match. Lewis tries to deal with this problem by the quasi-miracles strategy. He concedes that, since there is no law violation, there will be no miracles involved in the cover-up. Nevertheless, a complete cover up would be a remarkable coincidence and, as such, be a quasi-miracle (Ref. 7, p. 58–65).

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Lewis’s treatment faces problems. First, there are remarkable coincidences which take place in our world. We are in danger of making it less similar to itself — via Lewis’s similarity weighting — than another possible world. Although, as we have seen, Lewis adopts a technical notion of similarity which places the emphasis on certain similarities over others, I take it as a datum that nothing can fail to be more similar to itself than any other thing. Second, Lewis’s treatment introduces a questionable level of anthropocentricity in the assessment of counterfactuals. Remarkable coincidences are not — according to Lewis — simply very improbable events. Instead they are, in addition, what we count to be remarkable. Lewis’s reason for rejecting simple appeal to improbability is that since very improbable events occur in the actual world, we are in danger of making the actual world less similar to itself than some close-by worlds. The first problem I identified with Lewis’s approach simply took up this concern and applied it to the remarkable as well. Third, and finally, as John Hawthorne has pointed out recently, we are in danger of there being unfortunate trade-offs between the remarkable and improbable. For instance, we would have to accept that (11) If I were to toss a coin a million times, it would not come up either all heads or all tails is true but (12) If I were to toss a coin a million times, I would not get sequence S (where S is a particular random sequence of heads and tails) is false (Ref. 26, p. 400–402). Yet, P(all heads or all tails) is higher than P(S). A second approach also runs into difficulty. According to it, ‘If A were the case, then C would be the case’ is true if and only if (i) the vast majority of closest A-worlds are worlds in which C (ii) in the actual world, A and C (Ref. 27, p. 250–251). The intuitive idea is obvious. If C has only a high but not equal to one probability of being true given the antecedent is the case, C won’t be true in every close-by A-world. Nevertheless, it will be true in most close-by A-worlds. Unfortunately, this approach cannot be combined with Lewis’s account of the similarity weighting of worlds. If we can obtain more perfect match without law violation, then no close-by A-world will be a C-world. All close-by A-worlds will be worlds with perfect cover up.

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The first response to the problem we considered — Lewis’s — suggested strengthening the first condition of the similarity weighting by introducing the notion of a quasi-miracle. The second response suggested changing the analysis of counterfactuals. A natural third response is to weaken the perfect match condition or do away with it all together. The latter option is too radical because it would give us no circumstances in which to assess whether the consequent followed from the truth of the antecedent. So let us look at weakenings instead. In earlier work, Bennett has suggested that all that the assessment of counterfactuals requires is perfect match at the time of the truth of the antecedent (Ref. 28, p. 72–74). However, in his later work, Bennett supplied two good reasons for not going down this route. The first reason is that when we assert counterfactuals we typically assume that the circumstances at the time of the antecedent will be a little different guided by how the world might have evolved to arrive at the truth of the antecedent. Bennett gives the nice example of (13) If the German Army had reached Moscow in August 1941, it would have captured the city. In assessing the counterfactual, we don’t assume that the city would remain sparsely defended by inexperienced troops while the more experienced ones remain where they are fighting since-departed German troops marching on Moscow. Instead, we assume that the German troops had fought harder and the Soviet troops had fallen back (Ref. 27, p. 211–212). The second reason is that we also assert counterfactuals where we assume that the past leading up to the antecedent is more or less in place. Again, Bennett provides a nice example. (14) If that hill outside Syracuse had not been levelled last year, it would have been a superb site for a memorial to the Athenian soldiers who starved to death in their marble quarries. The counterfactual is only true because, in fact, Athenian soldiers did die in 413 BC in the way described (Ref. 27, p. 214). Instead, I suggest that the Nixon case reveals that we don’t value perfect match which fails to minimise departure from the distinct events (or their absences) that the truth of the antecedent of the counterfactual makes more probable given that the antecedent is actually false. Nixon’s pressing of the button makes the occurrence of the holocaust more probable than it would otherwise be. The claim is that if this is so it would not be appropriate to seek to retain perfect match with regard to this feature. Thus it is taken

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out of the calculation. As a result, (10) If Nixon had pressed the button, then there would not have been a nuclear holocaust, is false. There will also be events leading up to those involving the truth of the antecedent that end up being more probable than they would be if the antecedent is false. So the perfect match condition would not apply to these either. However, this is entirely appropriate and introduces no features not already present in Lewis’s original similarity weighting which relied upon small miracles to give rise to the truth of the counterfactual antecedent. The condition contains the phrase ‘given that the antecedent is actually false’ because, of course, we would not want to make the actual world potentially less similar to itself than some close-by worlds by removing a string of distinct events which actually occurred although were made less probable by the actually true antecedent. Our failure to value perfect match that does not minimise departures from what the truth of the antecedent would make more probable does not account for our intuitive verdicts regarding all ‘isolated’ versions of the future similarity objection. In the lottery case, travelling down path r2 does not raise the chance of the outcome being 17 since, presumably, it would have precisely the same probability as it had when the signal travelled down path r3 . The issues raised here are akin to those which are raised in standard cases of pre-emption and a similar solution suggests itself (see Ref. 11 for discussion of probabilistic causation and cases of pre-emption). Instead of appealing to the idea of making more probable, we should appeal to the idea of making more Σ-probable defined as follows. e1 makes e2 more Σ-probable iff there is some (possibly empty) Σ-set of actual (positive) events such that (i) if e1 were to occur without any of the events in Σ, it would be the case that ch(e2 ) is generally around x; (ii) if neither e1 nor any of the events in Σ occurred, it would be the case that that ch(e2 ) is generally around y; (iii) x > y (where ‘ch(e2 )’ should be read ‘chance that e2 occurs’). We would then formulate the restriction upon condition (B) of the similarity weighting, giving us (B*) as follows.

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It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails unless, in so doing, we fail to minimise departure from the distinct events (or their absences) that the truth of the antecedent of the counterfactual makes more Σ-probable given that the antecedent is actually false. In the lottery case, we would put in Σ the event of triggering randomising device B. In circumstances in which this even failed to occur, the signal travelling down the path to C would raise the chance of the winning ticket number being 17 over the spontaneous chance of that outcome (which might be equal to zero). In which case, it would not be appropriate to take the outcome across to the changed circumstances and (3) becomes false as desired. Appeal to Σ-probability retains the result we want regarding the Nixon case since there is a Σ for which Nixon pressing the button raises the chance of the holocaust, namely the null set. There are also, doubtless, others. The most striking feature of the proposal is that it appeals to a counterfactual in its characterisation of making more Σ-probable. This obviously raises the question of circularity. Clearly if the counterfactual could not be cashed out, then there would be a difficulty. We would be giving the semantics of counterfactuals partly in terms of a counterfactual to whom the semantics did not apply and nothing else was provided in its place. That is not the intention here. Instead, the counterfactual is used to summarise similarities which arise not due to the patterns of qualities in a particular world but rather those which arise due to patterns of qualities in a particular world and close-by worlds. Thus consider all the worlds with a significant amount of perfect match. There will be those in which there is no holocaust in which the laws are roughly as they are in our world. There will be those in which there is no holocaust and the laws are relevantly different to those in our world. There will be those in which there is a holocaust and the laws are roughly as they are in our world. The original clause, (B), ranks the first class of worlds as closer than the third class of worlds. The revised clause, (B*), sets aside this ranking since, in all the close-by worlds in which there is greater perfect match there is greater departure from distinct events that the truth of the antecedent makes more probable. As I have described things, this verdict can be simply read off the laws of nature at the various worlds. No fundamental appeal to counterfactual

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facts is required. Nevertheless, suppose that there were probabilistic dependencies not backed by law. This is something that the counterfactual theorist should concede since, as already noted, one of Lewis’s original motivations for adopting the counterfactual theory is that it allowed for the possibility of brute singular causation. In such cases, the laws won’t reveal the relevant probabilistic dependencies. Nevertheless, they would be revealed by the fact that sets of different worlds were close-by to the equivalent of the first and third classes of worlds. So the fundamental cashing out of the counterfactuals appealed to in the formulation of (B*) comes with the recognition that not simply the intra-world distribution of qualities sets up relations of closeness but also intra-regional distributions do — where regions are made up of a number of worlds (intuitively, worlds and the worlds which are close to them). A related concern with the proposal is that, in appealing to ‘make more probable’, I am appealing to a causal notion. In so doing, the charge would run, I undermine any attempt to analyse causation in terms of counterfactuals. The first point to make is that, even if my characterisation of making more probable was in fact an analysis of causation of probabilities, that would not present a problem. The issue is not whether we need to appeal to causation to characterise the similarity weighting for counterfactuals but rather whether we need to appeal to causation not understood in terms of counterfactuals to characterise the similarity weighting. As I noted earlier, Lewis distinguished our standard use of counterfactuals from a backtracking use. The standard use — characterised by his similarity weighting — made them appropriate for the analysis of causation and causal asymmetry. This does not vitiate the analytic appeal of counterfactuals on the grounds that the relevant notion of counterfactual dependence is a causal one. The proposed analysis of ‘making more probable’ appeals to counterfactuals of exactly the same character — in terms of eschewing backtracking and counterfactual dependencies between common effects — to which Lewis appeals in his original analysis of causation. Although I have said that it would not matter if the analysis of making more Σ-probable was an analysis of causation of probabilities, in fact it is not such an analysis for two reasons.11 First, a key component of c causing e is that the process linking c to e is actually complete and not just would be complete in different circumstances. If we consider circumstances in which the events mentioned in Σ are absent, it is possible that a process which, in fact, was incomplete, is now complete because the events mentioned in Σ actually served to inhibit the occurrence of events in that process.

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Second, it is a standard requirement that causes should be distinct from their effects. For the concern to arise with regard to my notion of making more Σ-probable, the effect would be the probability of a certain event, namely ch(e2 ). It is plausible, though, that this is none other than the causal circumstances including e1 given that a law relating to the chance of e2 holds. There is not some distinct event, e1.5 , which is the chance of e2 .e (B*) does not make (1) true. It just makes (6) false. This seems to me to be the key result. Our fundamental conviction is that it is wrong to say that there wouldn’t have been a holocaust (i.e., (6)) not that it is correct to say that there would have been (in an indeterministic world) (i.e., (1)). Nevertheless, there do seem to be circumstances in which we are inclined to assert (1). When this happens, context has added to our similarity weighting. It is of the fourth importance to minimise departures from the distinct events (or their absences) that the truth of the antecedent of the counterfactual would make highly Σ-probable if it were true given that the antecedent is actually false. It is of fourth importance, when it is, because we don’t want to minimise departures by supposing that the laws are changed. Call the similarity weighting with this added the contextually adjusted similarity weighting. I emphasise that this is in play in only certain contexts because there seem to be clear cases in which it would yield the wrong results. Suppose, to fix ideas, that ‘highly probable’ in the characterisation offered above is 90% or above and that there are 1,000,000 coin flippers. Consider the following counterfactuals. (F1) If I were to supply each coin flipper with a biased coin (giving rise to 90% heads), then coin flipper 1 would have tossed all heads. (F2) If I were to supply each coin flipper with a biased coin (giving rise to 90% heads), then coin flipper 2 would have tossed all heads. .. .. . . (F1000000) If I were to supply each coin flipper with a biased coin (giving rise to 90% heads), then coin flipper 1000000 would have tossed all heads. e These

last two paragraphs are written in response to an anonymous referee who raised the concern that my proposal had a circularity threat arising from the fact that ‘making more probable’ was a causal notion.

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Assume further that Agglomeration is true. P > Q, P > R . . . then P > Q & R & . . . Then (FALL) If I were to supply each coin flipper with a biased coin (giving rise to 90% heads), then all the coin flippers would have tossed heads. However, (FALL) is false. It would break the connection between the chance of a certain type of event and the frequency with which it occurs. The weakest point (in terms of commitments) that can be made against the application of the contextually adjusted similarity weighting in this case is simply that for high probabilities, the counterfactuals it would support would take it that the events mentioned in the consequent always occurred. It would be as if they had chance 1. I think that this shows that when we focus on overall patterns we drop the contextually adjusted element to the similarity weighting. The strongest point that might be made (in terms of commitments) is that there should be some link between chance and limiting frequencies which adoption of the contextually adjusted similarity weighting would hopelessly undermine. The connection is often put as follows. (L) Ch(e occurs) = p entails I4 (an E occurs) = p. The proportion of E-type events relative to a reference class of n events (where ‘n’ is a number) tends towards a certain limit as n gets larger and larger, namely p. Those who attribute chance to single cases and deny that chances are limiting frequencies cannot capture (L) as it stands. If 0 < p < 1, then it is possible that there is an infinite sequence of Es occurring and hence the proportion of Es does not correspond to the limiting frequency. Therefore, Ch(e occurs) = p cannot entail a certain limiting frequency. Instead, we may put in place of (L), (L*) If there were an infinite series of events or circumstances in which Chc (E occurs) = p, then it would be that I4 (an E occurs) = p. Lewis denies that (L*) is true on the grounds that there is no infinite sequence of outcomes that would occur if E (say coming up heads) had a certain chance. There are all kinds of sequences that would have a very small, perhaps infinitessimal, chance of occurring (Ref. 29, p. 90). However, the consideration Lewis offers is questionable, especially when we bear in

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Ω

mind his later rejection of ‘might’ with ‘not-would-not’. He allows that there are cases in which we would be inclined to say that something would not occur even though it might occur because there is some chance of it occurring. This is not just due to his appeal to quasi-miracles in the similarity weighting for counterfactuals discussed earlier but also, for instance, because of his treatment of counterfactuals with true antecedents and those mentioning unfulfilled chances in their antecedents (Ref. 7, p. 63–65). The reasoning in favour of (L*) rests upon a particular understanding of what would count as a violation of a law. Suppose that in the actual world a certain law, L, holds. In another possible world, the law may fail to hold in one of three ways. First, there may be the same pattern of events in the actual world and yet this is just an accidental correlation. No Humean would be happy with such a possibility if the actual world is Humean. Nevertheless, since Humean Supervenience is a contingent truth, there will be non-Humean worlds and, in these worlds, this first way in which a law may fail to hold must be allowed. For instance, Armstrong would have to allow that there may be two worlds, one in which (x)(Fx Gx) and N(F, G) and one in which simply (x)(Fx Gx). In the latter, there would be no law between F and G. Second, there may be a pattern of events which indicates that a different law holds and yet the pattern in question is consistent with the laws of the actual world. This type of case is best understood in terms of the Best System Analysis of Laws. According to Lewis, laws of nature are those universal or probabilistic generalisations which provide the best combination of strength, simplicity and fit with regard to the patterns of particular fact. The last is crucial for the case I am envisaging. In the finite case, the best fit is the one which makes the actual history most probable, in the infinite case, best fit is that which makes certain test propositions likely to be true e.g., those concerning the limiting relative frequency and which proportions occur exactly as often as each other (Ref. 30, p. 71–72). Either way, there will be patterns of events which, while they are consistent with certain laws holding, do not fit with them as well as other laws. Third, a law may fail to hold if a certain pattern of events is inconsistent with the laws. For instance, if the law says that all Fs are Gs, then there is something which is an F but not a G. Consider again a world in which the pattern of events doesn’t fit with laws assigning a certain chance to their pattern. For instance, a law says that Chc(E occurs) = p and yet it is not the case that I4 (E occurs) = p. If this counts as a law violation as far as the similarity weighting for counterΩ

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factuals is concerned, then this world will be further away from the actual world — where we assume the law holds — than one in which the pattern fits with the law. In which case, although there is some chance that the proportion of E-events is not p, it would not be the case that this proportion failed to be p. If we restrict our account of law violation to the third case in which laws fail to hold, then this result does not follow. It is a nice question what the most appropriate account of law violation is with regard to the failure of a law to hold at a world. If a Humean account of laws is necessarily true, the first way in which laws may fail to hold would be empty and the second way in which laws may fail to hold would be appropriately counted as a law violation. If laws are just patterns of qualities of a certain type, then the failure of this pattern to hold, in either the way that a deterministic law statement or the way that an indeterministic law statement would describe, alike count as violations of the law. There is nothing more to going against the law than a certain pattern failing to hold. On the other hand, if a Non-Humean Necessitarian account of laws is true, then there will be instances in which a law fails to hold in the first way. It would be hard to see how these would be ones in which the law is violated given that the pattern of events still hold. On the other hand, the second way in which the law may fail to hold would be empty. The existence of a pattern of events which is compatible with the law — however improbable this pattern may be — cannot be a pattern which violates the law. The law statement does not claim that the pattern will not be present. Humean and Non-Humean accounts of laws thus agree that the first way in which a law may fail to hold does not count as a case of law violation and that the third way does count as a case of law violation. They disagree over the second. For those of us who only hold that a Humean account of law is a contingent truth — at best — the second case is most plausibly considered to be a possible case of law violation depending upon what account of laws holds at a world. The proper development of a semantics for counterfactuals can go in one of two directions. We could appeal to the idea of law violation understood to exclude the second case and allow that, in worlds for which the Best System Analysis is true, the second type of case would also count as a case of law violation. Alternatively, we could appeal to failure of fit instead and adopt a uniform account which does not depend upon the correct theory of laws for a certain world.

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The attraction of adopting the latter approach appealing to failure of fit is that it would enable us to endorse (L*) as a necessary truth about the connection between chance and frequency. We can say that it is true that any pattern of E’s might occur in the infinite case when Ch(E occurs) has a certain value and nevertheless insist that if it did have that value a certain pattern would occur in the infinite case. Appeal to law violation — with different verdicts resulting for the second type of case described above — would have the upshot that (L*) is not true. It is not even obvious that it would be true if our world was one in which Humean Supervenience is true. That would depend upon whether the closest worlds to worlds in which Humean Supervenience is true are ones in which Humean Supervenience is also true — a matter by no means certain. 3. Causal Asymmetry A relation is symmetrical iff if Rab, then Rba. A relation is not symmetrical iff if Rab, then it doesn’t follow that Rba. A relation is asymmetrical iff if Rab, then not Rba. In the case of causation, if e1 causes e2 , it doesn’t follow that e2 causes e1 . However, in worlds of eternal recurrence, it is possible that e1 causes e2 and e2 causes e1 . So causation is not an asymmetric but a nonsymmetric relation. However, talk of this as a causal asymmetry is widespread and the phrase ‘causal nonsymmetry’ is ugly. So I shall hereafter talk of causal and counterfactual asymmetries. Nevertheless, it should be borne in mind that causal asymmetries do not imply that the relations are asymmetric but simply that there are asymmetries which explain why causation is not symmetric. If the denial of necessary connections between distinct existences is a contingent truth, then in some possible worlds, one asymmetry may simply be that e1 necessitates e2 but not vice versa. Nevertheless, if a counterfactual theory of causal asymmetry is true, this asymmetry of necessitation does not translate in any straightforward fashion into a counterfactual asymmetry. If e1 causes e2 , then trivially e1 occurs and e2 occurs. Thus, according to the standard semantics for counterfactuals, Lewis’s, both ‘if it were that e1 occurs, it would be that e2 occurs’ and ‘if it were that e2 occurs, it would be that e1 occurs’ are true. There is no asymmetry here in spite of the fact that the necessitation runs from e1 to e2 . Instead, attention focuses upon the claim that, in the basic deterministic case, (CA) If e1 were not to occur, e2 would not occur

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is true if e1 is the cause and e2 is the effect but not the reverse. In other words, bearing in mind that we are thinking of circumstances in which e1 necessitates e2 but not vice versa, the absence of e1 implies that e2 is not necessitated. Nevertheless, the absence of e2 only implies that e1 failed to necessitate e2 and not that e1 was absent. Counterfactual theorists usually provide a reductive analysis of how this asymmetry of absence versus absence of necessitation arises. Thus Lewis begins by noting that causes leave many traces. So when you take all their effects together, there is overdetermination of the presence of the cause. By contrast, effects don’t leave many traces on their antecedent causes. Rather causes combine to produce a particular effect. This difference interacts with the similarity weighting for counterfactuals. It is easier to cover up the impact of the absence of the effect in the direction of the putative cause than the absence of the cause in the direction of the putative effect. Thus, it is easier to secure perfect match in the effect–cause direction than it is to secure perfect match in the cause–effect direction. We retain the presence of the cause and just lose its capacity to necessitate the effect by either the cause–effect law failing to hold or one of the other elements in the causal circumstance for the effect failing to be present. Indeed, we don’t even have to suppose that e1 was present if the costs of obtaining perfect match are less by some other means (since we will be envisaging that some element of the causal circumstances of laws are different). All we need to assume is that it is not implied that e1 was absent because of the need for perfect match. Daniel Hausman makes what is, in effect, this point about lack of implication although he does not make it specifically with regard to the perfect match requirement but rather notes it more generally (Ref. 31, p. 115–118). By contrast, if the cause is absent, since perfect match is so hard to secure in the cause–effect direction, there is no reason for insisting on the retention of the effect, e2 . Of course, this is not the only story that may be told. As I have already noted, Hausman simply appeals to the fact that causes combine to cause effects to ground the asymmetry of absence/loss of necessitation. Nor need there be a story. The asymmetry of necessitation can be taken to be a primitive. The question for the counterfactual theorist will be whether, if there is a primitive asymmetry of necessitation, this is a proper basis for a counterfactual asymmetry. The discussion of the Future Similarity Objection in the previous section, and my adjustment of Lewis’s similarity weighting for counterfactuals, is directly relevant to this matter. The very facts which establish that a future similarity will not, in general, do are those which

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were taken by Lewis to be the basis of a counterfactual asymmetry. Thus my adjustment to the similarity weighting is, at the same time, a potential supplement to Lewis’s account of counterfactual asymmetry. In what follows, I will consider two cases which are challenges for Lewis’s account of causal asymmetry and discuss whether they are properly dealt with by the adjustment I have made. 3.1. Microphysical Causal Asymmetry? Huw Price has argued that the facts to which Lewis appeals to ground counterfactual asymmetries are not guaranteed to be present at the microphysical level. So either we have the wrong account of causal asymmetry or causation does not occur in microphysics. Consider the following set up (Fig. 1, where the axes, X, Y, represent directions in space).

Y

E

F

C

D

A

B X Figure 1.

A particle actually travels along ACE and produces a small explosion by being in place E. There are no other interactions. We are invited to assess the counterfactual.

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If particle P had been at D, then the explosion would not have occurred. Intuitively the counterfactual is true. For the antecedent to have been true, there would be a small miracle to shift the particle from C to D. As a result, we may assume that the path of the particle is now ACDF. However, Price suggests we could secure reconvergence by thinking of the particle as having (instead) the past BD and going on to CE to secure perfect match in the future. The miracle required to move the particle from D to C is just the same as the miracle required to move the particle from C to D. If this is what happened, then the counterfactual would be false since, if P had been at D, then the explosion would have occurred anyway (Ref. 32, p. 509–519). There are two plausible ways of dealing with this kind of case within the counterfactual framework. The choice depends upon whether or not we suppose that the laws governing the travel of the particle describe a phenomena which is time symmetric. If the answer is yes, then we should not suppose that the counterfactual is obviously true. There literally are two ways in which we could secure perfect match — either to the past or to the future. So it is not true that either if the particle had been at D there would have been an explosion or that there wouldn’t have been an explosion. Of course, it is more natural to hear the counterfactual ‘if the particle had been at D, there would not have been an explosion’ as true. That’s because we, in effect, take the counterfactual to have an unexpressed antecedent, namely, if the particle had been at D having travelled from A to C. With this unexpressed antecedent, one cannot maximise perfect match by supposing that the history is from B to D and we just need a miracle to get the particle to C. Rather we would need two miracles to have the particle end up at C, one to get it to D as the antecedent insists and one to get it back to C again. It is our knowledge of the past and our taking it to be fixed that determines which counterfactual seems most plausible. Nevertheless, it would be a mistake to suppose that we should ground causal asymmetry in terms of our asymmetric response to these kind of counterfactuals. We have an explanation of why we respond asymmetrically in terms of what we take as an unexpressed antecedent in the counterfactual. We would have no explanation of our symmetry of response once the details of the situation are pointed out to us and we recollect that the laws are time symmetric. Suppose that, instead, that the particle has an intrinsic direction of travel. In that case, we are disposed to hear the counterfactual ‘If particle P had been at D, then the explosion would not have occurred’ as true. The reason for this is that we count a miracle which is required to work against what the antecedent makes more Σ-probable more significant than

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a miracle that is required to make an antecedent true. By itself, condition (B*) of the similarity weighting cannot explain this asymmetry. The truth of the antecedent would appear to make both events subsequent to it and events prior to it more Σ-probable. However, this ignores the directionality introduced into the case. The direction of travel should be understood as a direction of chance. Thus the truth of the antecedent makes certain subsequent events have a higher Σ-chance but it does not give a higher Σchance to events leading up to the truth of the antecedent. This does not mean that the events leading up to the antecedent will not, in the context, have a certain probability given that the antecedent is true which they would not otherwise have. Just that the probability should not be thought of as an independent chance but rather a derivative from assignments of chance (see Ref. 33, p. 227–229, Ref. 34, p. 871–874, for the details of this position). If the probabilities given to the same types of events posterior and prior to the events mentioned in the antecedent are the same, this will mean that the laws themselves are time symmetric (in that they can be correctly applied forward and backward in time) even though the phenomena they describe is not intrinsically time symmetric due to the asymmetry of chance. Since the asymmetry of chance is intrinsic, non-macrophysical and, presumably, may include a chance of 1, then it is plausible that it may be viewed as a kind of asymmetric necessitation which, in the case of chance 1, introduces non-Humean logical connections between distinct existences: the power of the chance conferring events and the events to which they give chance 1. The revised similarity weighting would then explain our verdict on the counterfactual as follows. If we took the path to be B-D-C-E, then we would be securing perfect match in the future by ensuring that there are events which depart from that which the truth of the antecedent would more Σ-probable in terms of chance. By contrast, if we took the path to be A-C-D-F, the miracle that led to D would not involve events which depart from what the truth of the antecedent makes Σ-probable in terms of chance. The perfect match we would secure into the future is discounted by (B*) whereas the perfect match in the past is not. I don’t think that the distinction between probability and chance is without problems. For my purposes, though, it is enough to point out that some such distinction will be needed to constitute the direction of travel of the particle since the standard facts to which appeal to ground counterfactual asymmetry are unavailable.

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3.2. Tooley’s Inverted Universes In Price’s microphysical case, the asymmetry of overdeterimination which Lewis argued was the basis of counterfactual asymmetry was absent. However, what happens if the asymmetry goes against what we take to be the causal direction? Consider a universe, U1, made up of particles whose velocities determine the universe’s course of development over time. U2 is like U1 except that it begins at U1’s endpoint and works backwards with the velocities of the particles thereby reversed. The laws of U1 and U2 will be time symmetric. Many hold that Newtonian Laws display this feature in which case we could conceive of U1 and U2 being two Newtonian worlds. Tooley argues that if, in U1, c causes e, then in U2, e causes c. However, the very facts to which the counterfactual theorist appeals to explain why c is a cause of e in U1 won’t explain why e is a cause of c in U2. Indeed, the facts would establish that c is a cause of e in U2 too (Ref. 35, p. 224). For instance, in U1, let us suppose, causes have many consequences so making their absence hard to cover up. Effects have, in the direction of their causes, relatively few consequences. By contrast, in U2, it is the effects which will have the many consequences and the causes which have relatively few consequences. So if we consider the counterfactuals (FU2) If e hadn’t occurred, c would not have occurred, (BU2) If c hadn’t occurred, then e would not have occurred, then, by Lewis’s similarity weighting, in the U2-world, (FU2) would be false and (BU2) would be true. We will best secure perfect match by supposing that there was a miracle that ensured that c occurred anyway. There would be no need for additional miracles to ensure the occurrence of all the other consequences of e because there are none and we could secure perfect match in the future of c. Hence (FU2) is false. Moreover, since c has many consequences in the direction of the cause, e, there will be no possibility of securing perfect match by retaining e without many miracles covering up the absence of c with regard to all its other consequences. Thus (BU2) is true. Our revision to Lewis’s similarity weighting, (B*), explains our intuitive verdict with regard to the first of these counterfactuals, namely that (FU2) is true. I have indicated that perfect match is important unless it fails to minimise departure from that which the antecedent makes more probable. In worlds in which counterfactual asymmetry derives from the asymmetry of overdetermination, the revision will support the verdicts of Lewis’s

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similarity weighting with regard to counterfactual asymmetry. Tooley’s universes, though, are ones in which the proper characterisation of making probable is not to be understood simply in terms of counterfactuals based upon the asymmetry of overdetermination. The basis of making probable floats free of asymmetry to which Lewis appeals by appealing to the primitive chance-raising asymmetry mentioned in the previous section. The consequence of this is that the perfect match condition does not allow that we should secure perfect match by covering up the failure of e to occur and still producing c. By taking c to occur in the absence of e, we would not be minimising the departure from that which the truth of the antecedent makes more Σ-probable (understood in terms of chances), namely the absence of e. Since perfect match in the e, c direction is discounted, we would go to the next condition of the similarity weighting. There would be minor law violations if c was still the case. Hence (FU2) ends up true. (BU2) is more problematic. The very reasoning that led us to conclude that (FU2) is true would lead us to conclude that (BU2) is true. The revised perfect match condition rules out the importance of perfect match in the e-c direction. The no-widespread miracles condition rules out perfect match in the c-e direction. In which case, moving on to third condition, ruling out even small law violations, we should conclude that (BU2) is true. However, I don’t think this verdict is counterintuitive. In the U2 universe, vast numbers of overdetermining causes give rise to effects. It seems very natural to say that if the effect had not occurred, then these causes would not have. Considerations of perfect match or the like do not come into play. This demonstrates that appeal to our different verdicts for substitutions of causes and effects into the following simple counterfactual (CA) If e1 were not to occur, e2 would not occur will not be the basis of causal asymmetry in all cases. I don’t think that this demonstrates the failure of a counterfactual account of causal asymmetry but the importance of getting the counterfactual right. We should not focus on (CA) but rather (CAP)

(i) If e1 were to occur without any of the events in Σ, it would be the case that ch(e2 ) is generally around x. (ii) If e1 were not to occur without any of the events in Σ, it would be the case that ch(e2 ) is generally around y. (iii) x > y.

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In worlds in which chances have direction, if we substitute causes for e1 and effects for e2 , (CAP) will be true, but if we substitute effects for e1 and causes for e2 , (CAP) will be false. We still have a counterfactual asymmetry. It is just an asymmetry partly derived from chance rather than solely from the nature of the counterfactual itself. The revision of the similarity weighting together with the proposed asymmetry of chance in certain cases shows that there is a much more intimate connection between chance, counterfactual asymmetry and causal asymmetry than perhaps hitherto realised. We have seen, in our discussion of cases of microphysics and Tooley worlds that these various elements do not seem to come into conflict. Instead, for instance, asymmetric chances generate causal asymmetries where other components fail to generate any asymmetry. Equally, there seems little danger that one element will swamp the others and provide a more unified approach. Causal asymmetries are rooted in chance and the factors used to characterise the similarity weighting for counterfactuals. Pure counterfactual asymmetries can be based upon time symmetric chances. Other causal asymmetries can be based upon asymmetric chances. Each capture a common idea, roughly, that causes raise the chance of their effects over the (relative) background chance of the effect, where effects do not (Ref. 11, p. 120). None constitute a counterexample to a properly formulated counterfactual theory of causation. 4. Concluding Remarks: Methodological Implications I have been investigating the proper way to formulate the similarity weighting for counterfactuals. I argued that it would be best to appeal to a notion of failure of fit rather than law violation in the proper characterisation of the first and third clauses of the similarity weighting even though the distinction between failure of fit and law violation only had utility in worlds for which Humean Supervenience is false. Of course, Humeans can explain a sense in which a certain sub-pattern of events does not fit with the overall law. However, if laws are just particularly significant total patterns of events, then a total pattern which does not fit with the law just is a violation of the law. We can only understand the contrast of failure of fit with total pattern, as opposed to violation of law, with a non-Humean characterisation of law in mind. Equally, in placing a limit on the perfect match clause, I appealed to a notion of making more Σ-probable which allowed for the possibility of primitively asymmetric chances.

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Neither of these features threaten the compatibility of the doctrine of Humean Supervenience and, specifically, the denial of necessary connections, with the existence of causation. Their compatibility depends upon what a counterfactual analysis of causation requires within a possible world and not what possibilities it can capture in other worlds. One lesson to be learnt from this is that an analysis which reveals how certain phenomena may be realised in a world may appeal to notions whose role can only be properly understood by appreciating how the phenomena may be realised in worlds in which the phenomena cannot be realised in that way. Analyses which reveal how certain phenomena may be realised do not have to be framed in terminology which can be entirely understood by reference to the favoured ontology. Thus proponents of the counterfactual analysis of causation do not have to reject the possibility of causal relations unsupported by Humean differences, for instance, simple worlds in which there is no asymmetry of overdetermination or brute cases of causation in the form of persistence. Instead, they can be accepted as true of non-Humean realisers of causation. Rather than the counterfactual theorist being placed in the position of a dogmatist about whether certain things are possible, the opponent of the counterfactual theory is left to adopt the dogmatic position. They must deny that causation is present in the worlds in which Humean Supervenience and the denial of necessary connections are true. Counterfactual theorists can argue that the verdicts they favour are supported in this case because of the intuitive connection between causation on the one hand and counterfactuals (supplemented by the idea of chance-raising) on the other. The achievement, if they can pull it off, is that they can explain how counterfactuals may be true, and there be cases of objective chance-raising, in worlds in which Humean Supervenience is true. Proponents of the counterfactual theory can put the matter like this. OK, I agree that we do have the intuition that causation involves primitive asymmetric chance-raising. Nevertheless suppose that there is a world in which there is no such thing but there is asymmetric chance-raising grounded in other asymmetries. I say that in such worlds, there is causation. I ask you to defend the claim that there is no causation here and not just the claim that it does not fit your preferred intuition about causation. This seems to raise the bar against opponents to counterfactual theories motivated by claims about when causation is present in simpler worlds, inverted universes, microphysics and the like. By allowing Humean and non-Humean versions of their key notions, proponents of the counterfactual

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theory can both capture the intuitions of their opponents and explain how they should be generalised to the Humean cases. In this respect, the counterfactual theory of causation is in a favourable position when compared with other reductive programmes, for instance, Functionalism about the mind. Functionalism seeks to characterise mental states simply in terms of a certain causal or functional role in which reference to mental states is eliminated (e.g., Ref. 36, p. 433–435, Ref. 37, p. 261–264). The most famous argument in its favour appeals to the intuitive possibility that mental states such as pain may be realised in different ways, as a result of differences in the physical constitution of different creatures, while the distinctive pain-related causal role remains the same (Ref. 36, p. 436). It has even been allowed that non-physical substances such as ectoplasm may realise a system of functional states (e.g., Ref. 38, p. 412; Ref. 39, p. 293–294, 302–303). Hence most physicalists have insisted upon the contingent truth of the claim that mental states are physical states (e.g., Ref. 37, p. 266–267). I have likewise suggested that the counterfactual theory of causation may allow that causation is variably realised and that Humean Supervenience is a contingent truth. It is a familiar fact that opponents of Functionalism take it to leave something out about the phenomenal nature of the mind (e.g., Ref. 40). Thus there is thought to be an explanatory gap between functional states and phenomenal states (see e.g., Ref. 41, p. 93–104). The situation seems otherwise with the counterfactual theory of causation. There does not seem to be an explanatory gap between the truth of certain counterfactuals and the presence of causation. Rather the counterfactuals seem successfully to express the character of causation. The doubt primarily comes when we turn to different possibilities in which it is suggested there is causation without the relevant counterfactuals being true. It is this line of argument that I have questioned by suggesting that there may be Humean and NonHumean realisations of chance-raising each of which is entirely appropriate component to the characterisation of causation. There are two more general points that are suggested by my discussion. The first concerns the conditions which a successful analysis should meet. According to the classical picture, we should give an analysis of a concept in terms of necessary and sufficient conditions which themselves make no essential appeal to the concept in question. I have suggested that the proper characterisation of the similarity weighting for counterfactuals will make ineliminable appeal to counterfactuals. Yet for each realisation of the truth conditions of a counterfactual in a possible world there will be an

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ontological grounding of some kind or another. So it will always be possible to cash out the occurrence of a counterfactual in the similarity weighting in terms of some non-counterfactually specified sufficient condition even though counterfactuals are required to specify what is necessary about each sufficient condition. Thus, there can be circularity in the specification of the necessary conditions if there is none in the specification of sufficient conditions. The second point concerns the nature of metaphysics. Often, it is taken to be an investigation into highly general, fundamental and necessary features of reality. One or other theory of these features is normally taken to be uniquely true. If causation is variably realised, then although, by my lights there is a uniquely true theory of causation — the counterfactual theory — the way it is realised and hence the character it can display is open to variation. It abstracts from the different metaphysical positions which others say constitute the reality of causation e.g., those based upon natural necessitation, a powers ontology, Humean Supervenience and the like, and proposes that each can provide possible realisers of caustion. I think it pays to consider the extent to which this metaphysical pluralism is both coherent and attractive. Acknowledgments I would like to thank an anonymous referee for his or her very helpful comments on a previous draft of this paper and Rob Vanderbeeken for having the patience of a saint. References 1. N. Goodman, The Problem of Counterfactual Conditionals. Journal of Philosophy 44, 113–128 (1947). Reprinted in: N. Goodman, Fact, Fiction and Forecast. Cambridge, Massachusetts: Harvard University Press, 3–27 (1954). 2. E. Craig (Ed.), The Routledge Encyclopaedia of Philosophy. London: Routledge (1998, updated online). 3. S. Blackburn (Ed.), Oxford Dictionary of Philosophy. Oxford: Oxford University Press (1994, 1996). 4. T. Honderich (Ed.), Oxford Companion to Philosophy. Oxford: Oxford University Press (1995, 2005). 5. D. Hume, An Enquiry Concerning Human Understanding (Reprinted from 1777 edition with Introduction and Analytic Index by L. A. Selby Bigge, Third Edition with text revised and notes by P. N. Nidditch) (1748).

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6. D. Lewis, Causation. Journal of Philosophy 70, 556–567 (1973). Reprinted in: D. Lewis, Philosophical Papers, Volume 2. Oxford: Oxford University Press, 159–172. 7. D. Lewis, Philosophical Papers, Volume 2. Oxford: Oxford University Press (1986). 8. J. Ganeri, P. Noordhof and M. Ramachandran, Counterfactuals and preemptive causation. Analysis 56, 216–225 (1996). 9. J. Ganeri, P. Noordhof and M. Ramachandran, For a (revised) PCA analysis. Analysis 58, (1), 45–47 (1998). 10. M. Ramachandran, A Counterfactual Analysis of Causation. Mind 106, 263–277 (1997). 11. P. Noordhof, Probabilistic Causation, Preemption and Counterfactuals. Mind 108 (429, January), 95–125 (1999). 12. J. P. Wright, The sceptical realism of David Hume. Manchester: Manchester University Press (1983). 13. E. Craig, The Mind of God and the Works of Man. Oxford: Oxford University Press (1987). 14. G. Strawson, The Secret Connexion. Oxford: Oxford University Press (1989). 15. S. Blackburn, Hume and Thick Connexions. Philosophy and Phenomenological Research (1990). Reprinted in: S. Blackburn, Essays on Quasi-Realism. Oxford: Oxford University Press, 94–107 (1993); and reprinted in: R. Read and K. A. Richman (Eds.), The New Hume Debate. London: Routledge, with postscript, 100–112 (1990, 2000). 16. A. Heathcote and D. M. Armstrong, Causes and Laws. Noˆ us 24, 63–71 (1991). 17. D. Lewis, Counterfactual Dependence and Time’s Arrow. Noˆ us, 455–476 (1979). Reprinted in: D. Lewis, Philosophical Papers, Volume 2. Oxford: Oxford University Press, 32–52 (1986). 18. D. Lewis, On the Plurality of Worlds. Oxford: Basil Blackwell (1986). 19. D. Lewis, Void and Object. In: J. Collins, N. Hall and L. A. Paul (Eds.), Causation and Counterfactuals. Cambridge: Massachusetts, The MIT Press, 291–308 (2004). 20. D. M. Armstrong, What is a Law of Nature? Cambridge: Cambridge University Press (1983). 21. J. Divers and J. Melia, The Analytic Limit of Genuine Modal Realism. Mind 111 (441), 15–36 (2002). 22. K. Fine, Critical Notice of Counterfactuals by David Lewis. Mind 84, 451–458 (1975). 23. D. Lewis, Counterfactuals. Oxford: Basil Blackwell (1973). 24. D. Krasner and M. Heller, The Miracle of Counterfactuals: Counterexamples to Lewis’s Theory of World Order. Philosophical Studies 76, 27–43 (1994). 25. B. Kment, Counterfactuals and Explanation. Mind 115 (458, April), 261–309 (2006). 26. J. Hawthorne, Chance and Counterfactuals. Philosophy and Phenomenological Research 70 (2), 396–405 (2005).

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27. J. Bennett, A Philosophical Guide to Conditionals. Oxford: Oxford University Press (2003). 28. J. Bennett, Counterfactuals and Temporal Direction. The Philosophical Review 93, 57–91 (1984). 29. D. Lewis, A Subjectivist’s Guide to Objective Chance. In: R.C. Jeffrey (Ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press (1980). Reprinted in his (1986), Philosophical Papers, Volume 2. Oxford: Oxford University Press, 83–113 [page references in text to latter]. 30. A. Elga, Infinitessimal Chances and the Laws of Nature. Australasian Journal of Philosophy 82 (1), 67–76 (2004). 31. D. M. Hausman, Causal Asymmetries. Cambridge: Cambridge University Press (1998). 32. H. Price, Agency and Causal Symmetry. Mind 101 (403, July), 501–520 (1992). 33. D. H. Mellor, The Facts of Causation. London and New York: Routledge (1995). 34. P. Noordhof, Causation, Probability and Chance. Mind 107 (428, October), 855–875 (1998). 35. M. Tooley, Causation: Reductionism Versus Realism. Philosophy and Phenomenological Research 50, Supplement, 215–236 (1990). 36. H. Putnam, The nature of mental states. In: H. Putnam, Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge: University Press, 429–440 (1967). 37. S. Shoemaker, Some varieties of functionalism. Philosophical Topics 12 (1), 83–118 (1981). Reprinted in: S. Shoemaker, Identity, Cause and Mind. Cambridge: Cambridge University Press, 261–286 (1984), and in the second edition of Identity, Cause and Mind published by Oxford University Press, also 261–286 (2003). 38. H. Putnam, The mental life of some machines. In: H. Putnam, Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge: University Press, 408–428 (1967). 39. H. Putnam, Philosophy and our mental life. In: H. Putnam, Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge: University Press, 291–303 (1975). 40. N. Block and J. Fodor, What psychological states are not. The Philosophical Review 81 (2), (1972). Reprinted in: J. A. Fodor, Representations. Brighton: The Harvester Press, 79–99 (1981). 41. J. Levine, Purple Haze. Oxford: Oxford University Press (2001).

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DISENTANGLING CAUSAL PLURALISM

LEEN DE VREESE Centre for Logic and Philosophy of Science Ghent University, Belgium E-mail: [email protected] Causal pluralism is increasingly gaining interest as a promising alternative for monistic approaches toward causation. However, although the debate is scarcely out of the egg, the term ‘causal pluralism’ already covers diverse meanings. This creates confusion, and to remedy that confusion, it is necessary to discern different kinds of pluralistic approaches to causation and different possible positions within them. In this paper, I argue for a general distinction between conceptual causal pluralism, metaphysical causal pluralism and epistemological-methodological causal pluralism. I mainly focus on metaphysical approaches to causation and discern herein four possible positions: metaphysical causal constructivism, metaphysical causal monism, weak metaphysical causal pluralism, and strong metaphysical causal pluralism. Each of these positions are further related to their most obvious conceptual counterpart, specifically conceptual causal monism or conceptual causal pluralism.

1. Introduction Traditionally, philosophers concerned with causation have been reasoning from monistic presuppositions. They have supposed that causation is a univocal concept referring to a single kind of relation in the world. Recently, alternative approaches have emerged within the debate on causal pluralism. Causal pluralism indeed forms a promising alternative to causal monism, and the interest for this alternative view is steadfastly growing. However, although the literature on ‘causal pluralism’ is altogether still limited, the term already covers diverse meanings within this current literature. This creates confusion, which thwarts the fruitful development of this increasingly significant approach to causation. To remedy that confusion, it is necessary to discern different kinds of pluralistic approaches to causation and different possible positions within them. Therefore, I will try to make a good start in structuring and clarifying the debate, by introducing some distinctions in this paper. 207

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Generally, I discern three kinds of causal pluralism: conceptual causal pluralism, metaphysical causal pluralism, and epistemological-methodological causal pluralism. Each of these oppose their monistic counterparts. The literature in defense of causal pluralism focuses particularly on the first kind of causal pluralism: conceptual causal pluralism. Authors subscribing to conceptual causal pluralism maintain that our everyday notion of ‘causation’ cannot be described univocally, while authors subscribing to conceptual causal monism maintain that it can. I will briefly revise the arguments in defense of conceptual causal pluralism in section 2. The main aim of this paper is to clear up part of the confusion in the causal pluralism debate by discerning different possible positions with respect to metaphysical causal pluralism. This will be done by means of three central metaphysical questions concerning causation. Firstly, is causation a realistic notion, or is it a mental construct? Secondly, does causation only occur as a real relation at the fundamental level of reality, or does it also occur as a real relation between objects at higher levels of reality? And lastly, does causation consist in a single empirical relation, or does it consist in diverse empirical relations deserving the label ‘causal’ ? The possible answers to these questions lead to different metaphysical positions, which will be expounded and illustrated in section 3. Arguing for one or another metaphysical position is nonetheless not noncommittal. It carries implications for one’s conceptual approach to causation. In section 4, I will present the most obvious complementary conceptual approaches to the different metaphysical positions. Metaphysical causal pluralism will be discerned from epistemological-methodological causal pluralism in section 5, where I will briefly comment on the relations between the former and the latter. Section 6 will contain my final conclusions. 2. Conceptual Causal Pluralism Concerning our everyday notion of causation, only one central question guides the choice for or against causal pluralism: is our everyday notion of causation monistic or pluralistic? Since I am here concerned with causal pluralism, I will focus on the arguments in defense of conceptual causal pluralism. The following three arguments take a central place in the current literature defending conceptual causal pluralism: 1. All available monistic approaches to causation (e.g., manipulation approaches, probabilistic approaches, causal mechanism approaches, counterfactual approaches, etc.) have counterexamples and

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restrictions. Some of these approaches are even clearly inapplicable to certain domains of knowledge. (See e.g., Ref. 1.) 2. In some cases, even our everyday intuitions about whether a certain factor is really the cause of an event are ambiguous. If we had a clearly outlined, univocal notion of ‘causation’ at our disposal, this would not be the case. (See Ref. 2.) 3. In everyday reasoning and decision-making, we do not need to know what the ‘real’ causes are, for instance whether a probabilistic approach or rather a counterfactual approach points to the ‘real’ causal relations in the world. In practice, it mostly suffices to know that factor C is for example counterfactually dependent on factor E, or that there is a causal mechanism connecting C and E, etc. One does not need to know then whether these properties also define ‘real’ causation. (See Ref. 2.) It is the first kind of argument, for example, which has led Ned Hall to conceptual causal dualism.1 Specifically, well-known counterexamples to the counterfactual analyses of causation have led Hall to a distinction between causation as dependence and causation as production: “Causation, understood as a relation between events, comes in at least two basic and fundamentally different varieties. One of these, which I call ‘dependence,’ is simply that: counterfactual dependence between wholly distinct events. In this sense, event c is a cause of (distinct) event e just in case e depends on c; that is, just in case, had c not occurred, e would not have occurred. The second variety is rather more difficult to characterize, but we evoke it when we say of an event c that it helps to generate or bring about or produce another event e, and for that reason I call it ‘production’ ” (Ref. 1, p. 225). What forms the basis for Hall’s distinction? His analysis starts with those causal relations that form a counterexample for the counterfactual theory of causation, namely cases of overdetermination. Counterfactual dependence cannot form an argument for causation in these cases since several factors ensuring the effect are simultaneously present: “Suzy and Billy, expert rock-throwers, are engaged in a competition to see who can shatter a target bottle first. They both pick up rocks and throw them at the bottle, but Suzy throws her a split second before Billy. Consequently Suzy’s rock gets there first,

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shattering the bottle. Since both throws are perfectly accurate, Billy’s would have shattered the bottle if Suzy’s had not occurred, so the shattering is overdetermined” (Ref. 1, p. 235). In this case, Suzy’s throw is a cause of the shattering, but Billy’s throw is not. The shattering nonetheless does not depend on Suzy’s throw. Since if Suzy’s throw had not caused the bottle to shatter, it would have shattered anyway thanks to Billy’s throw. Hall argues that one should add three theses on causality to solve this problem: the thesis of transitivity, the thesis of locality, and the thesis of intrinsicness. The first states that causation is a transitive relation, the second that ‘causes are connected to their effects via spatiotemporally continuous sequences of causal intermediates’, and the latter that ‘the causal structure of a process is determined by its intrinsic, non-causal character’ (Ref. 1, p. 225). These three theses make up causation as production. The example above is indeed a case of ‘pure production’, in which dependence is of no concern. However, to be able to deal with cases of double prevention and omission, one should throw the three additional theses overboard. In these cases, counterfactual dependence is the only thesis that matters. Hall gives the following example of ‘pure dependence’: “Suzy and Billy have grown up, just in time to get involved in World War III. Suzy is piloting a bomber on a mission to blow up an enemy target, and Billy is piloting a fighter as her lone escort. Along comes an enemy fighter plane, piloted by Enemy. Sharpeyed Billy spots Enemy, zooms in, pulls the trigger, and Enemy’s plane goes down in flames. Suzy’s mission is undisturbed, and the bombing takes place as planned. If Billy hadn’t pulled the trigger, Enemy would have eluded him and shot down Suzy, and the bombing would not have happened” (Ref. 1, p. 241). In this example, the effect counterfactually depends on the cause, but there is no mechanism linking cause and effect. Billy’s pulling the trigger did not produce the bombing, but it was nonetheless necessary for Suzy to be able to execute the bomb attack. Hence, the occurrence of the bombing was dependent on Billy’s pulling the trigger. Hall’s consequent conclusion is that counterfactual dependence captures only one kind of causal relation and that another kind of causal relation exists which needs only the theses of transitivity, locality and intrinsicness but not the thesis of counterfactual dependence. The former are depen-

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dence relations, while the latter are production relations. However, typical causes are cases of dependent production rather than pure production or pure dependence. So although production and dependence are conceptually distinct, in the actual world their extensions overlap in most cases. This also explains why both kinds of causal relations are easily jumbled up and a single kind of causal relation is generally supposed. 3. Three Metaphysical Questions Let me turn to the central question of this paper: what about metaphysical causal pluralism? In other words, do metaphysical reasons exist to consider causal pluralism, or is pluralism with respect to causation only a conceptual matter? I discern three central metaphysical questions which should be answered and which quasi-automatically lead to certain positions with respect to the causal pluralism debate. A first question is whether causation is a real relation, or rather a mental construction. The answer to this question makes it possible to discern realistic from constructivist views on causation. Realists should answer a second question, namely whether ‘causation’ refers to a single kind of empirical relation, or rather refers to different kinds of empirical relations all labeled ‘causal’. I will call the latter position ‘strong metaphysical causal pluralism’. If one maintains, as most philosophers do, that ‘causation’ refers to only one kind of empirical relation in the world, the answer to a last question can determine whether one is a metaphysical causal monist on the one hand, or rather a weak metaphysical causal pluralist on the other hand. Namely, the question whether ‘causation’ refers to a relation which only exists between elements at the elementary level of reality on which all other causal relations then supervene, or whether causation is a real relation between all kinds of objects at all levels of reality. In the following subsections, I will take a closer look at the possible answers to these three questions and the resulting positions toward metaphysical pluralism. 3.1. Causation as a Realistic Notion Versus a Mental Construct A first metaphysical question to be posed is whether causation is not just a mental construct created by mankind. Is there after all some real kind of relation in the world to which our concept of ‘causation’ refers? Hume’s famous view on causation calls this into question,3,4 by asserting that causation is nothing more than constant conjunction in combination with

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temporal priority of the cause and spatiotemporal contiguity between cause and effect. It is the memory of past co-occurrences of the cause and effect that lead in new instances of the cause to the supposition that the effect will follow, and hence to the supposition of a constant conjunction between the cause and effect. However, men further suppose that the connection between cause and effect is necessary, but this necessity cannot be inferred from our perceptions. This convinced Hume that, from a philosophical point of view, causation has to be solely understood in terms of temporal priority, spatiotemporal contiguity and constant conjunction, and not in terms of a necessary connection. The idea of the necessity of a causal relation is a further construction of the human mind upon the more objective description of causation in terms of constant conjunction, temporal priority and spatiotemporal contiguity, but this latter description is closest to our perceptions and hence the one that enables consensus on what causation is. A similar view has more recently been proposed by Jon Williamson.5,6 In his view labelled epistemic causality, causation is also believed to be a mental construct. Williamson starts from the assertion that it is just handy for people to think in terms of cause and effect, and that this is also the reason why they do so, and not that there is something physical corresponding to the term ‘cause’. Williamson is nonetheless convinced that there is an objective reference point for the justification of our causal claims, namely the fullest knowledge of the world. The different views on causation as outlined in different causal theories, form what he calls different causal indicators. However, this variety of causal indicators does not imply a variety of concepts of causation, according to Williamson. Our causal beliefs are based on these several indicators, but all knowledge from all these indicators of causality would lead together to the fullest knowledge of the world. And it is precisely this fullest knowledge of the world which forms the objective reference point of what causation is, and which would deliver a monistic epistemic concept of causation. To sum up, Williamson maintains that causality is a feature of our epistemic representation of the world, and not a real part of the world itself. According to his view, causation further does not consist of a variety of concepts, but is rather one eclectic notion. Hence, just like Hume, Williamson defends the metaphysical view that causal relations are no real part of the world, but relations constructed on this reality by men. I will call this kind of position metaphysical causal constructivism. The real challenge for philosophers defending a constructivist metaphysical approach, is to clarify why it is nonetheless successful and/ or necessary to think in terms of cause and effect.

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In the case one defends the opposite position known as causal realism — namely that there ´ıs something physical in the world to which our notion of ‘cause’ refers — further metaphysical questions need to be answered. These questions and their possible answers will be expounded in the next two sections. To conclude this section, I first specify what causal realism is. In its strongest interpretation, causal realism can be described as follows: “Realism about causation requires two things. First, according to the realist, causation is objective, meaning that it is something that occurs in an ‘external reality’ as opposed to something that is merely subjective, a feature of our thoughts or perceptions alone (that is, merely an idea or a concept). The distinction between objective and subjective causation thus concerns the issue of whether or not causation is mind-independent. Second, according to the realist, causation involves some sort of necessity with respect to the connection between causes and effects. [. . . ] For now, let it suffice to say that by invoking necessity, realists of different stripes maintain that there is more to causation than mere constant or probabilistic conjunctions of events. Merely subjective accounts of causation hold that if there is such a thing as causal necessity, it is an idea or a concept only. Objective accounts hold that there is such a thing, and that it is a feature of the world quite apart from our ideas or concepts” (Ref. 7, p. 8). I think this definition captures clearly what causal realism involves. I have nonetheless presented the theories of Hume and Williamson above which both maintain that causation is a mental construction that can nonetheless be conceived as objective. Consequently, the definition would still be clearer when the terms ‘objective’ and ‘subjective’ were replaced with respectively ‘not-mental’ and ‘mental’. Further, the reverse claim can be found as well: Huw Price defends in Refs. 8 and 9 a view on causation which holds that causality is not a mental notion, but meanwhile neither fully objective. Price’s approach results in a rather weak version of causal realism. Regardless of whether one defends causal realism in a strong or in a rather weak sense, if it is accepted that something in the world exists to which our notion of cause refers, two further metaphysical questions obtrude themselves.

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3.2. Causation as a Single Versus a Plural Empirical Relation A second metaphysical question is whether our notion of ‘cause’ refers to a single kind of relation in the world or whether several kinds of empirical relations have to be discerned, although they are all labeled ‘causal’. This last option has been advanced by Ned Hall in Ref. 1. Hall interprets his distinction between production and dependence in the first place as a conceptual distinction, as it was presented in section 2. He nonetheless explicitly mentions the possibility to interpret his view as one making a metaphysical distinction: “A more subtle objection is the following: What I have really shown is not that there are two concepts of causation, but rather that there are two kinds of causation, two different ways in which one event can be a cause of another. That may well be right; certainly, I was happy to begin this paper by announcing that event-causation comes in two ‘varieties.’ I do not know how to judge the matter, because I am not sufficiently clear on what underlies this distinction between concepts and kinds. [. . . ] I am quite content to agree that I have (merely) shown that there are two kinds of causation — as long as those who insist on this rendering of my thesis agree that the two kinds answer to very different criteria and consequently require very different analyses” (Ref. 1, p. 255–256). Hall even advances the possibility that further research will demonstrate that even more empirical kinds of causal relations should be discerned. As far as I know, Hall is currently the only philosopher explicitly defending a dualistic position toward causation that can be metaphysically interpreted. It is clearly not at all easy to substantiate this kind of position, which I like to label strong metaphysical causal pluralism. Consequently, the opposite answer, namely that causation is a single kind of empirical relation, remains the most obvious view. John L. Mackie as well as Phil Dowe, for example, described causation as a single kind of empirical relation. However, a last metaphysical question divides their views.

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3.3. Causation as a Relation Between Elements at the Fundamental Versus at All Levels of Reality The last metaphysical question is whether causation is a relation only existing at the fundamental level of reality on which other ‘causal relations’ then supervene, or whether causation has to be interpreted as a real relation between all kinds of objects at all levels of reality. Phil Dowe follows the former route in the view on causation presented in Physical Causation.10 In this book, Dowe defends an approach to causation which is based on Salmon’s process theory: “The approach to be taken is to modify Salmon’s theory by introducing the concept of a conserved quantity. The central idea is that it is the possession of a conserved quantity, rather than the ability to transmit a mark, that makes a process a causal process” (Ref. 10, p. 89). This leads to the following central claims of Dowe’s own process theory: CQ1. A causal interaction is an intersection of world lines which involves exchange of a conserved quantity. CQ2. A causal process is a world line of an object which possesses a conserved quantity. “A ‘conserved quantity’ is any quantity which is universally conserved, and current scientific theory is our best guide as to what these are. Thus, we have good reason to believe that mass– energy, linear momentum, and charge are conserved quantities” (Ref. 11, p. 323). Dowe’s theory of causation in terms of ‘conserved quantities’ raises several questions. Most importantly, although Dowe presents his own, rather physical approach as superior to its opponents, it is not at all clear how to apply it to the knowledge from other scientific domains. Some information which he only obliquely hints to is crucial to understand Dowe’s point of view. It turns out that he underpins his approach to causation with a reductionistic metaphysical position: “. . . One answer is that the generality of ‘conserved quantity’ might allow this to be used as a testable conjecture in various fields of science. But it is unlikely that it would stand the test:

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conservation laws seem to be confined to the physical sciences. A more desirable option is to take a middle road and adopt a supervenience account such as that of Kim12 where causes supervene on conserved quantities13 ” (Ref. 14, p. 214–215). Peter Menzies summarizes this view of Jaegwon Kim, on which Dowe founds his own approach of causation, as follows: “There is a supervenient causal relation, Kim tells us, between the a’s having F and b’s having G just in case there are two events a’s having F ∗ and b’s having G∗ such that a’s having F supervenes on a’s having F ∗ , b’s having G supervenes on b’s having G∗ , and a’s having F ∗ causes b’s having G∗ . It is Kim’s view that all macrolevel causal relations are supervenient causal relations of this kind, where the causal relations at the base level relate microlevel events. . . . He sees the rationale for his view that all macrolevel causal relations are supervenient causal relations as lying in what he calls the thesis of microdeterminism, according to which the world is the way it is because the microworld is the way it is. He sees this thesis as urging us to look on the causal order of the macroworld as emerging out of the causal order of the microworld” (Ref. 13, p. 554). This metaphysical premise, according to which causation in the world has to be reduced to the domain of physics, clarifies the whole argumentation behind Dowe’s position in Physical Causation. I label this position which maintains that our notion of ‘causation’ refers to one kind of empirical relation at a single, basic level of reality metaphysical causal monism. The challenge for metaphysical causal monists, such as Dowe, lies in the justification of their metaphysical point of view. An important argument in defense of this point of view is that we should accept it if we take our physicalistic world view seriously.12 This argument is opposed by philosophers substantiating the claim that physicalism accommodates an ontological preconception with respect to physics which cannot be united with scientific knowledge and scientific practice (e.g., Stephen Webster,15 Nancy Cartwright,16 Michael Silberstein17 ): “The commonest justification of this position is simply to point out that higher level phenomena often cannot be predicted from a knowledge of the component part that constitute the lower level. Take water for example: its behaviour cannot be predicted simply from a knowledge of hydrogen and oxgyen [sic.]. For the

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anti-reductionist, this inability is not simply a result of ignorance. It is a matter of principle that every level has its own characteristic patterns and processes, particular to that level, and not replaceable by the patterns and processes of a lower level” (Ref. 15, p. 54). The latter conviction does not need to imply strong metaphysical causal pluralism, but can be accommodated with a position in between strong metaphysical causal pluralism and metaphysical causal monism, which I label weak metaphysical causal pluralism. This position entails that causation is a single kind of relation, which nonetheless occurs at all levels of reality as a real, and hence not-reducible, relation. John L. Mackie’s approach seems to belong to this category. Mackie defines causation, after John Stuart Mill, as a complex regularity: ¯ or JK L) ¯ are followed by P, and in F, “In F, all (AB C¯ or DGH ¯ or JK L). ¯ [. . . ] That is, all P are preceded by (AB C¯ or DGH some disjunction of conjunctions of factors, some of which may be negative, is both necessary and sufficient for the effect in the field in question” (Ref. 18, p. 63). ¯ Further, In this definition, negative causes are formally presented as X. F represents the causal field, which forms the background of the causal event, but is no part of the cause itself according to Mackie. He maintains that a theory trying to describe what causality is in the world, has to be concerned with these whole complex regularities. Although Mackie is further not very explicit about his metaphysical position, it becomes clear from his account that he would defend that causation consists of a single kind of empirical relation, in line with his conceptual approach. Unlike Dowe, he seems nevertheless convinced that this relation is present as a real relation in all domains of reality, what makes Mackie a weak metaphysical causal pluralist: “I insist that our concept is in several ways a bit indeterminate: ‘cause’ can mean slightly different things on different occasions, and about some problematic cases, for example of over-determination, we may be unsure what to say. But it is still a fairly unitary concept: we do not have one concept for physical causation and another for human actions and interaction (as someone might be forced to say who took our concept of physical causation to be that of regular succession); we can and do assert similar counterfactual necessity (and at times sufficiency) about fields of all different sorts” (Ref. 18, p. xi).

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4. The Relations Between Metaphysical and Conceptual Positions In the previous section, I discerned four possible metaphysical positions toward causation: metaphysical causal constructivism, strong metaphysical causal pluralism, weak metaphysical causal pluralism and metaphysical causal monism. Arguing for one or the other of these positions is not noncommittal. It carries implications for one’s conceptual approach to causation. Let me run through the various metaphysical positions again to point out what the most obvious complementary conceptual approach would be. In John Williamson’s case, it is the specific form of his theory in terms of epistemic causality which leads to what I interpret as a kind of conceptual causal pluralism, namely the conviction that we refer to a unitary epistemic concept by means of divergent causal indicators. Jon Williamson himself states that his view forms an improved monistic approach to causation which has the advantage of being able to deal with the epistemic usefulness of a variety of ‘causal indicators’ (causal mechanisms, counterfactuals, correlations, etc.). I think this interpretation of his own view on causation should be refined by introducing a distinction between conceptual causal monism/pluralism and epistemological causal monism/pluralisma . The term ‘conceptual’ is used as before to refer to our everyday concept(s) of causation, which guide(s) the way(s) we arrive at our everyday causal judgements. I further use the term ‘epistemological-methodological’ to refer to the meaning of causation from a knowledge point of view. I would prefer then to interpret Williamson’s approach as a combination of conceptual causal pluralism and epistemological causal monism: in daily practice, we make use of a variety of causal indicators, but once we possess the fullest knowledge of the world, one concept of causation would reveal itself from it. Consequently, causal theories explicate different everyday interpretations of the notion ‘cause’, that nonetheless indicate together a single — be it eclectic — epistemic concept. Another interpretation of a metaphysical causal constructivist theory of causation can just as well lead to conceptual causal monism. Hume for example maintained that only one concept of cause (in terms of spatiotemporal contiguity, temporal priority and constant conjunction) is good enough to serve as our concept of cause,3 since the other ways in which we are inclined to capture our notion of cause face epistemological problems. This revisionistic stance of Hume gets him

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go deeper into epistemological causal monism/pluralism in section 5.

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to defend a monistic conceptual approach to causation on the basis of his constructivist metaphysical position. Hence, in the case of metaphysical causal constructivism the choice for or against conceptual causal pluralism is entirely dependent on the specific premises of the causal theory defended. A thoroughly substantiated strong metaphysical pluralism, on the other hand, automatically forms a strong argument for the necessity of conceptual causal pluralism. Discerning production and dependence as two different kinds of causal relations in the world, as Ned Hall proposes,1 implies the need to have at least also this distinction in our conceptual apparatus in order to make appropriate causal judgements. Likewise, a thoroughly substantiated metaphysical monism automatically forms an argument in defense of conceptual causal monism. Hence, Phil Dowe’s conviction that causation only consists of a unique empirical relation at the fundamental organizational level of the world forces him to be revisionistic.14 His metaphysical conviction founds his rejection of all alternative approaches to causation in favor of his own approach in terms of causal processes and conserved quantities. In Ref. 19, Dowe nonetheless agrees that omissions and preventers can in practice not always be easily distinguished from genuine causes, although they are not physically connected to their effects and consequently are no genuine causes according to him. Dowe labels them ‘quasi-causes’, and states that it is even practically useful to treat quasi-causation as genuine causation. Furthermore, causation and quasi-causation seem to play very similar practical roles. According to Dowe, the unity of both lies in the fact that quasi-causation is, in essence, possible causation. Distinguishing them is nonetheless theoretically important. Since ‘causation’ appears in the definition of what ‘quasi-causation’ is, they cannot be treated as being the same. Hence, a description of genuine causation should throw cases of quasi-causation overboard. It follows that we should revise our notion of cause, such that quasi-causes are not included in our description. The most natural complement of weak metaphysical causal pluralism is also conceptual causal monism. In the quotation at the end of the former section, Mackie, for instance, clearly argues for a single, unitary concept applicable throughout all possible domains of application. However, things are not that straightforward, and some further comments are needed. The first comment concerns pragmatical considerations. Mackie creates some place for play which has to accommodate his view to pragmatical differences in causal judgements. According to his theory, in which a cause is supposed to be the factor which is necessary in the

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circumstances for the effect to occur, differences in everyday causal judgements can be attributed to the way we select ‘the’ cause from the factors of the disjunction of conditions: “The supposed distinction between conditions and causes can be adequately accounted for in these two ways: an alleged condition which is not called a cause, although if in the circumstances it had not occurred the result would not, either is part of the field presupposed in the view taken by the speaker of the result (and so is not a cause in relation to this field) or is a cause, but mention of this fact happens to be irrelevant, or less relevant than mention of some other cause of the same result, to some current purpose” (Ref. 18, p. 36). Pragmatical factors do not affect Mackie’s basic concept of cause, although they can affect the causal judgements resulting thereof. Apart from Mackie’s approach, pragmatical considerations can also be introduced to justify the defense of a monistic conceptual approach where a pluralistic approach seems more obvious and the reverse. Some metaphysical approaches seem to leave more room for this kind of considerations than others. Weak conceptual causal pluralism as well as metaphysical causal monism seem to be approaches that can easily be combined with pragmatically based conceptual causal pluralism. For example with regard to Dowe’s theory, one could argue that we will need a variety of concepts of causation for everyday causal reasoning as long as we do not possess enough knowledge to determine how specific causal relations in the macroworld depend on their underlying physical constitution. On the other hand, it seems much less obvious to argue for a combination of strong metaphysical causal pluralism with pragmatically based conceptual causal monism. However, the central conclusion is that it is utterly important to provide thorough pragmatical arguments to underpin atypical combinations. Further, one position which is possible in principle has nonetheless not been discussed. It forms no obvious point of view and is nowhere defended in the literature, as far as I know. It concerns a metaphysical position which defends that all causal relations have to be reduced to the elementary level but that diverse empirical kinds of causal relations nonetheless exist at that basic level. The most natural conceptual complement of such a position would clearly be conceptual causal pluralism.

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5. Epistemological-Methodological Causal Pluralism To conclude, I briefly indicate the importance of discerning conceptual and metaphysical causal pluralism from a third kind of approach to causal pluralism, namely what I label epistemological- methodological causal pluralism. The latter refers to the importance of a pluralistic view on causation for our scientific knowledge in general on the one hand, and for assembling causal knowledge in specific domains of science on the other hand. It will be clear that an epistemological-methodological approach to causation is not disconnected from conceptual and metaphysical approaches to causation. It is nonetheless important to value this line of approach as different from the others. Especially in the case of conceptual and/or metaphysical pluralism, certain questions become utterly important for the sake of our knowledge. What is the best way to acquire causal knowledge? Do the useful concepts of causation differ from domain to domain? Do we need a variety of causal concepts to achieve sufficient causal knowledge within a single domain? What are the useful concepts of causation for the different scientific domains? If causation is a single empirical relation, why do we possibly need a variety of causal concepts to gather scientific knowledge? Do scientists make use of a variety of concepts in practice? The answers to these questions will be affected by the conceptual and especially metaphysical position taken, but can on their turn affect the way causal knowledge is gathered and subsequently what causal knowledge is reached. This demonstrates again that arguing for certain conceptual and/or metaphysical positions, is not at all a noncommittal activity. 6. Conclusion ‘Causal pluralism’ is a very broad notion, covering entirely divergent approaches to causation. The conviction that causation is no single, univocal thing can lead to a wide area of alternative ‘pluralistic’ approaches to causation. Consequently, I argued that the confusion in the current debate on causal pluralism should be avoided by refining our view on causal pluralism. In the first place, one should make a clear distinction between three ways to approach the debate: from a conceptual point of view, from a metaphysical point of view or from an epistemological-methodological point of view. I focused in this paper on metaphysical approaches to causation and discerned four possible metaphysical positions: metaphysical causal constructivism, metaphysical causal monism, weak metaphysical causal pluralism and strong metaphysical causal pluralism. Each of these positions can be

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related to the most obvious conceptual counterpart, i.e., conceptual causal monism or conceptual causal pluralism. It is utterly important precisely to determine one’s position in the debate and to become aware of mutual connections between certain positions in order to improve the discussion. I hope to have offered a general framework that can help in creating more clarity. The further development of appropriate and fruitful pluralistic approaches should benefit from a refined view on what ‘causal pluralism’ can consist in. On the other hand, it is evident that the framework itself may also need further development in the course of the discussion, when new lines of argumentation are developed. Acknowledgments I am greatly indebted to Erik Weber and the referee for their insightful comments on earlier versions of this paper. The research for this paper was supported by the Research Fund of the Ghent University through research project BOF2001/GOA/008 and by the Fund for Scientific Research– Flanders through research project G.0651.07. Bibliography 1. N. Hall, Two concepts of causation. In: J. Collins, N. Hall, and L.A. Paul (Eds.), Causation and Counterfactuals. Cambridge, Massachusetts: The MIT Press, 225–276 (2004). 2. C. R. Hitchcock, Of Humean bondage. British Journal for the Philosophy of Science 54, 1–25 (2003). 3. D. Hume, An Enquiry Concerning Human Understanding (Originally published in 1748). Harvard Classics Volume 37, Online Edition (http://eserver.org/18th/hume-enquiry.html). New York: P.F. Collier & Son (1910). 4. S. Psillos, Causation & Explanation. Cambridge: Cambridge University Press (2002). 5. J. Williamson, Causality. In: D.M. Gabbay and F. Guenthner (Eds.), Handbook of Philosophical Logic, 2nd Edition, vol. 14. New York: Springer, 95–126 (2007). 6. J. Williamson, Causal pluralism versus epistemic causality. Philosophica 77, 69–96 (2006). Published 2008. 7. A. Chakravartty, Causal realism: Events and processes. Erkenntnis 63, 7–31, (2005). 8. H. Price, Causation in the special sciences: the case for pragmatism. In: D. Constantini, M.C. Galavotti and P. Suppes (Eds.), Stochastic Causality. Stanford: CSLI Publication, 103–120 (2001).

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9. H. Price, Causal perspectivalism. In: H. Price and R. Corry (Eds.), Causation, Physics and the Constitution of Reality: Russell’s republic revisited. Oxford: Clarendon Press, 250–292 (2007). 10. P. Dowe, Physical Causation. Cambridge, UK: Cambridge University Press (2000). 11. P. Dowe, Causality and conserved quantities: a reply to Salmon. Philosophy of Science 62, 321–333 (1995). 12. J. Kim, Epiphenomenal and supervenient causation. Midwest Studies in Philosophy 9, 257–270 (1984). 13. P. Menzies, Against causal reductionism. Mind 98, 551–574 (1988). 14. P. Dowe, Wesley Salmon’s process theory of causality and the conserved quantity theory. Philosophy of Science, 59, 195–216 (1992). 15. S. Webster, Thinking about Biology. Cambridge: Cambridge university press (2003). 16. N. Cartwright, The Dappled World. A Study of the Boundaries of Sciences. Cambridge: University Press (1999). 17. M. Silberstein, Reduction, emergence and explanation. In: P. Machamer and M. Silberstein (Eds.), The Blackwell Guide to the Philosophy of Science, Blackwell Philosophy Guides. Malden, Mass.: Blackwell Publishers, 80–107 (2002). 18. J. L. Mackie, The Cement of the Universe. A study of causation. Oxford: Clarendon Press (1974). 19. P. Dowe, Causes are physically connected to their effects: why preventers and omissions are not causes. In: C. Hitchcock (Ed.), Contemporary Debates in Philosophy of Science. Oxford: Blackwell, 189–196 (2004).

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MATHEMATICAL ENTITIES

LIEVEN DECOCK Faculty of Philosophy Vrije Universiteit Amsterdam, The Netherlands E-mail: [email protected] Since the dawn of philosophy in Ancient Greece, philosophers have discussed metaphysical problems concerning mathematical entities. For some important philosophers, from Pythagoras to Quine, this was even the most important metaphysical issue. However, questions concerning the metaphysical status of mathematical entities have been formulated and answered in various ways. In order to discuss the methodology of the contemporary metaphysics of mathematical entities, I will sketch a series of different related questions. It will transpire that each of these questions is somehow different from a methodological point of view. In the first section, I will discuss the question how mathematical entities can be described or identified unambiguously. In contemporary philosophy of mathematics, there is a cluster of problems concerning the unique characterisation of mathematical entities, especially numbers and sets. Other mathematical structures, such as groups, vector spaces, or manifolds can be precisely characterised in terms of numbers and sets, but for the latter, some persistent complications remain. Second, I will present the debate on the size of the mathematical universe. At present, there is a lively debate over the size of the set-theoretic universe, namely whether one should countenance axioms postulating the existence of large sets. Third, I will briefly sketch nominalism. In the last two decades, many philosophers of mathematics have devised strategies to avoid ontological commitment to abstract mathematical entities. Fourth, I will present a different tradition in the philosophy of mathematics, starting from Lakatos’ work and ending with contemporary social constructivism. In the fifth section, I will conclude with two general remarks on the methodology in the metaphysics with regard to mathematical entities. I will demonstrate that the different traditional metaphysical issues are present in contemporary philosophy of mathematics, and that the different styles of philosophising, i.e., logical analysis, conceptual analysis and naturalism are all present.

1. No Mathematical Entity With Identity Ever since Euclid’s Elements, mathematicians have aimed at a precise and unambiguous description of mathematical entities. The increased refinement in postulating and defining mathematical entities led to the axiomatisation of different branches of mathematics, e.g., geometry by Pieri and 224

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Hilbert, the natural numbers by Peano, the real numbers by Tarski, set theory by Zermelo and Fraenkel, etc. The language in which these axiom systems were expressed was first order logic, which was itself axiomatised by Frege, Peirce, Schr¨ oder, and Russell and Whitehead, and further streamlined in the following decades. Whitehead and Russell’s Principia Mathematica was a major attempt to encompass the complete realm of mathematics within a single framework, and in which all mathematical entities could be properly defined. However, several problems arose. It became clear that axiomatisation in first order logic was not sufficient for unambiguous description of mathematical entities. The notorious L¨ owenheim–Skolem theorem(s) made clear that all infinite axiomatic systems can be reinterpreted in unintended ways. For every axiom system, there is a large variety of possible reinterpretations going beyond isomorphic reinterpretation. Before the L¨ owenheim–Skolem theorem, mathematicians had already discovered the possibility of reinterpreting axiom systems, e.g., in the duality theorem in projective geometry. This theorem states that, if one reinterprets points as lines, the predicate ‘collinear’ as ‘concurrent’, and so on for all the primitive ideas in projective geometry, all theorems remain true. But this duality relies on the incidental isomorphism between the structure of lines and the structure of points in projective geometry. The L¨ owenheim–Skolem theorem proves that the possibility of such a reinterpretation is not incidental but inevitable. The first version of the theorem demonstrated that every axiom system intended to describe an overdenumerable domain (i.e., a domain with more elements than the natural numbers, e.g., the real number line) can be reinterpreted in the domain of the natural numbers with all theorems remaining valid. This implies that mathematics can be entirely interpreted in a denumerable domain, and thus that the set of the natural numbers suffices as the basic ontology for mathematics. Later versions of the theorem were stronger, and demonstrated that every theory (or axiom system) can be reinterpreted in a domain of arbitrary size (cardinality). The upshot is that axiom systems expressed in first order logic cannot uniquely determine the mathematical entities they are supposed to describe. The problem is not easily solved. One way out is by relying on standard or intended interpretations. One claims that the axiom system is meant to describe an intended mathematical structure, and that one can rely on a ‘background language’ to block the possibility of reinterpretation. It is thus assumed that one already understands the structure which one describes by means of a formal system. This strategy, of course, shifts the burden from

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philosophy of mathematics to epistemology. It is not entirely clear how to explain the background language from an epistemological point of view. The other way out is by challenging first order logic. George Boolos pointed out that second order logic, i.e., logic in which quantification over predicates is allowed, is less problematic than hitherto had been assumed,1 and that it can have a natural interpretation in natural language.2 Second order logic can to a great extent solve the problems caused by the L¨ owenheim–Skolem theorem. For arithmetic, the problem is solved immediately, since second order Peano arithmetic yields unambiguously the intended structure of the natural numbers. For set theory, the situation is a bit more complex. The second order version of the standard axiomatisation of set theory, i.e., ZFC, does reduce the ambiguity drastically, but not completely. The structure of the lower levels of the set-theoretic hierarchy is clearly determined, but an ambiguity over the higher reaches remains. A solution has been presented by Vann McGee,3 and consists in adding an extra axiom that removes the ambiguity. However, there remains room for debate concerning the acceptability of second order logic, and in set theory concerning the naturalness of McGee’s extra axiom. The elimination of ambiguity does not end with pinpointing the intended structure of an axiom system. New problems arise when one wants to compare the intended domains described in the various axiom systems. One can wonder how geometrical entities such as points and lines are related to numbers, how the real and natural numbers are related, and how the natural numbers and the sets in ZFC are related. There is no problem in relating the various mathematical entities; rather, there is an embarrassment of riches. One can easily show that there are straightforward reductions between the various mathematical realms. E.g., points in Euclidean geometry can be described by means of Cartesian coordinates, i.e., as triplets of real numbers. Real numbers can be described as sets of rational numbers. Rational numbers can be described as equivalence classes of ordered pairs of natural numbers. Natural numbers can be reduced to sets in ZFC. The various domains can thus easily be related so that all mathematical entities can in principle be reduced to sets. However, there are several possible reductions. For example, one can reduce the real numbers to sets of natural number as Cauchy series or as Dedekind cuts. Both reductions can express the structure of the real numbers. Also the natural numbers can in various ways be reduced to sets. There are at least three obvious ways, proposed by respectively Frege, Zermelo, and von Neumann. None of these reduction strategies is problematic, but still they lead to nontrivial differences. In the

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groundbreaking ‘What numbers could not be’ Paul Benecerraf put forward the problem forcefully.4 If natural numbers are in essence sets, then one can ask how they are related with regard to the basic relation of set theory, namely membership, or more concretely, whether 2 is an element of 4. If natural numbers were really and unambiguously sets, this question would be easy to answer. However, it turns out that the answer to this question critically hinges on the particular reduction one opts for. If one employs Zermelo’s definition, then every number is an element of its immediate successor, so that two is not an element of four. Von Neumann on the other hand defined the natural numbers as the sets of all their predecessors, so that two is an element of four. Thus a relatively elementary statement in mathematics has no unambiguous truth value; and moreover, none of the alternatives seems the most natural. This is a disconcerting result, since it jeopardises any straightforward equation of natural numbers and sets. One can easily find the structure of the natural numbers in set theory, but this does not justify an identification of natural numbers with sets. There is an even older identification problem in mathematics. If one is ontologically committed to physical objects and mathematical entities, one has to find ways to encompass both within a single universe. One way of doing this is by shoving the physical objects as Urelements into the set-theoretic hierarchy. Urelements are elements at the basic stage of the set-theoretic hierarchy, and are the elements of the first stage of real sets. The universe then consists of physical elements, sets of physical elements, sets of these sets, and so on. However, it is somehow counterintuitive that the set-theoretic universe and a forteriori mathematical entities should depend on the contingent physical objects in the world. For example, when using Frege’s definition of number two as the class of all pairs, one does not want the number two to change if a pair of shoes gets ruined. Another but less obvious way to relate physical objects and mathematical entities is by extending the mathematical reduction programme to physical objects, so that one ends with a (hyper-)Pythagorean universe. This strategy has been put forward by Quine in the mid-seventies.5,6 He proposed to identify physical objects with their space–time coordinates in order to obtain a universe containing mathematical entities only. Most philosophers however do want to keep the mathematical and physical realm separate, and this accords well with the dislike of mathematicians for impure set theory, i.e., set theory containing Urelements. However, on this view the description of the mathematical entities leaves open the possibility that some of these entities could be identical with physical objects. This so-called Caesar problem

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was first formulated by Frege (Ref. 7, § 56). The structural description of the natural numbers does not exclude the possibility that for example zero could be identical with the physical object Julius Caesar. This is of course most counterintuitive, but many axiom systems used for describing and identifying mathematical entities cannot bar this possibility. This cluster of problems led to the general acceptance of the view that a formal system cannot by itself determine the domain of objects it purports to describe. What numbers and sets are is not fully determined by axiomatic systems expressed in first order logic. This view has had important consequences for the methodology in the philosophy of mathematics in the last decades. Whereas the foundational programmes since Frege tried to define numbers unambiguously by means of a mixture of philosophical intuitions and technical logico-mathematical derivations, there is now a growing gap between the philosophical work and technical foundational work. On the one hand, mathematicians have concentrated on the study of the formal properties of axiom systems with a special focus on the fixation of unambiguous structures. Especially second order logic is regarded as useful in reducing multiple nonisomorphic interpretations of axiom systems. On the other hand, philosophical reflection has become detached from the ever more refined and complex foundational issues. If formalisation and axiomatisation can only lead to an unambiguous description of the structural relations between mathematical entities, and not to a direct characterisation of the entities themselves, this leaves room for other approaches involving the conceptual analysis of mathematical intuitions about concepts such as set, natural number, real number, etc.

2. The Size of Plato’s Heaven In addition to the identification problems, there is another set of questions where technical and philosophical considerations intersect. Throughout the history of mathematics, one sees a continued resistance to enlarging the domain of ‘real’ mathematical entities (often called Plato’s Heaven). Despite this resistance, the size of the mathematical realm has become increasingly large. Fibonacci’s introduction of Arabic numerals in Northern Italy led to fierce protest against the number zero, which, it was argued by opponents, could not be a genuine number, as it did not express any quantity. Similar objections were raised against negative numbers. Already in Ancient Greece, the discovery of lengths that cannot be expressed as ratios of natural numbers (e.g., the length of the hypotenuse of orthogonal triangles),

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had left Greek mathematicians/philosophers perplexed. Also the use of square roots of negative numbers led to opposition. Descartes called them mockingly ‘imaginary numbers’, a derogatory name that later became their standard name. However, in all these cases, the usefulness of these numbers led to a general acceptance after some time. Similar stories can be told for other mathematical structures. E.g., ever more mathematical ‘functions’ were countenanced. First, only functions described by algebraic equations were regarded as acceptable, but later on, ever more liberal definitions were employed, so that eventually functions were defined as arbitrary sets of pairs of real numbers (see Ref. 8, p. 116–128). The most remarkable stage in this development was Cantor’s work in the 1880s. Cantor studied mathematical properties of collections of real numbers. The work led him to a closer scrutiny of the notions of class and set. He was especially interested in the size of large sets of numbers; he compared the size of various sets. His major innovation was the postulation of various grades of infinity. Before Cantor, mathematicians had used a notion of infinity, but infinity was not used as an actual mathematical entity, let alone that one would have countenanced a multitude of infinities. The initial step in Cantor’s work was to regard the size of the natural numbers as an actual mathematical quantity, which he called ω. Subsequently, he allowed for transfinite operations on this quantity. He defined ordinal numbers by extending the counting progression to continue beyond ω. One can thus count 0, 1, 2, 3,. . . , ω, ω+1, ω+2,. . . , 2ω,. . . , 3ω,. . . . This process can be further extended. One can define a limit for this process, and call this ℵ1 , and then continue counting. One can continue this progression to immense lengths. In addition to this counting operation, Cantor used another operation to construct sets of ever greater size. He had proved that the power set of an infinite set, i.e., the set of its subsets, is always strictly larger than the size of this infinite set. This is not trivial, because surprisingly, Cantor had already discovered that many sets that seem different in size can be equal in size, which means that a one-to-one relation between the two sets can be constructed. E.g., one would expect that the set of rational numbers is vastly larger than the set of natural numbers, but actually, one can easily demonstrate that there is indeed a one-to-one relation between the two sets. However, by means of the power set operation, one does obtain a set that is strictly greater. Thus, also with a repetitive use of the power set operation, one can construct ever greater sets. Cantor’s exploration of the transfinite has led to a list of questions concerning the size of sets, the size of the set-theoretical universe, and in view of the possible reductions

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of all mathematical structures to set-theoretical structures, concerning the size of the mathematical universe. As was the case with the elimination of ambiguous identification, also questions related to the size of sets have been at the same time technical and philosophical, and also in this case, it seems as if some of these issues cannot really be decided on the basis of mathematical arguments only, so that philosophical arguments have come to play an important role in the justification of certain new set-theoretical axioms. At first blush, Cantor’s results may seem remote from mainstream mathematics, but his work had important repercussions with regard to the concept of number. One can demonstrate that the size of the set of real numbers has the same size as the set of subsets of the natural numbers. In view of Cantor’s theorem concerning the power set operation, we know that the set of real numbers is larger than the set of natural numbers. The following question then becomes most interesting: how much larger is the set of real numbers in comparison to the set of natural numbers; or, more concretely, are there sets with a size strictly greater than the size of the set of natural numbers and strictly smaller than the size of the set of real numbers? One could imagine that by means of transfinite counting, one would encounter such a new cardinal number. Cantor formulated the hypothesis that no such cardinal numbers exist, and thus that the first cardinal number larger than ω, i.e., ℵ1 , has the size of the power of the natural numbers, i.e., 2ℵ0 . This is the famous continuum hypothesis. This rather straightforward hypothesis led to another surprise in the middle of the previous century. It was proven by G¨ odel that the continuum hypothesis is compatible with ZFC, and it was proven by Cohen that also its negation is compatible with ZFC. The standard axiom system of set theory is unable to decide on the continuum hypothesis. The relative size of the set of the natural numbers in comparison to the size of the real numbers therefore remains indeterminate. The indeterminacy of the relative size of the set of real numbers versus the set of natural numbers leads to a more general problem, namely concerning the size of the set-theoretical universe. The proofs of G¨ odel and Cohen, together with new results in set theory by, among many others, Solovay and Woodin, have shown that ZFC can describe set-theoretic universes of different sizes. One can add new axioms or postulates that posit the existence of large cardinal numbers to the basic axioms of ZFC. One can thus lengthen the series of ordinals and thicken the subsets of cardinals. This situation has led to an interesting contemporary philosophical debate between minimalists and maximalists. On the minimalist side we

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find Quine and Ronald Jensen,a while the philosophical defence of maximalism is taken up by Penelope Maddy. The central disputed axiom is the axiom of constructibility ‘V = L’. Leaving technical details aside, the axiom states that the set-theoretical hierarchy is actually the smallest possible set-theoretical universe. There is room for philosophical debate, because there are few genuine mathematical arguments that can be used in the debate. Whereas the size of the mathematical universe and the thickness of the real number line may seem essential to the mathematical project, accepting or rejecting some large cardinal existence axiom has almost no practical implications for mainstream mathematics such as analysis, number theory, statistics, etc. Some set theorists rely on their own intuitions concerning the nature of sets and the real number line, so that their arguments are a form of conceptual analysis of concepts such as set, natural number, or real number. However, these intuitions are rather flimsy, and philosophers have tried to formulate more elaborate arguments. While pleading respectively for and against ‘V = L’, both Quine and Maddy appeal to methodological rules in mathematics. Maddy’s work is an elaborate attack on the axiom of constructibility, and thus a plea for a large set-theoretical universe. Her main arguments are based on an analysis of the history of mathematics and contemporary work in set theory, in particular in descriptive set theory. In Naturalism in Mathematics,8 she elaborates the historical argument. She compares the historical development in physics, namely the replacement of Mechanism by the Field Concept, with a development in mathematics, namely the replacement of Definabilism by Combinatorialism. She focuses on the concept of function, and shows that the definability requirement was gradually loosened. Maddy concludes that the superiority of Combinatorialism over Definabilism is likely to continue, so that one should reject the requirement that sets are constructible (definable). In ‘Believing the axioms’,10 she gave a more ‘sociological’ account. She presented a long list of actual ‘rules of thumb’ that set-theorists endorse and use in their research. One of the important rules was ‘maximize’, which implied that set-theorists believed in a large set-theoretical universe. Rather than assessing the strength of Maddy’s arguments, it is worthwhile to reflect on her philosophical

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discuss minimalism versus maximalism with regard to models of ZFC. Alternative set theories have been elaborated that can be quite minimal, e.g., Feferman’s predicative set theory.9

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methodology. Her approach in the philosophy of mathematics is naturalistic, which means that her philosophical position is a reflection on the actual and historical scientific practice in the field of mathematics. Therefore, it is remarkable that her major opponent in the discussion of the size of the mathematical universe is Quine, the founding father of naturalised epistemology. Quine’s argumentation in favour of ‘V = L’ is also naturalistic. Quine had argued that at least some mathematical entities must exist, because in our scientific theories, we quantify over numbers, and therefore one cannot deny that they exist. This summary of Quine’s position was put forward by Putnam (Ref. 11, p. 347), and the argument has been called the Quine–Putnam indispensability argument. The ground for the existence of mathematical existence is their indispensability in contemporary science. This way of putting it immediately leads to the question how many mathematical entities are needed in our scientific theories, and what we have to do with entities that are not really indispensable. As for the former question, at least a large number of mathematical entities is required. Quine points out that mathematical analysis is used in many scientific disciplines, and this implies that one needs at least a mathematical universe comprising sets of the size of the set of real numbers. As for the latter question, Quine urges that we should restrict ourselves to the smallest possible set-theoretical universe. In one of his late articles, he claimed that ‘V = L’ is a good halting point, and that other work in set theory should be regarded as mathematical recreation.12 His central argument is the maxim of relative empiricism: “Don’t venture further from sensory evidence than you need to” (Ref. 13, p. 138). The maxim can be regarded as a basic epistemic value in the scientific practice, so that Quine’s argumentation would be genuinely naturalistic. However, there is reason to believe that Quine’s strong endorsement of this principle is also motivated by an intuitive aversion of abstract entities. There is ample evidence that Quine has had an outspoken sympathy for nominalism.

3. Fear of the Abstract Quine’s loathing of abstract entities has been shared by many philosophers of mathematics since the 1980s. Nominalism has become fashionable especially since the publication of Hartry Field’s Science without Numbers.14 The (relative) success of Field’s nominalist construal of mathematical analysis attracted a lot of interest, and many nominalist reconstructions of mathematical and physical theories have been elaborated since.

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The nominalist’s aim is to avoid ontological commitment to mathematical entities. At first glance, this is quite counterintuitive. The use of mathematical entities, especially numbers, is ubiquitous both in common life and in science. Therefore, it is hard to imagine why one would want to dispel mathematical entities. However, if one would be able to continue to employ mathematics without actual commitment to mathematical entities, nominalism is already more attractive. Both from an ontological and epistemological point of view, commitment to mathematical entities is rather inconvenient. Platonism, i.e., commitment to mathematical entities, conflicts with the ontological intuitions of materialists. Since the resurging of materialism in the 1930s, many philosophers have repudiated immaterial, non-physical entities. Some materialists, such as Quine and Tarski, found it worrisome that ontological commitment to abstract entities seemed unavoidable, and would have welcomed scientific theories in which only quantification over concrete objects was necessary. However, ontological intuitions are flimsy and not strong enough as a motivation for mathematical reform, as Quine has stressed many times. The epistemological objection to mathematical entities is stronger. The argument goes roughly as follows: Human beings are concrete, physical beings, reference is a causal process, and therefore reference to abstract entities is impossible. In other words, the arguments states that our cognitive means are not capable of grasping abstract mathematical entities. Though in its strongest formulation,15 the argument critically hinges on Kripkes causal theory of reference, which has now become less influential than in the mid-seventies, the argument can be reproduced in various ways, all of which have a certain plausibility.b In consequence, several strategies for nominalistically reinterpreting theories have been devised. The first strategy is geometrical. The best example of this strategy can be found in Field’s Science without Numbers, though the strategy is much older. Goodman and Quine already introduced it in their ‘Steps toward a constructive nominalism’,17 but this early project foundered. Field managed to elaborate a geometrical interpretation of Newton’s gravitational theory. He tried to avoid the use of mathematical analysis and thus quantification over real numbers. Instead, he had his variables ranging over geometrical points and geometrical regions. Field argued that geometrical points and regions are concrete rather than abstract, so that quantification over these geometrical objects need not be regarded as quantification over b For

an extensive discussion of the epistemological arguments, see Ref. 16, p. 25–60.

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abstract mathematical objects. The predicates and relations in the theory are construed as physical predicates taking as arguments physical entities. Though various objections have been raised against Field’s work (Can the procedure be extended to the theory of relativity or quantum mechanics? Are geometrical entities not abstracts entities?, . . . ), it was a major step forward for nominalism. The second strategy is the modal strategy. Putnam’s ‘Mathematics without foundations’ (1967, reprinted in Ref. 11) was a major inspiration.c Putnam explained that the set-theoretical and the modal interpretation of mathematics are equivalent. For example, one can express Goldbach’s Conjecture in two ways. One can have the ontological, set-theoretical version, stating that there is no natural even number that is not the sum of two prime numbers. The modal version would state that given some basic mathematical axiom system AX, it is possible to derive a counterexample, i.e., a statement ¬ Goldbach, from AX. The set-theoretical version makes an existential claim, namely that a number with a certain mathematical property does not exist. The modal version can be interpreted nominalistically, since it only states that a certain mathematical formula can be derived from a set of mathematical formulas. One could for example interpret the modal statement as a statement about mathematical formulas, rather than about numbers.d In brief, Putnam demonstrated the equivalence of mathematical existence and mathematical constructibility. Putnam’s modal interpretation of mathematics has been used as an explicit nominalist strategy, especially by Geoffrey Hellman and Charles Chihara.18,19 Instead of regarding Putnam’s suggestion as an equivalence between two ways of expressing mathematical statements, modal nominalists only use the modal version as a way of eliminating existential statements. Modal strategies mostly employ elaborate translation schemes of existential mathematical statements into ontologically neutral modal statements. Both the geometrical and the modal strategies involve a considerable amount of technical work. Large sets of mathematical statements must

c However,

Putnam is not really regarded as the founding father of this strategy because the aim of the paper was not nominalism, and moreover, in other papers on the philosophy of mathematics, he defended quite different doctrines, such as the Quine–Putnam indispensability argument. d Another nominalistic interpretation is by using a set of concrete objects forming an ωsequence, see Ref. 11, p. 48. However, the modal interpretation does not necessarily lead to a nominalistic interpretation; realistic existential models for modal logic are actually more natural.

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be translated into statements not invoking quantification over abstract mathematical entities. This technical work is of a logical rather than a mathematical nature. The logical framework in which the mathematical statements are expressed must be replaced by a new framework. Most nominalist strategies have no repercussions for the mathematical practice. In addition to these highly technical reinterpretations, there are also less technical and more conceptual nominalist strategies. Most noteworthy is the strategy of tampering with the interpretation of the existential quantifiers. Since Quine’s ‘On what there is’,20 the existential quantifier has been countenanced as the locus essendi; the values of the variables bound by the existential quantifiers were said to exist. In some recent publications, philosophers of mathematics have tried to disconnect this interpretation of the logical framework in which mathematics is expressed from a more metaphysical notion of existence, and thus to replace Quine’s criterion of ontological commitment by a more metaphysically inspired criterion.21,22 Melia adopts a similar strategy;23 he argues that though mathematics is used in many scientific theories, one can regard it as a useful fiction. Mathematics can be used in a make-believe fashion, and the actual existential commitments can be withdrawn when the labour is done. In recent years, fictionalist approaches toward mathematics have become more acceptable. In these approaches, Quine’s logical criterion of ontological commitment is abandoned, which leads to a more conceptual analysis of the notion of existence in a mathematical context.

4. The Social Construction of Mathematical Entities The philosophical questions discussed in the previous sections are central questions in contemporary philosophy of mathematics. Though contemporary themes differ considerably from earlier ones, they have arisen as a natural continuation of a philosophical discipline defined by the three foundational schools of logicism, intuitionism and formalism. The continued development of formal logic and related disciplines such as set theory and model theory has given rise to ever new philosophical themes in this tradition. Some philosophers have taken issue with this formalist or logical approach in the philosophy of mathematics, and have put forward quite different issues. Most notable in this respect is the work of Imre Lakatos. Lakatos rejected the formalist tendency in the philosophy of mathematics, and elaborated on philosophical themes concerning the methodology of mathematics.24,25 His work became the basis of a separate tradition in

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the philosophy of mathematics. In Lakatos’s own work, metaphysical issues in the philosophy of mathematics are seldom raised.e His views are based on a close scrutiny of the historical development of mathematical concepts and theories. An adequate account of the actual mathematical practice is considered as more important that ideal reconstructions of mathematical theories. He described the development of mathematics as a competition between research programmes, and concentrated on processes of theory acceptance, most importantly mathematical proof. Lakatos’s philosophy of mathematics is embedded in the broader philosophy of science. The metaphysics of mathematics became important again in the Lakatosian tradition, because of later developments in post-Kuhnian philosophy of science. Whereas Kuhn and Lakatos elaborated their views on scientific methodology mainly on the basis on historical case studies, in later philosophy of science and in science and technology studies, the scientific practice was also considered from a sociological point of view, e.g., in the work of Latour, Barnes, and Bloor. In this sociological approach, the social interaction between scientists, the social institutions in science, and the power mechanisms in science were analysed without taking recourse to metaphysical notions such as truth, objectivity, reality. Scientific research was no longer seen as a quest for objective knowledge or a truthful description of reality, but as a struggle for scientific authority. The notions of knowledge, truth and reality became explananda, and were explained sociologically as strategic means for settling debates. Scientific theories and their entities are thus regarded as social constructs. Since the late seventies, this doctrine of social constructivism has led to the realism versus anti-realism debate (and subsequently to the so-called ‘science wars’ between the exact sciences and the social sciences). Realists and antirealists strongly disagree over metaphysical issues such as truth and reality. The anti-realism issue has been most heavily disputed with regard to physical theories and the entities they describe. But also mathematical theories and entities have been discussed. Some sociologists, e.g., Bloor,26 Sal Restivo,27 – 29 and Paul Ernest30 have analysed the social construction of mathematical theories and entities. Social constructivism claims that it can provide the best explanation of our acceptance of certain

e Lakatos

did not object to metaphysics; on the contrary, he did believe that metaphysical beliefs play a essential role in mathematical research programmes, see e.g., Ref. 25, p. 58–59.

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mathematical theories and the Platonic reality they describe.f For example, in a recent paper,31 Restivo analyses the ‘will to mathematics’, i.e., the belief in a transcendent mathematical realm, on analogy with social explanations of other beliefs in transcendent entitities, such as God. Of course, most traditional philosophers of mathematics, Platonists and nominalists alike, strongly condemn social constructivism in mathematics. From a methodological point of view, this controversy is particularly interesting, because the two parties involved use incompatible metaphysical methodologies. 5. Metaphysical Methodology In the previous sections, a variety of metaphysical issues with regard to mathematical entities has been presented. The overview has been composed in order to illustrate the diversity of methodological approaches in contemporary philosophy of mathematics.g In contemporary philosophy of mathematics, there is no unique type of metaphysical question, and moreover, there is no unique methodology for answering these metaphysical questions. In this concluding section, first, I want to relate the types of questions hitherto discussed to other types of questions in metaphysics in general; and second, I want discuss how and to which extent the traditional methodological approaches in metaphysics, i.e., logical analysis, conceptual analysis, and naturalism play of role in contemporary philosophy of mathematics. In each of the previous sections, a certain type of metaphysical question was raised, starting from specific ontological questions to the general f In

the philosophy of mathematics, there has been a long tradition of constructivism. Constructivism is a slightly more liberal version of intuitionism. The (epistemic) requirement that all mathematical notions and theorems should be explicitly ‘constructed’ put serious restrictions on the scope of mathematics. This constructivism is quite different from social constructivism. g The overview does not aim at a comprehensive and balanced overview of the various philosophical positions in contemporary philosophy of mathematics, which would be hardly feasible within the space of this paper. Rather, the aim was to illustrate the various topics and the concomitant methodologies with regard to the metaphysical discussion of mathematical entities. In consequence, some central themes and positions are underrepresented, such as logicism, intuitionism, structuralism, the study of the strength of axiom systems, etc. Some of these issues are of a foundational or epistemological nature, so that there are not of immediate interest for the metaphysical or ontological status of mathematical entities. For other themes, such as structuralism, an elaborate discussion would add (too) little with regard to the methodology of the metaphysics of mathematical entities.

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question of the desirability of a metaphysics of mathematical entities. In the first section, specific, detailed technical questions related to the identification of mathematical entities, and the relations between the various classes of mathematical entities, have been portrayed. In traditional metaphysics, these are ontological questions. In ontology, one tries to characterise the defining properties for certain categories of entities. Here, the ontological status of mathematical entities is at stake; or, in other words questions such as ‘What is a number?’, or ‘What is a set?’ are being answered. The identification problems typical for mathematical entities have an immediate bearing of the properties that define numbers and sets, and on the mutual dependencies between the various categories of entities, namely numbers, sets, and physical objects. In the second section, a more general metaphysical issue was at stake. The analysis of the ontological properties of individual mathematical entities was replaced by an analysis of the metaphysical properties of the realm of mathematical entities. The central question here is ‘What is Plato’s Heaven?’, and the contemporary debate especially focuses on the size of this realm. In the third section, the metaphysical questions no longer concern the properties of mathematical entities or the realm of mathematical entities, but their very existence. The nominalist project aims at the metaphysical elimination of mathematical entities and the realm to which they allegedly belong. Nominalists want to answer the questions ‘Do mathematical entities exist?’ and ‘Is there a Platonic Heaven?’ in the negative. This project has elicited a response by Platonists, arguing on metaphysical grounds that mathematical entities must exist. In the fourth section, the metaphysical project in the philosophy of mathematics was put in jeopardy. Throughout the history of philosophy, antimetaphysical reactions to elaborate metaphysical doctrines are a recurrent theme. Contemporary antimetaphysics is most outspoken in social constructivism. Social constructivists criticise the metaphysical attitude in mathematics, ‘the will to mathematics’, and try to explain this reaching for the transcendent in a sociological way. Therefore, we can conclude that the different traditional metaphysical issues are all present in the form of quite specific questions in contemporary philosophy of mathematics. In addition to the division of metaphysics into several types of questions, each with a particular methodology, one can also discuss the methodology in metaphysics along other lines. One can distinguish three major styles of philosophising that have been used in metaphysics in the last century. A first style is logical analysis; philosophical problems are solved by means of logical tools. Russell’s ‘On denoting’ is a paradigmatic case. Further

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metaphysical examples are Quine’s work on ontology or Kripke’s work on modality. The second style is conceptual analysis. Metaphysical issues are dealt with by means of a meticulous conceptual analysis of the ways in which some terms are used in common language. Prototypical representatives of this style are philosophers such as Jaegwon Kim or Frank Jackson. The third style is naturalism. Naturalists think that philosophy is not clearly separable form science, and that empirical data are relevant in philosophy, and also in metaphysics. Quine is often mentioned as the originator of this style, but only in the last two decades this style of philosophy has come to full maturity. As has been illustrated in the previous sections, in the contemporary metaphysical discussion of mathematical entities, the three styles are all present. Logical analysis has been the dominant style in the philosophy of mathematics since Frege up to now. Logicism aimed at the complete reduction of mathematics to logic. Therefore, the philosophy of mathematics has been the philosophical discipline where logical analysis has been applied most extensively. At present, long after the G¨ odel’s fatal blow to the logicist programme in the 1930s, logical analysis remains the dominant style in the philosophy of mathematics. The philosophical problems sketched in the first section concerning the identification of mathematical entities have in the first place been tackled by means of an ever more technical logical apparatus. Logical analysis is also important in the debate over the size of the mathematical universe, because logical consistency is the only indubitable objection against large set-theoretic universes. Also most nominalist strategies heavily rely on a logical reformulation of an existing axiomatic framework. In addition to logical analysis, conceptual analysis and naturalism have become increasingly important. Some central issues in the philosophy of mathematics are hardly decidable by means of even the most complex technical logical derivations. Decisions of this kind must rely on the mathematical intuitions of expert mathematicians. The analysis of these intuitions should be regarded as a form of conceptual analysis. Some instances of conceptual analysis have been briefly sketched, e.g., invoking a background language for clarifying the intended structure of an axiom system, relying on intuitions concerning sets or the real number line in debating the size of the mathematical universe, and in the nominalism–Platonism controversy, the conceptual analysis of the existential quantifier and the abstract/concrete distinction is important.

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The naturalist approach has existed for some decades in a tradition that is quite separate from mainstream philosophy of mathematics, i.e., in the Lakatos heritage and in social constructivism. These philosophers have often complained that mainstream philosophy of mathematics did neglect the actual practice of the working mathematician and have concentrated on philosophical themes that were of little concern in mathematical research and education, and are not debated in mathematical journals or taught at mathematical faculties. In recent years, the gap between the two traditions has to some extent been bridged. One can see that also in the more traditional philosophy of mathematics, naturalistic approaches, e.g., in the work of Maddy, have become acceptable or even desirable. In conclusion, there is a plurality of methods that are used in the philosophical debates concerning mathematical entities. Different metaphysical issues are at stake, and different styles of tackling these issues have been used. Moreover, it is rather unlikely that a reduction of this diversity or a quest for methodological unity would be beneficial in the metaphysical investigations concerning mathematical entities. Acknowledgments I would like to thank the members of the Epistemology and Ontology section of the Vrije Universiteit Amsterdam, in particular Arianna Betti and Wim de Jong. References 1. G. Boolos, On second-order logic. Journal op Philosophy 72, 509–527 (1975). 2. G. Boolos, To be is to be the value of a variable (or to be some values of some variables). Journal of Philosophy 81, 430–449 (1984). 3. V. McGee, How we learn mathematical language. Philosophical Review 106, 35–68 (1997). 4. P. Benacerraf, What numbers could not be. Philosophical Review 74, 47–73 (1965). 5. W.V.O. Quine, Wither physical objects. In: R. Cohen et al. (Eds.), Essays in Memory of Imre Lakatos. Dordrecht: Reidel (1975). 6. W.V.O. Quine, Facts of the matter. In: R. Shahan and C. Swoyer (Eds.), Essays of the Philosophy of W.V. Quine. Hassocks: Harvester Press (1977). 7. G. Frege, The Foundations of Arithmetic. (Transl. J.L. Austin. Evanston: Northwestern University Press (1980)) (1884). 8. P. Maddy, Naturalism in Mathematics. Oxford: Oxford University Press (1997).

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9. S. Feferman, Why a little bit goes a long way: logical foundations of scientifically applicable mathematics. Proceedings of the Biennial Meetings of the Philosophy of Science Association, 442–455 (1992). 10. P. Maddy, Believing the axioms. Journal of Philosophy 53, 481–511; 736–764 (1988). 11. H. Putnam, Mathematics, Matter, and Method. Philosophical Papers. Volume I. Cambridge: Cambridge University Press (1979). 12. W.V.O. Quine, Immanence and validity. Dialectica 45, 219–230 (1991). 13. W.V.O. Quine, The Roots of Reference. Open Court, La Salle (1974). 14. H. Field, Science without Numbers. Princeton: Princeton University Press (1980). 15. P. Benacerraf, Mathematical truth. Journal of Philosophy 70, 661–679 (1973). 16. J. Burgess and G. Rosen, A Subject with No Object. Oxford: Clarendon (1997). 17. N. Goodman and W.V.O. Quine, Steps toward a constructive nominalism. Journal of Symbolic Logic 12, 97–122 (1947). 18. G. Hellman, Mathematics without Numbers. Oxford: Clarendon (1989). 19. C. Chihara, Constructibility and Mathematical Existence. Oxford: Oxford University Press (1990). 20. W.V.O. Quine, On what there is. Review of Metaphysics 2, 21–38 (1948). 21. J. Azzouni, On ‘On what there is’. Pacific Philosophical Quarterly 79, 1–18 (1997). 22. J. Azzouni, Applied mathematics, existential commitment and the Quine– Putnam indispensability thesis. Philosophia Mathematica 5, 193–209 (1998). 23. J. Melia, Weaseling away the indispensability argument. Mind 109, 455–479 (2000). 24. I. Lakatos, Proofs and refutations. Cambridge: Cambridge University Press (1976). 25. I. Laktatos, Mathematics, Science and Epistemology. Philosophical Papers. Volume 2. Cambridge: Cambridge University Press (1978). 26. D. Bloor, Wittgenstein and Mannheim on the sociology of mathematics. Studies in the History and Philosophy of Science 4, 173–191 (1973). 27. S. Restivo, The Social Relations of Physics, Mysticism, and Mathematics. Berlin: Springer (1985). 28. S. Restivo, Mathematics in Society and History. Dordrecht: Kluwer (1992). 29. S. Restivo, J.-P. Van Bendegem and R. Fischer, Math Worlds. New York: SUNY Press (1993). 30. P. Ernest, Social Constructivism as a Philosophy of Mathematics. London: The Falmer Press (1991). 31. S. Restivo, The will to mathematics. Foundations of Science 11, 197–215 (2006).