Mereologies, Ontologies, and Facets: The Categorial Structure of Reality 1498524974, 9781498524971

Table of contents :
Dedication
Contents
List of Figures
List of Tables
Acknowledgments
Introduction: Theoretical and Applied Categories in Philosophy and Psychology • Paul M. W. Hackett
1 Categorization by the Animal Mind • Alison L. Greggor and Paul M. W. Hackett
2 Necessary Categories of Conscious Experience • Gal Yehezkel
3 On Limning the True and Ultimate Structure of Reality • Claire Ortiz Hill
4 A Category Semantics • Paul Symington
5 Giving Descartes His Due • Jonathan C. W. Edwards
6 Categorical Analysis in Pragmatism: Specialization in Science and the Role of Philosophy • Torjus Midtgarden
7 Declarative Mapping Sentence Mereologies: Categories from Aristotle to Lowe • Paul M. W. Hackett
8 Facet Methodology and Analysis: Mining the Unconquered Lands of Behavioral Sciences Research • Aharon Tziner
9 Divine Action, Ontological Dependence, and Truthmaking • Walter J. Schultz
Glossary of Terms
Index of Authors
Subjects Index
About the Editor and Contributors

Citation preview

Mereologies, Ontologies, and Facets

Mereologies, Ontologies, and Facets The Categorial Structure of Reality

Edited by Paul M. W. Hackett

LEXINGTON BOOKS

Lanham • Boulder • New York • London

Published by Lexington Books An imprint of The Rowman & Littlefield Publishing Group, Inc. 4501 Forbes Boulevard, Suite 200, Lanham, Maryland 20706 www.rowman.com Unit A, Whitacre Mews, 26-34 Stannary Street, London SE11 4AB Copyright © 2018 The Rowman & Littlefield Publishing Group, Inc. All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the publisher, except by a reviewer who may quote passages in a review. British Library Cataloguing in Publication Information Available Library of Congress Cataloging-in-Publication Data Names: Hackett, Paul, 1960- editor. Title: Mereologies, ontologies, and facets : the categorial structure of reality / edited by Paul M.W. Hackett. Description: Lanham : Lexington Books, 2018. | Includes bibliographical references and index. Identifiers: LCCN 2018015428 (print) | LCCN 2018019370 (ebook) | ISBN 9781498524988 (Electronic) | ISBN 9781498524971 (cloth : alk. paper) Subjects: LCSH: Categories (Philosophy) | Knowledge, Theory of. | Ontology. Classification: LCC BD331 (ebook) | LCC BD331 .M388 2018 (print) | DDC 111—dc23 LC record available at https://lccn.loc.gov/2018015428 ∞ ™ The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI/NISO Z39.48-1992. Printed in the United States of America

Jessica has relentlessly supported me in all of my work including that involved in this book and for this, and many other reasons, this book is dedicated to her.

Contents

List of Figures

ix

List of Tables

xi

Acknowledgments

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Introduction: Theoretical and Applied Categories in Philosophy and Psychology Paul M. W. Hackett 1 Categorization by the Animal Mind Alison L. Greggor and Paul M. W. Hackett

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2 Necessary Categories of Conscious Experience Gal Yehezkel

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3 On Limning the True and Ultimate Structure of Reality Claire Ortiz Hill

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4 A Category Semantics Paul Symington

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5 Giving Descartes His Due Jonathan C. W. Edwards

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6 Categorical Analysis in Pragmatism: Specialization in Science and the Role of Philosophy Torjus Midtgarden

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7 Declarative Mapping Sentence Mereologies: Categories from Aristotle to Lowe Paul M. W. Hackett

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Contents

8 Facet Methodology and Analysis: Mining the Unconquered Lands of Behavioral Sciences Research Aharon Tziner 9 Divine Action, Ontological Dependence, and Truthmaking Walter J. Schultz

161 201

Glossary of Terms

235

Index of Authors

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Subjects Index

249

About the Editor and Contributors

255

List of Figures

Figure 1.1 Hypothetical training and novel stimuli Figure 1.2 Mapping sentence for category usage in animals Figure 4.1 Potentiality and actuality in relation to the generic and the specific Figure 7.1 Declarative mapping sentence for Aristotle’s categories Figure 7.2 Declarative mapping sentence for Lowe’s four-category ontology Figure 7.3 Declarative mapping sentence for the hermeneutic consistency of a mapping sentence Figure 8.1 Diagrammatic display of mapping from a Set S to a Set T Figure 8.2 Geometric portrayal of a facet playing an axial role Figure 8.3 Geometric portrayal of the facet “Modality of Political Involvement” Figure 8.4 Example of a polarizing facet: “Areas of Life” Facet in Levy & Guttman (1978) Figure 8.5 Geometric portrayal of a facet playing a modulating role Figure 8.6 Flowchart of the SSA algorithm

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List of Tables

Table 2.1 The Conceptual Space of “Kant is a Bachelor” Table 2.2 The Conceptual Space “Deep Blue is Conscious that p” Table 2.3 The Conceptual Space of “Deep Blue is Conscious that it is in Pain” Table 2.4 The Conceptual Space of “Deep Blue is in Pain” Table 2.5 The Conceptual Dimension of the First-Person Pronoun Table 2.6 The Conceptual Dimension of First-Person Ascription of Consciousness Table 2.7 The Temporal Dimension of First-Person Denial of Consciousness Table 7.1a Components of a Mapping Sentence Table 7.1b Characteristics of a Mapping Sentence Table 7.2 Comparison of Attributes of the Declarative Mapping Sentence and the General Mapping Sentence Table 8.1 Pearson Product Moment Correlation Matrix for Achievement Motive Variables (Tziner & Elizur, 1985) Table 8.2 Twenty-One Occupational Reinforcers Used in the Study Table 8.3 Unrotated and Varimax-Rotated Loadings of the Occupational Reinforcers (Tziner & Elizur, 1985) Table 8.4 Intercorrelations among Twenty-One Occupational Reinforcers (Decimals Omitted)

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21 23 24 25 27 28 30 143 144 146 184 186 189 192

Acknowledgments

I have been involved in research into notions around categorical understandings of behavioral and experiential conditions of human and nonhuman animals for many years. Similarly, the idea behind this book of bringing together scholarship from psychological, facet theoretical, and philosophical realms has also developed over many years. As a consequence of this project’s longevity there are many people who I would like to acknowledge and thank for their contribution to the conception of and writing of this book. The most obvious and deeply felt gratitude must first be given to all of the authors who took time and expended considerable effort in preparing a chapter for this book. Without their dedication and commitment, over a protracted length of time, this book could never have been brought to completion. I believe that their depth of knowledge and the articulate manner in which they have been able to express this, has resulted in an eclectic and stimulating body of knowledge on psychological and philosophical understanding of categories. I would like to thank my editor at Rowman & Littlefield, Jana HodgesKluck, for her guidance during the preparation of the manuscript. I am deeply grateful to Professor Anna Marmodoro (who holds the chair of metaphysics in the philosophy department at Durham University and is a research fellow in philosophy at Corpus Christi College, University of Oxford) for inviting and facilitating my spending time with her at Oxford University. During this period I was able to commence the scholarship that underpins this manuscript. I am also grateful for the time she spent discussing my research with me.

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Introduction Theoretical and Applied Categories in Philosophy and Psychology Paul M. W. Hackett

The assignment of an individual event, object, state of being, and so on, to an experiential category is a fundamental activity carried out by both human and nonhuman animals. It appears that most and perhaps all living creatures will consciously, subconsciously classify the world in which they live. For example, events will be ascribed to categories such as this thing is dangerous, I can eat it, it is wet or dry, this is a specific type of bird that I am observing, and so on. So rudimentary are the process involved in categorizing that it is indeed impossible to imagine conscious awareness to exist without the presence of categories. As a consequence perhaps of the ubiquitous nature of categories a considerable body of academic writing has been brought forth on the subject of categories dating from the times of classical philosophy. Plato developed a categorical ontology (categories we use to structure our worlds) and Aristotle produced one of the earliest examples of a complex understanding of basic ontological categories. In his Categories, Aristotle proposed ten ontological categories to account for human experience (Aristotle and Ackrill, 1975, and for a contemporary consideration see, Klima and Hall, 2011). With increasing frequency and complexity, a number of other structured categorial ontologies have been proposed over the centuries since, including those by Lowe (2007), Westerhoff (2005), Chisholm (1996), and so on.1 Synonyms of the noun “category” are varied and include class, group, set, type, sort, kind, species, genre, and heading. If we consider the commonalities present between these synonyms it appears that a category can be seen to be a broad concept that refers to the bringing together of events within a conceptual scheme where the uniting of events simultaneously implies the division of the events from other events not in the category. A category is formed through the inclusion of events, objects, people, or xv

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things by characteristics they share. Events may be categorized under one category such that a feature that can be determined to characteristic of events, entities, and so on, that are characteristic of one category’s membership, cannot be a feature that determines membership of any other category. Thus, entities in the category of bird have feathers and flight while no entity in the category of cat can have feathers and flight. A category may be a discrete classification or may form a set of exhaustive classification classes, which together may classify all events, and so on. When philosophers are concerned with categories it is usually in terms of this latter form of definition in which cases they are cogitating upon the highest class of genera that may be thought of. On this understanding, a category set is complete when it is possible to mutually, exclusively, allocate all of the world’s entities under one of the specified categories (Audi, 2015). Examples of categories include the writing of Aristotle, who was the first philosopher to systematically discuss categories. He posited a ten-category ontology while Descartes identified a simpler two-category set of mind and matter. Categories are phenomena that may be thought of in a theoretical sense or they may be understood in terms of their application within substantive life areas. The authors in this book address categories in both of these orientations from a variety of disciplines. There are several noteworthy features of the present text. These include the provision of a philosophical account of contemporary scholarship in the area of categories. Furthermore, this book provides a comprehensive though focused presentation of philosophical categories complimented by philosophy’s sister disciplines; uniquely, the book also includes writing by psychologist and facet theorists that compliment, add to and challenge the body of philosophical knowledge developed. As well as developing theoretical understanding of categories authors uniquely provide accounts of the applied usage of categories in real-world settings. The book compliments competing books in the area through offering a distinct philosophical perspective that is modified by psychological understanding and applied within the real world where the book uniquely extends theoretical and applied knowledge within a philosophical/psychological/facet theory framework. Some philosophy monographs and textbooks include sections on categories and more commonly on ontology and mereology. Categories are not typically included as separate areas of interest in the psychological literature but are rather present throughout many academic areas of the discipline. As a consequence, many texts may be cited that include cursory attention to categories. Specialized volumes have addressed a similar content area within philosophy that more directly review a variety of philosophical perspectives on categories. Theses are all edited editions each of which takes a particular perspective upon categories. For example, Haaparanta and Koskinen’s (2012) edited collection, Categories of Being is the most comprehensive

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voice of modern day philosophical scholarship in this area with concentration upon the systematic presentation of the most superordinate or general categories of being. Drawing on philosophical thought from classic through twentieth-century philosophy Haaparanta and Koskinen present writing on the interrelations of metaphysics and logic. The present text does not attempt to present such a comprehensive overview of scholarship on categories but rather focuses upon philosophical and psychological voices upon categories and offers an applied orientation, applying as well as theorizing the realm of categories. The edited work by Gorman and Sanford (2004) take a comprehensive view in defining categories, cognitively, linguistically and in reference to morals. The authors come from a wide range of philosophical backgrounds that are reflected in their contributions. They also consider categories of different types and other category related questions as these are applied to several subdisciplines of philosophy: metaphysics, epistemology, ethics, and so on. Cohen and Lefebvre’s (eds.) (2017) text is the most comprehensive assembly of cognitive science research on categories. However, their book is also now a decade old and ignores much contemporary thought. Cohen and Lefebvre’s define categorization as a basic cognitive function and view categorization from linguistic, psychological, philosophical, neuroscientific approaches, and so on. Cohen and Lefebvre’s provide an interdisciplinary synthesis of knowledge from the different approaches they incorporate. As well as dealing with theoretical issues associated with categories, the current collection of essays provides an applied perspectives in philosophical research; contemporary research and scholarship in psychological research and consideration of facet theory. It does not however constitute an overly exhaustive review of the philosophy or cognitive science of categories. This is a scholarly text that provides an unique perspective of its subject area. The book is an edited collection of up to the moment essays that address critical aspects on the understanding of categories and categorical systems. The authors are all renowned experts in the area of their writing. Topics addressed include both contemporary advances in the understanding of perennial debates and latest thinking upon how scholars employ categories structure understanding of our experiences in the world in which we live. The book is set apart from the texts that exist by being written by academics from both philosophy and psychology, all of whom have developed their own distinct understanding and categorical based understandings and who present these within the appropriate historical context. The book is a collection of writings from selected academics at the fore of debates and understandings of categories in contemporary thought. The text provides a single source for contemporary scholarship in categories. The editor decided to assemble this collection as no single text that brings together expositions of categorical

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experiences for students and academics within the disciplines of philosophy and psychology. A central reason for my assembling this collection is that there is no text, which provides an empirically supported model for the integration of theoretical understanding of categories. The facet theoretical approach is a widely and consistently used systematic categorial approach in the social sciences: I have recently extended this approach into more philosophical and qualitative arenas and the proposed volume will further this extension through my own writing in this volume. In this book the authors undertake the comprehensive presentation of current thinking in the area of categorically structured ways of understanding the world around us. Authors are drawn from the domains of metaphysics, facet theory, and the broader areas of philosophy and psychology. Psychologists use the term construct and facets when describing the mental entities that are used to structure understanding of the everyday world around us. Philosophers, on the other hand, use the term of ontological category to describe our most basic or fundamental mental understanding of reality. Psychologists may speak about construct networks, webs or mapping sentences to epitomize the way in which constructs may interrelate while metaphysicians may describe this as a mereology. In this text the questions that are addressed include a consideration of ontological categories as basic units of meaningful categorization and construct networks and mereologies and their respective combinatorial existence. Through the presentation of the articles from the above perspectives the contemporary academic position of categories as a device for structuring our understanding of our daily lives is assessed. Furthermore, consideration is given to the basic nature of categories such as the often-assumed bipolar nature of categories; the mutual exclusivity of categories; the mereological arrangement of categories and the content of categories. Thus: how do we use categories to navigate our lives—ontological, personal, and social categories that are both metaphysical and psychological, where psychology is understood as a process that occupies an ontological space. This book presents not just a philosophical approach to the subject of categories but rather a multidisciplinary perspective is adopted that embraces and extends contemporary thinking about categories. Thus, categories are first presented as both human and nonhuman animals employ them. Essays are then included that are both applied and theoretical to various degrees and which reside in psychological, philosophical, and facet theoretical perspectives. BRIEF SYNOPSIS OF CHAPTERS After this introduction, in chapter 1 Alison Greggor and I consider that it appears to ostensibly be the case that all animals form categories, and employ

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categories in their daily lives. In this chapter we consider the notion of categorization as this applies to, and indeed typifies, animal behavior. While we concentrate upon nonhuman animals, the statements we make on many occasions apply equally well to our own species. The chapter constitutes an exposition of the manner in which nonhuman animals employ categories as these have been investigated in a wide variety of animals in both natural habitats and within the laboratory. We argue that forming categories allows animals to optimally sort and respond to their environment, which has been evolutionarily advantageous for individual animals and species. After presenting a brief review of category usage, we state that how an animal defines the categories it uses (through perceptual, functional, and abstract means) may be appreciated through reference to the speed, complexity, and flexibility of their category-based response, which in its turn is an indicator of the cognitive complexity the animals possess. To conclude, we assert that the formation and deployment of categorization skills in animals may best be investigated and understood through using a mapping sentence to design and analyze research. In chapter 2 Gal Yehezkel analyses the concept of self-consciousness in order to uncover its conceptual structure. The conclusions of this analysis describe some of the necessary categories of conscious experience. The concept of the self, the concept of consciousness, the concept of objectivity, the temporal distinctions between past, present, and future, and finally the idea of natural regularities, are found to be necessary categories for conscious experience, and hence describe the fundamental cognitive structure of selfconscious beings. Claire Oritz is the author of chapter 3. In her writing she notes how Edmund Husserl is known as the father of phenomenology, the science of intentionality. She notes however, that it is not well known that as a necessary complement to that science of subjectivity, he also fathered a science of objectivity, an austere scheme to limn the true and ultimate structure of reality free from acts, subjects, or empirical persons or objects belonging to actual reality, which shunned empiricism and embraced categoriality, essences and a fundamental, but anti-Kantian, cleavage between analytic truths. So, according to Hill, it is by embracing precisely what analytic philosophers have reviled and wanted to wipe out; he actually devised a plan to achieve what they have generally aspired to accomplish. However, she claims, Husserl’s strategy for keeping knowledge of reality from collapsing into a formless blob of facts became buried in the excitement, both negative and positive, generated by his phenomenology. In this chapter Hill digs through Husserl’s writings, especially those published by the Husserl Archives since the 1980s. In doing this she unearths the categorial skeleton that Husserl taught could uphold truly scientific knowledge of reality. Hill sets forth his theories about

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categoriality and examine their relation to his ideas about propositional logic, the inviolable differences between dependent and independent meanings, wholes and parts, set theory and Russell’s contradiction, his identification of categoriality and analyticity and his theory of manifolds, which he considered to be the ultimate consummation of all purely categorial knowledge. Ultimately, Hill suggests that once the pieces of Husserl’s theory about the categorial structure of reality are reassembled, philosophers can, and should, experiment with it as an alternative to the logical point of view used to prop up analytic philosophy, which, she claims, endeavored unsuccessfully to wipe out the very differences Husserl deemed revelatory of categoriality. The essay in chapter 4 is written by Paul Symington who offers a theory of meaning that is rooted in categoriality. In his writing he states that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. Symington goes on to build upon the virtues of David Lewis’s Possible World Semantics. However, Symington advances beyond problems that Lewis’s theory faces with its distinctly Aristotelian turn toward actuality and potentiality. Paul Symington claims that semantic integration of perception, logic, language, may result from a theory of categories. Going back as far as Aristotle and his Categories, Paul Symington claims in his chapter “categorial semantics” that three identifiable features are consistently present in categorial theories. In his essay he proposes a semantic theory that embodies categorial functionality and integrates the three features. The first of his features identify categories to be associated with the identification of their veracious characteristics that are meaningfully consistent. Secondly, when understood in terms of both their intension and extension, categories are very broad. The third of Symington’s features is that of providing a connection and focus of meaning in reference to an understanding of the real world as real and offer a fundamental structure to reality. Symington argues that categories offer a structure through which the basic or rudimentary properties for things in the world may be established. Moreover, categories, he claims, are needed to establish objective meaning. In his chapter he attempts to bring a theory of categories back to a position where they may unify the underlying aspects of the world, experience and reality. In the essay in chapter 5 Jon Edwards focuses upon René Descartes. Edward’s notes that despite being a key figure in the foundation of physical science, René Descartes has become a figure of derision in both neuroscience and philosophy of mind. His distinction between body and spirit is seen as the antithesis to a respectable “scientific materialism.” Edward’s claims that there is no doubt that Descartes’ physics contained specific flaws that were to be addressed by Hooke, Leibniz, and Newton in the decades after his death.

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However, Edward’s also claims that there are reasons for thinking that the popular interpretation of “Cartesian Dualism” is a complete misrepresentation of his position. Edward’s believes that Descartes was perhaps the most rigorous of all “physicalists” in that he insisted that both body and spirit were essential aspects of physics. Moreover, his distinction between spirit, in the sense of action or force, and matter, in the sense of solidity or exclusion from a space, has remained central to all physics and is now understood in terms of the Bose/Fermi dichotomy. In contrast, according to Edward’s, Descartes’s rigorous local causal analysis, present day theories of “emergence” of mental phenomena from “complex systems” are ungrounded and fail Popper’s criterion of testability. Edward’s concludes by stating that both physics and psychology may still have a lot to learn from Descartes. Torjus Midtgarden, in chapter 6, notes how Charles Peirce founded pragmatism at a time when the natural sciences were becoming ever more specialized. Both Kant and Comte inspired Peirce when he assigned philosophy the position of being the foundation of specialized empirical science. Midtgarden identifies a two conditions that constitute a foundational philosophical discipline. First, he presents a science classification provided by an epistemological analysis of sign-forms employed in scientific assertions or truth-claims. Secondly, Midtgarden presents a classification through presumed universal elements of an experiential phenomenological and ontological analysis of categories. Midtgarden notes how John Dewey defended Peirce’s categorial analysis in contrast with interpretations influenced by Logical Positivism. Midtgarden also analyses how Peirce influenced Dewey and the so-called ‘Transactional’ view on knowledge processes and modes of theorization in science proposed by Arthur Bentley. Midtgarden goes on to consider notions of methodological individualism in social science, associations between humans and nonhumans, and the formation of theory around human agency. In chapter 7 I examine Louis Guttman’s notions in reference to the novel application of the categorial research approach of facet theory and its principle component the mapping sentence, which have been traditionally been used quantitatively. In this chapter I focus upon my extensions of facet theory and the mapping sentence into the realms of qualitative and philosophical research. Mapping sentences are highly specific to allow the generation of discrete and applied research enquiries. I disassemble the content of the mapping sentence and the functioning of its parts is considered. Later, these components are brought together as what I call a declarative mapping sentence and I use this to allow examination of categorial ontologies by Aristotle and Lowe. Finally, I develop and illustrative declarative mapping sentence of the mapping sentence itself and I propose the declarative mapping sentence as an orientation to in-depth research.

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The content of chapter 8 provides another use of the facet theory approach. In this essay, Aharon Tziner introduces traditional facet methodology (after Guttman, 1954; 1957; 1959) and its associated mathematical and analytic procedures as a critical response to the phenomenon of inaccurate and weak definitions of variables that encompass investigated content domains. Tziner claims that such definitional problems, particularly in the field of social and behavioral sciences, mitigate against replication, impede accumulation of knowledge, and jeopardize the usefulness of research. Tziner suggests that the facet theory approach is a powerful methodology consisting of both data analysis and a research strategy that help to define systematically the boundaries, structure, and parameters of a conceptual domain under investigation: Facet theory, he claims, facilitates the choice of (observed) variables consistent with the objectives of the investigation, as well as the formulation of hypotheses that can ultimately be represented as points in geometric space. Tziner’s narrative presents both a review of the essentials and power of this methodology and a critical empirical comparison of a facet methodology (Smallest Space Analysis) with three alternative structure analyses. Questions which Tziner addresses include: Which variables embedded in the content domain are most interrelated and which are less associated? What is the structure of the entire set of interrelations among variables? What is the rationale for this structure? Ultimately, Tziner concludes that facet methodology is a rigorous tool that allows researchers, inter alia, to concentrate on a specific part of a domain, to specify the order of a facet’s elements and the relationship between them, to delineate the range of possible responses, and to facilitate a generation of hypotheses which, through an abundance of replications, serve to enhance the dynamic process of formal theory construction in social and behavioral sciences. In chapter 9, the final chapter, Walter Schultz presents a divine action account of the ontological dependence of contingently existing things of several types, namely, physical systems, their constituents and structures, and the laws that “govern” their coexistence, internal change, and interaction, together with an account of truthmaking for true propositions about such things. After presenting generic analyses of ontological dependence and truthmaking in the light of recent literature, Schultz provides a divine action ontology and then develops each notion in more detail in terms of the ontology. Such a dual account is metaphysically foundationalist, given that all things are ultimately ontologically dependent on what it assumes the fundamental existent to be. Since the “logic” of everything must lie in the logic of God’s action, according to Schultz, the referents of the fundamental concepts of science and mathematics must be ultimately related to God through ways God acts and through God’s awareness of his ability.

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NOTE 1. As well as philosophers, scholars from other disciplines and perspectives that are concerned with studying human behavior and experience have also taken categories into their scholarship. For example: child development (Rakison and Oakes, 2003); cognitive linguistics (Lakoff, 1990); cognitive psychology (Lamberts and Shanks, 1997); cognitive science (Cohen and Lefebvre, 2017); Neuropsychology (Forde and Humphreys, 2012).

REFERENCES Aristotle, & Ackrill, J.L. (1975) Aristotle’s Categories and De Interpretatione, Oxford: Oxford University Press. Audi, R. (2015) The Cambridge Dictionary of Philosophy (third edition), Cambridge: Cambridge University Press. Chisholm, R.M. (1996) A Realistic Theory of Categories: An Essay on Ontology, Cambridge: Cambridge University Press. Cohen, H., & Lefebvre, C. (eds.) (2017) Handbook of Categorization and Cognitive Science, Kidlington: Elsevier Ltd. Forde, E., & Humphreys, G. (eds.) (2012) Category Specificity in Brain and Mind, London: Psychology Press. Gorman, M., & Sanford, J.J. (eds.) (2004) Categories: Historical and Systematic Essays, Washington, DC: Catholic University Press. Guttman, L. (1954) A new approach to factor analysis: The radex. In P. Lazarfeld (ed.), Mathematical Thinking in the Social Sciences, Glencoe, IL: Free Press. ———. (1957) Introduction to Facet Design and Analysis. Proceedings of the Fifteenth Congress of Psychology, Amsterdam: North Holland Publishing. ———. (1959) A structural theory for intergroup beliefs and action. American Sociological Review, 24, 318–28. Haaparanta, L., & Koskinen, H.J. (eds.) (2012) Categories of Being: Essays on Metaphysics and Logic, Oxford: Oxford University Press. Klima, G., & Hall, A.W. (eds.) (2011) Categories and What Is Beyond (Proceedings of the Society for Medieval Logic and Metaphysics), Cambridge: Cambridge Scholars Publishing. Lakoff, G. (1990) Women, Fire, and Dangerous Things: What Categories Reveal about the Mind, Chicago: University of Chicago Press. Lamberts, K., & Shanks, D.R. (eds.) (1997) Knowledge, Concepts, and Categories, Cambridge, MA: The MIT Press. Lowe, E.J. (2007) The Four-Category Ontology: A Metaphysical Foundation for Natural Science, Oxford: Oxford University Press. Rakison, D.H., & Oakes, L.M. (eds.) (2003) Early Category and Concept Development: Making Sense of the Blooming, Buzzing Confusion, Oxford: Oxford University Press. Westerhoff, J. (2005) Ontological Categories, Oxford: Clarendon Press.

Chapter 1

Categorization by the Animal Mind Alison L. Greggor and Paul M. W. Hackett

BACKGROUND All animals categorize stimuli from the world around them, and this activity is vital in many areas of their lives (Asen & Cook, 2012). In its most basic form categorization does not even require a brain. Species ranging from sea anemones to humans sieve through the noise of their surroundings to identify and respond appropriately to food, predators, and members of their own species. Incorrect categorizations can be deadly if food opportunities are missed or if animals do not respond with the correct behavior toward predators or mates. Therefore, strong selective pressures have finely tuned animals’ abilities for detecting, categorizing, and responding to stimuli that are essential for their survival and reproduction. That being said, the categories that animals use range in complexity, as does the repertoire of behavioral responses that animals display toward them. Moreover, simply because animals demonstrate categorization behavior does not mean that they distinguish stimuli based on conceptual representations. Without a deeper understanding of the cognitive abilities involved in the formation of different categories, it is not always easy to predict which species will possess seemingly complex categories. For example, honeybees can be trained to solve foraging problems using abstract concepts such as “sameness” versus “differentness” (Avarguès-Weber & Giurfa, 2013). Meanwhile the pigeon is one of the best-studied and most prolific categorizers, and it can even categorize paintings of Monet versus Picasso (Watanabe, Sakamoto, & Wakita, 1995). Does this mean that bees, pigeons, and humans all categorize the world in a similar, cognitively complex way? The evidence would suggest not. In the case of bees, their abstract categorization abilities are limited to very specific flower-finding contexts. Meanwhile, many example of pigeons’ 1

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categories can be explained by rote memorization and overlapping perceptual similarity, rather than by rules or abstract concepts that generalize categories to new stimuli (Huber, 2001). Therefore, although impressive examples of categorization exist within the animal kingdom, not all animals deal with categories similarly. Very different neural architectures can produce seemingly similar categories, but often the basis of category formation—for example, whether category membership is defined by perceptual features, or abstract concepts—and the flexibility of category use differs between species. These differences are rooted in an evolutionary need for efficiently distinguishing aspects of the environment. The aspects of the environment that are most relevant for each species depends upon the niche that they occupy. Since distantly related species can occupy similar niches, similar categorization abilities, like many cognitive mechanisms, can be found in humans and other animals. A closer look into nonhuman categorization reveals which categorization abilities we are most likely to share. Additionally, a deeper investigation into the function and form of nonhuman categorization also highlights the important ways in which we differ. HOW RESEARCHERS STUDY ANIMAL CATEGORIZATION Since we cannot ask animals whether they consider two stimuli to be part of the same category, we have to determine their categories based on behavioral responses or neural firings. From a basic standpoint, if an animal behaves in one way toward one stimulus and in a different way toward another stimulus, the stimuli are not likely in the same category. In contrast, when animals have the capacity to differentiate between two types of stimuli, and they respond the same way to both of them, then it can be assumed that they are categorizing the two stimuli similarly. Animals’ category formation is most commonly tested in the laboratory. Animals can be trained to make categories based on scientists’ design, such that the perceptual features of stimuli and their presentation context can be tightly controlled. Beyond assessing whether animals can form categories with these methods, researchers often strive to understand what defines category membership. A key challenge researchers face is to distinguish animals’ discrimination based perceptual features from categorization based on deeper concepts. One way to determine whether an animal has a concept of something is by assessing how well they generalize their behavior to novel stimuli that share an abstract or conceptual relationship with the stimuli on which they were trained (see Figure 1.1).

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Figure 1.1  Hypothetical training and novel stimuli.

Assuming an animal had learned that the trained stimuli were rewarded, then the basis of category membership could be probed with presentations of each of the three novel stimuli. If category membership was based on texture alone, then only the first novel stimuli would elicit the same response as the training stimuli. If the animal had learned that membership was based on likeness of shape, then the first and second would elicit the same responses as the training stimuli. If membership was based on a more abstract relationship between stimuli, such as “larger object over similar small object” then the final novel stimulus would also elicit the same responses. HOW TO TRAIN CATEGORIES Discrimination training forms the basis of all category training, in which animals are rewarded for responding to one of two or more stimuli (Shettleworth, 2010). A procedure used often in pigeons involves rewarding pecking behavior toward one type of stimulus, and offering no reward for pecking when a different type of stimulus is presented (Huber, 2001). This type of instrumental training is called a go/no-go paradigm, and has been used for many decades (e.g., Herrnstein, Loveland, & Cable, 1976). Experiments such as these often train categories based on thousands of presentations. The farther the stimuli are away from each other perceptually, the faster the animal will learn to discriminate between them. Additionally, the greater number of exemplars an animal is trained on, the longer the training takes, but the better they are able to generalize the categories when encountering new stimuli.

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ABILITY DOES NOT DENOTE USE In the lab animals can be trained to categorize biologically irrelevant stimuli, but that does not mean that they would actually treat those stimuli differently in the wild, or that they understand that the lab stimuli they encounter, such as pictures or video, actually represent live categories. For example, various tests in pigeons show that they appear to process certain picture stimuli as abstract shapes and colors instead of objects, such as trees (Spetch & Friedman, 2006). Similarly, although baboons can distinguish pictures of human faces, they do equally well when those faces are inverted, which is not the case for people, and therefore it is unlikely they process them through the facial recognition system that humans use (Martin-Malivel & Fagot, 2001; Martin-Malivel, Mangini, Fagot, & Biederman, 2006). Finding that a species can categorize certain stimuli in the lab helps build a framework for species’ ability, but it must be backed up with research in the field to show that animals actually use the abilities they may have. Later in this chapter we will consider a framework that may assist in making clearer the findings from laboratory and natural settings, their similarities, differences, and interrelationships. HOW DO ANIMALS CATEGORIZE? Whenever an animal encounters something in its environment, the first categorization it makes is a simple one: is the stimulus familiar or novel? This distinction hinges on being able to discriminate between two stimuli based on their perceptual similarity (Blough, 2001). Certain types of stimuli are harder to classify for different species depending on their perceptual abilities. For example, humans are unable to distinguish light in the UV range, but many bird species can. Some birds, such as blue tits (Cyanistes caeruleus) have sex-specific color patterns on their feathers that individuals use to distinguish males from females (Andersson, Örnborg, & Andersson, 1998). With human eyes we are unable to make this simple categorization of male versus female that blue tits use on a daily basis. Stimuli are also going to be more or less distinguishable based on animals’ attentional and cognitive biases that transcend perceptual ability. For example, we have a bias to attend toward human faces. If we were asked to distinguish between familiar and unknown people based on pictures of their face or pictures of their feet, we would naturally do better at categorizing them based on faces, despite that fact that we are perfectly capable of seeing people’s feet. If an animal can perceptually distinguish between two stimuli, then the process of categorization can proceed. If the stimulus is a novel one, the animal must determine whether it fits within one of the known categories they

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possess. Is the new object food? Is the new location safe? Is the approaching individual friend or foe? The answer to these questions will depend upon how that animal sorts and organizes the world around them, which will differ according to the species, and that individual’s experience. While species differ in their categorization abilities, they also can differ in the extent to which their categories are encoded in their genetic makeup, or learned as a result of experience. Even in cases where categories emerge without prior experience, greater familiarity with stimuli often allows for better categorization simply because features become more distinguishable over time. This process is called perceptual sharpening, in which an individual forms a stricter category with greater experience (Shettleworth, 2010). An example of this can be seen in human language, in which native English speakers can make a clear distinction between the sound made by a “W” and a “V,” but Icelandic native speakers cannot, simply because they were not exposed to the two sounds when they were young. Experience aids in categorization because learned categories rely on shifts in attention, as good predictors of reward receive more attention on subsequent presentations (Mackintosh, 1973). However, animals may use different aspects of experience to help shape the categories they form. By examining what can define category membership—for example, perceptual similarity, functional similarity, or abstract relationships—it becomes clearer when and where animals use experience to help organize and respond appropriately to the world around them. PERCEPTUAL CATEGORIZATION Categorization often relies on distinguishing stimuli based on their perceptual qualities, such as separating objects by color or shape. In some cases only a few key features of a stimulus are used for categorization, even if other features are perfectly perceptible. For example, the red belly of a male stickleback fish elicits aggressive behavior in competing males. Yet male sticklebacks equally display aggression toward a “red belly” of a model, which does not well resemble a fish (Tinbergen, 1951). The red belly in this example would be called a “sign stimulus” (Shettleworth, 2010). Although the term has fallen out of popularity because it is often assumed to involve an innate category, in reality a sign stimulus can still be subject to learning, for example via perceptual sharpening (Hailman, 1967). Despite some of the potential problems with the term, the concept itself can be useful because it breaks down category membership into its most basic form, which can reveal intriguing insight into the cognitive biases that guide some forms of categorization. For instance, if the features of a sign stimulus are exaggerated beyond what would be found in nature, then the animals’ response is exaggerated,

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forming what is known as a supernormal stimulus (or supernormal releaser). A famous example comes from an experiment on the long-tailed widowbird (Euplectes progne), a species in which female mate choice is based on the length of the male’s tail (i.e., the category of “preferred male” is determined by tail length). When the males’ tails were experimentally elongated beyond what would be evolutionarily possible, the females preferred these males above all others that retained their normal tail length (Andersson, 1982). Therefore categorization of this form relies most heavily on predetermined preferences for a particular stimulus. Generally, when categories are based on perceptual likeness, the closer a novel stimulus mirrors known categories, the more likely it is to be easily classified. The cue similarity hypothesis places this concept in an evolutionary context, by proposing that animals will be more likely to respond to a novel cue the closer it resembles one to which their ancestors responded (Sih, Ferrari, & Harris, 2011). For example, fish are more likely to categorize the odor of a novel predator as dangerous, the closer the novel fish’s odor matches their natural predator (Ferrari, Gonzalo, Messier, & Chivers, 2007). In addition to the biases animals have toward certain stimuli, perceptual categories can also arise from learning. Many lab-based category experiments rely on this ability, which stems from discrimination learning (which is associative in nature) and stimulus generalization. In this way, perceptual categorization is not particularly cognitively demanding, so long as animals have the memory capacity to form simple associations between a type of stimulus and a response. Animals often rely on perceptual categories when rapid responses are needed. The eyes of a predator are often a reliable indicator of danger, but a decision to flee must be made rapidly if the prey identifies a predator. Thus objects that carry eye-like features are often avoided as if they were predators. Certain prey species, such as butterflies, exploit this tendency for rapid categorization of eye spots in order to momentarily deter their predators before they have time to fully categorize prey (Vallin, Jakobsson, Lind, & Wiklund, 2005). Despite the usefulness of perceptual categorization for quick and easy to learn categories, there are many instances in which animals need to categorize stimuli that do not resemble each other. FUNCTIONAL CATEGORIZATION Even if stimuli overlap in some perceptual feature, they are considered to form a functional category if they share a common association with an outcome (Shettleworth, 2010). For example, although a strawberry and a tomato both share the color red, they are also both part of the functionally equivalent

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“edible” category. Moreover, lettuce leaves would also be part of this same functional category despite not sharing any perceptual features with tomatoes or strawberries. Members of a functional category may not be immediately apparent without understanding the underlying meaning of the category itself. For example, it was found that Sykes’s monkeys (Cercopithecus albogularis) classify monkey calls as similar to each other and classify them differently from bird calls. These categories are not likely based on perceptual similarity because when people were asked to categorize the calls, they mixed the monkey and bird calls into categories made of both types of calls (Brown, Sinnott, & Kressley, 1994). Functional categories can be much more useful for animals that need to respond to many different types of things with the same type of behavior. An animal for example that only eats one type of food, would not need a functional category of food since it could rely solely on perceptual features to guide its foraging behavior. In contrast, a species such as a rat, which scavenges for a wide variety of food types, must be constantly updating its category of food. In such a case, being able to place dissimilar items into the same category is highly useful for remembering what is and is not edible on subsequent encounters. Yet, similar to perceptual categorization, the formation of functional categories can rely on simple associations that many animals are able to learn from experience. ABSTRACT CATEGORIZATION Abstract categories emerge not from any property of the stimulus alone, but from its relationship with other stimuli1 (Shettleworth, 2010). One example would involve classifying stimuli based on whether they consistently occur above or below something else (see Figure 1.1). Juvenile chimpanzees show spontaneous evidence of this ability (Thompson, 1995). Meanwhile corvids can do this quite easily (Mackintosh, 1988; Wilson, Mackintosh, & Boakes, 1985), but pigeons appear to need thousands of trials before they are able to do so (Katz, Wright, & Bodily, 2007). It is not yet clear what selective pressures have led to the occurrence of abstract categorization abilities. Until quite recently abstract categorization was assumed to be a marker of higher order mental representation. However, the fact that a range of species from honeybees to chimpanzees appear to exhibit this type of categorization implies that even relatively small brains are able to group stimuli in this way. Importantly, though, the appearance of a categorization ability in one context does not signify that the animal will be able to use it in others. Therefore while honeybees can distinguish between stimuli in a way that transcends their perceptual and functional features, they likely only do this

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in a limited number of contexts, whereas other species may be able to use these abilities across many areas of their lives. A look into where and how animals use the three types of categories helps us better understand what other factors may make categorization cognitively demanding. Furthermore, toward the end of this chapter, we will suggest a framework that could be used to design and interpret research that may facilitate such a complex form of understanding. WHEN IS CATEGORIZATION COGNITIVELY DEMANDING? While all animals have the ability to categorize stimuli, they do not do it with equal complexity, frequency, precision, or speed. As seen earlier, there are a number of different types of categories that range in how much they rely on perceptual features or a deeper concept learning. Many species can learn these category types. But how much do they actually use these abilities in their daily lives? The evolution of categorization abilities, and the actual categories animals use depend largely on the surrounding environment (Shettleworth, 2010). For example, male crickets sing their species-specific mating calls. Females must categorize the sounds of many species and respond selectively only to their own. Female crickets that share the auditory space with species that sing both above and below the sound frequency that they make respond only to experimentally produced sound that fits within their range. Meanwhile crickets that do not neighbor any species above their range respond to a broader category of sound (Symes, 2014). Thus although many cricket species are able to form a “mate” category based on perceptual characteristics of sound, the defining features of their categories depend upon the complexity of the species community in which they live. Over evolutionary time similar types of pressures arising from foraging challenges, species competition, and the social environment have contributed to the array of categorization abilities seen throughout the animal kingdom. NUMBER OF CATEGORIES Species differ greatly in the number of categories they create and the extent to which responses toward categories are graded based on levels of perceived category membership. For example, while some species respond similarly to all cues that indicate the presence of a predator, others have more flexible categories that depend on the type of predator present. In vervet monkeys (Chlorocebus aethiops), for instance, individuals make and respond differently to antipredator calls that their group mates make, depending on whether the

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call refers to an aerial or ground-based predator (Seyfarth, Cheney, & Marler, 1980). Such distinctions and separate categories have been advantageous for survival, since successful escape behaviors depend on responding differently to threats from above or below. While the evolutionary advantages of responding in the correct manner toward different predators are clear, category membership can be very specific in some species, even when not tied to such direct survival need. There is evidence that ravens, for instance, have categories relating to expected versus unexpected dominance interactions, and that they react differently when listening to audio playbacks of individuals violating the groups’ hierarchy, as opposed to interactions that confirm the existing hierarchy (Massen, Pašukonis, Schmidt, & Bugnyar, 2014). While such an ability is not as immediately related to survival as fleeing a predator, being able to categorize social interactions so precisely must have had an evolutionary benefit for ravens living in a close-knit social group with a strict dominance hierarchy. Category complexity can stem not only from the number of categories an animal makes, but also from the subtleties of category membership. Some species display graded categories, in which the same response changes intensity based on some feature of the stimulus that does not rely on stimulus intensity alone. An example of this would be responding to different levels of threat, based on context. For instance, although wild elephants are often subject to poaching, they only categorize people as dangerous in poaching contexts, but not in other contexts where people behave differently (Goldenberg, DouglasHamilton, Daballen, & Wittemyer, 2016). Other species, such as tufted titmice (Baeolophus bicolor), a small songbird, show a similar type of ability by responding warily to the presence of cats, but the extent of wariness depends on the head and body orientation of the cats (Book & Freeberg, 2015). While distinguishing species based on the number and detail of categories they create helps separate some species from others in their categorization abilities, the ability to form detailed categories alone does not necessarily denote cognitive capacity. For example, pigeons excel at learning categories, and retaining them, but having the ability to form such categories could rely more heavily on having a detail-oriented visual system rather than a higher level of intelligence. When investigating other aspects of category formation, such as how quickly animals learn new categories, the cognitive prowess of some species becomes clear. FLEXIBILITY AND RULE LEARNING IN CATEGORY ACQUISITION The flexibility with which animals acquire new categories can be an indicator of cognitive capacity. Broadly defined, intelligence involves the use of extractable rules to guide flexible behavior in the face of changing or

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uncertain conditions (Greggor & Thornton, 2016). Since category learning allows animals to more easily cope with novel stimuli, animals that more quickly and efficiently learn categories have been selected for greater intelligence in categorization contexts. In line with this hypothesis, birds from the crow family (corvids), which are considered to be more intelligent than many bird species (Emery & Clayton, 2004), are able to flexibly transfer a rule learned about one set of stimuli to a new set, while pigeons generally show no such ability (Wilson et al., 1985). Pigeons similarly underperform humans, macaques, and capuchin monkeys on rule-based categorization (David et al., 2012), suggesting that much of their categorization relies on rote-memory. Therefore even though pigeons may treat stimuli similarly to other species, the learning process underlying their categorization behavior can be markedly different. In their case, and in all other cross-species comparisons, the aim in identifying more cognitively challenging methods of categorization is not to crown a champion of categorization. Many species excel in different categorization contexts. However, by identifying abilities that require greater cognitive capacity than others, it helps shape our understanding of the animal mind, and the environments that have led to the development of abilities not dissimilar to our own. UNDERSTANDING THE COMPLEXITY OF CATEGORY USAGE IN ANIMALS Up until this point we have offered a series of examples of how animals employ categorization as a basic skill in their lives. In this concluding section we will suggest a way of integrating these findings. Our integrative model will take the form of a mapping sentence (see for example: Canter, 1985; Cohen, 2012; Hackett, 2014a, b, 2016; Hildebrandt, 1986; Levy, 1976, 1990), in the context of animal categorization, the mapping sentence is a précis that lists the underlying noun categories that animals employ to facilitate their daily lives along with indicators of category usage. This summary is stated in the mereological form of the mapping sentence for category usage in animals, which is shown in Figure 1.2. In the above mapping sentence the first thing to note is how to read the sentence. The reader starts at the beginning and reads along the sentence as if reading ordinary English prose. The first part of the mapping sentence that needs explanation is the “(x)” which designates a specific individual animal, animal group or species of animal that is the subject of the specific research being described in the mapping sentence. Upon reaching the first facet, that of ability, one of the elements is selected to be included in the sentence (select either: able, may be trained, unable). The procedure of reading continues

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Figure 1.2  Mapping sentence for category usage in animals.

through the connecting phrases until reaching the next facet, from which a single element is selected for this particular reading. This process is repeated until reaching the range facet. Within the range is embodied the criterion of evaluation or understanding that the mapping sentence encompasses and an element is not selected, but rather a given level is a reflection of the veracity of the declarative sentence that has been assembled by the particular selection of facet elements. Thus, the selection of a particular set of facet elements is assigned a value from the range facet that reflects the extent (in our case, high to low) of the event, object, or state of existence that is specified in the mapping sentence. We will now apply these general principles for understanding and reading a mapping sentence to the mapping sentence for category usage in animals. The facets that precede the range facet in the mapping sentence breakdown and specify the usage of categories in the specific animal. The facets that have been included, along with the elements within each of the facets, have been developed from the literature reviewed earlier in this chapter. Using these research-driven findings, the mapping sentence’s content facets (emboldened in Figure 1.2) stipulate that a specified ­animal’s use of categories (this may include humans) is understood in terms of: the animal’s ability to use categories; Some categorizing behavior in animals occurs in a natural setting of the animal, other categorizing (often complex) can be taught (see for example, Qadri, Sayde, & Cook, 2014), while some species or individual animals are not able to perform some categorizing tasks.

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the status of this ability; Some animals may form new categorizing abilities within a given context, others may deploy existing categorizing abilities for a specific situation. the type of expression through which a category is employed; The categories formed and used may be functional, perceptual, or abstract in their nature. the referent of this expression; Categories may be formed through either the differences or the similarities that exist between stimulus events. the situation within which the category is used; An animal may be observed to display the categorizing abilities that they possess in either a laboratory or within their natural habitat. the indicator employed to investigate category usage; The use categories that an animal uses may be evidenced through a variety of different outcome measures. These will take the form of measures of an animals’ speed of categorizing based task performance, the complexity of their categorical performance, or the flexibility (adaptability and transferability) of their use of categories in performing a task. Finally, these content facets, which define the content of category usage in animals, the range facet asserts that category usage in animals is associated with the level or extent (in terms of this being high to low) of the specified animal’s cognitive complexity. Thus, the mappings declarative statement is that an animals’ use of categories, as specifically determined through the particular combination of facet elements, is related to the complexity of cognition associated with that species. Kaplan (2014) cited research by Goldstone and Hendrickson (2010) when she stated that “we do not know enough (actually: next to nothing) on how animals categorize their environment” (Kaplan 2014, p 72). The mapping sentence is a categorial ontology that classifies how an individual animal or event in which an animal uses categorization may be understood through this formal declarative statement. The mapping sentence offers a clear depiction of the contextually based understanding of category usage in a manner that may also be used to facilitate further research. We suggest that studies need to be designed using the mapping sentence as a template. We make such a claim as it has been found in many other behavioral domains in which the mapping sentence approach has been used that the content area of interest has been clearly explicated and individuals and groups have been typified in terms of their relationship to the research

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domain taken as a whole. After having designed research using the above mapping sentence, analyses may be undertaken to reveal the relationships between the facets and their elements (the noun categories and the mutually exclusive forms the facets may take in reference to the topic of study). The combined roles of facets in relation to the range given in a mapping sentence are investigated using smallest space analysis (SSA). This procedure uses nonparametric measures of association to analyze data from research instruments that have been designed to exclusively incorporate elements from the facets specified in the studies mapping sentence. Graphical patterns of association then support or refute the veracity of the mapping sentence as a hypothesis of how a given event (in our categorization behavior) is experienced or deployed. Following the issuance and verification of a declarative statement in a mapping sentence, further analyses may be undertaken that demonstrate how individual’s animals can be typified by their full-profiles on the facet elements.2 Profile analysis is undertaken through partial order scalogram analysis (POSA). In POSA a profile is assembled for an individual respondent (animal) in terms of their responses to each of the facets in the mapping sentence. This analysis facilitates an understanding of the quantitative responses by an individual (for instance, the summated amount of category usage by an animal) and how the different types of categorical behaviors are realized in an individual participant (e.g., an individual animal’s differential usage of functional, laboratory based, transferable, etc.). Our mapping sentence is of course speculative. It has been developed in order to provide a declarative representation of categorizing behavior in animals. It has been developed through reference to the pertinent research findings regarding categorization in animals that were presented in the initial sections of this chapter.3 By designing research instruments (observations, measurements, lab tasks, literature reviews, meta-analyses) which incorporate single elements form each of the facets, it is possible to investigate the combined effects of the facets upon animals’ use of categories.4 SUMMARY AND CONCLUSIONS The exploration of categorization by the animal mind reveals several major themes: Many if not all animals appear to categorize, but they do not do so equally. The same procedures used to probe category learning can also help researchers understand how animals classify natural stimuli. Category membership can be based on perceptual, functional, or abstract similarity.

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Speed, complexity, and flexibility of categorization are indicators of cognitive capacity. There is still much to learn about how animals categorize the world around them, including their use of abstract concepts. Such research in future not only will help us understand more about the animal world, but also more about our own behavior, cognitive biases, and category construction. The mapping sentence for existential category usage in animals offers a theoretical model for understanding animal categorial behaviors. This mapping sentence template provides an explicit framework for the design of research to investigate categorization as a behavior in animals, including human beings. Through using the mapping sentence to design research projects to investigate different animal species’ use of categories will result in comparable research findings and has the potential for the development of cumulative knowledge about animals’ category usage. SSA and POSA analyses have the possibility to reveal much about the nature of category usage and how animals may be characterized by their combined use of different forms of categorical behavior. NOTES 1. The interrelationship between categorial behaviors is central to understanding the use of categories by animals. Later, we depict this interplay using a mapping sentence. 2. This research is part of the second author’s ongoing research program in the investigation of avian behavior using a facet theory approach. 3. See: Levy, 1976 for details on using a mapping sentence to coordinate a research project. 4. This is another component of Hackett’s current research.

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Chapter 2

Necessary Categories of Conscious Experience Gal Yehezkel

BACKGROUND The idea that there are necessary categories, that is, concepts, for conscious experience is ancient, and numerous thinkers have attempted to uncover the necessary ways in which a subject must conceive reality in order to be self-conscious, that is, to be conscious of his or her own experience.1 The difficulty of establishing any such list is apparent. Such an account must rely on a theory about the nature of concepts and the role they fulfill in cognition, on an explanation of the mysterious notion of self-consciousness, and on a conceptual analysis, which exposes the necessary conditions for conscious experience. In what follows I put forward a model of conceptual analysis, and implement this model in an analysis of the concept of self-consciousness, in order to uncover its supporting conceptual structure. The conclusions of this analysis describe some of the necessary categories of conscious experience. The concept of the self (for non-solipsist subjects), the concept of consciousness, the concept of objectivity, the temporal distinctions between past, present, and future, and finally the idea of natural regularities which connect different types of events in different times are found to be necessary categories for conscious experience, and hence describe the fundamental cognitive structure of self-conscious beings.2 In section 2, I begin my investigation by outlining the conceptual framework of my analysis. In section 3, I implement this framework in an analysis of the concept of consciousness. My analysis shows that this notion relies on a distinction between objective reality and the subject’s consciousness of it. In section 4, I explore the notion of self-consciousness, and show that the notion of the self (“I”) is necessary for self-consciousness for a non-solipsist 19

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subject. In section 5, I argue that in self-consciousness the subject is aware of himself or herself as a temporally extended point of view (consciousness) over objective reality, and hence that indexical temporal distinction are necessary for self-consciousness. In section 6, I show that in order to distinguish between one’s consciousness and objective reality, a subject must rely on the premise that objective reality is subject to natural regularity. In section 7, I summarize the conclusions of my analysis. CONCEPTUAL ANALYSIS Categories are concepts. However, rather than clarify the notion of a category, this definition raises the question: what are concepts and how do they relate to our experience? Rather than develop a full-blooded theory of meaning, in what follows I rely on some generally accepted features of language in order to offer a better understanding of the use of expressions in language in order to describe reality. This analysis not only suggests a better understanding of concepts and their relation to experience, but further enables us to extract necessary conditions for the meaningfulness of expressions in language. These conditions are the basis for the conceptual analysis, which is undertaken in the following sections. I should stress that this analysis relies on some as basic and undisputed as possible features of language, in order to secure conclusions, which are not committed to any specific theory of meaning, and can and should be accepted by any theory of meaning. I begin by clarifying the terminology I use. A concept is the meaning of a word (or an expression), that is, a sign in language. Whether the use of a word determines its meaning or its meanings determine its use, the meaning of a word is reflected in its use. In order to achieve better understanding into the nature of concepts it is therefore helpful to examine the use of words in language, and the necessary conditions for this use. Due to the fact my interest in this discussion lies in the use of language to describe the contents of experience, it is declarative sentences which are the focus of my analysis.3 These sentences express propositions (i.e., their meanings) which aspire to describe reality. These propositions are true if they successfully describe reality, and false otherwise.4 In order to uncover the function which a word fulfills in describing reality, that is, the meaning of that word, it is advisable to examine the necessary conditions for a word to contribute to the meaning of a sentence in which it appears. For it is sentences which are used in order to describe reality, and hence the (descriptive) meaning of a word is its contribution to the meaning of sentences in which it appears.5 Let us examine, for example, the sentence Kant is a happy bachelor. The word happy clearly contributes to

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the meaning of this sentence, as evidenced by the fact that the sentence Kant is a bachelor, which results from omitting this word, has a different meaning. The difference in meaning is shown by the possibility that the latter sentence expresses a true proposition while the original sentence expresses a false proposition. The word unmarried, on the other hand, clearly does not contribute to the meaning of the sentence Kant is an unmarried bachelor. This is evident from the fact that the proposition which results from omitting this word, that is, Kant is a bachelor, is logically equivalent to the original proposition. The reason for that is obviously the impossibility of a married bachelor.6 Notice that I do not argue that sentences which express logically equivalent propositions are synonymous. I argue that if two sentences, one of which results from omitting a certain word from the other (original) sentence, express logically equivalent propositions, the appearance of that word in the original sentence does not contribute to its meaning. A necessary condition for the meaningfulness of an appearance of a word in a sentence is therefore that its negation results in a sentence which expresses a contingent proposition. Thus, the appearance of a word in a sentence can be viewed as a coordinate of a conceptual dimension which includes different possibilities. That word is used, by appearing in the positive or in the negative, in order to map that dimension. For example, the proposition Kant is a bachelor is located in a conceptual space which includes the two dimensions which are described by Table 2.1. The word Kant is used in order to distinguish between Kant and other possible subjects who can be bachelors, while the word bachelor is used in order to distinguish between Kant being a bachelor and other marital statuses. The meaning of a word, that is, the concept, is therefore its use for mapping the different possibilities which are included in a certain conceptual scheme. This is a necessary condition for the meaningfulness of a word, that is, for the inclusion of a concept in a conceptual scheme. I should stress that this view of concepts does not contradict, for example, Kant’s conception of concepts as functions for organizing, or synthesizing, representations (B93). I do not attempt to present here a full-blooded theory of meaning, that is, a theory of meaning which also specifies what it is for a subject to possess a concept, but merely to describe a necessary condition for possessing a concept. Table 2.1 The Conceptual Space of “Kant is a Bachelor” Kant is a bachelor. Someone who is not Kant is a bachelor.

Kant is not a bachelor. Someone who is not Kant is not a bachelor.

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If a concept is a meaning of a word, does this definition imply that creatures that do not use a language also do not possess concepts? And if concepts are necessary for conscious experience, does that mean that creatures that do not use a language are not conscious of their experience? Rather than attempt to tackle these difficult questions, I would like to suggest a way to circumvent them. The previous analysis shows that the meaning of a word, that is, a concept, is its use for mapping different possibilities, that is, for making certain distinctions. Hence, a necessary condition for a subject to be able to possess a certain concept, for example, bachelor, is that the subject is able to find a use for the word bachelor. That is, the subject’s experience must include the necessary intricacy which is needed in order to find a use for the word bachelor for its description. Thus, the conceptual intricacy of our language, which gives meaning to a certain word, should reflect the structure of our experience. Thus, a conceptual analysis can expose necessary categories of experience, without assuming that that subject of experience fulfills the sufficient conditions for actually possessing a language. The only premise of this inquiry is that in order to possess a certain concept, that is, a certain use of a word, the subject’s experience must include the necessary intricacy for making the word useful, or meaningful, for its description.7 This premise is acceptable even if actual possession of a language is itself a necessary condition for conscious experience or even for experience per se. The necessary categories of conscious experience are therefore the meanings of the words which must find use in describing the contents of every possible conscious experience. CONSCIOUSNESS AND OBJECTIVITY The first question that should be asked is: what is a subject, who is conscious of his or her own experience, actually conscious of? What is the difference between, for example, a computer which can identify, relying on sensors, that a certain man, for example Garry, is using the computer (e.g., for security reasons), and a subject which does not only recognize that Garry is using the computer, but is also conscious of this recognition? To begin with, a necessary condition for ascribing any content of experience to a subject is that the subject should be able to make the distinctions which are reflected in the conceptual space in which the proposition, which is supposed to describe the content of this experience, is located. For example, the sentence Garry is using a computer includes (at least) three separate components, which relate to different conceptual dimensions, and are mapped by three different words Garry, using, and computer.8 Hence, a subject can

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be said to experience that Garry is using a computer only if he or she can distinguish between Garry and someone else (not-Garry), between using and not using something (e.g., just sitting in front of the computer), and between using a computer and using something else (e.g., a hammer). If the alleged subject of experience has no use for any of these distinctions for describing his or her possible experiences, it cannot be said that Garry is using a computer accurately describes the content of his or her experience. Obviously, this is a necessary condition, rather than a sufficient condition, for being conscious that Garry is using a computer. In conscious experience a subject is not only conscious, for example, that Garry is using a computer. He or she is also conscious of his or her experience, and hence that I experience that Garry is using a computer, or I am conscious that Garry is using a computer. The difference between the concept of experience and the concept of consciousness is mainly in their extension. The concept of consciousness is more inclusive than the concept of experience, and applies to all forms of awareness of things in the world, including our awareness of things which we do not experience, for example, my awareness of the existence of the wall behind me. Hence, if a subject experiences that p, he or she is also conscious that p, but not vice versa. The concept of consciousness is therefore more basic than the concept of experience, and will be the focus of my analysis.9 Allegedly, conscious experience requires the categories of the first-person (or the self), and consciousness. However, before committing to these conclusions, I suggest exploring some of the conceptual intricacy which supports first-person ascriptions of consciousness. I begin by focusing my attention on the concept of consciousness, and only later (in the next section) examine the first-person. In order to better understand what is involved in acknowledging that one is conscious, I begin by examining the ascription of consciousness to other subjects of consciousness, for example in the sentence Deep Blue is conscious that p. This sentence is located in a conceptual space which includes (inter alia) the possibilities which are demonstrated in Table 2.2. The word conscious is used in order to distinguish between awareness and unawareness of a certain fact p. It is a necessary condition for the meaningfulness of the word conscious, that is, for its being useful in mapping these possibilities, that p is an objective fact, that is, a fact that is independent of the subject’s consciousness. This is the case if p describes a physical fact, Table 2.2 The Conceptual Space “Deep Blue is Conscious that p” Deep Blue is conscious that p. Deep Blue is conscious that not-p.

Deep Blue is not conscious that p. Deep Blue is not conscious that not-p.

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for example, the fact that Garry is using a computer. In this case, there are indeed four conceptual possibilities, which are described by Table 2.2. However, suppose that p describes something subjective, that is, that cannot exist without the subject’s consciousness of it, such as its own pain. Allegedly, a sentence which ascribes consciousness of pain to Deep Blue (supposing that it can feel pain) is located in a conceptual space which is represented in Table 2.3. It is clear however that Table 2.3 does not describe four different conceptual possibilities. This is evident from the fact that propositions (A1) and (B2), and on the other hand propositions (A2) and (B1), are logically equivalent. For either Deep Blue is in pain, in which case propositions (A1) and (B2) are true, and propositions (A2) and (B1) are false, or Deep Blue is not in pain, in which case propositions (A1) and (B2) are false, and propositions (A2) and (B1) are true. There are only two conceptual possibilities which are represented in Table 2.3, which can be described by simple ascription or denial of pain, as in Table 2.4. As this analysis clearly shows, the concept of consciousness is useless in describing subjective facts. The meaning of words such as conscious, experience, see, hear, and so on, derives from their use in sentences which describe subjects’ awareness of objective facts, rather than subjective facts. The reason for this is simple. These concepts, much like the concept of knowledge, imply truth. Just as it follows from the proposition Garry knows that Deep Blue is a computer that Deep Blue is a computer, it follows from the proposition that Garry is conscious that Deep Blue is a computer that Deep Blue is a computer. If p is a subjective fact, which implies consciousness of it by a certain subject, it is impossible to distinguish between the subject’s consciousness of p and p—they are logically equivalent and describe the same conceptual possibility. Hence, ascriptions of consciousness are meaningful only if a subject is ascribed a consciousness of a fact which is independent of his or her consciousness. Concepts of consciousness, such as awareness, experience, and so on, are therefore conceptually tied with the concept of objectivity. It is impossible to find a use for these concepts unless they relate to what is independent of the consciousness of the subject to whom they are attributed. The meaning of the words conscious, experience, and so on, depends on their use for describing Table 2.3 The Conceptual Space of “Deep Blue is Conscious that it is in Pain” A1. Deep Blue is conscious that it is in pain. A2. Deep Blue is not conscious that it is in pain.

B1. Deep Blue is conscious that it is not in pain. B2. Deep Blue is not conscious that it is not in pain.

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Table 2.4 The Conceptual Space of “Deep Blue is in Pain” Deep Blue is in pain. Deep Blue is not in pain.

the objective reality, that is, the physical realm, rather than the mental realm. While the first necessary category for conscious experience is that of a consciousness, the second necessary category is therefore the category of objectivity.10 I stress again that I do not argue that a subject must have, in his or her vocabulary, the terms consciousness, and objectivity. The subject must however have the ability to make the necessary distinctions which are required for finding a use for these terms. This ability can be demonstrated in a variety of abilities in which the distinction between what a subject thinks of reality and reality itself is manifested. For example, it is reflected by a child’s ability to understand Little Red Riding Hood’s mistaken reference to the wolf as her grandmother, or a child’s attempt to lie, that is, to make another subject believe something the child knows is not true. Both cases rely on an understanding of the difference between what a subject thinks and what is objectively the case. SELF-CONSCIOUSNESS AND THE FIRST-PERSON In the previous section the discussion is limited to third-person ascriptions of consciousness. In this section I turn attention to first-person ascriptions of consciousness. For it seems that in order to be conscious of one’s own consciousness, the subject must be able not only to identify the content of his or her consciousness as contents of a conscious being, but also to correctly ascribe this consciousness to himself or herself, rather than to someone else. Notice that conscious experience requires a subject to identify himself or herself, out of all possible subjects of consciousness, using the first-person, rather than any other term which refers to himself or herself.11 For the subject may be able to identify that Garry is using a computer, and a subject, for example, Deep Blue, as the subject of this consciousness, but fail to recognize that I am Deep Blue. Thus, being able to experience p, and being conscious that a is conscious that p, does not guarantee an awareness that I am a, and therefore does not amount to a conscious experience.12 This brings me to the mystery of self-consciousness, which has plagued philosophers since Hume. The question is in what way a self-conscious subject is conscious of himself or herself. It is clear that a self-conscious subject is not merely a subject who identifies himself or herself. In order to achieve

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self-consciousness it is not sufficient, for example, for a subject to recognize himself or herself in the mirror as subject of consciousness. If a Siamese fighting fish it trying to attack its own mirror image, it is clear that it sees itself but fails to recognize that it is itself. Furthermore, an ape may recognize its image in a mirror, and far from attacking it, may even be able to use its image, for example, for recognizing and successfully removing a leaf from its head (which it cannot see directly). However, even this is not sufficient for self-recognition, just as the fact that I intentionally mirror the gesture of someone at the dinner table in order to remove a piece of food which is stuck to my chin does not imply that I am identifying him or her as myself. In order to be self-conscious it is therefore not sufficient for a subject to identify a certain subject of consciousness, even if that subject is himself or herself. In order to recognize a subject of consciousness as himself or herself the subject must be able to identify the unique position of this subject of consciousness, among all other subjects of consciousness, as the subject to which his or her own descriptions of consciousness should be attributed. For example, if a subject makes the judgment that Garry is using a computer, and is conscious of this consciousness as an consciousness, he or she will be able to ascribe to themselves this consciousness, and conclude that I am conscious that Garry is using a computer. However, not any self-ascription of experience constitutes self-consciousness. This brings me to the uniqueness of the singular first-person pronoun. In order to understand the uniqueness of the first-person, consider for example the following scenario. A child sees and reports that Garry is using a computer. The child then asked, Who sees that Garry is using a computer? The child then tries to find the answer by looking around, and might even find the right answer, for example by seeing his or her reflection in the mirror looking at Garry. The child then reports that I am seeing that Garry is using a computer. In this example however the child is using the first-person pronoun as if it was a third-person pronoun, and therefore this child is not self-conscious. For to be self-conscious one must acknowledge that every description he or she gives of reality reflects his or her point of view of reality. If the subject is aware of this fact, he or she will not need to attempt to empirically identify the correct subject of consciousness when asked to do so. In fact, the reason that no empirical identification process is involved is exactly why mistaken identification is impossible. While it makes sense to ask are you sure it is Deep Blue who sees that Garry is using a computer? it is senseless to ask are you sure it is you who sees that Garry is using a computer? This understanding of the uniqueness of the first-person is exactly the discovery which is reflected in Descartes’ Meditations (Descartes 1984, 17 [25]). It is impossible to doubt the existence of the self because its existence

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follows from every proposition which the subject holds. In fact, assuming that reality is described from the first-person point of view, it is possible to prove the existence of the subject by a reductio ad absurdum. Assume that I do not exist. It follows that I think that I do not exist, from which it follows that I think and hence that I exist. Since the conclusion of the arguments contradicts its premise, it follow that the premise is false, and therefore that I exist. Again we see that it is impossible to be wrong about the identity of the subject, not because it is impossible to misidentify the subject, through some mysterious fail-safe mechanism, but because no empirical identification process is involved. This is also the solution to Hume’s query about the missing impression of the self (1978, 251). Self-consciousness does not rest on the identification of any empirical fact, but is rather of a conceptual nature. Does this conclusion imply that the notion of the self is a necessary condition for self-consciousness? I believe that it is a necessary condition only for a subject whose conceptual scheme includes the possibility of the existence of other subjects of consciousness, that is, a subject who acknowledges the possibility of other subjects of consciousness. For the first-person is used in order to distinguish between the self and other subjects of consciousness.13 This function of the first-person is demonstrated in Table 2.5, which exposes the conceptual dimension in which the first-person pronoun is located. If the subject acknowledges the possible existence of multiple subjects of consciousness, a self-ascription of consciousness is indeed a necessary condition for self-consciousness. For in this case the subject must identify the correct subject of consciousness in order to be self-conscious, and for this purpose he or she must use the first-person pronoun. What happens, however, if the subject does not recognize the possible existence of other subjects of consciousness? In this case the first-person, that is, I, has no use, and therefore the subject has no notion of the self. This subject, which following Strawson (1959, 73) may be described as a true solipsist, would have no use for any index in order to distinguish between different subjects of consciousness, and therefore would simply say There is a consciousness that Garry is using a computer, instead of I am conscious that Garry is using a computer. A true solipsist has no concept of the self. This does not imply that a true solipsist cannot be self-conscious. In order to be self-conscious a true solipsist does not need to identify his or her own consciousness, due to the fact that a true solipsist only acknowledges his or her consciousness. All that a Table 2.5 The Conceptual Dimension of the First-Person Pronoun I am conscious that “Garry is using a computer.” Someone who is not me is conscious that “Garry is using a computer.”

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true solipsist needs in order to express his or her self-consciousness is the readiness to infer, from any proposition p, which the true solipsist accepts as true, the conclusion There is a consciousness that p, analogically to the readiness of a non-solipsist self-conscious subject to infer from any proposition p the conclusion that I am conscious that p. Thus a true solipsist can express the uniqueness of the only consciousness he or she acknowledges, as the consciousness from whose point of view every proposition he or she holds true is described. The surprising conclusion is therefore that the concept of the self, which is expressed by the first-person pronoun, is a necessary category for selfconsciousness only for non-solipsist subjects, such as normal human beings, who acknowledge the possibility of other subjects of consciousness. In order to be self-conscious, these subjects need to self-ascribe their experiences using the first-person.14 It is not a necessary condition for self-consciousness in a case of a true solipsist.15 The need for a category of the self, as a necessary condition for selfconsciousness for non-solipsist subjects, may further imply other necessary conditions. For example, Strawson argues that the concept of the self should be a concept of a person, that is, an entity who has both mental and physical characteristics (Strawson 1959, 87–116). This is due to the fact that ascribing mental predicates to others, which is a necessary condition for self-ascription of consciousness, is possible only if these subjects of consciousness are corporeal, for it is impossible to identify mental states directly. Exploring this suggestion is however beyond the scope of this investigation. SELF-CONSCIOUSNESS AND TIME I continue in what follows to extract the necessary conditions for self-ascription of consciousness, as demonstrated, for example, by the proposition I am conscious that Garry is using a computer, turning my attention to the firstperson ascription of consciousness. In order to examine the contribution of the word conscious, to the meaning of the sentence I am conscious that Garry is using a computer, let us examine the possibility of first-person denial of consciousness, as exemplified in Table 2.6.

Table 2.6 The Conceptual Dimension of First-Person Ascription of Consciousness I am conscious that “Garry is using a computer.” I am not conscious that “Garry is using a computer.”

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The word conscious is used in order to distinguish between things of which the subject is conscious and things of which the subject is not conscious. As the analysis in section 3 shows, the concept of consciousness implies truth. Hence, in order to meaningfully ascribe consciousness of p to a subject a, p must describe an objective fact, that is, a fact which is independent of a’s consciousness. Hence, in order to be self-conscious, that is, to be able to meaningfully ascribe to oneself a consciousness of p, the subject should be aware of the possibility that I am not conscious that p, but p. However, the difficulty that arises is that it seems that this possibility spells a contradiction. For from the premise that I am not conscious that p, but p, the subject can infer that p. If the subject is indeed self-conscious, he or she can hence conclude that I am conscious that p, which contradicts the premise of this argument. The difficulty before us is therefore to explain how a subject can be conscious of his or her own consciousness, given the trivial premise that his or her consciousness is limited to things of which he or she is conscious. Selfconsciousness requires a subject to be able to draw the distinction between his or her consciousness and the things of which he or she is conscious. This however seems to require the subject to be conscious of things that he or she is not conscious of, which is a contradictory condition. In order to understand how self-consciousness is nevertheless possible, let us examine another conceptual distinction which was so far ignored, that is, the temporal distinction. The sentence I am conscious that p is formulated in the present tense, and implies the distinctions between past, present, and future. Once these distinctions are laid bare, it is easy to explain the meaningfulness of first-person ascriptions of consciousness. For time allows a subject to acknowledge the limits of his or her consciousness without contradiction, as seen in Table 2.7. A subject is unable to draw the distinction between his or her consciousness and the things of which he or she is conscious in the present, as exemplified by proposition (2). However, no similar difficulty arises in propositions (1) and (3). Proposition (1) is explained by a subject’s ability to learn of a fact p of which he or she was not conscious in the past. In proposition (3), on the other hand, a subject predicts his or her future unawareness some facts. The meaningfulness of past and future first-person denials of consciousness can thus explain the meaningfulness of present first-person denials, and hence also of ascriptions of consciousness. The importance of the temporal distinctions between past, present, and future, in contrast to other temporal distinctions, such as dates for example, is twofold. First, these distinctions are relative to the time of their use by the subject, and hence describe reality from the subject’s point of view. They therefore accurately describe the contents of a subject’s consciousness.

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Table 2.7 The Temporal Dimension of First-Person Denial of Consciousness 1. I was not conscious that p, but p. 2. I am not conscious that p, but p. 3. I will not be conscious that p, but p.

Furthermore, these distinctions change in time, such that what was once present is later conceived to be past, and what is now future will later be conceived as present. Hence, the meaningfulness of past and present firstperson ascriptions of consciousness implies the meaningfulness of present first-person ascriptions of consciousness. Time thus enables a subject to be conscious to the limits of his or her consciousness, and thus become conscious of his or her existence as a consciousness, that is, it enables a subject to be self-conscious. This implies that a self-conscious subject conceives of himself or herself as a temporally extended point of view (consciousness) over objective reality. The temporal distinctions between past, present, and future are thus found to be another necessary category for conscious experience. OBJECTIVITY AND NATURAL REGULARITIES The analysis of the previous section shows that in order for a subject to be aware of his or her consciousness, the subject must be able to find a use for the distinction between his or her consciousness and the things of which he or she is conscious. The subject is able to make this distinction without contradiction in the past and in the future, as demonstrated in Table 2.7. In what follows I further explore necessary conditions for making this distinction. The difficulty of making the distinction between objective reality and the subject conscious of it is that if the subject was not conscious in the past that Garry is using a computer, it is unclear how he or she can be conscious of this fact now. The same difficulty applies to the future. For we need to explain how the subject can be conscious now that he or she will not be conscious that Garry will use a computer. Due to the fact that these difficulties are symmetrical, I focus in what follows on the necessary conditions for drawing this distinction in the past, and only later show how this the same solution applies to the future. The way we actually apply this distinction in the past is obvious. We rely on current evidence for previous occurrences of which we were not conscious at the time. For example, I did not see Garry using a computer, but I might (a) find my computer turned with Garry’s user account logged in, or (b) rely on a surveillance camera which clearly shows him using the computer, or (c) rely on the evidence of someone who saw him using the computer. What is common to

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these and other possible scenarios is that in each such example I can rely on current evidence in order to learn about past occurrences. A necessary condition for the validity of such inferences is a regularity which ties together occurrences in different times, such that an occurrence of a later event is a sufficient condition for an occurrence of an earlier event. For example, according to the first explanation (a), certain limiting conditions can enable me to conclude, based on the state of the computer now, about someone who used this computer in the past. According to the second explanations (b), current recording is reliable evidence of past occurrences. According to the third explanations (c), current memories can accurately describe past occurrences. Thus it is by relying on regularities which connect together occurrences in different times that we are able to extend our awareness to past events, of which we were not conscious at the time. The same explanation applies to the possibility of being aware now of future occurrences of which we shall not be aware in the future. If I know I am about to undergo a procedure in which I shall be anesthetized, I can know now both about the procedure that I am about to undergo and my future unawareness of it. Again, this example demonstrated that a reliance on regularities, which tie together events at different times, such that the occurrence of an earlier event is a sufficient condition for the occurrence of a later event, enable us to extend our consciousness to future occurrences. Although these examples show that the idea of natural regularities is sufficient for supporting the distinction between a subject’s consciousness and objective reality, they do not show that it is also a necessary condition for supporting this distinction. In order to show that natural regularities constitute a necessary condition for conscious experience it is necessary to show that only under the assumption that reality is subject to natural regularities can a subject find a use for the distinction between his or her consciousness and objective reality. To remind you, the difficulty we are facing is to explain a subject’s ability to be conscious of the distinction between his or her consciousness and objective reality, as exemplified for example in the proposition (1) I was not conscious that p, but p. In order to be self-conscious, a subject must be able to expand his or her consciousness beyond what he or she was conscious of in the past. There are two ways of gaining awareness of objective reality, direct and indirect. The direct way of gaining consciousness of objective reality is through sense perception. In sense perception one can gain knowledge of the truth of singular propositions, such as Garry is using a computer. This form of gaining awareness is direct, in the sense that it is not the conclusion of any inferential process. I can simply see, for example that Garry

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is using a computer. Can sense perception, or a similar ability to directly gain an awareness of objective reality, explain how a subject can learn that I was not conscious that Garry was using a computer, but Garry was using a computer? The first question that should be considered is whether it is possible to perceive the past. If it is only possible to perceive the present, sense perception alone cannot explain how a subject can now gain awareness of past occurrences of which he or she was not aware at the time. Sense perception however does allow us to perceive the past. For example, due to the speed of light, we actually always see past occurrences, and the further away from us they take place the more we see into the past. Since it is physically possible to gain knowledge of the past directly, can this alone explain the possibility of extending our awareness of past occurrences of which we were not aware at the time? The answer is negative. For although it is possible to directly perceive the past, a subject must be able to determine that his or her present perception describes a past occurrence. How can a subject who currently perceives for example that Garry is using a computer, determine the time of this occurrence? Since time itself cannot be perceived, it is only with the help of events in time that we can determine a temporal location, that is, their temporal relations to other occurrences. This is possible only by relying on natural regularities which help us to determine relative temporal relationships. For example, natural regularities help us to determine that, of the two photos which fell out of the family album, the one in which the kids are smaller is earlier. If there was no natural regularity involved here, it would have been impossible to determine their temporal relation. Watching a calendar or a clock does not circumvent the need to rely on natural regularities, for these methods of measuring time are likewise based on natural regularities. Identifying events as simultaneous with certain positions of the regular movement of a clock’s hands thus enables us to determine their temporal relations to other events. Building a systematic representation of objective reality, which is independent of our consciousness of it, based on our sense perception alone, is thus found to be impossible. It is necessary for a subject to rely on some indirect way of gaining awareness of objective reality in order to explain the possibility of extending our awareness of past occurrences of which we were not aware at the time. This is possible if a subject infers the existence of a past occurrence based on another occurrence which he or she perceives. Only if a subject is aware of a general regularity, which ties together occurrences of type F with occurrences of type E, such that if an event of type F occurs it is necessarily preceded, or followed, by an event of type E, is he or she able to extend their consciousness beyond what he or she directly perceives.

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These considerations show that in order to make the distinction between his or her consciousness and objective reality a subject must rely on the premise that objective reality is subject to natural regularities, which tie together occurrences at different times.16 This general regularity allows the subject to expand his or her awareness of objective reality beyond what he or she directly perceives, by allowing the subject to infer, based on occurrences at one time, about occurrences at different times. I should stress that I do not argue that the natural regularity which is revealed in this section as a necessary condition for conscious experience, necessarily constitutes a law of nature, that is, a general law which permits no exceptions. It might be argued, however, that natural regularities, such as those which appear in the previous examples, could only be explained by the existence of more basic regularities, that is, laws of nature. Although there is some force to this line of reasoning, my current interest is not metaphysical, and I will not attempt to explore this promising suggestion. CONCLUSIONS My analysis shows that in order to be self-conscious, that is, to be aware of one’s own contents of consciousness as one’s own contents of consciousness, a subject must be able to think of himself or herself as a temporally extended point of view over objective reality. The categories which are found necessary for this consciousness are the concepts of the self (for non-solipsist subjects), the concept of consciousness, the concept of objectivity, the temporal distinctions between past, present, and future, and finally the idea of natural regularities which connect different events in different times. In order to make sense of this conceptual intricacy, a subject must be able to find a use for these distinctions in the confines of his or her experiences. It is not only the conceptual structure which gives meaning to the contents of a subject’s experience, and enables the subject to be conscious of his or her experiences and of himself or herself as the subject of these experiences. In order to make sense of the intricate conceptual structure which is uncovered in the previous analysis, the subject must be able to find it a use in describing reality (from his or her point of view of reality). In this sense there is interdependence between the conceptual structure and the contents of a subject’s consciousness. Finally, I should stress that although the previous analysis shows that certain categories are necessary for self-consciousness, it is in no way shows that the categories which are uncovered so far in this analysis are sufficient for self-consciousness. Further analysis may show, for example, that not only temporal distinctions but also some spatial distinctions are necessary for

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self-consciousness. However, exploring this and other promising suggestions is beyond the scope of this investigation. NOTES 1. The most impressive and inspiring attempt is undertaken in Kant’s Critique of Pure Reason. Although it is commonly agreed that Kant’s arguments ultimately fail, my analysis show that some of his conclusions are nevertheless true. 2. I rely in this analysis on some of the conceptual analysis which I undertake in my book The Conceptual Structure of Reality (2014). It should be noted, however, that the context and purpose of the two inquiries are different. While the present inquiry attempts to expose the necessary categories of conscious experience, The Conceptual Structure of Reality is a metaphysical inquiry into the necessary features of reality. This difference is reflected, inter alia, by the reliance of the current analysis on presuppositions which are illegitimate in the context of a metaphysical inquiry (e.g., the seemingly trivial supposition that self-conscious beings do exist). This difference enables simplification of the current analysis. 3. This aspect of meaning can be called “descriptive meaning,” and contrasted with other aspects of meaning. This distinction can be understood as something analogous to Frege’s distinction between “sense” on the one hand and “coloring” or “tone” on the other (Frege 1970). 4. This claim should be understood as a truism, and is not committed to any theory of truth. 5. This confirms to Frege’s famous claim: “Only in a proposition have the words really a meaning” (Frege 1980, p. 71 (Sect. 60)). 6. A similar idea is found in Wittgenstein’s Tractatus Logico-Philosophicus (1963, proposition 4.461). See also Carruthers 1989, Chap. 6. 7. This demand should not be confused with the verificationist principle(s). To begin with, it is not limited to sentences, but rather applies to every expression in language. Furthermore, it does not argue that a necessary condition for the meaningfulness of a sentence is the possibility of verifying, or even confirming, this sentence in experience. 8. I should stress that this sentence actually includes more than three separate meaningful components, some of which are not even words (such as the order of the words and the tense). I do not attempt to offer in this context an exhaustive analysis of sentences in language. 9. It should be noted that the decision to focus on the concept of consciousness does not affect the conclusions of my investigation, but merely helps to simplify the analysis. Even if we begin the inquiry with the concept of experience, our investigation will soon lead us to the concept of consciousness. This is because experience implies consciousness, not only logically but also conceptually. Logically, the premise that a experiences that p implies that a is conscious that p. Conceptually, the concept of experience relies on the distinction between what is experienced and what is not experienced, and an awareness of this distinction requires the subject to

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be aware of things which he or she does not experience. This is possible only if the subject is conscious of things which he or she does not experience. Hence, conscious experiences implies that a subject is aware of himself or herself as a conscious being, as reflected, for example, in the sentence “I am conscious that ‘Garry is using a computer’.” 10. This conclusion reaffirms Kant’s conclusion in the Transcendental Deduction of the Categories (B129–B169), according to which self-consciousness requires the subject to be aware of an objective realm of reality. This conclusion was also defended in Strawson’s “Objectivity Argument,” (Strawson 1966, 97–112). However, these and other arguments, influenced by Kant and Strawson, all fail to establish the connection between self-consciousness and objectivity (Cassam 1997; Strawson 1999). 11. I later examine the possibility that the subject does not need to use any identifying term. 12. See also Perry (1979). 13. This conclusion is not new, as it was already drawn, in different terms and based on different considerations, by Strawson (1959, 99). 14. It is possible to imagine subjects who self-ascribe their experiences using proper names, but do so in the same unique manner in which a self-conscious subject self-ascribes his or her experiences in the first-person. That is, these subjects ascribe every proposition they hold true to themselves using their proper names. In this case, however, their proper name is used in the same way as the first-person in our language. Obviously, these subjects have the conceptual resources which are necessary for employing the first-person, and therefore can be said to possess the concept of the self. 15. My conclusion stands in contrast to Strawson’s conclusion in Chap. 3 (“Persons”) of Individuals (1959, pp. 87–116). 16. This is similar to Kant’s conclusion in his Second Analogy (B232–B256). Kant’s argument rests however on difference premises, and unfortunately fails to establish the connection between objectivity and natural regularities.

REFERENCES Carruthers, P. 1989. Tractarian Semantics. Oxford: Basil Blackwell. Cassam, Q. 1997. Self and World. Oxford: Oxford University Press. Descartes, R. 1984. “Meditations on First Philosophy.” In The Philosophical Writings of Descartes vol. II. Eds. and Trans. J. Cottingham, R. Stoothoff, and D. Murdoch, 3–62. Cambridge: Cambridge University Press. Frege, G. 1970. “On Sense and Reference.” In Translations from the Philosophical Writings of Gottlob Frege. Eds. and Trans. P. Geach and M. Black, 56–78. Oxford: Basil Blackwell. ———. The Foundations of Arithmetic. Trans. J. L. Austin. Evanston, IL: Northwestern University Press. Hume, D. 1978. A Treatise of Human Nature. Ed. L. A. Selby-Bigge. Oxford: Oxford University Press.

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Kant, I. 1933. Critique of Pure Reason. Trans. N. K. Smith. London: Macmillan. Perry, J. 1979. “The Problem of the Essential Indexical.” Nous 13:3–21. Strawson, P. F. 1959. Individuals. London: Routledge. Strawson, P. F. 1966. The Bounds of Sense. London: Routledge. Wittgenstein, L. 1963. Tractatus Logico-Philosophicus. Trans. D. F. Pears and B. F. McGuinness. London: Routledge & Kegan Paul. Yehezkel, G. 2014. The Conceptual Structure of Reality. New York: Springer. Strawson, G. 1999. “Self and Body.” Supplements to the Proceedings of the Aristotelian Society 73:307–32.

Chapter 3

On Limning the True and Ultimate Structure of Reality Claire Ortiz Hill

BACKGROUND Of Franz Brentano’s theory of intentionality, Willard Quine, the preeminent American, analytic, philosopher of the last half of the twentieth century, wrote in his chef d’oeuvre Word and Object, that one may accept the Brentano thesis either as showing the indispensability of intentional idioms and the importance of an autonomous science of intention, or as showing the baselessness of intentional idioms and the emptiness of a science of intention. My attitude, unlike Brentano’s, is the second. If we are limning the true and ultimate structure of reality, the canonical scheme for us is the austere scheme that knows no propositional attitudes. If we are venturing to formulate the fundamental laws of a branch of science, however tentatively, this austere idiom is again likely to be the one that suits (Quine 1960, p. 221).

Quine also considered that modern empiricism had to a large extent been conditioned by an ill-founded belief in a fundamental cleavage made by Kant between analytic truths grounded in meaning independently of matters of fact and synthetic truths grounded in fact. In “Two Dogmas of Empiricism,” he famously argued that it was a folly to look for such a boundary and that the idea that there was such distinction to be drawn at all was “an unempirical dogma of empiricists, a metaphysical article of faith” (Quine 1953, p. 37). Indeed, Quine made exposing and bewailing any suspicion of connivance with metaphysics one of the main planks of his philosophical program. He counseled philosophers to shun what he called curiously idealistic ontologies that repudiated material objects and he conjured up nightmare visions of the ontological crisis that would ensue were logicians to disobey his strictures and begin a retreat back into essentialism (Quine 1947, pp. 43, 47; Quine 37

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1956, p. 185; Quine 1960, Ch. 6; Hill 1997, Ch. 11; Hill 2012). Quine’s views were extremely influential and held sway for decades. Where FregeoRussello-Quineo (FRQ, pronounced “freak”) philosophy and logic prevailed it was long professionally necessary to philosophize within the power of them and few dared to contradict what seemed false in them. Now, it is not well known that Brentano’s most famous student Edmund Husserl also elaborated an austere scheme to limn the true and ultimate structure of reality. However, he did so in a perfectly un-Quinean way. He eschewed empiricism and made essences and a fundamental, but anti-Kantian, cleavage between analytic truths integral parts of his endeavor. Moreover, he wedded all this to his own nonautonomous science of intention. In short, he devised a plan to achieve what Quine and like-minded philosophers aspired to achieve by embracing everything they excoriated and wanted to wipe out. However, for a number of reasons, Husserl’s strategy for keeping knowledge of reality from collapsing into a formless blob of facts—or breaking apart into, for example, Quinean rabbit bits and pieces (Quine 1960, §12; Quine 1969, pp. 34–35, 48, 50)—became buried in all the excitement, both positive and negative, generated by his science of intentionality, and so its implications for logic and philosophy nowadays have barely been explored, if at all. Fortunately though, since the 1980s, the Husserl Archives has been publishing the material needed to recuperate the map of the underlying objective structure of reality that he drew. Here I use that material to outline his austere scheme for finding clarity with respect to the central traits of reality. In particular, I seek to dig up the parts and members of the categorial skeleton that he limned to uphold knowledge in a manner that stands in sharp contrast to the logical point of view that has propped up analytic philosophy, of which Quine was a preeminent exponent. NO MERE WALLOWING IN AN ORGY OF SUBJECTIVITY One of the main reasons why Husserl’s austere scheme has gone all but unstudied is that it is not sufficiently appreciated that for him logic had two sides. Subjective, transcendental logic had to find its necessary complement in pure, objective, formal logic, and the latter find its necessary complement in the former. For example, in Formal and Transcendental Logic, he tried to impress upon readers that logic turns both toward the deeply hidden subjective forms in which reason does its work and toward the objective order, toward ideal objects, toward a world of concepts, where truth is an analysis of essences or concepts and knowing subjects and the material world play no role (Husserl 1929, §8).

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Husserl definitely abandoned Brentano’s empirical psychology, but he held fast to his teacher’s theory of intentionality, out of which he developed the science of subjectivity that he called transcendental phenomenology, which is generally seen by both those have embraced it and those who have rejected it as being precisely the sort of autonomous science of intention that Quine and like-minded philosophers have so adamantly decried. However, Husserl’s science of intention was not autonomous, and he was not the lopsided philosopher generally thought by followers and foes alike to have spent most of his career cogitating only about subjectivity. Philosophy as Husserl conceived it was not the wallowing in an orgy of subjectivity that his detractors have imagined it to be. Once he abandoned empirical psychology, he spent the rest of his career fighting to overturn naïve psychologizing. He did ultimately throw himself wholeheartedly into extensive Cartesian-inspired investigations of the realm of transcendental subjectivity, of which he was unmistakably enamored, but in so doing he himself never lost sight of objective realities and strove to expose the ultimate, objective, structure of reality in a way that he hoped would keep explorers of the world of transcendental subjectivity from falling into the psychologizing errors he was determined to stamp out. Husserl in fact underscored the primacy of the objective side of logic. It is knowledge of formal logic, he stressed in Formal and Transcendental Logic, that supplies the standards by which to measure the extent to which any presumed science meets the criteria of being a genuine science, the extent to which the particular findings of that science constitute genuine knowledge, the extent to which the methods it uses are genuine ones (Husserl 1929, §7). The world constituted by transcendental subjectivity is a pre-given world, he explained in Experience and Judgement. It is a world that is determined and determinable in itself with exactitude, a world within which any individual entity is given beforehand as in principle determinable in accordance with the methods of exact science as being a world in itself in a sense originally deriving from the achievements of the physico-mathematical sciences of nature (Husserl 1939, §11). The realm of truth, he assured students attending his 1896 lectures on logic, is no disorderly hodgepodge. Truths are connected in systematic ways, governed by consistent laws and theories, and so the inquiry into truth and its exposition must be systematic. The systematic representation of knowledge must to a certain degree reflect the systematic representation grounded in the things themselves. All invention and discovery involves formal patterns without which there is no testing of given propositions and proofs, no methodical construction of new proofs, no methodical building of theories and whole systems. No blind omnipotent power has heaped together some pile of propositions P, Q, R, strung them together with a proposition S, and

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then organized the human mind so that the knowledge of the truth of P unfailingly must entail knowledge of S. Not blind chance, but the reason and order of governing laws reigns in argumentation (Husserl 1896, pp. 9, 13, 16–17). In his lecture courses on Allgemeine Erkenntnistheorie 1902/03 and Logik 1902/03, he taught that objectivity of thinking is grounded in purely logical forms. Pure logic, he told students, is the science of concepts and relations of concepts, of propositions and relations of propositions, of the possible forms grounded in these concepts and propositions. It defines the form concepts to which the objective content of all logical and all scientific thinking in general is subject and on whose basis they develop the laws of validity grounded in those form concepts. Science, in the objective sense, is a web of theories, and so of proofs, propositions, inferences, concepts, meanings, not of experiences (Husserl 1902/03a; Husserl 1902/03b). Purely logical, for Husserl, were the basic concepts of mathematics, the theory of cardinal numbers, the theory of ordinals, set theory, mathematical physics, formal pure logic, pure geometry, geometry as a priori theory of space, the axioms of geometry as a theory of the essences of shapes, of spatial objects, but also the pure theory of meaning and being, a priori real ontology of any kind (thing, change, etc.), the ontology of nature, the ontology of minds, natural scientific ontology, the sciences of value, pure ethics, the logic of morality, the ontology of ethical personalities, axiology or the pure logic of values, pure aesthetics, the ontology of values, the logic of the ideal state or the ideal world government as a system of cooperating ideal nation states, or the science of the ideal state, the ideal of a valuable existence, objective axioms relating to a priori propositions as truth for objects, as something belonging in the objective science of these objects, or of objects in general in formal universality, essence-propositions about objects insofar are they are objective truths and as truths have their place in a truth-system in general (Husserl 1906/07, §§18–19, 434–5; Husserl 1917/18, Ch. 11). Though Husserl’s science of subjectivity ultimately all but totally eclipsed his philosophy of objectivity, the latter is still there to be uncovered, and if we really want to understand Husserl’s contribution to FRQ logic and philosophy and how it may provide solutions to the still unsolved problems undermining it, it is really imperative to do so. In what follows, I want to do justice to his philosophy of objectivity, especially as spelled out in the lecture courses that have been published by the Husserl Archives since the 1980s. HUSSERL PINS DOWN THE CONCEPT OF CATEGORY Fundamental to Husserl’s philosophy of objectivity were his theories about categories. As an example of how a science dealing with a preestablished,

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determinate, categorial, field is constituted, he gave the original mathematical disciplines of the purely logical sphere which, according to him, had proceeded from given, purely logical basic concepts and axioms and directly perspicuous laws grounded in the essence of purely logical categories and thus, for instance, yielded the concept of cardinal number, the primitive laws of number given as directly perspicuous truths, and the dependent laws of number based on them (Husserl 1906/07, §19d). So it is imperative to sort through his various uses of the term “category” and to come to clarity about how he distinguished between the various concepts of categories that he juggled with as he labored to expose the structure of reality. A good place to begin is with his statement in Logical Investigation VI that one might “try to pin down the concept of category by saying that it comprises all objective form arising out of the forms, and not out of the matters, of conceptual interpretation” (Husserl 1900–01, VI §58). Later, in Introduction to Logic and Theory of Knowledge, he acknowledged that in the earlier work he had essentially spoken only about the logical forms, which he had called categorial forms, but that if categories were to be the basic forms of objectivity without regard to its changing matter, one was then obliged to distinguish between the logical categories and the metaphysical categories, that is the categories of thingness that investigate the categories and principles expressing the essence of what is real in general. Wherever it is a question of reality, in life and in all empirical sciences, he taught in that lecture course, we apply concepts seeming to belong necessarily to the idea of a reality. As examples of such concepts, he cited thing, real property, real relation between things, real whole, real part, cause and effect, real genus and species, state, process, coming into being and passing away, space and time, the basic categories in which what is real as such is to be understood in terms of its essence (Husserl 1906/07, §§21, 22, 23, 46). With respect to these essential categories of reality, he taught that reality as objectivity was subject to all forms and laws belonging to the essence of objectivity in general and that the theory of every real objectivity was necessarily subject to the laws belonging to the theory in general of any objectivity whatsoever. Of the a priori pertaining to the idea of reality as such, he considered all the totality of truths relating to the essential categories of reality to be a foundation and prerequisite for any further knowledge of reality, a necessary, common resource for the sciences of reality. Understood in that sense, he said, logic would encompass the whole of formal logic and could also be called a theory of science of the real. Formal logic, he maintained, would therefore be the science of this first a priori (Husserl 1906/07, §§22, 23, 46). However, although he saw that a priori connections ran from the formal domain into the domain of the real, he did not believe that metaphysical

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categories should be placed on a par with the purely logical categories, because purely logical concepts and principles abstracted from all cognitive material, and it was owing to that abstraction, owing to their fully undetermined universality as concerns matter, that they could relate to every possible field of knowledge, every possible science. Formal logic was to reach as far as the realm of matter-free—therefore, formal, and in the purest sense, mathematical—concepts as far as there was talk of things and objects in general, but only insofar as they were thought through the simple thinking forms. Metaphysics, even a priori metaphysics, could therefore not have any place there and was not to be constructed as a single science with formal logic. A strict line of demarcation had to be drawn between it and the sphere of formal logic, which was necessarily a distinct, strictly separate, discipline (Husserl 1906/07, §§22, 23, 46). He explained that the concept of formal logic as the most fundamental concept of logic of all had in fact been acquired by adopting the perspective of the idea of science in general, therefore, by accepting all the sciences as equivalent and declining to distinguish between them. In doing so, he said, sciences were found that specifically related to the different spheres of reality and other sciences, even completely formed and highly developed sciences such as pure mathematics that wholly excluded any relationship to any specific sphere of reality. What they had in common was pure form (Husserl 1906/07, §23). He regarded the formal character of logical analysis as consisting in the fact that it never deals with the material constitution of something, that it considers only the categorial form that it assumes in the judgment (subject form, predicate form, and so on), but in other respects remains completely indeterminate, just designated symbolically by S, by p, which only denote empty places that can be filled any way at all (Husserl 1939, §5c). He further illustrated what he meant as follows, If one ascends to a purely theoretical and a priori discipline having reference to . . . logical categories, therefore to all the concepts that determine the objective meaning of science in general and are inseparable from it, then it is clear without further ado that all of pure mathematics belongs in this sphere, that all purely mathematical disciplines, aside from the syllogistics traditionally dealt with in logic, are encompassed by pure logic as naturally conceived . . . all concepts belong in pure logic that are not to be assigned to a particular science limited to particular domains of objects, but to all sciences in general and are necessarily common to them, all concepts, therefore, that have this reference to objects in general in the most universal way . . . . The concept of cardinal number is such a concept, and every numerically determined cardinal number belongs among these concepts. One is something in general. Anything, no matter what it is, can posited as one . . . . And all numbers are built upon units. (Husserl 1902/03b, pp. 34–35)

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It was precisely the logical categories that were to be used to put together the skeleton for upholding science. Within them, Husserl made an extremely important distinction between the concepts and laws of the formal logical or meaning categories and those of the formal ontological categories. He explained that one of the jobs of formal logic was first to single out the constituent concepts belonging to the essence of a theory as such, something that leads to the group of concepts designated as meaning categories, namely, such concepts as that of proposition, judgment, concept, and generally all the concepts concerning the structure of judgments, simple and complex, and naturally also to the concept of truth, and so on (Husserl 1929, §27b). Closely connected with the categories of meaning, and wedded to them by ideal laws were, to Husserl’s mind, the correlative concepts of the formal object categories, the formal ontological concepts under which every object of every imaginable sphere of objects could in principle be brought and which included such concepts as object, state of affairs, quality, property, genus, multiplicity, cardinal number, magnitude, relation, unit, plurality, conjunction, existence, all of them kept free of cognitive material. “Object” was the master concept of formal ontology. It was the concept that determined the formal system of axioms and thus the system of formal categories (Husserl 1900–01, Prolegomena §67; Husserl 1913, §16; Husserl 1929, §27). As, Husserl said over and over, all the categorial concepts of formal logic, those of both the meaning categories and the formal ontological categories, were particularly characterized by the fact that they were independent of the particularity of any material of knowledge. For example, in Introduction to Logic and Theory of Knowledge, he stressed that, whereas matter and form are inseparable in the sphere of intuition and the actual givenness of objectivities, the possibility of considering formal relationships in their own right and of logical reflection upon them is, however, intellectually and meaningfully feasible precisely by positing what is material as undetermined and universal in thought. And, it is with this intellectual exclusion of matter, which is nothing other than formalization or mathematical universalization, that formal logic is constituted. It is operative in the sphere of pure determinations of form and of the laws pertaining to it. It deals with propositions in general, or proposition forms in general, inference forms in general, correlatively with states of affairs in general, with objects in general, with sets in general, with numbers in general, and so on (Husserl 1906/07, §23).

CATEGORIALITY, WHOLES AND PARTS Husserl’s theory of wholes and parts is a theory of what is dependent and what is independent (Husserl 1906/07, §22). In Logical Investigation IV, he

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very importantly maintained that the study of wholes and parts, therefore of what is dependent and independent, reveals the meaning categories (Husserl 1900–01 IV, §10). Independent, to his mind, were substantives, objects, arguments, particulars, members, parts. Dependent were predicates, properties, concepts, functions, universals, forms, sets, wholes. Predicates need subjects. Concepts need objects. Functions need arguments. Universals need particulars. Properties must be properties of something. Sets need members. Forms are incomplete, meaningless, unless they are forms of something. They need matter to make up a complete whole. And, for Husserl, categories were forms. He stressed that all knowledge presupposes both form and matter. Were all matter of knowledge imagined to be nonexistent, he taught, then the categorial would not make any sense, for logical form a priori points to matter to be formed, logicized, rationalized. Indeterminately universal, everything logical points beyond itself to something extralogical to be grasped logically, which must first be there for logical grasping to find something to grasp. All talk of objects in general would lose its meaning if objects were never really to be given at any time. The formal logic ultimately structuring the universe is pure form, but all form ultimately a priori refers back to some kind of matter—be it itself of a formal logical nature, such as multiplicities and numbers in mathematical universality—to be given form by means of it. Behind everything formal is the thought—however vague—of absolute particulars, therefore, of real particulars, and likewise of genera and species, of properties and relations of real particulars. Every proposition has both predicative forms expressed in form words and terms indicating what it is that is being spoken of. The terms may be categorial concepts (as is the case in every proposition of purely logical content), therefore, designate simple objectifications of forms and thus indicate only relative matter. However, the objectifications in question ultimately point back to original forms and to possible propositions in which those forms join terms that are no longer solely categorial in nature and so contain matter in the absolute sense (Husserl 1906/07, §22). According to Husserl’s theories, any instance of dependent meaning was accompanied by an essential law governing its need for completion by other meanings and establishing the ways in which they might be connected together that ruled out other possible combinations that would yield a jumble of meanings instead of one meaning. This impossibility of combining meanings in certain ways was not merely subjective, he insisted. It did not merely lie in our actual incapacity to achieve unity. It was objective, ideal, and grounded in the nature, the pure essence, of the realm of meaning. A priori insight into laws showed that certain combinations were ruled out by the very nature of the constituents of the pure patterns in question, that such constituents could only enter into definitely constituted meaning-patterns. Meanings, he repeated over and over, are governed by a priori laws that regulate the

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ways in which they can be combined with new meanings, the ways in which they can fit together and constitute a meaningful, coherent whole (Husserl 1900–01 IV, §10). It was an analytic truth, he explained, that the forms in a whole could not function as its matter or vice versa and this fact clearly carried over into the sphere of meanings. The pure elements of form in a concrete unit of meaning could never change places with the elements to which they give form and which also give the meaning its relation to things. For him, every concrete meaning was a fitting together of materials and forms and every such meaning fell under an ideal pattern that could be set forth in formal purity, and to every such pattern an a priori law of meaning corresponded. This law governed the forming of coherent meanings out of syntactical materials falling under definite categories having an a priori place in the realm of meanings. This took place in accordance with syntactical forms which were likewise fixed a priori and constituted a fixed system of forms (Husserl 1900–01 IV, §10). Bertrand Russell’s description of a propositional function standing on its own as “a mere schema, a mere shell, an empty receptacle for meaning, not something already significant” (Russell 1919, p. 157) might well be used to describe forms as Husserl saw them. Following him one might compare, albeit imperfectly, dependent meanings to a wineglass. Unless a wineglass contains wine it is just an empty receptacle. The wine and the glass go together to make the glass of wine. The role of the wineglass is such that it can only be replaced by another receptacle, never by the wine. By its very nature, the receptacle, the wineglass, as such cannot play the part of the wine. It cannot be a glass of wine and it obviously cannot be converted into wine. The wine is just as obviously dependent on a receptacle. If the latter is broken, the wine will come to be in a place not intended for it. CATEGORIALITY, NONSENSE, WIDERSINNIGKEIT1 Frege, Russell, and Husserl, the inventors of twentieth-century western philosophy, all concluded, that the fundamental differences between dependent and independent meanings ultimately prove inviolable because they are “founded deep in the nature of things” (Frege 1891, p. 41) in such a way that contradictions, paradoxes, antinomies, fallacies, nonsense, confusion, absurdity are bound to result when they are not respected (Hill 2010). In Logical Investigation IV, Husserl maintained that it was the primitive, essential distinction between dependent and independent meanings that formed the necessary basis for discovering the essential categories of meaning in which were grounded essential laws of meaning whose business it was to distinguish sense from nonsense by determining the a priori forms

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in accordance with which the meanings of the different meaning categories might combine into one meaning instead of producing chaotic nonsense (Husserl 1900–01 IV, Intro., §10). We can freely exchange expressions within a given category, he explained. Where nominal material stands, any nominal material can stand, but not adjectival, not relational, not completed propositional material. This is true of all meanings whatsoever. To illustrate this, he took the coherent, meaningful expression “this tree is green” and proposed formalizing the given meaning, the independent logical statement, to obtain the corresponding pure meaning form: “this S is p.” It is clear, he pointed out, that formalized in that way it could be interpreted in infinitely many ways. The statement “this tree is green” could be transformed. Any noun or noun phrase could be put in the place of “S” and any adjective in the place of “p” and a coherent, meaningful meaning and an independent proposition of the form indicated would be obtained. Such free exchange of expressions within a given category might yield false, dumb, or funny meanings, but it would necessarily yield coherent meanings (Husserl 1900–01 IV, §10). However, Husserl emphasized, we are not \ free in the way we bind meanings to meanings. Not just any meaning can be substituted for S or for p. Once we transgress the bounds of the categories of our meaning material, coherent meaning vanishes. Mere combinations of words like “a round or,” “king but or,” “a man and is,” “this reckless is green,” “more intensive is round,” “this house is equal” are nonsensical, meaningless, utterly incomprehensible. One can, he noted, substitute “horse” for “similar” in the relational form “a is similar to b,” but then one obtains only a sequence of words, in which each word has a meaning, but their meanings do not combine to give a coherent meaning to the whole expression. It is completely obvious that so combined no meaning exists, or can possibly exist, for them. They break the laws about what can be meaningful. Meaning itself is missing. When dependent meanings come to be in the places for independent meanings, the fundamental structure grounded in the differences between the two is broken, like the broken wineglass (Husserl 1900–01 IV, §§10, 12). In his course on Introduction to Logic and Theory of Knowledge, he taught that, since when proposition forms are arranged in a purely grammatical manner, the meaning components are assembled in specific ways, and it is clear that it is not some arbitrary rearrangement of the components that is yielding yet another proposition, by the same token the proposition forms express laws. The meaning components, or the components of the proposition categories, constitute a matter that can only be put and fit together in certain specific ways, or else no unitary whole can emerge, no coherent meaning result. So it is that one sees that a purely grammatical pattern of separating unitary meaning from nonsense, which is independent of truth

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and falsehood, prevails in the meaning sphere (Husserl 1906/07, §18b). He explained that, we cannot juggle with the elements of a significantly given, connected unity at will. Meanings only fit together in antecedently definite ways, composing other significantly unified meanings, while other possibilities of combination are excluded by laws, and yield only a heap of meanings, never a single meaning. The impossibility of their combination rests on a law of essence, and is by no means merely subjective. It is not our mere factual incapacity, the compulsion of our mental makeup, which puts it beyond us to realize such a unity. In the cases we here have in mind, the impossibility is rather objective, ideal, rooted in the pure essence of the meaning-realm. The impossibility attaches, to be more precise, not to what is singular in the meanings to be combined, but to the essential kinds, the semantic categories that they fall under. Wherever, therefore, we see the impossibility of combining given meanings, this impossibility points to an unconditionally general law to the effect that meanings belonging to corresponding meaning categories, and conforming to the same pure forms, should lack a unified result. We have in short an a priori impossibility. What we have said holds of course of the possibility of significant combinations as it holds of their impossibility (Husserl 1900–01, IV §10).

He considered that the job of a science of meanings is to construct meanings in accordance with essential laws, to discover the laws of combining meanings and transforming them, and to trace them back to a minimal number of independently elementary laws. It would be necessary first to identify the primitive meaning formations and to investigate their inner structure in order to identify the pure meaning categories that define the meaning and extension of what is indeterminate in the laws (Husserl 1900–01 IV, §13). He further maintained that the laws of meaning then provide logic with possible coherent, meaningful meaning forms whose formal truth or falsehood, reference to objects, Widersinnigkeit or lack thereof, is determined by logical laws (Husserl 1900–01 IV, Intro., §10). So it is that for him, the “sphere of the genuinely logical laws is based upon the purely grammatical sphere. In the sphere of meaningful (therefore purely grammatically established) forms, they separate those propositions that produce or do not produce possible truth according to their form, and also those are valid and not valid a priori and purely on the basis of form” (Husserl 1906/07, §18b). In the Prolegomena to Pure Logic, he explained that the pure truths of logic were all the ideal laws having their entire foundation in the meaning of the concepts that all science has inherited and that represent the categories of constituents out of which science is essentially constituted, that is to say that they are entirely founded in the meaning, essence, or content of the concepts of truth, proposition, object, property, relation, combination, law, fact, and so

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forth. Such laws are not to be violated, not because they would be false—be in conflict with some truth—but because they would produce Widersinnigkeiten. Any assertion whose content is at odds with principles rooted in the meaning of truth as such is self-cancelling or logically widersinnig, which means that its particular content, sense, meaning is in contradiction with the general exigencies of its own meaning categories, is in contradiction with what is rooted in the general meaning of those categories (Husserl 1900–01, Prolegomena §37). I have elsewhere tried to make certain of Frege’s, Russell’s, and Husserl’s ideas about the inviolability of logical form more tangible by describing some intertwined, problems that creep into reasoning when differences between dependent and independent meanings are not respected, namely, insidious problems with pseudo-objects, inference, substitutivity of identity, existential generalization, semantical paradoxes, type ambiguities of the kind Russell tried to evade through his theory of types, in other words much of what FRQ philosophers have been battling since Frege’s time (Hill 2010). RUSSELL’S CONTRADICTIONS The importance of Husserl’s insights into the inviolable differences between what is dependent and independent has for FRQ philosophy and logic can be illustrated by taking a look at some issues involved in Husserl’s ideas about sets and what is commonly called Russell’s paradox. Husserl viewed set theory as a mathematical discipline of the purely logical sphere. It was a matter of a rigorously scientific, a priori theory proceeding from purely logical concepts and axioms grounded in purely logical categories (Husserl 1906/07, 18d). For him, a set was a kind of whole and so was subject to the formal rules governing wholes and parts that stipulate that a whole cannot be its own part. So, viewed from the angle of his ideas about the differences between dependent and independent meanings, Russell’s contradiction about the set of all sets that are not members of themselves is just faithfully telling us that the set X of x’s is not a member of what it is a set of; what is predicated of an object is of a different logical type from the object itself; a concept is not an object; a function is not an argument; a whole is not a part; what is dependent is not independent. In short, logic is doing what logic is supposed to do (Hill 1997, p. 80). Husserl reasoned that it is part of the idea of set to be a unit, a whole, comprising certain members as parts in such a way that it is something new that is first formed by them. It belongs essentially to the concept of whole that no whole can contain itself as a part. So, as a kind of whole, a set is subject to the formal rules governing wholes and parts that stipulate that a whole cannot, without contradiction, be its own part. So no set can contain

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itself as a member. Sets are a priori different from their members (Husserl, Ms A 1 35). And he repeatedly relegated the set-theoretical paradoxes to the category of Widersinnigkeiten. For him, a set that contains itself as an element was widersinnig. By saying that the set of all sets that were not members of themselves is a Widersinnigkeit, Husserl explicitly put it into the same category as the round square, the golden mountain, and the present emperor of France. The formal logical construction “set of all sets that do not contain themselves as parts,” he argued, may not be presupposed to be about something that already exists. Just as it is contradictory for a whole to be its own part at the same time, so it is contradictory for a set to be its own member. It proceeds from the paradox that a set that contains itself as an element or a set that does not must be a Widersinn. The contradictions to which Frege’s logic leads illustrate Husserl’s points about sets and the non-substitutivity of what is dependent and independent concepts. Remember that Russell wrote to Frege in 1903 that, on functions in particular (sect. 9 of your Conceptual Notation) I have been led independently to the same views even in detail. I have encountered a difficulty only on one point. You assert (p. 17) that a function could also constitute the indefinite element. This is what I used to believe, but this view now seems to me to be dubious because of the following contradiction: Let w be the predicate of being a predicate which cannot be predicated of itself. Can w be predicated of itself? From either answer follows its contradictory. We must therefore conclude that w is not a predicate (Frege 1980, pp. 130–31).

True to his convictions that the fundamental differences between predicates and objects were inviolable and founded in the deep nature of things, Frege replied to Russell that “A predicate is predicated of itself” did not seem exact to him. A predicate, he explained, was as a rule a first-level function which requires an object as argument and cannot therefore have itself as argument (Frege 1980, pp. 132–33). When, late in his life, he was asked about the causes of the paradoxes of set theory, Frege answered that the essence of the procedure leading into a thicket of contradictions consisted in regarding the objects falling under F as a whole, as an object designated by the name “set of Fs,” “extension of F,” or “class of Fs” (Frege 1980a, 54–55). Russell acknowledged that the contradiction about the classes that are not members of themselves had shown him that classes must be something radically different from individuals (Russell 1956, p. 81). He came to believe that if one assumes that the class is an entity, one cannot escape the contradiction. As he explained, “if you think for a moment that classes are things in the same sense in which things are things, you will then have to say that the class consisting of all the things in the world is itself a thing in the world, and that

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therefore this class is a member of itself” (Russell 1956, pp. 81, 261; Russell 1973, p. 171). Early in his search for ways to evade (his choice of verb) the problem of the contradiction about the class of all classes that are not members of themselves, Russell thought that “the key to the whole mystery” was to be found by inventing (his choice of verb) a hierarchy of types. He said that it had become clear to him that the contradiction about the classes that are not members of themselves could only be avoided by realizing that no class either is or is not a member of itself, that the entire question as to whether a class is or is not a member of itself is nonsense. So, he invented a hierarchy of classes according to which the first type of classes would be made up of classes made up entirely of particulars, the second type made up of classes whose members are classes of the first type, the third type composed of classes whose members are classes of the second type, and so on. The types would be mutually exclusive, thus making the notion of a class being a member of itself meaningless (Russell 1973, p. 201; Russell 1903, §§104–105; Russell 1956, pp. 261–64). His hierarchy of types was to perform “the single, though essential, service of justifying us in refraining from entering on trains of reasoning which lead to contradictory conclusions. The justification is that what seem to be propositions are really nonsense” (Russell & Whitehead 1927, p. 24). Indeed, the contradictions that in Russell’s words had “infected logic and set theory” and “troubled students of symbolic logic and set theory” and that he had expended so much energy to “avoid” (Russell & Whitehead 1927, pp. vii, 1) were derived using a concept of set that allows one to form the expression “a set may be a member of itself,” which Husserl judged to be widersinnig. In contrast, Husserl would derive set theory analytically from the concept of set which, according to his theories, if it is to be mathematical would have to have a “set essence” in view. This set essence would be expressed in the relation between a set itself and its elements. He reasoned that an essence relation makes it impossible for the members of the relation to be identical. So it belongs essentially to the concept of set that no set can contain itself as an element without contradiction. Reasoning appealing to the notion of sets that do not contain themselves as members would therefore be entirely untenable. Blurring distinctions by allowing sets as dependent forms to be transformed into proper names breaks logical structure, which smooths the way for things to come into places not intended for them. Once logical structure is broken and meaning categories are violated trouble lies ahead in the form of failures inference, something I cannot go into further here, but have examined from various different angles in several writings, among them, Rethinking Identity and Metaphysics, On the Foundations of Analytic Philosophy (Hill 1997), “Incomplete Symbols, Dependent Meanings, and Paradox” (Hill 2003),

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“Reference and Paradox” (Hill 2004), “On Fundamental Differences Between Dependent and Independent Meanings” (Hill 2010), “Husserlian Sets or Fregean Sets (Hill 2013), “Husserl’s Way Out of Frege’s Jungle” (Hill 2015). CATEGORIALITY AND ANALYTICITY Husserl (not to mention Bernard Bolzano, Karl Weierstrass, Brentano, Georg Cantor, Frege, or Johnny-come-lately Quine in his famous “Two Dogmas of Empiricism”) rejected the way in which Kant had distinguished between analytic and synthetic truths. For instance, in Introduction to Logic and Theory of Knowledge, he reminded students that he had repeatedly said that no matter how proud Kant had been of the manner in which he had defined the concept of analyticity, it was altogether inadequate and really fundamentally wrongheaded (Husserl 1906/07, §23; Hill 2005). In Ideas I, he maintained that it was the purely logical as he defined it that determines the concept of the analytical as opposed to the synthetic (Husserl 1913, §10). In Logic and General Theory of Science, he explained that by analytic truths in the broadest sense, he understood “analytic concept-truths, therefore all pure categorial truths, therefore, the entire pure mathesis, pure logic, then however, also their a priori and empirical individuations, therefore, the analytic necessities.” He saw the pure categorial concept-truths as a whole as essentially belonging together and forming a single system of scientific disciplines to be dealt with under the broadest heading of formal logic, or analytics, or the mathesis universalis in Leibniz’ sense. He specified that in carrying the analytic and synthetic distinction over to deductive theories and disciplines, one obtains analytic (or categorial) and non-categorial or synthetic theories and disciplines, the latter breaking down into synthetic a priori ones and a posteriori ones. He maintained that all the analytic disciplines—which he defined as disciplines bringing all the laws to ultimate theoretical unity—belonging to the formal categories form a homogeneous unit, namely, analytics in a broader sense. So it is that Husserl identified analyticity and categoriality (Husserl 1917/18, §§45b, 47e, 50). This means that the categorial scaffolding he wanted have buttress scientific knowledge of reality was analytic. In the Logical Investigations, he defined analytic laws as unconditionally universal propositions that were free of any assertion, implicit or explicit, of individual existence and were grounded solely in formal categories, thereby unaffected by any material knowledge. They were composed exclusively of formal concepts and primitive or basic laws containing only formal categories, and were completely formalizable. As an example of such an analytic law, he proposed the analytic proposition that the existence of this house includes that of its roof, its walls and its other parts, for which the analytic

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formula holds that the existence of a whole W (A, B, C . . .) generally includes that of its parts A, B, C . . . . (Husserl 1900–01, III §12). To the question as to what was the essential line of demarcation within pure laws by which analytic laws set themselves apart from all other laws, Husserl once replied that the distinction permitting one to draw that line clearly was that between the material and the analytic-categorial, according to which meanings, propositions, judgments split into ones only containing formal-categorial terms and ones also containing material terms (Husserl 1917/18, App. XV). So it is that he further divided pure concept-truths not exclusively containing what he called “that remarkable group of pure concepts called the formal categories” into those that do not remain truths when their material concepts are replaced by pure categories and those that do. As examples of pure concepttruths falling into the first group, Husserl gave geometrical and kinematic axioms, which according to his theories were synthetic or synthetic a priori concept-truths, not analytic necessities. Into the second group he placed all a priori individuations of pure laws of meaning. As examples of these, he proposed: “Two colors the same as a third, are the same as one another,” as a particular instance of “Two objects the same as one and the same third one are the same as one another”; a real proposition such as, for example, “If something is red, then it is not not-red,” which is an extra-essential material truth corresponding to the formal law that, “If something is a, then it is not not-a, which is not essentially bound to the concept ‘red’, but holds for the property ‘red’, because it holds for arbitrary properties of arbitrary objects”; and the truth that “If one spatial distance is greater than a second one, then the latter is smaller than the former,” which is a particular instance of a universal principle holding not only for spatial distances, but for any magnitude, the concept of which is categorial (Husserl 1917/18 §45b). Every formal-logically valid inference as such, he added, is also characterized by the fact that it changes into a categorial law-truth when its material terms are replaced by indefinite terms of the corresponding categories. As an example, he gave, “If all humans are mortal and Socrates is a human, then Socrates is mortal,” which is merely a particular instance of the formal logical law, “If All A are α, and x is an A, then x is also α.” Every such inference, he concluded, is therefore an analytic necessity (Husserl 1917/18, App. XV). THE PROPOSITION CATEGORY AS THE HIGHEST LOGICAL CATEGORY Husserl thought that “the logical categories form precisely the source of all science as such, therefore, of all science in terms of its theoretical form.” And he maintained that those logical categories, the primitive concepts of pure

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logic, were grouped around the proposition category as the highest logical category (Husserl 1906/07, §§18a, 19d). Adopting the Aristotelian word for proposition, ‘apophansis,’ Husserl called the sphere of the proposition categories apophantic categories (Husserl 1906/07, §18a). As he explained to his students, From the standpoint that we adopted for the definition of apophantic logic, the idea of proposition was the basic category. In more common parlance, we could also say the idea of statement, of predication, and this insofar as it is a statement that something is or is not, the idea of a claim to validity or truth. What is grounded in the essence of the proposition as unit of validity is to be investigated. In certain ways, therefore, it is a matter of a logic of truth. Truth is simply true proposition. If we want to investigate what is grounded in the essence of truth, then we must go back to the propositional forms to be distinguished in essential ways. We therefore need a theory of forms of proposition. And based upon this as a higher level at which it is genuinely aimed, is the logical theory of laws: the laws of validity and nonvalidity grounded in the essence of these forms (Husserl 1906/07, §18c).

The basic trunk of the one pure logic, he stressed, is apophantic logic, by which he understood all the laws of essence pertaining to the idea of proposition. For him, this was a matter of laws making up the most universal, clearly indispensable basis for establishing norms for thinking, laws without which it would be meaningless to talk of truth and falsehood, attribution or non-attribution, assuming and inferring, therefore of yes and no, if and then, either, or, and so on (Husserl 1906/07, §18a, d). He saw the proposition category as separating into a series of separate categories of propositions that differ in terms of their formal constitution where various formal elements occur which, conceptually differentiated, produce a series of related categories of formal constituents of propositions. As examples of such constituents, he gave subject, predicate, attribute, is, not, if, then, and, either, or, plural, singular, all, some, a, and so on. Out of this are built, the propositional categories existential proposition, categorical, hypothetical, disjunctive proposition, conjunctive proposition, and so on (Husserl 1906/07, §18a). Every proposition as such, he explained, declares that something is or is not and in so doing lays claim to validity. However, this covers, a variety of particular cases which are expressed in different forms and grounded in the universal nature of the proposition as a unit positing an objectivity. So it is that propositions declare that something exists or does not exist, that a given property φ is or is not attributable to an object, that if φ is attributable to it, then another property ψ is or is not also attributable to it, or is not attributable to it because either one property or the other is attributable

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to it, if property φ is attributable to an S, property ψ must also be attributable to a Q, and so on. Laws grounded in the nature of these forms, laws of validity or lack of validity on the basis of mere form then pertain to these propositional forms and to the forms of their involvement in compound propositions. These form concepts and the laws accompanying them must be absolutely universal. These forms occur in concreto and the accompanying laws of validity are therefore applicable wherever propositions are stated, wherever they figure in theoretical structures, inferences, proofs, theories (Husserl 1906/07, §18a). Concepts such as proposition, valid and invalid proposition, truth and falsehood, Husserl pointed out, clearly have to be applicable always and everywhere. Concepts expressing the possible constituents of propositions in formal universality, for example, subject and predicate, universality and particularity, singular and plural naturally belong there, as well as, in general, all forms of propositions and possible systems of propositions that, irrespective of specific cognitive content, involve possibilities lying in the universal nature of the proposition of capturing arbitrarily determined contents in propositional form, therefore, of capturing them in meaning units that by their very nature lay claim to validity or truth. In contrast, however, concepts such as whole and part, relation and order, set, cardinal number, combination do not express essential forms of propositions, and the laws pertaining to them are not laws for truths grounded in the essence of the proposition in general. Rather, they a priori express possible object prototypes and what is grounded in their formal essence. They therefore must take a back seat to the concept of propositions (Husserl 1906/07, §18a). Importantly, Husserl considered that owing to the correlation of the concepts of proposition and state of affairs, concept and object, apophantic logic also in certain ways contains a formal ontology which, inseparably connected with the apophantic a priori—that of statement meanings—is the a priori of formal ontology. So, for example, if in virtue of this correlation between meaning and objectivity, one changed standpoints and adopted the standpoint on the side of objectivity, then corresponding to the theory of forms of propositions would be a theory of forms of the corresponding states of affairs (Husserl 1906/07, §18c). Every science’s entire theoretical content, he told students, is totally composed of meanings, is made up of propositions as units of meaning and validity that are complete in themselves (Husserl 1906/07, §18a). A theory, he wrote in the Prolegomena, is a certain deductive combination of propositions which are themselves certain combinations of given concepts, among them the concepts of concept, proposition, truth, and so on. (Husserl 1900–01, Prolegomena §67). To further their insight into the essence of pure logic, Husserl asked his students to reflect on the following:

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Scientific reasoning aims for truth. Truth is realized subjectively in judgment and is stated in statements. Every scientific theory is a system of statements. It is something complete in its own right and, as it is, lays claim to truth and falsehood. The starting propositions lay claim to this directly. The theory, the definitely formed web of propositions, lays claim to substantiating new truth indirectly, step by step. And the system itself lays claim to being true as a system. That means that everywhere one thing is linked to another by logical inference that is also stated, therefore, is also set down as true (Husserl 1906/07, §11).

As was his wont, to illustrate the role of propositions in a theoretical system, he asked his students to consider that of modern pure mathematics. As regards its essence, he explained to them, it is no more than a system of logically combined statement meanings, a system of propositions. This system states truths about a certain combination of facts, namely that of the mathematical facts making up the field of mathematics. This field is not given to us externally and apart from knowledge, but only in and by means of knowledge. And, it is scientifically given and known as far as it has been dealt with theoretically, as far as the subjects of the propositions refer, say, to numbers, the predicates to properties of numbers, or to relations between numbers, the combinations of propositions to combinations of properties and relations as regards cause and effect, as regards compatibility and incompatibility, and so on (Husserl 1906/07, §11).

Once the ideal of constituting a system of propositions in a field as basic principles is realized, then all the theoretical work is done. The propositions would be expressed algebraically. One could look at the form and say that it yields a deductive theory falling within the scope of a given mathematical prototype. All its possible formal consequences in formal universality have already been theoretically derived. It need only be applied (Husserl 1906/07, §19c).

THE ENTIRE CATEGORIAL FORM OF THE EDIFICE OF SCIENCE Husserl’s search for answers that he did not believe Brentano’s empirical psychology could provide led him to espouse metaphysical, epistemological, and logical views that Brentano—and Quine—deemed odious and despicable (Hill 1998). Brentano was wholly devoted to the austere ideal of a strict philosophical science as realized in the exact natural sciences (Husserl 1919, pp. 344–45). But, disenchanted with his teacher’s ideas, Husserl grew convinced that knowledge of the world of the natural sciences could not be definitive knowledge of reality, that although many worthwhile findings had been

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made through advances in the natural sciences, they did not provide definitive, ultimate, conclusive knowledge of the essence of nature and lacked the critical insight into the meaning of the fundamental concepts and fundamental principles needed to be clear about the sense in which their findings could be taken as expressions of ultimate being. The empirical sciences, he came to teach, are not creations of a purely theoretical mind, not based on absolutely scrupulously lain foundations in accordance with a rigorous logical method (Husserl 1906/07, §20; Husserl 1898/99, p. 233). He had come to hold that from the point of view of their form, all propositions, inferences, proofs, theories in the sciences are structured in a regular way and that that regularity is purely logical, so that, if the purely logical sphere has been developed to the proper extent, its concepts and laws make it possible in advance—and irrespective of actual scientific fields and any actual theories about them—to construct a priori forms of possible theories and possible sciences and subsequently make use of those theory forms and the regularity of their relations for actual theorizing about any a priori or empirical fields of knowledge defined step by step in the actual investigating of the world and awaiting theorization (Husserl 1906/07, §19c). Lifting out the elementary concepts that belong to the essence of the theoretical content of science in general and investigating the systems of laws grounded in them, one can obtain a group of disciplines embodying the direct and indirect conditions of the possibility of a theory and, in this regard, of a science in general. This is a matter of basic laws and disciplines developing out of them that all sciences can use in like measure and that no science can and may ever violate, because embodied there is precisely what is either directly constitutive of the science or is a pure consequence of it (Husserl 1906/07, §19c). Persuaded that belonging to the essence of science in general was the form of the theory, he went on to conclude that there must be a most universal theory of science of all, a theory of theory in general, a science of what is ultimately grounded in the essence of statements claiming validity, in the essence of the apophansis (Husserl 1906/07, §23). It was certain, he maintained, that the formal disciplines make up a self-contained unit and that taken all together they constitute a science of everything that with respect to its form belongs a priori to the essence of theory in general and can be developed scientifically there, or they constitute a theory of science, in so far as science must, by essence, contain theory, science being really only completed science in so far as it provides theory (Husserl 1906/07, §§22, 23). To build an ideal mathesis universalis as Husserl envisioned it, one must obtain a comprehensive set of completely direct axioms that are formally independent of one another and state all the direct law-truths pertaining to all the formal categories, both apophantic and formal ontological. The categories

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themselves being intertwined, their interconnections would have to be kept track of systematically, and the axioms laid down step by step. But, since mere axioms are not theories, the consequences would therefore have to be systematically deduced from the axioms. Each step of indirect thinking taken would have to be directly perspicuous, would only be valid if its law was valid and that law would have to occur among the axioms, therefore be directly warranted in and of itself (Husserl 1917/18, §59). All possible proof and theory forms a priori being thus outlined, Husserl envisioned the very same procedure as extending to the entire categorial form of the edifice of science. He was “ultimately striving after the ideal of an all-embracing theory of theories, of a science of all possible forms of deductive disciplines, or at least of a differentiation of main prototypes and of systematic, separate development of prototypes within a main prototype,” which if carried out with such completeness of the deductions that each possible form of a theoretical discipline falling within the scope of the main prototypes is already established and fully developed in advance would yield all theories before we even know the fields in which they will formulate and solve their problems (Husserl 1906/07, §19c). He described the goal of this modern “supramathematics” as being to obtain the disciplines belonging to the categories of proposition, concept, cardinal number, relation, equality, quantity, and so on and to all possible spheres of theories in an entirely new, unique way. Instead of everywhere purely holding on to the concepts and setting up for their own sake the axioms and out of them the mathematics pertaining to each sphere, it proves vastly more advantageous and infinitely more fruitful to set up a universal, and thereby hypothetical, theory of theories that defines the main prototypes of theories and constructs them completely in terms of their form, so that this mathematics itself is not to be effected anew for every preestablished purely logical or extralogical domain that in general admits of a mathematics, but is to be obtained by simple subsumption under the corresponding theory form (Husserl 1906/07, §19d).

This all-embracing theory of theories, of a science of all possible forms of deductive disciplines that Husserl was intent upon devising was his theory of manifolds, which he saw as the ultimate consummation of all purely categorial knowledge (Husserl 1917/18, §59). THE ULTIMATE CONSUMMATION OF ALL PURELY CATEGORIAL KNOWLEDGE So, for Husserl, all purely categorial knowledge culminated, in his words, in a “theory of theories, in a rational morphology and physiology of theories possible a priori, or correlatively speaking, in a rational discipline of the

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manifolds, of scientific fields that are exclusively defined by the form of their theoretical connections,” which therefore yields “a perfectly complete unit directly characterized by the fact that everything having to do with content is excluded on principle” (Husserl 1906/07, §23). He stressed that “every concept of a manifold and of a theory of manifolds is entirely built out of purely categorial concepts.” In answer to the question as to what he meant by “manifold,” he replied that to begin with, it was nothing more than an “aggregate” or a “class” of objects conceived in complete indeterminacy and universality. Now, those are, though, purely and simply categorial concepts. Furthermore, when we say we are stipulating of these objects of the presently fully undetermined class that there are certain connectives ±, and so on for them for which a+b = b+a, and so on then hold, then the concepts “certain” relation, sameness when changing the order of the relation, and so on in turn occur. Purely and simply logico-categorial concepts. Here, the sign “±” only means a sign for an indeterminately conceived relation and not, for example, for a relationship of quantities, or any other specific thing. Therefore, nothing leading outside the categorial sphere enters in here through the sign. We construct, therefore, purely logical concepts of possible objectivities (Husserl 1906/07, §19c).

He conceived of manifolds as pure forms of possible theories which, like molds, remain totally undetermined as to their content, but to which thought must necessarily conform in order to be thought and known in a theoretical manner. In manifolds, he explained, formal logic deals with whole systems of propositions making up possible deductive theories. It is a matter of theorizing about possible fields of knowledge conceived of in a general, undetermined way and purely and simply determined by the fact that the objects stand in certain relations that are themselves subject to certain fundamental laws of such and such determined form (Husserl 1906/07, §19; Husserl 1917/18, §§54–59). Universally speaking, he explained, the meaning of a theory of manifolds is, Let there be a domain in which the objects are subject to certain forms of relation and connection, for which axioms of such and such a form are valid, then for a domain formally constituted in this way, a mathematics of such and such a form would be valid, there would then result propositions of such and such a form, proofs, theories of such and such a form. Here, one does not actually have a domain, does not have actually given concepts, does not have actually given connections and relations, and finally does not have actual axioms, but is simply saying, if one had a domain, and if axioms of such and such a form obtained for it. The so-called axioms of such a mathematics calling itself axiomatic are, therefore, not actual axioms, actual propositions entitled to be validating truths. They are axiom forms that are to actual axioms precisely what proposition forms are to actual propositions.

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The thought S is P is not a proposition, but a thought that universally presents a proposition and presents it as having a certain formal prototype. If we say: Let there be a domain in which axioms of such and such a form hold, for example, an axiom of the form a+b = b+a, then I do not have an axiom, but am simply saying, let there be something such that for objects of the domain and for an unknown connective called +, commutativity applies. No truth is, therefore, advanced there. And, so the whole dependent theory is also simply the form of a theory. It really only says: From axioms of such a form (if axioms having such a form can be produced), theories would develop of such and such a codetermined form. If one actually finds a field of knowledge somewhere for which principles have the form required, then application to this field produces an actual mathematics forthwith instead of a hypothetical science form, a true and actual science (Husserl 1906/07, §19d).

Husserl saw the general theory of manifolds, or science of theory forms, as a field of free, creative investigation made possible once one realizes that deductions, series of deductions, continue to be meaningful and to remain valid when one assigns another meaning to the symbols. No longer restricted to operating in terms of a particular field of knowledge, one is free to reason completely on the level of pure forms. Operating within this sphere of pure forms, one can vary the systems in different ways. Nothing more need to be presupposed than the fact that the objects figuring in them are such that, for them, a certain connective supplies new objects and does so in such a way that the form determined is assuredly valid for them. One finds ways of constructing an infinite number of forms of possible disciplines (Husserl 1906/07, §19). In his course on Logic and Theory of Science, he explained that, All actual theories, therefore, also the analytic theories, can precisely be formalized in the sense of the theory of theories. Even syllogistic logic is not to be made an exception here. In its case, formalization even leads to a theory form that can be understood as a special case of the formal genus-type “arithmetic.” All the well-known algebraic propositions ab = ba, the laws of association, distribution, hold, and the brilliant Boole saw that two closed domains of ordinary syllogistic logic can be dealt with as if it were an arithmetic, only that the number series reduces to the numbers 0 and 1. All arithmetical laws are valid there if we but add the fact that 1 + 1 does not = 2, but = 1. If one knows nothing about the theory of theories that seems to be perfect nonsense, and it then seems absolutely strange when one hears of machines, of a kind of piano, that analogously permits one to resolve complex webs of syllogisms by means of a mechanical game, the way one can randomly mechanically carry out additions, multiplications, divisions, and so forth with calculating machines. However, the matter is no more miraculous there than here, and in syllogistic logic, the 0 and 1 are signs that have very little to do with the arithmetical 0 and 1. They are only selected, just as the signs +, ×, = are, in order to

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allow certain formal analogies to come to the fore and in further consequence to make perceptible the fact that the theory form agrees to the extent indicated with that of an arithmetic (Husserl 1917/18, §58).

So, in the methodology of manifolds, one speaks of numbers, but one does not speak, for example, of cardinal numbers, but anything for which formal axioms of the arithmetical prototype hold. If, Husserl taught, we drop the cardinal number meaning of the letters in the ordinary theory of cardinal numbers and substitute the thought of objects in general for which axioms of the arithmetical form a+b = b+a, a·b = b·a, and so on are to hold, we no longer have arithmetic, but a purely logical class prototype of theory forms to which, like innumerably many possible domains, the domain of cardinal numbers is also subject. In this case, it is no longer a matter of arithmetic, but of a class prototype of possible mathematics. One may speak of numbers in the formal sense, but they are not cardinal numbers, but objects indeterminately, universally defined by axiom forms as they are especially actually found for cardinal numbers. Here, as in every theory form or manifold form, the “axioms” are proposition forms that are constituent parts of the definition. For cardinal numbers, ab = ba holds. In constructing a manifold, though, one may just as well stipulate that ab ≠ ba, for example, ab = –ba, and likewise for the other basic principles (Husserl 1906/07, §§19b, d). This procedure, Husserl enthused, has proven “splendidly effective” and it was only owing to it that mathematics had become “a magnificent tool for investigating nature.” One can everywhere go back to the form and derive the whole system of consequences, or rather consequence forms, on the basis of the form, something which is very helpful since the same theory forms recur in different fields (Husserl 1906/07, §19c, d). However, in spite of all its advantages, Husserl realized that, because the theory of manifolds itself proceeds deductively, because it is based on pure analytic categories, and because its every step is subject to analytic laws that are not merely forms, thinking within the hypothetical reflection of theory forms cannot be exhaustive, the formal theory of manifolds cannot confirm all of analytics or the special domains of analytics we call arithmetics. In drawing an inference, some laws of inference belong to the inference. If it weighs the possibilities combinatorially when solving problems, it makes use of propositions for cardinal number and combination, and so on (Husserl 1917/18, §58). He further realized that although all fields of theoretical knowledge have a systemic form that belongs to formal logic itself, and so are particular instances of manifolds, not all sciences are theoretical disciplines that, like mathematical physics, set theory, pure geometry, or pure arithmetic, are characterized by the fact that their systemic principle is a purely analytical one.

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He recognized that sciences like psychology, history, the critique of reason, and, notably, phenomenology were not purely logical and so obliged philosophers to go beyond the analytico-logical model. When those not purely logical sciences were formalized and philosophers asked what binds the propositional forms into a single system form, they faced nothing more than the empty general truth that there is an infinite number of propositions connected in objective ways that are compatible with one another in that they do not contradict one another analytically (Husserl 1917/18, §54; Husserl 1929, §35a; Husserl 1908/09, p. 263; Husserl 1902/03b, pp. 31–43, 49). CONCLUSION With this account of Husserl’s theory of manifolds as “the ultimate consummation of all purely categorial knowledge,” I have sought to expose what might be viewed as the backbone of the true and ultimate skeleton that Husserl held up to philosophers to uphold truly scientific knowledge of reality. I have tried to show that the father of the science of intentionality also elaborated a formal logic that is as austere and free from acts, subjects, or empirical persons or objects belonging to actual reality as Quinean logic is, and that he manufactured it out of everything that Quine and those of his mind reviled and conspired to have ignored. He made essences, a fundamental cleavage between analytic truths, metaphysics, and integral parts of this endeavor. He renounced empiricism and espoused an idealistic ontology that repudiated material objects and surely would have fled Quine’s ontologies of rabbit parts, stages, and fusions, and river stages and kinship, person stages, where physical and mathematical objects, where are but myths relative to an epistemological view (Quine 1948, p. 19; Quine 1950, pp. 68, 70–71; Quine 1960, §12; Quine 1969, pp. 34–35, 48, 50). However, seduced by the siren of transcendental phenomenology, Husserl did not to pursue the issues, implications, and consequences of his ideas about formal logic as far as he could have. In 1917, he confessed to Hermann Weyl that despite of all the work he had devoted to the theory of functional judgments, of judgments with empty places, to distinguishing the different modes of the empty something, to implementing the fundamental distinctions between formal and factual ways of judgment, between proposition form and proposition or judgment, proof form and theory form and theory and the objective correlates associated with them, to his concept of complete manifolds, he had not pursued that train of thought completely to the end, because it had to be more important to him to develop his ideas about transcendental phenomenology (cited Husserl 1917/18, XXIII n. 1). In 1930, he wrote to Georg Misch that he had lost all the interest that formal logic and all real

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ontology had held for him in the face of a systematic grounding of a theory of transcendental subjectivity (cited Husserl 1917/18, XXIII, n. 4). As a result of Husserl’s manifest love for transcendental phenomenology, his pioneering, prophetic work in the field of formal logic was never furthered in a way that ever made much of an impact on FRQ, or even on his own followers. Nonetheless, the awareness that there is something about reality that cannot be manipulated at will, that for example, logic must be rooted in the ways in which being is structured or it will turn out illogical, may one day prove to be one of the principal lessons of twentieth-century analytic philosophy and phenomenology both. So, once the pieces of his theory about the categorial structure of reality are reassembled, philosophers can, and should, experiment with it as an alternative to FRQ philosophy and logic, which unsuccessfully tried to wipe out the very differences that he deemed revelatory of categoriality (Hill 1997; Hill 2004). It will surely one day prove to be one of the ironies of the history of philosophy that it is the study of the failings of phenomenology’s rival that has provided the key to understanding the importance of Husserl’s more lucid alternative.

NOTE 1. Hard problems surround the translation of the words ‘Widersinn’ and ‘widersinnig,’ ‘Widersinnigkeit.’ Although Husserl used these words in a perfectly normal way, they do not translate neatly into English. The word ‘wider’ means against, counter, contrary to, in opposition to. So a very literal translation of these words might be ‘countersense’ and ‘countersensical.’ Some have chosen to translate them thus; others have chosen ‘absurdity’ and ‘absurd.’ Husserl himself used ‘Absurdität’ and ‘absurd’ as synonymous with ‘Widersinn,’ and ‘Widersinnig’ (ex. Husserl 1900–01, LI I, §19; LI IV, Introduction, §12). ‘Widersinn,’ ‘Widersinnigkeit’ and ‘widersinnig’ may, however, be understood in the sense of paradox or contradiction and paradoxical, contradictory, illogical, which better suits our purposes here. In that case, these words fall into the family of ‘widersprechen’ (to contradict), ‘Widerspruch’ (contradiction), and ‘widersprechend’ and ‘widerspruchsvoll, two common German words meaning contradictory. Due to the problems, I have chosen to leave ‘Widersinn,’ ‘Widersinnigkeit,’ and ‘widersinnig’ in German.

REFERENCES Frege, Gottlob (1980) Philosophical and Mathematical Correspondence, Oxford, Blackwell. Hill, Claire Ortiz (1997) Rethinking Identity and Metaphysics, On the Foundations of Analytic Philosophy, New Haven CT, Yale University Press.

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——— (1998) “From Empirical Psychology to Phenomenology, Edmund Husserl on the ‘Brentano Puzzle’,” The Brentano Puzzle, R. Poli (ed.), Aldershot UK, Ashgate, pp. 151–67. ——— (2000) “Husserl’s Mannigfaltigkeitslehre.” Anthologized in Hill & Rosado Haddock. ——— (2003) “Incomplete Symbols, Dependent Meanings, and Paradox,” in Husserl’s Logical Investigations, Daniel O. Dahlstrom (ed.), Dordrecht, Kluwer, pp. 69–93. Anthologized in Hill & da Silva. ——— (2004) “Reference and Paradox,” Synthese 138(2) (January), pp. 207–32. Anthologized in Hill & da Silva. ——— (2005) “One Dogma of Empiricism,” in Experience and Analysis, Erfahrung und Analyse, Proceedings of the International Wittgenstein Conference on Held in Kirchberg am Wechsel, August 2004, M. E. Reicher & J. C. Marek (eds.), Vienna, ÖBV&HPT Verlag, pp. 30–38. Anthologized in Hill & da Silva. ——— (2010) “On Fundamental Differences Between Dependent and Independent Meanings,” Axiomathes, An International Journal in Ontology and Cognitive Systems 20, 2–3, online since May 29, 2010, pp. 313–12 (DOI 10.1007/ s10516–010–9104–1). Anthologized in Hill & da Silva. ——— (2012) “Cantor’s Paradise, Metaphysics and Husserlian Logic,” in Categories of Being, Essays on Metaphysics and Logic, L. Haaparanta & H. Koskinen (eds.), Oxford, Oxford University Press, pp. 217–40. ——— (2013) “Husserlian Sets or Fregean Sets?” Notae Philosophicae Scientiae Formalis, 2(1), pp. 22–32, May. http://gcfcf.com.br/pt/files/2013/07/HillClaire-Ortiz-NPSF-vol.2-n.1.pdf ——— (2015) “Husserl’s Way Out of Frege’s Jungle,” in Objects and PseudoObjects Ontological Deserts and Jungles from Brentano to Carnap, B. Leclercq, S. Richard & D. Seron (eds.), Berlin, de Gruyter, pp. 183–96. Hill, Claire Ortiz & G. E. Rosado Haddock (2000) Husserl or Frege? Meaning, Objectivity, and Mathematics, Chicago, Open Court. Hill, Claire Ortiz & Jairo José da Silva (2013) The Road Not Taken, On Husserl’s Philosophy of Logic and Mathematics, London, College Publications. Husserl, Edmund (1896) Logik, Vorlesung 1896, E. Schuhmann (ed.), Dordrecht, Kluwer, 2001. ——— (1898/99) “Aus der Einleitung der Vorlesung ‘Erkenntnistheorie und Hauptpunkte der Metaphysik 1898/99’,” in Husserl 1902/03a, pp. 225–55. ——— (1900–01) Logical Investigations, London, Routledge & Kegan Paul, 1970. ——— (1902/03a) Allgemeine Erkenntnistheorie, Vorlesung 1902/03, E. Schuhmann (ed.), Dordrecht, Kluwer, 2001. ——— (1902/03b) Logik, Vorlesung 1902/03, E. Schuhmann (ed.), Dordrecht, Kluwer, 2001. ——— (1906/07) Introduction to Logic and Theory of Knowledge, Dordrecht, Springer, 2008. ——— (1908/09) Alte und neue Logik, Vorlesung 1908/09, E. Schuhmann (ed.), Dordrecht, Kluwer, 2003. ——— (1913) Ideas, General Introduction to Pure Phenomenology, New York, Collier Books, 1962.

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——— (1917/18), Logik und allgemeine Wissenschaftstheorie, Vorlesungen 1917/18, mit ergänzenden Texten aus der ersten Fassung 1910/11, U. Panzer (ed.), Dordrecht, Kluwer (1996). My English translation, Logic and General Theory of Science, is forthcoming, Springer Verlag. ——— (1919) “Recollections of Franz Brentano,” Husserl: Shorter Works, P. McCormick & F. Elliston (eds.), Notre Dame IN, University of Notre Dame Press, 1981, pp. 342–49. ——— (1929) Formal and Transcendental Logic, The Hague, Martinus Nijhoff, 1969. ——— (1939) Experience and Judgment, London, Routledge and Kegan Paul, 1973. ——— (2016) Ms A I 35. Untitled, undated manuscript on set theory available at the Husserl Archives in Cologne, Leuven, and Paris, now partially published in German by Carlos Ierna and Dieter Lohmar as “Husserl’s Manuscript A I 35,” in Husserl and Analytic Philosophy, G. E. Rosado-Haddock (ed.), Berlin, de Gruyter, (2016), pp. 289–319. Quine, Willard (1947) “The Problem of Interpreting Modal Logic,” Journal of Symbolic Logic 12(2) (June), pp. 43–48. ——— (1948) “On What There Is,” in From a Logical Point of View (2nd rev.), New York, Harper & Row, 1961, pp. 1–19. ——— (1950) “Identity, Ostension, and Hypothesis,” in From a Logical Point of View (2nd rev.), New York, Harper & Row, 1961, pp. 65–77. ——— (1953) “Two Dogmas of Empiricism,” in From a Logical Point of View (2nd rev.), New York, Harper & Row, 1961, pp. 20–46. ——— (1960) Word and Object, Cambridge, M.I.T. Press. ——— (1969) “Ontological Relativity,” Ontological Relativity and Other Essays, New York, Columbia University Press, pp. 26–68. Russell, Bertrand (1903) Principles of Mathematics, London, Norton. ——— (1911) “The Philosophical Implications of Mathematical Logic,” The Monist 22 (October 1913), pp. 481–93. Cited here as found in his Essays in Analysis, London, Allen & Unwin, 1973, pp. 284–94. Partially translated in Husserl Ms A I 35. ——— (1919) Introduction to Mathematical Philosophy, London, Allen & Unwin. ——— (1956) Logic and Knowledge, Essays 1901–1950, London, Allen & Unwin. ——— (1973) Essays in Analysis, London, Allen & Unwin. Russell, Bertrand & A.N. Whitehead (1927), Principia Mathematica to *56, ­Cambridge UK, Cambridge University Press, second ed. (1964).

Chapter 4

A Category Semantics Paul Symington

BACKGROUND There are three recognizable features that consistently accompany a theory of categories going back to Aristotle’s treatment of the topic in his Categories.1 (1) Categories are associated with linguistic predicates. In fact, the words “category” and “predication” have the same etymological foundation. In this way, categories are equated with the activity of identifying things according to characteristics that can be rightly attributed to them. Since these characteristics are semantically consistent and able to be predicated of more than one thing, categories are often associated with universals. (2) Categorial terms are very “broad” when considered both (2a) intentionally and (2b) extensionally. (2a) The intension of a term is the meaning of the term, which helps fix the reference of the term and ideally identified with the necessary and sufficient conditions for the correct use of the term. If we think of predicates in terms of the meaning they express, they reveal a discernible hierarchical nature among them in such a way that some are said to “fall under” others.2 Predicate P is said to fall under predicate Q when the intension of Q is explicitly contained in the intension of P but not necessarily vice versa. For example, the predicate “giraffe” explicitly expresses what is expressed by the predicate “animal” and so “giraffe” falls under “animal.” Categories are associated with those predicates that have the most predicates that fall under them and so are most broad in nature. For Aristotle, these broad terms are “substance,” “quantity,” “quality,” “relation,” “place where,” “position,” “time when,” “habit,” “action,” and “passion.” 65

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(2b) The extension of a term is related to its reference;3 the particular things referred to when the term is used. If predicate P falls under predicate Q, any name of an object that has P correctly predicated of it also has Q accurately predicated of it, but not necessarily vice versa. This can be expressed within a set theoretic framework: suppose that set A has predicate P accurately predicated individually of each of its elements and set B has predicate Q predicated individually of its elements. When P “falls under” Q, all members of A will be included in B (although there might be some members of B not in A). When understood extensionally, categories are most broad in nature in that they refer to the largest sets (of real objects, which is addressed by condition “(3)” below). (3) Categorial terms provide a meaning nexus ordered to an understanding of the “real world as real.”4 Categories provide the fundamental ground of meaning so as to express the structure of reality. Classically understood, real objects—with which categories deal—were opposed to mental objects. Category theory provides a way of limning the isomorphic relationship between meaning and reality. In order for category theory to provide a fundamental theory of meaning flexible enough to account for this isomorphism, it must be concerned with perceptual content and the structure of human experience (psychology). In addition, a categorial theory will have to be integrated both with logic and the canons of reason, and the basic function of language. In fine, a category theory must provide not just a structure of reality, but also a radical theory of meaning articulating a plausible semantic intercourse with reality. In this chapter, I shall provide a semantic theory that incorporates a categorial functionality, which integrates these three features traditionally assigned to categories. There has been an inclination to favor “(1)” and “(2a)” over “(2b)” and “(3)” by philosophers when presenting theories of categories. I shall argue that categories should be thought of as providing semantic integration of the regions of perception, logic, language—including the sense and reference of our terms and the fundamental divisions of reality—and I shall do so in the context of a possible worlds truth functional theory of meaning as my point of departure. To wit, not only do categories provide the structure for determining fundamental properties for things in the world, but they also are essential in the determination of the very structure of objective meaning, which span both actual and possible objects of reference. By providing a way around intractable problems faced by recent semantic theories, I hope to bring categories back to its rightful place as key theory for unifying fundamental elements of the world, experience, and reality. David Lewis presented his “General Semantics” (1970) and with help from his possible world truth functional semantic theory,5 I present here a preliminary “Categorial Semantics.”

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The essence of categorial semantics is that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. SECTION I In order to make progress when investigating a semantic theory, one must distinguish two closely related questions: “What do our words mean?” and, “In virtue of what do our words have meaning?”6 In this section, I shall seek out an answer to the first question within the context of contemporary semantic theory, broadly and selectively, understood. In section “III.” I shall bring in the question about how words obtain meaning. The fundamental meaning of a sentence is related to the conditions under which, or the possible conditions under which, the sentence would be true.7 Just as the meaning of a sentence is related to the conditions under which the sentence is true, so too the meaning of the words fundamentally depend on the meaningful sentence as a whole that they compose.8 However, at the same time, in order to explain how humans are able to understand right away sentences not previous experienced, it is clear that there is a compositionality between the sentence’s words and the meaning of the sentence as a whole in such a way that the meaning of the sentence is built up from the meaning of its words (and the relations or structures that exist in and among them). In fact, the meaning of a sentence is a function of the meaning of the words that make it up. So, if someone has some knowledge both of the content of a given word and some rules (such as syntax, etc.) for using the word to build a meaningful sentence, one can anticipate new meanings at the sentential level, and ultimately at the truth conditional level. Since the meaning of a sentence is dependent on its truth conditions, it is important to identify a general theory of truth. According to Possible World Truth Functional Semantics (PWTFS) the meaning of a particular sentence is the conditions under which that sentence would be true in some possible worlds or state of affairs.9 For example, the meaning of the sentence, “A red bird flies swiftly” is the set of possible worlds in which “A red bird that flies swiftly” is true. Since this is an extension of the notion of the meaning of a sentence based on the truth conditions that hold in the actual world in relation to that sentence, and there are a vast number of possible worlds in which non-actualized sentences are true (and each of us have a sense of these broader possibilities) a more general (and plausible) theory of truth conditions is obtained. Since the truth value of complex sentences are determined by the semantic and truth functional elements of its constituents—regardless of the world that is being referred to—the truth conditions of sentences at a more complex level can be logically analyzed in virtue of its sentential parts.

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PWTFS ultimately establishes meanings as weighted toward a referential or extensionalist account. That is, meanings work by picking out the right sets of possible or actual objects from some specific set of worlds in which the sentence expressing the meaning is true. To use the example given above, “A red bird flies swiftly” means the function by which a set of possible worlds gives as its output the right set of objects as the conditions for the truth of the sentence namely, those in which a red bird flies swiftly. When one takes into consideration the theory of compositionality, the meaning of the sentence is all the possible worlds in which there is at least one object that exists in the intersection of the sets of red objects, of birds, of flying objects, and of swiftly moving objects. Advantages of this theory of meaning abound. In employing possible worlds for filling-out truth conditions—and consequently, meanings—some intentional functions seem to be obtained automatically from this analysis. A problem with purely extensional theories of meaning is that they are usually unable to distinguish intuitively different meanings for co-referring terms. To use Quine’s example, the extension of the term “animal with a heart” is identical to the term “animal with a kidney.” Since in the actual world there is no cordate being that is not a renate being, and vice versa, if the meaning of these terms is based purely on its extension in the actual world, then on a pure extensional theory the meanings will have to be identical. However, on PWTFS since there is a possible world in which some animal has a kidney with no heart and vice versa, the meaning of these terms are able to be distinguished and captured for each. In this way, more subtle meanings are captured indirectly: meanings are obtained for coextensive words through the diversity among worlds where even very similar sentences will turn out to have different truth-values. Another advantage of this view is that it does a good job at adumbrating the meaning of modality (necessity is a proposition that is true in all possible worlds, etc.). However, PWTFS has considerable problems facing it. After I spell out some of these, I shall build on its strengths in what I call a “categorial semantics.” SECTION II Problem 1: A sortalist theory is required to provide truth conditions for identity statements. A full theory of meaning needs to be able to give unambiguous answers to identity questions for most objects. However, as David Wiggins and others have argued, even if one presupposes a non-relative notion of identity, asking

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whether x and y are the same thing cannot yield an unambiguous answer. Such a question requires the identification of some sortal term—which answers the question, “The same what?”—in order to be able, in principle, to be answered.10 Similarly, in order to count something, one must count individuals as sorted by some kind. For example, one cannot simply count objects in a room, but one must count objects under some sortal concept (such as books, or pieces of furniture, or some combination). Due to the objective status of possible worlds and the principle of compositionality, sortals are required within each possible world, corresponding to each thing about which an identity claim can be made. Thus, not only are there objects in most possible worlds, but there are also sortals that correspond to these individuals. Specifically, objects will be in their respective sets if and only if they have sortal properties. Possible worlds are not intrinsically structured.11 However, in order for sentences to be true and to have meaning, there needs to be some principle that determines objects to the set in which they belong. For example, not only would the set of horses have something in common for their set membership but even the most fundamental particles and metaphysical simples need sortals associated with them in order to have identity and countability.12 Philosophers should seek to say something about that structure when theorizing about the meaning of sentences. Such a structure would work well with the theory of compositionality. Problem 2: It cannot handle substitutivity in certain propositional contexts. Genuine synonymy between two terms (say) is obtained by there being two sentences with so-called synonymous terms that are true in exactly all the same possible worlds. Yet, on PWTFS there are some contexts in which (otherwise) obviously synonymous terms yield different truth-values. For example, it might be true that “John believes that an actor works on a stage” but false that “John believes that a thespian works on a stage.” Thus, it seems that this view cannot be a sufficient account for the meaning of synonymous terms.13 Problem 3: It cannot handle transworld identity. That one and the same (identical) thing is understood in opposing states of affairs seems a part of the general meaning of sentences. If the meaning of a sentence were a function of possible worlds to that sentence’s truth, then it would be a mistake to think that there is no transworld identity for those objects named in the sentence. For example, it would seem that the meaning

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for the sentence “Sue is a medical doctor” should involve only Sue and those persons identical with her in the possible worlds that spell out the meaning of the sentence. The meaning of the sentence involves only Sue.14 A helpful account of meaning will include transworld identity.15 Problem 4: Something like mental content is required to support this theory of meaning. Given the theory of compositionality, it is more plausible to hold that meanings are built up from not only truth functional connectives and set theoretical sorting but also in some way through the lens of perceptual content. Due to the theory of compositionality, the meaning of a sentence is determined by the terms that make up the sentence. The truth functional features (such as the conjunction “and,” etc.) through which complex sentences are obtained are without content. The content for the terms comes from the basic meanings of the terms themselves. Such content is fundamentally related to, and commensurate with, perceptual content. If this were not the case, then it would seem possible for every possible world to be extremely different from the way it would be possibly perceived by us, in which case a theory of meaning would have nothing to do with our experience and perceptual interaction with the actual world. Thus, it seems that the fundamental meaning of our words includes some basic relationship to perceptual content. PWTFS takes a non-mentalist approach to semantics. However, it seems that some specific relationship to “mental content” is required for shaping up a theory of meaning for sentences in order to account for the fact that meaning is in some sense mind-dependent and integrated at the ground level with human intention, communication, and experience. Such a desideratum must be taken in light of the important distinction for a theory of meaning between what a sentence means, and that in virtue of which the sentence has meaning. Problem 5: Given “Problem 4” above, if a mentalist point of view is brought in there are puzzles in the interaction between the meaning of a sentence and what a person means by uttering a sentence. Involved with sentence meaning seems to be what the speaker of the sentence intends or understands the sentence to mean. Puzzles arise when considering especially the referential meaning of a sentence. On PWTFS, the reference of the sentence is fixed by the meaning of the terms as a function from possible worlds to the sentence’s truth. This can be different from what the speaker means. As a result, in the case where someone (mistakenly) utters the sentence, “Hens crow too early in the morning”—meaning it to be about

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the annoying practices of roosters—the sentence would literally be false, although it seems reasonable that since the speaker meant to refer to roosters, it should be true at the level of speaker intention. Thus, a theory of meaning that can integrate literal and speaker meanings would be advantageous. Problem 6: It lacks a robust account of propositional inference. A theory of inference based on the relationship among meanings instead of material truth conditions of possible worlds would be preferential since it is a more intuitive account of inference. Regarding logical inference, PWTFS strikes one as involving “logical luck” or “cosmic coincidence.” SECTION III We shall first look at the categorial semantic theory in general. In the next section, the theory will be investigated to see how it can handle individual sentences. Although Aristotle’s theory of categories is often associated with the specific list of them in the second chapter of his Categories, we take inspiration for categorial semantics in the structural insights about categories from his first chapter: Of things themselves, some are predicable of a subject, and are never present in a subject. Thus “man” is predicable of the individual man, and is never present in a subject . . . . Some things, again, are present in a subject, but are never predicable of a subject. For instance . . . a certain whiteness may be present in the body (for color requires a material basis), yet it is never predicable of anything. Other things, again, are both predicable of a subject and present in a subject. Thus while knowledge is present in the human mind, it is predicable of grammar. There is, lastly, a class of things that are neither present in a subject nor predicable of a subject, such as the individual man or the individual horse.16

This passage is understood to generate a matrix in which universals and particulars are matched with accidents and substance. However, Aristotle advances the matrix to show how they are integrated in such a way that primary substance (that which is neither predicated of another nor in another) is that upon which the others are founded. The universal exists in virtue of the particular and the accident exists in virtue of the substance. The dialectic of actuality and potentiality is a vital way for understanding these items in relationship to each other.17 On my view, the more universal a thing is understood to be from the individual substance, the more potentiality it expresses.

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Similarly, the more universal an accident is understood from its accidental particular, the more potentiality is also expressed.18 In order to illustrate the role of potentiality, we start from the ground up, imagining a nascent person seeing for the first time. What the person sees has a certain shape and color and appears to the person as such. As that person has more experiences with other shapes and colors, she starts to catch onto similarities and continuities among the variety of things of her experience. She begins to shift from an immanent and solipsistic awareness of images (adventitiously popping into her mind), in the broadening of her experience and grasping more common notions, to formulating a referential notion of these images. In other words, she proceeds from the notion of particular shapes and colors to the more general notion of “color” and “shape” to the categorial notion something like Aristotle’s “quality.” Through this process she realizes that included in the notion of a quality is the notion that any quality is a quality of something; specifically, the notion of a corporeal body in which the quality resides. In this way, the notion of reference to something substantial is realized as that in which the quality resides. The object is able to be seen by her from different sides and so provides some unity to the various qualities through which it is experienced. The various ways in which the dimensionality of the object is experienced yields general concepts for understanding such objects, and the notion of quantity as a category is realized.19 Like quality, quantity also has a reference to something else beyond it, which ultimately is quantity of a substance. Substance provides unity of the object over and above the diverse quantities and qualities associated with objects and both are understood to depend on it as that in which they exist.20 As with generic accidents such as quantity and quality, there is both a generic and more specific way of understanding a substance. Most generic is “substance,” simply speaking, which can be predicated of all substances; more specific than “physical substance” is “living” then “sentient” and finally “rational.”21 There are a few things that need to be explained about this account (and Figure 4.1) given above. The first is that potentiality becomes more salient as the level of “a this” or “bare particularity” is approached. “This” can be understood either in terms of primary unity or secondary unity in which “the this” is potentially referred to by the consideration of some quality or quantity such as “this thing” in which they inhere; or, it can be identified as potentially being the substance itself (rational animal) that is Obama, or Hillary Clinton, and so on. At such a level of deep potentiality it could be anything (in a fully modal and real sense) since this description—“this!”— applies generically to everything! Secondly, “this” has the semantic force of a basic referential focus or the ultimate target of the arrow of one’s conscious intentionality and as such serves as the basis of the referential

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Figure 4.1  Potentiality and actuality in relation to the generic and the specific.

function of language. All attributes are contained in the notion of being “a this” insofar as “this” is potentially rational, or sentient, and so on. The focus of rationality is “this” such that the rational is “this rational (thing)” as having a simple reference and gives it its status as a particular object (thing). Thirdly, potentiality is a function of vagueness. When something is being understood as a sentient thing, it is vaguely a particular sentient thing while not being any sentient thing in particular! “Sentient thing” is to be understood as itself a vague object that is ontologically indeterminate (it is vague which sentient thing it is and whether it a human being or a dog, etc.). Conversely, as you go higher in the hierarchy, the less vague things become. This is because higher in the hierarchy are specifying and determining properties of those that are lower in the hierarchy. This is seen in the fact that one does not experience in the real world “animals” as such but rather certain types of animals. At the highest level of actualization the object has “actual being,” which separates it from mere potential being: it actually exists as opposed to only possibly or potentially existing. In a manner of speaking, it is what differentiates the actual world from the merely possible world. Finally, one and the same thing has, objectively speaking, potentiality and actuality at different levels. Although potentiality can be separated-off from actuality as its own vague object, the vague object is (potentially) the same as the actual object except that the potentiality is an objectification of the actuality at a lower level of actuality. This is seen in the fact that when one sees a patch of color, although on one hand in itself it is vaguely just a patch of color that could be associated with any actual object, it is also the patch of color of an actually existing substance! Importantly to this theory is the fact that in an objective sense, a patch of color in itself is potentially some individual other than what it is: although it is actually the patch of color of the substance of Obama, as such, it is potentially something other than Obama, such as potentially the patch of color of Hillary Clinton or even of some inanimate

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object.22 Regarding unity, simple unity obtains when the different levels on the hierarchy are components of the same thing, whereas secondary unity is such that that which is at the lower level of the hierarchy refers to “the this” which is a substance as that in which it exists. Let us see how far set theoretical considerations can take us toward a clearer understanding of this theory. We begin with an actual substance, Barack Obama. He exists in the set of actual “thises.” He also exists in the set of actual substances, sentient beings, living beings, and rational beings. He also exists in the set of actual presidents. However, in virtue of his membership in these actual sets of various kinds, the “this” which is referenced to when he is actually being referenced is potentially a lot of other things. For example, to be a president is the actualization of the potential of “holding public office” and as such, since that potentiality is contained implicitly in this actualization, Obama is potentially something other than president that falls under that potentiality, such as being “secretary of state.” Deeper potentialities are present as one moves closer to the limit, which is that at the categorial level (in this case, quality). At a radical level, since Barack Obama is a “this” there is potentiality for the focus of reference of him to not refer to a human being at all, but possibly a star or tree. Of course, Barack Obama himself could never be a star or a tree since Barack Obama is essentially a human being and we think of his name attached to the continuing actually existing substance. Corresponding to the metaphysical structure of reality is the act and potency that exists in relation to human cognition, and it is at this point that we seek an answer to the question of how words obtain meaning. The categorial semantics holds a very broad—if not permissive—view of “acquaintance”;23 namely, that a necessary condition for being acquainted (in a semantic sense) with an actually existing object is for one to experience something that is potentially associated with the actually existing object. Suppose someone catches a glimpse of a patch of color that is speckled mixture of black and grey. It turns out that in actuality it is the color of Barack Obama’s hair. However, as such, since that patch of color is potentially the color of a rather large number of actual things that have that color, the perceiver of the patch of color has obtained a degree of acquaintance with all of those things. Similarly, say that one sees an animal approaching but one cannot make out exactly what kind of animal it is: as such it is potentially any number of actual animals that exist and in virtue of this one becomes acquainted to a degree with all of them.24 Words gain their meaning through a process of actualization of potentiality and potentiality of actualizations. Words are potentially meaningful, and the crispness of their meaning increases in relation to the deeper actuality that is obtained at the level of cognition.25

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SECTION IV In light of the analysis given in the last section, in this section I offer semantic analysis of a group of sentences, which serves as vehicle to explicating categorial semantics. (1) “Barack Obama is a human being.” Since the meaning of a sentence in categorial semantics is the function from the actualization of potentialities or the potentiality of an actualization to the sentence’s truth, the conditions for the truth of this sentence will be some potentiality named by Barack Obama that is actualized as a human being. Barack Obama needs to name an actual individual and so what is named by Obama requires the actualization of fundamental existence of “a this.” Beyond the actualization of an individual, further actualizations are required: it is not only a sentient living substance, but rational as well. When these conditions are met, the sentence is true. Like PWTFS, the meaning of this sentence is the conditions under which it is true, specifically, the condition in which Barack Obama is a human being, including all possible worlds in which the conditions are such that the sentence is true. On a logical analysis, the possible worlds in which this sentence is true are worlds in which the item named “Barack Obama” belongs to the set of human beings. If someone thought that this sentence meant that Barack Obama is a good chess player that person would not understand the sentence since the conditions are such that there are some possible worlds in which Barack Obama is a human being but is not included in the set of good chess players and yet the sentence is still true in those worlds. On a categorial semantics, meaning tracks the answer to the following inquiry: what actualization of some given potentiality needs to be realized in order for the sentence to be true? Specifically, the sentence is true when the actuality of some patch of color, and so on, which is potentiality Barack Obama is actually Barack Obama (according to secondary unity with this actually existing “this”) and “this” named by Barack Obama is both potentially a human being and actually a human being. Consequently, the sentence is meaningful both because the patch of color, even if it is not the patch of color of Obama, could have been, and the “this” identified through the patch of color is potentially a human being. What is the relationship between “human being” and “Barack Obama”? “Human being” is a description and “Barack Obama” is a name. However, “Human being” is a term associated with Barack Obama in an essential way such that every possible world in which there is Barack Obama, that thing named is a human being (or, while Obama exists, he is human). Associated with the meaning of Barack Obama is that of being a human being. The

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existence and identity conditions for a human being apply essentially to the existence and identity conditions of Barack Obama. So, we turn now to the next sentence to find its meaning: (2) “Although Barack Obama is President of the U.S. in 2015, he could have been just a U.S. Senator instead.” This is an interesting sentence since it has some unactualized potentiality associated with it. The antecedent of the sentence is clearly meaningful on categorial semantics: as president, there is an actualization of the potency of Obama to be president, and Obama himself is the actualization of a substance potentially being a human being. This corresponds with a person who has proceeded from potentialities to actualizations in their semantic grasp of the antecedent as well. She has proceeded from seeing a patch of color that is potentially a number of things to further actualizations and narrowing of that potentiality to the point where not only is the antecedent meaningful for her, but she also believes it to be true. Note as well that even if she wasn’t aware of the existence of Obama, and so did not believe it to be true, the sentence is still meaningful for her because she has acquaintance with human beings and presidents and so has acquaintance with Obama being president without believing it to be true. Finally, even if it is not meaningful for her, the sentence is still meaningful in itself since it is the case that at a most fundamental level “this thing,” no matter what it is actually is potentially Barack Obama, the human being, who is president. The consequent of the sentence is also meaningful. Although Obama is not actually a U.S. Senator in 2015, he is actually a human being. As such, he potentially is a president or a U.S. Senator. This is where the meaning is grounded in the potentiality of an actuality. Thus, since the meaning of the sentence is the function of the actuality of potentialities to the sentence being true, since Obama is a human being (as per “(1)” above) since human beings are potentially U.S. Senators in virtue of this, “(2)” is true under that condition of potentiality. Notice that the sentence is true only up to a certain level of actuality—the actuality such that Obama is a human being (which itself is actuality of more basic potentialities). Although Obama is actually a president and actually a human being, as a human being he is in potentially both with respect to being a president and to being a U.S. Senator. However, the name “Barack Obama” has a reference to “a this” as such and so does not stop with the being that actually is Barack Obama. Since Obama is not just a particular substance of a certain determination, he also is merely, and actually, “a this.” Since “a this” can be anything, the name “Barack Obama” picks out the thisness of Obama that could be a different actual thing than it actually is, although Obama specifically names only the actual thing that is Obama. To put it another way, thisness includes the meaning of

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potentiality, which can be anything. Yet, the thisness is that which is actually unified with the determinate sense as a potentiality for actuality. This point of view comes in handy when considering the meaning of the next sentence: (3) “A unicorn is cheerful.” The term “cheerful” would express an accident of a would-be unicorn. It refers to a substance beyond itself in which it exists. As described above, when properties (such as “cheerful”) is experienced, it is indifferent to which thing it modifies. But what about the reference of “unicorn”? Since a good number of rational things can be cheerful, the reference will be the vague object that includes rational beings—regardless of whether they exist or not (and so unicorns will potentially be such cheerful things). The meaning of this false sentence is still clear. The kind of thing that can be cheerful is something that is rational but there is required more actuality than what is expressed in the potentiality of the sentence in order to be true. Specifically, the potentiality of a rational animal would need to be realized by the further actuality of being equine; and this equine rational being would need to be cheerful. In this way the truth conditions are met and so the sentence is meaningful. Similarly, the sentence, (4) “The present king of the France is bald” is false. The meaning of this sentence is that the potentialities expressed in the sentence are actualized in a way that is true of the actual world. Although there are some potentialities that are grounded in actuality, it doesn’t go all the way to correspond to the actual state of affairs. Specifically, France potentially has a king but this state of affairs is not actualized. So, it is meaningful on a truth-theoretical perspective but false. The next sentence is a little bit more difficult than “(4)”: (5) “A square circle is an usual geometrical figure.” It is difficult because although square circle is what is being referred to in the subject of the sentence, square circles are impossible objects; in other words, there is no potency in the kind “geometrical figure” to allow for this. However, there is room to allow for a reference function for the subject of this sentence. The notion “this” is not something that requires the kind of unity appropriate for substances. Thus, someone could point to a set of books on a table and refer to that collection of substances as “this.” Thus, the subject of the sentence can have reference because in order to be “this” there is no required substantial unity. The sentence will be false, though, since the predicate expresses a notion of unity appropriate to a geometric figure. The meaning of the sentence will be that “this” is able to have actualities such that it is a square circle and will be unusual. Since “this” does not have the potentiality

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of the vague object geometric figure to be a square circle, the proposition will not only be false but necessarily false. Being a human applies to more than just Barack Obama, but to many others such as George Bush and Hillary Clinton. These individuals have a special link to this predicate such that they can be understood as properly falling under the predicate “human being.” This “falling under” clearly occurs at higher levels as well such as with the sentence: (6) “Every human being is an animal.” This is interesting in this respect because human being is a fuller actualization in itself than animal, which is a potentiality to be human. Thus, it will be true in virtue of the notion of human being and the level of actuality it contains. The meaning of the universal quantity of the sentence is uniquely obtained as well on categorial semantics. However, unlike modern logical perspectives on universal quantification in which there is no existential import, in order for the meaning of the sentence to be the function from the conditions for the actualization of potentialities or the potentialities of actualities to a sentence’s truth, “every” is proportionate to the actuality of the subject “human being” in the conditions for the truth of the sentence. Thus, “every” refers to all actual beings, and that they are all actually animals. A similar situation is true of sentences with particular quantity such as “Some human beings are happy,” in which what is being referred to includes at least one actual human being. The next sentence deals with synonyms. Extensionalist theories of meaning in which meaning is obtained solely through reference has a difficulty with sentences that involve substitutivity within propositional attitudes. This is true even for extensionalist theories of meaning that incorporate PWTFS principles into its theory. (7) “Although John believes that an actor works on a stage, John doesn’t believe that a thespian works on a stage.” On an extensionalist view, word meaning is the things that the words stands for. This approach is challenged when there are sentences in which a person is asserted as believing some proposition. Thus, although “(7)” seems like it should be true, it is not possible on an extensionalist account since there can be no difference between “thespian” and “actor” since in every possible world sentences with these words have the exact same truth value. On categorial semantics, the meaning of the sentence is as follows: with the true sentence that “John believes that an actor works on a stage” what is included is not only the actualities of basic potentialities that correspond to the fact that actors (or thespians) work on the stage, but also this is true regarding the meaning of the sentence to a particular person. On the one hand, human beings are in potentiality toward doing such things, such as performing on

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the stage, and at that level it is indifferent whether such a person is an “actor” or a “thespian.” On the other hand, the sentence is not just about the meaning of “An actor or thespian works on a stage,” but rather, John’s belief about it. It turns out that the categorial semantics can handle this additional condition because it ties in mental components of meaning; the meaning of “(7)” is related to actuality and potentiality in a complex way. Take a vital component of the sentence: “A thespian works on a stage.” This sentence is true, and so is meaningful, inasmuch as a human being has the potency to be a thespian and included in this actualization is the actualization of working on a stage. Beyond this, though, when belief about the sentence is considered, the meaning will now stand in potentiality to further actualization namely, the potentiality of this true sentence being believed by John. Understanding the meaning of the words of the sentence will be a necessary condition for belief. Thus, due to the diversity of words used, there is the possibility for a given sentence in which a belief is reported to be meaningful in that there is an actualization of possibility that is available despite the fact that for John himself the sentence “A thespian works on the stage” is not meaningful (because he is not aware of the conditions under which the proposition would be true). I should mention that categorial semantics has strong extensionalist features while being able to handle sentences like “(7).” This is because potentiality is derivative from what is actual, and what our language is fundamentally grounded in terms of meaning is actualities or the objects of reference in which potentialities lie. Also, the dynamic between the basic meaning of a sentence and the relationship that a person has to a sentence can be spelled out in terms of the act/potency relationship. (8) “Barack Obama is the Speaker of House of Representatives. Therefore, Obama is a U.S. citizen.” Questions about sentence meaning as it relates to implications among sentences are also handled by this categorial semantics. Regardless of whether potentialities are actualized or not, there can still be relations of inference among those sentences. That Obama is the president of the United States identifies actualities of potentialities that do not just include being a president of the United States but also being Speaker of the House. Included in the potentiality of Obama’s actually being a U.S. president is him being the Speaker of the House. Insofar as he could be a Speaker of the House he is a U.S. citizen such that if he actually was the Speaker of the House it would also be true that he is a U.S. Citizen. (9) “‘Barack Obama’ and ‘Barry’ are the same person” This involves the meaning of a statement of numerical identity. Identity has to do with full actuality of the potencies involved since when dealing

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with potencies one is not dealing necessarily with the same actual individual. For example, due to vagueness, there is no answer to the question of which person is picked out by the term “human.” Thus, the meaning of the sentence is such that in order to be possibly true, “Barack Obama” and “Barry” need to be the names for the same actual individual Barack Obama. The converse of Quine’s dictum “no entity without identity” is applied here: no identity without (actual) entity. (10) “Hens crow too early in the morning” (when the speaker means to refer to a practice of roosters). On extensionalist accounts of meaning, this sentence is simply false. However, on categorial semantics, there is some room to bring speaker meaning in to show that it can be a true sentence. In order for this to be possible, there needs to be some conditions of actuality of potentialities that determine the sentence as true. Prima facie, it seems that there can be no such conditions since no actual hens crow. However, if the meaning of the word “hens” is changed to mean “roosters” then the sentence would be true. Since word meaning is determined by a process of movement from potentiality to actuality in light of perceptual content—any given word is in principle in radical potency to the determination of meaning, and this is why they are understood to be established by convention—the meanings of words can change in light of speaker meaning (which is drawn from perceptual content). For example, the truth conditions for the sentence involves a chicken actualized by male sexual designation among other factors. In this case, the person asserting the sentence has a corresponding actualization of such a potency in mind (that is, they would deny that female chickens can crow). Therefore, the sentence is not only meaningful but also true due to his irregular use of the word “hen” in this instance. (11) “The summer run greasy as car before.” This sentence lacks meaning (and hence, truth value) due to the important role that syntax plays in indicating basic order among actuality and potentiality of elements of sentences together to be able to bring in a truth functional notion for meaning. Grammar and syntax, however, is posterior to the fundamental division of reality into the structures of categories, but a nice indicator (if not conclusively so) of this division.26 SECTION V Although much needs to be explored and fleshed out concerning the doctrine of categorial semantics, it is clear that it is a flexible and encompassing theory of meaning. Although it is able to deal with issues about the basic meaning of

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words, it also allows for a corresponding companion theory about how words gain meaning. In addition, the theory provides a way of plausibly integrating psychological (or at least cognitional metaphysical) factors with an objective (or extensionalist) semantics. It provides an alternative to possible worlds semantics, while building on it, but without inheriting some of the problems. It brings some clarity to the logical issues of inference and quantification. By utilizing intuitive notions of actuality and potentiality, it is both an extension of a traditional theory of categories and picks up on insights that are currently being developed in contemporary powers ontology.27 Ultimately, it satisfies the requirement of a semantic theory for sentences listed by Harman (1975, 42): (1) it provides a finite theory of truth for languages and it satisfies conditions resembling Tarsky’s “convention T.” Specifically, it takes Davidson’s advice that a theory of meaning “provides for every sentence s in the language under study a matching sentence (to replace ‘p’) that . . . ‘gives the meaning’ of s” (Davidson 1967, 309). (2) It minimizes novel rules of first order logic (on categorial semantics: it seems to save much of traditional logic at least). (3) It minimizes axioms (on categorial semantics: logical rules follow from an application of the act/ potency theory of meaning). (4) It interprets sentences as implying ordinary sorts of things (on categorial semantics: the experience of potentiality is grounded in basic perceptual experience). (5) It is compatible with syntax (on categorial semantics: categorial structure establishes syntactical potentialities). To sum up, I give the categorial semantic theory by way of an example of a Tarskian T-sentence: “Snow is white” if and only if snow is white.28 Snow is white is the condition under which the sentence “snow is white” is true. Snow is white when there is some potentiality to be snow and white and these are actualized. The meaning of the sentence “Snow is white” is partially grounded in a person experiencing something which has potentiality and that potentiality is actualized in such a way that what is experienced is snow and is white. Since snow being white makes the sentence “Snow is white” true, the sentence “Snow is white” is meaningful. Due to the theory of compositionality, the words in the sentence and their combination compose the meaning of the sentence and so they are in potentiality to be actualized by the meaning of the sentence as a whole. NOTES 1. For a helpful general overview of the topic and bibliography see Thomasson. 2. For a discussion of Frege’s view on the different senses of “is” see Hintikka & Knuuttila, p. ix. 3. Although some do not equate extension with reference. Oftentimes, extension is understood to mean just the objects in a set. For example, the extension of redness

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is just the set of red things (such as cardinals, etc.). In contrast, reference is often used to indicate not just objects but even aspects of objects. 4. For example, Aquinas divides being into real and mental being. Real being is being that is divided fundamentally by categories. 5. For a clear presentation of possible world as a foundation for semantics, see Jacobson, chapter 2, “Semantic Foundations.” Especially helpful is her use of set theory to explicate meaning as a function. 6. Lewis (1980), p. 18. 7. Davidson, p. 311. 8. This has been referred to as the “context principle” and can be found in Frege, section 60. 9. See Lewis (1970) and Weisler (1991). 10. Wiggins, Idenitity and Spatio-Temporal Continuity. 11. Or, what amounts to the same thing, they are fundamentally fractured and promiscuous. That is, there is a set for any conceivable collection of objects. 12. Although sortalists will recognize that at fundamental some of the prominent features of identity will breakdown, but not entirely. See Lowe, The Possibility of Metaphysics, chapter 3. 13. This objection is modified from Lycan (2008), p. 131. 14. Lewis (1986). 15. Lycan (1991, 517) makes a similar complaint. Working from a Montague inspired semantic theory, Cresswell, in contrast to Lewis, holds “the same basic individual can exist in more than one world, though its manifestations may be different in different worlds” (p. 94). 16. Aristotle, Categories. 17. It seems likely that Aristotle is at pains to show how these four items relate to each other in favor of an imminent realism that gives priority to individually existing substances to overcome a problem raised against the Platonic view of forms as transcendent and existentially removed from material things in Plato’s Parmenides. 18. The structure is very similar to the schema among Lowe’s (2006) four “categories,” except I add the relationship of actuality and potentiality as well. 19. It might seem strange that I am jumping right in without argument to some of the particular categories of Aristotle: quality, quantity, and substance. However, like myself find it plausible. For example, McMahon says the following: “the categories can be said to account for the major syntactic/semantic roles in language, and any term which can be taken as categorematic can in some sense be included within them.” Regardless of what the categories are in content (which is outside of the scope of this chapter), I am arguing for the truth of the structure of categories in terms of actuality and potentiality as a foundation for sentence meaning. 20. It is at this level that some developmental psychologists have described as the grasp of an essence of an object. Similarly, this is a movement from a process of identifying directly perceptual similarities to similarities in concept in which the similarities are hidden. Categorial semantics offers a perspective on the vexing issue for psychologist in clearly distinguishing between perceptual and conceptual categorization (Rakison and Oakes, 7).

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21. There are some significant differences between this view and Lakoff’s “Idealized Cognitive Models.” Unlike Lakoff, the category theory I am presenting has a metaphysical as opposed to a purely cognitive ground. Like the classical view of categories, the view I am presenting pertains to “extramental reality” as opposed to a mental framework. Also, whereas Lakoff’s account holds ICMs as abstract, they are not flexible enough to fit every situation. The view that I am presenting is flexible to fit every situation since they are equated with openness and potentiality to that which can be realized in reality (as opposed to the traditional notion of “abstract” that Lakoff is using as removed from reality). 22. An interesting feature of this theory is that on one hand, similar to Frege’s view of sense a potentiality is what the mind grasps, and the actuality of that potentiality makes the sentence true or false. A difference with Frege’s view is that on categorial semantics, in some and perhaps all cases, the sense and the object are one and the same. 23. Cf. Russell’s view of acquaintance as contrasted with knowledge by description. 24. Note that regarding the psychology of concept development, in moving from potentiality to actuality in one’s understanding of the world, young children will have an easier time distinguishing between things at more fundamental levels (the difference between a living and nonliving thing) than within higher stages of actuality (the difference between a dog and a tiger). This appears to line up with recent advances in developmental psychology: “18-month-old infants responded to the superordinatelevel categorical distinction between animals and vehicles but not to basic-level contrasts within these domains such as dogs versus horses” (Rakison and Oakes, 9). 25. As is clear, the objective of categorial semantics is to find deep properties and structures of language. However, instead of identifying a set of rules that pick out well formed sentences in which the “bracketing of deep structures was done in terms of fairly traditional grammatical categories” (Lycan 1986, 5), the categorial semantics method takes a combination of a metaphysical (including cognitional ontology) approach, which is facilitated by the notion of truth conditions. 26. Although he rejects a truth functional approach to semantics in favor of one grounded in the use of language, Braine agrees about the priority of semantics to grammar/syntax: “if we are presented with a stark choice between grammar dictating basic semantic structures or basic semantic structures dictating grammar, it is only the latter option that is credible. The only way in which the fundamental structures of speech can be “native” or innate is by their being dictated by the very structure of the activity of communication itself and by our understanding of the world so far as it is given in the general logic.” (p. 42). 27. See Marmadoro. 28. For a clear presentation of Davidson’s use of Tarsky’ theory of truth as applied to semantics, see chapter 2 of Larson & Segal.

REFERENCES Aquinas, Thomas. (1968) On Being and Essence. Armand Maurer (trans.). Toronto: The Pontifical Institute of Medieaval Studies.

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Aristotle. Categories. E. M. Edghill (trans.). http://classics.mit.edu/Aristotle/ categories.1.1.html Braine, David. (2014) Language and Human Understanding: The Roots of Creativity in Speech and Thought. Washington, DC: The Catholic University of America Press. Carnie, Andrew. (2013) Syntax: A Generative Introduction. 3rd Edition. Oxford: Wiley-Blackwell. Cresswell, M. J. (1973) Logics and Languages. London: Methuen & Co. Ltd. Culicover, Peter W. (1997) Principles and Parameters: An Introduction to Syntactic Theory. New York: Oxford University Press. Cumpa, Javier (ed.). (2010) Studies in the Ontology of Reinhardt Grossmann. New Brunswick: Ontos Verlag. Davidson, Donald. (1967) “Truth and Meaning.” Synthese 17(3): 304–23. Davidson, Donald and G. Harman. (1975) The Logic of Grammar. Encino, CA: Dickenson. Evans, Gareth, and John McDowell. (1976) Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press. Frede, M. (1987) Essays in Ancient Philosophy. Minneapolis, MN: University of Minnesota Press. Frege, G. (1980) The Foundations of Arithmetic. Evanston, IL: Northwestern University Press. Garfield, Jay L. and Murray Kiteley (eds.). (1991) Meaning and Truth: Essential Readings in Modern Semantics. New York: Paragon House. Harman, G. (1975) “Logical Form.” In Davidson and Harman. Hintikka, J. and S. Knuuttila (eds.). (1986) The Logic of Being. Reidel, Dordrecht. Jacobson, Pauline. (2014) Compositional Semantics: An Introduction to the Syntax/ Semantics Interface. New York: Oxford University Press. Kefer, Michel, and Johan van der Auwera. (1992) Meaning and Grammar: CrossLinguistic Perspectives. New York: Mouton de Gruyter. Lakoff, George. (1987) Women, Fire, and Dangerous Things: What Categories Reveal about the Mind. Chicago: The University of Chicago Press. Lasnik, Howard, et al. (2005) A Course in Minimalist Syntax: Foundations and Prospects. Malden: Blackwell Publishing. Larson, Richard, and Gabriel Segal. (1995) Knowledge of Meaning: An Introduction to Semantic Theory. Cambridge, MA: The MIT Press. Lewis, David. (1970) “General Semantics.” Synthese 22(1/2): 18–67. ———. (1986) On the Plurality of Worlds. Oxford: Basil Blackwell. Lowe, E. J. (2004) The Possibility of Metaphysics. New York: Oxford University Press. ———. (2006) The Four-Category Ontology: A Metaphysical Foundation for Natural Science. London: Clarendon. Lycan, William G. (1986) Logical Form in Natural Language. Cambridge, MA: The MIT Press. ———. (1991) “The Trouble with Possible Worlds.” In Garfield & Kiteley.

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———. (2008) Philosophy of Language: A Contemporary Introduction. 2nd Edition. New York: Routledge. Marmadoro, Anna. (2010) The Metaphysics of Powers: Their Grounding and their Manifestation. London: Routledge. McMahon, William. (2004) “Reflections on Some 13th and 14th Century Views of the Categories.” In Sanford & Gorman. Pasnau, Robert. (2011) Metaphysical Themes: 1274–1671. New York: Oxford University Press. Poole, Geoffrey. (2002) Syntactic Theory. New York: Palgrave. Radford, Andrew. (1997) Syntactic Theory and the Structure of English. New York: Cambridge University Press. Russell, Bertrand. (1912) The Problems of Philosophy. New York: Henry Holt and Company. Sag, Ivan A., and Wasow, Thomas. (1999) Syntactic Theory: A Formal Introduction. Stanford: CSLI Publications. Sanford, J. and M. Gorman (eds.). (2004) Categories: Historical and Systematic Essays. Washington, DC: The Catholic University of America Press. Symington, Paul. (2010) On Determining What There Is. New Brunswick: Walter de Gruyter. Symington, Paul and Jorge J. E. Gracia. (2010) “Grossmann and the Ontological Status of Categories.” In Cumpa. Thomasson, Amie. (2013) “Categories.” The Stanford Encyclopedia of Philosophy. Edward Zalta (ed.). . Weisler, Steven. (1991) “An Overview of Montague Semantics.” In Garfield & Kiteley. Westerhoff, Jan. (2005) Ontological Categories. Oxford: Clarendon Press.

Chapter 5

Giving Descartes His Due Jonathan C. W. Edwards

In the opening chapter of The Concept of Mind, Gilbert Ryle (1949) introduces the concept of category-mistake in relation to what he regards as the Cartesian view of mind as a “ghost in the machine.” Whether Ryle’s conception has much to do with Aristotle’s categories I am not sure. Nevertheless, it is a handy way of expressing the idea that serious errors in thinking can occur when a concept is assumed to belong to a type, or category, that does a certain sort of job in describing the world, when it belongs to another. Category-mistakes in this sense still get in the way, and none more so than the one that, I shall argue, Ryle wrongly accused Descartes of, and made a mess of himself: attributing the wrong jobs to “mental” and “physical,” and related pairs of terms. The case I wish to make starts in philosophy but is just as relevant to neuroscience and to practical clinical psychology. Category-mistakes about mind and body can directly impact people’s lives. Our understanding of the relation of the “mental” to the “physical” will have major gaps in it for some time to come but I think Descartes (1641a) is a better place to start than the now entrenched fashion for Descartes-bashing of which Ryle was almost certainly as much a symptom as a cause. The main points I wish to cover are as follows. Descartes’ division of entities into two dynamic types is in fact very consistent with modern physics. He got a number of details wrong but Leibniz (1714) did much to resolve these. The popular modern conception of “materialism” is naive in comparison to the perspectives of the people who invented physics. Ryle’s problem was that he too wanted an irreducible ghost, but worn outside, as a “person-ghost.” As illustrated by concepts such as “extended mind” (Clark and Chalmers, 1998) and “intersubjectivity” (Gallagher and Zahavi, 2008), this person-ghost entity, which holds no water in a neuroscience account, fares little better in alternative, less “reductive” approaches. Instead, we need a conception of a 87

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human being that allows phenomenal experience, reasoning, and complex internal dynamics to be interrelated in a rigorous, and I would argue neoCartesian, framework. Everything in neuropsychology points to events like “thoughts” and “percepts” arising from dynamic relations within the brain, and very likely rather small domains of the brain. Descartes makes mistakes but at least he worked within a coherent physics framework, in contrast to many present day neurobiologists. MAKING PROGRESS WITHIN A NEO-CARTESIAN FRAMEWORK MAY NOT BE AS DIFFICULT AS IS OFTEN ASSUMED What may be the key is that our phenomenal experience, which we rely on so much for building an understanding of ourselves, may be related to dynamics in very unexpected ways, involving multiplicity both of dynamic levels within the brain and of experience itself. We should expect nothing else looking at the anatomy, but intuitions about person-ghosts get in the way. When the mind goes wrong in ill health we are currently at a loss to provide a meaningful internal dynamic explanation that might help in treatment. We do not even have a clear idea what we mean by the dividing line between mental and physical illness. It is easy to say that “all illnesses are physical” but that does not help if we are unclear what the “physical” categorization means and how we intend it to encompass phenomenal experience. There are no easy answers but some hard Cartesian science might help. DESCARTES’ DUALITY Descartes is almost universally ridiculed in modern science and philosophy. Yet, often those doing the ridiculing appear to make exactly the mistake they incorrectly attribute to Descartes: a bogus distinction between types of dynamic, or causal relational, entity, or unit. Moreover, it is ironic that Descartes is in direct line between Galileo and Newton in the foundation of hardnosed science. He is certainly not an uncritical believer—the Meditations (Descartes, 1641) start with total skepticism. However unfamiliar to modern science his concept of a spiritual substance may seem, he does not shy away from the question of exactly how it fits into a causal chain. In contrast, present day neurobiological models of conscious thought mostly require that it arises by “emergence” for reasons unrelated to the rules of causation everywhere else. Did Descartes really make the error he is accused of? I see Descartes’ separation of spirit from matter as resting on four factors.

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The first is the “experiential” nature of spirit, at least for the spiritual “substance” itself. To be “a thinking thing” is, first of all, to sense or perceive. The second is that for Descartes all matter was inert. All action or change came from spirit. The thinking soul appears to determine bodily movement so must be spirit rather than matter. The third distinction, crucial to the way Leibniz (1714) moves on from Descartes, is that spirit appears to relate indivisibly to the world so has no dynamic parts, whereas matter relates mechanically, part by part, as in the ends of a lever or a key in a lock. The fourth is that, for Descartes, spirit could use logic and language in a way that seemed incompatible with simple mechanical interaction. (As Cottingham (2000) indicates, Descartes may have accepted that animals perceive and experience, but did not ascribe rational souls to them because they could not use logic or language.) The key question is to what extent Descartes was proposing, for human souls, a category of entity that was to be considered “outside physics.” I do not think he was. The experiences of observers are very often, but by no means always, bracketed out by calibration moves when studying dynamics in physical science, but if the “physical world” is the world that physics aims to describe, experience must be part of it. The observation that tests the rules always entails experience. In a sense experience appears in all physics equations as the left hand side. We read the equations as saying: “The nature of the experience you get, given by the left hand side, can be calculated from the dynamics described in the right hand side and appropriate context and calibration.” Moreover, Descartes assumed that experience itself must be part of causal dynamics. It is just that he could not see how it could involve material mechanics—echoed by Leibniz’s analogy of the mill. There has been a recent fashion for equating experience with action rather than the receiving of input. However, in all contexts other than analysis of internal brain events it is accepted that what we mean by experience is an event described in terms of some final influence of the world on to an experiencing unit (observer). As Descartes says, it is the opposite of an action—what he reasonably termed a “passion,” or aspect of passivity or being influenced. That is not to say that the event of experiencing may not also be describable as an action, when considered in terms of downstream effects from other points of view (as in the next paragraph) but that does not alter the fact that a pattern of experience only makes sense as a description in terms of something received by an experiencing unit. The redness of a tomato is not something offered up to the universe by some internal process. It is something offered to some observing unit with a particular point of view. People seem to forget that physics already has a very clearly defined place for experience, as Descartes understood.

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Since for Descartes all change or motion must be driven by spirit, spirit was integral to his physics, in the sense of causal dynamics, more or less in the form of “force” or “action.” Animals, as mere machines, would still involve both matter and spirit, to explain motion, but the spirit would be in the pervasive form he called God. Humans were different in that they had their own independent units of spirit, or force/action. Descartes seems to have been rather stingy in sharing out force units but the dichotomy of force and matter remains fundamental within physics to this day. So often it seems to be assumed that for Descartes, the soul and God are outside physics, or “non-physical,” yet the one place where Descartes mentions physics in the Meditations is in reference to legitimacy of arguments about the nature of God. That would seem unsurprising if you genuinely believe in an omnipotent God—physics would presumably have to be the study of His actions. One would expect physics for Descartes to be a comprehensive account of causal dynamics, or the reasons why things change, which would have to include spirit by definition. This seems to get forgotten. Ryle’s (1949, p8) analysis of “the origin of the category-mistake” does not do Descartes justice. Moreover, the regularity of mathematics and physics is the basis for Descartes’ argument for the existence of God. Descartes may use the term physics in a more restrictive sense elsewhere, but more or less to mean the practical business we would call engineering or mechanics, not to denote an ontological category. A similar double usage of the word occurs today. The idea that soul cannot be matter because it is indivisible in its dynamics seems to be at the core of the assumption that experience does not fit with mechanics. The unity of experience seems completely incompatible with an explanation in terms of infinitely divisible matter. For Descartes matter is always an aggregate of parts, each with a separate relation to other matter it may collide with. So souls differ from matter in being simples rather than composites. This turns out to fit neatly with the distinction between units of force and matter in modern physics, as indicated below. When it comes to using logic and language, Descartes seems to be similarly denying that this could be done mechanically. The advent of digital computers might seem to cast doubt on this but in fact neither computers nor brains make use of mechanically moving parts; they compute using electrical potentials. DUALITY IN MODERN DYNAMICS A translation of Descartes’ dichotomy into modern physics needs to be simplified here because a detailed analysis would be hugely complex, but a simple account can work reasonably well.

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Since the discovery of electromagnetism it has been clear that physics does indeed have a dichotomy of the spiritual/material sort, which is the dichotomy between elements of force and elements of matter. Building on Planck’s insight it has become clear that force comes in units as well as matter. In technical terms, this dichotomy corresponds to that between what are now considered Bose units and Fermi units (Feynman et al., 1964) but is readily apparent from everyday phenomena. Bose units, as in light (and in fact sound), do not form “extended” aggregates of “matter,” whereas Fermi units, such as electrons, do. The difference between the two rests on an element of the mathematical description such that possible Bose units can “double-up” (or more) to form stronger units whereas possible Fermi units exclude each other, so have to form aggregate arrays of single units. All dynamic units are in fact units of action or, in a sense, “spirit,” as Leibniz realized, but there is a genuine dichotomy of types that reflects Descartes’ reasons for making a division. Reference to present day physics can be criticized on the grounds of being anachronistic in relation to historical systems of natural philosophy. One has to be careful not to claim too much. However, I think the charge may often be a cover for something worse. The alternative tends to be an interpretation of historical figures in terms of the naive “materialism” of the mid-twentieth century based on a schoolroom appreciation of physics that would probably be far more alien to Descartes (if perhaps not to less perspicacious “Cartesian” followers). Modern schoolchildren are taught to believe that physics has discovered “particles of real stuff” that could not possibly have anything to do with something called God. The whole point of Descartes’ Meditations was to point out the naivety of exactly that sort of view to budding natural philosophers. The particles of real stuff in solar system atoms were abolished from real physics almost as soon as they were suggested by Rutherford. In the naive materialist view patterns of force or action, such as sound waves, might not be considered “real material stuff.” However, note that sound has never been considered outside physics. In modern physics with the recognition that all energy is partitioned into “quanta of action” the underlying units, entities or “substances” in light, sound, and matter are seen on an equal footing. Both are equally “real” or “physical.” Fermi units tend to carry rest mass. However, mass has only been considered the essence of “material stuff” rather recently. In the seventeenth century mass was understood to be a form of passive force (as it is) and the definition of matter for people like Descartes was “extension.” “Extension” is a specific term of art in early physics. It does not just mean related to a domain of space. Descartes indicates the meaning in Meditations in rather general terms, which may be why he takes pains to clarify in his letter to Hyperaspistes of the same year (Descartes, 1641b). For Descartes,

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extension effectively means antitypy or “ownership of a spatial domain” such that other material objects are excluded from that domain. For Descartes space is a property of matter such that it would be incoherent to suggest that a piece of matter could “enter the space” of another piece of matter. Matter is antitypic but light and sound are not. Leibniz’s concept may be broader in that he distinguishes extension as visible extent from antitypy as tangible extent but both draw the conclusion that extension implies spatially separated dynamic parts. For Descartes and Leibniz, it is a contradiction for any single indivisible dynamic unit to be extended. Extension entails different causal relations in different places (e.g., right and left ends), and hence dynamic divisibility. In accord with this, even Fermi units such as electrons or quarks are not in themselves extended. They are units of action focused on certain domains of space but other units can use that space. In a lead atom eighty-two electron orbitals make overlapping use of the perinuclear space. However, the dynamic relations of each with other orbitals are constrained in space and time through rules best known as “Pauli exclusion” with the effect that the next lot of eighty-two electrons around another lead nucleus have to move along to focus on a new domain of space, and so on. Thus, groups of Fermions have antitypic extension, that is form matter. So although Descartes’ apportioning of spirit was questionable he seems to have correctly picked out a basic difference between the dynamic structure of force and matter. Force units do not aggregate to form matter. Talk of Fermions and Bosons might seem distant from the biological scale of brain but, contrary to popular misconception, these units are not confined to a microworld. Bosons, in particular, can have domains at all scales. Sound waves are indivisible force units that can occupy huge domains. So there are good reasons to think that Descartes is not a “dualist going outside physics.” His dualism is well within the bounds of physics. Moreover, the famous problem of causal interaction between mind and body is empty. Even Leibniz got this wrong. “Interactionism,” relating units of force to units of matter, is what our physics is all about. Leibniz’s (1714) argument about conservation laws in Monadology #80 was a slapdash mistake. It seems remarkable that the myth of the problem of interactionism is so pervasive in philosophy of mind. A massless force can act on matter without violating conservation of momentum—what happens is that new movement in one direction by part of the matter is balanced by new movement in the opposite direction by another part—as in the recoil of a gun. Energy is conserved if one assumes that energy can be taken up and released by force units, which is pretty much what a force unit means in physics. It might be argued that in attributing free will to the rational soul Descartes goes outside the realm of physics. Free will is a difficult topic that I prefer

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not to say too much about but a Cartesian soul may simply be free in that it is a unit of action in itself, rather than just a manifestation of God’s action. That seems to leave us with the mundane conclusion that a Cartesian soul is a unit of force rather than matter. This is not unreasonable, as we now think of the brain dynamics associated with thought in terms of shifts in electromagnetic forces. When we go to sleep and thinking ceases it seems likely that certain force patterns disappear. We do not think that some matter disappears. The whole Descartes-bashing industry proves to be built on sand. Why then is contemporary neuroscience so motivated to keep Descartes out of the picture? If the problem of dualism is a myth, why is Descartes even mentioned? Why would it matter? Part of the answer may be that scientists wish to deny a (straw man) “supernatural” ghost within to ensure credentials in terms of an ingenuous concept of “materialism” and distance themselves from troublesome concepts like free will. But more specifically, it seems that neuroscientists claim that Descartes was wrong because they want to airbrush out any idea of an inner receiving unit. The watchword is that there is “no one place where everything comes together.” They are not arguing against dualism so much as against the specific dynamic model of a single receiving or perceiving soul element within the network of neurons. This has some justification and I will return to it later. But there is a difference between denying that there is one special place where everything comes together and denying that there are any places where enough comes together to explain the richness of experience. If nothing receives the signals neuroscientists study it is unclear why they should count as signals! RYLE’S ERROR The more I read The Concept of Mind the less clear I am what Ryle (1949) thought he was arguing. At one point he admits to be arguing that there is no other (spectral) machine inside the machine—no intermediary events within, that mediate events described at a “person” level. He claimed not to be antiscientistic but clearly science posits such internal events. Where I think Ryle may be right is in denying that there are events that exist in some sort of “mental realm” with no locus in space. It is certainly widely held that “phenomenal” or “experiential” events are not in space. Sometimes it seems to be suggested that they are not in time either but more often it is accepted that “thoughts” occur in a temporal sequence similar to that of other events. It is also widely held in philosophical circles that Descartes claimed that the soul was not in space. This is wrong, however, because Descartes tells us that the soul is centered on the pineal. It had a specific location for its interactions via tiny movements of nerves. What Descartes means

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when he says the soul is not extended is much more specific: that it does not take up or own a space, which is fine, since force units do not take up space. What I think Ryle may miss is that there is a very satisfactory basis for a principled distinction between a certain usage of “mental” and “physical” in terms of spatial location in epistemic terms. The difference between “thought” events and external events is that our brains have mechanisms for differentiating both in time, but only external events in space. To differentiate in space requires a movable sensor to calibrate the space. We make use of both eye and body/limb movements to calibrate the outside spatial world. Nothing inside the brain moves so we cannot allocate thoughts to any particular place within it. When we remember admiring a rose we can place the remembered external events in specific places. For the associated internal events, “our experiences,” we have the same time cataloguing but no spatial discrimination. So Ryle was right to deny a need to postulate some separate nonphysical ontological category of event within the head. But he was wrong to attribute this idea to Descartes, for whom all events that involved any sort of change had both “material” and “spiritual” components. He was also wrong to deny any category of internal events, because there is a valid epistemic category of internal events that the brain can infer through internal clocking mechanisms but cannot locate through senses. What seems particularly ironic about Ryle is that in a sense he is complaining about the opposite of what he claims to complain about. He is denying a machine within a ghost. He wants there to be rules of operations of “persons” that include dispositions and free will, that cannot be reduced to the workings of an internal machine. He wants the phenomenality, agency and indivisibility that Descartes wanted. He just wants Descartes’ soul to be worn outside, as a “person-ghost.” He tries hard not to posit anything ghostly, using behaviorist (with a small b) language, but behavior presumes something that behaves, a dynamic unit, which in Ryle looks yet more immaterial than in Descartes. The things that Descartes probably did get wrong—that the dynamics of human spirits are unique in category, and that there is one dynamic unit per person—Ryle retains. Worse still, he wants to divorce the dynamics from spatial location even in terms of brain. He wants a dynamics that, being defined purely externally, cannot be further analyzed in terms of local causal relation. Descartes did better than that. WHY IT MATTERS TO SCIENCE Although neuroscientists tend to think of Descartes’ preoccupation with defining dynamic entities as of no great practical relevance I think this is a

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mistake. There is a genuine practical problem to solve. Neuroscientists assert that a thought must be an event that fits within the framework of physics, and they see a denial of Descartes as consistent with that. Yet Descartes arrived at his ideas through a rigorous insistence on a local dynamic framework. In contrast, neuroscientists appear happy to consider thoughts to “emerge” from events distributed over the brain. The problem here is that physics requires all dynamic relations to be local. Locality gets subtle within single quanta of action but the rules are still rigorous, and, in particular, locality cannot be violated across a sequence of determinable events. In all contexts where physics is applied, other than neural models of consciousness, it is assumed that observation events obey the same locality laws as events that are observed. The astronomer must be at the right end of a telescope pointing in a certain direction, and at the right time, to observe certain stars. Predictions for him do not apply for another observer in another position at another time. To suggest that events can involve nonlocal causality once one is inside the head is to invent a “magical membrane,” as decried by Hurley (2006), within which dynamic rules mysteriously change out of all recognition. Descartes realized that nerves send messages and that for a soul to receive those messages the relevant nerves need to connect to it. He took locality to its logical conclusion. He had no need for “emergence.” Any claim that an observer’s experience emerges from a magical coalescence of independent events occurring in different parts of the brain raises serious concerns. There is no more reason in physics why the events in the cortex of the left and right hemispheres of a mother embracing her baby should be part of the same “physical thought event” than those of the cortex in the right hemispheres of mother and baby, which may be closer together and are functionally connected just as much as those in one brain, even if that connection is through sounds and caresses rather than electrical potentials and chemical diffusion. I am not a particular fan of either of the concepts of “extended mind” or “intersubjectivity” but what these ideas do bring home is that the Rylean person-ghost, qua dynamic entity, has no legitimacy, even in non-reductive approaches. A mother is as connected to her baby as her own right and left hemispheres are, in biophysics, and arguably in psychology. My wife may be aware of an increase in pain in my left knee (seeing me limp) before me, because I am used to it. I would deny that there is “shared experience” here but it makes clear that there is no magic personal boundary around events involved in sensations. As pointed out by extended mind enthusiasts, our sensations draw on antecedent interactions that go well out into the world. In contrast, when neurophysiologists allow events distributed in space in a brain, but only one brain, to be “a thought” or “an experience” there is a tacit acceptance of a person-ghost boundary. For events in both mother and baby’s

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brains to form a thought is considered absurd because of the magic boundary, which justifies arbitrary co-identification of distributed events. A much more pernicious dualism underpins this thinking than anything Descartes fell for. It might be argued that I am overstating the case, that we can allow for events to be “tied together as a thought” if they are involved in some dynamic pattern like a reentrant feedback loop. The problem is that this still contravenes locality. In fact, it is the worst-case scenario. Events in a feedback loop are related by causing each other—by being in determinate causal sequence. Determinate causal sequence is what makes events distinct, not co-identical. If anything, we should be looking to combine parallel, not sequential, events. If you try to give an account of the causal status of the combination of “tied together” sequential events you get both causal overdetermination and infinite regress in time. The only reason neuroscientists get away with such nonsense is that the workings of the brain are so complex nobody has any chance of making any specific testable predictions that would show the absurdity of current hypotheses. Why have neuroscientists become so convinced that subjective experience arises from events widely distributed over the brain? I think the answer is that there is a lot of good evidence that it does. But note that I used events in the plural. If you ask people to go back to why they reject Descartes they usually come up with the point that there does not appear to be any “one place where everything comes together.” What they fail to address is that there are millions of places where plenty of signals come together—many individual neurons have more than ten thousand inputs in the form of synapses. Coming together is not a problem. The problem is that neuroanatomy does not give us one special instance of coming together. So there should be no unique Cartesian soul. The question then is why we think there should be a single instance of subjectivity within a brain. The answer again seems to be this fixation on the person-ghost concept: the single subjective “I.” Yet we have no usable evidence for a single “I,” as Anscombe (1981) pointed out. William James’s (1890) discussion in Principles of Psychology is intriguing because it suggests that in the late nineteenth century this problem was understood better than today. Moreover, a number of people had obviously suggested the alternative possibility of multiple instances of subjectivity—in terms of polyzoism. James quotes a line of thought through Leibniz, Herbart and Lotze, against which he does not argue. He merely leaves it as “belonging to metaphysics.” Yet he himself argues this conclusion on the grounds of the locality of physics, describing an experience in a network of cells as not being a “physical fact” (i.e., nonlocal). The possibility of multiple sites of experience in a brain is important because it means that experience (without the indefinite article) can be

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distributed widely throughout brain tissue, yet individual experiential events can be entirely local—even to single cells. Multiplicity of subjectivity within a brain poses no physical or phenomenal inconsistencies. Crucially, absence of a sense of multiplicity is no argument because it is an oxymoron for a subject to be aware of another awareness. The upshot of all this is that if neuroscientists are seriously trying to address human conscious experience they need to start thinking about a way of making their theories compatible with physics. They need to propose precise domains for individual instances of experience. They need to shake off the specter of the Rylean person-ghost and start finding some Cartesian souls. They need to break out of their category-mistake. A NEO-CARTESIAN MIND/BRAIN SKETCH To embark on any comprehensive mind/brain theory within this text would be inappropriate. However, certain basic dynamic and phenomenal components can perhaps be assembled (focusing on input, which is the main concern here). A combination of basic anatomy, introspection and Hubel and Wiesel’s (1959) and other classic studies, leads us to believe that incoming sensory signals in cerebral cortex are integrated sequentially to generate more and more abstracted inferences about the dynamic properties of the world. We infer “objects” that belong to dynamic dispositional types, and the causal relations between these. It is also clear that there is competition for salience such that a high proportion of primary sensory signals are ignored. Many, including Baars (1997) and Dehaene (2014), have suggested that at some point a winning narrative emerges from early pathways and is “broadcast” widely throughout cerebral cortex so that it can be subject to parallel processing. In simple terms this winning narrative is “what I experience” at that time. There is also good evidence for sensory signals, perhaps at all levels of abstraction, being sent to pathways involved in emotional evaluative responses (with their own “feel”)—traditionally ascribed to the limbic system. Thus anything from a raw sense of a bad smell to realizing that one is not going to make an airport connection may invoke something like nausea. In addition, when internal body signals are received from enteroceptors we may simply feel nausea, with no idea why. Experience, value judgment, and rational inference interweave via complex overlapping pathways. A key aspect of the narrative that appears to be broadcast as “my experience” is a close correlation with that available to recall through short-term memory. It seems likely that “broadcast content” is held in some sort of recyclable stack that can provide replay. The content also tends to be available for speech pathways—for reporting. However, this “availability” depends on all

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sorts of additional priming cues and there may be no fact of the matter about what is “accessible” in the sense of Block’s (1995) access consciousness, other than what happens to be accessed in the current context. Apart from language, all of the above mechanisms, which involve allocation of token instances of input (a round red patch) to type categories (tomato) and also the use of learned type templates to interpret new token inputs in a top-down fashion, are likely to be found in other animals. What seems different about humans, and relevant to ideas of both moral responsibility and rational belief, may be something to do with an ability to retain the temporal token quality of input patterns such that we can think in terms of episodes (as proposed by Tulving (1972)) and also to construct hypothetical future token events from type concepts. (“That is the tomato I bought on Tuesday so it may be soft”: a mode of thinking maybe shared most with corvids!) As a result we expect each other to develop a sophisticated understanding of chains of dynamic token events both in the outside world and also within our own “minds,” where they are “thoughts.” The former we can register in space and time but the latter we can only register in time because we have no way of calibrating the “position of a thought,” other than somewhere within. This is the briefest of sketches of dynamic components but it already raises the question of where in all this there is subjectivity, or experience, and how does that experience relate to the various complex activities the brain performs in generating useful behavior in response to environmental stimuli. The specific point I would like to raise is that it is almost certainly wrong to look either for a single Rylean “person-ghost” in relation to these dynamics, or a single Cartesian inner ghost, because the parallel nature of the handling of “broadcast” material points strongly in the direction of a multiplicity of “ghost-units.” (Although Leibniz envisages multiple perceiving units in a brain, associated with different scales of structure, he too falls for a single dominant ghost-Monad.) Just as we are unable to attribute a position to thought events or experiences we cannot know whether it is one position or many—that is just as our brains have no way of analyzing how many violins are playing on a CD, we have no way of analyzing how many “experience events” contribute to our memory of having experienced. The (illusory?) sense of a single “self” must presumably be encoded in received signals just as much as a sense of the world, both “broadcast” to many receiving units. The fashion is to deny any ghosts. That seems to be justified by a claim that the ghostliness of phenomenal experience is nothing more than local physical interaction, yet at the same time there is a denial that the normal rules of locality for experience apply. More importantly, perhaps, denying that any inner site “receives” and “experiences” the “current broadcast narrative” is effectively to deny that broadcast material has any dynamic effect. It denies the fundamental premise of neuroscience—that the electrical impulses from

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cell to cell are signals involved in determining behavior. If nothing receives them, they are not even signals. The strange thing about models of broadcasting in neuroscience is that “consciousness” or “experience” is attributed to a distributed signal sending process. Yet both in everyday life and in physical science experience is always treated as a description of an input, or state of being influenced or receiving, rather than sending, and it seems that broadcasting must generate inputs at many sites. Further detail of this neo-Cartesian sketch is for speculation elsewhere (Edwards, 2005; Sevush, 2016). However, there is one technical detail that should probably be dealt with. Strictly speaking the electrical potentials of modern neurology, that arise from tiny ion fluxes, would replace the tiny movements of nerves or subtle fluxes of fluid that for Descartes “informed” the soul. We need whatever is influenced by these potentials to be a single dynamic unit rather than a material aggregate interacting mechanically by parts. I will simply point out here that in modern condensed matter physics force units (Bose modes) associated with structured aggregates of matter are well recognized. The ring of a bell is perhaps the most intuitive example. Objects as large as bells, and larger, are associated with indivisible force units like sounds. In a sense these (acoustic) modes are what make everyday objects, because there are dynamic modes of a coherent whole. It might seem odd for a Cartesian soul to be an acoustic unit or sound, but, like Descartes, we want to use the best physics of the day, not schoolroom materialism. If we accept that there are many places in a brain where current narrative comes together, rather than Descartes’ single site, then we have to accept that response to this content is distributed across many units. No single unit experiences and decides. Behavior is decided by the consensus of millions of neural events. This in some sense may provide a basis for Ryle having been right in saying that we have to consider “mind” in terms of the whole. But I think he was wrong to deny that any internal analysis relating this to inner experience was legitimate. My impression is that neurobiology is currently in a state of denial. It is easy to say that mind and brain are the same thing and that it is all both mental and physical. Yet, I believe that misses crucial distinctions about the way we use these words, at least in these contexts. We need to have a detailed understanding of the way in which different levels of neural dynamics involve experience, decision-making, and agency. WHY IT MATTERS TO SOULS LIKE US The argument that getting categories right in terms of mind and body is important to neuroscience need not interest everyone. What may be more

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important is that getting these categories right in caring for the sick may be of profound significance to people’s lives—potentially to any of us. Within philosophy, arguments for holding on to the concept of person tend to center around the idea that without individual free will and accompanying responsibility there can be no moral basis for justice and society would collapse. I find such arguments about justice strained but I think there is a more significant argument about “responsibility” to be had in the context of what we call “mental” and “physical” illness and the distinction between the two. However much the situation may be sanitized by complex medical jargon there is an undercurrent of feeling that some illnesses are “the fault of the person” and some are “the fault of the body.” Descartes is frequently invoked when debates are raging about the borderline between the two. Just as neurobiologists open a lecture with a dismissal of “homunculi,” clinical neuropsychologists start with an exhortation to be rid of “Cartesian dualism” only to follow with discussion overshadowed by the real bogey—the person-ghost. The “person” is frequently placed in a “social” framework that is supposed to explain everything, when in effect it makes the arguments so soft that you can get away with any theorizing you like. The current fashion is probably derived both from behaviorism and Freud. Behaviorism made the legitimate suggestion that if we cannot relate experience to specific internal dynamics the brain is best treated as an input-output black box. But with that came two weaknesses. It included a denial of the legitimacy of the concept of subjective experience. Yet almost all the useful information we have about human thought comes from reports of such experience. Moreover, in a Cartesian view experience is not epiphenomenal. It is part and parcel of local dynamics. The second weakness is that a black box approach stops us from making use of the limited understanding we do have of how experience fits with dynamics. We do understand about the hippocampus being important for memory and the amygdala for emotion. Ablative surgery for severe epilepsy makes use of reported experience relating (maybe indirectly) to the functions of tiny areas of brain. It has become clear that banning experience from science is counterproductive and illegitimate. Freud’s (1933) very different approach also had a broad justification in proposing a division of mental function into subdomains with different dynamic properties: subconscious, ego, and so on. Yet the concept of unconscious processing prior to presentation to conscious experience was well known in the seventeenth century. Both Descartes and Leibniz realized that there was preparation of material before a “soul” was aware of it. And whereas these earlier biologists had tried to identify local mechanisms, Freud in a sense just presents us with more mysterious “person-ghosts.” The key point, as I see it, is that the black box dynamics of the whole needs to be contrasted with a finer-grained account of internal dynamic units

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with appropriate attribution of subjective experience and rational functions. Neurobiology suggests that each instance of signal integration is on average one of about ten thousand. The strange thing is that nobody seems to accept that this should apply to experience as much as to computation. Experience is viewed not as a local event but smeared out in a “system”—the popular scientific jargon for person-ghost. Descartes recognized multiple levels of dynamic interaction within the brain. He had no real interest in a person as whole being. Within the brain, he saw that a putative soul cannot be entirely responsible for the content of its thought. It “thinks” in the sense of experiencing and responding to ideas but the genesis of the content of ideas must depend on the way nerves pass messages to each other en route. The soul can only think about the collated information the brain provides it with. His model is not quite right but is in the spirit of science. And it raises the point that we cannot consider a soul at fault for thinking something it has been erroneously told by the nerves around it. If we replace the single soul with many similar dynamic units, and perhaps hierarchies of such units, things begin to make more sense in terms of the empirical data we have from neurobiology and maybe clinical psychology as well. Going back to the list of features that characterize Descartes’ soul, we need to reconsider how experience, indivisibility, and rationality interrelate and give rise to what we call beliefs. An important issue is where beliefs, and in particular the putatively irrational beliefs that underlie a lot of mental illness, figure in this dynamic model, including phenomena ranging from feelings of worthlessness, through paranoia to auditory hallucinations and beliefs about external control. It is easy to attribute beliefs to a “person” but if in a mental illness there is no sense in which the “person” that was well, in the sense of a dynamic system with familiar dispositions, traits, or behaviors, still exists, is this the right approach? We use the term belief in at least two different ways, as noted by Crane (2013). A belief can refer to a dormant dispositional state of a brain even if never used: perhaps based on a trivial fact learned at school. It can also refer to the involvement of that belief in the formation of a conscious thought: perhaps when attesting to the fact in a game of Trivial Pursuit. Even for a healthy brain, however, the situation is yet more complex and inconsistent. Beliefs in the sense of dispositions to respond to stimuli almost certainly affect processing of incoming signals at an unconscious level. If you believe you put your glasses on the chair you may be completely unconscious of their presence on your nose. And conscious beliefs may not be associated with an appropriate behavioral disposition. Doctors often believe that they make decisions based on certain evidence when it can be shown that in practice they do not.

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Perhaps, the most characteristic feature of what we call mental illness is even greater inconsistency in the way dispositional and experiential aspects of belief relate to the world around us and to each other. The extreme case is typified by the term schizophrenia, implying a fragmentation of the various aspects of thought. If the mind is seen in terms of some global “system” with a single channel of experience and a single global computational sequence then such fragmentation is hard to understand. But if we recognize the multiplicity of these things it makes it much easier to see how discordance might arise. Perhaps, rather than seeing a unified self as being divided by disease we should accept that the normal “self” is divided, or at least multiplex. In disease consonance is replaced by dissonance. Even in a milder form of mental illness such as a mild depressive state what is often striking is the disconnection between rational discussion of adverse thoughts and the beliefs that underlie them. One can discuss all the reasons why a depressed person should not feel worthless and they may agree on the rational arguments but still believe they are worthless. This raises a particularly thorny question about the responsibility of the conscious mind for its thoughts. Do judgments arise at sites of experience as a result of presentation of “the evidence” or are sites of experience presented with the judgments as part of the narrative they experience? What is responsible? Without any clear theory of how internal units hosting experience relate to units involved in rational function and evaluation the sort of “analysis” frequently used in psychiatry seems suspect. Therapies intended to alter personal beliefs are very popular and although often termed “behavioral” they draw heavily on the idea of a person doing the believing. I realize that many psychiatrists are aware of these difficulties but at a time when it seems that anyone and their dog can set up as a psychotherapist I think they need highlighting. RESTORING CARTESIAN SOULS We are all agreed that experiences occur. To fit that into physics there must be some dynamic units in brain whose input signals encode experience. They cannot be anywhere else since it is not until you get deep into brain that information has been collated and interpreted in the sort of way our experiences are presented to us. The sound of a ringing tone can only be available to something that receives signals that have been integrated over a complex sequence across time and presented as a “brrr-brrr.” There is no coherent account of a person-ghost or “central nervous system” that hears these sounds. Descartes gets this right. The only problem is that Descartes assumes that experience within the brain is both unified and unique. The former seems hard to deny but the latter

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looks unrealistic. The suggestion made here is that Descartes’ soul should be replaced by those (several) dynamic components of the brain that receive those signals that carry the information in current awareness—salient, collated information. A number of neurobiological models invoke such a stream of information, as in Baars’s (1997) and Dehaene’s (2014) concepts of selected signals accessing dissemination as conscious thought. What is missing from these models in general is any account of exactly where these signals are received and processed and how many functional units are involved in this receiving and processing. The implication is that it is much more than the one envisaged by Descartes, but beyond that little is said. Current neuroscience indicates that the functional dynamic units in the brain are individual neurons, making them the most obvious domains for individual experiences, but things may prove more complex. What can reasonably be excluded is that sequences of events in reentrant circuits are domains of experience. If we accept that there must be dynamic units in the brain that receive signals with the semantic content that we ascribe to “our experiences” and resemble Cartesian souls in that sense and probably in being non-extended and indivisible, we want to know to what extent each of these units contribute to functions like reasoning, truth evaluation, and value judgments. One possibility that I think we have to consider is that the dynamic units that host our experiences are like what laptops call “clipboards.” Used for short-term memory, they may be nothing more than palimpsests on to which a “train of thought” is written, only to be wiped off in an instant. Phenomenal experience may be a quite separate stage in the process of thought from the other functions. Libet’s (1985) famous experiments might tend to support this in suggesting that decisions are made out of the frame of experience, and the conclusions shunted to experience later. Although possible, I think this is a relatively implausible and unparsimonious model. One can argue that at least some dynamic units receiving the content of our experience ought to be doing something useful with it in terms of logic or evaluation. And this need not be incompatible with the Libet result. What may be crucial to include is the rolling nature of the train of thought. A conclusion from experience 1 may be presented as experience 2 at the same site where it was derived. In a sequence of thoughts, experience may, by definition, always be of the conclusion from computing over the experience before. My hunch is that all three functions mentioned above—reasoning, truth evaluation, and value judgment—may occur in units supporting experience, but perhaps with rather different structures in different brain areas. In simple terms some units may have inputs implying a certain scenario plus signals from other units that have judged the scenario “bad” and respond with a rational inference. Others may do the reverse. Truth evaluation is particularly

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interesting in that it would seem to require comparison of two inputs with the judgment that they are equivalent. The experiences we discuss do not seem to involve such a double input of two matched patterns. Computers probably do not make such comparisons so may be a poor model for this type of brain event. The above scenario may be reminiscent of Marvin Minsky’s (1986) “Society of Mind,” except that the member units would be experiencing where Minsky’s were insentient. To extend the analogy a little one might think of these units as the members of the scholarly society we call the University (to borrow Ryle’s example) or perhaps more broadly, “Academia.” Over time individual members of this society are presented with material raising questions of logic, truth, or ethics that each solves in a particular way. The society progresses in understanding by incorporating solutions on the basis of standards such as consonance, parsimony, and utility. As understanding progresses not only do the questions change but solving skills do as well. Similarly in the brain it is likely that the way dynamic units respond to experience is refined through plasticity. A rider to this model is that all may not go well. Whether in the extreme case of totalitarian rewriting of history or the more pervasive sidetracking by self-interest or fashion, progress of understanding can take wrong turnings. Similarly, a rational individual may slip into destructive thoughts, whether of despair, paranoia or religious radicalization. In both cases what seems logical, what seems true, and what seems of value all play interrelated roles. If there was “one place where everything comes together” it might be hard to understand how disorder might arise. If, however, reasoning modules in the brain rely on other modules to deal with, for instance, value or truth, and experience reality accompanied by a misevaluation made by these other modules it is perhaps easier to see how a spiral of counterproductive thoughts may supervene. Spirals in and out of extreme thoughts are characteristic of conditions like bipolar disorder and probably feature in many mental health problems. And maybe, as when a brain suffers ill health, academic progress gets sidetracked by misevaluation. Brilliant insights may languish in obscurity for centuries. Maybe Descartes’ concept of the soul is a case in point. I have an eerie sense that we may live in an academic world suffering from a delusional state and that what is needed is some purging therapy to restore it to the healthy state we call the seventeenth century! REFERENCES Anscombe GEM. (1981) Metaphysics and the Philosophy of Mind: Collected Philosophical Papers Volume II. Oxford: Blackwell.

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Baars B. (1997) In the Theater of Consciousness. New York: Oxford University Press. Block N. (1995) “On a confusion about the function of consciousness.” Behavioral and Brain Sciences 18: 227–47. Clark A and Chalmers D. (1998) “The extended mind.” Analysis 58 (1): 7–19. Cottingham J. (2000) Descartes. Cambridge: Perfect Paperback. Crane T. (2013) “Unconscious belief and conscious thought.” In Phenomenal Intentionality. Ed. Kriegel U. Oxford: Oxford University Press. Dehaene S. (2014) Consciousness and the Brain. New York: Viking Press. Descartes R. (1641a, 1996) Meditations on First Philosophy. Translated by Cottingham J. Cambridge: Cambridge University Press. ———. (1641b, 2010) Letter to Hyperaspistes. Translated by Jonathan Bennett. Early Modern Texts: Selected Correspondence of Descartes at: http://www.earlymoderntexts.com/assets/pdfs/descartes1619_2.pdf Edwards JCW. (2005) “Is consciousness only a property of individual cells?” Journal of Consciousness Studies 12 (4–5): 60–76. Feynman R, Leighton RB and Sands M. (1964) Lectures on Physics. Boston: Addison-Wesley. Freud S. (1933) New Introductory Lectures on Psychoanalysis. Penguin Freud Library. London: WW Norton. Gallagher S and Zahavi D. (2008) The Phenomenological Mind. London: Routledge. Hubel DH and Wiesel TN. (1959). “Receptive fields of single neurones in the cat’s striate cortex.” The Journal of Physiology 148 (3): 574–91. Hurley S. (2006) Varieties of Externalism. In Extended Mind. Ed. Menary R. London: Ashgate. James W. (1890) Principles of Psychology. New York: Henry Holt and Co. Leibniz GW. (1714, 1998) “Monadology English translation.” In G.W. Leibniz, Philosophical Texts. Eds. Woolhouse RS and Francks R. Oxford: Oxford University Press. Libet B. (1985) “Unconscious cerebral initiative and the role of conscious will in voluntary action.” The Behavioral and Brain Sciences 8: 529–66. Minsky M. (1986) The Society of Mind. New York: Simon and Shuster. Ryle G. (1949) The Concept of Mind. Chicago: University of Chicago Press. Sevush S. (2016) The Single Neuron Theory. London: Palgrave Macmillan. Tulving E. (1972) “Episodic and semantic memory.” In Organization of Memory. Eds. Tulving E, and Donaldson W, pp. 381–402. New York: Academic Press.

Chapter 6

Categorical Analysis in Pragmatism Specialization in Science and the Role of Philosophy Torjus Midtgarden

A ROLE FOR PHILOSOPHY IN AN ERA OF SPECIALIZATION IN SCIENCE Several of the Classical American Pragmatists had training in some specialized science, in addition to being philosophers. The founder of Pragmatism, Charles S. Peirce (1839–1914),1 was educated as a chemist, while William James (1842–1910) was educated as a physician and became an internationally acknowledged psychologist. In an era of increasing specialization in the natural sciences but also in the younger human and social sciences, the Pragmatists exploited their specialist training in reflecting on the role of philosophy in relation to the sciences. Peirce’s later works provide a suitable starting point for considering such reflection. Peirce was influenced by Kant’s idea of philosophy as an architectonic system.2 Yet, in his later years he also adopted aspects of August Comte’s hierarchical science classification, in particular the idea that there are superordinate sciences that provide general principles upon which subordinate sciences are based.3 In later works Peirce outlined several science classifications where he attributes a foundational role to philosophy and also distinguishes between different philosophical subdisciplines. I will consider his development of two distinct science classifications that involve somewhat different conceptions of the most general and basic philosophical discipline. In the science classification considered in the first section below Peirce follows Kant in assigning a foundational role to epistemology. Moreover, he conceives of epistemology as an analysis of elementary forms of signs that are used in forming assertion or truth-claim in the sciences, and that he 107

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analyses in terms of his famous sign-typological triad: icon, index, symbol. In the second section below I consider Peirce’s later science classification where the foundational philosophical discipline is called “phenomenology”: its task is to analyze three categories that are taken to be universal elements in all experiential phenomena and that are termed “firstness,” “secondness,” and “thirdness.” In both this and the former science classification, however, philosophical disciplines are empirically based in everyday life experience, not in the specialized observations of natural or social science. Through analyzing such pre-specialized experience philosophy is to provide a basis for all specialized empirical sciences. In his classifications of the sciences Peirce also gives careful consideration to mathematics and to formal logic, to which Peirce gave pioneering contributions.4 He shares Comte’s view of the basic role of mathematics for all empirical or “positive” sciences, and his philosophical interest in formal logic resonate with the fathers of Analytic Philosophy of Language, Gottlob Frege and Bertrand Russell, as well as with their intellectual heirs in twentieth-century philosophy of science, the Logical Positivists. Nevertheless, the status Peirce assigns to these formal disciplines in his science classifications suggests important philosophical divergences. Contrary to Frege’s and Russel’s views, Peirce takes mathematics to be a prelogical and pre-philosophical discipline which has no need for logical foundations,5 but which rather provides a formal basis for conceptualization in philosophy. Further, in conflict with the views of the Logical Positivists Peirce holds that formal logic needs a foundation in philosophical analyses of pre-specialized experience, and thus in his three categories and the basic forms of signs. In order to trace the influence of Peirce’s categorical analysis in twentiethcentury philosophy I will in the third and last section below turn to Peirce’s fellow Pragmatist, John Dewey (1859–1952) and his reception of Peirce’s analysis. In his interpretation of Peirce Dewey not only defends Peirce’s categories against interpretations of Peirce influenced by Logical Positivism but he also adopts Peirce’s categories in his own thinking about the role of philosophy in relation to the specialized sciences. Together with his intellectual companion, Arthur Bentley, Dewey takes inspiration from Peirce in forming a philosophical view of knowledge process and of theorizing in the sciences, a view Dewey and Bentley call “transactional.” I will focus on two distinct “transactional viewpoints”; first, a view of modes of theorization of social action, involving rejection of methodological individualism, a view that has had some influence in contemporary sociology through Mustafa Emirbayer (1997). Secondly, linking up with Pragmatism’s Darwinian legacy, and arguing from a more general ontological perspective, a transactional view stresses that theorization of human agency must consider functional, as well as evolutionary continuities between human and nonhuman organisms, and

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humans’ dependencies on nonhumans. Although this latter viewpoint has Peircean credentials, Dewey develops it with greater awareness of society’s economic dependencies on nonhuman nature, and of how, through processes of production modern science and technology transforms conditions for the everyday life experiences philosophy is to study. PEIRCE’S TRANSFORMED KANTIAN ANALYSIS: ICON, INDEX, SYMBOL In his intellectual development Peirce follows Kant in assigning a certain foundational role to epistemology. An interesting example of the latter is his relatively late project in the mid-1890s of developing an epistemological analysis as a basis for formal logic, as well as for the increasingly specialized natural sciences and the emerging human and social sciences. Such endeavor can be seen as an attempt to update Kant’s idea of a foundational epistemological discipline in a new scientific context. Yet, Peirce turns to medieval sources in giving name to the epistemological discipline: he calls it “speculative grammar” after Thomas of Erfurt’s Grammatica Speculativa.6 Moreover, not only the name but also the methods and the subject matter of his epistemological analysis divert significantly from those of his German master. While the objective of the epistemological analysis is to provide a basis for logic and the empirical disciplines, methods are not used to reconstruct a priori elements of knowledge, nor are they capable of establishing infallible results. As for the subject matter, Peirce’s analysis considers constituent elements of any truth-claim or assertion.7 The foundational role of this analysis thus comes with a reflection on sign-elements that are tacitly assumed in making truth claims, and that enable scientists to learn to use a logical language in developing and testing truth-claims. As for the methods of analyzing such sign-elements, Peirce first derives certain general types of sign-elements from a rearticulation of his early definition of truth as the final consent (or the final opinion) of a community of inquirers.8 He now reformulates the latter in terms of the rational assent of what he calls “an investigating intelligence”: an agent capable of learning from experience and being a member of a “body of inquirers.”9 A crucial methodological step in Peirce’s analysis is thus a derivation from the reformulated truth definition of three types of signs used in assertions. Yet, Peirce introduces a peculiar combination of methods that blurs any sharp distinction between a priori and a posteriori justification since he has first defined an assertion by appealing to ordinary experience of language use. More specifically, he defines an assertion as a linguistic act that furnishes “evidence by the speaker to the listener . . . that the speaker

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believes something on a certain occasion” (CP 2.334). Furthermore, his derivations or “deductions” from the reformulated truth theory are tested and further articulated against observations “of the rudest kind” (CP 3.432) open to the eye of any competent language user. Such empirical basis, qualified as “rhetorical evidence” (CP 2.333), suggests Peirce’s Kantian background as well as his departure from the latter. First, by turning to observations of language use in non-scientific, everyday contexts, Peirce wants to avoid vicious circularity in his foundational project. He emphatically appeals to such “rudest” observations as a kind of nonspecialized experience, distinguishing it from any kind of evidence obtained through specialized disciplines for which Peirce’s analysis, in a noncircular way, is to provide an epistemological basis. In particular, Peirce’s qualification of his epistemology in terms of a non-psychologistic foundation of logic10 and of other branches of philosophy updates Kant’s foundational project in a new scientific context. Secondly, however, the appeal to observations of language use as rhetorical evidence suggests that only a “formally imperfect” kind of reasoning (CP 2.333) could be used in establishing the results of the analysis, and that the latter would not be immune to later modifications or even refutations. Different from Kant, then, the author and user of the methods at stake would not be claiming any infallible and a priori epistemic justification for the analysis.11 As for the content and outcome of the analysis, Peirce specifies three forms of signs in terms of his famous sign-typological triad: icon, index, symbol.12 While these three sign-forms parallel his phenomenological categories (which we consider below), their traits and functions are restricted to the kind of evidence giving act called “assertion.” Through ordinary observations of language use the sign-typological triad receives specification in terms of various kinds of linguistic, paralinguistic, or extralinguistic signs. Icons are thus specified as syntactical patterns that need to be apprehended in their capacity of mapping or “diagramming” a structured semantic content of an uttered sentence. In contemporary linguistic terms Peirce could here be seen to consider the iconicity of syntax—and to suggest that syntactic structure (on both phrase and clause level) is “relatively motivated” in the Saussurean sense.13 Capacity to comprehend the iconicity of syntax, Peirce argues, is a prerequisite for learning to use a formal, logical language. Further, indices are needed in order to establish what an assertion is about. Peirce had already in earlier writings argued that “what is the subject of discourse . . . can . . . not be described in general terms; it can only be indicated” (CP 3.363). Indices can be exemplified by paralinguistic signs (tone of voice) and extralinguistic signs (looks, gestures) showing that the sign-giver is asserting something about “the real world” and is not joking (CP 2.337). In other situations indices would be integral elements of practical instructions or “precepts” through which sign-giver and sign-receiver coordinate their

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activity in identifying the object(s) of their verbal discourse (CP 2.336). In such cases tokens of certain grammatical forms of expression (pronouns, proper names) would be used as part of a socially and practically instituted way of identifying objects. The epistemological upshot of this analysis is that, in science, as well as in everyday life, practical procedures must be followed in applying general propositions or sentences to individual objects of experience. In particular, Peirce takes the use of quantifiers in predicate logic to rely on shared precepts guiding the sign-giver’s and the sign-receiver’s selection of individual objects.14 Finally, turning to symbols Peirce not only focuses on conventionality as a defining trait of linguistic sign used in assertions. Against his Kantian background he sketches a semiotic counterpart to Kant’s account of the capacity of the understanding (Verstand) to synthesize representations (Vorstellungen).15 His analysis thus emphasizes that the sign-receiver, as well as the sign-giver, must be capable of virtually putting the various sign-elements of an assertion together in order to understand it, apply it, and ultimately give his or her assent to the claim raised through it. He therefore stresses the creative capacity on part of sign users to (re)synthesis sign-elements in novel combinations as a prerequisite for applying an assertion to objects of experience. Yet, the various sign-elements of an assertion would not only be of a linguistic kind but would in the case of indices involve coordinated practical efforts on part of sign-giver and sign-receiver. The capacity at stake would therefore not consist solely in, but would encompass, competence to distinguish and produce grammatically well-formed sentences. As for its general epistemological outcome, Peirce’s analysis of icons, indices, and symbols specifies conditions for engaging in any kind of specialized scientific inquiry. As suggested, such conditions would involve sign using skills acquired by being member in a prescientific linguistic community. However, Peirce’s speculative grammar further situates the epistemological analysis in a certain kind of learning community. More specifically, appealing to the medieval curriculum of trivium (grammar, logic, rhetoric) Peirce argues that students who are to embark upon a study of formal logic and any specialized science should reflect on the constituent elements of assertions together with a teacher.16 Such learning community would thus form a social point of transference for the learner in his or her passage from a prescientific to a specialized community of inquiry. A social and educational setting for reflecting upon iconic, indexical, and symbolic signs thus forms the immediate context of Peirce’s epistemological analysis and for understanding its foundational role. Moreover, such context qualifies both the validity and fallibility of the outcome of the analysis: only results that participants would be capable of assessing on the basis of pre-specialized “rhetorical evidence” could be discussed and affirmed. Hence, modifications and corrections are

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foreseen and expected in the career of Peirce’s speculative grammar. Yet, more surprisingly, within few years Peirce redefines and replaces the very foundational discipline of his architectonic system. Peirce’s Phenomenological Categories: Firstness, Secondness, Thirdness In several outlines shortly after the turn of the century Peirce relocates speculative grammar from its place as the most basic philosophical discipline in his science classification. What Peirce with a gesture to Hegel calls “phenomenology”17 is now to have the status as the most general philosophical discipline, only preceded by mathematics in the order of priority and generality. While his various outlines of a phenomenological analysis are rather sketchy, and are lacking the methodological sophistication of speculative grammar, phenomenology, too, is to be based on pre-specialized experiences of everyday life—but of the wider kind that any adult person would be capable of having in his or her waking hours.18 Even though Peirce fails to specify how the content and outcome of his phenomenological analysis is to be intersubjectively established, modifications and revisions of such outcomes would be expected. There are two reasons for this: first, his phenomenological analysis does not assume any infallible first person epistemic authority;19 secondly, its only theoretical input comes from mathematics which in Peirce’s classification only makes formal hypotheses but does not put forth or test truth claims as such.20 The new foundational discipline can be distinguished from other philosophical disciplines through a higher level of generality of its principles and its subject matter. Phenomenology is concerned with categories underlying and defining any kind of human experience, cognitive or noncognitive. Moreover, these are categories by which the three forms of signs studied by speculative grammar may be defined and further analyzed.21 In so far, the categories are not only more general than the forms of signs but they have a conceptually primitive status for Peirce’s sign-typological triad. We may here see a residue of a Kantian foundational discipline, in addition to the fact that Peirce’s categories have their historical point of departure in the table of categories in Kant’s first Critique.22 Yet, before considering how Peirce’s categories define his sign-typological triad, we note another way in which Peirce’s phenomenology is qualified as a philosophical discipline. Peirce evokes an ontological and Aristotelian-Scholastic tradition by defining his categories as “modes of being” (CP 1.23), not as “modes of signification” (which would rather pertain to the sign-forms of his speculative grammar). As “modes of being” the categories would not as such sustain human cognitive capacities for forming and assessing truth-claims (like the

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sign-forms of speculative grammar): they would rather constitute the various ways all phenomena in the world (including ourselves) are. Still, for any cognitive activity the categories would have a foundational role in conceptualizing and theorizing what truth claims are about. Nevertheless, based in pre-specialized experiences, and taking formal suggestions from mathematics (a mathematical logic of relations), such foundational role would concern the most generic traits of any experiential or thinkable entity. In particular, while Peirce himself at times employs an earlier version of his categorical distinctions in constructing a certain evolutionary metaphysics,23 such use of the categories must be distinguished from a phenomenological analysis in that the former would belong to a philosophical discipline of a lower level of generality.24 Let us now consider how the three categories are defined and distinguished. Firstness, in its most general and primary sense, is “what is positively there,” “regardless of what is absent,” past and present; and it is further what is “sole and unique,” involving no reference to, or comparison with any other phenomena (EP2: 150). As for its formal simplicity, the category is derived from the mathematical logic of relations and its monadic predicates (in distinction to dyadic and triadic relations or predicates).25 Both from its formal and experiential sources, its content is fixed ahead of any specialized research into psychological correlates of the category, and it is prior to any distinctions introduced by other philosophical disciplines. It has thus “pre-epistemological” status and concerns experiential modes of presentation, prior to inquiries into their possible representational or cognitive status. On the other hand, firstness in turn defines sign-elements analyzed by speculative grammar. In particular, as involving “no reference to other (or absent) phenomena” it may (in part) define the iconicity of verbal syntax (which diagrams the structured semantic contents of sentences) prior to any logical analysis of truth conditions expressed by a sentence or prior to methodological or empirical considerations of the representational capacities of sentences.26 Yet, as derived from pre-specialized ordinary experience, the phenomenological analysis provides further specifications of firstness in terms of experiential content and mode of presentation. Firstness is thus generically qualified as quality of feeling and as encompassing “myriad-fold varieties” of experiential or sensory modalities: “an odor, say a smell of attar, or . . . one infinite dead ache, [or] the hearing of [a] piercing eternal whistle” (EP2: 150). By emphatically appealing to pre-specialized experience Peirce distinguishes such modes of presentation from what psychology would make an object of research.27 His analysis further differs from classical epistemological analyses in its efforts to make a wide range of experiences, noncognitive as well as cognitive, an object of philosophical analysis.

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The category secondness is formally derived from the notion of dyadic relations in the mathematical logic of relations.28 Yet, abstaining from the latter’s technical specifications of forms of dyadic relations29 Peirce’s second category captures a rudimentary idea of a pair of reacting singulars.30 It is contrasted with firstness through the idea of an irreducible interconnection and duality of reacting singular phenomena. Yet, in an ontological sense, secondness remains relatively unspecified. Although Peirce sometimes contrasts it to firstness’ qualities of feeling by appealing to experiences of some external or “brute force,” his phenomenological analysis is careful not to qualify secondness in terms of a physical or material domain as such. One reason for this may be found in the order of priority of the science classification. Being prior to a metaphysics which sustains and justifies the division between natural and social science,31 the phenomenological account of secondness abstains from using received ontological dichotomies to qualify this category; say, those of body/mind, physical/psychological, nonhuman/human, or effective/ final causation. Peirce rather takes resort to more intuitive characterizations, such as “an element of struggle,” and he also introduces the more abstract distinction between agent and patient.32 The core idea of secondness is thus that of reacting pairs of singulars as a universal and irreducible trait of experiential phenomena. Yet, Peirce’s introduction of the category may also be seen as motivated by ontological controversies with a long history and that looms large in his works: the scholastic controversies of universal realism and nominalism.33 More specifically, since phenomena understood in terms of secondness would as such resist being subsumed under natural laws or lawlike generalizations, Peirce, a defender of variants of scholastic realism, can here be seen to give nominalism its due. Nevertheless, his qualification of the category by the more abstract agent/ patient distinction suggests that this category may also highlight starting points for inquiries into, and conceptualization of, different kinds of relationships or interactions between individual phenomena.34 Like firstness the second category, too, has a “pre-epistemological” status and it is used to define sign-forms analyzed by speculative grammar. In particular, secondness defines indices and the indexicality of verbal discourse. Recalling that the analysis of assertion considers various modes of (linguistic, paralinguistic, and nonlinguistic) indication, we may note that secondness provides opportunity for a more abstract and fine grained analysis of dyadic relationships involved by various modes of indication. The category enables separate and stepwise considerations of, for example, dyadic and dynamic relations involved by attention raising indices as such (tones of voice);35 dyadic relations defining cognitive connections established between indices and indicated objects (pointing gestures);36 and dyadic relations involved in furnishing verbally mediated information about an indicated object

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(propositional symbols).37 The phenomenological analysis may thus provide a more subtle consideration of how the reference of verbal discourse is established through levels or layers of nonlinguistic, paralinguistic and linguistic indications. Moreover, secondness, as well as firstness, provides resources for considering noncognitive and nonlinguistic ways in which human agents are embodied in the world of experience, and for considering how such embodiment forms a basis for cognitive activity. In analogy with the analysis of symbols in speculative grammar, the analysis of thirdness concludes the categorical analysis. Yet, thirdness is not so easily derived from pre-specialized experience; it is, Peirce admits, “further away from common sense” (EP2: 158). A formal and abstract approach therefore becomes more salient for the definition of this category. Peirce’s formal derivation of the category from a mathematical logic of relations is intrinsically connected to his argument for the irreducibility of triadic relations.38 Nevertheless, for phenomenology it is crucial that claims concerning the universality and irreducibility of the categories can be supported by considerations from pre-specialized experience. As for the empirical specification of thirdness, Peirce’s science classification leaves two ways open. First, thirdness may be indirectly derived from pre-specialized experience through other philosophical disciplines, such as epistemology (or speculative grammar), logic, or metaphysics. Secondly, the category may be further explored and confirmed by less general philosophical disciplines that are to provide principles for the main division of specialized empirical science, and that are termed “Physical” and “Psychical . . . Metaphysics”, respectively (EP2: 260). We shall briefly see how both these strategies are in fact applied, starting with the former. First, the formal and abstract derivation of thirdness provides conceptual input for a definition not only of a symbol but of what a sign is more generally. Hence, the idea of a sign is explicated in terms of an irreducible triadic relation between a representation, the object represented, and the interpretation or “interpretant” of the representation as representing the object. Thirdness is thus more formally defined as “mediating representation” (EP2: 161), a representation mediating between its object and its interpretation. Although this formal definition expresses a basic principle underlying almost everything Peirce wrote about signs, and gives occasion for specifying various types of “mediating representations,” the abstractness of such analyses creates problems for assessing Peirce’s phenomenology as an experiential discipline. While Peirce’s speculative grammar situates the analysis of symbols, indices, and icons in an epistemic learning community, allowing each participant to affirm and reflect on the sign-forms from his or her experience, an abstract analysis of thirdness, or of irreducible triadic structures, lacks such methodological and intersubjective basis. Nevertheless,

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due to such shortcoming, phenomenology may delegate to speculative grammar to investigate and recognize triadically structured signs on the basis of pre-specialized experience. In fact, in qualifying phenomenology’s abstract definition and divisions of triadic relations as “a priori descriptions” Peirce admists that the latter means little “until we have met with the different kinds [of triadic relations] a posteriori, and have in that way been led to recognize their importance” (EP2: 289). On the other hand, the abstractness of phenomenology’s analyses of triadic relations provides for a higher level of generality in identifying and recognizing a larger variety of nonlinguistic and linguistic sign-forms a posteriori.39 The phenomenologically supported sign-analysis may thus extend Peirce’s former epistemological sign-analysis by considering a variety of sign-forms on which scientific observation and theorization would be dependent, including diagrams (as variants of icons), different forms of proposition40 and reasoning.41 As mentioned above, phenomenology could delegate to the branches of metaphysics that distinguishes the domains of natural and social science to find an experiential basis for the claim of the universality and irreducibility of thirdness. As for the relevance of the category for the natural sciences the late Peirce often argues for the “reality of Thirdness” (EP2: 181) by qualifying the latter in terms of the reality of laws and regularities in nature. Claiming that “general principles are really operative in nature” (EP2: 183) he advocates a version of scholastic realism. From relatively simple examples within the reach of ordinary experience he argues that dispositional properties of inorganic things cannot be reduced, ontologically, to actual observable states of reacting singular phenomena,42 which would be instances of secondness. The reality of dispositional properties rather prove itself through what would happen under certain conditions that are typically specified and referred to by a subjunctive (or counterfactual) conditional sentence expressed in the future tense.43 More interpretive focus could been drawn, however, to ways in which Peirce’s analysis of triadic sign relations may be relevant for humanistic and social science research. A sign essentially involves an interpretant of the sign and of how it represents an object. A sign’s irreducible relation to an interpretant qualifies it as an “intellectual fact” (EP2: 171). In slightly different terms, a “three-subject fact is comprehensible and is analogous to an utterance, a speech” (CP 6.323, my emphasis). Yet, an interpretation of a verbal utterance is conditioned by shared norms and expectations. This is clearly shown by Peirce’s considerations of how acts of asserting or assenting to a proposition are made under a mutual understanding that telling a lie would be met with moral, and sometimes legal, sanctions.44 Such instances may suggest how language use involves irreducible triadic relations to socially (or institutionally) conditioned interpretants, as well as to objects. Indirectly,

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such instances may further suggest how, by neglecting socially conditioning elements, the analysis would tend to account for sign use in terms of dyadic relations defined, say, by an utterance and some psychological intention behind the former, or by a semantic relation between utterance’s verbal meaning and its reference. An even more convincing case of the irreducibility of thirdness is provided by the more formal example of two persons making a contract.45 Such institutionally bounded language use cannot be meaningfully analyzed simply in terms of sets of dyadic relations between reacting singular phenomena, or, more specifically, between signer and document, between the signers themselves, or between the signed document and successive acts of the signers. Rather, a triadic relation would here define the institutionally conditioned intent of the contract (interpretant), the contract (sign), and the state of affairs in the world the contract is about and is to regulate (object). A key to studying such acts is the intent since it is intrinsically connected not only to the contract and its content but to the state of affairs to be regulated. Like in an informal act of assertion the signing of a contract is binding on language users and has practical consequences if the norms at stake are broken, only that in the case of contracts such norms are expressively given through the contract’s intent “that certain conditional rules shall govern the conduct of [the contractors]” (CP 1.475). In either case, language use could be analyzed, to use a speech act theoretical distinction, in terms of illocutionary effects rather than merely by perlocutionary effects.46 Like Peirce’s interpretant illocutionary effects can only be accounted for by certain triadic relations,47 while perlocutionary effects may as such rather be analyzed as dyadic relations between linguistic acts and certain physical, physiological, or psychological reactions to those acts. In so far as thirdness would prove to be a basic element in the conceptualization of phenomena in social scientific research, as well as in natural science research, Peirce’s category analysis acknowledges and sustains methodological idealization involved in making phenomena intelligible. What to common sense would rather appear as instances of firstness or secondness to be marveled, feared, or suffered, would for scientific inquiry be phenomena that trigger further efforts to explain or interpret through hypotheses involving general notions.48 Such phenomena could be some surprising experimental results; an exemplar of some hereto unknown plant or animal species; or a newly discovered document reporting hereto unknown historical events—phenomena that must be related to other and already known phenomena through applying general notions of dispositions or of institutional norms and roles. Already in Peirce’s tenfold sign-classification, however, we note a certain asymmetry between thirdness and the other two categories. From a purely formal point of view thirdness presupposes the first and second category;

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yet, in Peirce’s classification of signs the third category rather “mediates” or integrates the other two categories.49 Hence, such account differs from the phenomenological analysis proper of the two first categories where the latter are defined and distinguishes as separate and irreducible categories. In so far, Peirce’s elaborate sign-analyses, rather than his more sketchy phenomenology, would seem to be drawn closer to Hegel’s philosophical system, where, on Peirce’s interpretation, “Firstness and Secondness must somehow be aufgehoben” (EP2: 177).50 This in turn raises the question of the point and purpose of phenomenological analysis proper of firstness and secondness, and of the status or role of phenomenology as a philosophical and foundational discipline in Peirce’s science classification. I will suggest two possible answers. THE ROLE OF PHENOMENOLOGY: REFLEXIVE, HEURISTIC, AND CRITICAL USES First, Peirce’s insistence on a distinct phenomenological mode of inquiry serves to highlight ways in which the natural and social or human sciences have their background and enabling basis in a vast reservoir of prescientific experiences. While researchers make theoretical idealizations and apply technical apparatuses for making specialized observations, they still take their point of departure in a world of everyday experience, and would need to return to it for qualifying and reinterpreting their theories or suggesting new hypotheses.51 Yet, although Peirce characterizes such experiential basis generally in terms of “common experience” (EP2: 196), his categorization of phenomena in terms of firstness and secondness stresses the vast plurality of qualitative experiences that would tacitly underlie or motivate researchers’ research problems; be they aesthetic sensibilities, selective focuses, personal sufferings, or struggles. Peirce further suggests, but fails to elaborate, that branches of philosophy such as aesthetics and ethics may exploit such diverse qualitative experiences in criticizing received beliefs that are not adapted to new social or technological environments, particularly beliefs that still linger in branches of philosophy.52 Secondly, in addition to its foundational role in his science classification, Peirce uses phenomenology in qualifying and criticizing other philosophical systems, past and present. More specifically, by qualifying basic concepts of other systems in terms of his categories he suggests a heuristic and critical role of phenomenology. Most often he applies the categories to Hegel’s system and he criticizes the latter for prioritizing thirdness at the cost of ignoring secondness and firstness. Yet, he sketches similar criticisms of other systems, such as “Cartesianism,” “Berkleyanism,” “Nominalism,” and “Kantianism.”53 Notably, he considers a doctrine with dominating and enduring influence in

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the English speaking academic world, particularly in ethics and economics: the hedonistic psychology of utilitarianism. His phenomenologically based criticism of hedonistic psychology is twofold. In so far as hedonistic psychology sets out to establish the achievement of pleasure and avoidance of pain as universal standards, this project should be analyzed in terms of secondness and thirdness, rather than firstness, despite the fact that pleasure and pain may at first seem to belong to the latter category, qualified as “quality of feeling.” From the perspective of the human agent, however, pain would consist in “a Struggle to give a state of mind its quietus” (EP2: 190) and would thus be an instance of secondness. On the other hand, seeking pleasure is connected to an intellectual effort of developing some general standard of action, and is more adequately seen to belong to the third category in being “allied to the consciousness of making a generalization” (EP2: 190). Interestingly, this critical argument parallels one of those presented by his fellow Pragmatist, John Dewey, in the latter’s more elaborate criticism of the hedonist psychology of marginal utility theory in economics.54 Peirce puts forth a second phenomenological argument against hedonist psychology based on considerations of firstness. Even if feelings play a significant role in human action, it would not be possible to identify a common quality in them in the manner assumed by the hedonist’s notions of pleasure and pain. Hence, in so far as there are phenomena associated with such labels they “do not mainly consist in any common Feeling-quality of Pleasure or any common Feeling-quality of Pain” (EP2: 190). Although Peirce is addressing what we more narrowly may call intra-subjective, rather than intersubjective, commonality, his phenomenological criticism of utilitarianism may be connected to his broader Pragmatist outlook on human agency. Both before and after outlining his phenomenology he distinguishes the pleasure/pain-distinction of the hedonist from a more primary level of organically conditioned and partly subconscious feeling.55 With reference to the latter Peirce foresees, but, again, fails to elaborate, that the phenomenological category of firstness would bear on an articulation of esthetical and ethical ideals in the normative sciences. It is with reference to such broader view of human agents as biologically conditioned sentient beings that Peirce’s categories bear on the philosophical thought of John Dewey, the most influential Pragmatist philosopher in first half of the twentieth century. THE TWENTIETH-CENTURY LEGACY OF PEIRCE’S CATEGORIES: DEWEY AND BENTLEY’S TRANSACTIONALISM The late Dewey’s interpretation of Peirce was crucially influenced by the first six volumes of Peirce’s Collected Papers that were published during the

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1930s.56 Through his reception of these volumes Dewey became attentive to Peirce’s later outlines of philosophical systems. Since the latter were primarily developed in writings that had not been published earlier, Dewey was now in a position to see more clearly the systematic plan behind Peirce’s often idiosyncratic terminologies. In a broader perspective, however, the publication of Peirce’s writings coincided with the emergence of a new dominating style of philosophy in America associated with Logical Positivism (or Logical Empiricism). In this context some of Peirce’s philosophical contributions were directly relevant for discussing the rising interest in formal language systems and the project of renewing Classical Positivism as a philosophy of science. Peirce’s Collected Papers not only included the various formulations of his famous pragmatic maxim for clarification of meaning, which was sometimes taken as an anticipation of a verificationistic criterium of meaning,57 but also his sign-classifications which served as a basis for his formal systems of predicate logic. Dewey and his intellectual companion Arthur Bentley could therefore use Peirce’s writings on signs in discussing the formal perspectives and distinctions of Rudolf Carnap, Ernest Nagel, and others. Dewey and Bentley further exploited resources in Peirce’s texts in forming a philosophical view they called “transactional” and that they thought could undermine the resurgence of received epistemological and ontological dichotomies Dewey had been fighting his whole intellectual career.58 TRANSACTIONALISM AND ITS PEIRCEAN LEGACY: AVOIDING ABSTRACT DICHOTOMIES Although Peirce’s architectonic systems were out of line with the new style of philosophy, Dewey nevertheless catches attention to basic traits of Peirce’s post-1900 outlines of a system. Dewey had himself in Experience and Nature (1925) engaged in an ontological inquiry aiming to capture “generic traits of existence,”59 and in the 1930s and 1940s he qualifies and defends Peirce’s phenomenological categories against Peirce’s critics. Dewey grasps the overarching aim of Peirce’s science classification as that of providing a philosophical basis for specialized empirical science. Such basis could be achieved, Dewey notes, not through “a system of axioms or self-evident truths,” but by an analysis of ordinary experience or “common sense” as “an affair of experience” (LW11: 481). In accordance with Peirce’s plan Dewey takes the primary analysis of the three categories to be provided by Peirce’s phenomenology, not his evolutionary metaphysics. Moreover, for Dewey in the 1930s it is crucial that firstness and secondness are not misunderstood or distorted in terms of classical or logical empiricist analysis of “sensations” or “sense data.” He thus defines firstness as “quality” or as

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“that which totally and intimately pervades a phenomenon or experience” (LW11: 90). In order to avoid the atomized and hypostasized units of an empiricist analysis he makes clear that firstness “characterizes any and every experience subject-matter, as far as that experience has unity and totality, wholly independent of the complexity of its ‘components’ and of the place of these components in the existential world” (LW11: 91). As for secondness, Dewey observes that its specification provides a fuller analysis of how experienced qualities are anchored in experiential process of interaction or reaction. Peirce’s secondness, Dewey points out,60 anticipates what William James (1912) called “the doublebarreledness of experience.” On Dewey’s interpretation of James, Peirce’s categorical analysis would thus accord with a broad Pragmatistic definition of the notion of experience in terms of a product-aspect (or content-aspect), as well as a process-aspect. Peirce’s secondness would encompass “what men do and suffer, what they strive for, love, believe and endure, but also how men act and are acted upon, the ways in which they do and suffer, desire and enjoy, see, believe, imagine” (LW1: 18). Dewey’s how/what-distinction correlates tightly with his experiencing/ experienced-distinction;61 and in the late stages of his philosophical thought, the use of these distinctions accords with his stress on the continuities between processes and products of inquiry.62 Through these distinctions, Peirce’s secondness points toward Dewey’s and Bentley’s own later distinction of knowing and the known,63 which, like the former distinctions, is coined to undermine received epistemological and ontological dichotomies: subject/object, mind/matter. Yet, making Peirce’s categories intelligible and agreeable in Pragmatist terms is not enough. How could Peirce’s analysis be applied in discussing the emerging emphasis on formal logic and on the language of science? It is important for Dewey to show that the “doublebarreledness” of secondness would undermine not only inherited epistemological or ontological dichotomies but also the need for abstract mediators between separate ontological realms suggested by such dichotomies. For intellectual descendants of Gottlob Frege and Bertrand Russell candidates for such mediators would be truth carriers; propositions or sentences, considered as abstract semantic entities. In particular, it is imperative for Dewey that instances of Peirce’s category thirdness are not assigned any such abstract mediating role. To consolidate Peirce’s Pragmatistic credentials Dewey spells out certain naturalistic dimensions of Peirce’s categorical analysis. He thereby situates the experiential specifications of firstness and secondness in a larger context of ongoing processes involving human organisms and their biophysical and social environments. Secondness is thus further explicated in terms of a “common transaction” of organism and environment as a “two-sided affair” (LW15: 147). On Dewey’s account of Peirce, human use of linguistic signs,

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cognitive as well as noncognitive use, would be rooted in such transactions. We recall that in Peirce’s tenfold classification of signs, the triadic relations that define linguistic signs incorporate secondness and firstness. Moreover, Dewey stresses that use of linguistic signs requires indices, and hence secondness, in order to establish their reference.64 To expressively avoid assumptions about separate ontological realms that propositions have to bridge or mediate, Dewey, together with Arthur Bentley, appeals to Peirce’s analysis of precepts (LW16: 11, 66).65 Precepts are instructions that through use of indices enable social action coordination required to achieve identification of an indicated object (or objects). To Dewey and Bentley Peirce’s analysis of precepts is particularly relevant since it accounts for the use of quantifiers in general sentences of a logical language in ways that do not call for abstract mediators in the sense of Frege or Russell.66 Dewey further considers thirdness as such. Through discussing other interpretations of Peirce, Dewey stresses how thirdness is defined by a triadic relation, and exemplified by linguistic signs. In particular, he attacks Charles Morris’ (1938) influential interpretation for having distorted Peirce’s thirdness. Famously, Morris translates Peirce’s general concept of the sign into three semiotic “dimensions” the first two of which are adapted to the studies of formal languages in Logical Positivism: the syntactical dimension of purely formal relations between signs; the semantic dimension of the relation of signs to objects; and, finally, the pragmatic dimension of signs’ relations to interpreters. Morris’ three dimensions, Dewey rightly points out, misrepresents Peirce’s concept of sign as defined by an irreducible triadic relation (between representation, object, and interpretant). In fact, Morris’ approach is “parceling out the triadic relation” and he obtains instead “three dyadic “dimensions” (LW15: 142). In particular, Peirce’s interpretant would in Morris’ “pragmatics” become cut off from a sign’s object, and the human uses of signs are thus reduced to an “extra-cognitive, extra-logical domain” (LW15: 143) of little or no concern for a philosophical analysis of enabling conditions for specialized empirical inquiry in the sense of Peirce’s speculative grammar.67 In considering thirdness Dewey is not so much concerned with the formal triadic sign-relation as such but rather focuses on Peirce’s specification of a sign’s interpretant in terms of a process of interpretation (or a “semiosis”68) where one sign (or representation) of an object is translated into another sign (representation). In fact, in his latest years Peirce provides a certain semiotic rephrasing of his early theory of inquiry;69 more specifically, he now requalifies one of his former definitions of truth phrased in terms of the final opinion (agreed on by inquirers) by now using terms like “the ultimate” or “final interpretant.”70 Peirce’s later use of the notion of interpretant thus makes explicit that processes of interpretation are socially embedded in communities of inquiry and interpretation.71 Yet, by also noting Peirce’s Pragmatistic

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qualification of interpretants of linguistic signs in terms of habits and habitchanges,72 Dewey further stresses that processes of interpretation are habitually embedded in a natural and social world.73 Stressing the contrast between Peirce’s and Morris’ respective accounts Dewey sums up: “according to [Peirce] ‘biological’ and ‘sociological’ facts are integral and indispensable factors of such [linguistic] signs—not something to be dismissed to a nonlogical and non-cognitive dimension” (LW15: 151). The idea of the social (and biophysical) embeddedness of linguistic signs is particularly attractive to Dewey and Bentley because it suggests ways of avoiding dependence on abstract dichotomies and mediators in philosophical inquiry into knowledge processes. Yet, acknowledging the social embeddedness of linguistic signs has methodological consequences for philosophical analysis. Instead of formulating a set of “axioms or self-evident truths” for an ideal language of science, Dewey and Peirce assume that sign-forms that are epistemically basic for scientific inquiry are already embedded in social practices or uses, like Peirce’s precepts. Epistemological analysis of such sign-forms takes acquaintance with their uses as a necessary starting point. In Peirce’s case we have seen that, while certain abstract derivations provide input to his analysis, acquaintance with sign use through “rhetorical evidence” (CP 2.333) is methodologically necessary to provide an analysis of assertions, and to test the outcomes of such analysis. Hence, an unavoidable circularity emerges, distinct from the vicious circularity Peirce expressively wants to avoid.74 Dewey and Bentley engage in similar kind of non-vicious circularity. In studying knowledge process, they refuse to provide a set of formal definitions or postulates independent in origin from the subject matter to be studied. Instead, and even openly, they accept the circularity involved in identifying a sign-form observed in actual use, taking it as “a behavioral event” (LW16: 69), and in qualifying such identification through further identifications of similar or contrasting uses.75 As in Peirce’s analyses and classifications of signs, such circular approach is not seen as a necessary evil; not unlike Martin Heidegger’s hermeneutical circle (2008: 194–5)76 Dewey and Bentley engage in, and exploit, such circularity in exploring and qualifying what is already interpreted or known by competent language users.77 TRANSACTIONALISM: MODES OF THEORIZING IN SCIENCE Dewey and Bentley further develop their Transactionalism to make it apply more directly to modes of categorization and theorizing in empirical science. Compared with Peirce’s science classification, it thus operates at a less general philosophical level than phenomenology and speculative grammar, more

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like Peirce’s metaphysics for the natural and social sciences. Dewey and Bentley distinguish their transactional view through qualifying and criticizing ontological schemes underlying scientific theorizing, which interestingly parallels Peirce’s heuristic use of his categories in qualifying other philosophical systems. In distinguishing their transactional view, however, Dewey and Bentley take their point of departure in August Comte’s three stages in science (and society): “the theological, the metaphysical, and the positive” (LW16: 97). First, hinting at Comte’s theological stage, they distinguish their position from a mode of theorizing they call “Self-Action” and which historically encompasses ways of accounting for organic and inorganic substances before the scientific revolution, relying on Aristotelian thought. Such mode of theorizing typically assumes “independent ‘actors,’ ‘souls,’ ‘minds,’ ‘selves,’ ‘powers’ or forces, taken as activating events” (LW16: 71) or “‘things’ as possessing powers of their own, under or in which they acted” (LW16: 66). In terms of Peirce’s categories (which Dewey and Bentley do not explicitly mention in this context) this mode would strikingly lack of consideration of secondness, a lack that Peirce himself finds typical of “The Berkeleyans for whom there are but two kinds of entities,—souls, or centers of determinable thought, and ideas in the souls” (EP2: 165). However, such lack of consideration could be seen to persist in twentieth-century social science: in Dewey’s and Bentley’s view, “the ‘mind’ as ‘actor,’ still in use in present-day psychologies and sociologies, is the old self-acting ‘soul’ with its immortality stripped off” (LW16:124). As the American sociologist Mustafa Emirbayer has pointed out lately, the “self-actional” model has reemerged in the methodological individualism of rational choice theory in particular (1997: 284). Dewey and Bentley further distinguish a second mode of theorizing they call “interaction.” Generally, theorization in the mode of interaction considers and allows for “presentation of particles or other objects organized as operating upon one another” (LW16: 71). Historically, such approach was initiated by Galilei and “took form under Newton as a system of interaction, marked especially by the third ‘law of motion’—that action and reaction are equal and opposite” (LW16: 67). Peirce, too, considers such mode of theorizing with reference to “Cartesianism of all kinds . . . and the metaphysics of the physicists of today” (EP2: 180). Peirce points out that this mode would stress secondness, as well as thirdness (in the sense of general laws or regularities), but would reject the reality of firstness (or of what John Locke called “secondary qualities”).78 Against the background of the two former modes of theorizing, “transaction” is introduced as the third mode. This mode should not simply replace that of “interaction,” but it would be a complementary mode of theorizing in contexts where analytic separation of single elements have become too rigid, and where

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categorization of general properties and relations, causal or other, have become too fixed, to do justice to phenomena. Dewey and Bentley see the third mode as having been initiated in recent developments in physics (relativity theory) and biology (ecology).79 By generalizing from such scientific developments they further define “transaction” in terms of “systems of description and naming [that] are employed to deal with aspects and phases of action, without final attribution to ‘elements’ or other presumptively detachable or independent ‘entities,’ ‘essences,’ or ‘realities,’ and without isolation of presumptively detachable ‘relations’ from such detachable ‘elements’” (LW16: 101–2). What facilitates comparison with Peirce’s categories, however, is that Dewey takes pains to make the transactional viewpoint intelligible by appealing to everyday life experience. When taking the term “transaction” in its everyday sense, Dewey points out, the single parties or parts of a commercial transaction are defined and sustained in terms of their roles and capacities in a transaction (as “buyers,” “sellers,” “goods,” or “commodities”), and they undergo changes in virtue of such roles and relations.80 In a similar fashion Peirce refers to social actions such as buying or giving as instances of thirdness that are to be analyzed in terms of irreducible triadic relations. While the individual elements of such actions could be seen to preserve their singular identities through time and space (as instances of secondness),81 understanding them as parts of a social action requires one to take one such element as receiving “a character which can neither exist nor be conceived to exist without the cooperation of the other two” (EP2: 171).82 Not for Peirce either, then, would it be sufficient or adequate to conceive such actions or transactions as instances of what Dewey calls “interaction” where individual elements would quasi-mechanistically retain their identities and natures unchanged. Yet, theorizing in the mode of transaction takes a further step and conceives the examples above as embedded in layers of context: commercial transactions are conditioned and enabled by economic activities, such as industrial production and financing, and they are further regulated through moral norms and legal institutions.83 Take another example, “a loan of money”: not only would the identities of borrower and lender mutually define each other, socially and morally, but taken as an economic transaction, the loan would be “identifiable only in the wider transaction of the full legal-commercial system in which it is present as occurrence” (LW16: 126). The requirement of institutional contextualizations in particular suggests how Transactionalism may accommodate Peirce’s analyses of thirdness through the cases of making a contract and informal acts of assertion. Through the appeal to layers of social and institutional contexts we may further begin to see how the requirement of categorizing “aspects and phases of action, without final attribution to ‘elements’ or other presumptively detachable or independent ‘entities,’ ‘essences,’ or ‘realities’” (LW16: 101–2) may receive further application in social science research. At least, Dewey’s (and Bentley’s)

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and Peirce’s considerations would involve criticisms not only of methodological individualism but of treating social attributes (class, gender, ethnicity) as independent realities or “essences” in accounting for social action.84 However, on a more general level, Transactionalism involves criticism of a division built ontologically into Peirce’s science classification: the division between natural and social or human sciences. It has become an urgent task for philosophy, Dewey argues in the late 1940s, to consider the various ways in which humans, individually and collectively or economically, depend on nonhuman nature. Dewey here qualifies “transaction” in terms of such dependencies: “human life itself, both severally and collectively, consists of transactions in which human beings partake together with non-human things of the milieu along with other human beings, so that without this togetherness of human and non-human partakers we could not even stay alive, to say nothing of accomplishing anything” (LW16: 243). Although this wider philosophical concern takes lessons from ecological research,85 and ecology inspired efforts to cross disciplinary boundaries, such as Egon Brunswik’s “psychological ecology” (LW16: 144n4), it also resonates with shared Pragmatist commitments of Dewey, James, and Peirce. As a generation of philosophers with Darwin as a main source of inspiration, the Classical Pragmatists made assumptions of evolutionary and functional continuities between human and nonhuman life. A key notion in considering such continuities in Peirce’s, James’s, and Dewey’s Pragmatism is that of habit. In his sketchy phenomenological analyses Peirce sometimes takes habit and habit-formation as examples of thirdness.86 Since phenomenology is to provide a more general foundation for science than metaphysics, which justifies the natural/social (human) science division, the specification of thirdness in terms of habit opens up for theorizing human agency in ways that cross disciplinary boundaries. Dewey reads Peirce’s philosophical use of the term “habit” along such lines by taking it to emphasize the integration of the human organism in her “world” (Dewey LW15: 151). Moreover, Peirce himself sometimes focuses on functional (not only evolutionary) continuities between humans and nonhumans in using his categories to criticize the mechanistic metaphysics stemming from Galilei and Newton. While recognizing secondness and thirdness, a mechanistic account of nature rejects the reality of firstness and thus fails to consider the sentience of habitual creatures, human and nonhuman. However, in recognizing firstness, Peirce argues, one cannot fail to see that both humans and nonhumans orient themselves in their environments through various sensory modalities and emotional responses, although in species-specific ways.87 He further suggests that, through such sensory modalities and emotional responses, human and nonhuman animals even directly engage each other.88 This phenomenologically based suggestion of continuities between humans and nonhumans anticipates Dewey’s transactional claim about human

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dependencies on nonhumans. Still, there are limitations in Peirce’s approach that are addressed by Dewey. While rooted in everyday life experience Peirce’s examples are drawn merely from his private experiences with domesticated pet animals. Dewey, however, in making a general point about human dependence on nonhumans, observes the economic exploitation of nature in “farming, mining, fishing, or manufacture” (LW16: 243), which suggests a public, rather than a private focus of concern. In an earlier text he comments that it makes a great difference to the life of a farmer “whether he is fond of [plants and animals]” that he uses to carry on his farming activity, or whether he regards the latter merely as means to ends lying wholly outside of the farming activities as such and of his affectional bond with the plants and animals (MW9: 113). On the face of it, Dewey is talking about the sentience of humans and about affective engagements between human and nonhumans; yet, given the economic context of farming generally and minding the rapid upscaling and mechanization of American agriculture,89 Dewey’s comment would thus also be about economic, technological, and political conditions for having an affectional experience and engagement with nonhuman nature. This suggest a further limitation of Peirce’s phenomenological approach rooted in the professed aim of his philosophical disciplines: these disciplines set out to analyze a necessary basis for specialized science in phenomena of everyday life, but they are not geared to reflect on how science and technology in turn massively invade, condition, and transform everyday life experiences.90 The latter aim, in addition to the former, is what Dewey suggests should be pursued by philosophy. Philosophy would thus need to consider and assess “the vast return wave of the methods and conclusions of scientific concern into the uses and enjoyments (and sufferings) of everyday affairs; together with an accompanying transformation of judgment and of the emotional affections, preferences, and aversions of everyday human beings” (LW16: 253). In particular, given the massive exploitation and destruction of nonhuman nature enabled by science and technology, philosophy needs to explore how technologically transformed conditions of human action and experience likewise affect our bonds to and valuations of nonhuman nature. A philosophical exploration of “the vast return wave” would thus be a valuable Deweyan complement to Peirce’s phenomenology. NOTES 1. References to Peirce’s works are to: (1) Collected Papers of Charles Sanders Peirce (Peirce 1931–58) with the abbreviation “CP” and where the number to the left of the decimal point indicates the volume and the number to the right of the paragraph; (2) The Essential Peirce (Peirce 1992–98) with the abbreviation “EP,” and where references are to the volume and page number follow; (3) Unpublished

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manuscripts in microfilm version that are indicated with “MS.,” and the numbers refer to those in Robin 1967. 2. See Murphey (1961: 1–3). 3. See EP2: 259, CP 1.180, 258, CP 3.427. 4. See Zeman (1986), Brady (1996), Dipert (2004). 5. For a brief developmental account of Peirce’s view of mathematics, see ­Midtgarden 2001. 6. See CP 2.206, 229, 332. See also MS 787: 10. 7. See CP 2.332–5, CP 3. 430. 8. See CP 5.311, 384, 407. 9. See MS 787: 5, 12–3, 17. See also CP 2.227, 333, CP 3.428. 10. See CP 3.432. 11. See Midtgarden (2001: 90–1). 12. For a more well-known introduction of this triad, see CP 2.247–9. 13. See Midtgarden (2002: 234). 14. See in particular CP 2.339, 357. Risto Hilpinen (1983) has interpreted Peirce’s account of quantifiers in terms of game-theoretical semantics. See also Midtgarden (2007: 589). 15. See Kant 1982 (1787): B 104–5. 16. See CP 3.428 and MS. 787: 4–5. 17. See EP2: 143–4, 268. 18. See EP2: 146, 259. 19. See Peirce’s rejection of Cartesianism and of the assumption of a faculty of intuition in the early epistemological article “Questions Concerning Certain Faculties Claimed for Man” (CP 5.213–63). 20. See EP2: 144, CP. 3.428. 21. See Peirce’s tenfold classification of Signs, EP2: 289–99. 22. See EP2: 148, CP 1.563. 23. See CP 6.7–35, 102–63. 24. Note how Peirce with reference to Hegel distinguishes between categories in a universal sense and categories as referring to “phases of evolution”: “Hegel was . . . right in holding that these categories are of two kinds, the Universal Categories, all of which apply to everything, and the series of categories consisting of phases of evolution” (EP2: 143). 25. See EP2: 427–8. 26. In one of Peirce’s most systematic classification of signs, he uses firstness (although not the word “Firstness” in this context but rather “First” and “Possibility”) in a technical and stepwise manner to define the syntax of a propositional symbol, a socalled Dicent Symbol (EP2: 295–6). Such a symbol requires through its interpretation (or “Interpretant”) an Iconic Legisign, where the latter has already been exemplified by “a diagram, a part from its factual individuality” (EP2: 294), and “Icon” has been defined by firstness (EP2: 291) and “Legisign” by thirdness (EP2: 291). Yet, even firstness has here initially been defined as an element of triadic relations (EP2: 289–290). 27. Sometimes he seeks to avoid the term “feeling” and rather defines Firstness through sense of quality, which would, for example, be “the sort of element that makes red to be such as it is, whatever anything else may be” (CP 8.267).

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28. For Peirce’s algebraic treatments of dyadic relatives, see for instance CP 3.492–8. 29. See for instance CP 3.590–600. 30. See EP2: 160–1. 31. See EP2: 259–60. 32. EP2: 150. 33. See for example his defense of scholastic realism in CP 5.312, 503–4. See further John Bohler’s discussion of Peirce’s relation to scholastic realism (2004). 34. See EP2: 170–171. 35. In Peirce’s terminology, this would be a “Rhematic Indexical Sinsign” (EP2: 294). 36. This would be what Peirce calls a “Dicent Sinsign” (EP2: 294). 37. This would be a “Dicent Symbol” (EP2: 295). 38. For a discussion of Peirce’s argument, see Hookway (1985: 97–101). 39. See Peirce’s tenfold classifications of signs, EP2: 289–99. 40. See EP2: 299. 41. See EP2: 297–9. 42. See EP2: 396, 401–2. 43. See EP2: 343, 354. 44. See EP2: 278, 311–2, CP 5.546. 45. CP 1.475. 46. See Austin 1962: 101ff. 47. In agreement with Peirce’s triadic sign-relation an illocutionary act would involve a socially (or institutionally) conditioned uptake (interpretant), an uttered propositional symbol or locutionary act (sign), the propositional content of which would be about something in the world (object). As for the latter, however, an illocutionary act would involve either a world-to-word, or a word-to-world direction of fit (see Searle 1979: 11–20). 48. See Peirce’s comment: “That single events should be hard and unintelligible, logic will permit without difficulty: we do not expect to make the shock of a personally experienced earthquake appear natural and reasonable by any amount of cogitation. But logic does expect things general to be understandable. To say that there is a universal law, and that it is a hard, ultimate, unintelligible fact, the why and wherefore of which can never be inquired into, at this a sound logic will revolt, and will pass over at once to a method of philosophizing which does not thus barricade the road of discovery” (CP 6.60). 49. “Not only does Thirdness suppose and involve the ideas of Secondness and Firstness, but never will it be possible to find any Secondness and Firstness in the Phenomenon that is not accompanied by Thirdness” (EP2: 177). See also EP2: 289–99. 50. “The truth is that pragmaticism is closely allied to the Hegelian absolute idealism, from which, however, it is sundered by its vigorous denial that the third category (which Hegel degrades to a mere stage of thinking) suffices to make the world, or is even so much as self-sufficient. Had Hegel, instead of regarding the first two stages with his smile of contempt, held on to them as independent or distinct elements of the triune Reality, pragmaticists might have looked up to him as the great vindicator of their truth” (CP 5.436, see also CP 8.268). 51. In addition, Peirce assumes that man has an evolutionary based capacity or instinct for making correct guesses from ordinary experience (see EP2: 443–5).

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52. See CP 5.513 and Midtgarden 2014. 53. See EP2: 179. 54. In his lecture notes from 1913 Dewey presents a broad range of arguments against the hedonist psychology of Marginal Utility Theory, and some of them are based on his own functionalistic psychological theory. According to the later, an object of desire, as pertaining to a conscious or deliberate state of mind, emerge out of conflicting impulses, and requires reflection and cognitive activity to bring the mental conflict to a solution. See Tilman and Knapp (1999: 302–3). 55. EP2: 258. 56. In 1935 Dewey’s engages in a philosophical defense of Peirce’s categorical analysis, in particular the category of firstness (see LW11: 86–95). The same year he reviews volume 5 of Peirce’s Collected Papers (see LW11: 421–5); and in 1937 he reviews all the first six volumes (see LW11: 479–85). 57. See Feigl 1949: 9. See Midtgarden (2007: 581) for an interpretation of Peirce’s later reformulations of his pragmatic maxim. 58. See Frank X. Ryan’s account of the cooperation between Dewey and Bentley (1997a, 1997b). 59. See in particular LW1: 50, 52. 60. LW15: 147. 61. See LW1: 18–9. 62. See in particular LW12: 15–21, where Dewey makes reference to Peirce’s early theory of inquiry (published in 1877 in the essay “The Fixation of Belief” [CP 5.358–487]). 63. See in particular LW16: 46–61. 64. LW15: 147–8. 65. See above and CP 2.330, 2.336. 66. See above and CP. 2.453. 67. Dewey and Bentley stresses that “Peirce introduced the word “interpretant,” not in order to maintain the old mentalistic view of thought but for quite the opposite purpose . . . to show how “thoughts” or “ideas” as subjects of inquiry were not to be viewed as psychic substances or as psychically substantial, but were actually processes under way in human living.” (LW16: 239) 68. See EP2: 411. 69. See Peirce’s essay “The Fixation of Belief” (CP 5.358–487). 70. See CP 8.184, 343. See also Hookway (1985: 139). 71. See LW15: 152. Few years earlier Dewey likewise pointed out that “C. S. Peirce is notable among writers on logical theory for his explicit recognition of the necessity of the social factor in the determination of evidence and its probative force. The following representative passage is cited: ‘The next most vital factor of the method of modern science is that it has been made social.’” (LW12: 484. The quote from Peirce is from CP 2. 502) 72. See in particular EP2: 418. 73. “Habit, operates in and through the human organism, but that very fact is to [Peirce] convincing evidence that the organism is an integrated part of the world in which habits form and operate” (LW15: 151). 74. See CP 3.432, MS 787: 15.

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75. For a complete overview of the various forms of circularity involved in Knowing and the Known, see Ryan (1997b: 1017–8). 76. See Midtgarden (2007: 582–3). 77. “We adopted circularity—procedure in a circle—openly, explicitly, emphatically . . . . We have nothing to apologize for in the circularity we choose in preference to the old talk-ways. We observe world-being-known-to-man-in-it; we report the observation; we proceed to inquire into it, circularity or no circularity. This is all there is to it. And the circularity is not merely round in the circle in one direction: the course is both ways round at once in full mutual function” (LW16: 62). 78. See Peirce’s more extensive account with reference to the ontology of classical Newtonian physics (EP2: 186–7). 79. In Physics Albert Einstein’s contributions involved the destruction of time and space as absolute Newtonian frameworks and “brought space and time into the investigation as among the events investigated” (LW16: 106). In biology, Dewey and Bentley point out, a rigid division between organism and its biophysical environment has been overcome in ecological studies (see LW16: 117, 120). 80. See LW16: 242. 81. See CP 3.460. 82. See EP2: 391. 83. See LW16: 243. 84. For a further account of the theoretical implications of Transactionalism for sociology, see Emirbayer (1997: 286–90). 85. See LW16: 117, 120. 86. See EP2: 269. 87. See EP2: 193. 88. See EP2: 193. 89. In the second edition of The School and Society, which was published in 1915, Dewey considers at length how implementation of new technologies and social division of labour through industrialization have transformed American agriculture in only one or two generations (see MW1: 6–8). He looks back at the times when farming was a purely a family based affair and all family members were trained and practically educated through “acquaintance with the plants and animals of the farm and garden acquired through actual living among them and caring for them” (MW1: 8). 90. Yet, sometimes Peirce does reflect on the transformation of everyday life affairs through science and technology, see CP 5.513 , CP 6. 564. For an interpretation of these reflections, see Midtgarden 2014.

REFERENCES Austin, J. L. (1962). How to do Things with Words. Oxford, England: Oxford ­University Press. Bohler, J. (2004). “Peirce and Medieval Thought.” In C. Misak (Ed.), The Cambridge Companion to Peirce (pp. 58–86). Cambridge, England: Cambridge University Press.

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Brady, G. (1997). The Contributions of Peirce, Schröder, Löwenheim, and Skolem to the Development of First-Order Logic. Ph.D. dissertation, University of Oslo. Dewey, J. (1969–1991). The Collected Works of John Dewey, 1882–1953, 37 vols., J. A. Boydston (Ed.). Carbondale: Southern Illinois University Press. The volumes were published as The Early Works: 1881–1898 (EW), The Middle Works: 1899–1924 (MW), and The Later Works: 1925–1953 (LW). (References are indicated by abbreviating letters [MW, LW] followed by volume and page number.) Dipert, R. (2004). “Peirce’s Deductive Logic: Its Development, Influence, and Philosophical Significance.” In C. Misak (Ed.), The Cambridge Companion to Peirce (pp. 287–324). Cambridge, England: Cambridge University Press. Emirbayer, M. (1997). “Manifesto for a Relational Sociology.” The American Journal of Sociology 103(2), 281–317. Feigl, H. (1949). “Logical Empiricism.” In H. Feigl and W. Sellars (Eds.), Readings in Philosophical Analysis (pp. 3–28). New York, NY: Appleton Century Crofts. Heidegger, M. (2008). Being and Time. (J. Maquarrie and E. Robinson, Trans.). New York, NY: Harper Perennial. Hilpinen, R. (1983). “On C. S. Peirce’s Theory of the Proposition: Peirce as a Precursor of Game-Theoretical Semantics.” In E. Freeman (Ed.), The Relevance of Charles Peirce (pp. 264–70). La Salle, IL: Monist Library of Philosophy. Hookway, C. (1985). Peirce. London, England: Routledge and Kegan Paul. James, W. (1912). Essays in Radical Empiricism. London, England: Longmans, Green and Co. Kant, I. (1982 [1787]). Kritik der reinen Vernunft. Stuttgart, Germany: Philip Reclam. Midtgarden, T. (2001). “Peirce’s Speculative Grammar from 1895–1896: Its Exegetical Background and Significance.” Transactions of the Charles S. Peirce Society 37(1), 81–96. ———. (2002). “Iconic Aspects of Language and Language Use: Peirce’s Work on Iconicity Revisited.” Semiotica 139(1–4), 227–44. ———. (2007). “Peirce’s Epistemology and Its Kantian Legacy: Exegetic and Systematic Considerations.” Journal of the History of Philosophy 45(4), 577–602. ———. (2014). “Pragmatism, Cultural Lags and Moral Self-Reflection.” In T. Thellefsen and B. Sorensen (Eds.), Charles Sanders Peirce in His Own Words (Semiotics, Communication and Cognition, vol. 14) (pp. 421–27). Hawthorne, NY, De Gruyter. Morris, C. W. (1938). Foundations of the Theory of Signs. (International Encyclopedia of Unified Science. 1[2]) Chicago, IL: The University of Chicago Press. Murphey, M. G. (1961). The Development of Peirce’s Philosophy. Cambridge, MA: Harvard University Press. Peirce, C. S. (1931–58). Collected Papers of Charles Sanders Peirce, 8 vol. C. Hartshorne and P. Weiss (Eds., vol. I–VI, 1931–5), A. Burks (Ed., vol. VII–VIII, 1958). Cambridge, MA: Belknap Press. ———. (1992–98). The Essential Peirce: Selected Philosophical Writings, 2 vol. N. Houser and C. Kloesel (Eds., vol. 1), Peirce Edition Project (Ed., vol. 2). Bloomington, IN: Indiana University Press.

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Robin, R. S. (1967). Annotated Catalogue of the Papers of Charles S. Peirce. Amherst, MA: University of Massachusetts Press. Ryan, F. X. (1997a). “The “Extreme Heresy” of John Dewey and Arthur F. Bentley I: A Star Crossed Collaboration?” Transactions of the Charles S. Peirce Society 33(3), 774–94. ———. (1997b). “The ‘Extreme Heresy’ of John Dewey and Arthur F. Bentley II: ‘Knowing and the Known.’” Transactions of the Charles S. Peirce Society 33(4), 1003–23. Searle, J. R. (1979). Expression and Meaning. Cambridge, England: Cambridge University Press. Tilman, R., and Knapp, T. (1999). “John Dewey’s Unknown Critique of Marginal Utility Doctrine: Instrumentalism, Motivation, and Values.” Journal of the History of the Behavioral Sciences 35(4), 391–408. Zeman, J. J. (1986). “Peirce’s Philosophy of Logic.” Transactions of the Charles S. Peirce Society 22(1), 1–22.

Chapter 7

Declarative Mapping Sentence Mereologies Categories from Aristotle to Lowe Paul M. W. Hackett

BACKGROUND The employment of category-based understandings of our existence is common in both our daily lives and in academic studies.1 In this chapter I place emphasis upon a categorial approach from the social sciences, namely facet theory.2 Research under this theory develops category-based understanding of our concepts of events, behaviors, states of affairs, and so on. The major tool used in facet theory is an explicit, structured mereology known as the mapping sentence. The mapping sentence is used to initiate enquiry, as a theoretical structuring device and often is the culmination of research as either an empirically and/or theoretically substantiated statement. I argue that mapping sentences are more easily and more thoroughly understood through an exploration of their constituent parts and an exposition of their philosophical, linguistic, and psychological structure. I also develop a distinction between two forms of mapping sentences: the mapping sentence or general mapping sentence and the declarative mapping sentence. The former has been used within facet theory research from the past seventy years and is represented in a large academic literature. The declarative mapping sentence, on the other hand, I have developed in my own research, principally over the last decade. I contrast these two linguistic mappings and consider their applicability to different forms of understanding. Illustrative declarative mapping sentences are presented and I design a declarative mapping sentence for the hermeneutic consistency of the declarative mapping sentence. I propose the declarative mapping sentence as an ontological and mereological structure for initiating and interpreting philosophical (and qualitative) scholarly endeavors. 135

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CATEGORIES ARE EVERYWHERE We all attempt to understand our experiences of the world around us, what we feel, conceive of and think about our lives and the activities we perform. This process often involves the forming of concepts or internal representations of experiential phenomena. Moreover, we frequently seem to find it useful to disassemble and subdivide our worldly experiences, where these disassemblies are often categorial in nature. I start this chapter by making the somewhat bold statement that a very large proportion of animal species (from rudimentary animals to highly sophisticated ones), in some way or another, form or employ categorization in their encounters with its world, and while I will not dwell upon the veracity of this claim, it serves as a useful starting point for my writing. Concepts are abstract ideas or mental images that have some form of correspondence to a class of events or things. In the chapter by Yehezkel in this book, states that, “categories are concepts.” Many species appear to employ what may be thought of as categorial concepts, such as humans, primates, and corvids (the crow family) and Psittaciformes (parrots), Petroica australis (New Zealand Robins) some other avian species, and so on. The formation of concepts is problematic to determine and is associated with the similar difficulty that scholars encounter when trying to determine which species possess consciousness. However, it is clear that animals, other than those listed above, employ categorization. My statement that all organisms form or at least employ categories even seems to hold true even when the organism that is being considered is a slime mold. These were originally thought of as fungi. However, of interest to this chapter is that slime molds usually live as single cells but have the ability to come together and form multicellular structures (see for example, Bonner, 2009). When these molds are grown within a maze, these extremely simple organisms categorize their encounters with their immediate environment as being paths that lead to food and paths that do not. Categorizing whether a chosen path leads to danger or to safety, to a food source or not, or in any other way as leading to something that is advantageous or disadvantageous, has obvious benefits at the level of the individual animal or organism and also in evolutionary terms. The categories that animals (and perhaps plants and other organisms) develop appear to emerge at different points of time in their growth. In animals, and especially human beings, these various types of categories have a neurological basis for their formation, which arise at specific stages of our maturation. Authors have noted how the human child progresses along a categorially segmented pathway upon which they initially form perceptual-motor activity based preverbal categories to classify their environments (Barsalou, 1999). Over the preceding two-decades there has also emerged a literature in which proposals have been offered to provide answers to questions about the

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neural location for various categories of knowledge. For example, Patterson et al. (2007), Lambon and Petersin (2008) offer models that posit a semantic a hub with radiating spokes and have located this bilaterally within the anterolateral portions lobes (ATLs). These authors claim that these hubs possess a similar structure in both lobes, while others (see Gainotti, 2012) posit these to differ between the two lobes, reflecting the verbal dominance of the left hemisphere of the brain and the sensorimotor supremacy in the right.3 Research that has provided a location for categorial knowledge in human beings, along with the fact that the brain structures are significantly different between different types of animals (e.g., between avian and primate species) raises interesting questions as to the how categorization differs between animals? With this stated, it should also be noted that these differences in neurological structures do not rule out the existence of mechanisms in category formation and usage which are shared across species. Neurobiological research into object recognition suggests that the basal ganglia implement this process in both primates and birds. Computational neuroscientific modeling suggests that the manner in which visual processing proceeds in humans also enables the interpretation of object recognition in pigeons. This supports the idea that vertebrate species of animals with only a distant evolutionary relationship possess communalities in their shape processing of objects (Soto and Wasserman, 2012). In what I have written so far I have provided an extremely brief snapshot of notions regarding the categorial abilities of human beings and other animals and I have suggested that there are similarities and differences between species. I have not attempted to provide a comprehensive or definitive review of this area but instead what I have done is to suggest that category formation and usage is ubiquitous among organisms from amoebas to primates. This being the case I feel justified in stressing the significance of categories and the importance of studying category formation and usage. With these claims in mind, in the following section I review an approach to the study of categories, namely facet theory. This review then forms the basis for my later exposition of a variety of category-based ontological systems. Categorial systems have long been present in philosophical and psychological research. For example, in psychology the most familiar category-based systems are probably those of George Kelly and his personal construct theory (Kelly, 2013) and Piaget in regard to child development (Piaget and Inhedler, 1969); in philosophy Aristotle’s Categories (Aristotle and Ackrill, 1975), and the ontological categories of Lowe (2007) and Chisholm (1996). At the heart of a categorial position is an assumption that breaking down human existence into conceptual subdivisions, categories, or subcomponents, avails peerless insight into what it means to be an individual person. The development of subdivisions of our experience is also used to facilitate appreciation

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of social activities and behaviors. Thus, it is implicitly proposed that through understanding the mereological nature of human behavior and experience we are able to better understand what it means to be human. CATEGORIES AND CONCEPTS Modularity refers to the characteristic that many entities possess, such as cognition, of being made from parts, or of being divisible into categories, that may be discretely identified and which function separately and/or in various combinations. Categories are divisions of people or things, most often in terms of shared characteristics. Concepts are ideas or notions, theories, hypotheses or beliefs, conceptions, or abstractions. Machery (2011) distinguishes concepts from categories by stating that a concept is a body of knowledge that is held in long-term memory whereas, a category is a class of event. Thus, knowledge can be about an event, object, or state of affairs, where these targets of our knowledge are external to the person who holds the category, while the concept itself is internal to the individual. When I attempt to define the word concept the first two terms that are of importance are idea and abstract. The fact that concepts are ideas or notions that are developed internally to, and held by, an individual does not mean other people cannot not share this concept, but rather that the concept is not independently present in the external world. Abstraction describes this lack of worldly presence and is another key feature of concepts, which emphasizes the lack of physicality or concreteness of these phenomena. Abstractness also stresses the theoretical nature of concepts and the verb to abstract even goes as far as to denote the action of removing something, shifting it away from reality. Concepts may also make reference to mental images that possess a relationship or correspondence with events, objects, or states of affairs usually in terms of their essential characteristics. Psychological theories of concepts that refer to their categorial nature have been widely written about (e.g., see Murphy, 2002; Machery, 2009, 2010). Machery (2009) distinguishes concepts from categories by stating that a concept is a body of knowledge that is held in long-term memory, where a category is a class of event. Thus, knowledge can be about a thing or object or happenings and encounters, where these targets of our knowledge are external to the person, while knowledge is internal to the individual categories are in the world (Machery, 2009). A concept (c) constitutes a body of knowledge (k) about event (x), where k of x is employed by default in cognitive process that in some manner involve x. The concept (c) that a person may hold about x (c of x) is therefore a subset of all their knowledge k of x and c of x is therefore that part of their k

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about x, and from which they categorize x. Thus, categorial knowledge about x enables us to understand an event that contains the concept of x. In such a situation we are able to use knowledge to enable categorization, induction, analogizing, understanding, and so on. Knowledge of x is relatively insensitive to context and consequently is employed by default such that occurrences of x cause k of x to be brought from long-term memory: When we think about the event x, our k of x is drawn upon. Thus, the concept of a bird is a subset of all of our knowledge about birds that we hold in our long-term memory and which is accessed regardless of context. We use this knowledge of all birds to categorize, speak of, form analogies about, and so on, a bird or birds. However, knowledge (k) about specific bird x, and the conceptual subsets (c of k) may be drawn upon within specific contexts, where k and c of x do not exist in isolation and are in dialogue with their surroundings. On this understanding, a concept may be conceived as being made up of several components that form an array of attributes that are possessed or present within the concept to a given extent. Furthermore, the concept itself is comprised of the two characteristics of categorical knowledge that may be used to describe the experiential nature of the concept. These characteristics are the existence or not of this category and the amount that this category is present within the concept. All of the interactions between these two features of existence and extent are also pertinent to understanding the concept where understanding may be context related and constitutes our knowledge of our knowledge (k of k and k of c). Furthermore, when we attempt to understand a concept we can do so by considering the array of pertinent categories associated with the concept taken together as in some way mapping the concept. Alternately, we can attempt to understand profiles of the extent of each category within a concept. Research that investigates the complexity and boundaries of complex events (such as cognition) require the use of sophisticated frameworks, structures, and tests of our understandings. In the next section I provide details of facet theory and propose this template for understanding complex events. CATEGORIAL CLASSIFICATION AND FACET THEORY Clare Beghtol (1995) noted how in the middle decades of the twentieth century two separate streams of one particular categorization framework were developed in the geographically distinct areas of the Indian subcontinent and the United States/Israel. In the former of these locations S.R. Ranganathan initially advanced, and then elaborated upon, what he called facet theory, which he located within his work in bibliographic classification systems. One hundred years ago in Brooklyn, United States, Louis Guttman (1947)

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originated what he also termed facet theory though this time it was advanced as an orientation within the behavioral sciences. Beghtol (1995) notes how both of these researchers used the phrase facet theory and called the major subdivisions of their respective theories facets, but that the precise realization of their analysis method differed as it grew out their work related needs. After reviewing the work of both Ranganathan and Guttman, Beghtol’s conclusions were that in both instances the facet analytic approaches used similar characteristics that recommend both of these to the formation of classification systems: this was, she said, particularly true of Guttman’s mapping sentence (see Shye et al., 1994, pp. 70–95). Facet theory (see Canter, 1985a for an overview, see Levy, 1994 for a theoretical summary) as devised by Guttman (1947)4 is an approach to social science research that, among other things, attempts to define concepts. From its start, facet theory research has been designed within a scientific rubric and has yielded quantitative data (see Canter, 1985a; Shye, 1978; Shye and Elizur, 1974; Borg and Shye, 1995). The approach has succeeded in providing empirically rooted definitions of a number of conceptually/psychologically broad areas of human performance such as: intelligence (Beauducel et al., 2001); attitudes (Vélez Latorre, 2013); values (Fisher, 2013); and so on, and a large number of more specific domains of human activity as diverse as: environmental concern (Hackett, 1995); advertising (Hestroni, 2000); merchandising virtual stores (Wo et al., 2015); the perception of fine art (Hackett, 2016, 2017); and students’ perception of learning environments (Alt, 2016). All facet theory research, and its explorations of research domains, has at its centre the structured categorial ontology/mereology known as the mapping sentence, which is the major methodological component of the research approach (see Canter, 1985b and Hackett, 2014 for details). The mapping sentence both represents and reflects the philosophical and theoretical underpinnings of facet theory and the facet theory approach to how research is designed and how information is collection and later analysed. The mapping sentence is both the major tool of facet theory and is also a series of structural/spatial hypotheses regarding the structure of the information being analysed. Canter (1985b) defines the sense in which I use the mapping sentence in this paper when he states, “A piece of facet research is a process of refinement, elaboration and validation of a mapping sentence.” (p. 266). The mapping sentence research instrument has shown itself to be an adaptable means through which to conduct and analyse research. Below, I attempt to facilitate an understanding of this approach to research by considering the components of the mapping sentence. I also review how the structure of the mapping sentence can be understood through reference to different academic perspectives, namely, philosophy, linguistics, and psychology. I also note some of the ways that even slight alterations of the mapping

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sentence can influence how information is gathered, the findings that arise and the formulation of theories. A declarative mapping sentence, as with all mapping sentences, is a formal statement of a substantive domain of interest, the people associated with this domain and a range along which the content will be related to subjects. The content is determined by specifying its major constituent components and the sub-elements of these components. Single elements from each subcomponent are combined to comprehensively delimit the domain. Information is then assembled from the specified subjects in terms of the determined response range. Facet theory assumes an implicit philosophical stance regarding its subject matter: human beings (Hackett, 2014). This standpoint conceives of human activities and understandings of these as being comprised of identifiable components and categories. Additionally, it envisages that appreciation of these parts and their interrelationships avails understanding of the broader life areas they constitute: Facet theory as an approach to understanding the world and its mapping sentence form a categorial ontology. In this chapter I consider how facet theory and the mapping sentence have been influenced and shaped by some of these assumptions. When I speak of the mapping sentence I am using the term mapping in a sense that is analogous to how this term is employed in mathematics.5 On this understanding, a mapping is a function that relates the facets6 (a set of inputs) in a mapping sentence, to set of possible outputs (values in the range facet). In this relationship each input (facet element combination) is precisely associated with a single output. This relationship is shown in the symbolic representation of the mapping sentence provided by duToit et al. (1986, p. 152):

X ABC  N ® R (7.1)

Often, the term of map embodies a particular function such as linearity. In category theory (Awodey, 2010) a mapping is a morphism7 rather than a function,8 indicated by an arrow relating objects to each other.9 In a mapping sentence an arrow leads from the categorial structure of the concept domain to the output or range domain. The range facet is analogous to another concept from mathematics, namely the codomain10 and it is into the codomain of range that all of the responses or reactions, that are delimited by the mapping sentence, fall. Mapping sentences are propositional in that they are statements or assertions that require an opinion to be expressed or a judgment to be made about a content area. In terms of formal logic, this expression will reflect the truth or falseness of the proposition. A mapping sentence is a linguistic category set that specifies and delimits the contents of a concept domain. Within each

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of the categories (facets) in the set is a further set of subcategories (elements) that constitute mutually exclusive states that the category may take.11 A mapping sentence is a declarative statement that becomes a propositional sentence with a mapping function when a specific element has been selected from each facet and combined to form a single sentence. Prior to the generation of a specific propositional mapping sentence, the flexible template for research design, analysis, and theory generation, is perhaps better thought of as a declarative statement or as a declarative mapping sentence, where declarative mapping is an ongoing and active process that comprehensively alludes to possibilities. Mapping sentences are both structured ontologies and structured mereologies. The concept of ontology, or the underlying nature of experience, is structured through the mapping sentence. The mapping sentence structured ontology explicates the basic levels of existence of a specified content area within a flexible though determinate structure. A structured mereology is a template-based depiction of the part-to-whole and part-to-part relationships within an area of content. Below, I discuss the meaning of, and the ways in which, these structures can be used to guide scholarship and research. DECLARATIVE MAPPING A declarative mapping12 is a comprehensive philosophical, qualitative, and/ or quantitative, depiction of a content domain. As with all mapping sentences a declarative mapping sentence comprises facets, elements with connective phrases that have been carefully chosen to meaningfully convey the facets’ mereological arrangement: the relationship between the facets and their relationship to the content of the concept domain of interest. In this chapter I employ the term hermeneutical as Heidegger (2008), and Gadamer (2004), used this in relation to a method of interpretation of knowledge and truth. On their definition I propose that facet theory and the mapping sentence constitute a hermeneutically consistent template, structured ontology, and structured mereology. The phrase hermeneutic consistency refers to the ability to achieve a reliable explanation in regard of an informational source. Hermeneutical consistency is achieved through the structural qualities of the mapping sentence ontology and mereology. As I have already alluded to, a declarative mapping sentence may become a full mapping sentence when a set of pertinent facets are selected and specified, an element is selected from each and all of the facets and these elements are brought together in the form of a propositional sentence. A declarative mapping differs from a general mapping sentence as it may or may not have a range facet as one of its components. Additionally, if it does have a range

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facet the elements from this facet may not apply to a specific question or instance but instead may address a broad conceptual area. However, for a declarative mapping to constitute a mapping sentence in the general sense necessitates that the mapping has been operationally defined in terms of a range facet with categorial elements that delimit (categorize) the declarative nature of the mapping. In the section below I provide further details about the components of a mapping sentence. COMPONENTS OF A MAPPING SENTENCE I list the parts of a mapping sentence in Tables 7.1a and 7.1b under the headings of: (a) sentence components (these are the actual parts of the sentence, Table 7.1a Components of a Mapping Sentence Sentence Component

Details

Concept or content domain

The overall area that a mapping sentence addresses. The area to which information that arises from the use of the mapping sentence refers. The person or group of persons who are the subject of the mapping sentence. The person or group of persons to whom investigations undertaken using a mapping sentence framework pertain. The categories within the concepts, variables, objects of interest, and so on that are addressed by a mapping sentence. The object components of a mapping sentence. The connective words and phrases that join together a mapping sentence’s content words or phrases. A type of functor that specifies the range of responses as being of possibility to necessity.

Subject (category of participation)

Content words or phrases (category of content)

Functor (category of linguistic links) Modal and/or auxillary verb (linguistic category of the possibility of truthfulness) Assessment criterion (linguistic category of elements that causes the content to address the range) Range of response (category of responses to the content)

A word or phrase that specifies the criterion of the evaluation that is present in a mapping sentence (not to be confused with the range of responses, see below). A specification of the range of observations or responses that will be gathered in order to interrogate the content of the mapping sentence in reference to its subject(s). The legitimate values that will be employed to assess the veracity of the sentence for the subject(s).

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Table 7.1b Characteristics of a Mapping Sentence Implicit Structural Processes

Details

Ontology

The content words and phrases in a mapping sentence as these constitute the most fundamental aspects of the research addressed by the mapping sentence. The above definition of ontology applied to an ontology that is about or of ontology. The interrelationships between the components of a mapping sentence. An understanding of the effects and products of these interrelationships. The above definition of mereology applied to a mereology that is about or of mereology.

Meta-Ontology Mereology Meta-Mereology

the choices made regarding the selection of words, phrases, and concepts to fill these components determines the questions being asked in a mapping sentence and the type and breadth of answers produced); (b) implicit structural processes (these are attributes of the mapping sentence that arise from the structure of the sentence and the interrelationships between the components of the sentence). CONNECTIVE ONTOLOGY An often neglected part of the mapping sentence are the connective words and phrases that are used to logically or rhetorically join the elemental content of the facets to each other, to subjects and to a range of responses. These words perform a similar role to that of the mathematical functor. Rudolf Carnap (1937) originated the term functor in a linguistic context (see, Mac Lane, 1971).13 In this situation, factors embody a mapping or structure between object components of a sentence. Within a mapping sentence, the difference between the words used to specify the content of a concept domain, (the facets and their elements), and the functional words and phrases that also provide the sentence’s meaning (the functors) are important.14 Functors cement the sentence together and structure the relationships between content words (facets and elements). Functors are words that often possess ambiguous meaning, or even have little meaning, when considered in isolation or out of the context of the sentence within which they are contained. In a mapping sentence without functors, the content words (facets and elements) would have either little meaning or volatile meaning. A functor assists in facilitating the grammatical and semantic connections between the content words. Functors in mapping sentences are also able to convey subtleties in experience. Functors usually take the form of conjunctions, pronouns, prepositions, particles, interjections, auxiliary verbs, or grammatical articles (for an

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exposition on function words, see, Corver and Riemsdijk (2013) and Klammar et al. (2012) for a general commentary on English grammar).15 THE MODALITY OF A MAPPING The mapping of a domain of content words and functors to an end product, outcome, consequence, result, and so on may involve auxiliary verbs that often take the form of modal verbs, which expresses the necessity to possibility of the declarative sentence’s enactment. For example, in a mapping sentence for research into a person’s performance upon a test of cognition, the verb that is being tested within the mapping sentence may be that of, for example, performance upon the test. Here, performance will be modified by the modal verb of may, must, can, could, and so on perform the test tasks. Thus, we may consider the following example of a mapping sentence: Person (x) can perform the numerical task that is assessed through a written output within a limited timeframe, to a specified level of correctness. Within this mapping sentence the criterion that is being assessed is of performance (given in small capitals) and this verb is modified by the modal quality of can (emboldened). The facet elements are in italics while the facets are underlined (the facet elements may be selected from a plurality of facet elements for each facet). The range over which the assessment is made (small caps italics) and is of correctness. Modal logic is an extension of classical forms of logic through the inclusion of a qualifier. Instead of using the modal verb in this mapping sentence of “can” I could have chosen this to be “usually,” and so on. From this example it is apparent that a modal within a mapping sentence’s functors can have a very significant effect upon the sentence’s efficacy and veracity, especially when the modality is one of truth (truth modalities are known as alethic modalities). Epistemic modalities qualify a mapping sentence’s statement through the inclusion of words such as “knows.” Temporal modalities are also of extreme importance to consider when designing a mapping sentence. These modalities include qualifiers such as: “it was,” “it has always” or “it will be.” Deontic modalities convey an obligation and include words such as permissible and obligatory. Finally, a mapping sentence may be modified through a doxastic modality, which would necessitate the incorporation of words that indicate a belief. USING THE TWO FORMS OF MAPPING SENTENCE Up until this stage of this chapter I have been concerned with the attributes, the composition and characteristics of mapping sentences. In the following

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section I now consider the similarities and differences in the characteristics of declarative mapping sentence and general mapping sentence (these are listed in Table 7.2). Furthermore, I address differences and similarities in the information that each employs in its analyses and the type of results that each typically generates. The first thing that I must state is that both forms of the mapping sentence are, or at the very least contain, an argument: they are forms of propositional logic (Pospesel, 1974). Both kinds of mapping sentences are related to the notions present in fuzzy logic.16 This is because, as Priest put it in his introductory text, fuzzy logic is “ a kind of logic in which sentences take truth values that may be any number between 0 and 1” (Priest, 2001, p. 112). When addressing the general mapping sentence this statement possesses absolute truth as a numerical value is gathered to test the veracity of the sentence’s structure. In the declarative mapping sentences, the applicability of Priest’s statement is less literal, where extent of truth is lesser to greater rather than numerical determined. However, in both mapping sentence forms, the fuzzy logical dictum that truth comes in degrees rather than being totally present or totally absent, is applicable to the sentence’s range facet. Furthermore, as with the application of the two forms of mapping sentence, in fuzzy logic an assessment of the degree of truth is assigned to each proposed sentence. To this point I have discussed the components of the mapping sentence and have proposed the declarative mapping sentence as a framework. I now turn to the application of the declarative mapping sentence to design and interpret qualitative and philosophical research.

Table 7.2 Comparison of Attributes of the Declarative Mapping Sentence and the ­General Mapping Sentence Declarative Mapping Sentence

General Mapping Sentence

Concerned with variables and concepts from a single content universe. Concerned with all possible variables in a content universe. Guides the categorization of all content and other variables from a multivariate content universe. May address any form of information that possesses a categorical structure. Mainly involves the analysis of qualitative and theoretical data but may involve quantitative data. Facilitates the generation and analysis of primary data and the analysis of secondary data.

Concerned with variables and concepts from a single content universe. Concerned with variables sampled from a content universe. Guides the stratified sampling of content variables from a multivariate content universe. Is concerned with multivariate human experiences responses. Is concerned with the analysis of quantitative data. Concerned mainly with the generation and analysis of primary data.

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Qualitative and Philosophical Facet Theory Over the past few years I have been advancing the conception of a qualitative or philosophical facet theory. This approach, as I have briefly commented upon, stands next to but is differentiated from, quantitative facet theory approaches. To these ends I have been undertaking qualitative analyses of content domains employing the mapping sentence to guide research conception, research design, data analysis, and theory development: all of these activities evaluate the adoption of a facet theory mind-set. In this research I positioned facet theory as a philosophical orientation regarding its subject matter: the behavior of and understanding of human beings (Hackett, 2013, 2014, 2016b). The declarative mapping sentence is an important component of a qualitative or philosophical facetted approach. It is the broad and propositional nature of the declarative mapping sentence that differentiates it from the strictures of empirical veracity that must be present in the traditional, general mapping sentence. Here I should clarify what we mean by the word qualitative. The term “qualitative facets” has already appeared in the facet theory literature, however this has been used to mean a qualitatively arranged facet rather than a linear or quantitatively ordered facet. I do not employ this understanding of qualitative as a form of nonlinear analysis and representation. Rather, in this chapter, and in my ongoing research, I use the term qualitative in the more usual social science sense as meaning rich narrative and observational data. Under this definition, there is an implication for the researcher to gather narratives, observations, visual records, and other forms of nonnumerical data where the subsequent analyses of these data sets takes the form of attempting to establish reliable and valid interpretative hermeneutics. DECLARATIVE MAPPING SENTENCES AS STRUCTURED MEREOLOGIES AND ONTOLOGIES Philosophically, a declarative mapping sentence constitutes a structural ontology when it has been developed to address any substantive area of research and understanding. The term ontology, when used by a variety of disciplines that have incorporated ontology into part of their lexicon and ways of thinking, has been ambiguously defined. In philosophy for instance, ontology is a branch of metaphysics concerned with the nature of being (see, Poli and Seibt, 2014); within logic the term ontology refers to the set of entities that a given theory assumes beforehand; in technology an ontology provides a systematic explanation of existence; within information and computer sciences ontology is the rigorous designation of existent components

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(sorts, characteristics) and their inter-associations. To some extent the above definitions demonstrate that there are common elements in the meaning of ontology. These commonalities imply ontology to refer to being and to the components (often these are basic or fundamental components) of existence, where these components are perhaps instantiated a priori to consideration of a content area. However, the ways in which the term ontology has been defined and used with a variety of meanings requires me to provide a precise definition of how I will use this term. Thus, to eliminate any possible confusion, ontology is defined as: “The study and formal explication of a domain of content in terms of its more rudimentary or basic categorial components as these may be understood at this fundamental level and as their meaning may be further revealed through consideration of more sub-ordinate, particular or evident categorial entities.” A structured ontology brings together the concept of ontology or the underlying nature of experience, with notions of structure. This is of value as a structured ontology explicates understanding of the basic units of experience within a determinate structure within which ontological components may vary. Under the definition of ontology we have provided, a declarative mapping sentence is clearly a form of structured ontology. The term mereology is defined within metaphysics as “any theory of part hood or composition” (Harte, 2002, p. 7). However, as with the term ontology, mereology has slightly different definitions dependent upon the discipline of usage.17 The declarative mapping sentence may also be seen as a device for exploring mereological arrangements within a content area. The declarative mapping sentence is a mereology such that it proposes a compositional identity for a content domain, where composition is the relation between a whole and its specific parts, in which parts form the whole and where the whole is nothing more than its parts: the whole is its parts (see Cotnoir and Baxter, 2014). As with the term ontology, in order to avoid confusion and misinterpretation I provide a definition of mereology as: “The systematic and explicit investigation, analysis and understanding of the relationships within a structured ontology, in terms of the part to part, part to whole, part to context and background and part to observation range, relationships: where and when context and background are essential and inherent components of the existence and realization of the structured ontological system; where changes in the background and context would result in significant differences in the structured ontological system, and where the specification of a different range of observations would significantly alter the content of the structured ontology and/or the nature of knowledge present within the structure.” When facet theory addresses a content domain by either gathering qualitative information or through embodying what may be thought of as a facet

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theoretical philosophy, there are two major implications associated with adopting the above definitions of ontology and mereology: “A declarative mapping sentence constitutes the unification of a specified structured ontology and a mereological account of this structure.” “A declarative mapping sentence provides a hermeneutically consistent account of a specified domain of interest.” “The declarative mapping sentence explicitly develops hermeneutically consistent knowledge through its status as a structural ontology and structured mereology.” My usage of the phrase hermeneutic consistency, hermeneutical refers to a specific interpretive methodology as understood through the writing of Heidegger (2008) and Gadamer (2004). These authors were interested in knowledge and truth and in their work the phrase hermeneutic consistency refers to the ability to achieve a coherent explanation of an informational source. Qualitative facet theory provides an interpretation of a content domain that has the potential to achieve hermeneutic consistency due to its framing explorations and interpretations within the structure of the declarative mapping sentence. In the rest of this chapter I put forward three mapping sentences that illustrate the form and use of the declarative mapping sentence, the first of which is of Aristotle’s Categories. ARISTOTLE’S ONTOLOGY The utility of a nonnumerically based, qualitative facet theory, with the conceptual rigor that the declarative mapping sentence is able to offer, is illustrated in my consideration of Aristotle’s Categories (Aristotle and Ackrill, 1975) and the declarative mapping sentence that I developed to present this category system (Hackett, 2014). In this situation, both Aristotle’s Categories18 and my declarative mapping sentence of the Categories are ontological devices. In Figure 7.1, I offer a declarative mapping sentence for Aristotle’s Categories, which I have adapted from earlier versions of this declarative mapping sentence (Hackett, 2014, 2016b). This declarative mapping sentence provides an account of the Categories that explicitly displays Aristotle’s ontology. Additionally, the sentence uniquely suggests a potential mereological relationship between categories parts-to-parts and parts-to-whole. In this mereology I provide a hypothesis for the structure of Aristotle’s ontology and suggest the mapping sentence as a structure for ongoing debate.

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Figure 7.1  Declarative mapping sentence for Aristotle’s categories (Adapted from Hackett, 2014).

LOWE’S ONTOLOGY An ontology that has a very different composition and structure to that of Aristotle’s is E.J. Lowe’s (2007) four-category ontology. According to Lowe, his ontology grew out of Aristotle’s Categories but is made up of less than

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half the number of ontological components that Aristotle identified. Furthermore, Lowe’s ontological units are completely different and less specific when compared with Aristotle’s. However, as with Aristotle, Lowe commences his ontology with two fundamental differences. First he distinguishes between entities that are substantial and non-substantial, secondly he differentiates between particulars and universals. Lowe arranges these in a twoby-two configuration that results in four fundamental categories: substantial particulars (objects); non-substantial particulars (modes); non-substantial universals (attributes); and substantial universals (kinds). Lowe portrays his four categories (kinds, objects, modes, and attributes) as an ontological square, which, he says, provides, “a uniquely satisfactory metaphysical foundation for the natural sciences.” (Lowe, 2007 p. 16) through representing its metaphysical underpinning. Lowe claims that through the inclusion of four categories this structure has an explanatory prowess that other, more economical ontologies, are unable to achieve. Lowe demonstrates how his categorial system can offer an integrated explanation of many aspects of the human condition including: causal powers, natural laws, dispositions, and so on. In the declarative mapping sentence for Lowe’s ontology (Figure 7.2) I offer a transparent representation of Lowe’s conceptions of basic existence. The mapping sentence demonstrates not only the ontology’s structure but also the mereological interplay of ontological elements.

Figure 7.2  Declarative mapping sentence for Lowe’s four-category ontology.

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Both of the declarative mapping sentences above explicitly acknowledge and incorporate, in their respective subjective background facets, the active role of the person who is reading and attempting to understand either Aristotle’s or Lowe’s ontological structures. Furthermore, in both mapping sentences, the verb that is being tested is that of understanding. In these sentences understanding is qualified using an auxiliary verb in the form of the modal verb of may. The two declarative mappings are similar both in the verb and modal verbs that form the active process in the sentences and they share similar ranges into which I have mapped these processes. The content facets are very different between the two sentences but the similar ranges shows how similar, or at least comparable, knowledge may arise when using mapping sentences with similar ranges over which the sentences are evaluated. The actual content facets and their respective elements are obviously very different between the two sentences and clearly evidence the differences in the thinking of Lowe and Aristotle. Each of the two declarative mapping sentences proposes a possible combination and arrangement for the ontology. Within each mapping I have suggested possible theoretical structural interrelationships that need further research to investigate their respective veracities: The declarative mapping uniquely proposes a hypothetical framework that allows the systematic investigation of interrelations between ontological elements. One aspect of the declarative mapping sentence that I have not included in the present introductory examples, but which I could have readily incorporated, are background facets. Background facets may take a variety of different formats but all allow for the inclusion of pertinent influences of external factors upon the content domain of interest while not having to alter the content of the domain itself. For instance, in investigating Lowe’s ontology and we may believe that a certain characteristic of the individual reading the ontology may have a significant impact upon their understanding of this. An example of this may be whether or not the reader possessed a degree in philosophy. In this instance we may include this characteristic of the individual as a background facet and then evaluate understanding for these two groups of individual. This is a somewhat frivolous example but often the consideration of background facets can have a major impact on the development of knowledge. MAPPING A DECLARATIVE MAPPING SENTENCE As is now apparent, the mapping sentence is at the heart of both traditional quantitative and philosophical considerations and qualitative explorations of facet theory approaches to research and knowledge development. The mapping sentence is the basis for facet theoretical investigations, structural hypothesis

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testing, and theory generation and as a stand-alone approach to investigations. The declarative mapping sentence is able to specify an area of research interest in such a way as to define the important aspects of an area and their interrelationships. To further illustrate the structure and use of the declarative mapping sentence I now propose what may be thought of as a meta-mapping sentence that demonstrates the hermeneutic consistency of the understanding that arises from nonnumerical research that is organized through using a declarative mapping sentence. This is a meta-mapping sentence as it is a mapping sentence about mapping sentences and therefore has two range facets: the range of the declarative mapping sentence and a response range of the meta-mapping sentence. This declarative meta-mapping is shown in Figure 7.3. The response range facet delimits the process incorporated in the mapping sentence as the extent to which a declarative mapping sentence is a structured ontology that is able

Figure 7.3  Declarative mapping sentence for the hermeneutic consistency of a mapping sentence.

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to avail hermeneutically consistent understanding of its content domain. This range is chosen as it is broad while being specific and both of these qualities are valuable for a declarative mapping sentence that is as theoretical as the meta-mapping in present example. The range facet of the declarative mapping sentence itself delimits understanding of the ontology to be more to less when applied in a particular instance. The mapping’s subjective aspect, person (x), is taken to be any person or group of persons reading the mapping sentence. The background facet is stated but no elements are included as these must be determined for a specific enquiry. The combinatorial arrangements of the content ontology facet and connective ontology facet are the determinants of the conditions that will be observed in the range facet. Thus: • The subjective facet specifies who is reading the declarative mapping sentence; • The background facet lists background characteristics of the instantiation of the ontology; • The content ontology and connective ontology facets (through the selection of the subdivisions of facet elements) specify the content of the mapping sentence ontology; • The mereology facet characterizes the nature of the relationships that are extant within the mapping sentence ontology to be—either part-to-part (facet/facet element-to-facet/facet element) or part-to-whole (facet/facet element-to-mapping sentence); • The range facet specifies the epistemological characteristics of the observations that constitute the mapping sentence’s logic. CONCLUSIONS Contained within a declarative mapping sentence are its subjective focus, an explanatory argument put forth in the sentence’s content, and a range of specified observations. A declarative mapping sentence thus assigns a condition from the range, for each combination of the qualitative elements in its explanatory argument to a specified subject (person or persons). The content of qualitative elements contain the substantive meaning embodied in the sentence’s declaration. The content’s facets are both explanatory and indexical; they form a thematic argument that is evidential and discursive. To illustrate this process, let us imagine that Sarah (the focus) is assigned the quality of criticality, as this is determined through some appropriate empirical or theoretical procedure to be her experience of a specified genre of art. Using the declarative mapping sentence allows a network of observations

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to be assembled where the foci (subject) and/or the content (facet and facet elements) may be systematically combined so as to comprehensively address the specified content domain. Altering the subjective focus of the sentence provides a wider understanding of the applicability of findings to other populations. Systematically varying the explanatory argument (content facets) allows for the observation of other attributes associated with the content of the declarative mapping sentence. In this chapter I have provided support for claims regarding the potential of qualitative research that is undertaken within a facet theory rubric. I have also claimed utility for the use of a declarative mapping sentence as a purely philosophical outlook when attempting to understand human experience by offering a declarative mapping sentence as a philosophically coherent approach to understanding metaphysical ontologies. Facet theory and declarative mapping sentences form a precise though flexible framework that can be used to design research and writing within philosophical research and other qualitative endeavors. NOTES 1. I thank Karl Frank for his critical input and thoughtful comments upon the work that went into this chapter. Parts of this chapter appeared Hackett P.M.W. (2016) Facet Theory and the Mapping Sentence as Hermeneutically Consistent Structured Meta-Ontology and Structured Meta-Mereology. Frontiers in Psychology, Section Theoretical and Philosophical Psychology, 7:471. doi: 10.3389/fpsyg.2016.00471 2. Facet theory is an approach to research that has been used to explore many aspects of human behavior and experience using quantitative methods and statistical data analysis (e.g., Shye and Amar, 1985). The facet approach will form the foundation for this chapter. 3. Moreover, the use of verbal labels enables abstraction of concepts to be present along with a greater categorical complexity. Whereas, the categories associated with an animal’s perceptual-motor explorations and understanding of the world appear more rudimentary. 4. Louis Guttman formulated facet theory as a way of conducting and coordinating research systematically and in a way that employs scientific principles. Thus facet theory requires: the formal definition of a research area prior to commencing the research; that this definition takes the form of classifications (facets) for the research area; that hypotheses are stated to associate observations with content (facets). The above requirements are fulfilled by the development of a mapping sentence for an area of research. Furthermore, the employment of the mapping sentence promotes comparable research and the development cumulative knowledge and theory generation.Louis Guttman originated and developed facet theory in as a statistical approach to quantitative data (Guttman, 1968, 1977) and in terms of regularities in human behavior (Guttman, 1980, 1982).

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5. In this context, mapping is frequently shortened to map. 6. In his authoritative text, Canter (1985) states how a facet is constituted as a “labeling of a conceptual categorization underlying a group of observations” (p. 22). 7. Morphism may be defined as an abstraction of a function or a mapping between two events which may preserve the structure of the mapping. 8. A function may be defined as a relation between a set of inputs and allowable outputs. 9. The term mapping was used by facet theory’s originator Louis Guttman to relate the content of a mapping sentence to its range facet, with Guttman employing an arrow to indicate this relationship. 10. A codomain may be defined as a set that possesses all of the values of a function. 11. In this chapter I will consider the mapping sentence, as defined above, as a structured meta-ontology and as a structured meta-mereology (Hackett, 2016). 12. A declarative mapping may also be called a declarative mapping sentence, as a declarative mapping statement, a propositional mapping, as a mapping statement, or as an overall mapping sentence. There are likely to be many other forms of nomenclature that may specify the status of a declarative mapping but in this chapter we will simply call this as a declarative mapping. 13. Of relevance to the chapter, functors have found usage in the area of category theory (Simmons, 2011). 14. This distinction is made in a more general linguistic sense by Fries (1952). 15. Function words may, or may not, be of a type that can be changed in their form to express a specific grammatical function through tense, mood, person, gender, number and so on (e.g., through inflection, conjugation, declension). 16. Fuzzy logic is a form of multiple-valued logic (infinite-valued logic) which grew out of the work of Zadeh (1965), on fuzzy sets. For more details see Bergmann (2008). 17. For example: in philosophy (Henry, 1991); in science (Calosi and Graziani, 2014); in logic and mathematics (Urbanaik, 2013); in semantics (Moltmann, 2003). 18. Aristotle’s ten Categories are: (1) Substance (οὐσία); (2) Quantity (ποσόν); (3) Quality (ποιόν); (4) Relation (πρός); (5) Place (ποῦ); (6) Time (πότε); (7) Being-in-aposition (κεῖσθαι); (8) Having (ἔχειν); (9) Action (ποιεῖν); (10) Affection (πάσχειν).

REFERENCES Alt, D. (2016) “Students’ Perceived Constructivist Learning Environment: Empirical Examples of the Comparison between Facet Theory with Smallest Space Analysis and Confirmatory Factor Analysis.” European Journal of Psychological Assessment, July 10, 2016, 1–12. doi: http://dx.doi.org/10.1027/1015–5759/a000358 Aristotle, & Ackrill, J.L. (1975) Aristotle’s Categories and de Interpretatione, Oxford: Oxford University Press. Awodey, S. (2010) Category Theory, Oxford Logic Guides, 49, Oxford: Oxford University Press.

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Barsalou, L.W. (1999) “Perceptual Symbol Systems.” Behavioral and Brain Sciences, 22, 577–660. Beauducel, A., Brocke, B., & Liepmann, D. (2001) “Perspectives on Fluid and Crystallized Intelligence: Facets for Verbal, Numerical, and Figural Intelligence.” Personality and Individual Differences, 30(6), 977–94. Beghtol, C. (1995) “Mapping Sentences and Classification Schedules As Methods of Displaying Facets.” In Schwartz, R.P., Beghtol, C., Jacob, E.K., Kwasnik, B.H., & Smith, P.J. (eds.) Proceedings of the 6th ASIS SIGICR Classification Research Workshop, October 8, 1995, Chicago, IL: ASIS SIGICR. Bergmann, S. (2008) An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems, Cambridge: Cambridge University Press. Bonner, J.T. (2009) The Social Amoebae: The Biology of Cellular Slime Molds, Princeton, NJ: Princeton University Press. Borg, I., & Shye, S. (1995) Facet Theory: Form and Content (Advanced Quantitative Techniques in the Social Sciences), Thousand Oaks, CA: Sage Publications, Inc. Calosi, C., & Graziani, P. (eds.) (2014) Mereology and the Sciences: Parts and Wholes in the Contemporary Scientific Context, New York: Springer. Canter, D. (ed.) (1985a) Facet Theory: Approaches to Social Research, New York: Springer Verlag. Canter, D. (1985b) “How to Be a Facet Researcher.” In Canter, D. (ed.) Facet Theory: Approaches to Social Research, 265–76, New York: Springer Verlag. Chisholm, R.M. (1996) A Realistic Theory of Categories: An Essay on Ontology, Cambridge: Cambridge University Press. Corver, N., & Riemsdijk, H. (2001) “Semi-Lexical Categories.” In Riemsdijk, H., van der Hulst, H., & Koster, J. (eds.) Semi-Lexical Categories: the Function of Content Words and the Content of Function Words, 1–20, New York and Berlin: Mouton de Gruyer. Cotnoir, A.J., & Baxter, D.L.M. (eds.) (2014) Composition as Identity, Oxford: Oxford University Press. duToit, S.H.C., Steyn, A.G.W., & Stumpf, R.H. (1986) Graphical Exploratory Data Analysis. New York: Springer Verlag. Fisher, Yael. (2013) “Exploration of Values: Israeli Teachers’ Professional Ethics.” Social Psychology of Education: An International Journal, 16(2), 297–315. Fries, C.C. (1952) The Structure of English, New York: Harcourt Brace. Gadamer, H.G. (2004) Truth and Method (Wahrheit und Methode), New York: Crossroad. Gainotti, G. (2012) “The Format of Conceptual Representations Disrupted in Semantic Dementia: A Position Paper.” Cortex, 48, 521–9. Guttman, L. (1947) “Scale and Intensity Analysis for Attitude, Opinion and Achievement.” In Kelly, G.A. (ed.) New Methods in Applied Psychology: Proceedings of the Maryland Conference on Military Contributions to Methodology in Applied Psychology held at the University of Maryland, November 27–8, 1945, under the auspices of the Military Division of the American Psychological Association. College Park, MD: University of Maryland. ———. (1968) “A General Non-metric Technique for Finding the Smallest Coordinate Space for a Configuration of Points.” Psychometrica, 33, 469–506.

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———. (1977) “What Id Not What in Statistics.” The Statistician, 26, 81–107. ———. (1980) “Recent Structural Laws of Human Behavior.” The Bulletin of the Institute of Communications Research (Keio University), 114, 1–12. ———. (1982) “What Is Not What in Theory Construction.” In Hanser, R.M., Mechanic, D., & Hauer A. (eds.) Social Structure and Behavior, 331–48, New York: Academic Press. Hackett, P.M.W. (1995) Conservation and the Consumer: Understanding Environmental Concern, London: Routledge. ———. (2013) Fine Art and Perceptual Neuroscience: Field of Vision and the Painted Grid, New York: Psychology Press. ———. (2014) Facet Theory and the Mapping Sentence: Evolving Philosophy, Use and Application, Basingstoke: Palgrave Macmillan Publishers. ———. (2016a) Psychology and Philosophy of Abstract Art: Neuro-aesthetics, Perception and Comprehension, Basingstoke: Palgrave McMillan Publishers. ———. (2016b) “Facet Theory and the Mapping Sentence as Hermeneutically Consistent Structured Meta-Ontology and Structured Meta-Mereology.” Frontiers in Psychology, Section Theoretical and Philosophical Psychology, 7. doi: 10.3389/ fpsyg.2016.00471. ———. (2017) The Perceptual Structure of Three-Dimensional Art, Springer Briefs in Philosophy, New York: Springer. Harte, V. (2002) Plato on Parts and Wholes: The Metaphysics of Structure, Oxford: Oxford University Press. Heidegger, M. (2008) Being and Time, New York: Harper Perennial Modern Classics. Henry, D.P. (1991) Medieval Mereology, Amsterdam: B.R. Grüner Publishing Company. Hestroni, A. (2000) “The Relationships between Values and Appeals in Israeli Advertising: A Smallest Space Analysis.” Journal of Advertising, 29(3), 55–69. Kelly, G.A. (2013) A Theory of Personality: The Psychology of Personal Constructs, New York: W. W. Norton & Company. Klammar, T.P., Schulz, M.R., & Volpe, A.D. (2012) Analyzing English Grammar (7th Edition), London: Pearson. Koval, E., & Hackett, P.M.W (2015) “Hermeneutic Consistency, Structured Ontology and Mereology as embodied in Facet Theory and the Mapping Sentence.” Paper Presented at the Fourteenth International Facet Theory Conference, Fordham University, New York City, USA, August 16th–19th, 2015. Lambon, R.M.A., & Patterson, K. (2008) Generalization and differentiation in semantic memory insights from semantic dementia. Annals of the New York Academy of Sciences, 1124, 61–76. Levy, S. (ed.) (1994) Louis Guttman on Theory and Methodology: Selected Writings, Dartmouth Benchmark Series, Aldershot: Dartmouth. Lowe, E.J. (2007) The Four-Category Ontology: A Metaphysical Foundation for Natural Science, Oxford: Oxford University Press. Machery, E. (2009) Doing Without Concepts, Oxford University Press. ———. (2010) “Précis of Doing without Concepts.” Behavioral and Brain Sciences, 33, 195–244, doi:10.1017/S0140525X09991531

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Mac Lane, S. (1971) Categories for the Working Mathematician, New York: Springer Verlag. Moltmann, F. (2003) Parts and Wholes in Semantics, Oxford: Oxford University Press. Murphy, G.L. (2002) The Big Book of Concepts, Cambridge, MA: The MIT Press. Patterson, K., Nestor, P.J., & Rogers T.T. (2007) “Where Do You Know What You Know? the Representation of Semantic Knowledge in the Human Brain.” Nature Reviews Neuroscience, 8(12), 976–87. Piaget, J., & Inhedler, B. (1969) The Psychology of the Child, New York: Basic Books. Poli, R., & Seibt, J. (2014) Theory and Applications of Ontology: Philosophical Perspectives, New York: Springer. Pospesel, H. (1974) Propositional Logic: Introduction to Logic (volume 1), Upper Saddle River, NJ: Prentice Hall. Priest, G. (2001) Logic: A Very Sort Introduction, Oxford: Oxford University Press. Ranganathan, S.R. (1933) Colon Classification, Madras: Madras Library Association. Shye, S. (1978) Theory Construction and Data Analysis in the Behavioral Sciences, San Francisco: Jossey-Bass. Shye, S., & Amar, R. (1985) “Partial-Order Scalogram Analysis by Base Coordinates and Lattice Mapping of the Items by their Scalogram Roles.” In Canter, D. (ed.) Facet Theory: Approaches to Social Research, 277–98, New York: Springer Verlag. Shye, S., Elizur, D., & Hoffman, M. (eds.) (1994) Introduction to Facet Theory: Content Design and Intrinsic Data Analysis in Behavioral Research (Applied Social Research Methods), Thousand Oaks, CA: Sage Publications, Inc. doi: http:// dx.doi.org/10.4135/9781412984645.n6 Simmons, H. (2011) An Introduction to Category Theory, Cambridge: Cambridge University Press. Soto, F.A., & Wasserman, E.A. (2012) “Visual Object Categorization in Birds and Primates: Integrating Behavioral, Neurobiological, and Computational Evidence within a ‘General Process’ Framework.” Cognition, Affective and Behavioral Neuroscience, 12, 220–40. doi:10.3758/s13415–011–0070-x Urbanaik, R. (2013) Leśniewski’s Systems of Logic and Foundations of Mathematics, New York: Springer. Vélez Latorre, L. (2013). “La Educación Inclusiva en Docentes en Formación: Su Evaluación a Partir De La Teoría De Facetas.” Folios: Revista De La Facultad De Humanidades, 37, 95–113. Wo, L., Kim, A., & Koo, J. (2015) “Co-design Visual Merchandising in 3D Virtual Stores: A Facet Theory Approach.” International Journal of Retail and Distribution Management. Volume, 43(6), 538–60. Zadeh, L.A., (1965) “Fuzzy Sets.” Information and Control, 8(3), 338–53. doi:10.1016/ S0019–9958(65)90241-X

Chapter 8

Facet Methodology and Analysis Mining the Unconquered Lands of Behavioral Sciences Research Aharon Tziner

Any meaningful investigation in the behavioral sciences necessitates, a priori, an exhaustive delineation of the domain of study; otherwise, at best, the conclusions we infer about relationships among the variables we uncover may be fallacious and erratic. Because of poor conceptual definitions of content domains, it is not uncommon that findings of studies in behavioral sciences are barely replicable, thereby hampering accumulation of knowledge. To circumvent this obstacle in behavioral research, the late Louis Guttman (1954; 1957; 1959) conceived of the facet methodological approach and a set of mathematically based procedures that achieved two major goals. These were (a) data analysis and (b) the provision of a research strategy for conceptualizing the domain of investigation, tools that, respectively, facilitated choice of variables consistent with the objectives of the investigation and the formulation of hypotheses. The key instrument in this approach is the mapping sentence. In a mapping sentence, multiple, mutually exclusive categories (named “facets”) define the content universe of scrutiny. The mapping sentence connects these independent elements of the facet to form a statement that reads as an ordinary sentence. If the mapping sentence withstands empirical examination, it becomes a valid representation of the content domain, thereby leading to the generation of a theory (Canter, 1985; Shye, Elizur & Hoffman, 1994). A further notion inherent to the facet methodological approach is the observational system comprised of observational questions, each operationalizing a permutation of the facet’s elements. An observational question, along with a range of possible responses, constitutes a variable. The observed variables are just samples from the content universe, and they can be represented as points in the 161

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geometric space. Respondents’ replies to these observational questions or items are analyzed with appropriate data—analytic procedures devised especially in the context of this approach—and the results are correspondingly plotted in the geometric space. We can then infer the structure of the entire concept from these points. Essentially, the facet approach provides a way (a) to define conceptually a content domain as a universe of observations, (b) to depict the relationships embedded in the domain, and (c) to assess the replicability of the hypotheses. Facet methodology derives its roots from mathematics. Thus, we shall first review some pertinent terms. MATHEMATICAL TERMINOLOGY Sets The word “set” means a collection of items or objects. Within a set, objects are called elements. Usually, sets are denoted by capital Latin letters, printed in boldface type. For instance, B, G, T; whereas the set of positive integers 1, 2, 3, 4 . . . is designated by N. Formally, such a set is depicted as follows in equation 8.1:

N = [1, 2, 3, 4, ...] (8.1)



Small Latin letters such as s, t, and u usually denote the elements of a set. By s ∈ S we mean that “s is an element of S” or “The element s belongs to the set S.” A useful shorthand notation of a set is: S = [ x / x has the property of P ] (8.2)



where, “S is the set of all elements x, each of which has a property P.” For instance, suppose that the property one wishes to express is “even number” or “possessing a car”; then: S = [ x / x is any even number ] (8.3.1)

or

S* = [ x / x is any person who possesses a car ] (8.3.2)

If, in addition, a and b are two elements of a set, the notation (a, b) is termed an ordered pair consisting of a and b. This notion enables us to define the Euclidean plane as

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éë p / p = ( x, y ) where x, y R ùû (8.4)

which means, “All ordered pairs p = (x, y) comprising two elements x and y, each encompassed by set of real numbers, R.” Furthermore, the distance between any two pairs (x1, y1), (x2, y2) in this plane is defined as:

2

2

d = ( x1 − x 2 ) + ( y1 − y 2 ) (8.5)

CARTESIAN PRODUCTS Let S be a set so that S = [s /s ∈ S] and let T be another set defined as:

T = [ t / t Î T] (8.6)

The product term S×T will thus contain all ordered pairs of elements (s, t) of which the first element always belongs to S and the second element always pertains to T. The formal notation for this is:

S ´ T = [p / p = ( s, t ) so that s Î S, t Î T] (8.7)

which constitutes a Cartesian product of the set S by the set T. We may also extend the product to more than two terms. Assuming that S1, S2, ….…. Sn (n c2, this formulation led to the hypothesis that the region including the variable of which c1 was an element would be generally closer to the region of variables of which c2 was an element, in contrast to the region of variables of which c3 was an element. This sort of hypothesis about the existence of order among contiguity regions is termed second-order hypothesis (Shye, 1978). Facet of Axial Role When a facet has the role of generating contiguity regions arranged in a certain order, it is called an axial facet. The hypothesis would thus state that the geometric representation would be portioned into a sequence of nonintersecting regions produced by some ordering principle. Each region contains variables of one struct (facet element), while the whole set of regions falls along an axis in the geometrical space (see Figure 8.2). Hackett (2014) stated that the elements of an axial facet form an approximation of linearity derived from the rankings of correlations between pairs of question items, which represent the various structuples. Question items that are closer to each other linearly would be perceived more similar than those further apart. Such a type of facet is illustrated in Levy’s (1979) study of political involvement. Levy noted the axial role of her facet, which she termed modality of political involvement. The two elements of the facet were the instrumental element (attend home circle, discuss political issues) and the cognitive element (express interest in political issues). Levy’s empirical evidence showed that an upper stratum had formed of instrumental involvement variables; while the lower stratum along the axis was generated by cognitive involvement variables (see Figure 8.3). This vertical order corresponds to a hierarchy from the more instrumental or active involvement to the purely

Figure 8.2  Geometric portrayal of a facet playing an axial role.

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Figure 8.3  Geometric portrayal of the facet “Modality of Political Involvement.” Copyright © 1979 by D. Reidel Publishing, Dordrecht, Holland.

cognitive. Stated non-mathematically, taking active steps shows more of a political involvement than merely expressing interest in political affairs. Facet of Polarizing Role A content facet may be specified to be circularly ordered. This specification leads to the hypothesis that the facet plays a polarizing role, namely each struct or element of the facet corresponds to a different direction in the geometric space. A facet is designated polar when three or more lines originating at the same pole (namely, the center) separate the space by moving in different directions, whereby each slice of the pie corresponds to one of the facet’s structs. Stated succinctly, in a polar facet, the structs (elements) are arranged geometrically as wedge-shaped sections with a common origin (Hackett, 2014). An example of a polar facet was depicted in Levy and Guttman’s (1978) exploration of adjustive behavior. One of their facets comprised “areas of life” such as social, leisure, health, and economic. Since the researchers could not point to any order of priority among this facet’s elements, each area of life was expected to correspond to a different direction emanating from a common origin. The hypothesis was that a geometric portrayal of these areas of life would reveal wedge-like regions and, indeed, the hypothesis proved tenable in light of the empirical evidence (see Figure 8.4). Hence, when no order exists between the regions corresponding to the study of a facet—that is, when no one facet element necessarily exerts a higher primacy than any other element—such a facet could be hypothesized to play a polar (or polarizing) role. Facet of Modulating Role When an order does exist, however, between the elements of the facet, in the sense that some elements are placed centrally while others are located

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Figure 8.4  Example of a polarizing facet: “Areas of Life” Facet in Levy & Guttman (1978).

progressively more at the periphery, the facet plays a modulating role. The corresponding partition of the geometric space appears in the form of circular bands around a common origin, so that the variables (i.e., question items) most highly intercorrelated fall toward the center, while the progressively less intercorrelated are positioned further away toward the edge (see Figure 8.5). Levy (1981) has argued that when the order of one facet holds also for a second facet, but without possessing the same substantive meaning or direction, the former facet is expected to play a modulating role. In such a case,

Figure 8.5  Geometric portrayal of a facet playing a modulating role.

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two points that lie at an equal distance from the center will be closer to each other, because the regions are closer together in a circular order. An example of modulating facets appears in Levy and Guttman’s (1980) work on medical treatment media. Respondents were asked to express attitudes for or against private medical practice in hospitals. One of the authors’ facets was modality of behavior, containing three structs: affective, cognitive, and instrumental. As hypothesized and depicted geometrically, the instrumental modality variables appeared in the outer band; the affective modality variable surrounded the origin, and the cognitive modality variable was located in the intermediate band. Tziner and Elizur (1985) employed the same facet, modality of behavior, and identical structs (affective, cognitive, and instrumental), in a questionnaire study designed to ascertain the structure of the achievement motive. The facet also played a modulating role; however, the study produced a different order of regions. Empirically, the variables were depicted geometrically with instrumental variables comprising a band around the center, affective variables encircling the instrumental variables, and cognitive variables comprising the outer band. The reversal in order is difficult to explain. Perhaps, one should bear in mind that the facet modality of behavior plays different roles under different circumstances. For instance, in Levy’s (1979) article on political involvement, the facet performed an axial role, while in Elizur and Guttman’s (1976) paper on attitudes toward work and computers, the facet took a polarizing role. Seemingly, the specific role this facet performs depends on the notions of order played by the other content facets in the design. Moreover, after Levy (1981) we can argue that there are no guidelines to facilitate prediction of the order of cognitive, instrumental, and affective modalities. Once again, it is the researcher’s intuitive insight and the state of the art in the literature that strongly influences what role facets will take. TWO-FACET STRUCTURES Radex One of the best-known two-facet structures is the radex generated by one facet playing a polarizing role, and the other facet performing a modulating role. In Tziner and Rimmer’s (1984) examination of an extension of Guttman’s model of ability tests, the radex structure of the ability tests was yielded by a combination of the polarizing role played by language of presentation (Facet A) and the modulating role played by mental operation (Facet B). The elements of facet A reveal a polar facet because they do not express any

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notion of order among the different types of language presentation: figural, verbal, and numerical, nor are any of these forms of presentation “higher” or “lower,” or “greater” or “less,” than any of the other forms. Therefore, as expected, each of the presentation languages corresponds to a different direction in a geometric portrayal. They emanate from a common origin and partition the space into three wedge-like regions. Similarly, as anticipated, the elements of facet B can be mapped to show a partition of a geometric space. However, the elements (or structs) of facet B do convey an order. In the inner circle around the origin, the variables (ability tests) have in common the struct rule of inference. The variables in the other bands share the structs cognitive rule applying, clerical rule applying, and concrete role applying, respectively. The radex structure is manifested in that the variables (ability tests) requiring rule of inference tend to be more closely located to one another, even though they are presented in different languages. Furthermore, these variables are at a higher proximity to each other than to other variables presented in the same language. For instance, there is a higher degree of closeness between “verbal analogies” test and “Raven’s matrix” test than between “verbal analogies” and “words identification” tests, even though words identification and verbal analogies pertain to the same presentation language (i.e., verbal), whereas Raven’s matrix belongs to the figural language. In a recent investigation of coping mechanisms and stress, Rabenu, Elizur, & Yariv (2015) demonstrated empirically that the total structure of this domain could be represented with a radex. The two facets were: A—modalities of coping (a1 = cognitive; a2 = emotional; a3 = instrumental) playing a modulating role, and B—coping directions (b1 = change the; b2 = accept the; b3 = withdraw from) playing a polarizing role. Notably, Lingoes (1981) contended that the origin or center of the radex could not be determined solely on the basis of the geometry of the configuration or by mathematical considerations. He argues that it is quite possible, for example, to interpret a radex structure from points plotted near the periphery of the configuration (much like the solar system in our galaxy). For Lingoes (1981), the center of a radex is dictated solely by substantive considerations. Duplex If the content domain has two facets, each playing an axial role, the resulting structure is a duplex. For illustration, relating to their study of children’s value structure, Bilsky, Doring and Groenen (2015) posited that two facets were needed to analyze value structure: A—interests (a1 = social; a2 = personal), and B—objectives (b1 = promotion of gain; b2 = prevention of loss).

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They hypothesized that the joint action of these two facets would result in a duplex of Schwartz’s (1992) values. Promotion of Gain Objective

Prevention of Loss Objective

Social interest

• Universalism • Benevolence

Personal interest

• Hedonism • Stimulation • Self-direction

• Security • Conformity • Tradition • Achievement • Power

A further example can be found in Tziner and Elizur’s (1985) investigation of the achievement motive. Reportedly, an empirical double-ordered system—that is a duplex structure—properly spanned the universe of the achievement motive concept. One facet described the type of confrontation, namely, the individual’s readiness to confront a challenge and cope with it. Structs of this facet included coping with difficult tasks, accepting personal versus shared responsibility, and coping with uncertain outcomes. Other structs were readiness to consider different aspects of the situation, and readiness to match answers to challenges, such as calculating risks, solving problems, and fulfilling needs. The second facet classified the various aspects of achievement according to time. Certain aspects are suggested, mainly before the task is performed, such as being uncertain and calculating risks. Other aspects are reflected during task performance, such as coping with difficulty and solving problems. Responsibility and satisfying the need to succeed are achievement aspects, basically related to the after stage. THREE-FACET STRUCTURES Cylindrex A cylindrex is a structure that emerges in one of two cases. One instance is when the content domain has two facets, one playing an axial role and the other a polarizing or modulating role. The other instance is when the domain has three facets, two forming a radex and the third an ordered facet perpendicular to it. In the latter type, the circular arrangement of the items repeats itself at each segment for stratum of the axis. An example of the first instance is provided by Levy (1979). In her study of political involvement, facet A—mode of behavior (a1 = discuss; a2 = interested; a3 = attend political organizations) was hypothesized to play an axial role, while facet B—political issue (b1 = social; b2 = economy;

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b3 = security; b4 = in general) played a modulating role. The empirical data corroborated the existence of a cylindrex of political involvement comprised of these two facets, one involving the mode of involvement, and the other gauging involvement in different areas debated in a political arena (see Tziner, 1987, p. 66). As an example of the second instance, consider if a third axial facet were added to the radex in Tziner and Rimmer (1984) study—namely mode of test administration (consisting of elements c1 = individually, and c2 = in group). In such a case, a cylindrex would emerge (see Tziner, 1987, p. 65). Conex A conex represents a special case of a cylindrex that reflects a particular kind of dependence between the two facets, two parts of which may extend to both sides of the structure without limits. An illustration of a conex appears in Elizur and Guttman’s (1976) exploration of the structure of attitudes toward work and computers (see Tziner, 1987, p. 67). In this study, the ordering facet of referents corresponds to a geometrical ordering of variables along a simple gradient: the computer staff is at one extreme, and the other employees at the opposite extreme. This order reflects the extent to which each of the referent echelons are involved in, and affected by, the introduction of the computer. The computer staffers nearest to the computer appear at the top, while individual employees, whose proximity to the computer is the least, are at the bottom of the conex. In addition, the higher the progress up the axial facet, the closer the structs of the second facet are clustered. Mode of behavior proved to play a polarizing role, as hypothesized. This is manifested in that each stratum corresponding to one of the structs of the axial facet becomes narrower as it moves up to the top of the conex. Porex represents a combination of two modulating facets (Shkoler, Rabenu, Vasiliu, Sharoni, & Tziner, 2017). HYPOTHESIS TESTING: DATA PROCESSING VIA SMALLEST SPACE ANALYSIS Subjection of a hypothesis to empirical scrutiny is as central to facet analysis as it is to any method of scientific research. In facet analysis, however, it is the empirical structure (or at least one aspect of it) that is scrutinized to see if it corresponds to, or confirms, the hypothesis. The facet hypothesis, we recall, predicts how the variables, arranged in a mapping sentence, will appear when depicted geometrically. The empirical aspect explored is known as the “intercorrelation matrix” of the variables.

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Statistical methods designed specifically to analyze empirical structures in facet analysis include Smallest Space Analysis (SSA)—and its variation, Faceted SSA or FSSA (see Shye, 1998)—Multidimensional Scalogram Analysis (MSA), and Partial Order Scalogram Analysis (POSAC). Of the three, SSA is most useful and is discussed at length below. SSA allows researchers to evaluate the extent to which the geometric structures, hypothesized from the mapping sentence, are borne out by the empirical data. Elaboration of MSA and POSAC is available elsewhere (Kedar & Shye, 2015; Shye, 2015; Shye, Elizur & Hoffman, 1994). SSA: AN OVERVIEW SSA (Guttman, 1968; Lingoes, 1973) is a nonmetric, multidimensional scaling procedure that geometrically represents the “correlation matrix”, based on the order of magnitude of the intercorrelations between the variables. Such variables include questionnaire items and cognitive ability tests, among others. SSA portrays the variables as points in a Euclidean space. The intercorrelations of the variables, which serve as the empirical measure of similarity between them, are expressed in that space by distances between pairs of points. Therefore, two points are closer together if the correlation between the corresponding variables is higher. Conversely, when the correlation between the two variables is low, they are farther apart, and the distance between their geometric points should be relatively large. The dimensionality of the space is set so that the rank of the distance between the points representing variables in space has a maximum relationship to the rank of the correlation coefficients. Expressed formally, if rij is the observed correlation between variable i and j, and if dij is the calculated distance between these two variables for the smallest space, then SSA attempts to find the space with the minimal number of dimensions in which the following inequalities are preserved: dij < dk1 whenever rij > dk1 (i, j, k, l = 1, 2,….., n). Order among the correlations is thus preserved in the smallest Euclidean space, and the absolute size of the input correlation coefficients can be reproduced from the scattergram of the rij on the dij (Shepard diagram) printed by the computer. Such a chart indicates how well rij = f(dij), where f is a monotonically decreasing function. The goodness of fit between the smallest possible Euclidean space and the correlation matrix is numerically measured by a coefficient termed coefficient of alienation (conceptually, this parallels Young’s S-STRESS [Young & Lewyckyj, 1979] or Kruskall’s [1964] STRESS coefficients). The coefficient of alienation is defined as (1 – r2)1/2, where r is a rank-order correlation between the intercorrelation of the variables and their

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corresponding geometrical differences: The smaller the coefficient of alienation, the better the fit. Zero represents a perfect fit. In practice, however, a coefficient of alienation smaller than .15 is considered a good fit (Guttman, 1968), while one ranging between .15 and .20 is considered a reasonable fit (cf. Elizur, 1984). SSA ALGORITHM The algorithm underlying SSA consists of the following phases: i. Starting Configuration In the first phase, the algorithm matches points in a Euclidean space to the variables of the study. In this starting configuration, each point is represented by initial coordinate estimates x1i1 and x1j1. Distance estimates are computed from the coordinate estimate as follows:

(

)

1/ 2

2 d1ij = éS x1i1 - x1 j1 ù ëê ûú

(8.13)

In this phase, rank images of the data are also computed. In other nonmetric multidimensional scaling methods, such as that of Young (1979), rank images are referred to as disparities. Rank images pij are values computed nearly as equal as possible to the distance estimate dij, subject to the constraint that they are monotonically related to the original intercorrelations. That is,

rij < rk1 ® pij ³ p k1 for all i, j, k, l. (8.14)

Since pzy (for any z or y) are computed to mirror the rank order of the data points, they are termed rank images. ii. Standardizing Distance and Coordinate Estimate Here the first iteration begins. At the start of this iteration, as well as at the outset of all the following iterations (if there are any), the coordinate estimates and distances from the starting or previous configuration are standardized, so that the sum of the squares of distances equals 1.00 (i.e., Σ d2ij = 1). For the coordinate estimates to be expressed on the same scale as the distances, each coordinate estimate must be multiplied by the same constant.

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iii. Nonmetric Phase In the third stage, the nonmetric stage, the rank images are computed using standardization distances from the previous iteration and the original intercorrelations. A series of passes through the data (described below) constitutes the major portion of the nonmetric phase for a single iteration. Each rank image is set equal (Guttman, 1968) to one of the current distance estimates. Specifically, if the pair of variables (i, j) corresponds to the nth largest correlation pij, then the corresponding rank image pij(m+1) is set equal to the smallest distance estimate (where m denotes iteration order and m = 1 is to where the starting configuration is referred).

(

)

1/ 2

2 d1n ij = éS x1n i1 - x1n j1 ù êë úû

(8.15)

If a variable pair (i, j) corresponds to the second largest correlation pij, then pij(m+1) is set equal to the second smallest distance estimate, and so forth, until the variable pair (i, j), corresponding to the smallest correlation, is reached. The corresponding rank image is set equal to the largest distance. It is important to note that in this phase the estimates of variables coordinates, or estimates of distance, do not change; only the rank image pij changes. When this phase is completed, the rank images will satisfy the weak monotonicity constraint:

rij < rk1 ® pij ³ p k1 for all i, j, k, l. (8.16)

iv. Metric Phase The metric phase follows the nonmetric phase. It uses the rank images computed in the nonmetric phase pij(m+1) plus the estimates of distance from the previous iteration dijm plus the coordinate estimates from the previous iteration Xi1m to obtain new coordinate estimates Xi1m+1. From these new coordinate estimates, new estimates of distance can be obtained. The rank images remain unchanged in this phase. Assuming that the distances are standardized, this phase is first designated to minimize the coefficient of alienation. Then, following Lingoes and Roskam (1973), the new coordinate estimates are computed as follows:

p ( m + 1) d ijm (8.17)

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Figure 8.6  Flowchart of the SSA algorithm.

To avoid division by zero, this ratio is set arbitrarily to 1, if dijm = 0.00. Iteration continues until an improvement in the coefficient of alienation from one iteration to the next falls below some suitable number set by the researcher. The algorithm can be represented in a slightly changed version of the diagram (Davison, 1983), drafted for nonmetric multidimensional scaling procedures (see Figure 8.6). FACET SSA While partition patterns can often be detected or verified by inspection and drawn by hand, an algorithm testing for each of the types of planar facets (e.g., radial, axial) has been created and programmed (Borg & Shye, 1995). Shye (2014) states that, “Given a set of variables, pre-classified by the researcher, and given the 2D SSA of this set of variables, FSSA finds, for each of the planar facet types, the one specific partition of that type that best separates the points in the space obtained, so that points pertaining to a class of variables fall as closely as possible into one region. The goodness of fit of the obtained separation is called the separation index (SI) and is computed by:



SI = 1 - ( loss function ) / ( normalizing function ) , (8.18)

where the loss function is made up of the sums of the distances of each deviant point from its prescribed region, and where a deviant point is one that does not fall in the region assigned to its class. The normalizing function represents the typical loss function for a set of points randomly (uniformly) distributed in the square 100*100. The normalized loss function (i.e., the ratio) falls roughly on a scale between 0 and 1, where 0

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represents a perfect separation, with each class of points falling entirely into its assigned region. Hence, the resulting SI falls between 0 and 1, with 1 indicating a perfect separation by the pre-specified content classification of the variable. (Note that the loss function and the SI are not based on the number of deviations, but on their sizes.) An intuitive interpretation of the value of SI , say SI = 0.95, could be this: The sum total of the deviations is (about) 5% of what they would have been if the points were scattered at random. It is important to realize that with this procedure, FSSA produces two measures of goodness of fit. The one (represented by low values of SI) is one of the loss functions of MDS/SSA, (e.g., stress or coefficient of alienation) that assesses how well the distances in the obtained MDS/SSA space of the given dimensionality reflect the input similarities (e.g., correlations). The other measure (represented by high values of SI) assesses how well the obtained space-partition separates variables according to their input content classification (content facet)” (pp. 2131–32).

HOW TO READ SSA OUTPUT The most compelling evidence of whether the empirical structure of the relationship among the variables conforms to the hypothesized structure appears when the hypothetical topological structure is superimposed onto the SSA depiction. The examination of the SSA output begins with an inspection of the intercorrelations matrix. To the extent that the following conditions are fulfilled by all variables, positive or zero intercorrelations are expected to emerge:1 1. Variables relate to a common object of exploration (i.e., they concern the same observation or content domain); 2. Variables have the same range of responses (e.g., “5” being very high to “1” being very low) and reflect the same direction (with low figures at one extreme of the range to indicate low preference or disagreement with a statement, and with high figures at the other extreme to indicate high preference or agreement with the statement); 3. The population of the respondents was not selected artificially, specific to the domain of inquiry.2 The first principle to be applied is the principle of contiguity (Foa, 1958; Guttman, 1965) which states that the geometric space in the SSA outcome should be partitionable into regions that reflect the facets and their structs. According to this principle, variables that share the same facet structs should be more highly correlated and thus closer together in multidimensional space than variables that do not share the same facet structs. For example, in Tziner

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and Elizur’s (1985) study of the achievement motive, the three variables entitled “preference for tasks involving uncertainty”; “satisfaction with tasks involving uncertainty”; and “undertaking tasks involving uncertainty,” shared the same structuple (b1, c1). Consequently, we would expect them to be closer to each other than to other variables in the space, an expectation that was, in fact, upheld by empirical data. Furthermore, the more similar the variables are to each other in terms of their facet structs, the higher their expected intercorrelations. The consequence of this principle is that an inverse relationship is predicted between (a) similarity of variable structuples and (b) their distance within the special representation of their correlations. Indeed, an inspection of the intercorrelation matrix in Tziner and Elizur’s (1985) article reveals that most of the variables that share two structs have a markedly higher intercorrelation than those sharing only one struct (see Table 8.1). Table 8.1 reveals that most of the encircled correlations, representing variables that share two structs (b1 & c1; b1 & c2; b1 & c3; b2 & c1; b2 & c2; b2 & c3) are of a higher magnitude than the correlations in the triangles, which represent variables that share only one struct (b1 or b2 or c1 or c2). Moreover, an inverse relationship exists between the similarity of the variables and the spatial representation of their correlation, as predicted. Table 8.1. Pearson Product Moment Correlation Matrix for Achievement Motive Variables (Tziner & Elizur, 1985)

Copyright © 1985 by John Wiley & Sons Ltd.

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The division of the structure into regions is accomplished through boundary curves introduced to aggregate the variables according to the structuples of the mapping sentence. However, variables of a region do not always cluster together. In most studies, the variables employed are only a sample of all conceivable items in the domain of observation. Because they comprise points everywhere in a geometric representation, some variables at the edge of one region may correlate less with other variables of the same region than with certain variables at the edge of neighboring regions. An important feature of SSA is its relative insensitivity to variations in variable sampling. Thus, two different selections of items from the same observation domain can be expected to result in their small spaces having identical partition patterns (Shye, 1978). This is true even though the correlation matrices are different. Different correlations lead to considerable variations in variable positioning from one sample to another. Hence, almost identical configurations in the SSA plots can correspond to two considerably different intercorrelation matrices. Comparison of Facet Methodology-Driven Analysis and Alternative Structure Analyses Ultimately, having reviewed facet methodology-driven analysis, one wishes to know how the methodology stands up to a comparison with other methods commonly used to study underlying structures in behavioral sciences, such as factor analysis and cluster analysis. Such a comparison was conducted in the context of an ongoing exploration and survey of work values structure (based on 546 interviewees), under the aegis of the Israel Institute of Applied Social Research.

INSTRUMENT Interviews were conducted with a questionnaire structured to provide ample representation of occupational reinforcers, such as pay, work hours, working condition, advancement, and type of work. The full list of the twenty-one items used is presented in Table 8.2. Subjects were asked to indicate the extent to which each of the reinforcers was important to them regarding satisfaction at work. The responses ranged from six (very important) to one (very unimportant).

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Table 8.2. Twenty-One Occupational Reinforcers Used in the Study 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Responsibility Job security (permanent job) Benefits and social conditions (vacation, sick leave, pension) Recognition for doing good work Esteem (that your valued as a person) Influence in the organization Achievement in work Advancement (chances for promotion) Influence at work Coworkers, fellow workers who are pleasant and agreeable To do complete and meaningful work Supervisor (a fair and considerate boss) Job status Company policy Use of knowledge and ability in your work Job interest (your work is interesting and well-liked by you) Independence in work Pay (the amount of money you receive) Convenient work hours Work conditions (comfort, cleanliness, absence of noise, heat/cold, odors, etc.) Contribution to society

Note: Items were presented in alphabetical order in Hebrew. Copyright © 1984 by the American Psychological Association.

DATA ANALYSIS METHODS Three comparative methods were employed, namely: 1. Young’s Nonmetric Multidimensional Scaling (MDS) Analysis Young’s nonmetric multidimensional scaling (MDS) method (Young & Lewycky, 1979) was developed to study the structure of underlying data. The basic data usually processed are proximity measures denoting similarity and dissimilarity, the basic assumption being that the proximity data is a monotonic function of the distances between pairs of items in Euclidean space. For a given matrix of a proximity measure between items (e.g., correlation coefficients), ALSCAL software maps items into a space of prescribed dimensionality by deriving from the data the corresponding coordinates in space. One of the important features of Young’s ALSCAL—the computer program for his nonmetric MDS algorithm—is the fit measure for assessing the degree to which the item coordinate estimates of the geometric configuration reproduce the rank order of the original proximity data. The goodness of fit measure is termed S-STRESS.

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Since the configuration generated by the computer is often uninterpretable, a rotation of the original coordinates is frequently necessary. Two approaches are possible. One approach is objective, called varimax (Kaiser, 1958) or equimax (Saunders, 1960) rotation. If this approach does not yield an interpretable solution, Davison (1983) strongly recommends using a hand rotation, which is a subjective approach. 2. Hierarchical Cluster Analysis Hierarchical cluster analysis is built on a distance model; like Young’s MDS method, it analyzes proximity data. However, hierarchical cluster analysis differs fundamentally from Young’s MDS and other MDS techniques in that the relationship it derives between the proximity data and the distances often cannot be expressed by a linear or even monotone function. In addition, cluster distances are not spatial distances as in MDS. Hierarchical cluster analysis is based on the assumption that proximity data is monotonically related to distances in the ultrametric space (see Davison, 1983, pp. 208–11, for a detailed explanation.) Lastly, while in MDS the coordinate dimensions of the solutions are continuous, in cluster analysis they are discrete (Aldenderfer & Blashfield, 1984). Cluster solutions are not usually represented in terms of stimulus coordinates, but rather in terms of stimulus groupings such as tree diagrams, named dendograms (Lorr, 1983). 3. Factor Analysis In most cases, this method also processes measures of proximity, and like MDS, it yields the representation of the stimulus structure in terms of spatial coordinates called factor loadings. In factor analysis, the proximity data are presumed to relate to coordinates by a function in the form of Σ [Xik, Xjk], where Xik, Xjk stands for coordinates, whereas in Young’s MDS they relate to coordinates by a monotone and a completely different function in the form of [ Σk | Xik – Xjk | p] 1/p. Since a solution originally generated by factor analysis is rarely interpretable, a rotation to ensure achievement of the simplest factor structure should be used. A factor structure in its simplest form is possible when each variable has nonzero loadings on only one common factor. Of the many types of rotations possible, the two best known are orthogonal rotation and oblique rotation. The former imposes the restriction that the factors must be uncorrelated, while the latter allows correlations among the factors. Although oblique rotation is more general than orthogonal rotation, insofar as it does not arbitrarily

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impose factor independence, it is less often invoked because introduction of independence between factors often makes interpretation more difficult. When orthogonal rotation is engaged, it is customary to use Kaiser’s (1958) varimax solution, which maximizes the variance of the squared loading for each factor. (For further explanation, see Kim & Mueller, 1978). A major deficiency of factor analysis is its factor indeterminacy, which refers to an inherent property of this statistical method to yield many different scores, all of them perfectly satisfying the factor model (Steiger & Schonemann, 1978).3 FINDINGS OF THE FOUR STRUCTURE ANALYSIS APPROACHES 1. Multidimensional Scaling Approach The graphic representation of the ALSCAL output is plotted in Tziner (1987, p. 110). Four clusters are readily discernable, only after having hand-rotated the original configuration by 65°. The upper left quadrant (I) contains reinforcers which might be perceived as having the potential to satisfy esteem and independence needs, invoking Maslow’s (1968, 1970) terminology. The upper right quadrant (II) is comprised of reinforcers pertinent to satisfying existence needs, borrowing Aldenderfer’s (1972) concept. In the lower right quadrant (III) are the reinforcers that may be categorized as relatedness needs fulfillers (also in Aldenderfer’s terminology). The lower left quadrant (IV) spans reinforcers that satisfy selfactualization needs (a notion borrowed from Maslow’s needs hierarchy). The goodness of fit for the configuration shows an S-Stress coefficient of .27, which indicates a moderate degree of fit between the original intercorrelations of the reinforcers and their corresponding geometric representation in the two-dimensional plot. 2. Factor Analysis The factor structure of the occupational reinforcers (i.e., their factor loadings), resulting from the unrotated principal component analysis and the orthogonal rotation varimax criterion solutions (Kaiser, 1958), are depicted in Table 8.3. Upon inspection of the results, it is easy to see that the conclusion reached by Davison (1983) is substantiated in the present case. The unrotated solution yielded a general factor in which all the variables—occupational reinforcers—have high positive loadings; nevertheless, an interpretation is barely

2

.12 −.03 −.24 .39 .53 .25 .07 −.04 .26 −.42 −.16 −.12 .21 .20 .12 .25 .43 .21 .08 −.01 −.15 1.28 .08 .06

−.34 .26 .38 −.09 −.13 −.26 −.25 .10 −.26 .00 −.31 .11 .15 −.12 −.44 −.14 .07 .58 .55 .59 −.29 2.01 .12 .10

.06

.02 −.10 −.16 .06 .11 −.26 .00 −.15 −.25 −.11 .02 −.25 −.39 −.29 .31 .44 .24 .12 .27 .26 .47 1.25 .08 .05

.51 .42 .13 −.02 −.07 .20 .20 .02 −.04 −.17 −.17 −.25 −.20 −.08 −.31 −.28 .01 −.21 −.01 .19 .24 1.02 .06 .79

.86 .75 .90 .79 .82 .72 .73 .74 .73 .81 .79 .77 .87 .66 .86 .83 .80 .91 .70 .75 .76 16.57 1.00

Factor I Factor II Factor III Factor IV Factor V Communalities h

Responsibility .68 Job security .70 Benefits & social conditions .81 Recognition for good work .79 Esteem .71 Influence in the organization .69 Achievement in work .79 Advancement .84 Influence at work .73 Coworkers .77 Meaningful work .80 Supervisor .78 Job status .78 Company policy .72 Use of knowledge and ability .68 Job interest .69 Independence .75 Pay .69 Work hours .56 Work .54 Contribution to society .61 Contribution of factor 11.01 Proportion of common .66 variance Proportion of total variance .52

Reinforcers

Unrotated Factors Loadings

.52

.32 .32 .39 .23 .11 .64 .43 .53 .70 .35 .41 .61 .81 .70 .30 .23 .40 .37 .10 .01 −.09 4.02 .24 .10

.19 .29 .55 .74 .83 .14 .34 .45 .20 .78 .61 .54 .26 .23 .33 .19 .00 .14 .16 .18 .41 3.83 .23 .06

.08 .53 .62 .24 .16 .06 .17 .41 .06 .24 .06 .31 .36 .15 .00 .31 .51 .83 .79 .83 .16 3.65 .22

.06

.21 −.11 −.10 .23 .23 .18 .32 .13 .31 .14 .44 .12 .12 .22 .79 .79 .53 .25 .18 .04 .48 2.58 .16

Factor I Factor II Factor III Factor IV

Rotated Factors Loadings

Table 8.3 Unrotated and Varimax-Rotated Loadings of the Occupational Reinforcers (Tziner & Elizur, 1985)

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possible. Only the rotated solution allows us to make sense of the findings. Drawing on the arbitrary rule of thumb that a component is not assigned to a particular factor unless its factor loading exceeds a .50 lower limit value, we may conceptualize the emergent factors as follows: Factor I encompasses extrinsic reinforcers (“bureaucratic rewards”), provided by management, that promote increased employee status, influence, and involvement in decision-making in the organization. Factor II predominately reflects “psychological growth,” even if in an impure way. Reinforcers such as “benefits” and “supervisor” are allocated to this factor, although they do not fit the core essence determined by the majority of other elements. This illustrates one of the major deficiencies of factor analysis: Even following rotation, factors are not entirely homogenous, a situation that obviously hinders interpretability. Factor III indicates preference of instrumental (material) reinforcers, including pay, work hours, and conditions, thereby resembling an almost identically named component of the SSA facets (see below). Factor IV, which includes “use of ability” reinforcers, reflects the importance of opportunities for self-aggrandizement; it is similar in content to a reinforcer mentioned by Lofquist and Dawis (1978) with the same label. Additionally, it appears that the factors, “safety,” “achievement,” and “autonomy,” previously found by Lofquist and Dawis, merged here to yield one single factor—Factor V—that incorporates reinforcers such as “security,” “achievement,” and “responsibility.” In conclusion, the ambiguity incurred by factor analysis, whereby the same element is assigned to more than one factor, applies not only to Factor II. The other factors share the same notorious problem. For instance, the elements “security,” “benefits,” “influence in the organization,” and “supervisor” each belong concurrently to two different factors. The above five factors, which account for 79 percent of the explained variance, might be deemed work values, following the definition formulated by Lofquist and Dawis (1978). 3. Hierarchical Cluster Analysis Using SSA software (Bar, Goodnight & Sall, 1979), the hierarchical analysis of the twenty-one occupational reinforcers results in the dendogram depicted in Tziner (1987, p. 119). Six major and meaningful clusters appear to span adequately the entire universe of employed reinforcers, accounting for 81 percent of the explained variance. These groupings or clusters may also be deemed to represent work values. From left to right, cluster I—reflects the importance attached to obtain autonomy; cluster II—authority; cluster III—self-aggrandizement; cluster IV—social relations; cluster V—safety, while cluster VI consists of material

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reinforcers. Interestingly, this cluster structure partially resembles the factor structure of work values uncovered by Lofquist and Dawis (1978) in that the two share three out of six work values (autonomy, safety, and self-aggrandizement). We can then also generate a structure where the modalities of one of the SSA facets are replicated. This is done when reinforcers of cluster I through III are merged into a grouping labeled “cognitive,” cluster IV is renamed “affective,” and clusters V and VI are grouped as “instrumental.”4 4. Smallest Space Analysis The map in Figure 8.6, which depicts the structure of occupational reinforcers, reveals that the space is easily partitionable into six regions, which can be perceived as work values based on the Lofquist and Dawis’ (1978) definition (Tziner, 1987, p. 115). The regions are created by the joint action of two facets; one might be termed “modality of occupational reinforcers” and the other, “type of reinforcerperformance relationship.” The former facet groups the reinforcers into three classes: instrumental (extrinsic), which are concrete and practical (e.g., work hours, work conditions, benefits); social or affective, which deal with social relations (e.g., coworkers, supervisor); and cognitive (intrinsic), comprising reinforcers such as interest, achievement, responsibility, and independence. The latter facet classifies reinforcers as either resources or rewards (noncontingent and contingent). Noncontingent rewards, such as benefit plans and free transportation, comprise occupational reinforcers or “system rewards” earned merely through membership in the organization, independent of work performance (Katz & Kahn, 1978). They exist mainly to motivate individuals to join the organization and work there. Contingent rewards are provided in exchange for work performance and are occasionally contingent on advancement, status, or recognition. It is worth noting that the facet “type of reinforcer-performance relationship,” that cuts across the modality facet, orders the conceptual space from the center to the periphery: Reinforcers perceived as more directly linked to performance (rewards) are nearer the center of the map, whereas resources are in the peripheral area of the map. A facet that divides the space from the center outward in two concentric rings is designated, after Guttman, a modulating facet. The modality facet that separates the space by regions along lines emanating from the same pole in different directions is a polarizing facet. The configuration formed by the components of both facets acting together (three of the polarizing facet X 2 of the modulating facet) is a radex structure (Guttman, 1954). The coefficient of alienation 0.26 obtained for the configuration indicates a moderate degree of fit between the original correlations of the occupational reinforcers in Table 8.4 and their corresponding geometric distances in the two-dimensional plot.

Responsibility Job security Benefits and social conditions Recognition for good work Esteem Influence in the organization Achievement in work Advancement Influence at work Coworkers Meaningful work Supervisor Job status Company policy Use of knowledge and ability Job interest Independence Pay Work hours Work Contribution to society

39 53 15 18 32 62

49 51 37 49 44 50 48 57

70

43 62

48

– 55 48

1

44 54 58 34 44 41

63 32 50 44 56 52 46 17

65

41 41

45

– 80

2

41 50 74 48 61 38

75 41 68 57 77 63 51 26

50

57 45

69

–

3

48 50 44 46 30 49

75 49 64 69 49 49 52 49

64

90 51

–

4

45 42 34 31 32 48

61 41 70 63 51 46 32 49

56

– 41

5

Copyright © 1984 by the American Psychological Association.

16 17 18 19 20 21

8 9 10 11 12 13 14 15

7

5 6

4

1 2 3

37 51 33 26 26 39

58 79 44 50 46 53 39 47

58

–

6

63 56 42 32 24 43

71 66 56 67 43 53 50 55

–

7

49 55 69 41 43 37

– 60 62 53 58 68 60 51

8

47 56 32 36 26 39

– 51 67 59 64 56 47

9

44 36 41 36 46 49

– 73 76 59 49 48

10

60 53 29 40 20 61

– 63 54 68 61

11

46 39 58 36 40 38

– 80 55 55

12

37 65 64 47 37 18

– 71 48

13

Table 8.4 Intercorrelations among Twenty-One Occupational Reinforcers (Decimals Omitted)

39 52 42 30 28 39

– 51

14

76 47 43 09 21 67

–

15

– 76 56 36 26 42

16

– 65 50 43 44

17

– 67 64 22

18

– 74 34

19

– 37

20

–

21

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Of interest, the coefficient is almost identical to the one found in the multidimensional scaling analysis. RESULTS AND DISCUSSION Having reviewed the various methods, we note that the work value structure is substantially dependent on the analysis method employed. Notably, some overlap between the outcomes is evident, such as the “safety” value produced by both factor analysis and cluster analysis, or the “instrumental” value yielded by Guttman’s SSA, Young’s MDS (labeled “existence”), and factor analysis. Nonetheless, the discordance between the various structures substantially exceeds their similarity, which explains why previous studies based on different analysis methods reveal conflicting work value structures (see for example Elizur, 1984 vs. England, 1975 vs. Lofquist & Dawis, 1978). With respect to the exploration of the structure of work values, and in terms of parsimony, the underlying question remains as to which of the four analysis methods is most productive. Young’s MDS, for instance, extracted the fewest number of work values (four), whereas Guttman’s SSA and hierarchical cluster analysis revealed six work values. Note that the SSA solution was sharply interpretable without relying on a rotation, as was required by the MDS solution; the latter could not generate a meaningful configuration without the hand rotation of the original (raw) outcome.5 The results of the hierarchical cluster analysis were not surprising considering Davison’s (1983) conclusion that the number of dimensions required to reproduce a set of data is relatively large because hierarchical cluster analysis uses many simple two-valued dimensions to reproduce the structure. MDS, in comparison, uses a few complex multivalued dimensions to accomplish the same goal. In the same vein, factor analysis results appeared poorest in terms of interpretability. Even after rotation, the emergent solution was poor because many of the reinforcers loaded high on more than one factor, thus rendering interpretation difficult. Comparing (a) the various solutions for percentage of variance (applicable to factor and hierarchical cluster analysis) and (b) the goodness of fit of the emergent configuration to the initial similarity data matrix (applicable to SSA and MDS), it is evident that hierarchical cluster analysis has provided a slightly better grouping of reinforcers than factor analysis. Furthermore, SSA generated configurations equally suitable since their goodness of fit coefficients (alienation and S-Stress) are at about the same size. The assumption of linear relationships between variables that holds for factor analysis, and the inherent requirement that variables be measured at least at the interval

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level (Kim & Mueller, 1981), may account for the difficulties associated with interpretability revealed with this method, in contradistinction to SSA and MDS (Schiffman, Reynolds & Young, 1981). There also remains a question concerning the statistical conclusions about work value structure obtained via SSA and MDS. No tests have yet been devised to compute the probability that a number of different samples would essentially exhibit the same structural configuration. Nonetheless, Rabenu, Elizur, and Yariv (2015) assert that when the underlying structure of a conceptual universe or a set of variables turns out fuzzy, only facet methodology and analysis procedures can yield clearly interpretable results. Notably, however, Greenbaum, Bacon-Kaufman, and Alyagon (2015), take a different stance. They studied learning disability, attention deficit, and hyperactivity disorder, and their respective relationships to adjustment of college students, using three different approaches to data, two analytic procedures deriving from facet methodology, namely, FSSA and POSAC, and structural equation modeling (SEM). The findings led the researchers to conclude that the three different approaches to data complement each other. SEM helped elucidate the strength of relationships among variables, while analytic procedures deriving from facet methodology (FSSA and POSAC) shed light on the underlying structure of those variables. Hence, a tenable conclusion may be that none of the competing analysis procedures is superior to the others, but rather that one complements the other. Stated differently, each approach uncovers unique insights, unaccounted for by the other methods. Each adds a unique share to our understanding of a scrutinized conceptual universe. CONCLUDING REMARKS Investigations in the field of social and behavioral sciences are usually conducted in order to shed light on the structure of various aspects of human behavior, such as attitudes, response patterns to mental tests, or affective responses. As indicated, too often, researchers initiate investigations with a collection of casually selected variables or concepts. Neglecting the essential need to approach empirical study by formulating a reliable definitional basis upon which to conduct empirical observations mitigates against meaningful replication of studies and hampers the accumulation of valuable bodies of knowledge. Facet theory approach is a powerful methodology that helps to define systematically the boundaries, structure, and parameters of a conceptual domain. It specifies how this definitional system relates to the empirical structure of observations. In particular, facet methodology addresses the following questions: Which variables embedded in the content domain are most interrelated

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and which are less associated? What is the structure of the entire set of interrelations among variables? What is the rationale for this structure? The foremost advantage of arriving at an initial definition of the whole domain of study is that researchers can then decide to concentrate specifically on a part of the domain, knowing that they still possess a rigorous tool that facilitates the decision as to which variables to exclude. In essence, researchers need to be able to justify focusing on a particular subset of variables. Furthermore, this approach facilitates the estimation of the effects that omission of variables will have on generalization from the empirical findings. The facet theory approach has thus advanced the novel notion of sampling—and defining—the entire domain of relevant study in much the same way as subjects are sampled from a particular population. Facet methodology further enables the generation of hypotheses, as it lends itself to specifying the order of a facet’s elements and the relationship between them, and it delineates the range of possible responses. All these components, linked by verbal connectives, produce the mapping sentence, the framework within which the entire empirical exploration is conducted. It is worth recalling that any facet design and mapping sentence should be regarded as an open system. When an inappropriate or insufficient correspondence exists between the hypothesized and empirical structures, facets or their structs may be omitted or trimmed, and others may be added. SSA, and its variation FSSA, serve as the statistical device for ascertaining the extent to which the whole array of intercorrelations among variables is represented by a spatial pattern of distance, which maps the a priori specified structure of the domain of observation. The more the conceptual and empirical structures correspond, the more effective is the selected facet structure in describing the investigated theme. While variants of SSA—MSA and POSAC—partition or order the space of respondents into contiguous regions according to common traits, SSA (FSSA) similarly partitions or orders the space of variables into such regions. Inasmuch as facet methodology is mainly oriented to systematic definition of the domain of study, and to investigation of the correspondence between its hypothesized and empirical structures, SSA is more useful than MSA and POSAC in reaching this goal. The fruitful partnership of SSA and facet methodology, which has demonstrated the corroboration of many structural hypotheses, explains why among all facet analysis procedures, it is the most commonly invoked. As a last comment, we note that no corroboration is ever absolute proof of a specific facet design’s veracity. Rather, researchers are advised to conduct an indefinite series of empirical replications aimed at accumulating more recurrences of the correspondence between the facet’s definitional system and the empirical observations.

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In sum, facet methodology and analysis provides a powerful means for enhancing the dynamic process of formal theory construction in social and behavioral sciences. AUTHOR NOTE The author acknowledges having reproduced in this article texts (entire paragraphs) from his book: Tziner, A. E. (1987) The facet analytic approach to research and data processing. New York: Peter Lang, with the permission of Peter Lang Publishing. NOTES 1. This requirement was termed First Law by Guttman (1965, 1967). First Law is always concerned with the sign of correlation among variables. Second Law calls for an inspection of the relative sizes of correlations, which warrant regional hypothesis derivation. 2. An example of artificial selection is found in Levy and Guttman’s (1975) exploration of youth values for personal well-being. Two of the values that tapped religiosity turned out negatively related to many other values in the sample of religious school students. These respondents constitute an artificial population deliberately selected with respect to religious items. 3. The analytical methods—nonmetric multidimensional scaling (MDS) analysis, factor analysis, and hierarchical cluster analysis—are not discussed at length. It is assumed that readers already possess a basic knowledge of these procedures. For details, see Aldenderfer & Blashfield (1984); Davison (1983); Kim & Mueller (1978). 4. To establish the psychometric soundness of the instrument employed here, internal consistency coefficients (Cronbach’s α) were computed for the reinforcer groupings obtained via three of the four methods of analysis. (The fourth, SSA, has only partially conduced to this calculation, since two of the six regions revealed did not contain solely one component.) As the results were virtually similar for all three methods, it is worthwhile only to report the reliability of the reinforcer clusters ranging between α=.75 and α=.90. This constitutes a more than satisfactory level of reliability. 5. It is also possible, however, that Young’s MDS did not function optimally with the present data, which was not obtained in a dissimilarity or proximity measure form, as is usually the case in studies employing MDS.

REFERENCES Aldenderfer, C.P. (1972). Existence, Relatedness, and Growth: Human Needs in Organizational Settings. New York: Free Press.

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Aldenderfer, C.P., & Blashfield, R.K. (1984). Cluster Analysis. Beverly Hills and London: Sage. Bar, A.J., Goodnight, J.H., & Sall, J.P. (1979). SAS User’s Guide. Raleigh, NC: SAS Institute. Bilsky, W., Borg, I., Janik, M., & Groenen, A.P. (2015). “Children’s value structure— Imposing theory based regional restrictions into an ordinal MDS solution.” In A. Roazzi, de Souza, & W. Bilsky (Eds.), Facet Theory: Searching for Structure in Complex Social, Cultural, and Psychological Phenomena (pp. 23–37). Recife: Editura, UFPE. Bilsky, W., Doring, A.K., & Groenen, P.J.F. (2015). “Assessing the fit of each item of the ‘Picture—Based Value Survey for Children’ into the theoretical structure of values.” In Borg, I., & Shye, S. (1995). Facet Theory: Format and Content. Thousand Oaks, CA: Sage. Canter, D. (Ed.) (1985). Facet Theory. New York: Springer. Davison, M.L. (1983). Multidimensional Scaling. New York: Wiley. Elizur, D. (1979). “Assessing achievement motive of American and Israeli managers: Design and application of a three-facet measure.” Applied Psychological Measurement 3, 201–12. ———. (1984). “Facets of work values: A structural analysis of work outcomes.” Journal of Applied Psychology 69, 379–89. Elizur, D., & Guttman, L. (1976). “The structure of attitudes toward work and technological change in our organizations.” Administrative Science Quarterly, 21, 611–22. England, G.W. (1975). The Manager and His Values: An International Perspective from the US, Japan, Korea, India, and Australia. Cambridge, MA: Ballinger. Fisher, Y. (2015). “The wave syndrome: A career span of principal’s self-efficacy.” In A. Roazzi, de Souza, B.C., & W. Bilsky (Eds.), Facet Theory: Searching for Structure in Complex Social, Cultural, and Psychological Phenomena (pp. 198–216). Recife: Editura, UFPE. Foa, V.G. (1958). “The contiguity principle in the structure of interpersonal behavior.” Human Relations 11, 229–38. Greenbaum, C.W., Bacon-Kaufman, E., & Alyagon, M. (2015). “A comparison of structural equation modeling (SEM) and Facet Theory (FT) approaches to theory and data analysis: Understanding the adjustment of learning disabled college students in Israel.” In Shye, S., Solomon, E., & Borg (Eds.), The 15th International Facet Theory Conference Proceedings (pp. 75–83). New York: Fordham University Press. Guttman, L. (1954). “A new approach to factor analysis: The radex.” In P. Lazarfeld (Ed.), Mathematical Thinking in the Social Sciences. Glencoe, IL: Free Press. ———. (1957). “Introduction to facet design and analysis.” Proceedings of the Fifteenth Congress of Psychology. Amsterdam: North Holland Publishing. ———. (1958). “What lies ahead for factor analysis?” Educational and Psychological Measurement 18, 497–515. ———. (1959). “A structural theory for intergroup beliefs and action.” American Sociological Review 24, 318–28.

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———. (1965). “The structure of interrelations among intelligence tests.” Proceedings of the 1964 Invitational Conference on Testing Problems (pp. 25–36). Princeton: Educational Testing Services. ———. (1968). “A general nonmetric technique for finding the smallest coordinate space for a configuration of points.” Psychometrika 33, 469–506. Hackett, P.M.W. (2014). Facet Theory and the Mapping Sentence: Evolving Philosophy, Use and Application. Hampshire: Palgrave Macmillan. Kaiser, H.F. (1958). “The varimax criterion for analytic rotation in factor analysis.” Psychometrika 33, 187–200. Katz, D., & Kahn, R.L. (1978). The Social Psychology of Organizations (2nd ed.). New York: Wiley. Kedar, Y., & Shye, S. (2015). “The measurement of distributive justice attitudes: Multiple scaling by POSAC analysis.” In Shye, S., Solomon, E., & Borg (Eds.), The 15th International Facet Theory Conference Proceedings (pp. 96–105). New York: Fordham University Press Kenny, C., & Canter, D. (1981). “A facet structure for success evaluation of ward designs.” Journal of Occupational Psychology 54, 93–108. Kim, J.O., & Mueller, C.W. (1978). Factor Analysis: Statistical Methods and Practical Issues (7th ed.). Beverly Hills, CA: Sage. Kruskall, J.B. (1964). “Multidimensional scaling by optimizing goodness-of-fit to a non-metric hypothesis.” Psychometrika 29 (1–28), 115–29. Levy, S. (1979). “The cylindrical structure of political involvement.” Social Indicators Research 6, 463–73. ———. (1981). Lawful roles of facets in social theories. In I. Borg (Ed.), Multidimensional Data Representations: When and Why? (pp. 65–107). Ann Arbor, MI: Mathesis Press. Levy, S., & Guttman, L. (1975). “On the multivariate structure of wellbeing.” Social Indicators Research 2, 361–88. ———. (1978). “The conical structure of adjustive behavior.” Paper presented at the Ninth International Sociological Congress in Upsala, Sweden. ———. (1980). Attitudes Toward Private and Public Medical Treatment in Hadassah Hospital. Jerusalem: Israel Institute of Applied Social Research (Hebrew). Lingoes, J.C. (1973). The Guttman-Lingoes Nonmetric Program Series. Ann Arbor, MI: Mathesis Press. ———. (1981). “Testing regional hypotheses in multidimensional scaling.” In I.Borg (Ed.), Multidimensional Data Representations: When and Why? (pp. 65–107). Ann Arbor, MI: Mathesis Press. Lingoes, J.C., & Roskam, E. E. (1973). “A mathematical and empirical analysis of two multidimensional scaling algorithms.” Psychometrica 38, (Supplement). Lofquist, J.H., & Dawis, R. (1978). “Values as second-order needs in the theory of work adjustment.” Journal of Vocational Behavior 12, 12–9. Lorr, M. (1983). Cluster Analysis for Social Scientists. San Francisco: Jossey Bass. Maslow, A.H. (1968). Toward a Psychology of Being (2nd ed.). New York: Van Nostrand Reinhold. ———. (1970). Motivation and Personality (2nd ed.). New York: Harper & Row.

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Rabenu, E., Elizur, D., & Yaniv, E. (2015). “The structure of coping with stress: Comparison between SSA and Factor analysis.” In A. Roazzi, de Souza, B.C., & W. Bilsky (Eds.), Facet Theory: Searching for Structure in Complex Social, Cultural, and Psychological Phenomena (pp. 167–82). Recife: Editura, UFPE. Rabenu, E., & Tziner, A. (2016). “Employee resilience: A faceted analytical approach.” Industrial and Organizational Psychology: Perspectives on Science and Practice 9, 480–5. Shkoler, O.,Rabenu, E., Vasiliu, C., Sharoni, G., & Tziner, A. (2017). “Organizing the confusion surrounding workaholism: New structure, measure and validation.” Frontiers in Psychology. Saunders, D.R. (1960). “A computer program to find the best fitting orthogonal factors for a given hypothesis.” Psychometrika 25, 207–10. Schiffman, S.S., Reynolds, M.L., & Young, F.W. (1981). Introduction to Multidimensional Scaling. New York: Academic. Shkoler, O., Rabenu, E., Vasiliu, C., Sharoni, G., & Tziner, A. (2017). “Organizing the confusion surrounding workaholism: New structure, measure and validation.” Frontiers in Psychology 8, 1803. doi: 10.3389/fpsyg.2017.01803 Shye, S. (Ed.) (1978). Theory Construction and Data Analysis. San Francisco: Jossey—Bass. ———. (1991). “Facet theory and its applications.” Jerusalem: Megamot, 33 (3–4). A special issue in memory of Louis Guttman. (Hebrew, with abstracts in English). ———. (1998). “The systemic life quality model: Comparative analysis of concepts and scales.” Megamot (special issue on salutogenesis), 39, 149–69. ———. (2014). “Faceted smallest space analysis (Faceted SSA; FSSA).” In A.C. Michalos (Ed.), Encyclopedia of Quality of Life and Wellbeing Research (pp. 2133–34). Dordrecht, Netherlands: Springer. ———. (2015). “New directions in facet theory.” In Shye, S., Solomon, E., & Borg (Eds.), The 15th International Facet Theory Conference Proceedings (pp. 147–62). New York: Fordham University Press Shye, S., Elizur, D., & Hoffman, M. (1994). “Introduction to facet theory: Content design and intrinsic data analysis in behavioral research.” Applied Social Methods 35, London: Sage. Shye, S., Solomon, E., & Borg (Eds.), The 15th International Facet Theory Conference Proceedings (pp. 23–34). New York: Fordham University Press. Schwartz, S.H. (1992). “Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries.” In M. Zanna (Ed.), Advances in Experimental Social Psychology 25 (pp. 1–65). New York: Academic Press. Tziner, A.E. (1987). The Facet Analytic Approach to Research and Data Processing. New York: Peter Lang. Tziner, A., & Elizur, D. (1985). “Achievement motive: A reconceptualization and new instrument.” Journal of Occupational Behavior 6, 321–9. Tziner, A., & Rimmer, A. (1984). “Examination of an extension of Guttman's model of ability tests.” Applied Psychological Measurement 8, 59–69. Young, F.W., & Lewycky, R. (1979). ALSCAL 4 user’s Guide (2nd ed.). Chapter Hill, NC: Data Analysis and Theory Associates.

Chapter 9

Divine Action, Ontological Dependence, and Truthmaking Walter J. Schultz

I: BACKGROUND This chapter1 presents a divine action account of the ontological dependence of contingently existing things of several types—namely, physical systems, their constituents and structures, and the laws that “govern” their coexistence, internal change, and interaction—together with an account of truthmaking for true propositions about such things.2 (The term “physical system” can be used to refer to tree, a dog, a person, a table, a molecule, a particle, or any more complex portion of the physical universe that includes such things.) Three tasks face the formulation of any such dual account. The first is to specify an ontology. Some ontologies deny that relations are fundamental.3 Therefore, if the ontology permits ontological dependence to be understood as a real, external relation between entities, then the second task is to indicate the nature of the relata in both ontological dependence and truthmaking in terms of the ontology. If the ontology precludes real external relations, then ontological dependence will be explained in non-relational terms, and this will affect its account of the relata in truthmaking. The third task is to state—again, in terms of the ontology—the necessary and jointly sufficient conditions involved in each notion. Section II of this chapter develops generic analyses of ontological dependence and truthmaking in the light of recent literature. Section III provides a divine action ontology and then develops each notion in more detail in terms of the ontology. Such a dual account is metaphysically foundationalist, given that all things are ultimately ontologically dependent on what it assumes the fundamental existent to be. Section IV is a summary of these concepts.

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II: GENERIC NOTIONS OF ONTOLOGICAL DEPENDENCE AND TRUTHMAKING Ontological Dependence Assuming that physical systems, their constituents and structures, and the laws that “govern” their coexistence, internal change, and interaction are ontologically dependent, how might ontological dependence be analyzed? In this section, I gradually develop a generic analysis, which reflects the current salient proposals, their shortcomings, and then the revisions that appear in the literature. “Ontological dependence” is an expression whose conceptual content is narrower than that of “grounding.” Since I am concerned only with what may be classified as physical things, I set aside the considerations that usually arise when the grounding concepts are applied to mental, linguistic, mathematical, and abstract things. Perhaps, the notion of ontological dependence that I intend is closer to what Aizawa and Gillett (2016) call “vertical relations.” To get started let the variable x stand for a token of any of the four types of entities mentioned above. For example, let x be some physical system, such as a molecule of ordinary table salt, sodium chloride (NaCl). Alternatively, let x stand for some scientifically recognized structure of such systems (e.g. the lattice of NaCl molecules forming a grain of salt) or let x represent some regularity of sequences of states of such physical systems. Let the variable y stand for any entity. We may begin by proposing that x ontologically depends on y if (1) x is not identical to y, and (2) x cannot exist, be the thing x is, and be the kind of thing x is unless y exists, is the thing y is, and is the kind of thing y is.4 Condition (2) combines a distinction between a thing’s existence being dependent on something else and its identity (i.e., its unique configuration of properties) being dependent on something else. Existence and identity are given together, because even if they are conceptually separable—as Aquinas argued in chapter 4 of Being and Essence—it remains a matter of significant dispute whether they are metaphysically separable.5 Can a physical thing exist without having the properties it has that together render it the thing it is distinct from every other existing thing? Nevertheless, these two, that is, (2a) existential dependence and (2b) identity dependence, will be addressed separately. Existential Dependence Condition (2a) “x cannot exist unless y exists” expresses the modal–existential element of ontological dependence. The existence of a given molecule of

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water H2O requires the existence of the two atoms of hydrogen (H) and the one atom of oxygen (O). That molecule cannot exist without those atoms. Replace the atoms with others of the same kind and you would have a molecule of water, but it would be a different molecule. Where a given x is dependent on a definite y—as in these cases—ontological dependence is called “rigid existential dependence” (RXD).6 What follows is usually given as a definition, represented formally as a biconditional. Nevertheless, I state it as a conditional proposition. I then attempt to identify other necessary conditions. Only after having identified a set of necessary conditions that are generally thought to be jointly sufficient, will it be expressed as a biconditional.7 (RXD) If x’s existence depends on y’s existence, then x cannot exist unless y exists. Since ontological dependence involves some sort of metaphysical necessity, RXD is often formalized as follows:



∀x∀y ( x / y →( Ex → Ey ) ) or ∀x∀y ( x / y → ( Ex ⇒ Ey ) ) (9.1) Read: “For any entities x and y, if x’s existence depends on y’s existence, then necessarily, if x exists, then y exists.”

However, the formalization expresses logical necessitation, which is a relation between propositions about the entities in question. In other words, the formalization of RXD says that “If x ontologically depends on y, then the proposition entails the proposition .” However, as such, it only reflects the metaphysical necessity in ontological dependence, which is a relation between the entities themselves. It does not explain anything. Therefore, the question remains: Why cannot x exist if y does not? If x exists, then why must it be that y exists? What is desired is an explanation of how x is related to y in a way that accounts for the apparent necessity in ontological dependence. An answer based on some version of possible worlds semantics of this formalization or given in terms of a supervenience relation is inadequate, because, at best, it would simply report a correlation or covariance, for example, “Every world in which x exists, y exists.” RXD fails to explain the modal-existential element in the concept of ontological dependence. In other words, while the proposition logically necessitates the proposition , the kind of necessity in ontological dependence “runs the opposite direction” (so to speak) from y to x. A better explanation than those given in modal logical or supervenience terms—and one which applies to our example—is that the dependence in

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question is a matter of the axioms of mereology. A whole ontologically depends on it parts. However, Anna Marmodoro observes that, in physical cases like those being considered in this chapter, “[although] there is ontological dependence between subjects (where the subjects can be properties, or substances, or parts) . . . ontological dependence is not a relation,” adding that “Aristotle explains [this type of] ontological dependence with the notion of [what she calls] ontological containment.”8 In other words, a given molecule of water H2O depends on the existence of the two atoms of hydrogen (H) and the one atom of oxygen (O) that constitute it; it “contains” them in the sense of its being a composite and they are its parts. It “contains” them mereologically.9 In both cases, the composite depends on its constituents. Kathrin Koslicki calls this “constitutive essential dependence.”10 This second answer accounts to some extent for the metaphysical necessity involved in ontological dependence, but not sufficiently. Where x is a composite physical system of some sort, a more satisfying explanation should account for the apparent relations between x’s constituents that give x the structure it exhibits as a composite. For example, while the existence of a molecule of water H2O requires the existence of the two atoms of hydrogen and the one atom of oxygen that constitute it, nevertheless—in addition to its constituents—it has structure and its existence requires that structure. If it did not have that structure—that pattern of combination of constituents—it would not exist as the kind of thing it is. As Koslicki writes, Specimens of the kind H2O molecule come into existence when two hydrogen atoms and one oxygen atom enter into a particular configuration . . . mereologically complex objects, in order to be specimens of a particular kind, must satisfy certain structural requirements . . . .11

But then, one might ask, “On what does that structure depend?” On what, for example, does the lattice structure of the NaCl molecules in a grain of salt ontologically depend? This question assumes that, not only are physical systems themselves—and their constituents—ontologically dependent on something, but also that the existence of scientifically recognized structures of such systems also depend on something. Thus, an adequate answer to the earlier question “Why cannot x exist if y does not?” will address the issues of both constitution and structure. Another way to express the question, “On what does the structure ontologically depend?” is to ask, “Why do the constituents of these types combine in that very pattern with regularity?” The question can be applied “all the way down” to whatever happens to be the fundamental constituents of a physical system and the structures of their combinations, whether particles, fields, or something else. Kenneth Aizawa and Carl Gillett, for example, include the

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“Neo-Causal” approach in their taxonomy of research traditions ontological dependence—what they call “vertical relations.”12 Conceptualizing ontological dependence as involving causation affects the notions of emergence and reduction, at least where physical system x exhibits characteristics that are not mere sums of the characteristics of its constituents and its structure. The formation of a molecule of sodium chloride NaCl is an example. The molecule of NaCl is dependent on—but not reducible to—one Na cation and one Cl anion, because its characteristics, including its dispositional properties, are not due merely to the sum combination of the two atoms and their characteristics. The one Na cation and one Cl anion are more than mere parts of the whole. The molecule of NaCl results from some combinatorial process. Although the factor (or factors) that brings the constituents together may or may not be the factor that holds them together, it seems causal. This applies to both chemical and biological mechanisms, suggesting that, when considering physical systems, treating ontological dependence categorically as noncausal dependence may not be entirely justified and may deserve reconsideration. In short, it looks as though an account of the ontological dependence of physical systems may be supplemented with a notion of causation to account for emergence and reduction. IDENTITY DEPENDENCE It is an analytic truth with empirical application that, unless a physical system is self-existent, it ontologically depends on something else. Peter Simons calls this “strong rigid dependence.”13 Accordingly, where y is not a constituent of x and yet x’s composition and dispositional properties somehow depend on y, analyses of ontological dependence may be supplemented in terms of identity conditions expressed as follows: (ID) If x depends for its identity on y, then there is a two-place relation F such that it is part of the essence of x that x is related by F to y.14 If x’s essence—whatever it is that amounts to x’s particularity or that makes x the thing it is and the kind of thing it is—is at least in part given or determined by a relation to something else that does not constitute x, then x cannot exist unless it is so related to that something else. For metaphysical foundationalists, the task is to describe a conceptually possible, theoretically sufficient y and the relation F that links x to y. In section II, relation F will be given in terms of divine action that accounts (1) for what it means to exist, (2) for any structural unity that may be involved between constituents, (3) for some regularity of sequences of states of such physical systems, and (4)

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for the time of x’s existence relative to y’s. I will argue that a theoretically sufficient y is a creating, sustaining agent. It is not merely that such an agent exists, but also that that agent confers existence according to plans, and it is this relation that accounts for the metaphysical necessity expressed by the modal—existential element as well as accounting for the kind of thing x is and the very thing x is. In sum, it is generally acknowledged that, while extant analyses of ontological dependence provide conditions that are individually necessary for existence, it remains as an open research project to provide a list of collectively sufficient conditions, satisfying our general sense of the metaphysical necessity involved in ontological dependence: “Why cannot x exist if y does not?”15 TRUTHMAKING It is a fair approximation to say that truthmaker theorizing arose largely over recalcitrant problems in the correspondence Theory of Truth, where correspondence is understood as an external and isomorphic relation of representation between a proposition and what it is about—usually some aspect of reality.16 A commitment to classical correspondence entails what is now commonly called, the Truthmaker Principle: (TM) For every proposition p: p is true if and only if there is a y such that y is a truthmaker for p (i.e., y makes p true).17 Letting “T” be the formal unary predicate expressing the property, is true, and letting “M” be the formal binary predicate expressing the relation, makes true, (TM) may be formalized as:

"p ( Tp « $y ( Myp ) ) (9.2)

It might be objected that there is an implicit necessity in the truthmaking relation and that this implicit necessity is not reflected in the formalism. The necessity in truthmaking is ontological and it is expressed implicitly by the predicate, “M.”18 The task is to describe M. Nevertheless, one way of rewriting the formal statement of (TM) using modal operators would be this:

∀p  ( Tp → ∃y ( < Ey > → < Tp > ) ) (9.3)

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Read: “For any proposition p, necessarily, if p is true, then there exists some entity y, such that the proposition entails the proposition

”.19

While this formal statement reflects the necessity implicit in truthmaking, given the standard semantics of modal logic, it does not fully express it. While, given TM, every true proposition p logically necessitates its truthmaker y, the element of necessity in making true “runs the opposite direction” from y to p. In short, the relation of truthmaking M is more than the mere correlation reported by a semantics of modal logic. Furthermore, both the logical necessitation and supervenience approaches to truthmaking report correlations without providing metaphysical explanation.20 David Liggins says of the general grounding approach to truthmaking that “a noncausal dependence is at present only dimly understood. In particular, its metaphysics is unsettled.”21 Jonathan Schaffer holds the grounding relation to be “primitive” and “unanalyzable.”22 Section III of this chapter offers a divine action alternative to these judgments, providing the needed metaphysical explanation. The first thing to do is to settle on the relata of the relation. What kinds of entities are the truthbearers and the truthmakers? To address these questions, notice that (TM) entails Truthmaker Maximalism (MAX), which is simply the “left to right” conditional constituting the biconditional of (TM). (MAX) For every proposition p: if p is true, then there is a y such that y makes p true (i.e., p has a truthmaker).23



∀p (Tp → ∃y ( Myp )) (9.4)

It is widely recognized that the most difficult cases for (MAX)—and hence for (TM)—are negative existential propositions (or “negative existentials” for short), be they singular (e.g., Santa Claus does not exist) or general (e.g., There are no unicorns). (MAX) indicates that there exists a truthmaker for every true proposition. If is true, then there is something that makes it true, but “Santa Claus” does not refer to anything real. There is no entity in the world that makes these tokens of these kinds of propositions true.24 So, what could such truthmakers be? I shall address this in a moment. A second difficult case for a theory of truthmaking are counterfactual conditional propositions (or “counterfactuals” for short), such as were one to place a teaspoon of salt in water, it would dissolve. What is it that makes this and its related disposition attribution, NaCl is water soluble, true?

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To sum up this section, a generic notion of ontological dependence includes both a modal-existential element and an identity element, and a generic notion of truthmaking retains the basic intuitions of the classical correspondence theory. Hence, a logically consistent, dual theory should accomplish two tasks. The first is that, whenever entity x is ontologically dependent on entity y, where y is not a constituent of x, the theory should provide a metaphysical explanation of the apparent necessity in the relation, accounting for x’s existence, for the kind of thing x is, and for x’s identity. The second is that it should describe the relation of truthmaking in a way that explains its implicit metaphysical necessity, makes sense of the idea that there is a kind of correspondence between a true proposition and the reality it depicts, and accounts for the truthmakers for negative existentials and counterfactuals. III. A DIVINE ACTION APPROACH Divine Action On the basis of scripture, Christians (Catholic, Eastern, and Protestant) hold that God the Father, through and for Christ the Son, freely created the world, continually sustains it, reveals himself through it, providentially guides it, and is redeeming it. In other words, God’s works of creation, sustenance, self-disclosure, providence, and redemption are all according to his plan for his purposes in Christ. If true, it follows that God’s acting is the dynamic, underlying reality of all things. Moreover, since God is self-sufficient (Latin, a se), and aseity is incommunicable, we may summarize this as follows: God’s existence-conferring action alone is the dynamic, underlying reality of all things.25 Since this chapter concerns God’s action only as it pertains to the physical world as represented by science and mathematics, the fundamental truth about the universe may be stated as follows: (G) God is acting (conferring existence) according to his plan for his purposes in Christ. God’s existence-conferring action is the mediating—though not ultimate— ontological ground of all things and upon which all things are ontologically dependent. This view of divine action treats God as being neither physically temporal, nor atemporal, but rather metaphysically temporal. Garret De Weese calls this view of God’s temporal nature, “omnitemporality,”

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according to which there is a “causal succession of mental states in God’s conscious life” rooted in God’s aseity.26 What is needed now is to relate the mediating ground of divine action to the ultimate ground. This brings us to what might be called a “divine action ontology.” Ontology In metaphysics, an ontology is a complete list of the fundamental kinds of things there are.27 If God’s existence-conferring action alone is the dynamic, underlying reality of all things, no created thing, its putative powers or laws of nature can be self-existent (a se). The question is whether any ontology can at least be postulated, if not extracted, from the idea that the ultimate fundamental and real things are only God and the ways God confers existence according to plan coupled with the idea that all created things are somehow ontological dependent on these. What we have is a divine action “process” ontology comprising five categories: God, an ordered domain of possibilities, dispositions, forces, and structures. Taking each in its turn, let me elucidate. The God of the Hebrew-Christian Scriptures, who—as a tri-unity of persons (Father, Son, and Holy Spirit)—is eternally, inexhaustibly, and uniquely self-sufficient and thus the only ontological ground of all things ad extra. God is ontologically unanalyzable and metaphysically necessary. God is one of a kind, sui generis. The ordered domain of possibilities is the content and extent of God’s representational awareness of God’s ability ad extra, constituting the domain of all possibilities in the form of an infinite array of alternative histories for a universe (not of a universe). One such history is God’s composite plan in Christ, which I will call “the actual world.”28 God confers existence according to the actual world, God’s plan. Given creation ex nihilo, the universe is nothing—nothing but God’s acting in a multifaceted, coordinated way, according to his plan. It is an ordered sequence of world states (which are not propositions) that constitutes the history of our physical existence (past, present, and future). As such it is only one of an infinite array of alternative histories or “possible worlds.” This infinite array is God’s representational awareness of His ability ad extra. Each representation—each aspect of God awareness of his ability ad extra—is a representation, not of something that already exists, rather for something to exist. To reiterate, (G) God is conferring existence according to his plan for his purposes in Christ. What we perceive and conceive to be dispositions, forces, and structures are ways God confers existence to the universe according to plan. Dispositions are God’s commitments to confer existence on condition. Forces are God’s constant existence-conferring action. Structures are God’s unifying, coordinated action. Both the actual world and the ways God confers

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existence are governed by and subordinated to God’s original ultimate end in creation.29 This is not to say that such things are illusions. They are real. Both the empirical content of our perceptions and the propositional content of our conceptions of dispositions, forces, and structures are legitimate and our ordinary and scientific experience is valid, though subject to corrections and revision.30 Clarifying Note on “Existence-Conferring Divine Action” This idea of existence-conferring divine action may be rendered more vivid considering the difference between willing that x and willing x. Applied to God, willing that x is willing as planning and willing x is willing as achieving. Planning involves an intention to achieve something. It involves a representation for an achievement, which in this case is a state of creation. By contrast, willing x is not a representation for an achievement, it is an achievement. Applied to God, it is a divine act that realizes a state of the universe. It is a realization of one of God’s plans. This can be understood on the analogy of a person’s imagining a scenario. In fact, imagining a scenario may be the perfect—perhaps only—applicable analogy. Imagining a scenario is not planning, it is willing as achieving. Whatever a person so wills (in this sense) exists, albeit, only in his or her mind as an intentional object. The scenario exists at a given moment only because it is willed and only as long as it is willed. Thus, a worthy “explanation of how we can literally and realistically think of God as acting”—something William Alston (1993) challenged Christian theologians and philosophers to pursue—is to think of God’s creating and sustaining action as God’s “imagining” the universe into existence.31 With this clarification in mind one can understand that, in relation to his plan, the various ways God acts should be understood in two senses: intentional and actual. In the intentional sense, they are eternally existing commitments. It is as though God says to himself, “This is my plan and I will enact it as follows: at any stage, upon the satisfaction of conditions C at that stage, I will perform some type of existence-conferring A-ing. I will supplement A-ing by types of constantly B-ing and I will co-ordinate what I do.” However, as God enacts his plan, such ways God acts (understood intentionally) are episodically realized, rendering the dynamic, composite cosmos. Clarifying Note on “Contingent Existence” The idea of existence-conferring divine action can now be used to give a precise definition of contingent existence.32 Contingent existence is a matter

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of being created and sustained by God and involves moments of existence. Whether time and space are continuous or discrete remains unsettled.33 Nevertheless, we may justifiably assume that existence comes in discrete quanta, whether as Planck-scale regions of space-time, as spontaneous collapses of wave functions, as disturbances in general-covariant quantum fields, or as elementary events—whichever interpretation of fundamental physics you prefer.34 Thus, a moment of existence of an entity involves some duration. Let it be a Planck moment, which is thought to be the minimum, physically possible duration. From this notion of a moment of existence and, given that aseity is incommunicable, the idea that the universe, or any component thereof, either begins to exist before—or continues to exist after—God’s efficacious, existenceconferring volition that it exist is thereby ruled out. The universe—in part and as a whole—is such that the divine existence-conferring act and the result of such must be simultaneous. Therefore, a contingent object’s existence is both the divine action and the result of it, simultaneously. We then have this principle: There can be no time t* prior to t (the discrete moment of God’s existenceconferring action) such that physical system x exists at t* apart from God’s existence-conferring action and there is no t* after t such that x exists at t* apart from God’s existence-conferring action. Thus, when God confers existence—whether minimally at a Planck volume for a Planck moment, or macroscopically (which we perceive in terms of objects, properties, and relations) or comprehensively, rendering the entire universe over some duration—every scale it is a simultaneous duality (or complementarity) of divine action/result of action. The universe in its existence, constitution, and dynamics is like a scenario—an intentional object— that God imagines according to plan. Hence, we now have this metaphysical analysis of contingent (i.e., physical) existence (CE): (CE) For any contingent object (i.e., physical system) x and time t, x exists at t if and only if x at t is the act/result of God’s creating x according to plan. This five-category ontology and its notion of the existence of a contingent object is non-Aristotelian in that physical existence is creation ex nihilo and that there cannot be any a se causal powers. While active and passive dispositional properties and the events that occur as manifestations of combinations of them are theoretically legitimate in empirical explanation, they are not brute (i.e., self-existent fundamental) realities. Rather, they are ways God confers existence. Aseity is incommunicable and contingent existence is a

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duality of divine existence-conferring act/result. This ontology serves as the conceptual basis of the accounts of ontological dependence and truthmaking given below. Ontological Dependence Revisited With this five-category ontology in hand we can now revisit and develop the generic notion of ontological dependence presented in section I. Rigid existential dependence (RXD) can now be stated as follows: (DXD) x’s existence requires God’s existence = df x cannot exist unless God exists. As stated, (DXD) is incomplete. First, it does not include the time of the existence of the ground of x relative to any of the times of the existence of x over the duration of its life. Whatever happens to be one’s preferred view of God’s temporal nature relative to the temporal nature of creation—atemporal, sempiternal, or omnitemporal—God is at least portrayed in Scripture as “from everlasting to everlasting.” Therefore, we must emend (DXD) to express this and do so in relation to the time of a contingent object’s existence, which is given in (CE). Thus, letting t be a Planck moment we have this revision: Divine existential dependence (DXDt) x’s existence depends on God’s existence x cannot exist at any moment t of its existence unless both 1. God exists at t, and 2. God exists before x exists at t. Some accounts of ontological dependence treat ontological priority as an explicit necessary condition. If God is atemporal, the term “before” may be taken to express ontological priority. If God is sempiternal, the term expresses both ontological priority and temporal priority. If God is omnitemporal (as is presumed in this proposal), the term “before” expresses both physical and metaphysical temporal priority as well as ontological priority. (DXDt) is still incomplete because God’s existing (even necessarily existing) merely before and at x’s existence does not fully account for x’s existing. It does not yet answer the main question we posed at the outset: Why cannot x exist if y does not? Our sense of ontological dependence contains the idea that x exists in some sense because of some relation in which it stands since it cannot be self-existent. It is not merely in virtue of some kind of invariant correlation. Historic Christian thought holds that x’s existence requires God’s willing x’s

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existence—God’s conferring existence to x. Furthermore, God does not do so without reason. Rather, God confers existence to everything for purposes according to plan and this is what gives a thing its identity. These considerations should be made explicit. To that end, consider the received, generic notion of identity dependence: (ID) x depends for its identity on y = df There is a two-place predicate “F” such that it is part of the essence of x that x is related by F to y.35 Therefore, since on my view a thing’s identity lies in God’s plan for it, the definition should be emended so that F denotes a real relation given in terms of divine, existence-conferring action for purposes according to a plan. The identity of a contingent object is God’s complete plan for it.36 This plan includes representations for each state the thing is in throughout the duration of its existence. These representations are for all of its so-called properties and relations, some of which make it the kind of thing it is. To reiterate, a thing is a structure of dispositions and forces over time, so that what appear to be parts of things are themselves matters of God’s existence-conferring action for purposes according to plan.37 Thus, we do have “objects” or “individuals”; they are real and we negotiate our lives accordingly. Nevertheless, they are ultimately processes; each being nothing but the act/result of God’s sequentially conferring existence according to plan. But since this also includes time, we have: Divine identity dependence (DID) x depends for its identity on God = df The essence of x is such that, for every moment t in the entire existence of x, x at t is the act/result of God conferring x’s existence at t according to plan. What was relation F in (ID) is now, in (DID), x’s moment-by-moment dependence entirely on God’s purposeful, planned, existence-conferring action. A corollary to (DID) is that the ultimate ontological grounds of things cannot be analyzed merely as a composite of those things or simply in terms of those things. Something must account for the nature of the parts or elements and for the composite itself having just that unity or structure. Those structures are God’s unifying, coordinated, existence-conferring acting according to plan. It was noted in section II of this chapter that, an account of the ontological dependence relation should explain why x cannot exist, be the particular thing it is, and is the kind of thing it is unless y exists, is the thing it is, and is the kind of thing it is. That is, an ideal account would explain the metaphysical necessity involved in the ideas. Accordingly, the divine action account of ontological dependence of this chapter may now be stated: For any contingent entity x and moment t, x at t is ontologically dependent on God at t if and only if

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1. Divine existential dependence (DXDt) x cannot exist at any moment t of its existence unless both (a) God exists at t, conferring existence to x at t, and (b) God exists before t, planning to confer existence to x at t, and 2. Divine identity dependence (DID) The essence of x is such that, for every moment t in the entire existence of x, x at t is the act/result of God conferring x’s existence at t according to plan.38 This definition accounts for the metaphysical necessity expressed by the modal-existential element. Every x’s existence is solely a matter of God’s commitments, plans, and purposes, and he alone is self-sufficient. God acts accordingly and nothing can resist God’s actions, hence the necessity. Moreover, since God’s plan for the universe includes everything we perceive or conceive as an object, property, or relation, this definition accounts for the kind of thing x is and the very thing x is.39 It follows that there can be no such thing as “ontological momentum,” “temporal inertia,” or “existential inertia.”40 Every created thing ontologically depends only on God, God’s plan (which is part of God’s awareness of his ability ad extra), and God’s existence-conferring action. However, there is a paradox in God’s existence-conferring action. At any moment of x’s existence—considering x only as the “result” aspect of the duality of God’s existence-conferring action—x stands in an ontological dependence relation to God. Nevertheless, at that same moment, the “act” aspect of the act/result duality of God’s conferring x’s existence at t is not properly a relation to x, it is x. Since God is self-sufficient and aseity is incommunicable, the existence and nature of every “thing” can only be what God wills it to be at that moment; nothing more and nothing less. Nothing can exist apart from God’s existence-conferring action. Therefore, nothing can even be considered except as now being created. Under this divine action account there cannot be at least two relata and one relation as there are in the standard notion of a relation. In addition to—or “over and above” God’s existence-conferring act—there just cannot be one more relatum, and then a relation of that relatum to God’s act. In the “act” aspect of the act/result duality, ontological dependence is not a relation; God’s efficacious willing ad extra is an intrinsic property, because it cannot be extrinsic.41 Contingent Objects as Processes The ontology presented here as reflected in its account of ontological dependence treats a contingent object as real and having an identity; nevertheless, an object is a process of divine action. In terms of the “result” side of the act/ result complementarity, a persisting object is a passive continuant. In terms

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of the “act” side of the act/result complementarity, a persisting object must be a process of divine action. This ontology therefore differs from standard “entity” ontologies. Ordinary experience, standard extensionalist logic, and much of basic science take the world to be a matter of objects having properties and standing in relations.42 Martin (1996) says, “My aim is to make do with things, properties and relations that make up and are the constituents of situations or states of affairs, all of which would be first-order.”43 Quine (1948) advocates a prescriptive approach to ontological commitment whose first step is to regiment a theory’s basic claims in first-order logic, which of course is extensional.44 So, naturally, some efforts to spell out ontological dependence will come out along these lines. Nevertheless, it is a matter of dispute whether what appear to be contingent objects really are objects; whether objects are fundamental. Could they be structured wholes, bundles of properties, relatively invariant manifestations of a network of causal powers, irreducible relations?45 Or are they processes? Campbell (2015) explains that the “entity” approach to the dynamics of the universe holds that stability is basic and it is change that requires explanation. The “process” approach holds that change manifests metaphysically fundamental processes or dynamism and it is stability that needs explanation.46 On my proposal, physical systems are compositional processes—dispositional structures of lower-level dispositions “all the way down” to elementary particles which are themselves structures of dispositions without ground in any physical categorical base.47 Robert Disalle writes, Almost from the beginning of general relativity [Weyl and Eddington saw it] as a theory of the geometrical structure of the world. [General Relativity] . . . represents the geometry of space-time as a function of the mass-energy distribution. . . . At the very least, we can identify a common metaphysical principle uniting general relativity with special relativity and Newton’s theory: space-time is an objective geometrical structure that expresses itself in the phenomena of motion [which is] a dynamical structure whose states depend on the states of the matter and energy within it.48

Mauro Dorato suggests that given one version of the Ghirardi, Rimini, Weber interpretation of quantum mechanics GRWf, “it is reasonable to follow [J. S.] Bell and assume that physical spacetime, [is to be] regarded as the set of all ‘flashes’, or localizations, occurring at a precise location at a certain time . . . it is the collection of such localization events that constitute both physical space-time and the world around us . . . space-time is simply derived out of quantum events.”49 Given wave function realism, the universe over time is fundamentally the sequential “collapses” of the universal wave function. Given covariant loop quantum gravity, the universe is a manifestation

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of a general-covariant quantum field, because these are “all that exist in nature.”50 Thus, there is good reason to suppose that the universe at any moment of its existence is the manifestation of a complex disposition.51 As Johanna Seibt remarks, “The current facile recourse to ‘particulars’ does not yet seem legitimate.”52 There are at least two non-physicalist ontologies available to account for these changing states of mass/energy, understood as manifestations of a complex disposition. The first, is neo-Aristotelian and explains processes in terms of substances and causal powers.53 The second, defining ontological dependence in terms of divine action, such “localizations” are the elementary micro-creations of God, which—when combined in increasingly and exceedingly complex ways—constitute the entire universe over time. In other words, this mass-energy distribution—as a whole and every state of every system in particular—at every moment is nothing other than God’s coordinated acting according to plan. What we perceive or individuate as macroscopic objects are relatively invariant structural features of processes over time, whose identities lie in God’s plan. All of this depends on the ways God confers existence, which in turn appear to us as dispositions, forces, and structures. Dispositional properties manifest within a range. Some aspects of the universe are constant. Molecules exhibit a certain structure. The regularities, constants, and recurrent patterns of God’s existence-conferring actions are the laws of nature. What Roland Omnès (2005) wrote is relevant and suggestive: The fundamental laws of nature are pure mathematical forms accounting for the phenomena though providing no cause for them and showing no action. The laws expressing the regularities of reality are much more accessible to understanding than reality itself. They are prior to mathematics, however, just as reality is absolutely prior to anything.54 If God’s sustaining action is the reality that is “absolutely prior to anything,” then the “laws expressing the regularities of reality” are expressing the regularities of God’s acting. In short, objects, properties, and relations are—in reality—nothing but the complex existence-conferring actions of God. The act/result duality and complementarity of God’s existence-conferring action, which like the GRWf “flash” ontology, the elementary events of Causal Set and Loop approaches to quantum gravity compositionally yield the macroscopic objects of ordinary experience. Truthmaking Revisited Realist truthmaker theorists hold that a truthmaker is some entity in the world.55 In this chapter, that entity is real, but it is not in the world; it is some constituent of God’s knowledge. The extent of God’s knowledge is infinite;

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there is nothing God does not know. The nature of God’s knowledge is eternal, perfect, unmediated self-awareness. Thus, God is directly aware of his ability ad extra. More than that, since God is perfectly aware of his ability ad extra, creational possibilities are real possibilities solely by virtue of God’s ability ad extra. Thus, God’s awareness of his ability, must include a representation of every creational possibility. God’s representational awareness of his ability ad extra (1) constitutes the collection of all real possibilities (i.e., it is all the “things” of various kinds and relations, which—were he to create any of them—would be his work ad extra), (2) is a structure; it is an ordered domain of possibilities in the form of an infinite array of alternative histories for a universe. The Actual World and World States Recall that one history for a universe—among the many that constitute the ordered domain of possibilities—is God’s plan, the actual world. The actual world is God’s representation for the universe, not of the universe. God’s knowledge of history is his awareness of his plan. Let the constituent plans, which are representations for a state of the universe and collectively constitute the actual world, be world states. Assuming physics at the Planck-scale is correct, let an atomic world state be God’s representation of the content of a Planck cell (a three-dimensional irregular hodon) at a Planck moment (a chronon). Let a representation for the entire universe at a Planck moment be a total world state. The actual world is a strict, linear order of compossible total world states. A composite world state is any combination of atomic world states without a regional or temporal gap. Therefore, God’s representational knowledge—an ordered domain of possibilities—is a mereological, non-set theoretical, structure of world states. Proposition A proposition is the informational (or information-like) content of an occurrent, intentional mental state or “attitude.” As informational content, a proposition is an abbreviated, synoptic representation. As an aspect of an occurrent, intentional mental state, a proposition involves an actual intentional object; it is the content of a particular kind of attitude toward the thing (or some aspect thereof) that one is thinking about.56 For example, Sally was thinking about the recent sunny weather and is convinced that the garden needs to be watered. The intentional object is the effect of recent weather on the garden and the proposition is .57 There are several competing views of propositions and this is not the place to rehearse the alternatives.58 Nevertheless, whereas most theistic

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philosophers and theologians hold to the abstract object view, mine is an occurrent content view. Given the divine action ontology presented earlier, a proposition cannot be a platonic abstract object, because only God is selfexistent; only God is the fundamental reality. A person may look out the window and think, It is raining. Then later, that person may remind himself that “When Marie said, ‘Il pleut,’ she had in mind what I had in mind when I said, ‘It is raining.’” Thus it is that the nearly irresistible phenomenology of our reflective experience leads us to think that such apparently shared content is a necessarily existing abstract object. However, as the content of an occurrent mental state of a created agent, a proposition exists briefly and contingently. That same content in the minds of two different people at two different times is not a matter of the metaphysical nature of the proposition itself. It is a matter of God’s existence-conferring action. To make this more precise, a proposition is a structure of concepts and expressed by an indicative sentence in a context of utterance or inscription. It is the information (or information-like) content of an intentional mental state of a created consciousness, and (as such) it is given as a manifestation of a complex disposition. In other words, a proposition is the informational content of an occurrent propositional attitude, which in turn is a manifesting cognitive disposition of a created agent. Such dispositions are features of a human’s expressed capacity to represent. However, the manifestings of these dispositions are nothing other than God’s acting (conferring existence) according to plans which are aspects of his self-awareness. In sum, the occurrent content view treats a proposition as the informational aspect of the manifestation of a cognitive disposition.59 These dispositions are features of a human’s capacity to represent and to predicate.60 Dispositions themselves are one of the ways God confers existence. There is therefore a crucial difference between propositions (what a created agent has in mind about something that exists in some sense) and world states (what God has in mind for something to exist). Composite world states are like propositions or states of affairs, but they are not conceptually identical to them. The standard view is that propositions (and possible worlds as maximal propositions or states of affairs) are the content of both created agents’ thoughts and God’s.61 On the standard view, propositions are necessarily existent abstract objects. However, on the account advocated here, a proposition is the informational content of an occurrent propositional attitude, which in turn is a manifesting cognitive disposition of a created agent. Such manifestings are nothing other than God’s acting. The informational content of a person’s belief, therefore, cannot be as detailed as God’s self-awareness. To put it another way, while humans apprehend physical objects by means of propositions, physical objects are processes (i.e., manifesting dispositional properties) just as human mental states are processes. However, for God,

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physical objects and human mental states are God’s acting and rooted ultimately in God’s self-awareness. Truthmakers Specified To make this more precise, let K be God’s knowledge. Let the expression consisting of lowercase letter p in brackets [p] be the world state or aspect k of God’s knowledge K represented by the proposition, p. Thus, “[p]” and “k” denote the same thing. Because the existence of a concrete state of affairs x or physical system x is a matter of God’s conferring existence to x according to his plan—of which k is a constituent—we can say: “p represents k” even though seldom does a created agent think this is what p represents. Thus, in general, for any extant proposition p, 1. p is true if and only if what p represents as being the case is included in God’s knowledge K.

Tp « K  [ p ] (9.5)

This is the general form. However, it is not quite accurate because a true proposition is always relevant to at least one history, unless it is about God. Since the universe is a matter of God’s conferring existence, for propositions regarding the physical world, 2. p is true if only if what it represents as being the case is included in the actual world, which is included in God’s knowledge.

Tp « K  éëa  [ p ]ùû (9.6) Read: “God knows the actual world includes the state denoted by p”

A proposition is either purely false or fictionally false. If a proposition is a contradiction or a false idea about God—for example, God does not exist—it correlates to no constituent of God’s self-awareness. Its world state is not included in any history for a universe. Its world state is metaphysically impossible. It is purely false. Thus,62 3. p is purely false if and only if God knows that

Fp « K  éë ~ $w : w  [ p ]ùû (9.7)

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Read: “God knows that no alternative history includes the state denoted by p.”

In general, when what is asserted is false, but not purely false, it is fictionally false: 4. p is fictionally false if and only if God knows that the actual world does not include the world state picked out by p, but that it was within the range of his ability.

Fp ↔ K ⊃  α ⊃ [ p ] ∧ ∃w ≠ α : w ⊃ [ p ] (9.8)

Read: “God knows that the actual world does not include the state denoted by p, but that it is included in a different alternative history.”

Perhaps, the most important examples of fictionally false propositions are mathematical propositions that have no actual world correlate, but yet are elements of a mathematical structure. Mathematical structures are the propositional content of logically consistent axiom systems or (algebraic or differential) equations. They are logically possible but nevertheless may or may not correlate with real structures. Saunders Mac Lane asserted that “Mathematics consists in the discovery of successive stages of the . . . structures underlying the world and human activities in that world, with emphasis on those structures of broad applicability and those reflecting deeper aspects of the world.”63 I am proposing that all of the “structures underlying the world” are real structures—regularities in the ways God sustains creation. Furthermore, each of these real structures is a feature of one other real structure which is God’s plan in Christ. God’s plan and God’s ways of acting according to plan exhaust the category of real structures. Accordingly, true mathematical structures represent either the actual world (which is a structure) or substructural aspects of it or regularities in the ways God acts (which are structures), all of which are things God knows. For example, we are assuming that the actual world is God’s plan in Christ and is an infinite, strict linear order of discrete, total world states. If the assumption is correct, then there is an ontological correlate of the natural numbers sequence. In other words, the actual world is a real structure and the propositional content of second-order Dedekind-Peano Arithmetic (PA2), for example, is a true mathematical structure. It is true along with the sentence of PA2, o + o = o′′ (that is, “1 + 1 = 2”). Thus, if a mathematical proposition (an axiom or theorem of a logically consistent theory) correlates with a real structure, it is true. If it does not correlate with a real structure, but with a merely possible structure (an aspect of a history or histories God did not

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choose to enact) then, since it is logically consistent, it is fictional. In short, a mathematical proposition is true if and only if what makes it true is a real structure. Thus, Zermelo-Frankel set theory ZFC, though logically consistent, is not true. It is fictionally false because it has no correlative real structure, that is, it correlates to nothing in the actual world. In sum, this theory is trivalent: besides being true, a proposition can be either purely false or fictionally false. If a proposition p is false God knows something regarding what it represents: either that it is impossible (thus purely false) or merely possible (thus fictionally false). Thus, a logically consistent theory (mathematics, or a narrative, or an elaborate imagination) is either true (if all of its propositions are true) or it is fictional (if some of its propositions are not true and none of them represent a metaphysical impossibility). If p is true, some aspect of God’s representational awareness of his ability ad extra (which includes God’s plan) is its truthmaker. In short, truthbearers are propositions and truthmakers are constituents of God’s knowledge. Now that we have an account of the relata in truthmaking, let us turn to the relation of truthmaking. It was noted earlier that there is an implicit necessity in the truthmaking relation M. The truthmaking relation between a true proposition and God’s knowledge has three aspects. The first is that a true proposition p has the property, truth, in virtue of the existence of some constituent of God’s knowledge k, which either is or includes what p ultimately represents. The reality in truthmaking is the reality of God’s knowledge. The second aspect is that, as the content of an intentional mental state, a proposition p exists only as God confers existence to it and to the cognitive agent who thinks it. Third, the truthmaking relation also involves (G) God is conferring existence according to his plan for his purposes in Christ, because (G) is that in virtue of which p exists. Thus, for any true proposition p, we have this account of the truthmaking relation: Truthmaking (M) For any true proposition p and constituent k of God’s knowledge K, k makes p true over duration if and only if (1) k either is or includes what p represents, (2) p’s being the content of some created agent’s occurrent propositional attitude over is itself a world state included in the actual world, and (3) (G) God is conferring existence according to his plan for his purposes in Christ. The pertinent point for the relation of truthmaking is that a proposition is— at the same time—both an aspect of a realized divine plan and the content of an occurrent propositional attitude. Thus, the makes true relation is a matter of what God plans and does and the is true property holds episodically in a temporally indexed sense, referred to by the symbol .64 We have this revision in (TM):

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Revised Truthmaker Principle (RTM): For every p: p is true only if there is a k, such that k is a truthmaker for p.

"p ( Tp « $k ( Mkp ) ) (9.9)

The makes true relation here differs from the standard views or intuitions about truthmaking because propositions under this view are not platonic objects. This renders the theory more complex, because a proposition’s existence involves a duration of time. Taking the actual world to be a representation for the universe that preexists the universe provides a way to not only to handle this added complexity, but also a way to synthesize two views of time referred to as the “A-theory” and the “B-theory.” Time The A-theory (sometimes called the presentist, dynamic, or tensed view of time) holds that the apparent distinction between the past, the present, and the future is objectively real, though only the present moment is real. The B-theory (sometimes called the eternalist, static, or tenseless view of time) holds that all times and their contents are equally real and stand in an earlierthan relation to each other. In this theory, the temporal structure of God’s plan is B-theoretic and each component is real. Every world state is eternal and necessary and stands in a B-theoretic relation to others. However, from our A-theoretic perspective as creatures “within the flow” of God’s universesustaining actions, there are propositions that were true in the past, others that will be true in the future, and some that are true now. Here we have a theory that preserves (TM) by saying what the relation of truthmaking is in a way that explains our sense that there is a correspondence between the content of indicative sentences and the reality they depict, when that content is true. Moreover, since God’s eternal awareness includes every world state that involves some agent’s occurrent mental state that has p as content, God is aware of all propositions. Letting sets be God’s collections, the set of all propositions is included in this eternal awareness. It is an objectively existing set, existing as an aspect of God’s eternal awareness of his ability ad extra. The question now is whether this adequately accounts for negative existentials. Ontological Dependence and Truthmaking Applied Having developed both ontological dependence and truthmaking in terms of one ontology, we can now see how they apply. Consider Pauli’s Exclusion

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Principle. As a sentence regarding a law of coexistence, it says: “There are no quantum systems in which two fermions occupy the same quantum state simultaneously.” When it is an occurrent proposition, it is a negative existential. In addition to the requirement that what it represents is an aspect of God’s intentional knowledge as part of God’s plan, what makes it true is that God’s plan itself—the actual world—does not include any state in which two identical fermions occupy the same quantum state within a quantum system simultaneously and (G) God is conferring existence according to his plan for his purposes in Christ. God plans and acts accordingly. There is order and regularity, and nothing can prevent or alter God’s acting according to his commitments. So, the principle appears to us as a necessity; a law. Moreover, God knows what his plan includes and what it does not. What grounds the pattern of physical systems that Pauli’s Exclusion Principle describes is both the content of God’s plan (i.e., the actual world) and (G), just as the existence and nature of an existing fermion—an atom of helium–3 (3He), for example—is grounded in what the actual world includes and also in (G). One Implication I argued that for any true proposition p, there is some k in God’s knowledge K that makes p true. However, given the nature of a proposition as the content of an occurrent propositional attitude or mental state, both (DXDt) and (DID) apply. That is, p cannot exist at any time t of its existence unless both (a) God exists at t and (b) God exists before t, and the essence of p is such that, for every t in the entire existence of p, it is the act/result of God conferring p’s existence at t according to plan. This in turns reveals the fundamentality commitment of this theory: God and God’s existence-conferring action.65 IV. SUMMARY The aim of this chapter was to provide a divine action account of the relations of ontological dependence and truthmaking from one ontology. Basic Assumption It does so on the assumption that (G) God is acting according to his plan for his purposes in Christ. God’s acting is the dynamic, underlying reality of all things. Ontology This assumption is reflected in the following five-category ontology: (1) God, (2) an ordered domain of possibilities is the content and extent of God’s

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representational awareness of God’s ability ad extra, constituting the domain of all possibilities in the form of an infinite array of alternative histories for a universe (not of a universe), (3) dispositions are God’s commitments to confer existence on condition, (4) forces are God’s constant, existence-conferring action, and (5) structures are God’s unifying, coordinated existenceconferring action. Ontological Dependence The divine action account of ontological dependence for physical systems and laws of nature in terms of existence and identity is this: For any contingent entity x and moment t, x at t is ontologically dependent on God at t if and only if (1) Divine existential dependence (DXDt) x cannot exist at any moment t of its existence unless both (a) God exists at t, conferring existence to x at t, and (b) God exists before t, planning to confer existence to x at t, and (2) Divine identity dependence (DID) The essence of x is such that, for every moment t in the entire existence of x, x at t is the act/ result of God conferring x’s existence at t according to plan. Every created thing ontologically depends on (is grounded in) God, God’s intentional knowledge, and God’s existence-conferring action. Truthmaking Given (G), letting p be any proposition understood as the content of an occurrent, intentional mental state of a created agent, and letting what p represents be some constituent k in God’s knowledge K, the divine action account of truthmaking for propositions is this: Truthmaking (M) For any true proposition p and constituent k of God’s knowledge K, k makes p true over duration if and only if (1) k either is or includes what p represents, (2) p’s being the content of some created agent’s occurrent propositional attitude over is itself a world state included in the actual world, and (3) (G) God is conferring existence according to his plan for his purposes in Christ. This supports a revision in (TM): Revised Truthmaker Principle (RTM): For every p: p is true if and only if there is a k, such that k is a truthmaker for p.



"p ( Tp « $k ( Mkp ) ) (9.10)

Hence, the traditional generic idea holds: “truth depends on being.” (RTM) explains our sense that there is a kind of correspondence between the content

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of indicative sentences and the reality they depict, when that content is true. The problem of negative existentials is addressed because truthmakers are constituents of God’s knowledge. Lowe and Rami (2009) observe that “the explication of the truthmaking relation is presumably the most difficult task for a truthmaker theory.”66 We now have such an explication, if divine action is admitted into our framework of possibilities. In 1935, Albert Einstein wrote the following to Erwin Schrödinger, “The real difficulty lies in the fact that physics is a kind of metaphysics; physics describes ‘reality’. But we do not know what “reality” is; we know it only by means of the physical description.” Metaphysical foundationalists hold that, at some point, physical description “bottoms out” so to speak, calling for a philosophical posit (naturalist or religious), which should address the issues coherently and consistently. In the end, we may not know what reality is, but this chapter assumed that whatever it is, it is being sustained by God. The underlying reality is neither platonic, nor Aristotelian, nor physicalist; it is not an infinite divisibility of elementary particles, nor a complex structure of a variety of self-sufficient basic “powers.” Rather, the underlying dynamic reality is God’s acting and only God’s acting. Since the “logic” of everything must lie in the logic of God’s action, the referents of the fundamental concepts of science and mathematics must be ultimately related to God through ways God acts and through God’s awareness of his ability. NOTES 1. I want to thank Martin Pickup, Lisanne Winslow, Elyse Kallgren, Anna Marmodoro, and others from the Metaphysics of Entanglement and Power Structuralism in Ancient Ontologies projects who attended my talk at the University of Oxford for helpful comments which improved this chapter and precluded many errors and needless confusion. 2. For two helpful introductions to both ontological dependence, see Correia and Schnieder (2012) and Tahko (2015), and for truthmaking see Beebee and Dodd (2005) and Lowe and Rami (2009). Vallicella (2002), uses the term “grounding” as I am using “ontological dependence.” 3. See Heil (2016), Lowe (2016), Marmodoro and Yates (2016), and Simons (2016). 4. Some analyses add, “y is prior to—or ontologically more fundamental than— x.” This condition is explicit in the account divine existential dependence given in the next section. 5. See Vallicella (2002). 6. See Correia (2008), 25 and Tahko (2015), 93–119. The aims of this chapter do not involve or require discussion of “generic existential dependence” and “generic essential dependence.”

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7. This strategy precludes the result that x would be dependent on every necessarily existent entity y when applied to abstract object, which in most realist ontologies are necessarily existent entities. 8. Marmodoro and Yates (2016), 6. 9. A similar view is found in Fine (1995), where y would be a constituent of x’s essence. 10. Koslicki (2005), 190. 11. Koslicki (2010), 197, 235. 12. Aizawa and Gillett (2016), 1–38. 13. Simons (1987), 295. If x depended on more than one particular thing—that is, on some things or others of some type—then, ontological dependence would be “strong generic dependence.” 14. This is similar to Tahko (2015), 101, who treats this as a definition. 15. It is widely acknowledged that there may be more than one type of ontological dependence, where either each are categorically distinct or else are variations of species under one genus. 16. Lowe and Rami (2009), 2. Accordingly, Johanna Seibt (2008) says that “An ontology is a theory of truthmakers for a certain natural or scientific language,” 134. 17. Ibid., 3. By not stipulating that there is exactly one truthmaker for each truth, TM does not entail isomorphic correspondence. 18. Armstrong (2004), 5. 19. Beebee and Dodd (2008), 2. 20. For other criticisms see Schaffer (2008). 21. Liggins (2012), 270. 22. Schaffer (2009), 364. 23. It also includes Truthmaker Purism: (PUR) For every proposition p: if p has a truthmaker, then is true. "p (Tp « $k (Mkp)) 24. For a clear statement of the problem of negative existentials, see Lowe and Rami (2009), 15. See also Beebee and Dodd (2008) in several places from several authors. For an alternative analysis, see Crane (2013), 71–75. 25. At least since the early eighteenth-century philosophers have argued that aseity is incommunicable Clarke (1988 [1704]), 61: “No powers are impossible to be communicated, but only those which imply self-existence and absolute independence.” Kvanvig and McCann (1988), 49: “Created things can have no capacity for self-sustenance.” This claim is standard for many systematic theologians. Vos (2012 [1896]), for example, writes “[Scripture represents] that the creature although possessing a real existence, nevertheless at no moment and in no respect can be independent of God. If it existed of itself [i.e., were a se], then so far as its being is concerned it would like God.” 184. 26. De Wesse (2004) 239–255. 27. For an introduction, see Ney (2014), Macdonald (2005), and Lowe (2002). For a more advanced treatment, see Poli and Seibt (2010). 28. Treating the actual world as God’s plan is neither new nor widely accepted by Christian philosophers. Leibniz, of course, is credited with first proposing the idea in the seventeenth century, but his view differs from that developed in this chapter. Most

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theistic philosophers understand “the actual world” to refer to a structured, composite abstract object whose constituents are either propositions or states of affairs. See Schultz (2014). 29. The concept of an original ultimate end is precise and important. See Edwards (1989) and Schultz (2013). 30. See Schultz (2009) and Schultz and Winslow (2014). 31. This satisfies what Alston (1993) says he desires by taking the notion of God’s acting “seriously and realistically.” It satisfies what Oakes (1977) claimed was needed to avoid pantheism. 32. As previously stipulated, this chapter pertains to the ontological dependence of contingent entities. Nevertheless, given the five-category ontology of this chapter, socalled necessarily existent entities either do not exist necessarily (e.g., propositions) or are accounted for in terms of the ordered domain of possibilities described above (e.g., numbers, sets). 33. For discussion of the debate on regarding discrete time, see Van Bendegem (2011), 145–162. For the debate on discrete space, see Hagar (2014). 34. See Ghirardi, Rimini, and Weber (1986) and Dorato and Esfeld (2010) for wavefunction collapse, Vidotto and Rovelli (2014) for quantum fields, and Dowker (2006) for elementary events of causal sets. 35. Tahko (2015), 101. 36. This is similar to Leibniz’s idea of a complete concept. Something similar is also expressed in scripture. Psalm 139: “In your book were written, every one of them, the days that were formed for me, when as yet there was none of them.” 37. This account is similar to Vallicella (2002), 269, “(PT) Necessarily, for any contingent individual x, x exists if (i) there is a necessary y such that y is the paradigm existent, and (ii) y, as the external unifier of x’s ontological constituents, directly produces the unity/existence of x.” The differences are that, in addition to defining “existence” in terms of existence, he treats universals as constituents which “necessarily exist.” But they cannot exist on this account (see above under clarifying note on “contingent existence”). Secondly, Vallicella does not provide an account of what x’s ontological constituents (i.e., a “thin particular” and necessarily existing universals) are in terms of his “paradigm existent.” 38. Notice that the definition entails that x is distinct from y and that y is prior to, or ontologically more fundamental than, x. 39. This may be fruitfully and favorably compared to what James Ross (9180) holds: “When I say creatures are metaphysically dependent upon God, I mean that there is no possible world where a thing other than God exists where its being is not independent upon God’s will or where some characteristic the creature has, including its continued existence, is not accounted for by God’s active willing it to be that way,” 620. 40. See Menzel (1987), 366 and (2001), 71; Kvanvig and McCann (1988), 41; and Feser (2011), respectively. 41. This answers Adams (2015). 42. Bigaj and Wüthrich (2016), 8. 43. Martin (1996), 60.

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44. Quine (1948). 45. Koslicki (2008), Lombardi and Dieks (2016), Marmodoro (2013), Rickles and Bloom (2016), and Seibt (2010). 46. Campbell (2015), 1–2. See also Smolin (2005), 49–65. 47. The issue of apparently ungrounded dispositional properties has attracted an increasing amount of attention in recent years not only from the standpoint of theoretical physics, but more so from contemporary analytic metaphysicians and philosophers of science. Mumford (1998) and (2006) and Lombardi and Dieks (2016). 48. DiSalle (2006), 15–16. 49. Dorato (2006), 150–151; Bell (1987), 45; and Dorato and Esfield (2010). 50. Vidotto and Rovelli (2014), 18. 51. See Vidotto and Rovelli (2014), Vidotto (2015), (2013). 52. Seibt (2010), 52. 53. For just a sampling, see Harre and Madden (1975), Kistler and Gnassounou (2005), Handfield (2009), Marmodoro (2010), Mumford and Anjum (2011), Ellis and Sankey (2012), Groff and Greco (2013), Tahko (2013), and Novotný and Novák (2014). 54. Omnés (2005), 157, 163. 55. Schaffer (2010) holds that it is the world. 56. This differs from Armstrong (2004), 16 “possible intentional objects.” 57. Tim Crane, The Objects of Thought (Oxford: Oxford University Press, 2013), 7. 58. See Hanks (2009). 59. This view seems to be equivalent to a rough synthesis of the views of King (2007), Soames (2010), and King, Soames, and Speaks (2014). It differs in that a proposition is occurrent and ontologically dependent on God’s acting. 60. It follows that propositions are gross abbreviations of divine thoughts. They cannot be as detailed as God’s knowledge of the thing. Propositions play a different representational role in the mind of a created agent than world states play in the mind of God. 61. See Menzel (2001). 62. The expression ‘Fp’ is equivalent to ‘T~p.’ 63. Mac Lane (1981), 471. 64. For appropriate technicality, see Schultz and Winslow (2013). 65. Schaffer (2008), 18–19. 66. Lowe and Rami (2009), 24.

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Vidotto, Francesca. [Talk]: A Relational Ontology from General Relativity and Quantum Mechanics (May 21, 2015, University of Oxford). http://www.philosophy-of-physics.ox.ac.uk/tag/thursday-seminars/; www.philosophy-of-physics. ox.ac.uk/2015/04/23/philosophy-of-physics-research-seminars-tt-2015/ Vidotto, Francesca. [Talk]: Atomism and Relationalism as guiding principles for Quantum Gravity (July 2013, Perimeter Institute, Waterloo, Canada). https://arxiv. org/abs/1309.1403; http://www.hef.ru.nl/~fvidotto/materials/papers/Vidotto_Chicago_13.pdf; https://www.researchgate.net/publication/256441434_Atomism_ and_Relationalism_as_guiding_principles_for_Quantum_Gravity Vidotto, Francesca and Carlo Rovelli, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory. (Cambridge, UK: Cambridge University Press, 2014). Vos, Geerhardus. Reformed Dogmatics, Volume One: Theology Proper. Richard B. Gaffin, Jr. (trans. and ed.). (Lexham Press, (2012 [1896]).

Glossary of Terms

Accident:  That which exists in another and does not express an essential property of thing that it exemplifies. Acquaintance:  A condition in which one has mental content that encompasses not only actual content but also potential content associated with individuals. Actuality:  A state of a “this” which excludes what the thing could be in favor of what a thing is. Algorithm:  An algorithm is a process, set of rules, or finite number of steps to be followed in mathematical calculations (or other problem-solving operations), especially by a computer. It frequently involves repetition of an operation (iteration). Categorial Semantics: The theory of meaning articulated in this paper, which asserts that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. Category:  A broad characterization of things that provide a sense of the real. Coefficient of Alienation:  This is a statistic that measures the lack of linear association between two variables. It represents the proportion of variance in the dependent variable that is not accounted for by the independent variable(s). It is computed by taking the square root of the difference between 1 and the square of the correlation coefficient 1 - r2. Compositionality:  A semantic theory that holds that the meaning of the sentence as a whole is made up of meaning of the parts of the sentence. Conditional Proposition:  A compound proposition of the form “If p then q” which is false when p is true and q is false and otherwise true. Content Variables:  The content variables are selected from the content universe of a specific piece of research. The content universe is the indefinitely 235

236

Glossary of Terms

large hypothetical set of variables relevant to the investigation, based upon the definition of the construct being researched. The domain of the investigation is the Cartesian product of all the facets used to depict the study, combined with a description of the population to be observed (Guttman and Greenbaum, 1998). Contiguity Regions:  In facet theory these hypotheses posit the existence of “contiguity regions” of the elements of each facet. This contiguity implies that every element of a facet is represented by a separate region or area in the geometric configuration, and all variables representing a structuple in each region share an element in common. Convention T:  Tarsky’s semantic theory of truth in which for any sentence “p,” “p” is true if and only if p. Euclidean Space: In geometry, a two- or three-dimensional space within which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula. Existential Import: Propositions which can be true only if the objects of the proposition actually exist. For example, if there are no unicorns, the proposition “Some unicorns are cheerful” is false due to existential import. Extension:  The meanings of a term which are the particular things referred to when the term is used. Facet(s):  In a mapping sentence, multiple, mutually exclusive categories, named “facets,” define the content universe of scrutiny. A facet is a set of attributes (variables) that together represent underlying conceptual and semantic components within a content universe. Shye, Elizur and Hoffman (1994, p. 23) define the facet as a “set that plays the role of a component set of a Cartesian set.” In mathematical terminology the word “set” refers to a collection of items or objects. Within a set, objects are called “elements.” Facets are proposed by the investigator and are comprised of elements that define the different values logically describing the variations within a facet (Brown, 1985, p. 22). To be effective, the elements of each facet must be mutually exclusive, and different facets must be conceptually distinct from each other. (Guttman and Greenbaum, 1998) FACET ELEMENTS (SEE FACET(S)) Facet (Types and Structures of) Axial Facet:

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237

An axial facet generates contiguity regions arranged in a specific order, which is geometrically represented as a sequence of nonintersecting regions produced by some ordering principle. Each region contains variables of one struct (facet element), while the whole set of regions falls along an axis. Conex: The conex structure has a similar appearance to the cylindrex. However, the conex is narrower at one of its ends than it is at its other: The radex at the base of the cylindrex is broader and less focused than the radex at the other end of the cylindrex, which is more focused and results in a cone shape. Cubex: A cubex is formed through combining three simply ordered facets, which results in a cube like structure. Cylindrex: A cylindrex is a structure that has two forms. First, a two-facet cylindrex results from combining an axial facet with a polarizing or modulating facet. Second, a three-facets cylindrex is the result of combining polarizing facet and a modulating facet in the form of a radex with a perpendicular ordered facet: The circular (radex) arrangement of the items repeats itself at each segment as stratum along the axis. Duplex: A duplex is formed by the combination of two axial facets. Modulating Facet: When some elements of a facet are positioned centrally while others are located progressively more at the periphery, the facet plays a modulating role. The corresponding partition of the geometric space appears in the form of circular bands around a central origin, so that the variables most highly intercorrelated fall toward the center, while the progressively less intercorrelated variables are positioned further away from the origin. Polarizing Facet: A facet may be circularly ordered. This specification leads to the hypothesis that the facet plays a polarizing role, where each struct or element of the facet corresponds to a different direction in the geometric space. A facet is designated polar when three or more lines originating at the same pole (center) separate the space by moving in different directions, so that each wedge corresponds to one of the facet’s structs. In a polar facet, the structs (elements) are arranged geometrically as wedge-shaped sections with a common (central) origin (Hackett, 2014). Porex: A porex is a combination of two modulating facets. Radex: A radex is formed by the combination of a polarizing facet with a facet performing a modulating role. 

238

Glossary of Terms

Facet(s) (Varieties of):  Mapping sentences consist of three basic varieties of facets: (a) population, (b) content, and (c) range. Population: designates the population of persons or events that will be sampled. Domain: together with the facets that classify the content of the variables (ABC . . . N), make up the domain of the mapping sentence. Range: the range (R) is the set of response or observational categories specified as being relevant to the investigation. It depicts all possible appropriate responses that could be observed for a given universe. Facet Elements (order of):  These hypotheses predict the order of facet elements. Once a specific facet order is hypothesized, a third hypothesis is made possible, predicting a similar order among the corresponding contiguity regions in the geometric configuration. Facet Hypotheses:  In facet analysis, hypotheses are not merely representations of the way a set of variables is structured; rather, hypotheses almost always depict how the variables (structuples) will appear when portrayed geometrically: they predict how the empirical data will look when plotted or mapped on paper, in accordance with the definitional system—the mapping sentence. Facet Theory (FT): FT is a systematic approach to facilitating theory construction, research design, and data analysis for complex studies, that is particularly appropriate to the behavioral and social sciences. FT is based on (1) a definitional framework for a universe of observations in the area of study; (2) empirical structures of observations within this framework; (3) a search for correspondence between the definitional system and aspects of the empirical structure for the observations. The development of FT and Facet Design is reviewed from early scale analysis and the Guttman Scale, leading to the concepts of “mapping sentence,” “universe of content,” “common range,” “content facets,” and nonmetric multidimensional methods of data analysis. In FT, the definition of the behavioral domain provides a rationale for hypothesizing structural relationships among variables employed in a study (Guttman and Greenbaum, 1998). Function:  Originating in mathematics, it is a relation among inputs in which each input can only be related to one unique output. In other words, a given input cannot have different outputs. Generic:  A type of concept that requires further specification in order to more fully capture entities. Due to its vagueness, it is related to potentiality. Geometric Space:  A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points. The points in a line are said to be incident with the line.

Glossary of Terms

239

Instrumental Training: From the term “instrumental conditioning,” this form of training involves changing behavior based on rewarding behaviors one wants to encourage, and punishing behaviors one wants to encourage. Rewards can be both the addition of something good or the cessation of something bad. Punishments are the opposite. Intension:  The meaning of the term, which helps fix the reference of the term and ideally identified with the necessary and sufficient conditions for the correct use of the term. Mapping:  A mapping is a rule that, to each member of one set, assigns a unique member of another set; in mathematics that means assigning elements in one set, or domain, to elements in another set, or codomain. Mapping Sentence:  The mapping sentence is one of the basic features and primary tools of FT (see Guttman, 1959, 1971; Borg, 1982; Canter, 1985; Levy, 1990; Borg & Shye, 1995). The mapping sentence posits a formal definitional framework for the design of a specific piece of research. It is a hypothesis of the pertinent variables in the research project and their interrelationships and offers a basis for testing of the theorized structure for the relationships between the study’s variables. The mapping sentence defines a priori exactly what is being studied—the population, the content variables, and the range of the possible responses, serving as the definitional and conceptional base of the problem to be studied (Guttman and Greenbaum, 1998). Shye (1978, p. 413), stated that a mapping sentence is “a verbal statement of the domain and of the range of a mapping, including verbal connectives between facets as in ordinary language.” It always consists of two main parts: a formal part made up of the facets and a less formal part comprising the phrases linking the facets together (Shye, 1978, pp. 179–80; Levy, 1990). Mentalism:  The meaning of terms are fundamentally determined by the mental contents of speakers. Name:  A linguistic label given to an object in order identify it. Necessity:  Something that is true in every possible world. Niche:  Implied in the ecological sense to differentiate animals based on habitats? N-Tuples or Structuples:  In FT terminology, n-tuples are finite ordered lists (sequences) of n objects where n is a nonnegative integer. Also called “structuples,” probably because their role consists of structuring the domain of investigation. There is only one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair. Ordered Pair (2-tuples or sequences):  In mathematics, a pair of objects (a,b) is said to be an ordered pair if the order in which the objects appear in the pair is significant. Thus, the ordered pair (a,b) is different from the

240

Glossary of Terms

ordered pair (b,a) unless a=b. If the pairs are unordered pairs, then the pairs (a,b) and (b,a) are equivalent. Perceptual Content:  Mental content that specifically has perception as its origination. Positive Integers:  The positive integers, or natural numbers, are the numbers 1, 2, 3, . . . . Possibility:  Something that is true in at least one possible world. Possible World:  A maximally inclusive situation, which is so complete and comprehensive that it can be described as a world. The only difference between a possible world and the actual world is that the latter actually occurs. Possible World Truth Functional Semantics: A theory of meaning in which the meaning of a particular sentence is the conditions under which that sentence would be true in some possible worlds or state of affairs. Potentiality:  A condition of a “this” by which it can be a number of distinct things it might not actually be or possess a number of distinct characteristics it might not actually have. Predicate:  An expression that signifies some characteristic that can be asserted of a subject. For example, the predicate “tall” can be asserted of “Abe Lincoln.” Primary Unity:  The substance taken without its accompanying accidents. Propositional Attitude: The consideration of a particular mental state as it relates to a proposition. For example, someone can have an attitude of doubt, belief, and so on about a certain proposition. Quality:  An accidental characteristic of substance that indicates the disposition of the substance. Quantification:  An indication of generality in a proposition. Typical quantities of propositions are “all” and “some.” Quantity:  An accidental feature of a substance by which it has parts outside of parts and dimensionality. Rote Memory:  When learning occurs as an isolated association via repetition, without relation to context, or emotion Secondary Unity: The state of a substance along with its accidental characteristics. Set Theory:  Set theory is a theory from mathematics concerned with mathematical logic. Set theory addresses sets, which are well-determined collections of objects and items. While any form of object may be gathered into a set, it is usual for set theory to be used with mathematically relevant objects. Smallest Space Analysis (SSA): SSA is an analysis procedure from FT. SSA allows researchers to evaluate the extent to which the geometric structures, hypothesized from the mapping sentence are present in empirically

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collected data. SSA is a form of nonmetric multidimensional scaling (MDS) where variables and their intercorrelations are geometrically portrayed in space. SSA graphically presents the relative sizes of the observed relationships between variables in terms of the proximity of variables in this space of multiple dimensions. Thus, two points are closer if the correlations between the corresponding items are higher. SSA attempts to find the space with the minimum number of dimensions in which the rank order of relations will be preserved (Guttman and Greenbaum, 1998). Sortal:  A classification criterion by which individuation conditions are established for objects. Specific:  A technical term for types of concepts that are a production of a genus and specific difference. It corresponds to actuality. SSA Algorithm:  The algorithm underlying SSA consists of the four phases: Starting configuration; Standardizing distance, and coordinate estimate; Nonmetric phase; Metric phase. Iterations continue until an improvement in the coefficient of alienation from one iteration to the next falls below some suitable number set by the researcher. Substance:  Something that does not exist in another thing: For example, a dog or a tree is a substance. This:  A technical term that identifies the basic potentiality to be anything that could be and is a particular. Truth Function:  A function in which if a truth value is the input, it will always have a truth value as an output. For example, p & q will have a truth value if p has a truth value and q has a truth value. Truth Value:  The property of a proposition as either true or false. Vagueness:  A situation in which a proposition is neither exactly true nor exactly false about the situation. For example, at certain point of time and place it is neither exactly true nor exactly false that the sun has set. REFERENCES Borg, I. (1982) Some Basic Concepts of Facet Theory, in Davies, P.M., & Coxon, A.P.M. (eds.), Key Texts on Multidimensional Scaling, 193–228, London: Heinemann. Borg, I., & Shye, S. (1995) Facet Theory: Form and Content (Advanced Quantitative Techniques in the Social Sciences), Thousand Oaks, CA: Sage Publications, Inc. Brown, J. (1985) An Introduction to the Use of Facet Theory, in Canter, D. (ed.) Facet Theory: Approaches to Social Research, 17–58. New York: Springer Verlag. Canter, D. (ed.) (1985) Facet Theory: Approaches to Social Research, New York: Springer Verlag. Guttman, L. (1959) A Structural Theory for Intergroup Beliefs and Action. American Sociological Review 24, 318–328.

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Guttman, L. (1971) Measurement as Theory. Psychometrika 36, 329–347. Guttman, R., & Greenbaum, C.W. (1998) Facet Theory: Its Development and Current Status. European Psychologist 3(1), 13–36. Hackett, P.M.W. (2014a) Facet Theory and the Mapping Sentence: Evolving Philosophy, Use and Application, Basingstoke: Palgrave McMillan Publishers. Levy, S. (1990) The Mapping Sentence in Cumulative Theory Construction: Wellbeing as an Example, in Hox, J.J., & deJong-Gierveld, J. (eds.), Operationalization and Research Strategy, 155–177, Amsterdam: Swets and Zeitlinger. Shye, S. (1978) Theory Construction and Data Analysis in the Behavioral Sciences, San Francisco: Jossey-Bass. Shye, S., Elizur, D., & Hoffman, M. (1994) Introduction to Facet Theory: Content Design and Intrinsic Data Analysis in Behavioral Research. Applied Social Methods 35, London: Sage.

Index of Authors

Ackrill, J. L., xv, xxiii, 137, 156 Adams, S., 227–28 Aizawa, K., 202, 204, 226, 228, 229 Aldenderfer, C. P., 187–88, 196–97 Alston, W., 210, 227, 229 Alt, D., 140, 156 Alyagon, M., 194, 197 Amar, R., 155, 159 Andersson, M., 6, 14 Andersson, S., 4, 14 Anjum, R. L., 228, 231 Anscombe, G. E. M., 96, 104 Aquinas, T., 82, 83, 202 Aristotle, xv–xvi, xx–xxiii, 65, 71–72, 82, 87, 135, 137, 149, 150–52, 150, 156, 204 Armstrong, D. M., 226, 228, 229 Asen, Y., 1, 14 Audi, R., xvi, xxiii, 8, 9, 101 Austin, J. L., 35, 129, 131, 168 Avarguès-Weber, 1, 15 Awodey, S., 141, 156 Baars, B., 97, 103, 105 Bacon-Kaufman, E., 194, 197 Bar, A.J., 190, 197 Barsalou, L. W., 136, 157 Baxter, D.L.M., 148, 157 Beauducel, A., 140, 157

Beebee, H., 225, 226, 229 Beghtol, C., 139, 140, 157 Bell, J. S., 99, 215, 228, 229 Bentley, A., xxi, 108, 119–25, 130, 131, 133 Bergb, M. E., 15 Bergmann, S., 156, 157 Biederman, I., 4, 16 Bigaj, T., 227, 229–31 Bilsky, W., 171, 176, 197, 199 Bird, A., 229 Blashfield, R. K., 187, 196, 197 Block, N., 98, 105 Bloom, J., 228, 231 Blough, D. S., 4, 15 Boakes, R., 7, 17 Bodily, K. D., 7, 16 Bohler, J., 129, 131 Bolzano, B., 51 Bonner, J.T., 136, 157 Book, D. L., 9, 15 Boomer, J., 15 Borg, I., 140, 157, 171, 182, 197, 198, 199, 239 Brady, G., 128, 132 Braine, D., 83, 84, 229 Brentano, F., 37–38, 39, 51, 55, 63, 64 Brocke, B., 157 Brown, C. H., 7, 15, 236, 241 243

244

Index of Authors

Bugnyar, T., 9, 16 Burgess, A., 229 Cable, C., 3, 16 Calosi, C., 156, 157 Campbell, R., 215, 228, 229 Canter, D., 10, 15, 140, 156, 157, 159, 161, 171, 197, 198, 239 Cantor, G., 51, 63 Carnie, A., 84 Carruthers, P., 34, 35 Cassam, Q., 35 Chalmers, D., 87, 105, 232 Cheney, D., 9, 16 Chisholm, R.M., xv, xxii, 137, 157 Chivers, D. P., 6, 15 Clark, A., 87, 105 Clayton, N. S., 10, 15 Cohen, E. J., 10, 15 Cohen, H., xvii, xviii Comte, A., xxi, 107, 108, 124 Cook, R. G., 1, 11, 14, 15, 16 Correia, F., 225, 229, 230 Corver, N., 145, 157 Cotnoir, A. J., 148, 157 Cottingham, J., 35, 89, 105 Crane, T., 101, 105, 226, 228 Cresswell, M. J., 82, 84 Crossley, M. J., 15 Culicover, P. W., 84 Cumpa, J., 84, 85 Daballen, D., 9, 15 David, S. J., 10, 15 Davidson, D., 81, 82, 83, 84 Davison, M. L., 182, 187, 188, 193, 197 Dawis, R., 190, 191, 193, 198 Dehaene, S., 97, 103, 105 Dennett, D., 229 Descartes, R., xvi, xx–xxi, 26, 35, 87–96, 99–104, 105 Dewey, J., xxi, 108–9, 119–27, 130, 131, 132, 133 Dieks, D., 228, 230 Dipert, R., 128, 132

DiSalle, R., 215, 228, 229 Dodd, J., 225, 226, 229 Dorato, M., 215, 227, 288, 299, 230 Doring, A.K., 176, 197 Douglas-Hamilton, I., 9, 15 Dowker, Fay, 227, 230 duToit, S.H.C., 141, 157 Edwards, J.C.W., xx, 87, 99, 105, 227, 230 232, 253–54 Elizur, D., 159, 161, 170, 175, 177, 178, 179, 180, 184, 184, 189, 193, 194, 197, 199, 236, 242 Ellis, B., 64, 228, 299 Emery, N. J., 10, 15 Emirbayer, M., 108, 124, 131, 132 England, G.W., 131, 132, 133, 193, 197 Evans, G., 84 Fagot, J., 4, 16 Feigl, H., 130, 132 Ferrari, M. C. O., 6, 15, 16 Feser, E., 227, 230 Feynman, R., 91, 105 Fine, K., 9, 230 Frege, G., 34, 35, 45, 48, 49, 51, 62, 63, 82, 83, 84, 108, 121, 122 Freud, S., 100, 105 Friedman, A., 16 Fries, C.C., 156, 157 Gadamer, H.G., 142, 149, 157 Gainotti, G., 137, 157 Gallagher, S., 87, 105 Garfield, J. L., 84, 85 Ghirardi, G. C., 215, 227, 230 Gillet, C., 202, 204, 226, 228 Giurfa, M., 1, 15 Gnassounou, B., 228, 299, 230 Goldenberg, S. Z., 9, 15 Goldstone, R.L., 12, 15 Gonzalo, A., 6, 15 Goodnight, J.H., 190, 197 Gorman, M., xvii, xxiii, 85

Index of Authors

Grace, R. C., 15 Gracia, J. J. E., 85 Graziani, P., 156, 157 Greenbaum, C.W., 194, 197, 236, 238, 239, 241, 242 Greggor, A. L., xvii, 1, 10, 15 Groenen, A.P., 171, 176, 197 Groff, R., 228, 230 Guttman, L., xxi, xxii, xxiii, 139, 140, 155, 156, 157, 158, 161, 165, 166, 168, 169, 170, 171, 173, 174, 175, 178, 179, 180, 181, 183, 191, 193, 196, 197, 198, 199, 236, 238, 239, 241, 242 Haaparanta, L., xvi, xvii, xxiii, 63 Hackett, P.M.W., vii, xv, 1, 10, 15, 135, 140, 141, 147, 149, 155, 156, 158, 172, 173, 198, 237 Hagar, A., 227, 230 Hailman, J. P., 5, 16 Hall, A.W., xv, xxiii, 159 Handfield, T., 228, 230 Harman, G., 81, 84 Harre, R., 228, 230 Harris, D. J., 6, 16 Harte, V., 148, 158 Heidegger, M., 123, 132, 142, 158 Heil, J., 225, 230 Hendrickson, A.T., 12, 15 Henry, D.P., 85, 105, 156, 158 Hestroni, A., 140, 158 Herrnstein, R. J., 3, 16 Hildebrandt, L., 10, 16 Hill, C. O., xix, xx, 37, 45, 48, 50, 51, 55, 62, 63 Hilpinen, R., 128, 132 Hintikka, J., 81, 84 Hoffman, M., 159, 161, 179, 199, 236, 242 Hookway, C., 129, 130, 132 Hubel, D. H., 97, 105 Huber, L., 2, 3, 16 Hume, D., 25, 27, 35

245

Hurley, S., xxiii Husserl, E., xix–xx, 38–62, 63, 64 Inhedler, B., 137, 159 Jacobson, P., 82, 84 Jairo José da Silva, 63 Jakobsson, S., 6, 17 James, W., 96, 105, 107, 121, 126, 132, 227, 231, 232 Janik, M., 171, 197 John, G., 69, 78, 79 Kahn, R.L., 191, 198 Kaiser, H.F., 187, 188, 198 Kant, I., xix, xxi, 20, 21, 21, 34, 35, 36, 37–38, 51, 107, 109, 110–12, 118, 128, 132 Kaplan, G., 12, 16 Katz, D., 191, 198 Katz, J. S., 7, 16 Kedar, Y., 179, 198 Kefer, M., 84 Kelly, G.A., 137, 157, 158 Kenny, C., 171, 198 Kim, A., 159 Kim, J.O., 188, 194, 196 King, J. C., 46, 77, 228, 230 Kistler, M., 228, 229, 230 Kiteley, M., 84, 85 Klammar, T. P., 145, 158 Klima, G., xv, xxiii Knapp, T., 130, 133 Knuuttila, S., 81, 84 Koo, J., 159 Koskinen, H. J., xvi, xvii, xxiii, 63 Koslicki, K., 204, 226, 230 Koval, E., 158 Kressley, R. A., 7, 15 Kruskall, J. B., 179, 198 Kvanvig, J. L., 226, 227, 230 Lakoff, G., xxiii, 83, 84 Lamberts, K., xxiii

246

Index of Authors

Lambon, R. M. A., 137, 158 Lasnik, H., 84 Larson, R., 83, 84 Lefebvre, C., xvii, xxiii Leibniz, G. W., xx, 51, 87, 89, 91–92, 96, 98, 100, 105, 226, 227 Leighton, R. B., 105 Levy, S., 10, 14, 16, 140, 158, 168, 170, 172, 173, 174–75, 174, 177, 196, 198, 239, 242 Lewis, D., xx, 66, 82, 84 Lewycky, R., 179, 186, 199 Libet, B., 103, 105 Liepmann, D., 157 Liggins, D., 207, 226, 230 Lind, J., 6, 17 Lingoes, J. C., 176, 179, 181, 198 Lofquist, J. H., 190–91, 193, 198 Lombardi, O., 228, 230 Lorr, M., 187, 198 Loveland, D. H., 3, 16 Lowe, E. J., xv, xxi, xxiii, 82, 84, 135, 137, 150–51, 158, 225, 226, 228, 231 Lycan, W. G., 82, 83, 84 McCann, H. J., 226, 227, 230 Macdonald, C., 226, 231 Machery, E., 138, 158 Mackintosh, N., 5, 7, 16, 17 MacLane, S., 231 Mac Lane, S., 144, 159, 120, 228, 231 Madden, E. H., 228, 230 Mangini, M. C., 4, 16 Marler, P., 9, 16 Marmodoro, A., xiii, 204, 225, 226, 228, 230, 231, 232 Martin, C. B., 215, 227, 231 Martin-Malivel, J., 4, 16 Maslow, A. H., 188, 198 Massen, J. J. M., 9, 16 Massin, O., 231 McDowell, J., 84 McMahon, W., 82, 85 Menzel, C., 227, 228, 231 Messier, F., 6, 15

Midtgarden, T., xxi, 107, 128, 129, 130, 131, 132 Minsky, M., 104, 105 Misch, Georg, 61 Moltmann, F., 156, 159 Morris, C. W., 122, 123, 132, 230 Mueller, C. W., 188, 194, 196, 198 Mumford, S., 228, 231 Murphey, M. G., 128, 132 Murphy, G. L., 15, 138, 159, 229 Nestor, P. J., 159 Ney, A., 226, 231 Novák, L., 228, 231 Novotný, D. D., 228, 231 Oakes, L. M., xxiii, 7, 17, 82, 83 Oakes, R., 227, 231 Omnés, R., 228, 231 Örnborg, J., 4, 14 Pasnau, R., 85 Pašukonis, A., 9, 16 Patterson, K., 137, 158, 159 Peirce, C. S., xxi, 107–27, 128, 129, 130, 131, 132, 133 Perry, J., 35, 36 Piaget, J., 137, 159 Poli, R., 63, 147, 159, 226, 231, 232 Poole, G., 85 Pospesel, H., 146, 159 Priest, G., 146, 159 Qadri, Muhammad, A. J., 11, 16 Quine, W., 37–39, 51, 55, 61, 64, 68, 77, 80, 215, 228, 231 Rabenu, E., 166, 170, 176, 178, 194, 199 Radford, A., 85 Rakison, D. H., xxiii, 82, 83 Ranganathan, S. R., 139–40, 159 Raven, M. J., 176, 231 Reynolds, M. L., 194, 199 Rickles, D., 228, 231

Index of Authors

Riemsdijk, H., 145, 157 Rimini, A., 215, 227, 230 Rimmer, A., 169, 175, 178, 199 Robin, R. S., 128, 133 Rogers, T. T., 159 Rosado Haddock, G. E., 63, 64, 254 Roskam, E. E., 181, 198 Ross, J. F., 227, 232 Rovelli, C., 227, 228, 233 Russell, B., xx, 38, 45, 48–49, 50, 64, 83, 85, 108, 121–22, 229, 231 Ryan, F. X., 130, 131, 133, 232 Ryle, G., 87, 90, 93–95, 97, 98–99, 104, 105 Sag, I. A., 85 Sakamoto, J., 1, 17 Sall, J. P., 190, 197 Sands, M., 105 Sanford, J., xvii, xviii, 85 Sankey, S., 228, 229 Saunders, D. R., 187, 199, 120, 231 Sayde, J. M., 11, 16 Schaffer, J., 207, 226, 228, 232 Schiffman, S. S., 194, 199 Schmidt, J., 9, 16 Schultz, W. J., viii, xxii, 201, 227, 228, 232 Schwartz, S. H., 157, 177, 199 Searle, J. R., 129, 133 Segal, G., 83, 84 Seibt, J., 147, 159, 216, 226, 228, 231, 232 Sevush, S., 99, 105 Seyfarth, R., 9, 16 Shanks, D. R., xxiii Sharoni, G., 178, 199 Shettleworth, S., 5, 6, 7, 8, 16 Shkoler, O., 178, 199 Shye, S., 140, 155, 157, 159, 161, 172, 179, 182, 185, 197, 198, 199, 236, 239, 241, 242 Sih, A., 6, 16 Simmons, H., 156, 159

247

Simons, P., 205, 225, 226, 232 Sinnott, J. M., 7, 15 Smolin, L., 228, 232 Soames, S., 228, 230, 232 Socrates, 52 Solomon, E., 197, 198, 199 Soto, F. A., 137, 159 Spetch, M. L., 4, 16 Steyn, A. G. W., 157 Strawson, G., 35 Strawson, P. F., 27, 28, 35, 36 Stumpf, R. H., 157 Symes, L. B., 8, 17 Symington, P., vii, xx, 65, 85 Tahko, T. E., 225, 226, 227, 228, 232 Thomasson, A., 81, 85 Thompson, R., 7, 17 Thornton, A., 10, 15 Tilman, R., 130, 133 Tinbergen, N., 5, 17 Tulving, E., 98, 105 Tziner, A., viii, xi, xxii, 161, 166, 169, 175, 177–78, 183, 184, 184, 188, 189, 190, 191, 196, 199 Urbanaik, R., 156, 159 Vallicella, W. F., 225, 227, 232 Vallin, A., 6, 17 Van Bendegem, J. P., 227, 232 van der Auwera, J., 84 Vasiliu, C., 178, 199 Vélez Latorre, L., 140, 159 Vidotto, F., 227, 228, 233 Volpe, A. D., 158 Vos, G., 226, 233 Wakita, M., 1, 17 Wasow, T., 85 Wasserman, E. A., 137, 159, 232 Watanabe, S., 1, 17 Weber, T., 215, 227, 229, 230 Weisler, S., 82, 85 Westerhoff, J., xv, xxiii, 85

248

Weyl, Hermann, 61, 215 Whitehead, A. N., 50, 64 Wiesel, T.N., 97, 105 Wiklund, C., 6, 17 Wilson, B., 7, 10, 17 Winslow, L. D. A., 225, 227, 228, 232 Wittemyer, G., 9, 15 Wittgenstein, L., 34, 36, 63 Wo, L., 140, 159 Wright, A., 7, 16, 229 Wüthrich, C., 227, 229, 230, 231

Index of Authors

Yaniv, E., 199 Yates, D., 225, 226, 230, 231, 232 Yehezkel, G., vii, xix, 19, 36, 136 Young, F. W., 179, 180, 186–87, 193, 194, 196, 199 Zadeh, L. A., 156, 159 Zahavi, D., 87, 105 Zeman, J. J., 128, 133

Subjects Index

abstract categorization, xix, 1–5, 7–8, 12, 14, 136 abstractness, 115–16, 138 accident, 71–72, 77, 235, 240 acquaintance, 74–76, 83, 123, 131, 235 actuality, xx, 67, 71, 73, 73–83, 235, 241 aggregate, 58, 90–92, 99, 185 algorithm, 180–82, 182, 186, 235, 241 analyticity, xx, 51 animals, xv, xviii, xix, 1–14, 65, 68, 73–74, 78, 83, 89–90, 98, 126–27, 131, 136–37, 239 animals, human, xv, xvii, 1–2, 4–5, 10–11, 11, 14, 73–74, 78, 89–90, 98, 126–27, 136–37 animals, nonhuman, xv, xviii, xix, 2, 126–27 antitypy, 92 the a priori, 41, 45, 54, 195 Aristotle’s categories, vii, xv, xvi, xx, xxi, 65, 71–72, 87, 135, 137, 149–51, 151, 156 attributes, 73, 107, 126, 139, 144, 145–46, 146, 151, 155, 236 axioms, 40–41, 43, 48, 52, 56–60, 81, 120, 123, 204, 220, 236

behavioral responses, 1, 2, 194 behaviorism, 100 biases, 4–6, 14 boson, 92 broadcasting (neural), 97–99 Cartesian space, xxi, 91, 168–69 categorical semantics, 83 categories: different species and, 1–2, 4–5, 7–10, 12, 14, 136–37; flexible, 8–9, 66, 83, 142; functional, xix–xx, 5–7, 12–13, 66, 80, 108, 126; number of, xv, 8–9, 43, 57, 60, 128, 151; perceptual, xix, 2–8, 12–13, 66, 80–82, 136, 155 categorisation: abstract, 1–2, 5, 7–8, 12–14, 123; animal, xix, 1–2, 4–14, 136–37; human animal - non categorization, rule based, 2, 10; incorrect, 1 category / categories, necessary, vii, xix, 19, 22–23, 25, 28, 30–31, 33–34, 41, 45, 47, 74

249

250

Subjects Index

category: complexity, xv, xix, 8–10, 12, 14, 139; construction, 14, 49; flexibility, xix, 2, 9, 12, 14; generalization, 6, 114, 119; learning, 5–6, 8–10, 13; membership, xvi, 2–3, 5, 8–9, 13, 69; abstract relationships, 5, 13, 114; functional similarity, 5, 13; perceptual similarity, 2, 4, 5, 6, 13; category-mistake, 87, 90, 97 number, 8–9, 41; theory, xvi, xvii–xviii, 40, 41, 48–50, 51, 53–58, 60, 61–62, 65–67, 69, 71, 73–74, 80–81, 83, 119, 124–25, 130, 135, 137, 139, 140–42, 235; usage, ix, xvi, xix, 10–14, 11, 137 Classification, xvi, xxi, 107, 108, 112, 114–15, 117–18, 120, 122–23, 126, 139–40, 155, 165, 166, 183, 241 coefficient of alienation, 179–83, 191, 235 cognitive, xvii, xix, xxiii, 1–2, 4–6, 8–10, 12, 14, 19, 42–43, 54, 83, 112–15, 122–23, 130, 138, 166–67, 172–73, 175–76, 179, 191, 218, 221 complexity, xv, xix, 1, 8–10, 12, 14, 121, 139, 155, 222 compositionality, 67–70, 235 concept of mind, the, 87, 93 concepts, xxii, 1–2, 14, 19–22, 24, 33, 38, 40–44, 47–49, 51–54, 56–58, 72, 87, 93, 95, 98, 103, 118, 135–36, 138, 140, 143–44, 146, 155, 166, 194, 201, 202, 218, 225, 238, 241 conceptual: analysis, 19–20, 22, 34; dimension, 21, 27–28, 28;

scheme, xv, 21, 27; structure, xix, 19, 33 conditional proposition, 203, 235 connective ontology, 144–45, 154 conscious experience, xix, 19–20, 22–23, 25 consciousness, xix, 19–20, 22, 23–35, 95, 98–99, 119, 136, 218 constitutive essential dependence, 204 content variables, 146, 235, 239 contiguity regions, 171–72, 183, 236–37 convention T, 81, 236 dependence, xxii, 33, 123, 127, 178, 201–6, 208, 212–16, 222–24 differentness, 1 discrimination training, 3 divine action, xxii, 201, 207–14, 216, 218, 223–25 dualism, 92–93, 96, 100 elements, of facets, 11–13, 141–42, 144–45, 152, 154–55, 166–68, 173, 175–76, 178, 190, 195, 236–38 empiricism, xix, 37–38, 51, 61, 120 essentialism, 37 evolution, xix, 2, 6, 8–9, 108, 113, 120, 126, 128–29, 136–37 evolutionary advantage, 9, 136 experience, vii, xvii–xx, xxiii, 5, 7, 13, 19–20, 22–26, 28, 30–31, 33–35, 39–40, 66–67, 70, 72–73, 77, 81, 88–90, 93–104, 108–16, 118, 120–21, 125, 127, 129, 136–38, 142, 144, 146, 148, 154–55, 167, 210, 215–16, 218 extended mind, 87, 95 extension, xviii, xx–xxi, 23, 47, 49, 65–68, 78–81, 91–92, 145, 175, 215, 236 Euclidean: plane, 162; space, 179–80, 186, 236

Subjects Index

evolution of categorization, 8 existential: dependence, 202–3, 212, 214, 224–25; import, 78, 236; extension, xviii, xx, 23, 49, 65–68, 91–92, 145, 175, 236 faces, 4 facet: axial role, 172, 172, 175–77; background, 152, 154; elements, 11–12, 145, 154–55, 168, 171, 236, 238; order of, 171, 238; hypotheses, xxii, 13, 140, 152, 155, 161–62, 170–73, 177–79, 195, 236, 238–39; modulating role, 173–78, 174, 237, 250; polarizing role, 173, 175–76, 178, 237; range facet, 11–12, 141–43, 146, 153–54, 156, 170 facet theory (FT), xvi—xviii, xxi–xxii, 14, 135, 137, 139, 140, 141, 142, 147–49, 152, 155–56, 168, 194–95, 236, 238; philosophical, xvi, xvii, xviii, xxi, 135, 137, 140–42, 147, 152, 155; qualitative, xxi, 135, 142, 147, 149, 152, 155 facet(s), xvi–xviii, xxi–xxii, 10–14, 135, 137, 139–49, 152–56, 161–62, 165–79, 172, 173, 174, 182–85, 190–92, 194–96, 236–39; connective ontology, 144, 154; content ontology, 154 firstness, 108, 113–15, 117–22, 124, 126, 128–30 first-person, 23, 25–30, 27, 28, 30, 35 foraging, 1, 7–8

251

form, xxi, 40–48, 53–61, 82, 90–92, 107–16, 123, 131, 145–49, 169, 176, 187, 216, 219, 235, 237, 241 formal logic, 38–39, 41–44, 51, 58, 60–62, 108–9, 111, 121, 141 function, xvii, 2, 20, 21, 27, 44, 45, 48–49, 68–69, 73, 75–78, 82, 100–2, 110, 131, 138, 141–42, 145, 156, 164–68, 179, 182–83, 186–87, 196, 211, 215, 235, 238, 250 functors, 144–45, 156 fuzzy logic, 146, 156 gender categories, 126, 156 generic, xxii, 72, 73, 113, 120, 201–2, 208, 212–13, 224–26, 238 genetic, 5 geometric space, xxii, 162, 173–74, 176, 183, 237–38 ‘Ghost in the Machine’, 87, 93–94 hermeneutical consistency, 142, 149 hermeneutic circle, 123 human animal differences, 2, 4, 137 hypothesis testing, 178, 239 icon, 108–11, 113, 115–16, 128 ideality, 37–38, 40, 43, 44–45, 47, 55–57, 61, 83, 117–19, 123, 129, 213 identity dependence, 202, 205, 213–14, 224 illocutionary effects, 117 independence, 186, 186–87, 189, 191, 192, 226 index, 20, 27, 108–10, 114, 154, 182, 221 indivisible, 90, 92, 99, 103, 250 intension, xx, 65, 239 intentionality, 37–39, 61, 72 interactionism, 92 interpretant, 115–17, 122–23, 128–30, 250

252

Subjects Index

laboratory test, 2, 4 language, xx, 5, 20, 22, 34, 66, 73, 79, 81–83, 89–90, 94, 98, 108–10, 116–17, 120–23, 175–76, 226, 239 laws, xxii, 33, 37, 39–41, 43–47, 51–54, 56, 58–60, 92, 95, 114, 116, 124, 151, 201–2, 209, 224 learning, 5–6, 8–10, 13, 109–111, 115, 140, 194, 240 linguistic category, xvii, 65, 114–17, 135, 141, 143 logical positivism, xxi, 108, 120, 122 Lowe’s ontology, xv, 150–52, 151 manifolds, xx, 57–61 mapping, xviii, xix, xxi, 10, 11–14, 21–23, 110, 135, 137, 139–156, 143, 144, 146, 161, 164–67, 169–71, 178–79, 185, 195, 236, 238–40 mapping, of a mapping, 10, 143, 144 mapping sentence, xix, xxi, 10–15, 11, 30, 135, 140–149, 143, 144, 146, 150, 151–56, 151, 153, 161, 165, 167, 169–71, 178–79, 185, 195, 236, 238–40; ability, 10–12; indicator(s), xix, 10, 12, 14; range, 11–13, 141–48, 143, 144, 152–54, 156, 169–70, 238–39; referent, 12; situation, 12, 144, 149, 169, 240; status, 12, 149, 156; type, 12, 143, 144, 146, 171 mapping sentence, declarative, xxi, 135, 141–42, 143, 144, 146–50, 146, 150, 151, 151, 152–54, 153, 155–56 mapping sentence, general, 135, 142, 146, 146 materialism, xx, 87, 91, 93, 99 mathesis universalis, 51, 56

meaning, xviii, xx, 7, 20–24, 28–30, 33–34, 37, 40, 42–48, 50–56, 58–60, 62, 65–71, 74–83, 88, 91, 117, 120, 142, 144, 147–48, 154, 161, 174, 186, 189, 190, 192–94, 192, 193–94, 235, 232, 235, 236, 239, 240; theory of, xx, 20–21, 40, 66, 68, 70–71, 80–81, 235, 240 meaningfulness, 20–21, 29–30 meditations on first philosophy, 26, 88, 90, 91 memory, short-term, 97, 103 mentalism, 239 mental (versus physical), 25, 28, 61, 87–88, 99–100, 202, 218–19, 223 mereology, xvi, 135, 140, 142, 144, 148–49, 154, 156, 204 meta-mapping, 153–54 metaphysics, xvii–xviii, 37, 42, 50, 61, 96, 113–16, 120, 124, 126, 147–48, 207, 209, 225 morphism, 141, 156 natural regularities, xix, 19, 30–33, 35 negative existential, 207, 223 neural, 2, 99, 137 neuron, 93, 96, 103 neuroscience, 87, 93, 98–99, 103 New Zealand robin (Petroica australis), 136 n-tuples, 163–64, 168, 239 objective reality, 19–20, 25, 30–33 objectivity, xix, 19, 22, 24–25, 30, 33, 35, 40, 41, 53, 54, 63 objects, xv, xix, 4–6, 37–38, 40, 42–44, 47–49, 52, 58, 60, 61, 66, 68, 69, 72, 77, 79, 81–82, 92, 97, 99, 111, 114, 116, 122, 124, 137–38, 141, 143, 151, 162, 204, 211, 213–16, 218–19, 222, 228, 236, 239, 240, 241 observer, 89, 95

Subjects Index

253

ontological: containment, 204; dependence, xxii, 201–8, 212–18, 222–27; ontology, xv–xvi, xxii, 12, 40, 43, 54, 62, 81, 83, 141, 140–42, 144, 147–56, 151, 201, 209, 211–12, 214–16, 218, 222–23, 226, 227; structural, 140, 142, 144, 144, 147, 149, 152 ordered pair (2-tuples or sequences), 162–63, 239–40

136–38, 140, 142, 144, 144, 152, 153, 154, 168, 186, 187, 196, 205, 209, 213–16, 218, 235 profile analysis, 13 proposition, 21–22, 24, 27–29, 31, 34–35, 39, 43–44, 46–47, 51–54, 57–61, 68, 78–79, 116, 141, 203, 206–8, 217–24, 226, 228, 235–36, 240–41, 249, 251 propositional attitude, 218, 221–24, 240 propositional sentence, 142 pure logic, 40, 42, 47, 51, 53, 54

paintings, 1 partial order scalogram analysis (POSAC), 13–14, 179, 194–95 passion (Cartesian), 89 perception, 31–32, 66, 140, 210, 240 perceptual sharpening, 5 personal construct theory, 137 phenomenology, xix, 39, 61–62, 108, 112, 115–16, 118–23, 126–27, 218 point of view, xx, 20, 26–30, 33, 38, 56, 70, 77, 89, 117 polyzoism, 96 positive integers, 162, 240 possible world, xx, 66–70, 73, 75, 78, 82, 227, 239–40 possible world truth functional semantics, 67, 240 potentiality, xx, 67, 71, 73–83, 73, 235, 238, 240, 241 pragmatism, 107–08, 126 predicate, 28, 42, 44, 48–49, 53–55, 65, 66, 71–72, 78, 111, 113, 120, 206, 213, 128, 240 preimage, 164 preverbal categories, 136 primary unity, 72, 240 problem solving, 60, 177, 184, 235 process, xv, xviii, xxi–xxii, 4–5, 10–11, 26–27, 31, 41, 72, 74, 80, 82, 89, 97, 99–103, 108, 121–23,

quality, 43, 65, 72, 74, 82, 98, 113, 119–20, 128, 145, 154, 156, 240 quantification, 78, 240 quantity, 57, 65, 72, 78, 82, 156, 240 reality, xviii, xix–xx, 5, 19–20, 25, 26–27, 29–35, 37–39, 41–42, 51, 61–62, 66, 74, 80, 83, 104, 116, 124, 126, 129, 138, 206, 208–9, 216, 218, 221–23, 225 recognition, 4, 22, 26, 91, 95, 137, 186, 189, 191, 192 reward, 3, 5, 190, 191, 239 rote memorization, 2 rule learning, 9–10 Russell's paradox, 48–50 Sameness, 58 secondary unity, 72, 74, 75, 240 secondness, 108, 112, 114–16, 118–22, 124–26, 129 selective pressures, 1, 7 self, xxi, 7, 19–20, 23, 25–31, 33–35, 98, 124, 195 self-ascription, 26–28 self-consciousness, xix, 19–20, 25–29, 33–35 set, elements of a set, 162, 252 set inclusion, xv; intersection, 68;

254

Subjects Index

set difference, xx, 48–49, 51; Cartesian product, 163–64, 168–70, 236; set(s), xv–xvi, 10–11, 40, 43–44, 48–50, 54, 56, 60, 66–70, 74–75, 77, 81–83, 117, 123, 138–39, 141–42, 147, 156, 161–70, 164, 172, 182, 193–95, 203, 215–17, 221–22, 227, 235–41 set theory, xx, 40, 48–50, 60, 82, 221, 240 sign, xxi, 5, 20, 58, 108–18, 120, 122–23, 129, 196 sign stimulus, 5 similarity, 2, 4–6, 13, 179, 184, 193 slime mold, 136 smallest space analysis (SSA), 13–14, 179–80, 182–83, 182, 185, 190–91, 193–96, 240, 241 solipsist, 19, 27–28, 33, 72 sortal, 68–69, 82, 241 specific, xv, xx–xxiii, 1, 4, 8–12, 11, 20, 42, 46, 54, 58, 68, 70, 72, 73, 91 speculative grammar, 109, 111–15, 123 spirit, xx–xxi, 88–92, 101, 209 SSA algorithm, 180, 182, 241 stimuli, ix, 1–8, 3, 10, 13, 98, 101, 165, 166 structuples, 168–72, 184–85, 238, 239 structure, xv, xvii–xx, xxii, 19, 22, 33–34, 26, 37–43, 37, 46–47, 50, 54, 56, 62, 66–67, 69, 74, 80–83, 92, 98–99, 103, 110, 113, 115–16, 135–37, 139–42, 146–53, 155–56, 162, 167, 170–71, 175–79, 183–88, 191, 193–95, 201–2, 204–5, 209–10, 213, 215–18, 220–22, 224–25, 227, 236–39 subjective, 24, 38, 44, 47, 55, 96, 100, 101, 115, 119, 152, 154–55, 168, 187

subject of consciousness, 26–27 substance (Cartesian), 88, 91, 124, 252 supernormal stimulus, 6 symbol, 108–9, 115, 128–29, 221 thirdness, 108, 112, 115–19, 121–22, 124–26, 128, 129 third-person, 25–26 time / temporal, 19, 29–30, 30, 32–33, 93, 98, 145, 212, 221, 222 training, 3, 3, 107, 239 transactionalism, 119–20, 123, 125, 126, 131 transcendental phenomenology, 39, 61–62 truth, xx, xxi, 24, 29, 31, 34, 38–40, 43, 45–48, 52–55, 59, 61, 66–71, 75, 77–78, 80–83, 103–4, 107, 109–10, 112–13, 121–22, 129, 141–42, 145–46, 149, 205–8, 221, 224, 226, 235, 236, 240, 241 truth function, 241 truthmaker principle, 206, 222, 224; maximalism, 207 truthmaking, xxii, 202, 206–8, 212, 216–17, 221–25 truth value, 67, 78, 80, 241 two-facet structures, 175; conex, 178, 237; cylindrex, 177–78, 237; duplex, 176, 177, 237; porex, 178, 237; radix, 175–78, 191, 237 vagueness, 73, 80, 238, 241 vertical relations, 202, 205 wholes and parts, xx, 43–44, 48, 252 widersinnigkeiten, 49

About the Editor and Contributors

Jonathan C. W. Edwards is an Emeritus Professor of Medicine at University College London. Since 2005, he has been interested in the overlap between the biophysics of perception and philosophy of mind. He has a particular interest in the Enlightenment scholars of the seventeenth century and specifically Leibniz and Descartes. His own work focuses on the importance of biophysical events in individual neurons to phenomenal representation within the brain. The central motivation for this work is the premise that correspondence between phenomenal experience and physical dynamics must be consistent with the principle of locality in order to lead to any testable hypothesis. Alison L. Greggor’s research focuses on how animals perceive, interact with, and learn about humans and the changes we make to the environment. She has studied species ranging from crabs to crows and champions the use of animal cognition principles in aiding biodiversity conservation. Alison received her PhD in Psychology from the University of Cambridge as a Gates scholar, and was a postdoctoral researcher in biological sciences at Dartmouth College. She is currently working for San Diego Zoo Global as a postdoctoral associate in recovery ecology. She is located in the Keauhou Bird Conservation Center in Hawaii. In this work she oversees research that is conducted to enable the successful reintroduction of extinct in the wild Alalā or Hawaiian Crow (Corvus hawaiiensis) and other reintroduction avian programs. Paul M. W. Hackett main area of research is in categorical ontologies and specifically on how events may be classified in this manner and how an individual person or event may be understood through formal declarative statements of their ontological profiles. He has developed the qualitative or 255

256

About the Editor and Contributors

philosophical facet theory approach and has applied this to the study of many forms of behavior including: place experience; health; art; philosophical writing; and so on. Paul is also interested in the application of ontological accounts of nonhuman animal behavior. He has over 170 publications and PhDs in psychology and fine art practice. He is a visiting professor of health research methods at the University of Suffolk, a visiting professor in psychology at the University of Gloucestershire, a visiting researcher in psychology at Cambridge University and a professor in the School of Communication at Emerson College. Appointments he has held include those at Oxford University, Birmingham University, Cardiff University, and Tufts University. Claire Ortiz Hill holds a B.A. in Philosophy and an M.A. in Comparative Literature  from the University of California, Riverside and a Maîtrise and Doctorate from the University of Paris, Sorbonne. She has specialized in the Austro-German roots of twentieth-century philosophy, with a particular emphasis on Husserl’s philosophy of logic and mathematics.  Her  publications include  Word and Object in Husserl, Frege and Russell; Rethinking Identity and Metaphysics; Husserl or Frege? (with G. E. Rosado Haddock); The Roots and Flowers of Evil in Baudelaire, Nietzsche and Hitler; The Road Not Taken (with Jairo da Silva), and over fifty articles. She is a religious hermit with the Archdiocese of Paris. Torjus Midtgarden (born 1962) is professor at the Centre for the Study of the Sciences and the Humanities at the University of Bergen. His research interests are Social and Political Philosophy and American Pragmatism, in particular the philosophy of Charles S. Peirce and John Dewey. He has published articles on pragmatism and its relevance for contemporary philosophy in journals such as Transactions of the Charles S. Peirce Society, Journal of the History of Philosophy, European Journal of Social Theory, Philosophy and Social Criticism, Semiotica and Revue Internationale de Philosophie. Walter J. Schultz holds a B.A., M.A., and Ph.D. in Philosophy (University of Minnesota) with doctoral specializations in mathematical logic and economic theory. He studied economics with Leonid Hurwicz who won the Nobel Prize in Economics in 2007. Dr. Schultz is currently Professor of Philosophy/Scholar-in-Residence and the University of Northwestern in St Paul. He has been influenced by the eighteenth-century theologian/ philosopher Jonathan Edwards. For the last fifteen years has been developing a new kind of formal semantics for systems of logic grounded in an alternative modal metaphysics. It affects the way the basic concepts of mathematics and science should be understood.

About the Editor and Contributors

257

Paul Symington (Ph.D.) is Professor of Philosophy and Director of Scholarly Excellence at Franciscan University of Steubenville. He is the author of over a dozen articles and a book entitled, On Determining What There Is. His main areas of research are in metaphysics and medieval philosophy. Aharon Tziner (Ph.D., Labor Studies, Tel Aviv University) is a full professor of management and organizational psychology, former dean of the School of Business Administration, and founder of the MBA program and M.A. in organizational behavior and management of health systems programs, present dean of the School of Behavioral Sciences and senior vice-rector at Netanya Academic College. He has published 111 refereed articles, six book chapters, and six books with several thousand citations. He is and has been an editorial member many renowned journals in organizational behavior, management, human resources, economics, business, psychology. He is a member of the Academy of Management, APA, IPA, and SIOP and has been associated with: University of Montreal City; CUNY; Tel Aviv University; Bar-Ilan University and held visiting appointments at: SUNY; University of Minnesota; Ben-Gurion University. He is a leading authority on human resources management, organizational behavior, management, and organizational psychology. Gal Yehezkel is a senior lecturer at the Department of B.A. in Liberal Arts and Sciences, The Sapir Academic College, Israel, and a member of the Department of History, Philosophy, and Judaic Studies, The Open University of Israel. His main areas of research are philosophy of language and Metaphysics. He is the author of The Conceptual Structure of Reality (Springer, 2014).