The Oxford Handbook of Metaphysics (Oxford Handbooks)

THE OXFORD HANDBOOK OF

METAPHYSICS Edited by

MICHAEL J. LOUX AND

DEAN W. ZIMMERMAN

OXFORD UNIVERSITY PRESS

OXFORD UNIVERSITY PRESS

Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © the several contributors 2003

The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2003 First published in paperback 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Antony Rowe Ltd, Chippenham, Wiltshire ISBN 0-19-825024-X ISBN 0-19-928422-9 (Pbk.)

978-0-19-825024-1 978-0-19-928422-1 (Pbk.)

13579108642

ACKNOWLEDGEMENTS

Thanks are due to Peter Momtchiloff, who provided help and encouragement at every stage of this project. Thanks also to Margaret Jasiewicz, Cheryl Reed, Tina Elkins, Linda Lange, and David Manley, who worked on the preparation of the manuscript. And special thanks to Noell Birondo, who handled the page proofs and oversaw the final stages of the project.

CONTENTS

Notes on the Contributors

x

Introduction

1

MICHAEL J. Loux DEAN

W.

ZIMMERMAN

PART I UNIVERSALS AND PARTICULARS 1.

Nominalism

11

ZOLTAN GENDLER SZABO

2.

Platonistic Theories of Universals JOSHUA HOFFMAN AND GARY S. ROSENKRANTZ

3. Individuation E.

75

J. LOWE

PART II EXISTENCE AND IDENTITY 4. Identity

99

JOHN HAWTHORNE

5. Existence, Ontological Commitment, and Fictional Entities

131

PETER VAN INWAGEN

PART III MODALITY AND POSSIBLE WORLDS 6. The Problem of Possibilia KIT

FINE

161

Vlll

CONTENTS

7. Reductive Theories of Modality

180

THEODORE SIDER

PART IV TIME, SPACE-TIME, AND PERSISTENCE 8. Presentism

211

THOMAS M. CRISP

9. Four-Dimensionalism MICHAEL

10.

C.

REA

Space-Time Substantivalism GRAHAM NERLICH

11.

Persistence through Time

315

SALLY HASLANGER

PART V EVENTS, CAUSATION, AND PHYSICS 12.

Events

357

PETER SIMONS

13. Causation and Supervenience MICHAEL TOOLEY

14. Causation in a Physical World HARTRY FIELD

15. Distilling Metaphysics from Quantum Physics TIM MAUDLIN

435

CONTENTS

IX

PART VI PERSONS AND THE NATURE OF MIND 16. Material People

491

DEAN W. ZIMMERMAN

17. The Ontology of the Mental

52 7

HOWARD ROBINSON

18. Supervenience, Emergence, Realization, Reduction

556

JAEGWON KIM

PART VII FREEDOM OF THE WILL 19.

Libertarianism CARL GINET

20.

Compatibilism and Incompatibilism: Some Arguments

613

TED WARFIELD

PART VIII ANTI-REALISM AND VAGUENESS 21.

Realism and Anti-Realism: Dummett's Challenge MICHAEL J.

22.

Loux

Ontological and Conceptual Relativity and the Self ERNEST

665

So SA

23. Vagueness in Reality TIMOTHY WILLIAMSON

Index

717

NOTES ON THE CONTRIBUTORS

Thomas M. Crisp, Assistant Professor of Philosophy at Florida State University. Hartry Field, Professor of Philosophy at New York University. Kit Fine, Professor of Philosophy at New York University. Carl Ginet, Professor of Philosophy Emeritus at Cornell University. Sally Haslanger, Associate Professor of Philosophy at the Massachusetts Institute of Technology. John Hawthorne, Professor of Philosophy at Rutgers University. Joshua Hoffman, Professor of Philosophy at the University of North Carolina at Greensboro. Jaegwon Kim, Founce Professor of Philosophy at Brown University. Michael J. Loux, Schuster Professor of Philosophy at the University of Notre Dame. E. J. Lowe, Professor of Philosophy at Durham University. Tim Maudlin, Professor of Philosophy at Rutgers University. Graham Nerlich, Professor of Philosophy at Adelaide University. Michael C. Rea, Associate Professor of Philosophy at the University of Notre Dame. Howard Robinson, Member of the Faculty of Philosophy at the Central European University. Gary S. Rosenkrantz, Professor of Philosophy at the University of North Carolina at Greensboro. Theodore Sider, Associate Professor of Philosophy at Rutgers University. Peter Simons, Professor of Philosophy at Leeds University. Ernest Sosa, Elton Professor of Natural Theology and Professor of Philosophy at Brown University. Zoltan Gendler Szabo, Associate Professor of Philosophy at Cornell University. Michael Tooley, Professor of Philosophy at the University of Colorado at Boulder.

NOTES ON THE CONTRIBUTORS

Xl

Peter van Inwagen, O'Hara Professor of Philosophy at the University of Notre Dame. Ted Warfield, Associate Professor of Philosophy at the University of Notre Dame. Timothy Williamson, Professor of Philosophy at Oxford University and Fellow of New College. Dean W. Zimmerman, Associate Professor of Philosophy at Rutgers University.

INTRODUCTION MICHAEL

J. LOUX

DEAN W. ZIMMERMAN

ITs detractors often characterize analytical philosophy as anti-metaphysical. After all, we are told, it was born at the hands of Moore and Russell, who were reacting against the metaphysical systems of idealists like Bosanquet and Bradley; and subsequent movements in the analytic tradition-logical positivism and ordinary language philosophy-made the elimination of metaphysics the cornerstone of their respective philosophical agendas. The characterization is not, however, completelyaccurate. For one thing, the earliest movement in the tradition-the logical atomism of Russell and the early Wittgenstein-was thoroughly metaphysical in its orientation. To be sure, the metaphysics at work there was conservative, lacking the speculative excesses and obscurantist jargon of the idealists; but no less than the idealists, the logical atomists were concerned to provide a comprehensive account of the ontological structure of reality. For another, while card-carrying positivists and ordinary language philosophers were officially committed to the view that the claims of the traditional metaphysician are somehow problematic (perhaps meaningless; perhaps, just confused), the fact is that philosophers from both movements continued to deal with the problems confronting traditional metaphysics. Of course, they were anxious to conceal this fact, parading their work as talk about logical syntax or as conceptual analysis; but no one was fooled; and in any case, their attacks on metaphysics were themselves anchored in theses (typically theses expressing a radical form of anti-realism) that were no less metaphysical than the views they sought to undermine.

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Still, it remains true that for much of its early history analytic philosophy was inhospitable to traditional metaphysics; and it cannot be denied that in the heyday of logical positivism in the 1930S and 1940S or in the post-war period when the ordinary language philosophy of the later Wittgenstein was most influential, it was not fashionable to bill oneself as a metaphysician. But by the early 1960s prejudices against metaphysics were beginning to soften. This change in attitude was due to the work of philosophers who were willing to address metaphysical questions in spite of the long-standing prejudices. Philosophers like Arthur Prior, Roderick Chisholm, and Wilfrid Sellars come to mind here; but two philosophers were especially influential in the rehabilitation of metaphysics-W. V. o. Quine and P. F. Strawson. They had their roots in the anti-metaphysical traditions they helped undermine. Quine came out of the tradition oflogical positivism, and Strawson was originally a representative of the ordinary language tradition. Both attempted to show that there is a project in metaphysics responsible philosophers can in good conscience undertake. For Strawson, the project was what he called 'descriptive metaphysics'. According to Strawson, the aim of descriptive metaphysics is the systematic characterization of the most general categorial or structural features of the conceptual scheme in terms of which we talk and think about the world. Quine, by contrast, focused on the ontological commitments associated with accepting a body of discourse. His famous slogan 'To be is to be the value of a bound variable' was supposed to provide a criterion by which the metaphysician can determine just which kinds of entities we commit ourselves to by endorsing a given body of statements. Both philosophers were highly influential, each on his respective side of the Atlantic. Strawson's conception of descriptive metaphysics was attractive to philosophers-typically British philosophers-who grew up in the tradition of conceptual analysis; whereas Quine's notion of ontological commitment appealed to philosophers-typically American philosophers-schooled in the more formal logistic approaches characteristic of the logical positivist tradition. The upshot was that philosophers no longer felt the need to conceal their interest in metaphysical issues, and there was something like a revival of traditional metaphysics. In Britain the revival had a distinctively Kantian flavour. Philosophers posed metaphysical questions by asking about the presuppositions of this or that conceptual practice-our identification and reidentification of particulars, our ascription of spatio-temporallocation, our use of the classificatory concepts at work in predication. Questions about the objectivity of the concepts structuring those practices were central here, and those questions naturally unfolded into more general questions about the nature of realism and the possibility of anti-realist theories of meaning and truth. In the United States the revival of interest in metaphysics was expressed in the more self-consciously ontological idiom of categories. Initially, philosophers followed Quine's lead in asking whether our beliefs (either those expressed in our best scientific theories or those at work in our day-to-day confrontation with the world)

INTRODUCTION

3

commit us to the existence of abstract entities. And if they do, are those abstract entities things like sets whose identity conditions can be given in straightforwardly extensional terms, or are we committed to things like properties and propositions? And these questions led to others. Those who endorsed the existence of properties faced questions about individuation. If there are such things as properties, how are they related to familiar concrete particulars? Are the latter just bundles of properties, or do particulars constitute an irreducible ontological category? And since propositions are the sorts of things that are said to be necessary, possible, contingent, and impossible, those who endorsed the existence of propositions found themselves forced to confront questions about modality. Do we need to follow Leibniz and appeal to a special category of objects-possible worlds-to explain how modal claims can be true or false? And if so, how do particulars figure in the story? Are they the sorts of things that can exist in different possible worlds? And what does that tell us about their ontological structure? The range of legitimate metaphysical questions kept expanding, and soon philosophers in this tradition were asking all the old questions. What is the nature of time? What is it for an ordinary object to persist through time? What is the nature of space? Do events constitute an irreducibly basic kind of object? If so, what are they like and what are their identity conditions? What is causation? Are there any uncaused events? In both Britain and the United States the revival of metaphysics was gradual. At first, there was a piecemeal character to work in the field. With rare exceptions, philosophers were wary of large-scale metaphysical theories-the construction of comprehensive ontological schemes, theories about the nature of and relations among the most abstract categories under which absolutely everything falls, and the use of this ontological machinery to settle issues about mind-body relations, causation, philosophy of religion, and so on. Comprehensive, ontology-driven metaphysics was associated with the names of the idealists whom Russell and Moore had effectively defeated-McTaggart, Bosanquet, Bradley, Royce, Joachim. The systematic realist metaphysics of Russell and Moore themselves (the Moore of Some Main Problems of Philosophy), and of other realists like Samuel Alexander, Roy Wood Sellars, H. H. Price, D. C. Williams, and C. D. Broad, had been made to seem misguided and outdated first by the arguments of the logical empiricists, then by the harangues of Wittgensteinians and other ordinary language philosophers; and so an impressive body of non-idealist systematic metaphysics was ignored and then forgotten. We suspect that, past mid -century, few philosophers really believed that the standard verificationist arguments against the meaningfulness of metaphysical claims were any good. Nevertheless, systematic metaphysics continued to languish. It was typical of those who began to raise the old metaphysical questions during the 1960s and 1970S to proceed cautiously, addressing now this metaphysical problem, now that. Their caution was understandable; after the idealists were routed, the most prominent builders of metaphysical systems were Whitehead, Bergson,

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and Paul Weiss. Despite their evident genius, whatever insights they had into metaphysical problems were invisible to analytic philosophers. Indeed, they seemed to many to serve as an object lesson: This is what happens when you try to do metaphysics in the grand manner. They and their admirers produced bodies of work that followed the same recipe used by the nineteenth-century idealists: (i) set forth your own baroque ontological scheme in a new, peculiar jargon; (ii) claim that it is radically opposed to all preceding metaphysical systems; and (iii) explain its intricacies in a series of ever longer books, introducing as many undefined technical terms as possible. By the mid-1980s a new generation of philosophers was coming to the study of metaphysics. These philosophers had no first-hand knowledge of the positivist or ordinary language attacks on metaphysics. For them, the attacks were quaint episodes from a distant past rather than serious theoretical challenges. Accordingly, they were not in the least apologetic about doing metaphysics, nor were they content with a piecemeal approach to metaphysics. Unlike many of their predecessors, they were willing to attempt the construction of comprehensive ontological theories, building upon the work of such trailblazers in the rehabilitation of systematic metaphysics as Roderick Chisholm, David Armstrong, and David Lewis. Quine's criterion of ontological commitment was very important to philosophers like Chisholm and Lewis. Both are rightly regarded as champions of a chastened approach to metaphysics, one that neither shies away from the traditional problems of ontology, nor falls back into the arcane, untethered system-building that had given metaphysics a bad name; and both regarded Quine's criterion as an antidote to the besetting sins of traditional metaphysicians. The approach to questions of ontological commitment defended by Quine in 'On What There Is' (1948) was already in place by 1939, when Chisholm and Quine overlapped at Harvard (Chisholm a graduate student, Quine a young professor). In the hands of Chisholm, Lewis, and their heirs, Quine's criterion of ontological commitment is understood to be something like this: If one affirms a statement using a name or other singular term, or an initial phrase of 'existential quantification', like 'There are some so-and-sos', then one must either (1) admit that one is committed to the existence of things answering to the singular term or satisfying the description, or (2) provide a 'paraphrase' of the statement that eschews singular terms and quantification over so-and-sos. So interpreted, Quine's criterion can be seen as a logical development of the methods of Russell and Moore, who assumed that one must accept the existence of entities corresponding to the singular terms used in statements one accepts, unless and until one finds systematic methods of paraphrase that eliminate these terms. The metaphysics of Chisholm and, later, Lewis look nothing like Quine's, however. For Quine, it is the deliverances of science alone that should determine our ontological commitments. As Chisholm saw it, this was the decisive point at which he departed from Quine and took inspiration from Moore: Why not assume, in the

INTRODUCTION

5

seminar room, the same things we take ourselves to know in everyday life? Why are we suddenly not entitled to them? Lewis, and the younger generation of metaphysicians who came into their own in the 1980s, by and large side with Chisholm and Moore. Once all our ordinary convictions are taken into account, the traditional problems of metaphysics return with a vengeance, as they do not for Quine. As a result, ontology must be responsive to other areas of philosophy; a particular ontological scheme shows its adequacy by its usefulness in the resolution of problems elsewhere. Desiderata for an ontological scheme include both simplicity (a point about which Quine would agree) and scope. One metaphysical system is superior to another in scope in so far as it allows for the statement of satisfactory philosophical theories on more subjects-theories that preserve, in the face of puzzle and apparent contradiction, most of what we take ourselves to know. One presupposition of the version of Quineanism invoked by Chisholm and Lewis is that the nature of the ontological categories is somewhat opaque to us. There is still hope for ontology, however, since our fallible intuitions about the subject can be tethered in this way to success elsewhere, in the resolution of philosophical problems concerning better-known matters. The differences between Quine's starting point and that of Chisholm, Lewis, and the rest lead to greater differences down the line. With only (a small subset of) the sciences yielding truths for the ontologist to consider, Quine can rest content with an austere naturalism: although one cannot accept the mathematics needed for science without set theory, no further 'queer entities' need be recognized; there is only space-time and its particular contents, and sets of such things. Chisholm, Lewis, and company have many more truths to consider, and more apparent paradoxes to resolve. They have generally found it very difficult to arrive at metaphysical theories satisfying both desiderata of simplicity and scope without giving up Quine's insistence upon a purely extensional language and logic. Lewis was able to retain extensionality, but at great cost-the positing of an extravagant ontology of concrete, spatio-temporally disconnected universes, which he defended by an explicit appeal to Quinean principles of ontological commitment. His attitude toward the contents of our world, however, remained staunchly materialist, and not substantially different from that of Quine. Chisholm, unlike Lewis, rejects Quine's logical scruples, taking at least one intentional (mental) and intensional (non-extensional) notion as a primitive. He also concludes that the only way to retain most of what we think we know about persons is to admit that they are very special: they have causal powers unlike those found elsewhere in nature, they can 'grasp' or conceive of abstract objects, and their persistence conditions are mysteriously different from those of ordinary physical objects. Such conclusions make his metaphysics unacceptable to Quine and other naturalistically inclined philosophers. Although there is much in the metaphysics of both Chisholm and Lewis that their critics find mysterious or unbelievable, both systems include solutions to a host of philosophical puzzles, and stand as a challenge to be met by anyone

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who would defend metaphysical naturalism and nominalism while rejecting Lewis's vastly enlarged physical ontology. Most philosophers today who identify themselves as metaphysicians are in basic agreement with the Quinean approach to systematic metaphysics exemplified in the work of Chisholm and Lewis. Indeed, it is probably not much of an exaggeration to say that to day's crop of metaphysicians can be divided fairly exhaustively into those most influenced by the one or the other. That division is reflected in the debates discussed in the chapters that follow. Those chapters approach the field topically. Each focuses on a fundamental metaphysical issue; the aim is to provide an account of the nature and structure of the debate over the issue. But the chapters are not merely about metaphysics; they are also exercises in metaphysics with authors attempting to advance the debate over the relevant issues. The first three focus on the traditional dichotomy of universal and particular. Zoltan Szabo discusses nominalistic accounts of the phenomena central to the debate over universals; whereas Joshua Hoffman and Gary Rosenkrantz focus on Platonistic accounts of universals. E. J. Lowe closes Part I by discussing problems surrounding the individuation of particulars. Next, there follows a pair of chapters on very general ontological issues. John Hawthorne deals with the concept of identity, and Peter van Inwagen discusses the phenomenon of ontological commitment and attempts to show how the case of fictional discourse is to be accommodated. Modal issues have been pivotal in recent analytic metaphysics. Here, the central debate has been between those endorsing non-reductive theories of modality and those insisting on reductive accounts of modal phenomena. In his contribution Kit Fine deals with approaches of the first sort; whereas Ted Sider examines approaches of the second sort. In addition, discussion of non-reductive theories can be found in Hoffman and Rosenkrantz's chapter on Platonistic theories of universals. Part IV focuses on issues bearing on the metaphysics of time and space. One important debate on the nature of time pits what are called presentists against those who construe time as a fourth dimension on a par with the three spatial dimensions. Thomas Crisp examines presentist theorists; whereas Michael Rea discusses fourdimensionalism. In his chapter, Graham Nerlich discusses issues bearing on the debate over the status of space-time. Finally, Sally Haslanger discusses the different approaches to questions about persistence through time and their theoretical roots in the metaphysics of time. Part V deals with a series of interrelated issues about events, causation, and physical theory. In the first chapter Peter Simons discusses recent debates about the existence and nature of events. Michael Tooley and Hartry Field each contribute a chapter on causation. Tooley focuses on broader issues about the analysis of our concept of causation; whereas Field examines the more particular case of causation in physical theory. Finally, we have a chapter by Tim Maudlin on the metaphysical implications of quantum mechanics.

INTRODUCTION

7

The next three chapters focus on questions about the metaphysics of persons and the mental. Dean Zimmerman examines materialist accounts of persons. His chapter is followed by two more general discussions of the metaphysical status of the mental. The first, by Howard Robinson, focuses on general ontological questions about the nature and structure of perceptual and conceptual episodes. The second, by Jaegwon Kim, considers the way questions about supervenience and reduction have come together in recent attempts at providing materialist accounts of intentional phenomena. Then we have two chapters on the problem of freedom of the will. Carl Ginet examines libertarian approaches; whereas Ted Warfield discusses compatibilist accounts of freedom. Part VII bears broadly on realism and attempts to delineate alternatives to realism. Michael Loux discusses the very influential debates over realism and anti-realism that originated with Michael Dummett and dominated the British philosophical scene in the 1970s, 1980s, and early 1990S. Ernest Sosa considers approaches to questions about realism that have their origin in facts bearing on ontological relativity. Finally, Timothy Williamson attempts to layout the central features of metaphysical debates over the nature of vagueness.

PAR T

I

UNIVERSALS AND PARTICULARS

CHAPTER 1

NOMINALISM /

/

ZOLTAN GENDLER SZABO

1. INTRODUCTION ARE there numbers? What about directions, sets, shapes, animal species, properties, relations, propositions, linguistic expressions, meanings, concepts, rights, values, or any other abstract entities? There are two sorts of answers to such questions: straight ones and oblique ones. The straight answers are typically introduced by the expression 'of course', as in 'Of course there are, otherwise how could sentences like "2 + 2 = 4" and "There is something Napoleon and Alexander have in common" be true?' and 'Of course there aren't, for how could we even know or speak of things that are causally inert?' The oblique answers are usually headed by the locution 'well, you know', as in 'Well, you know that really depends on whether you take this to be an internal or external question' and 'Well, you know that actually depends on whether you mean "exist" in a thick or thin sense: Analytic philosophers tend to feel a strong inclination towards the clear-cut. But ontology-and especially the ontology of the abstract-is an area in which it is hard to dismiss oblique lines. The nominalist sticks with straight negative answers: she unqualifiedly rejects abstract entities of any sort whatsoever.! The nominalist's equally straight opponent

Thanks to Tamar Szab6 Gendler, Benj Hellie, Harold Hodes, Ted Sider, and Scott Spiker for comments and criticism. I 'Nominalism' is often used in another sense as referring to the doctrine that there are no universals. In the traditional medieval sense of the word, nominalism is the doctrine that whatever

12

ZOLTAN GENDLER SZABO

is the anti-nominalist,2 who accepts at least one type of abstracta. On the face of it, their views are clear opposites. Nonetheless, both expend a good deal of effort fending off a variety of oblique answers seeking a middle ground between their VIews. Nominalism is certainly not the most surprising eliminativist thesis-there are some who deny the existence of ordinary material objects, mental states, or persons-but it is among the most radical of those widely held. Nominalism does away with so many kinds of putative entities that the ontology it yields may not even be properly described as a desert landscape. After all, aren't landscapes, at least in one of the perfectly legitimate senses of this word, abstract? Nominalism is a divisive doctrine. Proponents often concede that they are fighting an uphill battle, but justify their insistence with an appeal to ontological conscience; opponents tend to be sceptical about the sincerity of such appeals. They suspect that nominalism is indeed much like a desert: an uncomfortable place whose main attraction is that it is hard to be there. Some of this clash is no doubt the result of a genuine conflict in philosophical temperament, but there is another source as well. Contemporary nominalism grows out of a number of different traditions, each contributing its distinct understanding of the key terms of the nominalist thesis. The intensity of many philosophers' belief in the absurdity of nominalism is partly the result of the seeming simplicity and underlying ambiguity of the position. To bring out the perplexing character of nominalism, consider the often voiced concern that the view appears to be a self-undermining. For suppose that a nominalist-call him Nelson-just told you that there are no abstract entities. How should Nelson describe what he did? Did he say something? Certainly not, if saying something amounts to expressing a proposition. Did he utter something? Clearly not, if uttering something requires the articulation of a sentence type. Did he try to bring you to share his belief? Obviously not, if sharing a belief requires being in identical mental states. Of course, Nelson is not likely to be moved by all this. After all, there is a nominalistically acceptable way of describing what happened: he produced meaningful noises and thereby attempted to bring you into a mental state relevantly similar to one of his own. There is no mention of propositions, sentences, or shareable beliefs here, and still, in an important sense, we are told precisely what was going on. Nevertheless, that we can find such an alternative way of talking is by no means exists is particular, and nothing but particular. According to nominalists, generality belongs to certain nominal expressions alone, and it belongs to them only in the sense that they may apply to more than one particular. The origin of the term 'nominalism' is subject to serious scholarly dispute; cf. Courteney (1992). 2 The term 'Platonism' is occasionally used in the literature in the sense I employ'anti-nominalism'. Unfortunately, it is also often used in a richer sense, when it carries additional commitment to the mind-independence of abstract entities. Since neither sense of 'Platonism' has much to do with Plato's metaphysics, I have opted for a neutral term.

NOMINALISM

13

a complete response to the concern about self-undermining. For the questions raised were merely bypassed, not answered. We can raise them again: When Nelson produced those meaningful noises, did he say something? did he utter something? did he try to bring you to share his belief? If the answer is no, Nelson must tell us just how we ended up in a massive error in thinking the commonplace thought that Nelson did say something by uttering a sentence and that we might have ended up sharing his belief. If the answer is yes, he has to explain how that concession is supposed to be compatible with his renunciation of abstracta. How Nelson answers this challenge is crucial for a full understanding of his position. I will begin (Section 2) with a good deal of clarification. Participants in contemporary debates surrounding nominalism tend to share certain assumptions about what ontological commitment amounts to, how the abstract and the concrete are to be distinguished, and what objects in general are. It is good to have these assumptions on the table. Then (Section 3) I turn to a discussion of nominalist attitudes towards the apparent commitment ordinary thinking and speech carry to abstracta. This is followed by a survey of some of the most influential arguments for nominalism (Section 4) and against it (Section 5). The chapter ends (Section 6) with a brief look at some oblique answers to the ontological question about abstracta. I will make no attempt to resolve the issues here, but my anti-nominalist inclination will no doubt show throughout.

2. THE NOMINALIST THESIS The debate about nominalism concerns the question whether there are abstract entities. The terms of this question-'there are', 'abstract', and 'entity'-are all subject to interpretative disagreements. I will start by examining them one by one.

2.1

Are There ...

The standard view nowadays is that we can adequately capture the meaning of sentences like 'There are Fs', 'Some things are Fs', or 'Fs exist' through existential quantification. As a result, not much credence is given to the idea that we must distinguish between different kinds or degrees of existence. 3 When we talk 3 Commitment to a univocal quantificational analysis of existence claims need not be taken as entailing the rejection of fundamental categories in metaphysics. But the distinction cannot be ontological: entities in the different categories exist in the same sense of the word.

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about whether there are cheap hotels in New York and when we talk about whether possible worlds exist, there is no fundamental difference in logical form between the claims at stake. If this much is agreed upon, alternative conceptions of ontological commitment must be presented as alternative views about quantification. 4 There are all sorts of exotic existential quantifiers in formal languages: some are interpreted substitutionally; some can bind predicate-, function-, or sentencevariables; some bind all variables within their scope unselectively. There are formal languages, for example those of intuitionistic, free, and quantum logic, where certain classical inferences are invalid. There is no serious question about the coherence of the semantic rules governing such languages. s But this does not settle the deeper question whether these formal devices have anything to do with anything we ordinarily think or say. The usual line of defence against employing non-standard quantification to capture our existential idioms goes back to Quine. It relies on two claims. First, that the interpretation given to the classical objectual first-order existential quantifier is just this: there are things that are thus and so. Secondly, that the ordinary existential idioms are univocal: there is only stylistic difference between saying that there are things that are thus and so and saying that thus and sos exist (Quine 1969: 106). Both claims are widely endorsed, both are plausible, both are nonetheless questionable. We do tend to say when elucidating the meaning of the material conditional that we interpret