Ways a World Might Be: Metaphysical and Anti-Metaphysical Essays

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WAYS A WORLD MIGHT BE

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Ways a World Might Be METAPHYSICAL AND ANTI-METAPHYSICAL ESSAYS

ROBERT C. STALNAKER

Clarendon Press · Oxford

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 Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto 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 ©Robert C. Stalnaker 2003 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2003 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 this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available ISBN 0-19-9251487 (hbk.) ISBN 0-19-9251495 (pbk.) 1 3 5 7 9 10 8 6 4 2 Typeset by Kolam Information Services Private Limited, Pondicherry, India. Printed in Great Britain on acid-free paper by Biddles Ltd., Guildford & King's Lynn

In memory of Louis O. Mink Carl G. Hempel H. Paul Grice David K. Lewis

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Preface All but two of the papers included in this collection have been previously published. I thank the editors and publishers for permission to reprint them. Details of the sources are given on page xii. In most cases, the papers have been only lightly edited, but Chapter 3—a dialogue on impossible worlds—has been expanded in response to comments by David Lewis, and postscripts have been added to Chapters 5 and 8 on some technical issues discussed in those papers. Thanks to Andy Egan for invaluable editorial assistance in preparing the papers and updating the references, and for advice on matters of both substance and detail. Thanks to Peter Momtchiloff of Oxford University Press for his good advice about the selection of papers, among many other things, and for his support. I can't thank by name all of the many teachers, colleagues, and students who have helped me to get clearer about the issues discussed in these papers, so let me thank them collectively, and mention just a few who stand out. Saul Kripke must take some of the blame for the preoccupation with possibilities that is evident in the papers in this collection, since I was ﬁrst brought to appreciate the clarifying power of the framework of possible worlds in his seminar at Princeton in 1964–5 (where ideas about Wittgenstein on following a rule mingled with the ideas that were later to take form in Naming and Necessity). The inﬂuence of his arguments in Naming and Necessity on my ideas about the relations between modal, semantic, and epistemological concepts will be evident throughout these papers, most explicitly in Part IV Four of the papers were originally written for festschrifts, and I am indebted to the philosophers celebrated in those collections – Paul Benacerraf, Ed Gettier, Ruth Marcus, and Sydney Shoemaker – all people with remarkable philosophical minds who have inﬂuenced my thinking on metaphysical matters through their work, their example, and philosophical discussion over the years. The paper on supervenience (Chapter 5) grew out of a metaphysics seminar at MIT taught jointly with Judy Thomson, and my thoughts about this issue and others in metaphysics have beneﬁtted from her incisive arguments and analyses. Ned Block's insights into questions about consciousness and concepts have helped me to see many things I hadn't seen before. Collaboration with Ned, ﬁrst on a seminar on consciousness, and then on a joint article (Block and Stalnaker 1999), was important to my understanding of issues both about metaphysical and conceptual possibility, and about

viii

PREFACE

phenomenal consciousness. Some of the ideas in Chapters 10, 11, 12, and 13 have their source in that collaboration. Anyone who spends his or her time thinking and writing about philosophical problems develops, along the way, a cluster of prejudices and preoccupations, methods and styles of argument that constitutes, one hopes, a general view of things. Where it comes from and how it develops is hard to say, but the examples provided by teachers and colleagues that we both follow and react against obviously play a crucial role in shaping our philosophical personae. The four philosophers to whose memory this book is dedicated played a particularly important role in my own philosophical development, both through the substance of their ideas and arguments, and by the force of their personalities. Let me say a little about each of them. Louis Mink was my main undergraduate teacher of philosophy at Wesleyan University. He was at the center of the intellectual life of the university, and had many students who went on to distinguished careers in philosophy. Louis had an insatiable intellectual curiosity, and showed us how to think philosophically about everything. With him I studied Kant and St Augustine, Collingwood and logical positivism, the philosophy of history and social science, among other things. He fed my ambivalence about metaphysics by getting me to appreciate both the richness of the philosophical tradition and the power of the logical empiricist critique. Louis has always been, for me, a model of what a philosopher should be. I ﬁrst encountered the work of C. G. Hempel in high school, browsing in James R. Newman's anthology, The World of Mathematics. His essays reprinted there, ‘On the Nature of Mathematical Truth’ and ‘Geometry and Empirical Science’ struck me as models of clarity and good sense, as they still do, and helped to draw me into philosophy. When I got to graduate school I beneﬁtted from his lively seminars, patient and painstaking comments on my work, his writings on explanation, conﬁrmation and concept formation, and most of all from his example of clarity of mind, intellectual integrity, and generosity. I was fortunate to be his student and teaching assistant. Paul Grice was never my teacher or departmental colleague, but I got to know him when he made an extended visit to the University of Illinois, where I was teaching, in 1970, and during a memorable summer institute at Irvine in 1971. I had earlier been able to attend just one of his William James Lectures, but I vividly remember the intellectual excitement of the occasion, the feeling that we were watching a great philosophical mind in action. Grice was an opportunistic and experimental thinker, eclectic in his methods and interests, following out lines of thought to see where they led him. But a coherent philosophical vision emerged – a view about the relations between language, thought, and action – that has greatly inﬂuenced my own way of thinking about these issues.

PREFACE

ix

I began corresponding with David Lewis in 1968, when we discovered that we had developed, independently, similar theories of counterfactuals, and we had many fruitful and enjoyable discussions over the years from that time until just before his death in 2001. David was, of course, an unabashed metaphysician, and one might think that he was untroubled by the kind of mixed feelings about the subject that I have expressed, but he did say, in the introduction to his ﬁrst collection of papers: ‘I should have liked to be a piecemeal, unsystematic philosopher, offering independent proposals on a variety of topics. It was not to be’ (Lewis 1983a: ix). In a sense, it was to be, for even though David's many philosophical contributions grew out of his metaphysical system, and ﬁt together with remarkable coherence, he was careful to show us when an analysis or an argument was detachable by one who didn't buy into the whole system. His work was widely applied, both within and outside of philosophy, by researchers who would not have thought that metaphysics could be relevant to their work. The inﬂuence of David's work, and I hope of his example as well, will be seen in every paper in this collection. Those who knew these four philosophers will agree that they were radically different from each other in personal and intellectual style, but they are all paradigm cases of philosophers, and had much in common. They all had a passion for philosophy, and a focus on philosophical issues. Style and method emerged from grappling with them. While each had his own philosophical agenda, they were all adept at seeing things from other points of view, and were generous and effective in showing others how to advance their own projects. They all had a sense of humor and a sense of fun: they knew how to take philosophy seriously without taking themselves too seriously. They saw, and helped us to see, that philosophy is an activity that is both enjoyable and worthwhile. Cambridge, Massachusetts January 2003

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Contents Details of ﬁrst publication Introduction I.Ways and Worlds 1. Possible Worlds 2. On what Possible Worlds could not be 3. Impossibilities II.Carving up Logical Space 4. Anti-essentialism 5. Varieties of Supervenience III.Identity in and across Possible Worlds 6. Counterparts and Identity 7. Vague Identity 8. The Interaction of Modality with Quantiﬁcation and Identity IV.Semantics, Metasemantics, and Metaphysics 9. Reference and Necessity 10. On considering a Possible World as Actual 11. Conceptual Truth and Metaphysical Necessity V.Subjective Possibilities 12. Comparing Qualia across Persons 13. What is it like to be a Zombie? 14. On Thomas Nagel's Objective Self References Index

xii 1 23 25 40 55 69 71 86 109 111 133 144 163 165 188 201 217 219 239 253 277 283

Details of First Publication A preliminary version of ‘Possible Worlds’ was published in Nous, 10 (1976). The version reprinted here is chapter 3 of my Inquiry (Cambridge, Mass.: Bradford Books, MIT Press, 1984), 43–58. Reprinted with the permission of Basil Blackwell Ltd and the MIT Press. ‘On what Possible Worlds Could Not Be’, in Adam Morton and Stephen Stich (eds.), Benacerraf and his Critics, (Oxford: Basil Blackwell Ltd., 1996). Reprinted with the permission of Basil Blackwell Ltd. ‘Impossibilities’, Philosophical Topics 24 (1996). Reprinted with the permission of the editor. ‘Anti-essentialism’, Midwest Studies in Philosophy 4 (1979). Reprinted with the permission of the editor. ‘Varieties of Supervenience’, Philosophical Perspectives 10: Metaphysics (1996). Reprinted with the permission of Basil Blackwell Ltd. ‘Counterparts and Identity’, Midwest Studies in Philosophy, 11, Studies in Essentialism (1987). Reprinted with the permission of the University of Minnesota Press. ‘Vague Identity’ in David Austin (ed.), Philosophical Analysis (Dordrecht: Kluwer, 1988). Reprinted with the kind permission of Kluwer Academic Publishers. ‘The Interaction of Modality with Quantiﬁcation and Identity’, in W. Sinnott-Armstrong, D. Raffman, and N. Asher (eds.), Modality, Morality and Belief: Essays in honor of Ruth Barcan Marcus (Cambridge: Cambridge University Press, 1994). Reprinted with the permission of Cambridge University Press. ‘Reference and Necessity’, in Crispin Wright and Bob Hale (eds.), Blackwell Companion to the Philosophy of Language (Oxford: Basil Blackwell Ltd., 1997). Reprinted with the permission of Basil Blackwell Ltd. ‘On considering a Possible World as Actual,’ Proceedings of the Aristotelian Society (2001). Reprinted with the permission of the editor. ‘Conceptual Truth and Metaphysical Necessity’ is published here for the ﬁrst time. ‘Comparing Qualia across Persons’, Philosophical Topics26 (2000). Reprinted with the permission of the editor. ‘What is it Like to be a Zombie?’, in John Hawthorne and Tamar Szabo Gandler (eds.), Conceivability and Possibility (New York: Oxford University Press, 2002). Reprinted with the permission of Oxford University Press. ‘On Thomas Nagel's Objective Self ’ is published here for the ﬁrst time.

Introduction This collection includes most of the papers I have written over the past twenty years on metaphysical topics. Most have been published before, but two are published here for the ﬁrst time. The papers were written for speciﬁc occasions to address a diverse range of particular issues, but—a familiar phenomenon—on rereading the papers together I discover certain common themes that were not always recognized at the time. In this introduction, I will comment on the big picture, as I now see it, that helps to connect the papers to each other. ‘I thought metaphysics was dead’ someone (not a philosopher) said to me when I described the work of one of my colleagues as metaphysics. It did seem to be so for a while, but metaphysics came back to life in the second half of the twentieth century, and it ﬂourishes today among the heirs of the philosophical tradition that began with a rejection of metaphysics. It is an interesting question why this ﬁeld of study should have fallen and risen, in our time, in the way that it did. There is nothing new about the downs and ups of metaphysics. It has always been controversial just what this ﬁeld of study is about, and whether it has a subject matter at all. Metaphysics is supposed to be the study of being. Its problems are not about how we think about the world, or what we can know of it, but about what the world is like in itself, at the most abstract level—about the structure of the universe, about what exists. But all cognitive disciplines—physics, history, mathematics, geology, economics— are concerned with what exists, and with the characteristics of the things within their domains. Is there really anything substantive to be said at a completely general level, a level that transcends even the most general empirical science, about what the world is like? And if there is, what gives philosophers the expertise to address such questions? How can a priori reﬂection and argument yield substantive truths about the world? The difﬁculty in answering this kind of challenge, along with the apparent fruitlessness of debates at the time about realism and ontology, motivated the logical empiricists, during the ﬁrst half of the twentieth century, to argue that metaphysical statements were literally meaningless—devoid of cognitive content. Their argument was grounded in a theory of meaning— or an idea for a theory of meaning—that was supposed to provide a criterion to distinguish both empirical propositions and propositions true or false in virtue of meaning from statements that, despite an appearance of meaningfulness, failed to express propositions at all. The logical empiricist also had a strategy for diagnosing the source of the illusion of meaningfulness that metaphysical statements had: metaphysics was the result of equivocation between empirical statements and meaning-ﬁxing stipulations.

2

INTRODUCTION

The theory of meaning, of course, was veriﬁcationism. ‘Stating the meaning of a sentence amounts to stating the rules according to which the sentence is to be used, and this is the same as stating the way in which it can be veriﬁed (or falsiﬁed). The meaning of a proposition is its method of veriﬁcation.’1 It was central to the idea of veriﬁcationism that the rules determining the meanings of words were the result of the decisions of the user of those words. ‘Grammatical rules are not found anywhere in nature, but are made by man and are, in principle, arbitrary; so you cannot give meaning to a sentence by discovering a method of verifying it, but only by stipulating how it shall be done. Thus the logical possibility of veriﬁcation is always self-imposed.’2 The story of the failure of veriﬁcationism is a familiar one. Attempts to make the standard precise resulted in criteria that were either too restrictive, so that paradigm cases of theoretical statements of science were judged to be meaningless, or too permissive, leaving loopholes through which arbitrary, uncontroversially meaningless sentences would be judged to be meaningful. The project of giving a reductive analysis of meaning failed on its own terms as shown by the criticisms of its proponents. And it was recognized by those proponents that a major source of the problem was the holistic character of veriﬁcation. The logical empiricists retreated to less ambitious projects such as clarifying the structure of empirical theories, and stating necessary constraints on the logical relations between theoretical and observation languages, but they retained the centrality of the distinction between matters of discovery and matters of stipulation or decision, and they retained the idea that metaphysics resulted from equivocation between the two. So Rudolf Carnap, in his classic late paper, ‘Empiricism, Semantics and Ontology’,3 distinguished two kinds of questions concerning theoretical frameworks: internal questions are questions to be answered within the framework by the methods that it sanctions, while external questions are questions about the fruitfulness of the practice of using the framework. External questions, properly conceived, are practical questions that call for a decision. Metaphysics is the result of confusing the two kinds of question, treating what are really practical questions about how to talk or think as if they were theoretical questions about what the world is like. One can, for example, ask whether numbers, propositions, or physical objects exist, but these questions make sense only as internal questions within the appropriate framework. Such questions, understood this way, are trivial, and not what the metaphysician who raises them has in mind. The realist, idealist, or nominalist, Carnap argued, ought to put his point, not as a claim about what there is, but as a proposal or recommendation about what kind of linguistic practice to engage in.

1

Schlick (1936/1941: 341).

2

Ibid. 351.

3

Carnap (1950).

INTRODUCTION

3

Even if one is free to choose whether or not to adopt a certain theoretical framework, the choice will not be an arbitrary one. It will be motivated by a judgment that the framework will prove fruitful, and such judgments are not made in a vacuum. If all reasoning and judgment must occur within some rule-governed linguistic framework, as Carnap believed, then we will need a meta-framework in which to state and justify our decisions about how to theorize. Carnap said little about how frameworks are individuated, or how one distinguishes, in practice, reasoning within a theory from reasoning in some meta-framework, and it is not clear that there is a nonarbitrary distinction to be made. If one's decision is to accept, or not, a whole language together with a theory stated in it, as Carnap's holistic picture suggests, then it is not clear that there is a basis for distinguishing the decision about what the rules of one's language shall be from judgments about which of the statements of the language correctly describe the world. This kind of consideration was the basis for W. V. Quine's critique of the dogmas of (logical) empiricism.4 Quine's critique was more radical than the other internal criticisms of veriﬁcationism, and precipitated a major shift in the way metaphysics was viewed, but Quine was nevertheless an internal critic who was sympathetic to the general aims and spirit of the logical empiricist project. The shift in perspective should not obscure the extent to which Quine shared Carnap's conception of philosophy, and the extent to which his critique grows out of the logical empiricist picture. Speciﬁcally: ﬁrst, Quine accepted the root idea of veriﬁcationism. It is because meaning, to the extent that we can make sense of meaning, must be explained in terms of veriﬁcation or conﬁrmation that the epistemological holism that Quine shared with Carnap was relevant to the critique of the analytic/synthetic distinction. Second, Quine agreed with Carnap's pragmatism: one chooses theories and theoretical frameworks based on their fruitfulness. But according to Quine's more thoroughgoing pragmatism, the fruitfulness of a theory is a reason to believe that it is true. Third, and most important for our purposes, Quine agreed with the idea behind the empiricist diagnosis of metaphysics—that it arises from the conﬂation of semantic and factual questions. But this diagnosis takes on a different character when one conjoins it with the thesis that there is no non-arbitrary, theory-neutral way to distinguish factual from semantic questions. Quine would have agreed that to be clear in our inquiries, and to avoid misunderstandings, we need some kind of distinction, at least in context, between questions about what the world is like, and questions about how the words we use manage to make the claims about the world that they seem to make, but if we give up the idea that the contents of our empirical claims are ﬁxed a priori by wholly arbitrary stipulations, then the way we make this distinction, particularly in inquiries about fundamental theoretical matters, may itself be a

4

Quine (1951a).

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INTRODUCTION

matter of contention. The mix of semantic and factual issues that results in metaphysics is unavoidable. As Quine noted, ‘the quest of a simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of ultimate categories, a limning of the most general traits of reality.’5 Quine was explicit, in ‘Two Dogmas’, in noting that one of the upshots of his critique of the analytic/synthetic distinction was an opening of a place for speculative metaphysics. In the picture that emerges from Quine's critique, there are no external questions in Carnap's sense. We do choose linguistic frameworks in which to formulate our claims, and we judge them by their fruits, but in laying down their rules, and regimenting our theories in them, we are using the conceptual resources we ﬁnd ourselves with, and tinkering with them from within. We can ask about our practice of theorizing, and about the relations between our theories and the world, and when we do so, we are asking questions that are external in a different sense: we view ourselves and our theories as objects in the world we are theorizing about. Presupposing the theoretical account of the world that we accept, we ask about how the fact that we are theorists of the kind we are with theories of the kind we have is to be described and explained. As Quine put it, we ‘ponder our talk of physical phenomena as a physical phenomenon, and our scientiﬁc imaginings as activities within the world that we imagine’.6 If we are able to explain how we and our theorizing ﬁt into the world as we take it to be, then this will provide support for that conception of the world, but this kind of externalist account of how our theories manage to say things about the world involves a kind of circularity. It provides no neutral standpoint from which people with radically different general theoretical beliefs can ﬁrst agree about what they mean—about what their apparently conﬂicting theoretical claims say—and then discuss whether those claims are true. My reason for sketching this old story is that the themes that I see recurring in the papers included in this collection are all echoes of the Quinean picture that resulted from his critique of logical empiricism. First, you will ﬁnd in these papers an ambivalence about metaphysics that is reﬂected in the subtitle of the collection. Like Quine, I try to walk a line between realism and a Carnapian pragmatism. We cannot avoid ontological commitments in our choices of languages and frameworks, but we still evaluate such choices, as Carnap argued, on whether it is fruitful to theorize in a language which seems to require those commitments. Second, you will ﬁnd in these essays a preoccupation with the interplay of semantic and metaphysical questions. When two philosophers disagree, or seem to disagree, about fundamental matters, there is often a question whether they are talking past one another. We cannot separate semantic from substantive questions before we begin to theorize, but we still seek, in our philosophical

5

Quine (1960: 161).

6

Ibid. 5.

INTRODUCTION

5

theorizing, to separate, in context, questions about how to talk, or about how we in fact talk, from questions about what the world is like. That is one of the aims of Quinean regimentation, and it is an issue in most of the papers in this collection. Third, you will ﬁnd throughout these papers the kind of externalist perspective reﬂected in Quine's approach to semantic and metaphysical questions. We understand our own theorizing, and more generally our perspective on the world, not by building a conception of the world from within, but by locating ourselves and our cognitive activities in the world that we are talking and thinking about. I was slow to realize the extent to which I am a follower of Quine since the particular way he developed his picture—the conceptual tools that he found useful—were radically different from those that I found myself using. In particular, Quine was notoriously critical of modal logic, of the semantic apparatus used to interpret it, and more generally of any attempt to explain anything in terms of intensional entities—attributes (as contrasted with sets), relations in intension, propositions. But the possible worlds framework and the account of propositions that it provides are central to all of my attempts to come to terms with metaphysical issues. Quine's rejection of modal and intensional notions ﬁts naturally with his skepticism about analyticity and a priori knowledge and truth, and there are tensions in any attempt to use the possible worlds framework to carry out a philosophical project that is Quinean in spirit, tensions that are apparent in many of the essays in this collection. But there are in any case tensions in a philosophical project like Quine's own that takes as its central focus the relations between theorists and their theories and the world that they theorize about, but that tries to talk about these relations without using any notion of the content of the theories—of what the theories say about the world. The possible worlds framework helps to make some of the tensions explicit, and I think it also provides some resources for resolving them. If the possible worlds framework proves fruitful for clarifying our beliefs about what there is and about how we represent what there is, as I think it has, then a good Quinean should be willing to take it seriously. Before turning to some remarks on the different topics discussed, I should take note of another philosopher whose ideas ﬁgure prominently in the papers in this collection. David Lewis can, I think, also be regarded as a neo-Quinean, but one who picked up on different aspects of the Quinean legacy. While my Quine is a veriﬁcationist at heart, and a reluctant metaphysician, Lewis's Quine breaks more radically with the positivist past (or perhaps recovers a latent metaphysical impulse in positivism, for Lewis regarded Carnap as a great metaphysician). While my Quine is ‘no champion of traditional metaphysics’,7 and pushes ‘the maxim of shallow analysis’ (‘if it doesn't itch, don't scratch’),8 Lewis's seeks a systematic and uniﬁed

7

Quine (1966: 127).

8

Quine (1960: 160).

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INTRODUCTION

account of what there is. Lewis shared Quine's materialist and nominalist inclinations, as well as his holistic methodology, even if he reached very different conclusions from Quine about what there is. Both Lewis and I parted company with Quine in embracing the centrality of possible worlds, but we gave very different accounts of what possible worlds are. And while we both explained propositional content in terms of possible worlds, we gave contrasting accounts of how thinkers and speakers are related to the contents of their thoughts and speech acts. A fruitful mix of agreement and disagreement between Lewis and myself on many issues, both substantive and methodological, will be evident throughout these essays.

1. Ways and worlds All of the papers in this collection are, in one way or another, about possible worlds, but those in the ﬁrst section focus directly on questions about what kind of thing they are. I started talking about possible worlds, ﬁrst to give a semantic analysis of conditional propositions, and then to represent speech contexts and intentional content, without giving a lot of thought to questions about their nature. It didn't occur to me that one might think of them literally as worlds—as parallel universes similar in kind to the totality of ourselves and all our surroundings—until I heard criticisms that took me to be committed to things of that kind, and then read David Lewis's endorsement of this account of possible worlds. Although I professed to have no ontological conscience, I realized that I had to address the question of what, if not things of this kind, I was committing myself to by talking about possible worlds. There is a simple puzzle that anyone who takes possible worlds seriously needs to address. The possible worlds theorist is committed to two theses that seem to contradict each other: ﬁrst, the theory says there is a plurality of possible worlds (at least more than one). But second, it says that only one possible world is actual—the rest are merely possible. But merely possible things don't exist, so contrary to the ﬁrst thesis, there is only one possible world. Lewis's conception of possible worlds—modal realism or possibilism— and the one I defend—actualism—give contrasting solutions to this puzzle. Both say that the source of the puzzle is an equivocation; they agree that the claims that there are many possible worlds, and that there is only one possible world are each true in one sense, and false in another, but they locate the equivocation at a different place. For the modal realist, the equivocation is on the domain of the quantiﬁer. When our quantiﬁer is unrestricted, then the statement that there are many possible worlds is true, but our quantiﬁer is very often restricted to a proper subclass of what exists—the things that actually exist, and when the quantiﬁer is interpreted in this restricted way, the statement says something false. This diagnosis is

INTRODUCTION

7

not available to the actualist about possible worlds, since he holds that what is actual coincides with what is real, and so that unrestricted quantiﬁcation is the same as quantiﬁcation over what is actual. For the actualist, the equivocation is on the kind of thing one is referring to when one uses the term ‘possible world’. The things we are talking about when we say that there are many possible worlds are possible states of the world, or ways that a world might be. When we say that there is only one world—the actual world—we are talking about something that is in one of those states. There exist many ways a world might be, and these ways actually exist. But there is only one of these ways that is instantiated, and so only one universe that is one of the ways. If it is worlds themselves we are talking about, then it won't be true to say that nonactual worlds exist, no matter how wide one takes the range of one's quantiﬁer to be. What is required for this actualist response to the puzzle to work is that possible worlds be the kind of thing that may have instances, but that may exist without instances. That is, possible worlds—or to avoid the ambiguity, possible states of the world—are properties of a certain kind. Lewis called the possible worlds of the actualist account ‘ersatz worlds’. This is good rhetoric, but the actualist should resist the label: it is like calling the property of being the present king of France an ersatz king, as if the uninstantiated property were a pretender to the throne. But behind Lewis's rhetoric are good reasons, given his metaphysical beliefs, for rejecting the actualist conception of a possible world. For Lewis, properties are nothing but sets.9 If ways a world might be are sets, with their instantiations (if any) as members, then there will be many ways a world might be only if there are many universes to distinguish the different unit sets that are these properties. Ironically, it was a taste for desert landscapes inherited from Quine—a rejection of universals and an identiﬁcation of properties with their extensions—that led Lewis into what some regard as the jungle of modal realism.10 An advantage Lewis claimed for modal realism, and denied of the actualist account, is that it provides the materials for a reductive analysis of all modal notions. Whether his theory, if correct, would provide such a reduction is controversial, but I am prepared to concede it, and also to agree that the actualist account fails to give an eliminative analysis of modal notions. But it seems to me that modal notions are basic notions, like truth and existence, which can be eliminated only at the cost of distorting them. One clariﬁes such notions, not by reducing them to something else, but by developing one's theories in terms of them.

9

Lewis did recognize a primitive distinction between natural properties and arbitrary sets of individuals, but he regarded this as a distinction between certain sets of individuals and others.

10

Not that it is clear sailing for the actualist account of possible worlds if one accepts universals. Many metaphysical theories of universals have a problem with fundamental properties that are uninstantiated.

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INTRODUCTION

The contrast between my view of possible worlds and Lewis's is not just a difference in basic metaphysical commitments. My aim was to separate a commitment to possible worlds from any speciﬁc metaphysical theory at all. I see the apparatus of possible worlds, not as a metaphysics, but as a framework for representing one's commitments, and for clarifying disagreements between people with conﬂicting commitments. The basic assumption that informs all of my attempts to come to terms with metaphysical questions is that what it is to represent the world—to say how things are—is to locate the world in a space of possibilities. One understands what someone else is saying by understanding how that person is distinguishing between the possibilities, as one takes those possibilities to be. The concept of a possibility— a way a world might be—is to be explained functionally—as what one is distinguishing between when one says how things are. Saying something more substantive about the character of logical space—about the distinctions there are to be made between the possibilities—is done by formulating and clarifying speciﬁc theories. Just as understanding the concepts of truth and existence tells you little, by itself, about what exists, or what is true, so understanding the concept of possibility tells you little of interest about what possibilities there are. Chapter 1, ‘Possible Worlds’, was my ﬁrst attempt to articulate an actualist view of possible worlds, to contrast it with Lewis's, and to explain possible worlds in terms of their role in the representation of content. The second chapter, written about twenty years after the ﬁrst version of the ﬁrst, develops further the contrast between actualism and modal realism, focusing on questions of modal epistemology that are a problem both for Lewis's theory and for the one I defend. In the third paper in this part—a dialogue on impossibilities—Lewis (or rather his ﬁctional counterpart Louis) appears as an ally rather than an opponent. Although the explicit topic of the dialogue is the existence of impossible worlds, my real concern was the light that the discussion of this issue might shed on the role of possibilities in the representation of content, and on the problem of characterizing the limits of logical space. The aim was also to display (or to caricature) some of the difﬁculty of separating semantic from metaphysical questions.

2. Carving up logical space There is little to be said, if one wants to remain completely neutral, about what possible worlds there are, and what they are like. There is no way to describe a space of possibilities except by distinguishing between the possibilities—by carving up logical space. Even the most abstract characterization of a space of possibilities makes metaphysical commitments, but the aim in any speciﬁc representation of the structure of a space of possibilities is to remain as neutral as one can on issues in contention in the context in question. My aim, in the papers in Parts II and III, is to ﬁnd and develop

INTRODUCTION

9

representations of the space of possible worlds that make sense of certain metaphysical theses about the relations between individuals and their properties. My aim, for the most part, was not to defend the theses, but to see if they can be given clear and coherent expression. ‘Anti-essentialism’, the oldest of the papers in this collection, uses a problem about essentialism to motivate a framework for the representation of properties that goes beyond the kind of representation provided by the basic possible worlds framework. Properties, on a thin conception of property, are just ways—any ways—of grouping individuals. In a simple possible worlds model, one can identify properties with functions from possible worlds to sets of individuals—the extensions of such functions are the members of the domain of the world that instantiate the property in that possible world. But to make sense of a certain anti-essentialist doctrine, we need a more robust conception of property—not just a grouping of individuals, but something about the individuals in virtue of which they are grouped. The representation I used identiﬁes intrinsic properties with the regions of a quality space, and identiﬁes possible worlds with location functions that map a set of possible individuals into the space. (The reader should be warned that the term ‘logical space’, elsewhere used to refer to the space of possible worlds, is in this paper used to refer to a property space.) This kind of model provides a distinction between a thick and a thin (or sparse and abundant) notion of property that is intuitively motivated, and that is needed to make sense of the anti-essentialist doctrine. By using sets to represent properties, this conception of properties and relations does as well as an extensional theory in modeling structural relations between properties, but since the members of the sets are different from the individuals that instantiate the properties, it represents the independence of properties from their instantiations. Is this a theory of universals (or a framework for such a theory)? There is an extensive contemporary literature about the problem of universals, one that I have not engaged with, mainly because it overstimulates my Carnapian inclinations. Universals, according to David Armstrong and, following him, David Lewis, are by deﬁnition ‘repeatable entities wholly present whenever particulars instantiate them’.11 They are parts, but non-spatio-temporal parts, of their instances. Are there such entities? If I ask myself whether, say, the property red is wholly present, or only partially present in a red rose, or whether the property is a part of the rose, I lose my grip on the game we are playing. I think it is unhelpful to deﬁne universals in terms of these obscure features, since it labels as nominalistic any theory that denies that there are things of this kind, even if it is committed to properties that are independent of their instances. And building these features into the deﬁnition contributes to the appearance that arguments against a

11

Lewis (1999: 8–9, n. 2).

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INTRODUCTION

particular theory of universals such as Armstrong's have a wider target than they in fact have. The quality space model is not nominalistic in any reasonable sense, but it suggests that properties are not things that ﬁt the Armstrong deﬁnition. If the property red is a region of a property space in which a red rose is located, then to say that the property is part of the rose, wholly present in it, would be like saying that Texas is a part of George W. Bush, wholly present in him, whenever he is at home on his ranch in Crawford. Isn't it rather that Bush is wholly present in Texas on those occasions? The spatial model is perhaps only a metaphor, but it suggests a conception of property that is an alternative both to Armstrong's theory of universals and to Lewis's identiﬁcation of a property with the class of its instantiations. The framework sketched in this paper is just the start of a project that remains undeveloped. The model of a possible state of the world as a function locating possible individuals in a quality space is simplistic in many ways, some of which are pointed out in the paper, but I think it has the potential to be embellished and complicated in ways that might throw light on questions about the nature of properties and the relations between individuals and their properties. The other paper in this section, ‘Varieties of Supervenience’, is also concerned with properties, and the way we carve up logical space in terms of them. Its speciﬁc concern is with the relations between different ways of carving up a space of possibilities. Some levels of description seem more basic than others, and less basic descriptions often seem to be, in some sense, redundant. They don't describe further features of the world, but some of the same features in different ways. This is obviously a vague idea in need of clariﬁcation. One way to pin it down (a way that was standard at a time when it was thought that all philosophical problems were problems about language) is in terms of the reduction of theories: one deﬁnes the terms of a less basic theory by the terms of the more basic one, and using those deﬁnitions, shows that the ﬁrst theory can be deduced from the second. But many philosophers concluded that a reductionist thesis of this kind was too restrictive to capture the intuitive idea since it mixed semantic claims about the expressive resources of theories with metaphysical claims about the relations between sets of properties. Supervenience is a conceptual tool, or a family of conceptual tools, designed to separate out the purely metaphysical part of a reductionist thesis. The rough idea is that one set of facts or properties supervenes on another if possible worlds, or possible individuals, exactly alike with respect to one kind of property or fact are necessarily exactly alike with respect to the other. Much of the paper is devoted to trying to get clear about the technical issues involved in making supervenience precise, and about the relations between different kinds of supervenience, and different interpretations of those notions. I try to distinguish an interpretation of supervenience that is

INTRODUCTION

11

more reductionist in spirit from one that takes supervenience to be some kind of primitive metaphysical relation, but I have to concede that this distinction remains somewhat elusive. I argue that global supervenience, as it is often deﬁned, needs reﬁnement in order to close an unintended loophole, and try to state precisely the relation between global and strong supervenience. I discuss the sense in which a supervenience thesis may be contingent. The paper concludes by looking at the role of the notion of supervenience in the dialectic of philosophical argument. I did not begin this project with a skeptical agenda, but this exploration did lead me to the conclusion that the concept of supervenience is less clear and clean than is often supposed. While I think the point of this conceptual tool is to help separate semantic from metaphysical questions, it is not clear that one can apply the notion at all without making strong and controversial metaphysical assumptions. In particular, the picture that guides our intuitions about supervenience seems to presuppose that there is an ultimate most basic space of properties—the fundamental properties and relations which sufﬁce to determine a complete possible world. Even if it is reasonable to think that there is such a basic property space, it is clear that it is an empirical question what these properties and relations are like.

3. Identity in and across possible worlds The papers in Part III use a version of counterpart theory, and an actualist interpretation of it, to try to throw light on some issues about identity and predication. The original version of counterpart theory was developed by David Lewis in the context of modal realism. The thesis is that possible individuals exist only in one possible world, though they have counterparts in other worlds, and the modal properties of individuals will be a function of the properties of their counterparts. So, for example, according to Lewis's counterpart theory, it will be true that Aristotle might have died in infancy if and only if Aristotle has a counterpart in some possible world who died in infancy in that world. Modal realism, if one accepts it, provides one compelling motivation for counterpart theory: if other worlds are really worlds, then it seems obvious that Aristotle could not be in more than one of them. But an actualist might also have reason to be a counterpart theorist. A second motivation for counterpart theory, compatible with actualism, is a reductionist attitude toward individuals—a bundle theory that holds that the identity of an individual is supervenient on its qualitative character and location. On this conception of individuals—a version of anti-essentialism different from the one discussed in Chapter 4—one needs to explain the way individuals are identiﬁed across possible worlds in terms of the qualitative characteristics that they have within the worlds, which a counterpart relation would do, if it were explained in qualitative terms.

12

INTRODUCTION

The version of counterpart theory that I explore in the three papers in the third section has neither of these motivations. My aim was not to defend a metaphysical theory at all, but to develop a framework for representing some puzzles about identity across possible worlds, puzzles that some philosophers take to support the idea that identity is in some sense contingent. Many philosophers (for example Ruth Marcus, David Wiggins, Saul Kripke) have argued that it makes no sense to say that the identity relation is contingent: that there is or could be a pair of individuals that instantiates the identity relation, but that might have existed without instantiating that relation. If the relation is really identity, then the only pairs that are candidates to be examples of contingent identity are those with the same thing in both places. An example would have to be a pair that, in some counterfactual world, failed to be in the extension of the identity relation, even though a existed in that world. But the identity relation is, by deﬁnition, the relation that includes in its extension (in any given world) for every a that exists in that world. There are identity statements that are contingent (such as ‘The inventor of bifocals was the ﬁrst postmaster general of the United States’), but their contingency is explained by the fact that one or both of the terms in the statement might have referred to different things. And there are equivalence relations different from identity that might be confused with it. But, it seems, no coherent metaphysical doctrine, no matter how outlandish, can make literal sense of the thesis that the identity relation is contingent. I don't dispute this argument, and the counterpart semantics that I develop validates the thesis that identity is an essential relation. My aim in ‘Counterparts and Identity’ was not to defend the coherence of the thesis that the identity relation can be contingent, but to make sense of a family of puzzles about identity across possible worlds that have motivated some philosophers to defend the thesis that identity can be contingent, and to see if there is a coherent metaphysical view in the vicinity. The puzzles are familiar: the ship of Theseus, and cross-world versions of it, the statue and the clay, sorites-like puzzles that suggest that identity across worlds is nontransitive. All of these puzzles describe possible situations in which it is controversial whether certain cross-world identity statements are true. A ﬁrst step to getting clear about such puzzles would be to have a framework in which we can give a clear representation of the phenomena without begging the questions at issue. So if it is in dispute whether ship A in world x is the same as or different from ship B in world y, then we want representations of the worlds that separate, to the extent that it is possible, the relations of cross-world identity from internal descriptions of the character of the individuals in their worlds. The second step is to note that if we are actualists, then we have to grant that when we talk about domains of individuals that exist in other possible worlds, we are not talking literally about sets of individuals

INTRODUCTION

13

themselves, since some possible individuals do not actually exist, and there are no individuals that do not actually exist. Talk of a merely possible individual, according to an actualist, is loose talk about a possibility that there be an individual different from any that actually exists. Domains used to represent such possibilities will be sets, not of individuals themselves, but of representatives of some kind for individuals: essences, or roles, or ways an individual might be. (Just as actualists distinguish ways a world might be from a world that is that way, so they need to distinguish the way an individual might be from an individual that is that way.) Questions about whether one possible individual, a member of the domain of some counterfactual possible world, is identical with a possible individual in another world are questions about whether one representative represents the same individual as another. In a standard modal semantic theory, the individuals represented will be identical if and only if the representatives are identical, but it is open to individuate the representatives in a different way, and that is what an actualist counterpart theory does. One motivation for doing so is simply to provide a perspicuous framework for describing the puzzle cases, but in doing so, one also generalizes the modal framework and makes room for some new responses to the puzzles. The framework does not allow for contingent identity, but it does allow for contingent distinctness, and for something that sounds very close to contingent identity: the existence of distinct things that might be identical, but only contingently so. These claims may be bizarre and unacceptable, but I argue that such possibilities cannot be shown to be incoherent in the way that contingent identity can be. They need to be rejected, if they are to be rejected, on metaphysical grounds. There is no question that the counterpart semantics is formally coherent, but one may argue that it makes apparent sense of certain theses only by reinterpreting the language in which the theses are stated. Perhaps counterpart theory does not really mean identity by the identity sign; perhaps the apparently bizarre metaphysical claims it shows to be coherent are just bizarre ways of saying familiar things. A large part of the burden of the defense of the coherence of the theory is to argue that the relation it calls identity is really identity—the relation that holds between anything and itself, and not between anything and anything else—and that what the theory calls predication is really predication. There is no knockdown argument for these claims, but their plausibility is supported by showing that both the logic and the semantics of the extensional theory of identity and predication are perfectly standard, and the modal semantics provides a smooth generalization of the extensional theory. Whether or not the metaphysics makes sense in the end, I think the attempt to stretch basic concepts to accommodate it, while preserving their central features helps to throw light on modal predication and variable binding. It also helps to bring out some of the contrasts between modal realism and actualism, since the actualist setting of the theory is central to the argument.

14

INTRODUCTION

A minor change in the standard argument for the incoherence of contingent identity yields an argument that the identity relation cannot be vague. But just as there can be contingent identity statements when the referring terms in them refer contingently, so there can be vague identity statements if the referring expressions in them can be vague. Some apparently vague identity statements seem to involve identity across worlds or times. Can cross-world identity relations be vague? Might it be indeterminate, for example, whether a certain table in another possible world is the same table as a certain actual one, where the possible table is made in the same way at the same time as the actual table out of mostly but not entirely the same stuff? It is argued, in the second paper in Part III, ‘Vague Identity’, that the counterpart semantics can help to clarify such questions. If so-called cross-world relations between individuals are really relations between some kind of representatives of individuals, and not between individuals themselves, then the so-called cross-world identity relation need not be identity, and even if identity itself cannot be vague, a relation of this kind might be. Analogies between times and worlds are familiar, and the puzzles about cross-world identity all have temporal analogues. These two papers discuss both analogies and disanalogies between cross-temporal and cross-world identities. The distinction between actualism and possibilism is in many ways analogous to the distinction between a presentist and a four-dimensionalist view of time, though the formal analogy does not imply that there is any conﬂict between actualism about worlds and four-dimensionalism about time. Few of us are modal realists—even David Lewis acknowledged that the thesis that there are other possible worlds as real as our own diverges from common opinion. On the other hand, almost all of us are realists about space, holding that distant places are just as real as our local one. About other times—particularly future times—it seems that common opinion is ambivalent: we tend to think of time sometimes as space-like and sometimes as world-like. I am not sure which is the right way to think of it, or even whether this is really a metaphysical difference, and not just differences in the form of representation, but I suspect that in any case some metaphysical puzzles about time arise from shifting between the two. The counterpart semantics has some technical interest that is independent of its metaphysical interpretation and motivation. The third paper in Part III uses that semantics to show the independence of some logical principles that involve the interaction of quantiﬁers and modal operators. Speciﬁcally, it is shown that there are principles that are valid in the classical semantics, but that are not theorems of the logic that results from a combination of a complete extensional quantiﬁcation theory with a complete modal propositional logic. Surprisingly, it turns out that completeness proofs for the most general modal logics with respect to a counterpart semantics are relatively simple and straightforward, and that one can get a

INTRODUCTION

15

transparent completeness proof for the classical semantics by seeing it as a special case of the counterpart semantics.

4. Semantics, metasemantics, and metaphysics General issues about the relation between semantics and metaphysics take center stage in the three papers in Part IV. My central premise throughout has been that we understand the informational or propositional content of thought and speech in terms of the way we distinguish between possibilities. Metaphysics concerns the distinctions there are to be made between possibilities, while semantics—more broadly, the study of the intentionality of both thought and speech—is concerned with our capacity to represent and distinguish between the possibilities. The two kinds of questions are inextricably intertwined, since we cannot address the metaphysical questions without exercising our capacities to represent, and the interpretation of metaphysical claims may depend on our account of those capacities. On the other hand, we cannot theorize about our representational capacities except from the perspective of some view of what logical space is like, and where in it we are located. But despite the difﬁculty of disentangling these two kinds of questions, we need to try to avoid, in context, the confusion that can result from equivocating between them. The ﬁrst paper in this Part, ‘Reference and Necessity’, is an interpretation of what I take to be the central line of argument in Saul Kripke's groundbreaking lectures, Naming and Necessity. It is argued that the most important accomplishment of this work was to separate semantic questions about reference from metaphysical questions about the objects of reference. I begin by distinguishing two kinds of semantic questions, which I label descriptive and foundational. (In the two later papers in this Part, I adopt David Kaplan's terminology—semantic vs. metasemantic—for what is essentially the same distinction.) Descriptive semantic questions ask what the semantic value of certain expressions or kinds of expression are. Foundational or metasemantic questions ask what the facts are in virtue of which expressions have the semantic values they have. The thesis that proper names are rigid designators is an answer to a descriptive question about names, while a causal theory of reference is an answer to the foundational or metasemantic question about what it is that explains why names have the referents that they have. Both kinds of semantic questions are distinguished from metaphysical questions about the essential properties of individuals and kinds. Kripke, as I interpret him, argues (convincingly, in my view) that equivocation between the two kinds of semantic questions is part of what motivates a description theory of names, and that equivocation between semantic and metaphysical questions is part of what motivates resistance to intuitively natural metaphysical views about the essential properties of individuals and kinds.

16

INTRODUCTION

The other two papers in Part IV discuss the use of a two-dimensional modal semantic framework to clarify issues about the relation between conceptual and metaphysical questions. Ideas from Kripke's Naming and Necessity also ﬁgure prominently in these two papers, since this application of the two-dimensional modal framework was to a large extent a response to Kripke's arguments that there are necessary truths knowable only a posteriori, and contingent truths that are knowable a priori. Different philosophers have used the apparatus in a similar way to describe the phenomena that Kripke brought out, but have drawn different conclusions about its interpretation and signiﬁcance. In these two papers, I contrast my understanding of the framework with those of Frank Jackson and David Chalmers. In two-dimensional modal semantic models, the sentences of an appropriate formal language are associated with what I have called propositional concepts, which are functions from possible worlds to propositions, where propositions are themselves functions from possible worlds to truth-values. If an utterance that occurs in a given possible world is (somehow) associated with a propositional concept, then one can deﬁne in terms of it two different propositions. If c is the propositional concept, and x is the possible world in which the utterance u takes place, then c(x) is what Frank Jackson calls the C-intension expressed by u in x. The second proposition, which Jackson calls the A-intension expressed by u, and which corresponds to what I have called the diagonal proposition of the propositional concept, is the proposition that is true at any world y if and only if c(y) is true at y. C-intensions are determined by a propositional concept only relative to a possible world, while A-intensions are determined by the propositional concept alone. This apparatus is used to explain the divergence of modal and epistemological distinctions in roughly the following way: there are no propositions that are both necessary and a posteriori; or both contingent and a priori; rather, a necessary a posteriori statement is one with a C-intension that is necessary, but an A-intension that is contingent. Contingent a priori statements exhibit the opposite combination: their A-intensions are necessary, while their Cintensions are contingent. This kind of account aims to reconcile an explanation of the epistemological distinction in modal terms with the divergence between the modal and epistemological distinctions. But how are utterances and acts of thought associated with propositional concepts? Different philosophers who agree on this kind of explanation for the phenomena disagree about how this question is to be answered. My use of this apparatus was motivated by the observation that whatever the details of the descriptive semantics, if an utterance or an act of thought expresses a proposition, then the truth-value of what is expressed in the act will depend on the facts in two different ways: ﬁrst, the content—what is said or thought—will depend on the facts; second, if what is said or thought

INTRODUCTION

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is a contingent proposition, then its truth-value will depend on the facts. If this is right, then one can use the twodimensional framework as a descriptive apparatus for representing these two kinds of dependencies. A propositional concept, deﬁned for a set of possible worlds in which a given utterance event takes place, will represent the way that the content of the utterance depends on the facts. The semantics for the language may be one-dimensional, on this use of the apparatus, but the semantics itself may vary from world to world. When we ‘consider a world as actual’, in evaluating the truth-value of what someone is saying or thinking, we adopt the hypothesis that the speaker or thinker and we are speaking and thinking from within that possible world, and so we interpret the person's speech in terms of the semantics that applies in that possible world. In contrast, if we are ‘considering a world as counterfactual’ in evaluating what a person is saying relative to that world, we use the actual semantics, and not the semantics of the world in question. It is because semantics may vary from world to world that the two methods of evaluation may differ. I labeled this way of using and interpreting the two-dimensional apparatus ‘metasemantic’ because the facts on which what is said depends are the metasemantic facts—the facts in virtue of which the sounds or marks we make, or the states of our brains, have the representational properties that they have. I contrast this interpretation with what I call a ‘semantic’ interpretation of the same two-dimensional apparatus which holds that a proper descriptive semantics for the languages we happen to speak will be a two-dimensional semantics, associating propositional concepts with its sentences. Our languages get a two-dimensional interpretation because they contain what are in effect generalized scope devices—reference-ﬁxing mechanisms that allow us to describe a proposition (the C-intension) and to assert that it is true even if we are ignorant of exactly what proposition it is. On this interpretation, it is in general only the Aintension and the propositional concept associated with a thought or an utterance to which the speaker or thinker has cognitive access. That is why it is the modal status of the A-intension that determines the epistemological status of the utterance. My main aim in Chapters 10 and 11 is to bring out the signiﬁcance of the contrast between the two interpretations of the two-dimensional apparatus. The difference matters, I argue, for our understanding of the epistemological concepts—a priori and a posteriori—and their relation to the modal concepts, necessity and contingency. The semantic interpretation of the two-dimensional apparatus identiﬁes a priori truth with the necessity of the Aintension. In contrast, while the metasemantic interpretation can make sense, in context, of the paradigm examples of the contingent a priori, it does not provide or require any general account of a priori truth. On the metasemantic interpretation, where the semantics may vary from world to world, nothing will be a priori in this sense unless the domain of possible worlds relative to which the

18

INTRODUCTION

propositional concepts are deﬁned is restricted in some way. The absence of a general characterization of a priori truth, and of any reliance on such a notion, might be regarded as a disadvantage by some, but those of us who are antecedently skeptical of this notion should regard it as an advantage. The notions of a priori knowledge and truth—things that are in some sense knowable independently of experience—seems to me even more obscure and problematic than the semantic notion of analytic truth. Even if we can distinguish conceptual analyses from synthetic claims, it seems reasonable to think that we evaluate the plausibility of both in a holistic way—by how well they ﬁt together into a satisfactory general account of our experience, broadly construed. I suspect that the notion of the a priori is a mix of different notions, some of which are probably essentially tied to parochial epistemological projects. The different notions may come together in certain cases, creating the illusion that at least sometimes we know what we are talking about when we talk about the a priori. So it may be that paradigm logical truths are a priori in all reasonable senses, while some other candidates (for example, ‘vixens are female foxes’, ‘arthritis is a disease of the joints’, ‘I exist’, ‘there are physical objects’) are a priori in some senses, and not in others. If we can get along without any of these notions, so much the better. The semantic interpretation that I argue against takes the phenomenon of necessary a posteriori truths to be the result of relatively superﬁcial linguistic facts. Frank Jackson suggests that it arises from an optional descriptive-semantic mechanism that happens to characterize natural languages: a mechanism of reference ﬁxing. He suggests that we might have a ‘reference-ﬁxing-free language’ that had the expressive power to ‘say how things are in some detail’. but that would contain no necessary a posteriori truths at all.12 But if the reference-ﬁxing mechanisms are part of the metasemantic story, they are not optional: they are part of an account of what constitutes the fact that our utterances and internal states are able to have representational properties at all. On the account I defend, the paradigm examples of necessary a posteriori truths are a mark of a general and inevitable feature of intentionality, of the fact that we can represent the possibilities we distinguish between in describing the world only in terms of the resources—properties, relations, events, and individuals—that the actual world provides us with. Questions about the nature of those resources are empirical questions, so there will inevitably be empirical questions about what the possible worlds are like and whether there are possible worlds ﬁtting certain descriptions. The two-dimensional framework, on this way of understanding it, can help to describe and clarify the way that questions about what is possible and what is true interact, and can help to separate semantic from factual questions in context, but it can't provide a presupposition-free

12

Jackson (2001: 620–1).

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canonical language in which to give an absolutely neutral characterization of the space of possibilities.

5. Subjective possibilities The three papers in the ﬁnal section are about the problem of accounting for a subject's point of view, and of relating it to our account of the way the world is, and the possible worlds are, in themselves. One way to understand a subjective point of view is to try to take that point of view—to see the world from the perspective of the subject. A different way is to consider what objective conditions something in the world has to satisfy in order to be a subject—what a thing must be like for there to be, in some sense, ‘something it is like’ for that thing. Just as, following Quine, we may ‘ponder our talk of physical phenomena as a physical phenomenon’, so we may ponder the fact that we are the kind of thing that can experience the world from a certain point of view as a fact about the world that we experience. Our metaphysical (and scientiﬁc) theories are, for the most part, theories about what the objective world is like in itself. To be defensible, they must provide an adequate account of everything we ﬁnd there, including—perhaps especially— the fact that we are phenomenally conscious beings that experience this world from the inside. But it is controversial just what needs to be shown to show that a metaphysical theory (for example, materialism) succeeds in giving a satisfactory account of subjective experience. Are there facts of a distinctive kind about conscious subjects that are accessible only from the subject's point of view, or at least accessible only to one who has the imaginative capacity to take on the subject's point of view? If so, are they irreducible objective facts that must be included in a complete account of the way the world is in itself? These papers explore some aspects of this problem. The papers in this section are all very recent. For a long time I avoided the issue of consciousness, afraid of sinking in the bog. (I sometimes fear, when I hear certain philosophers talk about phenomenal consciousness, that I am one of the zombies—creatures that lack this property, even though they are physically and functionally exactly like conscious beings—and that this is why I ﬁnd them hard to understand. Some may ﬁnd conﬁrmation for this fear in the content of these papers.) I was drawn into these issues by their connection with the more abstract metaphysical issues discussed in the other papers, and with issues about intentionality that continue to puzzle me. In particular, questions about supervenience, and about the relation between conceptual and metaphysical possibility, are obviously relevant to arguments about whether a materialist theory can account for our conception of ourselves as conscious subjects. And the idea of a possible world considered as actual that is part of the intuitive explanation of the two-dimensional modal framework is the idea of a world considered from within—from the point of view of a subject in it.

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INTRODUCTION

‘Comparing Qualia across Persons’ is about the puzzle of the inverted spectrum, and Sydney Shoemaker's attempt to reconcile the intelligibility of the inverted spectrum with a functionalist and materialist theory of the mind. The general issue here is the relation between consciousness and representation—between the intentional and the qualitative content of an experience. I am also interested in Shoemaker's argumentative strategy, which plays on the relation between intrapersonal and interpersonal comparisons. Against Shoemaker, I defend the old-fashioned view that comparisons of the qualitative character of experience across persons are meaningless (at least if the qualitative character of experience is understood to be conceptually independent of representational properties). The aim is not to ‘quine qualia’—to defend an eliminativist attitude to such properties—but to argue for the intelligibility and plausibility of a view of them as part of a purely relational structure, and to suggest that to the extent that we can make sense of interpersonal comparisons of qualitative experience, it is because our conception of qualitative character is conceptually connected to representational content. ‘What is it Like to be a Zombie?’ examines a familiar argument from the conceivability of zombies to their possibility. I argue, ﬁrst, that one cannot escape the argument by claiming that there are possible worlds—zombie worlds—that are conceivable but metaphysically impossible. The problem is that all materialists agree that there are possible worlds that the dualists call ‘zombie worlds’, and they agree that these worlds are not only conceivable, but metaphysically possible. They just disagree that these possible worlds are properly described as ‘zombie worlds’. But second, I argue that while there is a sense in which it is conceivable that there be zombie worlds, the inference from conceivability in this sense to possibility works only if materialism is assumed to be in fact false, and so the conceivability of zombies provides no argument against materialism. The general picture promoted is this: ‘consciousness’ refers to a property we ﬁnd ourselves with, and that we perhaps know we have by having it. But our being conscious beings provides no special access to the nature of that property. Hypotheses about that have to be evaluated, like hypotheses about the nature of anything else we ﬁnd in the world, by how well they ﬁt with our overall theory of the world. The last and most recent paper is about an intriguing but elusive conception of the self proposed by Thomas Nagel, or at least that is where the paper begins. It is also about the informational content of the things we say and think when we talk about ourselves and our place in the world. And in the end, it is about Mary, Frank Jackson's notorious character who knows all there is to be taught about color, but has never experienced it. Nagel's discussion of the objective self begins with the expression of a general feeling of puzzlement about one's place in the impersonal world, and with this speciﬁc puzzle about it: when a person says who he or she is (when, for example, I say ‘I am RS’), it seems that the person states a fact,

INTRODUCTION

21

and it is an objective fact in the sense that what is said is true or false independently of what the speaker thinks. But it seems that our conception of an objective world leaves no room for such facts, since a complete description of the world as it is in itself will not single out any particular person as me. No matter how complete the objective description, it will not, by itself, tell me who I am. There is a familiar semantic diagnosis that tries to use an account of indexical or self-locating belief to solve the problem. Nagel rejects the semantic diagnosis because he thinks it does not get to the heart of the matter. Against Nagel, I argue that a version of it can dissolve this particular puzzle, though there is still work to be done to clarify the semantic account, and there are plenty of problems that remain about the relation between a subject and the world he or she inhabits, questions about exactly what the subjective facts about the way we experience the world tell us about what the world is like in itself. If one asks about the truth-conditions for indexical or self-locating statements, there is no puzzle—nothing could be simpler: if EA said ‘I am a philosopher’, on June 5, 1953, then she said something that is true if and only if EA was a philosopher on June 5, 1953. But what is the content of her statement? It has been convincingly argued that the information a speaker conveys with indexical expressions is not captured in a correct statement of their truthconditions in timeless, impersonal terms. That is, the belief EA expressed and what she told her audience, when she said that she was a philosopher on that occasion, was not the same as the belief she would have expressed if she had instead said ‘EA is a philosopher on June 5, 1953’, for she might have believed what she said without knowing the date, or that she was herself EA, and her audience might have understood her ﬁrst-person, present-tense statement without knowing these things. To dissolve the puzzle, and to help clarify the general problem, the semantic diagnosis needs an account of subjective or contextual informational content, and I make some suggestions about how to understand this idea. While he is dissatisﬁed with a semantic dissolution of the problem, Nagel is clear that he rejects an opposite kind of response—an ontological view that objectiﬁes self-properties. I describe a response of this kind that claims that each of us has a distinctive and irreducible objective self-property that only the possessor of the property can be acquainted with. This view is a kind of caricature that I don't think anyone would defend, but it illustrates a pattern and helps to deﬁne the issue. And I tentatively suggest at the end of the paper that this is a pattern that may be exempliﬁed in the objectiﬁcation of the phenomenal character of experience. The signiﬁcance of the question about subjective and contextual information for metaphysics is this: our conception of the world as it is in itself—our metaphysics—depends on our conception of the space of possibilities in which we locate the world. We draw conclusions about the

22

INTRODUCTION

character of that space from our judgments about the distinctions that need to be made between possibilities in order to make sense of our knowledge and beliefs. But the phenomenon of indexical or self-locating knowledge and belief brings out that our cognitive states are about our place in the world as well as about what the world in itself is like. We need to get clear about the kind of cognitive states that essentially involve the subject of those states in order to be clear about exactly what the distinctions we make between epistemic possibilities tell us about the world. Subjective information is obviously very important to us subjects, and there is a strong temptation to believe that our experience reveals to us facts that are, on the one hand, objective facts about the impersonal world, but on the other hand facts that are deﬁned in terms of a subject's point of view, and accessible only to that subject. Perhaps there are facts that are both objective and essentially subjective in this way, for example about ‘what it is like’ for someone or something to see colors, or to be a bat. But perhaps the idea that there are is an illusion that arises from a mistaken inference from the undeniable reality of our subjective experience to the conclusion that it needs a distinctive and irreducible place in our account of the world as it is in itself.

PART1 Ways and Worlds

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1 Possible Worlds (1976/1984) According to Leibniz, the universe—the actual world—is one of an inﬁnite number of possible worlds existing in the mind of God. God created the universe by actualizing one of those possible worlds—the best one. It is a striking image, this picture of an inﬁnite swarm of total universes, each by its natural inclination for existence striving for a position that can be occupied by only one, with God, in his inﬁnite wisdom and benevolence, settling the competition by selecting the most worthy candidate. But in these enlightened times, we ﬁnd it difﬁcult to take this metaphysical myth any more seriously than the other less abstract creation stories told by our primitive ancestors. Even the more recent expurgated versions of the story, leaving out God and the notoriously chauvinistic thesis that our world is better than all the rest, are generally regarded, at best, as fanciful metaphors for a more sober reality. J. L. Mackie, for example, writes, ‘talk of possible worlds…cries out for further analysis. There are no possible worlds except the actual one; so what are we up to when we talk about them?’13 Larry Powers puts the point more bluntly: ‘The whole idea of possible worlds (perhaps laid out in space like raisins in a pudding) seems ludicrous.’14 These expressions of skepticism and calls for further analysis are of course not directed at Leibniz but at recent uses of parts of his metaphysical myth to motivate and give content to formal semantics for modal logics. In both formal and philosophical discussions of modality, the concept of a possible world has shown itself to have considerable heuristic power. But, critics have argued, a heuristic device should not be confused with an explanation. If analyses of modal concepts (or of the concept of a proposition) in terms of possible worlds are to be more than heuristic aids in mapping the relationships among the formulae of a modal logic, the concept of a possible world itself must be explained and justiﬁed. Although it is commonly taken to be an obvious truth that there really are no such things as possible worlds—that the myth, whether illuminating or misleading, explanatory or obfuscating, is nevertheless a myth—this common opinion can be challenged. That is, one might respond to the possible worlds skeptic not by explaining the metaphor but by taking the

13

Mackie (1973: 84).

14

Powers (1976: 95).

26

WAYS AND WORLDS

story to be the literal truth. David Lewis responds in this way, and he cites common opinion and ordinary language on his side: I believe there are possible worlds other than the one we happen to inhabit. If an argument is wanted, it is this: It is uncontroversially true that things might have been otherwise than they are. I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way that they actually are. On the face of it, this sentence is an existential quantiﬁcation. It says that there exist many entities of a certain description, to wit, ‘ways things could have been’. I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities which might be called ‘ways things could have been.’ I prefer to call them ‘possible worlds’.15 Lewis does not intend this as a knockdown argument. It is only a presumption that the sentences of ordinary language be taken at face value, and the presumption can be defeated if the naive reading of the sentences leads to problems which can be avoided by an alternative analysis. The aim of the argument is to shift the burden to the skeptic who, if he is to defeat the argument, must point to the problems which commitment to possible worlds creates, and the alternative analysis which avoids those problems. Lewis does not think the skeptic can do either. The rhetorical force of Lewis's argument is in the suggestion that possible worlds are really not such alien entities as the metaphysical ﬂavor of this name seems to imply. The argument suggests not that ordinary language and our common beliefs commit us to a weighty metaphysical theory, but rather that what appears to be a weighty metaphysical theory is really just some ordinary beliefs by another name. Believing in possible worlds is like speaking prose. We have been doing it all our lives. But for this to be convincing, the shift from ‘ways things might have been’ to ‘possible worlds’ must be an innocent terminological substitution, and I do not believe that, as Lewis develops the concept of a possible world, it is. To argue this point I will state four theses about possible worlds, all defended by Lewis. Together they constitute a doctrine which I will call extreme realism about possible worlds. It is this doctrine against which the skeptic is reacting, and against which, I shall argue, he is justiﬁed in reacting. I believe the doctrine is false, but I also believe that one need not accept or reject the theses as a package. The main burden of my argument will be to show the independence of the more plausible parts of the package, and so to defend the coherence of a more moderate form of realism about possible worlds, one that might be justiﬁed by our common modal opinions and defended as a foundation for a theory about the activities of rational agents.

15

Lewis (1973: 84).

POSSIBLE WORLDS

27

Here are Lewis's four theses: 1. 2. 3.

4.

Possible worlds exist. Other possible worlds are just as real as the actual world. They may not actually exist, since to actually exist is to exist in the actual world, but they do, nevertheless, exist. Other possible worlds are things of the same sort as the actual world—‘I and all my surroundings’.16 They differ ‘not in kind, but only in what goes on at them. Our actual world is only one world among others. We call it alone actual not because it differs in kind from all the rest, but because it is the world we inhabit.’17 The indexical analysis of the adjective ‘actual’ is the correct analysis. “The inhabitants of other worlds may truly call their own world actual if they mean by ‘actual’ what we do; for the meaning we give to ‘actual’ is such that it refers at any world i to that world i itself. ‘Actual’ is indexical, like ‘I’ or ‘here’ or ‘now’: it depends for its reference on the circumstances of utterance, to wit, the world where the utterance is located.18 Possible worlds cannot be reduced to something more basic. ‘Possible worlds are what they are and not another thing.’ It would be a mistake to identify them with some allegedly more respectable entity, for example a set of sentences of some language. Possible worlds are ‘respectable entities in their own right’.19

The ﬁrst thesis, by itself, is compatible with Lewis's soothing claim that believing in possible worlds is doing no more than believing that things might have been different in various ways. What is claimed to exist are things which ordinary language calls ‘ways things might have been’, things that truth is deﬁned relative to, things that our modal idioms may be understood as quantiﬁers over. But the ﬁrst thesis says nothing about the nature of the entities that play these roles. It is the second thesis which gives realism about possible worlds its metaphysical bite, since it implies that possible worlds are not shadowy ways things could be, but concrete particulars, or at least entities which are made up of concrete particulars and events. The actual world is ‘I and my surroundings’. Other possible worlds are more things like that. Even a philosopher who had no qualms about abstract objects like numbers, properties, states, and kinds might balk at this proliferation of fullblooded universes which seem less real to us than our own only because we have never been there. The argument Lewis gives for thesis (1), identifying possible worlds with ways things might have been, seems even to be incompatible with his explanation of possible worlds as more things of the same kind as I and all my surroundings. If possible worlds are ways things might have been, then the actual world ought to be the way things are rather than I and all my surroundings. The way things are is a property or a state of the world, not

16

Ibid. 86.

17

Ibid. 85.

18

Ibid. 85–6.

19

Ibid. 85.

28

WAYS AND WORLDS

the world itself. The statement that the world is the way it is is true in a sense, but not when read as an identity statement (compare: ‘the way the world is is the world’). This is important, since if properties can exist uninstantiated, then the way the world is could exist even if a world that is that way did not. One could accept thesis (1)—that there really are many ways that things could have been—while denying that there exists anything else that is like the actual world. Does the force of thesis (2) rest, then, on a simple equivocation between ‘the actual world’ in the sense that is roughly captured in the paraphrase ‘I and all my surroundings’ and the sense in which it is equivalent to ‘the way things are’? In part, I think, but it also has a deeper motivation. One might argue from thesis (3)—the indexical analysis of actuality—to the conclusion that the essential difference between our world and the others is that we are here and not there. Thesis (3) seems to imply that the actuality of the actual world—the attribute in virtue of which it is actual—is a worldrelative attribute. It is an attribute which our world has relative to itself but which all other worlds have relative to themselves too. But the moderate realist conception of possible worlds seems to conﬂict with this world-relativity, or contingency, of the property of actuality; if possible worlds are abstract ‘ways things could have been’, then there is something distinctive about one of them, which constitutes its actuality: it is the one which corresponds to the world itself. Lewis argues that any ‘moderate version of modal realism comes to grief in the end’ for this reason. Referring to abstract ‘ways things could have been’ as ‘ersatz worlds’, he argues that, on the moderate realist account, ‘the actualized ersatz world is special, since it alone represents the one concrete world. And it is special not just from its own standpoint, but from the standpoint of any world. So it is noncontingently special, since contingency is variation from world to world. But it is part of the theory that the actualized ersatz world is the special one. So it seems to turn out to be a noncontingent matter which of the ersatz worlds is actualized.’20 The mistake in this argument, I think, is in the italicized statement. It is a special fact about ‘the actual world’ (the way things are) that it alone corresponds to the one concrete world. But this is a contingent fact, which means that from the standpoint of other worlds, it is not a fact. From the standpoint of a counterfactual possible world, that world has the special property of being the one and only ‘way things could have been’ that corresponds to the concrete world. But does this not mean that, looking at things from an objective, absolute standpoint, merely possible people and their surroundings are just as real as we and ours? Only if one identiﬁes the objective or absolute standpoint with a neutral standpoint outside of all possible worlds. But there is no such standpoint. The objective, absolute point of view is the

20

Lewis (1979: 533).

POSSIBLE WORLDS

29

view from within the actual world, and it is part of the concept of actuality that this should be so. We can grant that ﬁctional characters are as right, from their points of view, to afﬁrm their full-blooded reality as we are to afﬁrm ours. But their point of view is ﬁctional, and so what is right from it makes no difference as far as reality is concerned. My point is that the semantic thesis that the indexical analysis of ‘actual’ is correct can be separated from the metaphysical thesis that the actuality of the actual world is nothing more than a relation between it and things existing in it. Just as one could accept the indexical analysis of personal pronouns and be a solipsist, or accept the indexical analysis of tenses and believe that the past exists only as memory and the future only as anticipation, one can accept the indexical analysis of actuality while excluding from one's ontology any universes that are the way things might have been. Let me see if I can use the analogy between the present time and the actual world (an analogy that Lewis obviously has in mind) to make my point a little clearer. Pretend for the moment that we accept an Augustinian thesis about time, the one expressed in the following quotation: At any rate it is now quite clear that neither the future nor the past really exist. Nor is it right to say there are three times, past, present, and future. Perhaps it would be more correct to say: there are three times, a present of things past, a present of things present, a present of things future. For these three exist in the mind, and I ﬁnd them nowhere else: the present of things past is memory, the present of things present is sight, the present of things future is expectation. If we are allowed to speak thus, I see and admit that there are three times, that three times truly are. By all means continue to say that there are three times, past, present, and future; for, though it is incorrect, custom allows it. By all means say it. I do not mind, I neither argue nor object: provided that you understand what you are saying and do not think future or past now exist. There are few things that we phrase properly; most things we phrase badly; but what we are trying to say is understood.21 Now suppose we are trying to give a semantic analysis of tenses. Is our pretended metaphysical belief about time compatible with the standard semantic account—the one that says, for example, that at any time t a future tense statement is true at t just in case the corresponding present tense statement is true at some t′ later than t? I think it is, provided we understand the times in terms of which our past and future tense statements are interpreted as things which exist in the present. That is exactly how Augustine does understand them. Just as we needed to distinguish two senses of ‘possible world’, so the Augustinian theory needs to distinguish two senses of time. There is the sense in which ‘neither the future nor the past really exist’, and the sense in which, ‘if we are allowed to speak thus’, we can correctly say ‘that three

21

Augustine (399/1943: 276); (Bk. 11, ch. 20).

30

WAYS AND WORLDS

times truly are’. The future and the past (in the latter sense) exist in the present (former sense), which is to say that they exist. So they are available as resources for the interpretation of tensed statements. Only the present really exists (we are supposing). So the word ‘now’ picks out the time that is uniquely real (that is uniquely realized). But, one might object, do not speakers in the past, and in the future, who say ‘only the present really exists’ refer to their own times, and do they not speak the truth? Yes, they did, or will, refer to their own times, and they did, or will, speak the truth. But the fact remains (according to our hypothesized metaphysics) that their times do not exist now, which is to say that they do not exist at all (except as memory or anticipation). The fact that those times were or will be real does not show that they are real. I do not want to defend the Augustinian theory of time, or even a less idealistic version that substitutes traces and potentialities for memory and anticipation. My only point is that Augustine and his metaphysical opponents who believe that other times are as real as our own might share the same semantics for tenses. The correctness of the standard semantics for tenses and temporal indexicals is not, in itself, a refutation of a theory that denies the reality of other times. The thesis that the actual world alone is real is superﬁcially analogous to the Augustinian thesis that the present alone is real—that all else, or all that appears to be else, is an aspect of the present. But the Augustinian thesis has content, and can be coherently denied, because it says something substantive about what alone is real. In effect, it says that the actual world is a moment of time. But the thesis that the actual world alone is real has content only if ‘the actual world’ means something other than the totality of everything there is, and I do not believe that it does. The thesis that there is no room in reality for other things than the actual world is not, like the Augustinian thesis, based on a restrictive theory of what there is room for in reality, but rather in the metaphysically neutral belief that ‘the actual world’ is just another name for reality. The extreme realist will, of course, deny this. He must hold that the indexical ‘actual’ picks out, not the whole of reality, but only a part of it. But what part? How do I draw the boundaries around that part of reality which is appropriately related to me to be part of my actual world? I do not think the extreme realist can give a satisfactory answer to this question. Presumably, any part of reality that is spatially or causally connected with something in the actual world is itself part of the actual world. No one thinks that other possible worlds are literally ‘out there’ in space (like raisins in a pudding), or that we might communicate with merely possible beings. But if other possible worlds are causally disconnected from us, how do we know anything about them? If the truth or falsity of our modal claims depends on the existence of things and events which are causally disconnected from us, then even the simplest claims about what is possible are unveriﬁable speculations.

POSSIBLE WORLDS

31

My point is not a veriﬁcationist one. I am not bothered by the fact, freely admitted by Lewis, that there may be some modal facts—facts about what is possible—which we can never know. My worry is that I do not see how, on Lewis's account, there can be any other kind of modal fact. I do not see how we could ever have any reason to believe that a proposition we know to be false was nevertheless one that might have been true. As Lewis says in the argument quoted above, ‘I believe, and so do you, that things could have been different in countless ways.’ But we also believe that this belief is a reasonable one, and not a speculation about what is going on in some place so far away that it is not even part of our universe. It is the reasonableness of modal beliefs which I think Lewis's extreme realism cannot account for. In the course of defending his version of modal realism, Lewis makes some general remarks about his conception of the methodology of metaphysics. The particular problem with extreme realism that I have just pointed to derives, I think, from a limitation in that methodology. Let me quote some of Lewis's remarks: One comes to philosophy already endowed with a stock of opinions. It is not the business of philosophy either to undermine or to justify those preexisting opinions, to any great extent, but only to try to discover ways of expanding them into an orderly system. A metaphysician's analysis…succeeds to the extent that (1) it is systematic, and (2) it respects those of our pre-philosophical opinions to which we are ﬁrmly attached. Insofar as it does both better than any alternative we have thought of, we give it credence.… So it is throughout metaphysics; and so it is with my doctrine of realism about possible worlds.…Realism about possible worlds is an attempt, the only successful attempt I know of, to systematize preexisting modal opinions.22 There is much in this conception of metaphysics that seems to me right, but I think we must ask more of our philosophical theories. They must not only systematize preanalytic opinions, but also help to explain the source of those opinions and their role in our practical activities. We want to know not only what it is to believe that things might have been different in various particular ways, but also why those beliefs make a difference to inhabitants of the actual world. We want to know why it is reasonable to have such beliefs, and why it is reasonable to use them in the way we do. Even if extreme realism were to succeed in providing an elegant systematization of modal opinions, it would, I think, preclude a plausible explanation of the practical signiﬁcance which we believe those opinions to have. The moderate realism whose coherence I am trying to defend accepts theses (1) and (3), and rejects thesis (2). What about thesis (4)? If we identify possible worlds with ways things might have been, can we still hold that they are ‘respectable entities in their own right’, irreducible to anything more fundamental? Some may believe that even if a moderate realism about

22

Lewis (1973: 88).

32

WAYS AND WORLDS

possible worlds is coherent, one buys the added plausibility which it has over extreme realism only at the cost of incurring the obligation to give some further analysis or explanation of the concept of a possible world. If there were possible worlds, in the sense of other things like me and my total environment, then they could perhaps be referred to and quantiﬁed over even if not much more could be said about them than that they are other things like our actual universe. As concrete objects, they can stand alone, if they stand at all. One would need no justiﬁcation for including them in one's theory of reality other than that they are there. But the moderate realist believes that the only possible worlds there are—ways things might have been—are (like everything that exists at all) elements of our actual world. They obviously are not concrete objects or situations, but abstract objects whose existence is inferred or abstracted from the activities of rational agents. It is thus not implausible to suppose that their existence is in some sense dependent on, and that their natures must be explained in terms of, those activities. Thus Mackie, discussing possible worlds analyses of conditionals, writes, possible situations, or possible worlds, just because they are not actual (or may not be actual) do not stand on their own, do not exist independently.…People can consider possibilities; but the possibilities exist only as the contents of such considerings…‘possible situations’…cry out for some further analysis. This analysis must be given in terms of what people do.23 The claim that possible worlds are dependent on actual human activities and the demand that possible worlds be explained in terms of such activities are vague, but their general intent and motivation are clear enough. I shall try to respond to this concern by locating claims about possible worlds in a theory of rational activities. But I want to resist a more speciﬁc demand with the same motivation: this is the demand, which Robert Adams argues must be met if we are to escape commitment to extreme realism, that ‘if there are any true statements in which there are said to be nonactual possible worlds, they must be reducible to statements in which the only things there are said to be are things which are in the actual world, and which are not identical with nonactual possibles.’24 Unless the reminder that by ‘possible world’ we mean nothing more than ‘way things might have been’ counts as such a reduction, I do not see why this should be necessary. Two problems need to be separated: the ﬁrst is the general worry that the notion of a possible world is a very obscure notion. How can explanations in terms of possible worlds help us to understand anything unless we are told what possible worlds are—and told in terms which are independent of the notions which possible worlds are intended to explain? The second problem is the speciﬁc problem that believing in possible worlds and in the

23

Mackie (1973: 90, 92).

24

Adams (1974: 224).

POSSIBLE WORLDS

33

indexical analysis of actuality seems to commit one to extreme realism, which is obviously false. Now to point to the difference between a way our world might have been and a world which is the way our world might have been, and to make clear that the possible worlds whose existence the theory is committed to are the former kind of thing and not the latter, is to do nothing to solve the ﬁrst problem; in fact, it may make it more acute since it uses a modal auxiliary to explain what a possible world is. But this simple distinction does, I think, dissolve the second problem, which was the motivation for Adams's demand for an analysis. Not only is an eliminative reduction of possible worlds not necessary to solve the second problem, it also may not be sufﬁcient to solve the ﬁrst. I shall argue that the particular reduction that Adams proposes—a reduction of possible worlds to propositions—by itself says nothing that answers the critic who ﬁnds the concept of a possible world obscure. His reduction says no more, and in fact says less, about propositions and possible worlds than the reverse analysis that I am defending—the analysis of propositions in terms of possible worlds. Adams's analysis is this: Let us say that a world-story is a maximal consistent set of propositions. That is, it is a set which has as its members one member of every pair of mutually contradictory propositions, and which is such that it is possible for all of its members to be true together. The notion of a possible world can be given a contextual analysis in terms of worldstories.25 For a proposition to be true in some or all possible worlds is for it to be a member of some or all world-stories. Other statements that seem to be about possible worlds are to be replaced in a similar way by statements about world-stories. There are three undeﬁned notions used in Adams's reduction of possible worlds: proposition, consistent, and contradictory. What are propositions? Adams leaves this question open for further discussion; he suggests that it might be answered in various different ways. Little is said about them except that they are to be thought of as language-independent abstract objects, presumably the potential objects of speech acts and propositional attitudes. And it is, of course, assumed that they have truth-values. What is consistency? The notion used in the deﬁnition of world-story is a property of sets of propositions. Intuitively, a set of propositions is consistent if it is possible for all its members to be true together. We cannot, of course, explain this intuitive idea in terms of the existence of a possible world in which all of them are true. Presumably, consistency will be a primitive notion, but we must be sure that the world-story theory includes some constraints on it which ensure that it has the right properties. Two

25

Ibid 225.

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WAYS AND WORLDS

assumptions that are necessary, and that should be uncontroversial, are the following: (W1)The set of all true propositions is consistent. (W2)Any subset of a consistent set is consistent. What is a contradictory? This relation between proposition might be deﬁned in terms of consistency as follows: A and B are contradictories if and only if {A, B} is not consistent, and for every consistent set of propositions Γ either Γ ⋃ {A} or Γ ⋃ {B} is consistent. The theory tacitly assumes: (W3)Every proposition has a contradictory. These deﬁnitions and postulates yield a minimal theory of propositions. It is minimal in that it imposes no structure on the propositions except what is required to deﬁne the standard propositional relations such as compatibility, implication, and equivalence, and to ensure that these relations have the right properties. Implication, for example, can be deﬁned in a familiar way: A implies B if and only if a set consisting of A and a contradictory of B is not consistent. (W1) and (W2) ensure that implication, deﬁned this way, has the right properties. For example, it is transitive, reﬂexive, and preserves truth. This minimal theory is not, however, sufﬁcient to justify what Adams calls ‘the intuitively very plausible thesis that possibility is holistic rather than atomistic, in the sense that what is possible is possible only as part of a possible completely determinate world’.26 The assumptions we have made so far do not imply that every consistent set of propositions is a subset of a world-story,27 so to ensure that the theory satisﬁes the principal thesis that motivates it, we must add the following as an additional postulate: (W4)Every consistent set is a subset of a maximal consistent set. It will be useful to compare this reduction of possible worlds to propositions with the competing reduction of propositions to possible worlds. What is at stake in choosing which of these two notions to deﬁne in terms of the other? Adams refers to the ‘not unfamiliar tradeoff between non-actual possibles and intensions (such as propositions); given either, we may be able to construct the other, or do the work that was supposed to be done by talking about the other’.28 But the two proposals are not equivalent. Part of what distinguishes them is an elusive question of conceptual priority, but

26

Adams (1974: 224).

27

In the earlier published version of this paper I claimed otherwise. Philip Bricker, in his dissertation (Bricker 1983), pointed out my mistake in assuming that (W4) followed from (W1)–(W3). Bricker's dissertation contains a clear, detailed, and interesting investigation, both technical and philosophical, of the relation between proposition-based theories such as Adams's world-story theory and world-based theories such as the analysis I am defending.

28

Adams (1974: 228).

POSSIBLE WORLDS

35

there are also more substantive differences, both in the structure imposed on propositions and possible worlds and in the questions left to be answered by further developments of the respective theories. One might think that a reduction of possible worlds to propositions was more appropriate than the reverse since propositions are more familiar entities than possible worlds, and analysis should explain the less familiar in terms of the more familiar. However problematic propositions may be, we can still point to particular examples of them (like the proposition that Gerald Ford became President of the United States in 1974), and to facts about them with which we are familiar (for example, that the above-mentioned proposition is believed by Richard Nixon, and that it entails that Gerald Ford became either the President or the Vice-President in 1974). Possible worlds, on the other hand, are a philosopher's invention and are further removed from the phenomena of speech and thought. So they are more in need of analysis. I think this reasoning is based on a mistaken assumption about the point and content of a philosophical analysis. An analysis makes a claim about a relation among concepts which, if accepted, can be informative in either direction, or in both directions. It may be as helpful in explaining an obscure concept to reduce other things to it as to reduce it to other things. This would not be true if an analysis were like a stipulative deﬁnition of a previously meaningless sign, but normally all the terms involved in a philosophical analysis are terms that we understand, to some extent, prior to the analysis. What is more important than familiarity for choosing the order of an analysis is the question of structure. Normally, one would expect to analyze the more highly structured set of entities in terms of a less highly structured one so that the analysis might help to explain the structure. Propositions are highly structured. One proposition can be stronger or weaker than another, or equivalent to it, compatible or incompatible with it, related to it as contrary or contradictory. These relations give rise to questions about the identity conditions for propositions, about closure conditions for the set of all propositions, about whether some propositions are constructed out of others. Possible worlds, on the other hand, are relatively unstructured. One may, for some purposes, want to deﬁne relations between possible worlds, like resemblance in some respect or other, or accessibility of some kind, but such relations are not essential to the concept of a possible world in the way that relations like entailment and compatibility are essential to the concept of a proposition. A minimal theory of propositions and possible worlds needs an account of the propositional relations, but it can get along without an account of relations between possible worlds. Both of the theories that I am comparing impose structure on the set of propositions, but in the minimal world-story theory that structure derives from a primitive and unexplained concept of consistency. In contrast, the

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possible worlds analysis of propositions yields deﬁnitions of consistency and the other propositional relations in terms of elementary set-theoretic relations between the sets of possible worlds determined by the propositions. Whether one accepts these deﬁnitions as explanations of the propositional relations may depend on whether, in the end, one accepts the concept of a possible world as having intuitive content and an independent role to play in a theory; but even if possible worlds are totally opaque postulated entities, the possible worlds analysis of propositions still imposes a structure on the set of propositions which can be tested against intuitions about propositions, and against theoretical assumptions about the role of propositions in a theory of mental states and linguistic actions. If we set aside questions of conceptual priority—of which concepts and principles should be primitive and which deﬁned or derived—what are the differences between the two theories we are comparing? The world-story theory is weaker, leaving open questions which are settled by the possible worlds analysis of propositions. The following two theses are consequences of the possible worlds analysis but not of the world-story theory; the ﬁrst is a closure condition; the second concerns identity conditions. (W5)For every set of propositions Γ there is a proposition A such that Γ implies A, and A implies every member of Γ. (W6)Equivalent propositions are identical. Are these consequences of the possible worlds analysis welcome or not? Thesis (W5) seems reasonable on almost any theory of propositions and propositional attitudes. What it says is that for every set of propositions, there is a proposition which says that every proposition in the set is true. Whatever propositions are, if there are propositions at all then there are sets of them, and for any set of propositions, it is something determinately true or false that all the members of the set are true. If one is willing to talk of propositions at all, one will surely conclude that this determinately true or false thing is a proposition. It may not be possible to express all such propositions since it may not be possible, in any actual language, to refer to all such sets; it may not be humanly possible to grasp them. But if this is so, it is surely a contingent human limitation which should not restrict the range of potential objects of propositional attitudes. So I will assume that the world-story theorist will want to add thesis (W5) to his theory. Thesis (W6) has some notoriously problematic consequences, but it is also a thesis for which there are independent arguments.29 If the world-story theorist accepts these arguments, then he will want (W6) in his theory as well. It is compatible with the minimal theory, so he can add it as a further postulate.

29

Both the problematic consequences and the independent arguments are discussed in Stalnaker (1984: ch. 1).

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37

If (W5) and (W6) are added as postulates to the world-story theory, then it becomes equivalent to the possible worlds analysis with respect to the structure it imposes on the set of propositions. For every set of world-stories, there will be a unique proposition that is a member of just the world-stories in the set. This means that every function from possible worlds (or world-stories) into truth-values will correspond to a unique primitive proposition which is true just where the function takes the value true, and false just where the function takes the value false. It seems that the sole difference that remains between the two theories is that one takes as primitive what the other deﬁnes. And even this difference will be eliminated if we make one more change in response to a question about the further development of the world-story theory. The next question for the world-story theorist is this: can he say more about his fundamental concept, the concept of a proposition? In particular, are there some basic propositions out of which all the rest can be constructed? The usual way to answer this kind of question is to model basic propositions on the atomic sentences of a ﬁrst-order language; propositions are constructed out of individuals and primitive properties and relations in the same way that sentences are constructed out of names and predicates. But this strategy requires building further structure into the theory. There is another way to answer the question which needs no further assumption. We can deduce from what has already been built into the world-story theory that there is a set of propositions of which all propositions are truth-functions: this is the set of strongest contingent propositions—those propositions which are members of just one world-story. It is thus a harmless change, a matter of giving the theory a more economical formulation, to take these to be the basic propositions. (This change does not foreclose the possibility of a further reduction of what are here called basic propositions to propositions even more basic. Any alternative reduction can be expressed as a further reduction of this kind; this is why this move is harmless.) We can then deﬁne propositions generally as sets of basic propositions (or, for a neater formulation, call the basic elements propositional elements and let their unit sets be the basic propositions. Then all propositions will be things of the same kind.) A nonbasic proposition will be true just in case one of its members is true. This reduction has the added advantage that it allows us to deﬁne the previously primitive property of consistency, and to derive all of the postulates. With these primitive notions and assumptions eliminated, the worldstory theory looks as good as the theory that takes possible worlds as primitive and deﬁnes propositions. This is, of course, because it is exactly the same theory. I have gone through this exercise of changing the world-story theory into the possible worlds analysis of propositions in order to make the following points. First, the minimal world-story theory with which I began is indeed a minimal theory, a theory that assumes nothing about propositions except

38

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what is required to capture the principal intuition of the theory: that something is possible only as part of a possible completely determinate situation. But second, every step in the metamorphosis of this minimal theory into the possible worlds analysis is motivated either by uncontroversial assumptions about propositions (such as that truth-functions of propositions are propositions) or by the pragmatic picture of propositional attitudes, or by theory-neutral considerations of economy. If this is right, then the possible worlds analysis is not just one theory which gives propositions the identity conditions which are motivated by the pragmatic picture. More than this, it is the whole content of that analysis to impose the minimal structure on propositions which is appropriate to a theory which is guided by this conception of propositional attitudes. Anyone who believes that there are objects of propositional attitudes and who accepts the assumptions about the formal properties of the set of these objects, must accept that there are things which have all the properties that the possible worlds theory attributes to possible worlds, and that propositions can be reduced to these things. Is the form of realism about possible worlds that I have been defending really realism? It is in the sense that it holds that statements about what is possible are to be explained in terms of quantiﬁcation over possible worlds, and that some such statements are true. It is in the sense that it claims that the concept of a possible world is a basic concept in a correct account of the way we represent the world in our propositional acts and attitudes. But on the other hand, the moderate realism I want to defend need not take possible worlds to be among the ultimate furniture of the world. Possible worlds are primitive notions of the theory, not because of their ontological status, but because it is useful to theorize at a certain level of abstraction, a level that brings out what is common in a certain range of otherwise diverse activities. The concept of possible worlds that I am defending is not a metaphysical conception, although one application of the notion is to provide a framework for metaphysical theorizing. The concept is a formal or functional notion, like the notion of an individual presupposed by the semantics for extensional quantiﬁcation theory. An individual is not a particular kind of thing; it is a particular role that things of any kind may occupy: the role of subject of predication. To accept the semantics for quantiﬁcation theory is not to accept any particular metaphysics of individuals, even though one may use the resources of that semantic theory to help clarify one's metaphysical commitments. Similarly, a possible world is not a particular kind of thing or place. The theory leaves the nature of possible worlds as open as extensional semantics leaves the nature of individuals. A possible world is what truth is relative to, what people distinguish between in their rational activities. To believe in possible worlds is to believe only that those activities have a certain structure, the structure which possible worlds theory helps to bring out.

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39

Let me develop the analogy between domains of possible worlds and domains of individuals to try to make my point clearer. One may think of quantiﬁcation theory as a framework for representing, once and for all, one's total ontological commitment. To do this is to assume that there is one big domain of discourse—the domain of what there is—which gives the intended interpretation of quantiﬁcation theory. To be, then, is to be a value of a bound variable, under this interpretation. But one can reject this metaphysical interpretation and still accept the referential semantics for quantiﬁcation theory. One can deny that there is a domain of all there is, of which all the domains of discourse in particular contexts are subdomains. One can deny that it makes sense to ask ontological questions outside of a particular context. Analogously, one may choose to put a metaphysical interpretation on the concept of a possible world, assuming that there is one domain of all metaphysically possible worlds from which the restricted domains relevant to interpreting different kinds of possibility and necessity are drawn. But one may also reject that interpretation, and the coherence of the metaphysical questions which it raises, without rejecting a realistic understanding of possible worlds semantics. One may say that in particular contexts of inquiry, deliberation, and conversation, participants distinguish between alternative possibilities, and that they should do so is deﬁnitive of those activities. It does not follow from this that there is a domain from which all participants in inquiry, deliberation, and conversation must take the alternative possibilities that they distinguish between.

2 On what Possible Worlds could not be (1996) 1. Introduction According to David Lewis's modal realism,30 the actual world is only a proper part of a reality that consists of many parallel universes that are spatially and temporally disconnected from each other. The actual world is deﬁned indexically as that part of reality that stands in some spatio-temporal relation to ourselves. Talk about what is merely possible, according to this thesis, is not talk about what might have existed but does not; instead, it is talk about what does exist, but only in some different part of reality than the one we inhabit. Merely possible cabbages, kings, and croquet games are things of the same kind as the actual cabbages, kings, and croquet games that inhabit our world; their nonactuality consists simply in their being located somewhere else. Modal realism is really two theses, one semantic and one metaphysical. The semantic thesis is that claims about what is possible or necessary should be analyzed as claims about what is true in some or all of the appropriately individuated parts of reality. The metaphysical thesis is that there exists a plurality of parts of reality individuated in this way—a plurality that is full enough to make true many of our ordinary beliefs about what is possible and necessary when those beliefs are interpreted in accordance with the semantic thesis. It is a familiar objection to the semantic part of the thesis of modal realism that if it were true, then it would not be possible to know any of the facts about what is merely possible, or to have any reason to believe any modal claims about what is merely possible. If the semantic part of the thesis were true, it is argued, then the metaphysical part would be an unsupported and insupportable speculation. For example, it seems that we can know, or at least have reason to believe, such claims as that the Federal Reserve Board might not have voted to raise interest rates on a particular occasion on which they in fact did vote to raise interest rates. But on Lewis's analysis, this claim entails that there is a parallel universe, spatio-temporally disconnected from ours but similar to it, in which there is a Federal Reserve Board populated with counterparts of the members of the actual Board who

30

See Lewis (1986a) for a systematic exposition and defense of modal realism.

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met as the actual members did, but who voted not to raise interest rates. How could one know that, and why should the reasons we have for believing that the Board might not have raised interest rates be reasons for believing in the existence of such people and events? This epistemological objection to modal realism may seem to parallel closely Paul Benacerraf's dilemma about mathematical truth and knowledge.31 Benacerraf saw a tension between the demand for a plausible account of what mathematical statements say and a defensible account of the way we know that what such statements say is true. If we take the statements of, say, number theory at face value, then we will interpret them as statements about a domain of entities—the numbers—which lack spatio-temporal location, and with which no one can be causally related. But if that is what mathematical statements are about, then it is not clear how it is possible to know that any of them are true. Lewis points out the parallel between the epistemological objection to modal realism and Benacerraf's dilemma, and exploits it in his response to that objection. We can agree, I think, that if modal realism is no worse off than Platonism about such things as sets and numbers, then it will ﬁnd itself in better company than many critics suppose. My aim in this paper is to explore the analogy between mathematical Platonism and modal realism, and between Benacerraf's dilemma and the epistemological objection. I think the parallels, as well as the contrasts, are illuminating, and may help to clarify both modal realism and the general problem of modal epistemology. I will ﬁrst sketch Benacerraf's reasons, as I understand them, for thinking that there is a prima facie conﬂict between a straightforward account of mathematical truth and a reasonable account of mathematical knowledge, and Lewis's response to it. Second, I will sketch a strategy for responding to the dilemma, and argue that this strategy does not suggest a parallel response to the epistemological objection to modal realism. Finally, I will look at a more general problem for an epistemology of necessary truth.

2. The dilemma, and Lewis's response It seems to be a reasonable constraint on an adequate philosophy of mathematics that it should explain mathematical statements as genuine statements making claims that are true or false. And we should expect a semantics for mathematical statements to be continuous with a semantics for statements in general. In particular, one should expect existential statements about sets, functions and numbers to be interpreted with the same referential truth-conditional semantics that we use to interpret existential statements about tables and chairs, quarks and photons, symphonies and

31

Benacerraf (1973).

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ON WHAT POSSIBLE WORLDS COULD NOT BE

rock bands. But on the other hand, we should also expect our account of mathematical knowledge to be continuous with our account of knowledge in general. The procedures we use to evaluate and justify mathematical statements should be explained by a general account of knowledge, together with our account of mathematical truth; we should be able to explain why, if mathematical statements say what our semantics says they say, those methods and procedures are appropriate ways of telling whether they are true. Benacerraf argues that some philosophical accounts of mathematics—Platonistic accounts—give a natural semantics but allow for no plausible epistemology; others—what he calls combinatorial accounts, such as formalism and conventionalism—may account for the mathematicians' methods and procedures, but fail to give a plausible account of what is said by the statements justiﬁed by those methods and procedures. Benacerraf poses the problem, but does not offer a solution. We are not invited just to opt for one or the other horn of the dilemma. Instead, it is suggested that we need to ﬁnd some kind of reconciliation—some account that respects both the prima facie account of mathematical truth and the need to explain mathematical knowledge. ‘Ultimately I will argue that each kind of account has its merits and defects: each addresses itself to an important component of a coherent overall philosophic account of truth and knowledge.’32 Why, according to Benacerraf, is there a conﬂict between a straightforward Platonistic account of mathematical statements and the facts about the way we evaluate and justify those statements? The central reason is that the straightforward semantics explains truth in terms of reference or satisfaction, and (Benacerraf argues) genuine reference requires a causal connection between an act of reference and the object of reference. But the objects hypothesized by a Platonistic account of mathematical statements are not the kinds of things with which the speakers in a mathematical discourse, or anyone else, can be causally related. Lewis's response to Benacerraf's dilemma is to accept the Platonistic semantics, but to reject the assumption that reference requires a causal transaction with the referent. Then once the precedent is set, we can move on from numbers and functions to possible cabbages, kings, and croquet games. If reference and knowledge are sometimes possible in the absence of causal connection, one can no longer refute a thesis simply on the ground that it implies we can have knowledge of a certain domain without interacting with it. The proponents of the epistemological argument against modal realism reject the parallel between mathematical objects and possibilia, realistically construed. They insist that reference to and knowledge of concrete things requires causal interaction, even if reference to and knowledge of abstract things does not. But, Lewis responds, why should the line between what

32

Benacerraf (1973: 666).

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requires causal interaction and what does not be drawn in terms of this distinction (a distinction, Lewis adds, that is none too clear in any case)? Instead, we should say that reference to and knowledge of contingent facts requires causal interaction, while knowledge about modal reality does not. In the context of modal realism, this is to say that indexical knowledge, or knowledge of one's own place in reality, requires causal interaction with that part of reality we are in, but impersonal knowledge does not. According to this line, a causal requirement for knowledge of an existential proposition depends, not on the kind of thing that is said to exist but only on whether it is claimed to exist in the knower's own part of reality. One might have knowledge, without causal connection, of the existence not only of numbers, sets, and functions, but also of objects, such as sidewalks, that are concrete.

3. Liberal Platonism I am inclined to agree with Lewis that Platonism about mathematical objects does not imply that knowledge of such objects requires causal interaction with them, and so that Benacerraf's dilemma, in the form in which it is presented, can be dissolved. But I still feel the force of the epistemological objection to modal realism. The challenge is to explain the disanalogy between reference to and knowledge of numbers and reference to and knowledge of cabbages, kings, and croquet games that are alleged to exist in spatio-temporally disconnected parts of reality. I once tried to meet this challenge by sketching a cheap or liberal version of Platonism, a way of reconciling a straightforward semantics with mathematical epistemology that could not be extended to a defense of modal realism. According to my liberal Platonist, one begins with the facts of mathematical discourse—the existence of a practice involving activities that seem to resemble assertion, inference, argument. One notes that if a Tarskian semantics is given for the products of the discourse (hypothesizing a domain of things of the kind that the discourse seems to be talking about), then that semantics helps to explain facts about the discourse, for example that people tend to try to assert and accept what is true, according to the semantics, and to make and endorse inferences that preserve truth. Now, the liberal says: if we agree that this is a legitimate practice, that its (perhaps evolving) standards for evaluating the products of its discourse are relatively clear, then isn't this sufﬁcient reason to accept that the practice really is a practice of making assertions, and its semantics really tells us what the statements say? Can't we, with a clear conscience, engage in this practice, and endorse some of the existential statements that meet its standards, without making some further supernatural assumptions about causal interaction with a realm of immaterial entities?

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Then the liberal (incautiously) said, ‘the existence of numbers is just constituted by the fact that there is a legitimate practice involving discourse with a certain structure, and that certain of the products of this discourse [statements that have an existential form] meet the standards of correctness that it sets.’33 Hartry Field rightly took my liberal Platonist to task for this last statement, which suggests that he has mislabeled his position, a position that Field suggested would be more accurately described as a kind of linguistic idealism.34 But my liberal's last statement was careless. The position that he was trying to espouse was in the spirit of Carnap's ‘Empiricism, Semantics and Ontology’.35 In trying to defend the thesis by saying, from an external point of view, what numbers are, he distorted the view, and violated his Carnapian principles. I think the thesis, more carefully stated, really is a version of Platonism, and not a kind of linguistic idealism—at least it accepts the two theses that Field takes to deﬁne Platonism: that numbers, functions, and sets exist, and that they are ‘mind-independent and language-independent’.36 Speaking from within the practice, one might ask counterfactual questions about the entities whose existence one has endorsed, and if one does, one will surely afﬁrm that those entities would have existed even if no one had ever thought about them, or engaged in a practice of talking about them. The Carnapian, like all of us, will say that a statement would not have been meaningful if the language of which it is a part had not existed, but that is compatible with agreeing that what it says might still have been true.37 Our liberal Platonist need not follow Carnap in making a sharp distinction between internal and external questions—questions asked from within a framework, and purely practical questions about whether to adopt or endorse the framework. Let us suppose that our post-Carnapian liberal Platonist, having read Quine, recognizes that all questions are asked from within some linguistic context, and that the questions, ‘is it reasonable to adopt the framework of numbers?’ and ‘are there numbers?’ are not so easily separated. But we can still distinguish questions that are external in the sense that they are questions about the practice, or the framework, that is at issue. The kind of external perspective I have in mind is like the one

33

The liberal's incautious statement is taken from Stalnaker (1988: 119).

34

Field (1989).

35

Carnap (1950).

36

Field (1989: 1).

37

Compare: Barry Stroud (1984: 192) asks ‘whether it is Carnap's view that the statement we can now make and understand about mountains in Africa would no longer be true if we abandoned the thing language, or would not have been true if we had never adopted it’. If Carnap were to allow himself to take such counterfactuals seriously, he surely would deny that the existence of characteristics of mountains in Africa depends on anyone's linguistic practices, and there is no reason why he could not say the same thing in the formal mode: that true statements that we in fact make would still be true even if we did not make them, or even have a language in which they could be made. Questions about the truth of those counterfactuals should be regarded by Carnap as internal questions asked in the context of the thing language, and answered according to its rules.

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Quine adopts at the beginning of Word and Object when he says: ‘I propose…to ponder our talk of physical phenomena as a physical phenomenon, and our scientiﬁc imaginings as activities within the world that we imagine.’38 Without pretending that we are stepping outside of the world, or setting aside our commitments, we can still describe ourselves, our discourse, and the fact that we make the commitments we make as features of the kind of world we believe ourselves to be in. It is in this kind of inquiry that the causal theory of reference has a place. When we ask: ‘how must a speaker's use of a name be related to a person or physical object in order for the object to be the referent of the name?’ we are pondering our acts of referring as phenomena within the world to which we refer. Now when our liberal Platonist ponders his and our talk of mathematical objects as an activity within the world that we imagine, he ﬁnds that it is an activity with reasonably well-deﬁned rules and procedures. He further ﬁnds that it is an activity that is usefully described and systematized as a practice that involves making assertions and inferences using expressions that have a Tarskian semantics. Since the practice in question is one that the liberal Platonist engages in, and since he is a good Quinean who believes that to be is to be the value of a bound variable, he feels free to refer to the members of the domain—the numbers—in giving the semantics for the discourse. But now we ask, still viewing the practice as a phenomenon that is a subject of empirical inquiry, ‘how must a speaker be related to the numbers in order to be in a position to refer to them?’ It is with this question that the disanalogy between mathematical and empirical discourse emerges. The liberal Platonist says that the legitimacy of the practice does not presuppose that there is any story to be told, in our empirical theory of the practice, about an external relation between acts of reference and the referents. The liberal was tempted to put the point by saying that the existence of numbers is just constituted by the fact that the practice is a legitimate one with a certain structure and well-deﬁned standards, but this had the false consequence that numbers were contingent objects whose existence was dependent on the existence of the activity of talking about numbers. The point is rather that the commitment to numbers is just constituted by the endorsement of the practice with this structure and standards. One might be inclined to think that the liberal Platonist is trying to occupy a middle ground that is not really there—that his position is simply an equivocation between a thesis that is not really realism, and a version of Platonism that is not distinguishable from Lewis's—a thesis about mathematical objects that can provide a precedent for a defense of modal realism against the epistemological objection. Let me address the two sides of this objection in turn.

38

Quine (1960: 5).

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ON WHAT POSSIBLE WORLDS COULD NOT BE

First, is the liberal Platonist's thesis really realism, rather than some kind of ﬁctionalism, instrumentalism, or quasirealism? I don't think it would be appropriately assimilated to ﬁctionalism, since a ﬁctionalist position requires a commitment to the intelligibility of a thesis that, if true, would make the ﬁction fact. The liberal might grant the intelligibility of something like Gödelian Platonism—the thesis that there is a realm of entities with which we have causal contact through a quasi-perceptual faculty of mathematical intuition—but it would seem gratuitous to interpret the liberal's thesis as the thesis that we are pretending that some such theory is correct. The liberal denies not only that such a story is true, he denies that it is needed to make sense of the content of mathematical claims. More plausibly, one might argue that the liberal is really an instrumentalist who does not take mathematical truth seriously. Benacerraf notes, in his criticism of conventionalism, that to give a real truth-conditional semantics for a language, it does not sufﬁce simply to sprinkle the word ‘true’ onto some well-deﬁned subset of the sentences. ‘Suppose now that the language is set theory, in some ﬁrst order formalization.…Let those [sentences] with an even number of horseshoes be “true”.’ Such a trivial sprinkling might, Benacerraf notes, be ‘parlayed into a truth theory’, at least a theory that had the form of a truth theory. But to be a theory that is really about truth, ‘the explanation must proceed through reference and satisfaction and, furthermore, must be supplemented with an account of reference itself ’.39 What is required, Benacerraf suggests, is the kind of external explanation of the relation between acts of reference and referents that the liberal Platonist denies is required. Now I agree that the matching of the word ‘true’ with expressions, and even the possibility of formulating an account of the matching in a recursive theory that has the form of a Tarskian truth deﬁnition, is not sufﬁcient to justify saying that we are really talking about truth. But it is not clear that it is a causal account of reference that is what is required to distinguish genuine from counterfeit semantics. One might instead focus on the practice of assertion. One needs, for a division of expressions into two classes to count as an account of truth, to connect that assignment with the way the expressions are used in some practice that involves something that looks like assertion and reasoning—some explanation of the role of the distinction between the sentences matched with ‘true’ and those that are not in some kind of cognitive and communicative enterprise. The account of the epistemology of mathematics answers to this demand, and sufﬁces, the liberal Platonist argues, to justify the straightforward truth-conditional semantics. One might argue that simply because the liberal Platonist rejects the demand for any answer to the external question about the relation between his acts of ‘reference’ and the objects of reference, his position is best called

39

Benacerraf (1973: 677).

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by another name—‘quasi-realism’ rather than ‘realism’.40 To this suggestion, the liberal Platonist might reply, with some exasperation: ‘This is just the kind of issue that Carnap taught us was meaningless. We agree about what to do: about what practices are legitimate, about what to say within those practices, and about what to say in answer to the external questions about the practice as an activity within the world. All we disagree about is whether to call it “realism”. Have it your way: if you want to deny that I am making an ontological commitment, I won't object. I have no stake in any metaphysical label; I simply want to defend the legitimacy of the practice, and of the theoretical account of it provided by the straightforward semantics.’ Whether it is called ‘realism’ or ‘quasi-realism’ the liberal Platonist's thesis does seem to meet Benacerraf's requirement that sentences such as ‘There are at least three large cities older than New York’ be seen to have the same semantic structure as sentences such as ‘There are at least three perfect numbers greater than 17’,41 or more generally that ‘the semantical apparatus of mathematics be seen as part and parcel of that of the natural language in which it is done’.42 If we succeed in defending the liberal Platonist against the charge that he isn't really a Platonist, we will face the charge that he is not really a liberal. We have not yet succeeded in distinguishing our Platonist's way of rejecting a causal requirement for reference to and knowledge of mathematical objects from Lewis's way of rejecting a causal requirement for reference to and knowledge of possible things and worlds. ‘Your liberal responds to Benacerraf's dilemma exactly as I do,’ Lewis might say: by rejecting the general demand for a story about how this kind of evidence can be evidence for that kind of claim. My view [Lewis might continue] is that epistemology should be naturalized epistemology. We should do it by describing the methods that we in fact use to form and justify our opinions of various kinds, by systematizing these methods and bringing them into reﬂective equilibrium. If our most plausible semantic hypothesis tells us that a certain bit of discourse is about things that speakers are not causally connected to, and if epistemological principles that seem on reﬂection to be reasonable tell us that we can know about such things, then there is no reason that we should not accept both the semantics and the epistemology. Isn't that just what your liberal Platonist thinks? Why, then, should he change his tune when he turns from mathematics to modal realism?43

40

The ‘quasi-realist’ is Blackburn's name for a person who, ‘starting from a recognizably anti-realist position, ﬁnds himself progressively able to mimic the intellectual practices supposedly deﬁnitive of realism’ (Blackburn 1993: 15).

41

Benacerraf (1973: 663).

42

Ibid. 666.

43

Cf. Lewis (1986a: 113–15).

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Of course Lewis will agree that the liberal Platonist might, in assessing the costs and beneﬁts—in bringing his epistemological and semantic beliefs into reﬂective equilibrium—decide that numbers pass the test—are worthy of belief—while possibilia, realistically construed, do not. But, I think Lewis would argue, he cannot use the general epistemological objection to justify this assessment without making some principled distinction between the two kinds of non-contingent objects. I think there is a difference between the liberal Platonist's defense of existential commitment without a causal connection and Lewis's, but it is difﬁcult to pin down. The source of the difference is that my liberal Platonist, unlike Lewis, is still, in his heart, a veriﬁcationist. He has given up attempts to articulate an empiricist criterion of meaningfulness, since he recognizes that there is no neutral, non-question-begging language in which to describe the procedures by which we verify and conﬁrm statements. But he continues to hold onto the idea that answers to questions about how we justify our beliefs, and about how we must be related to things in order to have beliefs about them, tell us something about the contents of the beliefs, and about the natures of the things.44 The liberal Platonist cannot say what he is tempted to say—that the existence of numbers is just constituted by the fact that there is a legitimate practice involving discourse with a certain structure, since that statement distorts the commitments of the practice by implying that numbers are contingent objects that would not exist under certain counterfactual circumstances. But he can say that commitment to numbers is just constituted by an endorsement of the legitimacy of the practice, and that the account of the epistemology of number theory—of how we are related to the numbers we know about—tells us something, not only about the conditions under which it is reasonable to believe in those things, but also about the extent and nature of the commitment that one makes when one endorses the practice, and afﬁrms the belief. The answer to the Quinean external question about how we must be related to objects in order to refer to and know about them should be seen as part of an answer to a question about what those objects are like. One is therefore not free to combine the epistemological account of the way we must be related to numbers in order to know about them with just any account of the nature of the numbers themselves. Lewis will agree, of course, that the story told by a theory about the nature of the objects to which the theory is committed must be compatible

44

Lewis makes clear, in a remark in a footnote, his lack of sympathy with the idea that there is some conceptual connection between our conception of the nature of a thing and our beliefs about how one may know about it. Commenting on a proposal of Michael Dummett to distinguish between abstract and concrete things in terms of ‘how we could understand their names’, Lewis says that even if such a distinction can be drawn, ‘it tells us nothing directly about how the entities on opposite sides of that border differ in their nature. It is like saying that snakes are the animals we instinctively most fear—maybe so, but it tells us nothing about the nature of snakes’ (Ibid. 82, n. 56).

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with the story told about the way the speakers afﬁrming the theory are related to those objects. But just what constraints does the ontology put on the epistemology? I am inclined to say that what distinguishes the liberal Platonist from the modal realist is that the latter, but not the former, makes speciﬁc claims about the nature of the entities whose existence is afﬁrmed that are incompatible with the account of the way knowers are related to the objects. The modal realist insists that possible persons and physical objects are persons and physical objects, things of the same kind as actual persons and physical objects, things that exist in space and time (though not, in all cases, our space and time) and that interact causally with other persons and physical objects. But those are the sorts of things knowledge of which requires a kind of explanation—an answer to the Quinean external question—that the modal realist's theory does not allow for. It is the liberal Platonist's veriﬁcationist principles that lend support to this last claim. He holds that we understand what it is to be a physical object or a person partly by understanding how one must be related to one in order to know things about it. That, I think, is why there seems to be a conﬂict between the insistence that possibilia are things of the same kind as contingent physical objects, and the claim that they are things whose existence we can know about in the way we know about things of a very different kind, such as numbers, functions, and sets. Of course Lewis will reject the assumption that there is a conceptual connection between the way we know about things and our conception of the nature of those things. In the end, I have to grant that I have no general principle that the modal realist must accept that will permit liberal Platonism about numbers, but exclude commitment to real but merely possible cabbages, kings, and croquet games. The modal realist will insist that we know about the existence of all persons and physical objects (actual or merely possible) in the same way, a way that requires no causal connection with them. Knowledge of the existence of actual things is distinctive, not because of the nature of the things, but because it is indexical knowledge—knowledge not just of the existence of the things, but of the fact that we stand in a particular relation to them. According to this picture, all impersonal ontological beliefs are to be justiﬁed on a priori grounds. Some may ﬁnd this picture hard to swallow, and for those who do, I think that even if the liberal Platonist line I have sketched does not give us a decisive refutation of modal realism on its own terms, it does at least offer a plausible strategy for defending a kind of realism about mathematical objects that does not provide a precedent for an analogous defense of modal realism. But there remains an epistemological puzzle about how we know about possible worlds, whether one is a modal realist or not, and whether or not one is able to swallow Lewis's epistemological picture. I will conclude by sketching this more general problem about knowledge of necessary truth.

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4. Content and necessary truth I suggested above that to distinguish a genuine truth-conditional semantics from a mere division of sentences into two classes, one labeled with the word ‘true’, one should focus not on the explanation of reference, but on the practice of assertion. It is because assertion is not simply the game of trying to name the true that an assignment of truth-values to the sentences is not in itself sufﬁcient to provide a basis for an account of this and other speech acts. An explanation of assertion requires a notion of the contents of the sentences used to make assertions—of the information that the sentences can be used to communicate. One thing wrong with Benacerraf's example of an arbitrary assignment of truth-values to the sentences of the language of set theory (based on the number of horseshoes in some formalization of those sentences) is that the ‘semantics’ assigns truth-values without telling us what the sentences are supposed to say. The ‘truth’ assignment tells us nothing about why one might ‘assert’ one or another of the sentences that one judges to be ‘true’, or what effect it might have if one did. But whatever the details of one's semantics, if all the sentences in the part of the language in question are either necessarily true or necessarily false, then it is not clear how to give an account of content or information for those sentences. A semantics for sentences that express contingent propositions will give rules that determine the truth-values for those sentences as a function of the facts, and so will say how those sentences might convey information about the facts on which their truth depends. But if the semantic rules determine truth-values unconditionally, then it is harder to see how the sentences might be used to say something about what they are about, and how the semantics might be distinguished from an arbitrary assignment of truth-values. Behind Benacerraf's dilemma is a problem more general than a problem about Platonistic ontology, a problem that could not be resolved either by simply accepting a deviant semantics, or by hypothesizing a Gödelian faculty of mathematical intuition, unless one of these moves was a way of explaining mathematical propositions as propositions that were in some way contingent. The problem is to explain how necessary truths can have content. According to Lewis, one of the virtues of modal realism, one of the beneﬁts to weigh against the costs, is that it provides us with an account of the contents of propositional attitudes and speech acts. Among all the possible worlds, there will be a certain subset—the doxastically or epistemically accessible possible worlds—that are the ones compatible with some agent's beliefs or knowledge. The set of doxastically accessible worlds should not be

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thought of as deﬁned by the propositions that the agent believes. Rather, Lewis suggests, we should ‘characterise the content of knowledge or belief from the outset in terms of something like the epistemically or doxastically accessible worlds’.45 An explanation of belief should begin with an account of how the facts about a person's internal functional organization and causal relations with his or her external environment determine a set of doxastically accessible worlds. Then a proposition is believed (at least implicitly) if it is true in all of those possible worlds.46 How, on this conception of belief, is one to explain the possibility of inconsistent belief, or of failures to believe all the necessary consequences of one's beliefs? We must recognize, Lewis says (and here I am in agreement with him), that belief attributions may describe a person's state of belief in some kind of indirect way. ‘The connection of belief sentences [sentences attributing belief] with belief as characterized by doxastic alternatives is complicated and multifarious.’47 Part of the answer to this question, according to Lewis, is that beliefs may be fragmented and compartmentalized: one may believe several propositions separately without having integrated them into a single belief state. But while this might explain how it is possible to believe several different propositions without believing some consequence of them, it cannot, by itself, explain how one might fail to believe a necessary truth. There is just one necessary truth, on this conception of content, and it is true in all possible worlds. Even if our beliefs are characterized by several nonintegrated sets of doxastic possibilities, a necessarily true proposition still must be true in all of them, so to account for the possibility of ignorance and error of necessary truths, we need to recognize a different way in which belief attribution is ‘complicated and multifarious’. Failure to believe a necessary truth, Lewis suggests, is not failure to believe the proposition it expresses, but rather failure to believe-true a sentence expressing it. Doubt and error about a necessary truth expressed by some sentence depends on the believer not fully understanding what the sentence says.48

45

Ibid., 28.

46

This is not quite right. In order to account for de se, or indexical beliefs—beliefs about one's time and place within a particular possible world—Lewis argues that contents of belief should be properties, or sets of centered worlds, rather than sets of possible worlds. But I think we can ignore this complication in this context without distorting the issues at hand.

47

Ibid. 34.

48

As Lewis makes clear, one can't use that-clauses to deny belief, or attribute ignorance, in a case where the subject has no idea what the sentence means. But when the subject has a ‘pretty good idea’ what a sentence means, but has failed to see that it expresses a necessary truth, then one may use the sentence, in indirect discourse, to describe the situation.

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This notion of content, and this kind of explanation of attitude attributions in the case where the content clause expresses a necessary truth, suggest a perspective on propositions about modality itself that is different from the perspective suggested by the possible worlds story. This story seems to suggest a domain of objects that makes our modal propositions true or false in the way that the domain of animals makes our zoological statements true or false. There are zoological facts about the domain of animals. We might ask whether things meeting certain conditions are in this domain. (Are there any unicorns—or at least horse-like animals with one long horn growing out of their foreheads? No, nothing like that.) It might seem that the modal realist believes that in a similar way there are modal facts about the domain of possible worlds. Can't we ask about whether there are possible worlds meeting certain conditions? (Are there any worlds with water that has a chemical composition different from H2O? No, nothing like that.) But the correct answers to all such questions will be necessary truths. The content of any such answer will be the same as the content of a sentence of the form P-or-not-P. Sentences of this form obviously tell us nothing about the character of the domain of all possible worlds: no matter what that domain is like, the union of any subset of it with its complement will be the whole set, and this will sufﬁce to ensure that provided that the sentence that goes in for P expresses some proposition, then the corresponding sentence of the form P-or-not-P will characterize the whole domain of all possible worlds. If there were a doubt about whether a sentence of that form expressed a true proposition, it would be a doubt about what the sentence said—about whether it expressed the proposition that it in fact expressed—and not a doubt based on any ignorance of what the possible worlds are like. The same will be true for any sentence expressing a necessary truth. If it is true that there might have been talking donkeys, or that it is necessary that water is H2O, or that there are inaccessible cardinal numbers, then each of these claims expresses this same proposition, and so what these sentences say also tell us nothing about the character of the possible worlds. Any ignorance or mistake about the truth of such statements will be ignorance or mistake about the relation between the statement and the proposition, and not about the proposition itself. The idea of the possible worlds analysis of content is that the content of a statement should be understood in terms of the possibilities the statement rules out. On this kind of account, there can be no substantive characterization of the whole domain of possibilities, since a substantive characterization would be a characterization that distinguished the way the domain of all possible worlds is from the way it might instead have been. The Tractarian Wittgenstein had this conception of content, and he clearly recognized this problem posed by it for an account of the content of necessary truth and for a characterization of the space of possibilities. His talk of what can be shown, but not said, is an attempt to address the problem, but it doesn't really help

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since showings must have content as well as sayings. As Frank Ramsey said, ‘what we can't say we can't say, and we can't whistle it either’.49 According to Lewis's way of reconciling this account of content with the fact of ignorance and error about modal truths and deductive relations, we can fail to know a necessary truth, or falsely believe an impossible proposition, only by failing fully to understand some sentence that expresses it. Knowledge and ignorance of modal truths (truths that seem to be about the character of the possible worlds, as well truths of mathematics) are to be explained as semantic knowledge and ignorance—knowledge and ignorance of facts about the relation between the expressions we use to state modal truths and the content of those truths. If this is right, then there is no information about the character of modal reality itself, considered independently of the way we think and talk about it. The picture that the thesis of modal realism suggests of a domain of possibilia, divided up into worlds, about which we can have substantive opinions, is thus difﬁcult to reconcile with the conception of content that, according to Lewis, provides one of the beneﬁts of the possible worlds theory. Empiricists used to say that necessary truths were true by convention, or true in virtue of meaning, or true because of the relations between our ideas—not because of the nature of anything in reality. Lewis's modal realism seems to be a conception of modal truth that is at the opposite extreme. ‘Why’, Lewis once asked, should it be human conventions that create and destroy facts about what is possible? All that human conventions can do is to select one verbal expression rather than another to enjoy the privilege of truth by virtue of the facts about the possibility of worlds. In just the same way, human convention selects one verbal expression rather than another to enjoy the privilege of being truth by virtue of the facts about tomorrow's weather.50 Conventions match sentences with propositions, but the propositions, whether necessary or contingent, are true independently of the conventions. But on Lewis's account of content, there is only one necessary proposition—the set of all possible worlds—and knowing that it is true—knowing that the actual world is in this set—does not require knowing any facts about modal reality. On Lewis's account of what we are doing when we attribute knowledge and ignorance of what appears to be modal fact, we are talking about knowledge and ignorance of the relations between sentences and the propositions they express. The conventionalist account of necessary truth and Lewis's are not so far apart as they at ﬁrst appear to be. I think this account of content helps explain both why mathematical Platonism is appealing, and why it has seemed problematic. Platonism seems to be a way of characterizing the content of mathematical statements—of giving them a subject matter—since it suggests a picture according to which

49

Ramsey (1929/1990: 146).

50

Lewis (1969: 207).

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they are contingent. If one thinks of mathematics as being about a domain of entities, then it is hard to resist the temptation to believe that the domain might not have existed. The Platonist's ontological commitment, one is tempted to think, is constituted by his exclusion of the possibility that there is no such domain of objects. But then the Platonist adds that the domain is one that exists necessarily, and so no such possibility has been excluded after all—no such commitment has been made. Perhaps it is better to say, as the liberal Platonist does, that the ontological commitment is not really a commitment to the exclusion of a possibility, and so is not a commitment that requires a defense in terms of some external relation between acts and objects of reference. If true mathematical claims are necessarily true, then there are no facts, about a domain of entities, or about anything else, that make the proposition they express true. They would be true no matter what the facts were. But one may still be ignorant of the answers to questions about the consequences of the rules and procedures by which certain sentences are matched with the necessarily true and the necessarily false propositions (the proposition that is true if and only if the actual world is located somewhere in the space of all possible worlds, and the proposition that is false if and only if it is). Proof, calculation, construction, and other kinds of mathematical inquiry and argument are ways of answering this kind of question. Lewis's account of content is separable from his modal realism. An actualist about possible worlds (one who believes that what are called possible worlds are not really worlds, but are possible states of the world—properties that the world might have had) can understand content in the same way, and can use the same strategies that Lewis uses to reconcile this conception of content with the fact of ignorance and error about modal truths and deductive relations. I have, elsewhere, defended this account of content and the strategies Lewis endorses, and I think it suggests a plausible way to address Benacerraf's problem about how to reconcile a straightforward semantics for mathematical discourse with the facts about way the sentences interpreted by such a semantics are established and refuted. But I don't think this account of content, and these strategies, are compatible with modal realism. Recall that according to Lewis's theory, all purely objective, impersonal beliefs—all beliefs about what there is in reality and not about the believer's place in that reality—are beliefs whose contents are necessarily true or necessarily false. But the necessarily true proposition does not really say anything. The information conveyed by sentences that express it is information about something else—something not impersonal and objective, but about the relation between the believer's language and the world. It seems that according to a theory that includes both modal realism and the possible worlds account of content, reality as it is in itself is something one cannot talk or think about. I don't think this is a consequence that a realist should be happy with.

3 Impossibilities (1996/2002) 1. Introduction Possible worlds I think we should be willing to accept, at least if they are given a sober actualist explanation. There are possibilities, different ways things could have been, or could still be. But impossible worlds, impossibilities, ways things could not have been—that is too much to swallow. Why make this invidious distinction? Impossible worlds have their defenders: William Lycan, for example, claims that ‘semantics needs impossible worlds’ and that there are no good reasons for recognizing nonactual possibilities that are not reasons for recognizing impossibilities as well.51 Others have defended impossible worlds as a dialectical move, agreeing with Lycan that possibilities and impossibilities stand or fall together, but tying them to each other only to lend weight to the rejection of both. The dialectical move is preﬁgured in Quine's arguments against Wyman, his ﬁctional Meinongian: All the rank luxuriance of Wyman's universe of possibles would seem to come to naught when we make a slight change in the example and speak not of Pegasus but of the round square cupola on Berkeley College. If, unless Pegasus were, it would be nonsense to say that he is not, then by the same token, unless the round square cupola on Berkeley College were, it would be nonsense to say that it is not.…Can we drive Wyman now to admitting also a realm of unactualized impossibles?52 More recently, such dialectic arguments have been used to criticize David Lewis's modal realism.53 I don't ﬁnd either these dialectical criticisms or the heroic defenses of the impossible at all persuasive, but I do think that arguments about this issue are revealing of some of what is at stake in the commitment to possibilities. The friends of possible worlds differ from each other on a number of dimensions—there are contrasting accounts of what possible worlds are and of what explanatory work they are capable of doing that the arguments over impossibilities help to bring into focus. I will try to

51

Lycan (1994: 39).

52

Quine (1961: 5).

53

See, for example, Naylor (1986). Yagisawa (1988) argues for the conditional thesis that if modal realism is acceptable at all, an extended realism that accepts impossible worlds as well should also be acceptable, leaving it to the reader whether to use this thesis ‘as the ﬁrst premise of the modus ponens, or the ﬁrst premise of the modus tollens’ (p. 203).

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lay out some of the twists and turns in the argument over impossibilities by recounting a dialogue between two philosophers. It is controversial whether this dialogue really took place. According to one of the participants it did, but whether he is right or not, it is clear that both he and his interlocutor are at best merely possible beings, and so in any case the discussion did not actually take place. The reader may see some resemblances, maybe even counterpart relations, between the characters and actual philosophers, but they should see contrasts as well. I want to make clear that these resemblances and contrasts are not my responsibility—they are just features of that part of modal reality that I have chosen to describe.

2. The dialogue WILL: I understand the position of those ontological puritans, the Quineans, whose preference for desert landscapes drives them to skepticism about everything other than what exists, but I am surprised that a possibilist like you, a Meinongian at heart with no fear of the incredulous stare, should balk at the impossible. I know of no argument for the existence of merely possible worlds that is not matched by a parallel and equally compelling argument for the existence of impossible worlds. LOUIS:

Before getting to the main issue, let me correct a misunderstanding. I am no Meinongian. In fact, I share Quine's skepticism (if this counts as skepticism) about everything other than what exists. But like Quine, I don't regard the claim that there are no nonexistent things (or the slogan ‘to be is to be the value of a bound variable’) as a commitment to an austere ontology—it is just a reminder that we should all be clear and unequivocal about our ontological beliefs, whatever they are. In his classic paper, ‘On What There Is’, Quine ﬁrst criticizes his ﬁctional Meinongian, Wyman, not for his bloated ontology, but for his misleading characterization of that ontology. ‘Wyman’, he says, ‘…is one of those philosophers who have united in ruining the good old word “exist”. Despite his espousal of unactualized possibles, he limits the word “existence” to actuality—thus preserving an illusion of ontological agreement between himself and us who repudiate the rest of his bloated universe.’ Quine then generously cedes the word ‘exist’ to Wyman, falling back on ‘is’. ‘So much for lexicography,’ he says, ‘let's get back to Wyman's ontology.’54 Now I have no quarrel with Quine on this—I have no inclination to refrain from applying the word ‘exist’ to everything there is to talk about or quantify over. But of course while I endorse Quine's methodological point, and accept his terms for the debate about ontology, I have plenty of disagreements with him about what there is.

54

Quine (1961: 3).

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WILL:

Okay, I'll agree that you are a clearheaded and unequivocal Meinongian, unlike Quine's Wyman. But my question remains—why possible worlds but not impossible worlds? LOUIS:

My problem is that I don't understand what I would be admitting if I admitted that there were impossible worlds or things. Here is how I understand the word ‘possible’: What is possible is what is true in some world or what is in the domain of some world. The role of the modiﬁer ‘possible’ in ‘possible world’ is not to restrict the class of worlds to a subset meeting some additional condition. The only role of the modiﬁer is to make clear that by ‘world’ I don't mean something like a planet within the actual world. ‘Possible world’, as I understand it, is otherwise just a redundancy, like ‘existent entity’. So what I mean by ‘possible world’ is what you impossibilists mean by ‘world’. You distinguish a proper subset of the set of worlds that you call ‘possible’. What I need to be told before I understand your impossibilist thesis is what it is that distinguishes this subset from the rest of the worlds.

I see your use of the word ‘possible’ as being like Wyman's use of the word ‘exist’: ‘Exist’, for Wyman, is a predicate that (according to him) picks out a proper subset of the domain of things there are. As Quine argued, to understand Wyman we need to be told what that predicate means—what distinction he is using the word ‘exist’ to make. I am inclined to reply to you as Quine did to Wyman: By using the word ‘possible’ to distinguish between the possible worlds, you are ruining the good old word ‘possible’. I'll give it to you, but you owe me an explanation of what distinction between the worlds (the things that I am inclined to call ‘possible worlds’) you are using the word ‘possible’ to make. Once that is clear, then I can consider whether I think there are any worlds that don't meet the condition—worlds that are not possible in your sense. WILL:

I don't agree with you about who is ruining terminology, but I agree that we should not argue about who gets the word ‘possible’, and I am happy to accept the burden of explaining the difference between the worlds I call ‘possible’ and those I call ‘impossible’. It is simple: impossible worlds, in my sense, are worlds in which some contradiction is true. Whatever the terminology, the substantive metaphysical question between us is whether there are any worlds (or in your misleading terminology, any possible worlds) in which contradictions are true. LOUIS:

If that is what you mean, then I have an argument that there are no such things as impossible worlds, at least if I am allowed to make the assumption that the actual world is not an impossible world. (This last assumption, I grant, may be controversial in some circles—it might be argued that quantum mechanical phenomena, or United States politics in the 1990s, tend to support the thesis that our world is impossible—but

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I assume that you agree with me that the actual world is one of the possible worlds.) Here is the argument: Suppose there is a world w in which both P and ∼P are true. Let us introduce a modal operator ‘in w’ that is interpreted by the following semantical rule: ‘in w, P’ is true in any world x if and only if P is true in w. So by this rule, ‘in w, P’ and ‘in w, ∼P' are both true in the actual world. But ‘in w, ∼P’ is logically equivalent to ‘∼ (in w, P)’. So a contradiction will be true in the actual world. We ourselves must afﬁrm a contradiction in order to describe an impossible world. But this implies that there are no impossible worlds, for, to quote David Lewis from whom I have borrowed this argument, ‘There is no subject matter, however marvellous, about which you can tell the truth by contradicting yourself.’55 WILL: I am not impressed, or convinced, by this argument. You are just begging the question. I grant you that if all worlds were possible, then the inference from ‘in w, ∼P’ to ‘∼(in w, P)’ would be valid, but clearly the inference loses all plausibility as soon as we entertain the idea that there are impossible worlds.56 LOUIS:

We are making some progress, at least, since we have reduced our metaphysical disagreement to a disagreement about the validity of a logical inference, and this question we should be able to settle. I have given you the semantical rule for my operator ‘in w,’ and presumably you don't object to that. The only other relevant symbol is the negation sign, which I thought had a pretty clear and uncontroversial semantics, at least for those of us who accept classical logic. My assumption about the meaning of ‘∼’ is this: ∼P is true if and only if P is false. Or in other words, the set of worlds in which ∼P is true is the complement of the set of worlds in which P is true. I learned this rule early in my ﬁrst logic class years ago. I suppose one might use the symbol differently, but it is hard to see how any metaphysical question could turn on whether we stick with the traditional truth-table account of the negation symbol. Now isn't it clear that, given this rule for negation, I am right about the equivalence of ‘in w, ∼P’ and ‘∼(in w, P)’? If so, isn't my argument against impossible worlds, as you have deﬁned them, a good one?

55

See Lewis (1986a: 7, n. 3). William Lycan replies to this argument in Lycan (1994: 40).

56

Will is following William Lycan in responding this way. But another defender of the impossible, Takashi Yagisawa, seems to accept Lewis's argument and to embrace the contradiction. He rejects Lewis's claim that no subject matter is so marvelous that we can tell the truth about it by contradicting ourselves. ‘Why can you not tell the truth about an impossible thing by contradicting yourself? … What else would you expect? Impossible things are impossible’ (Yagisawa 1988: 203). If Yagisawa also accepts Will's criterion for an impossible world—a world in which a contradiction is true—then it seems to follow that the actual world (and by similar reasoning every possible world) is impossible. I am tempted to call this a reductio of the position, but believers in actual impossibility will obviously not think that the reduction of some claim to absurdity is a reason to reject it.

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WILL:

As Ronald Reagan used to say, ‘There you go again’ Once again, you are begging the question. I agree that if we restrict our attention to the possible worlds, then the set of worlds in which ∼P is true will be the complement of the set in which P is true; but this rule will not apply generally if there are impossible worlds, which is what is in dispute. Impossible worlds are inconsistent, and for the most part are not deductively closed, so it can't be assumed that the set of worlds in which P is true is the complement of the set in which ∼P is true. LOUIS:

Impossible worlds are not consistent and not deductively closed? What could that mean? What is it for a world to be consistent or inconsistent, deductively closed or not? Imagine the citizens of some impossible world establishing empirically that the cat is on the mat, and that if the cat is on the mat, then the dog is asleep, and then discovering, to their horror, that the dog is not asleep. The headline in the National Enquirer blares: ‘TOP SCIENTISTS FIND WORLD NOT DEDUCTIVELY CLOSED.’ But even if you can make sense of your attribution of these logical properties to worlds, I don't see that this matters, since the rule for the negation operator doesn't assume anything about the nature of the worlds that are in the set of all worlds, and so cannot be begging any questions about what kinds of worlds there are. Let the worlds be as bizarre and ill-behaved as you like. No matter what worlds you allow into your set of all worlds, none of them will be in some subset of them and also the complement of that subset. Surely you won't deny that my rule is clear and coherent, whether or not there are impossible worlds. So how am I begging the question against them? Are we just arguing about terminology again—about who gets to deﬁne the symbol ‘∼’? Paraphrasing Quine one more time, you are ruining the good old symbol ‘∼’—Wyman at least ruined only one word and left others for Quine to use to state his views. I am worried you will take away my whole vocabulary before we are ﬁnished. Okay, you can have the tilde, since nothing hangs on how a bit of logical notation is used (though you owe me an explanation of what you mean by the tilde). But I fear you are going to want to take over the word ‘contradiction’ as well. I started by asking for an explanation of the distinction between the worlds that you are calling ‘possible’ and the ones you are calling ‘impossible’. You answered by explaining it with the help of the word ‘contradiction’, and I thought I understood. But now I ﬁnd that we don't mean the same thing by ‘contradiction’, so I am no longer sure what you are saying or whether we are disagreeing at all. Let me try to see if I can describe our dispute, and my puzzlement about it, in neutral language. You claim that there is a distinction between two classes of worlds: there is an inner set that you call possible and that is assumed to include the actual world, and an outer set that you

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call impossible. Let's call the inner set the boring worlds and the outer set the weird worlds. So far, I have no objection, though I have lots of questions. (What, for example, is the status of the claim that the actual world is boring and not weird? Is this an empirical fact?) But set aside for the moment the question of what distinguishes the two sets. We can say this about the use to which you want to put the distinction: we will use it in our interpretation of a one-place sentence operator, the tilde. It will be a constraint on the interpretation of this operator that within the set of boring worlds, ∼P shall be true if and only if P is false, but in worlds in the weird set, this need not hold. (How is this symbol interpreted relative to the weird worlds? That remains to be speciﬁed.) Call the proposition expressed by ‘∼P’ a quasi-negation of P (since we agree that it coincides with negation at least for the boring worlds), and call the conjunction of any sentence and its quasi-negation a quasi-contradiction. Let us specify the rule for ‘∼’ so that every weird world will have at least one quasi-contradiction true in it. Now you seem to take our dispute to be about whether there are any weird worlds, any worlds in which quasi-contradictions are true, but I am not in a position to deny that, since you have told me nothing about what makes a world weird. I am certainly willing to grant that however the weird worlds are distinguished from the boring ones, if there are any weird worlds, then for some interpretations of ‘∼’ that ﬁt the constraints speciﬁed, quasi-contradictions will be true in them. But I am still in the dark about what these worlds are like. So as I said at the start, it is not that I disagree with your metaphysics—I don't see that you have yet given me any metaphysics to disagree with. WILL:

Hold on—let's not get carried away with this question-begging talk of quasi-negation and quasicontradictions. I don't owe you an explanation for my use of the tilde, since I am using it exactly as you are. That truth-table rule that you learned in your ﬁrst logic class is ﬁne with me (for at least one kind of negation). Like you, I assume that the tilde is a truth-value reverser: ∼P is true if and only if P is false. My difference with you is not over the tilde, or the deﬁnition of ‘contradiction’. It is rather that I allow for the possibility of statements that are both true and false—for truth-value gluts (and perhaps also for truth-value gaps). The rule for negation that you know and love is compatible with the truth of a contradiction. P & ∼P will be true, given the classical rules for negation and conjunction, whenever P is both true and false. An impossible world might be deﬁned as a world in which some proposition is both true and false. This will be equivalent to saying that a contradiction is true in it. LOUIS:

Now I am really confused. It seems now that it is the good old words ‘true’ and ‘false’ that you are ruining, and given the crucial role that those words play in semantics, that threatens to throw everything into disarray. (Not that I see how this move helps you anyway. If P is

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both true and false in some impossible world w, then ‘in w, P’ will be both true and false in the actual world, indeed in all possible worlds. So it still seems to follow that all worlds are impossible.) But my real problem is that I have no idea what it could mean to say that a proposition is both true and false. Let me explain my puzzlement by saying how I understand truth and falsity. Our aim in communicating is to locate the actual world within some subspace of the space of all possible worlds. A proposition is no more than such a subspace, or subset, and to assert a proposition is just to locate the actual world in that subset. To say that a proposition is true at or relative to a possible world x is just to say that x is in the subset that constitutes that proposition. To say that a proposition is true simpliciter is to say that the actual world is in the subset. ‘True’ and ‘false’ are just labels that help to tell this story. The proposition is identiﬁed with its truth conditions, which is to say with the possible circumstances that, if realized, would make it true, which is just to say the possible worlds that are included in the set that constitutes the proposition. Now if we want to allow propositions to be both true and false, relative to some world, we can't think of them this way. To accommodate truth-value gluts, we might take the value of a sentence to be, not a single subset of the set of worlds, but instead a pair of such subsets: a truth set and a falsity set. Call them D-propositions (‘D’ for double). For well-behaved D-propositions, the one set will be the complement of the other, but not all D-propositions will be well-behaved. (It seems that it will be required, however, that all D-propositions be well-behaved relative to the boring worlds. Each of those worlds will be included in any proposition's truth set if and only if it is excluded from the falsity set.) Now it is clear enough what these D-propositions are, but what is their point? What is it to assert or believe one of them? Suppose world w is in both the truth and falsity sets for some D-proposition P. If I assert P, what am I saying about w? If I believe P, is w compatible with my beliefs or not? And if one is to allow ill-behaved Dpropositions at all, why are they restricted to pairs of sets that are well-behaved relative to the boring worlds? This doesn't help explain the metaphysical difference between worlds that you are asking me to believe in, so I am still in the dark about whether I should believe in the kind of world that you are calling impossible. WILL:

First, let me respond to your parenthetical point—that truth-value gluts won't avoid your argument that all worlds are impossible. I think the problem is that I have not been careful enough in giving my deﬁnition of an impossible world, but the problem is easily remedied. We should say that an impossible world is one about which a contradiction is true. Your operator, ‘in w’ is just a device for turning a proposition that is really about what goes on in world w into a proposition that is true in

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different worlds. Since ‘In w, P’ is about world w (assuming that P is), the fact that it is both true and false in the actual world won't make the actual world impossible. LOUIS:

Fair enough, provided you can give me an explanation of the notoriously difﬁcult notion of aboutness. On my understanding of proposition—as a set of worlds—it would make no sense to say that a proposition is about one world rather than another, but you will presumably want some more ﬁne-grained notion. If you can explain what it is for a proposition to be about a world, you will avoid the conclusion that all worlds are impossible, but you are still stuck with the consequence that belief in impossible worlds commits you to the actual assertion of a contradiction. But anyway, my main concern is to understand the metaphysical distinction that you are claiming exists between the boring and weird (or possible and impossible) worlds. WILL: Let's look at an example, just to try to be more concrete about what impossible worlds (or weird worlds, to adopt your weird terminology) are like. Quine, in his argument with Wyman, referred to (in some sense of ‘referred to’) the round square cupola on Berkeley College. A world containing a building with a round square cupola would be an impossible (or weird) world. My claim is that there are such worlds, or at least that you have no reason to rule them out. But you, as I understand you, are denying the existence of such worlds. Isn't this a clear metaphysical disagreement? LOUIS:

This does not help me very much. My problem is still in understanding exactly what sort of world you are asking me to believe in. As I understand the meanings of the adjectives ‘round’ and ‘square’, they pick out disjoint parts of logical space. On this understanding, when you tell me that a certain weird object is, in its weird world, round, you are telling me that it is not square there. But then you tell me that it is square there. As in the case of the simple contradictions, it seems that you must contradict yourself to describe the possible—sorry, I mean impossible—world you are trying to get me to believe in. Now I am an open-minded person who does not want to be dogmatic about the limits of logical space. I am prepared to learn that I was wrong to think that the properties round and square are incompatible. For all I know, logical space is richer and more ﬂexible than I am capable of imagining, allowing for a possibility that I would recognize (if only I could understand it) as including things that are both round and square at the same time. But to admit this would be to admit that round squares are perhaps possible after all, and that is not what you are asking me to believe. Your example serves its purpose only if roundness and squareness really are incompatible properties. So you are not asking me to make room in logical space for an object that is both round and square in the sense you intend. You

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want me to make room for it only in illogical space. I would understand you if you were asking me to expand my conception of the possible—to admit that there are weird and wonderful possibilities beyond those I have imagined, or even could imagine. But I haven't, in this discussion, said anything substantive about the limits of the possible, so you can't be asking me to go beyond those limits. You seem to be telling me that whatever worlds I admit, there are some other ones as well, and this is what I ﬁnd hard to grasp. WILL: Perhaps I was wrong to begin by trying to argue from within your modal realist perspective, suggesting that you, with your conception of possibilities, ought to ﬁnd room for impossibilities as well, when my real point is that a good theory of possible worlds (one that does not have the drawback of being outrageously false) ought to allow for them. I should perhaps admit that your concretist conception of a world as a very large parcel of real estate compels you to rule out impossible worlds. But we actualists have no problem making sense of them—they might be understood, for example, as inconsistent sets of propositions. And if you are right that modal realism can ﬁnd no room for impossible worlds, so much the worse for your modal realism. In the weighing of costs and beneﬁts of concretism versus actualism it seems to me that it is a beneﬁt of actualism that it can accommodate impossible worlds. (They are useful, for example, for explaining counterfactuals with impossible antecedents and perhaps for giving a semantics for propositional attitudes that can account for inconsistent belief.) LOUIS:

Modal realism (or concretism, as you like to call it) we can argue about another time. I think the particular disagreement we have been having today is independent of that issue. As for the existence of inconsistent sets of propositions, I hope that is not what we have been arguing about. I have no inclination to deny the existence of sets of propositions that are inconsistent, and if you think they can do some explanatory work for you in semantics, go right ahead and use them—you need not reject modal realism to have recourse to sets of propositions, either maximally consistent ones or those that fail to be either consistent or deductively closed. But you can't buy any metaphysics by calling such sets ‘worlds’.

As I see it, the crucial difference between us concerns the role of possible worlds in the explanation of possibility (and more generally in the explanation of propositions and relations between propositions). More speciﬁcally, the issue is whether we should analyze worlds in terms of propositions or propositions in terms of worlds. While I am perfectly comfortable with sets of propositions, one reason I resist the identiﬁcation of possible worlds with sets of propositions is that I think propositions are sets of possible worlds. It may be that my modal realism is one

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thing that motivates a preference for an analysis in this direction, but some actualists would agree with me on this question, and I think the real motivation for it is a conception of propositional content that is not tied to modal realism. The starting point is the familiar idea that the intentional content of a statement or thought is its truthconditions, where truth-conditions are the way that the world would have to be for the statement or thought to be true. One knows what a statement says to the extent that one is able to form some conception of the distinction between the kind of world that would make it true and the kind that would make it false. If one has succeeded in forming a conception of a world that would, if realized, make the statement true, then one has succeeded in showing it to be possible. Now whatever one's metaphysical theory about the nature of worlds—whether one thinks of them as large parcels of real estate, to use your words, or as a kind of actually existing way the world might or might not be—the following will be true: If there is a domain of all the worlds, then one can interpret modal operators in terms of unrestricted quantiﬁcation over this domain: necessity is truth in all worlds, ‘Possibly ___’ is true in any world if ___ is true in some world. That is what I mean when I talk of metaphysical possibility, but if you want to interpret possibilities and impossibilities in a different way—in terms of restricted quantiﬁcation—that is ﬁne with me. And if you do, I shouldn't even accuse you of ruining good old words, since modal words—‘possible’, ‘may’, ‘might’, ‘could’, ‘must’, ‘ought’, etc.—are most commonly interpreted in terms of some proper subset of the possibilities, a set deﬁned by an accessibility relation between worlds (the worlds compatible with the laws of nature that hold in the actual world, or with what Pierre knows there, or with Igor's moral obligations all being satisﬁed, for example). All I need to know is what the basis is for your restriction. But whether your concept of impossibility is based on restricted or unrestricted quantiﬁcation, it seems to me hard to escape the conclusion that at least some impossible statements will come by their impossibility by being true in no world at all, possible or impossible. For you surely will agree that a proper semantics explains truth-conditions in terms of compositional rules, and that whatever possibilities and impossibilities are available for semantics to appeal to in its explanations of the content of a complex statement as a function of the meanings of its component parts, there might be statements that are true in no possible or impossible world. Of course, one can be ignorant or mistaken about what is possible in this unrestricted sense. One may be under the illusion that one has conceived of a possibility when one has not. Since statements, and other kinds of representations, represent possibilities in complex ways, it may take some effort to see what a statement says, and the effort may reveal that a statement that one thought described a coherent possibility in fact does not—that despite ﬁrst appearances there are no conditions under which it

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would be true. That is what it is to discover, or come to believe, that a proposition is impossible in this sense. It is not that one forms a conception of a kind of situation that would make the statement in question true but judges that kind of situation to be one that fails to meet some metaphysical condition. Rather, one fails to turn up any situation, or ‘world’, at all. WILL:

So are you suggesting that statements describing impossibilities are meaningless—devoid of content—sentences with no truth-conditions? If so, you are following the precedent of ‘wily Wyman’, who tried to escape Quine's reductio by saying that the phrase ‘round square cupola’ is meaningless. As Quine said, the doctrine that contradictions are meaningless has a long history, but I am inclined to agree with him that ‘it has no intrinsic appeal’ and has ‘severe methodological drawbacks’,57 such as, for example.… LOUIS:

Wait—sorry to interrupt, but I don't want you wasting your time refuting a doctrine that I have no inclination to defend. Of course contradictions are meaningful. Contradictory statements and thoughts succeed in expressing a proposition—one that is true under no conditions. On the picture I am trying to sketch, the meaning of a statement is something like a recipe for determining truth-conditions. One may know the meaning of a complex statement—know the recipe for determining its truth-conditions as a function of the meanings of its components and the compositional rules—without yet having done the computational work to discover what those truthconditions are (or whether there are any conditions under which it would be true). There is perhaps an ambiguity in the expression ‘truth-conditions’ that is responsible for the inclination some philosophers have had to say that contradictions are meaningless. The recipe for computing the content of a statement as a function of the meanings of its parts (plus context) is a statement of the conditions under which the statement would be true, and so this recipe might reasonably be called ‘the truth-conditions of the statement’. In this sense, any statement with a determinate meaning will have truth-conditions. But even if a statement has truth-conditions in this sense, it still may be that the result of the computation of the recipe is that there are no conditions under which it would be true.

WILL: Okay, I get this distinction, but I am still suspicious of your picture, partly because I am not sure I understand what it is to ‘form a conception of a world that would, if realized, make a statement true’. How do we form a conception of the worlds in which a certain statement is true except by describing the worlds, and doesn't the statement itself do that? (The kind of world that would, if realized, make ‘there is a round square

57

Quine (1961: 5).

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cupola on Berkeley College’ true is a world in which there is a round square cupola on Berkeley College.) The reason we know we have not formed a conception of a possible world in which the statement is true is that the statement describes an impossibility. So I don't see how your picture provides us with any criterion for possibility. LOUIS:

I have to agree with you—I would not pretend to have given a criterion for possibility—a general way of settling disputes about what is possible. But I think the issue is about how to understand questions about what is possible, and not how to settle them. Suppose two philosophers are arguing about whether time travel is metaphysically possible, whether Aristotle—the man himself—could have been an artichoke, whether water could have been something other than H2O, whether physical space could have seventeen dimensions. If I think of such questions your way, then the problem is to decide whether the worlds which we agree there are and in which these conditions are realized are located in the inner set of possible worlds or the outer set of metaphysical impossibilities. Once you have told me more about how you make this distinction, I will know how to go from there. If I think of the questions my way, then the problem is to determine whether an expression succeeds in representing a kind of world at all. The focus of our dispute or inquiry shifts from the status of the worlds to the meanings of the expressions and the rules for interpreting them. When we disagree about whether some statement could possibly be true, we are arguing about what the statement says.

WILL: I ﬁnd it ironic that you, the consummate metaphysician who takes modal claims to be claims about the properties of a domain of parallel universes, should be arguing that disputes about what is metaphysically possible are really disputes about the meanings of words or at least about what statements say. Are you sure you are not a closet logical empiricist who believes that all necessity is a matter of convention? LOUIS:

I take it to be a triviality that the truth of any statement depends on two things: what it says, and whether the world is as it says. That is, it depends on what the truth-conditions are and whether those conditions are satisﬁed. If the statement is true under all conditions, or under none, then we know whether the world is as the statement says simply by determining what it says. So arguments about what is metaphysically necessary or possible are inevitably arguments about what a statement says. If this is the point that the slogan ‘all necessity is a matter of convention’ is trying to make, then I agree with it. But the truth of propositions themselves (including the necessary and impossible propositions) does not depend at all on any conventions. WILL: Let me see if I have this straight. Consider a statement like ‘Either donkeys talk or they do not’. Applying the truth-functional rules that you are so fond of, we learn that the proposition expressed by this statement

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is the one that is the union of some subset of the set of all possible worlds with its complement. Obviously, this proposition tells us nothing, either about the world or about modal reality—about what sorts of worlds are included in the space of all possible worlds. But your conception of content implies that any necessarily true statement, any true statement about what is common to the whole of modal reality, or any statement about what is possible (any statement about what worlds are included in the space of all possible worlds) will say nothing more than this trivial tautology. They all have exactly the same content, and so once we understand what they say we see that they too tell us nothing about what the space of all possible worlds is like. So you have given us these modal riches—a plenitude of possible universes—but your conception of content seems to imply that modal reality is impossible to characterize. Is this right? (Maybe you should change your name from Louis to Ludwig and make dark and delphic pronouncements about the limits of language and the limits of the world.) LOUIS:

No, I am afraid that is not my style, but it is right that the necessary proposition is one that is true no matter what the world is like, and so it tells us nothing about reality, modal or otherwise. This may be surprising, but I don't think it is as mysterious as you suggest. The conception of content that I have been trying to defend assumes that a proposition is a way of distinguishing between possibilities—that the only way to describe the world is to distinguish a way it is from other ways that it might have been. Since there is no other way modal reality might have been, one cannot say something informative about the character of modal reality as a whole by asserting the proposition that is true in all possible worlds. But that does not mean that one cannot talk at great length about what the possible worlds, actual or otherwise, are like. One describes modal reality by distinguishing parts of it from other parts. The possible worlds differ from each other on many dimensions, so there is much to be said about contrasts between the different possible worlds. So I see no need to be mystical about logical space, or modal reality, or to add a contrasting set of impossible worlds in a vain attempt to talk about the limits of the possible from some point of view beyond them.

WILL: I can't say that I am convinced, but since it is clear that the author of our dialogue is on your side in this dispute, I must leave you with the last word. Perhaps we can continue our discussion some time when he is not around.58

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After the original version of this dialogue was in press, I received some detailed comments from David Lewis who, while ﬁnding Louis a kindred spirit, thought that Will could have done a better job defending his side of the story. In this expanded version of the discussion, I have followed some of Lewis's suggestions, though I am not sure that I have done as well on Will's behalf as Lewis would have liked. In any case, Louis was not moved.

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PART II Carving up Logical Space

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4 Anti-essentialism (1979) Aristotelian essentialism, according to Quine, is the doctrine that things may have some of their properties necessarily, not relative to how the things are described, but absolutely. To accept some form of this metaphysical doctrine is to adopt an ‘invidious attitude toward certain ways of uniquely specifying x…as somehow better revealing the “essence” of the object’.59 Further, Quine has argued, one is forced to accept this doctrine if one quantiﬁes into modal contexts; ‘so much the worse for quantiﬁed modal logic,’ he concludes. ‘By implication, so much the worse for unquantiﬁed modal logic as well.’60 Most contemporary modal logicians have responded to Quine's arguments by accepting the tie between quantiﬁed modal logic and essentialism, and by embracing essentialism. Rather than ‘so much the worse for quantiﬁed modal logic’, they conclude ‘so much the better for essentialism’. This reversion to metaphysics is supported ﬁrst by a semantics that gives an explanation of essential attribution and shows it to be formally coherent, and second by intuitive examples that show that the invidious distinction lamented by Quine is well entrenched in our ordinary ways of regarding things. But although this is the majority reaction, there are those who wish to reconcile quantiﬁed modal logic with Quine's rejection of essentialism—the rejection of a discriminatory distinction between two ways that a thing may be related to its properties. It is a program of this kind that I want to discuss. If the anti-essentialist accepts an explanation of necessity in terms of possible worlds, then he has an account of essential properties whether he wants one or not. An essential property is a property that a thing has in all possible worlds in which it exists. An accidental property is a property that a thing has in the actual world, but lacks in some other possible world. But the anti-essentialist can still try to remove the discriminatory feature of essentialism to which Quine objects. He can do this in either of two ways: ﬁrst by arranging to have all properties be essential properties in the sense deﬁned; second, by trying to set up his theory so that none of them are. In both cases, essential attributions are meaningful (and thus the conclusion of Quine's arguments is not contradicted). But the problem of distinguishing

59

Quine (1961: 155).

60

Ibid. 156.

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true essential attributions from false ones is avoided in the ﬁrst case by making them all true, and in the second by making them all false. A philosopher who responded to Quine in the ﬁrst way was Leibniz. According to him, every property of every individual is constitutive of its essence, and hence only existence is contingent. A modern descendant of this kind of anti-essentialism is David Lewis's counterpart theory. According to Lewis's theory, individuals have counterparts—things that resemble them more than anything else—in other possible worlds, but each individual itself exists in only one possible world. Hence no individual can have accidental properties in the sense deﬁned above: properties that it lacks in some other possible world.61 The second kind of anti-essentialism I shall call bare particular anti-essentialism. This theory holds, roughly, that for every individual and every property, there are possible worlds in which the individual has the property and possible worlds in which it does not. For the sake of consistency, this generalization needs some qualiﬁcation—for example, tautological properties like being self-identical will be exceptions—but this is the rough idea. The main problem in the development of this idea is to make clear and precise just what qualiﬁcations are necessary. The ﬁrst thing I want to argue is that even after the relevant qualiﬁcations are made, one cannot make semantical sense out of bare particular anti-essentialism within the framework of the standard semantics for modal logic. In this respect, the bare particular theory contrasts with the Leibnizian version of anti-essentialism. The latter doctrine has a formal semantics which can be seen as a special case of the standard possible worlds theory. The second thing I want to do is to suggest an alternative to the standard semantics that can make sense out of the bare particular theory. The alternative semantics will not require that the anti-essentialist doctrine be true, but that doctrine will be embodied in a simple formal condition which is very naturally imposed on the models deﬁnable within the alternative semantics. My primary aim in pursuing this project is not to defend the bare particular thesis, which seems to me most of the time to be implausible. But while I doubt that this metaphysical doctrine is true, I think the fact that it does not even make sense within the framework of extensional semantics is a symptom of a limitation of that semantics. My real aim is not to argue against essentialism, but rather, by giving a formally coherent account of a contrasting doctrine, to raise some new questions about essentialism and to make clearer what the essentialist is committed to. I shall begin on an intuitive level with the qualiﬁcations that are required in the thesis that all

61

I do not want to suggest that David Lewis's theory is motivated by anti-essentialism. His counterpart relation, together with a different analysis of essential and accidental properties, reintroduces the invidious distinction.

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properties of all objects are accidental properties. There are three kinds of qualiﬁcations—three kinds of unobjectionable essential attributes. Each of these kinds of properties has been discussed by Ruth Marcus or Terry Parsons in articles on essentialism and modal logic.62 First, any property that is necessarily an essential property of everything is an unobjectionable essential property from the point of view of the bare particular doctrine. Such properties as being self-identical, being either a kangaroo or not a kangaroo, being colored if purple in no way limit the logical potential of any individual, or distinguish between different kinds of individuals. Hence they do not conﬂict with the spirit of the anti-essentialist thesis. Second, certain relational properties that are deﬁned in terms of speciﬁc individuals may be essential properties without conﬂicting with the intuitive idea behind anti-essentialism. Ruth Marcus has called these referential properties. For example, the following are attributes that everyone should admit are essential to Babe Ruth: being identical to Babe Ruth, being either identical to Babe Ruth or fat, being fat if Babe Ruth is, being the same weight as Babe Ruth. Even if there are possible worlds in which Ruth is a kangaroo, a tricycle, or a billiard ball, even if he has no essential nature which constrains the qualitative characteristics that he might have had, still, in all possible worlds he will have the properties mentioned above, since these properties are deﬁned so that Babe Ruth could not lack them without lacking his own identity. It might, of course, be controversial whether or not a given property was a referential property in this sense. According to an operationalist, for example, the property being one meter long would be one, since the operationalist believes it is deﬁned as the property of being the same length as x, where x is a particular object. The standard meter bar is essentially one meter long, if the operationalist is right, but this does not prevent it from being, in other possible worlds, very very long or very very short. Third, the so-called world-indexed properties invented by Alvin Plantinga are unobjectionable examples of essential properties.63 Call the actual world Kronos. Then being snub-nosed-in-Kronos is deﬁned as the property that something has in any world if and only if it has, in Kronos, the ordinary accidental property of being snub-nosed. All snub-nosed people are essentially snub-nosed-in-Kronos, but being saddled with such an essential property puts no constraints on the qualitative characteristics that an individual might have had. The problem is, now, to reconcile the bare particular thesis, qualiﬁed in these ways, with quantiﬁed modal logic. To carry out this job we must incorporate the qualiﬁcations and the intuitive distinctions on which they rest into a formal theory. This problem has been attacked from a

62

See Marcus (1967), Parsons (1967), and Parsons (1969).

63

Plantinga (1970).

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proof-theoretic point of view by Terence Parsons. He asked in his paper, ‘Essentialism and Quantiﬁed Modal Logic’,64 what axioms are necessary to a sound and complete anti-essentialist theory—a theory that has as a consequence the denial of each objectionable essential attribution? But the axiom set that Parsons provides in answer to this question has the following unusual feature: there are sentences (for example, ∃x□Fx ⊃ ∀x□Fx) which are theorems even though some substitution instances of them (for example, ∃x□Rxy ⊃ ∀x□Rxy) are not theorems. What this means is that the atomic predicate ‘F’ does not represent an arbitrary property as is usually the case, but only an arbitrary property of a certain sort. Since the second sentence is a non-theorem, there must be some legitimate interpretations in which it is false. But then if we could interpret the predicate ‘F’ in the ﬁrst sentence to mean what ‘R_y’ means in the interpretation which falsiﬁes the second, then we could have an interpretation in which the theorem is false. But since theorems must be true in every legitimate interpretation, that interpretation of the predicate ‘F’ will have to be ruled out. Thus the predicate ‘F’ does not stand for an arbitrary property. This consequence is not in itself objectionable, but it puts an additional burden on the semantics for the theory. If all and only the theorems are to be valid—true in every legitimate interpretation—then the rules for interpreting the sentences of the language must make a distinction between those properties that are appropriate to be values for the atomic predicates and those properties that are not. The required distinction, of course, is the distinction between intrinsic, qualitative characteristics on the one hand, and referential and world-indexed properties on the other; it must be assumed, at least, that all the atomic predicates express properties of the ﬁrst sort. But this distinction is presupposed and not explained in Parsons's account. The notion of an atomic predicate cannot contribute to such an explanation since it is a purely syntactical notion and cannot by itself do a semantical job. To complete the task of reconciling anti-essentialism with quantiﬁed modal logic, we need a distinction on the semantical level between those propositional functions that can be values for atomic predicates and those propositional functions that cannot. In the now standard formal semantics for ﬁrst-order modal logic, truth-values for the sentences are deﬁned relative to possible worlds. Each possible world has a domain of individuals—the individuals that exist in that world. Possible worlds and individuals are the only primitive semantical elements of the theory—the only elements necessary to deﬁne the models that serve as the subject matter for the sentences of the language being interpreted. Other semantical notions such as properties and relations, individual concepts and propositions are identiﬁed with functions deﬁned in terms of individuals and possible worlds. For example, a proposition is

64

Parsons (1969).

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deﬁned as a function from possible worlds into truth-values, or equivalently, as a subclass of the class of all possible worlds. Properties are represented as singulary propositional functions—functions that take an individual as argument and a proposition as value, or, equivalently, functions that take a possible world as argument and a set of individuals as value. Intuitively, on this account, a property is a rule—any rule—for determining a class of individuals, given the facts. Any procedure for selecting individuals, whatever its basis, is a property of the individuals selected. In terms of this extensional account of properties (extensional in the sense that properties are deﬁned by their extensions in different possible worlds), what corresponds to the intuitive distinctions between referential and purely qualitative properties, and between world-indexed and world-independent properties? Nothing. All properties are referential in the sense that they are deﬁned in terms of the speciﬁc individuals that have them. All properties are world-indexed in the sense that they are deﬁned in terms of the speciﬁc possible worlds in which things have them. While one can, of course, make a distinction between essential and accidental attributes in terms of the standard semantical framework, one cannot ﬁnd any independent distinctions corresponding to the intuitive ones needed to state a coherent version of the anti-essentialist thesis. Thus there is no satisfactory way, without adding to the primitive basis of the semantical theory, to state the thesis as a further semantical constraint on legitimate interpretations of the language of modal logic. There is one unsatisfactory way that should be mentioned just to be put aside. One could simply stipulate that in legitimate interpretations of anti-essentialist modal logic, atomic predicates always must express purely accidental properties (properties that no individual has essentially). In terms of propositional functions, this stipulation comes out as the requirement that the interpretation given to any one-place predicate be a propositional function that takes a contingent proposition as value for every argument. But even if a constraint of this kind were formally adequate,65 it would be subject to the following objection: this requirement does not prevent objectionable essential attributions from being true; it just prevents them from being expressed in the language that is being interpreted. No limitation is placed on the model structures for the language—on the allowable subject matter for its statements. The limitation placed by the constraint is a limitation solely on what can be said about the structures in the language. This is a theory, not for an anti-essentialist, but for an embarrassed essentialist. It is no more an account of anti-essentialism than the traditional Victorian response to venereal disease—don't talk about it—was a cure.

65

The constraint suggested would be necessary, but not sufﬁcient. It does not rule out the possibility that some deﬁned monadic predicates such as (Fx∨Gx ) be nonuniversal, but essential to some things.

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What the standard semantics lacks is an account of properties that deﬁnes them independently of possible worlds and of individuals. If we are to make sense of the bare particular theory, a property must be not just a rule for grouping individuals, but a feature of individuals in virtue of which they may be grouped: not just a propositional function, but something that determines a propositional function. This independent speciﬁcation of properties and relations is what I shall add to the semantics. It will give us a formal representation of the intuitive distinctions on which the doctrine depends. The account of properties and relations that I shall borrow and incorporate into the possible worlds theory was developed by Bas van Fraassen.66 He regarded it as an alternative account of modality to the possible worlds account. In contrast, I shall treat it as a supplement to the standard theory. He considered the main virtue of his theory to be that it avoided metaphysical commitments and questions. In contrast, I shall use it to raise metaphysical questions that cannot be raised within the standard theory. Properties, on van Fraassen's account, are represented by regions of a logical space, or quality space. For example, the color spectrum might be a dimension of such a space; the color red would then be identiﬁed with a region deﬁned by a segment of the color dimension. The temperature scale might be another dimension. The relation warmer than would be identiﬁed with a set of ordered pairs of points of the space deﬁned by this dimension. The basic semantic elements of the models for the languages interpreted by van Fraassen's theory are two independently speciﬁed sets—an arbitrary set representing the points in logical space, and a domain of individuals. The individuals are assigned properties by a location function—a function that maps the individuals into the logical space. Each individual is thus located at a speciﬁc point in logical space, and in this way gets a speciﬁc color, shape, temperature, mass, and so forth. The language is interpreted by assigning to each one-place predicate a subset of the points in logical space. Such a predicate is satisﬁed by an individual just in case the location function locates the individual at one of the points included in the value assigned to the predicate. If the predicate is to mean is red, then its value will be the region of logical space deﬁned by the relevant segment of the color dimension. The open sentence ‘x is red’ will be satisﬁed by an individual just in case the individual is located somewhere in that region—just in case the location function colors it some shade of red. This account generalizes to cover n-place predicates and n-ary relations in the obvious way. There are no possible worlds in van Fraassen's semantics, but there is a semantical construct that looks a lot like one: the location function—the

66

Van Fraassen (1967). Lambert and van Fraassen (1970) generalize the logical space theory in a way different from the way I shall suggest.

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function that determines all the properties of all the individuals, and all the relations that hold between them. There is only one such semantical construct in each of the models deﬁned in van Fraassen's theory, but there is no reason not to consider many location functions at the same time—alternative ways that individuals might have been located in logical space. To do so, we need introduce no new semantical primitives into the theory. Besides considering many location functions at once deﬁned on the same logical space, the only other change I shall make in van Fraassen's theory is to substitute a domain of possible individuals for the ordinary domain. This change allows the domains of the different possible worlds—the sets of individuals located by the different location functions—to be different from each other.67 This is all we need for a semantic analysis of anti-essentialist modal logic. A model structure for the language will consist of just two elements: ﬁrst, a set H representing the points in logical space, and, second, a domain D representing the possible individuals. The set of all possible worlds is not a primitive element of the model; it is deﬁned in terms of the others. The set of possible worlds is the set I of all functions mapping some subset of D into H. The formal representation of a possible world, then, is a function that selects a subset of the set of all possible individuals to be actual, or to exist relative to that possible world, and that determines all the properties that the members of that subset are to have, and all the relations that are to hold among them. Let me now show how this very simple semantical framework meets the speciﬁc problem that we encountered in trying to make sense of the bare particular doctrine within the standard semantics. That is, let me show how this framework yields a distinction between those propositional functions that express intrinsic properties and those that do not. Since the models in our semantics contain both possible worlds and possible individuals, we can deﬁne, relative to any model, the class of all singulary propositional functions—the class of all functions from possible worlds into sets of individuals. It should be clear that every property (every region of logical space) determines a unique propositional function in the following way: given any property, the value of the corresponding propositional function, relative to a given possible world, will be the class of individuals that have the property in that possible world—the individuals that are located in that region of logical space by the location function that

67

The move from actual to possible individuals is a signiﬁcant additional commitment. A motivation of van Fraassen's original theory was to give a non-metaphysical interpretation to the picturesque but objectionable notion of a possible individual; in his theory, possible individuals were replaced by points in logical space. I am here reintroducing the metaphysical commitment, which I agree is objectionable. A further development of the theory might reduce possible but non-actual individuals to some sort of construct out of the other elements of the model structure.

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represents the possible world. Thus every property determines a unique propositional function, and the correspondence is one–one: distinct properties never determine the same propositional function. But it is not the case that every propositional function corresponds to an intrinsic property, for the classes of individuals selected by a propositional function in the different possible worlds need not all come from the same region of logical space. Among the propositional functions, or properties in the broad sense, that do not correspond to regions of logical space are, of course, just those that the anti-essentialist wants to distinguish from full-ﬂedged intrinsic properties. For example, referential properties such as being the same weight as Babe Ruth will clearly not correspond to regions of logical space. As the Babe waxes and wanes, moving up and down the weight scale from world to world, the class of people weighing the same as he will likewise move about in logical space. World-indexed properties like being snub-nosed-in-Kronos will also correspond to no particular region, since the noses that are, in fact, snub may grow to be aquiline, or Roman, or disappear altogether in alternative possible worlds. And if we consider a tensed version of logical space theory in which things may change their location in logical space over time as well as across possible worlds, then we can distinguish time-indexed properties, as well as world-indexed properties, from intrinsic properties. Being grue, for example, would not correspond to a single region of logical space (at least assuming that being green does), but to different regions at different times. Thus the logical space possible worlds semantics yields a representation of the distinctions needed to make sense of bare particular anti-essentialism. With a relatively straightforward interpretation of the formal language in terms of this kind of semantical structure, we can validate all the axioms proposed in Parsons's version of anti-essentialist modal logic. Since one-place atomic predicates must express properties in the narrow sense (regions of logical space), while open sentences with one free variable in general may sometimes express propositional functions that do not correspond to properties in the narrow sense, we have a semantic explanation for the failure of the substitution principle. Now we can ask, should any subset of possible individuals located anywhere in logical space be said to determine a possible world? One might want to rule out some of these formal constructs as not representing genuinely possible counterfactual situations. But if one does rule some of them out, one will need a philosophical justiﬁcation; and if one rules none of them out, one has a real bare particular theory. Thus, while the formal machinery I have sketched does not by itself commit one to anti-essentialism, it does make the doctrine clear, relative to the semantical primitives of the theory, and it does put the burden on the essentialist to justify his opposition. From a pre-systematic, intuitive point of view, there is strong motivation for taking on this burden. If one does not, one is forced to admit that some

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pretty bizarre propositions about particular individuals are possibly true. I am not thinking just of such alleged possibilities as that Babe Ruth be a prime number or a social class. Even if we take the relevant domain of possible individuals to include just possible persons and physical objects, there is something implausible about the assumption that any of them might have had the properties of any other. But it is not easy to see why this is implausible. Just to see how the philosophical debate might go, I shall look at just one kind of property, and at some arguments that might be advanced for the claim that properties of this kind are essential to the things that have them. Saul Kripke has suggested that the common names of natural kinds express essential properties.68 The paradigm examples are the names of animal species. Kripke argues that the names of such kinds, unlike ordinary property expressions, are referential terms—terms whose denotations are determined by the causal connections holding between our uses of the term and the actual individuals that are members of the kind. ‘Human being’, then, is like a proper name of the natural class to which we all belong. There is a way to interpret this claim so that it is not incompatible with the bare particular doctrine. It may be taken as a purely linguistic claim that certain commonplace predicates are in fact world-indexed properties (indexed to the actual world) rather than properties in the narrow sense—properties that correspond to regions of logical space. On this interpretation, Babe Ruth would be essentially human, but this would not prevent him from looking just like a billiard ball, or, in fact, from being just like a billiard ball all the way through. This purely linguistic essentialism is surely not the view of the natural kind theorists. They want to hold that natural kind predicates are essentially tied both to their actual denotations and at the same time to the structural and qualitative features that determine the real basis for the natural classiﬁcation. This double tie is not just a linguistic thesis, but serves to constrain the movement of individuals in logical space. What is its justiﬁcation? Why not be more liberal and let the Babe roam freely through the lower reaches of logical space? I cannot think of any point in making the counterfactual supposition that Babe Ruth is a billiard ball; there is nothing I can say about him in that imagined state that I could not just as well say about billiard balls that are not him, and if he does have the logical potential to be a billiard ball, it is of no interest that he does since on the bare particular theory this does not distinguish him from anything else. But that this alleged possibility is uninteresting is not sufﬁcient reason to judge it impossible. Before Kripke himself exposed the fallacy in such arguments, one might have reasoned as follows: the supposition that Babe Ruth is a billiard ball implies a denial of the common presuppositions that make reference to him

68

Kripke (1972).

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possible. Hence such a supposition is self-defeating. This argument confuses the limits on conjectures about what might, in fact, be with limits on suppositions about what might, contrary-to-fact, have been. It is perhaps true that if someone proposed that maybe Babe Ruth really was a billiard ball, then I could reasonably conclude that that person could not possibly be talking about the thing that I refer to with that name. But this is beside the point. The conditions that make the expression of a proposition possible need to hold in the world in which the proposition is expressed, but not necessarily in the world about which the proposition is said to be true. With assertions and conjectures, these worlds coincide, but with contrary-to-fact suppositions they are explicitly distinguished. Hence there is no incoherence when the content of such a supposition implicitly denies the possibility of its own expression. The causal theory of reference for natural kind terms might be thought to provide an argument for the conclusion that such terms express essential properties. Kripke and others have argued—persuasively, I think—that the conﬁguration of traits that is necessary to being, say, a kangaroo, is not determined by the meaning of the word ‘kangaroo’, but must be discovered by a theoretical and empirical investigation into the nature of the actual creatures. The meaning of the word determines, roughly, its extension, and the facts about the members of the extension then determine the features that are essential to the kind. Actual kangaroos thus play a necessary part in ﬁxing the nature of their kind. This is not, however, by itself a sufﬁcient reason for concluding that being a kangaroo, with all that entails, is essential to the individuals that are in fact kangaroos. Kripke has shown how we might use a particular individual (like a standard meter bar) to ﬁx the reference of a property expression (like being one meter long) without connecting the property necessarily to the object. Even though the standard in a sense deﬁnes the measure, it still can be true that that object might have been longer or shorter than one meter. In the same way, actual kangaroos might ﬁx the reference of the kind without being essentially members of it. The case for essentialism, I suspect, rests not on such general arguments, but on case-by-case intuitions about which descriptions seem to capture genuine possibilities and which do not. This is, however, a shaky basis since it is hard to separate the intuition that a proposed possible situation is too bizarre to be interesting from the intuition that it is too bizarre to be possible. And it is hard to separate intuitions about different kinds of possibility: epistemic, causal or temporal, metaphysical. It may be that the theory that best accounts for our intuitions and practices is one that explains away some of the judgments that we are all inclined to make about particular cases. I do not have such a theory. I do not even know which side I am on in the dispute over essentialism. Perhaps someone with stronger metaphysical convictions than I can develop an argument within the framework that I am recommending.

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Instead of arguing about essentialism, I shall conclude by making some general remarks about possible developments and applications of this account of properties and relations. First remark: the distinction between properties narrowly conceived and propositional functions in general is roughly analogous to the distinction between possible individuals (thought of as existing in many possible worlds) and individual concepts in general (functions from possible worlds into individuals). Just as some singular terms, such as ‘the fattest man in America’, are non-rigid designators—terms that express variable individual concepts, or pick out different individuals in different possible worlds, so some predicates may be non-rigid property designators—predicates that correspond to different intrinsic properties in different possible worlds. There was a tendency in some of the early explorations into the semantics for modality to conﬂate individuals with individual concepts, and some clariﬁcation resulted when the distinction was appreciated. But the mere drawing of a distinction between individuals and individual concepts did not by itself solve the metaphysical problems about the nature of individuals, or answer the linguistic questions about which singular terms were rigid designators and which were not. All it did was to give clear expression to some of these questions, and to their alternative answers. In the same way, the semantics I have sketched does not claim to solve metaphysical problems about the nature of intrinsic properties, or answer linguistic questions about which ordinary predicates express them. It does not lay out the structure of a particular logical space, or give criteria for making the distinctions in application that the theory allows for. So, for example, although the account provides for a representation of the distinction between properties like being grue and those like being green, it does not claim to give an answer to Goodman's riddle on its own terms. There is no formal reason why one could not construct a logical space with grue as a region of it. It would obviously not be our logical space, but the semantics offers no criterion or argument to justify this claim. The account I have proposed does change the focus of Goodman's puzzle: it takes the emphasis off the predicates—items of language—and puts it on a larger conceptual structure which lies behind them and in terms of which they are understood. It suggests that it is this non-linguistic conceptual structure that is entrenched and projected. But as to exactly how this happens, the abstract semantical framework is silent. It is at best the form of a philosophical theory, and not the theory itself. I should add, however, that the theory is less abstract than the simple possible worlds theory since it gives at least some structure to the possible worlds. And there is, I think, considerable potential for further development—for saying more about the structure of logical space, and thus more about the relationships among properties and among possible worlds. We have called logical space a space, but have not yet exploited the spatial

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metaphor. So far, logical space is just a set of points. One may want to say more about the relationships among the points—about the topological and metric properties of the space. One property (region) may be adjacent to another, or separated from it (as red is next to orange, but separated from green). Disjoint regions may be comparable with respect to their area (non-red is a much bigger region than red). The appropriateness of adding such structure will depend on two things: ﬁrst, whether there is direct intuitive support for the distinctions required; second, whether the structure can be used to explain facts about our cognitive behavior such as the inductive inferences that we judge to be reasonable and the way we evaluate counterfactuals. Since we do, sometimes at least, think of properties in terms of a spatial metaphor, the imposition of spatial structure on the properties will, I think, ﬁnd intuitive support. And it seems to me likely that such structure could help to explain some of the semantic determinants that have been postulated in the semantics for counterfactual conditionals, and in inductive logic: on the one hand, comparative similarity of possible worlds; on the other, measures of the ‘logical width’ of properties and the grouping of properties into ‘families’. The application to Carnapian inductive logic seems particularly appropriate. For just as the notion of a possible world is the semantical child of the syntactical notion of a state description, so the notion of a point in logical space is the semantical child of Carnap's syntactical notion of a Q-predicate, or maximal predicate, which played an important part in the development of his inductive logic. In both cases, the move to the semantical notion frees the theory from a dependence on language. Second remark: although the logical space account of properties and relations is a very abstract and ﬂexible one which by itself says little about the nature of properties, there is one substantive consequence of the formal theory—a consequence that some might want to deny. The following principle must hold in any application of the framework as it stands. All relations are grounded in intrinsic properties in the following sense: if one speciﬁes all the intrinsic properties of a set of individuals, one thereby speciﬁes all the relations that hold between them. To give all the intrinsic properties of some object is just to say what point in logical space it occupies, and the relations holding among a set of objects are determined by their locations in logical space. Might one deny this principle? Some who hold a relational theory of space will want to deny it. Such a theory says that spatial location is itself relational. That is, to give the location of an object in physical space is just to say something about its relations to other objects. According to some versions of this theory, there may be no properties that the objects have independently of other objects in virtue of which they stand in the spatial relations they stand in. To represent such a theory in terms of the logical space account of possible worlds, we must assume that logical space is itself in part conventional.

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That is, we must assume that sometimes distinct location functions differ only conventionally, and thus represent the same possible world. For example, let the three diagrams shown on page 83 represent three distinct location functions locating the same three objects in a two-dimensional Euclidean space. Now one might say that because the distance relations between the objects are the same in these three representations, they all represent the same situation. The point of saying this is not just that the coordinates are conventional—that it is conventional which point in the space is called the origin and in what direction the x-axis is drawn. That would be true even if an absolute theory of space were correct. The point would be that there is no non-conventional identiﬁcation of points in the space across possible worlds. To say that the origin of the coordinate system in one world is the same point as the origin in another is to make a purely conventional stipulation. To put this possibility into the formal theory, we add to the model structure an equivalence relation deﬁned on the location functions. To say that i is equivalent to j is to say that the location functions i and j represent the same possible world. A real intrinsic property (as opposed to a merely conventional intrinsic property) can then be deﬁned as a region of logical space that is invariant with respect to this equivalence relation. That is, region F represents a real property if and only if for every member d of the domain of individuals and every pair of equivalent location functions i and j, i locates d in F if and only if j locates d in F. Real as opposed to conventional relations could be deﬁned in the same way. In the relational theory of space, spelled out in this way, no intrinsic spatial properties would be real (except the property of being located somewhere in space), but some spatial relations would be real. There are, of course, more and less extreme versions of such a theory, depending on how the equivalence relation is deﬁned. The principle that all relations are grounded in intrinsic properties does not by itself commit one to an absolute theory of physical space. Leibniz seems to be someone who accepted this principle while at the same time denying that spatial location is an intrinsic property. But I think that to reconcile these two doctrines one would be forced to the conclusion that physical space as a whole is some kind of merely ideal construction out of the non-spatial properties of things. That is, I suspect that to reconcile the two Leibnizian doctrines, one must adopt an extreme version of a relational theory of space—the kind of theory that it seems Leibniz, in fact, held. Final remark: since the apparatus I have deployed here is shamelessly metaphysical, which goes against all my more positivistic instincts and training, I shall close with an anti-metaphysical comment. Sometimes I am tempted to believe that there is only an actual world. But we do represent to ourselves pictures of ways that things might be, or might have been, and this practice is not just the idle exercise of our imaginations; it is central to

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some of our more serious activities such as giving scientiﬁc explanations of how and why the actual world works the way it does. The semantical account that I have sketched is intended as one of the ways that we construct such representations of how things might have been. We do it, the account suggests, by making a conceptual separation between the things that inhabit our world and the properties that things have there, and then imagining the individuals with different properties, and the properties instantiated by different individuals. But, of course, it is all grounded in the actual world, and in what we know and how things appear to us. Logical space is not given independently of the individuals that occupy it, but is abstracted from the world as we ﬁnd it. Posed from this point of view, questions about essentialism, and about the identiﬁcation of properties across possible worlds, are questions about how far it is useful, or possible, to carry this process of abstraction. How different can we imagine the facts being before we lose our grip on the structure of properties and relations, and on the individuals, that were abstracted from the facts? This is not, I think, a question that is metaphysical in any sense that is either objectionable or honoriﬁc, but is a question about how we understand and ﬁnd our way about in the world.69

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Versions of this paper were presented to the University of North Carolina Philosophy Colloquium at Chapel Hill in 1972, and at Princeton University in 1973. The paper began as a response to Parsons (1969) and I beneﬁted from his useful comments at Chapel Hill.

5 Varieties of Supervenience (1996) 1. Introduction ‘Supervenience’ has been deﬁned in a variety of ways, and different and conﬂicting things have been said about the relations between different supervenience concepts. The concepts have been deployed in the discussion of a range of different philosophical problems, and for a number of different purposes. Sometimes a concept of supervenience is used to formulate a thesis to be defended: for example, a version of materialism about the mind, or of internalism about intentional or experiential states, a Humean thesis about necessary connection, a ‘reductionist’ thesis about personal identity. Sometimes it is used to clarify or sharpen a problem by spelling out the common ground between conﬂicting theses. Contrasting theses in metaethics or the philosophy of mind, for example, may agree that evaluations, or attributions of mental states, are supervenient on natural, or physical, facts. Contrasting theses about criteria for personal identity may agree that facts about identity across time are supervenient on momentary mental and physical states, and causal relations between them. Sometimes a concept of supervenience is used to raise a problem rather than to solve one: how, for example, can moral properties be supervenient on natural properties, and yet not be analytically entailed by them? My aim in this paper will be a modest one: to get clearer about some of the dimensions on which different supervenience concepts differ, and about the role that they play in the formulation of philosophical problems and theses. It is not my intention to defend or attack any particular supervenience thesis, but only to explore the abstract concepts of supervenience, and the intuitive ideas that motivate them. On the abstract deﬁnitions, I will make some claims, but my main concern is with the intuitive ideas and philosophical applications. As the leading maven of supervenience, Jaegwon Kim, has emphasized, supervenience is a philosopher's technical term—we can deﬁne it as we like to suit whatever philosophical purpose we have for it. There does, however, seem to be an intuitive idea that the technical concepts are trying to articulate and make precise, and that plays a role in evaluating the different deﬁnitions. In fact, I think there are two different intuitive ideas that motivate the attempts to articulate concepts of supervenience, ideas that

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there is some tension between. I will begin by trying to say, in a rough and uncritical way, what those ideas are, as I understand them, and what some of the different philosophical projects are to which these ideas have been thought to be relevant. Then I will sketch some of the different deﬁnitions of supervenience, and discuss the relations between them. Next, I will look at the concepts of necessity relative to which all of the supervenience concepts are deﬁned. I will conclude by raising some questions about the role of concepts of supervenience in the dialectic of metaphysical argument and analysis.

2. Two intuitive ideas of supervenience A supervenience thesis, on one way of understanding the notion, is a reductionist thesis. To say that the A-properties or facts are supervenient on the B-properties or facts is to say that the A-facts are, in a sense, redundant, since they are already implicitly speciﬁed when one has speciﬁed all the B-facts. A-facts are not facts ‘over and above’ the B-facts, not something ‘separate’. To state an A-fact, or ascribe an A-property, is to describe the same reality in a different way, at a different level of abstraction, by carving the same world at different joints. To borrow a metaphor from Saul Kripke, if all the facts are supervenient on the B-facts, then God, when he creates the world, is ﬁnished when he has determined all the B-properties of things. It is not that others—God's apprentices perhaps—ﬁll in the picture by adding the Aproperties. There is nothing more to be done. Here are some relatively uncontroversial examples of supervenience theses for which this way of understanding the notion seems appropriate: 1.

2.

Many of the terms and concepts of meteorology and geology are not to be found in the linguistic and conceptual repertoire of the physicist, but it seems clear that the meteorologist and the geologist are studying purely physical processes and events. The vocabularies of their sciences are different ways of talking about aspects and parts of the same reality that the physicist is concerned with. Whatever might be said about the possibility of reducing those special sciences to physics, it seems reasonable to suppose that the meteorological and geological facts are supervenient on the microphysical facts. After having arranged all the particles and their physical properties and relations throughout history, God does not have to add cold fronts and hurricanes, mountains, oceans, and tectonic plates. It is controversial just what colors are—how they are related to the physical properties of light and the reﬂectance properties of surfaces, to the physiological properties and perceptual capacities of perceivers, and to the phenomenological character of their experience. But it does not seem controversial that color properties (to the extent that there are such things as color properties) are supervenient on some or all of the properties and relations of the different kinds mentioned. There are no ‘further facts’ about

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the colors of things, over and above facts about their optical properties, and how they affect perceivers. Historians may describe events and states in terms of the behavior of complex collective entities: the German army invaded Belgium, the House of Representatives voted to impeach the President, the crowd became angry as rumors of a massacre by government troops spread through it. It seems reasonable to suppose that such claims, if true, are made true by facts about the behavior and patterns of behavior, along with intentions, beliefs, and feelings, of particular individuals. And it is not that new properties of the complex collective entities ‘emerge’ from the interaction of individuals, like spontaneous combustion. The properties of and relations between social wholes are constituted by the properties and relations of the relevant individuals.

There are philosophical theses that are more controversial than these, but that seem to be claims of the same kind. I will give two examples: (1) David Lewis describes the doctrine that he calls ‘Humean supervenience’ as follows: All there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. …We have geometry: a system of external relations of spatio-temporal distance between points.…And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else is supervenient on that.70 (2) Derek Parﬁt does not, so far as I know, use the term ‘supervenience’, but a thesis he calls ‘reductionist’ seems to be a thesis of this kind: ‘A person's existence just consists in the existence of a brain and a body, and the occurrence of a series of interrelated physical and mental events.’ Persons are not ‘separately existing entities’, and there is no ‘further fact’ about personal identity over and above such facts.71 But while some, such as Lewis and Parﬁt, would happily describe their supervenience theses as versions of reductionism, others take pains to distinguish supervenience from reduction. The idea of supervenience is, for example, supposed to help us articulate a nonreductionist version of materialism. Jaegwon Kim takes it as at least a putative component of the concept of supervenience that it ‘be consistent with the irreducibility of supervenient properties to their base properties’,72 although he also argues against the coherence of nonreductive materialism. In what way is a supervenience thesis supposed to be less demanding than a corresponding reductionist thesis? In at least two ways. First, a reductionist thesis was traditionally construed as a semantic thesis: reduction is a relation between theories or languages. One theory is reducible to another if (a) all the terms

70

Lewis (1986b: ix–x).

71

Parﬁt (1984: 211, 210).

72

Kim (1993: 140).

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of one are deﬁnable in terms of the other, and (b) given the deﬁnitions, the reduced theory is derivable from the theory to which it is reduced. In contrast, a supervenience relation is supposed to be metaphysical, and not semantic: it is a relation between sets of properties or facts, and not between theories or languages.73 Second, reduction is point to point, while supervenience is holistic. A reduction requires that each term of the reduced theory be given a deﬁnition in terms of the theory to which it is reduced, while a supervenience claim says only that all of the properties from one set somehow determine the properties of the other. Traditional reductionist programs were motivated at least in part by the metaphysical intuition that one kind of fact is, in some sense, the only kind of fact that there really is. But a reductionist thesis might fail for reasons that are irrelevant to this motivation, even in cases where the underlying metaphysical intuition is uncontroversial. For example, a special science, such as meteorology, might be irreducible to physics in part because physical theory does not purport to be, or to entail, a complete description of physical reality. It is not the job of physical theory to describe the particular arrangements of physical forces and particles, but the subject matter of a special science will depend on such particular facts—on the way matter happens to be distributed and organized in a particular corner of the solar system. And if boundary conditions, ceteris paribus qualiﬁcations, and assumptions about the domain of application of a special science are tacit presuppositions of the practice of applying its theory rather than explicit consequences of it, it may be that the theory fails to be reducible even to physical theory supplemented with a speciﬁcation of particular conditions. So traditional reductionism makes a metaphysical claim, but also carries with it some metaphysically irrelevant semantic baggage. The concept of supervenience is supposed to be a concept that helps to isolate the metaphysical part of a reductionist claim—to separate it from claims about the conceptual resources and explicit expressive power of theories we use to describe the world. The separation of metaphysics from semantics is not easy to accomplish, and some of the tensions and obscurities in the concept of supervenience may derive from the failure to have achieved a clean separation. But whether it succeeds or not, I think this is one of the things that the concept of supervenience is designed to do. There is, however, another side to the story. Consider, not materialism or Humean supervenience, but the thesis that moral and evaluative properties are supervenient on natural properties. The problem of the relation between evaluative and natural properties was, after all, the problem that motivated the introduction of the concept of supervenience into contemporary

73

Although in some inﬂuential early discussions of the general concept of supervenience, and its application to the clariﬁcation of a materialist thesis, the notion was deﬁned in terms of predicates, and languages or models of them. See for example, Haugeland (1982) and Hellman and Thompson (1975).

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philosophical discussion. The intuitive explanations of supervenience sketched above seem inappropriate—or at least tendentious—when applied to the use of the concept in this case. G. E. Moore, certainly, was at pains to deny that ascriptions of intrinsic evaluative properties were just a different way of talking about the same facts that we talk about when we ascribe natural properties. According to Moore, natural properties entail evaluative properties, but the necessary connection between natural and evaluative is synthetic and substantive. If Moore's thesis is properly described as a supervenience thesis, then it cannot be right to identify supervenience with reduction, even a liberal version of reduction that succeeds in isolating the purely metaphysical component of that idea. If the concept is to apply to such theses, a supervenience relation must be, in some cases at least, a metaphysical relation between distinct sets of properties or facts. The distinction between two ways of understanding supervenience that I am trying to make is elusive. When one retreats from the traditional, more restrictive versions of reductionism, then it becomes more difﬁcult to distinguish a reductionist conception of supervenience from the view that supervenience is a sui generis metaphysical relation between distinct families of properties. If G. E. Moore accepts the supervenience of intrinsic evaluations on natural properties, how is he different from the ethical naturalist, who argues that evaluative properties just are natural properties, while at the same time rejecting the possibility of analytic deﬁnitions of evaluative expressions in terms of an unproblematically descriptive vocabulary? Or consider the emergentist philosophers of mind from the ﬁrst half of this century that Jaegwon Kim and others have recently brought back onto the philosophical stage. As Kim describes it, ‘the doctrine of emergence, in brief, is the claim that when basic physicochemical properties achieve a certain level of complexity of an appropriate kind, genuine novel characteristics, such as mentality, appear as “emergent” qualities.’74 These philosophers (who, as Kim notes, sometimes used the term ‘supervenience’ to characterize their thesis) seem to be dualists, since the emergent mental properties are ‘genuine’ and ‘novel’. But how are they different from materialists, such as Donald Davidson, who reject the possibility of reductive deﬁnitions of the predicates we use to ascribe mental properties? To clarify the distinction, we will have to say more about exactly how supervenience is deﬁned, and also more about the nature of properties, and the nature of the necessity relation that connects supervening properties with the properties on which they supervene.75

74

Kim (1993: 134).

75

The distinction I am pointing to between two intuitive ideas of supervenience is close to a distinction made by Terence Horgan between supervenience and what he calls ‘superdupervenience’—‘ontological supervenience that is explainable in a materialistically acceptable way’. I ﬁnd much to agree with in Horgan's insightful discussion, but I would rather not tie the distinction to materialism, which is just one application of the concept of supervenience. If one requires, for superdupervenience, only that the supervenience relation be explainable in some way compatible with one's basic metaphysical commitments, then there will presumably be no room for a positive use of a concept of supervenience weaker than the superduper kind.

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3. Strong and global supervenience I want now to set aside, for the moment, the difﬁcult metaphysical questions on which I think the intuitive motivation and interpretation of supervenience depend in order to get some more precise concepts to evaluate. If we take for granted the relevant sets of properties—the ones that putatively supervene, and the ones on which they are supposed to supervene—and if we take for granted a notion of necessity, then we will have the materials to make the concept precise, relative to those notions, in a way that is neutral on the elusive interpretative contrast that I have tried to point to. Or rather, we will have the materials to make several different supervenience concepts precise. Kim and others have distinguished a weak from a strong concept of supervenience, and both of these have been distinguished from a third notion, global supervenience. There has been controversy about the relations between these different concepts, particularly about the relation between strong and global supervenience. Kim originally argued that they were equivalent, but then was convinced by counterarguments that global supervenience was a weaker relation. In the end, he concluded that the relation between the two concepts was not something that could be settled on formal grounds (he suggested that the question might depend, for example, on the correctness of certain closure conditions on the set of metaphysically possible worlds). I will argue that while the two notions are not in general equivalent (that is, it is not true that for any sets of properties A and B, A globally supervenes on B if and only if A strongly supervenes on B) it is nevertheless true that every global supervenience thesis is formally equivalent to a strong supervenience thesis, and that this equivalence is independent of any metaphysical assumptions. But to get this result, one needs the right deﬁnition of global supervenience, and this will require closing a small loophole in the usual deﬁnition. All of our supervenience concepts will be deﬁned for two given sets of properties, A and B properties. They are all modal concepts, deﬁned in terms of a given notion of necessity, or a given set of all possible worlds. The rough idea of all of them is that A supervenes on B if the A properties necessarily depend on the B properties. With weak supervenience, individuals within any one possible world can differ with respect to an A-property only if they differ with respect to some B-property. With strong supervenience, individuals in the same or different possible worlds can differ with respect to an A-property only if they differ with respect to some B-property. And with global supervenience, two whole possible worlds will differ with respect to the distribution of the A properties of individuals only if they

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differ with respect to the distribution of B properties. More precisely, here are versions of the usual deﬁnitions: 1. 2. 3.

A strongly supervenes on B iff for any worlds w and z, and for any objects x and y, if x has in w the same Bproperties that y has in z, then x has in w the same A-properties that y has in z.76 A weakly supervenes on B iff for any world w and any individuals x and y in the domain of w, if x has, in w, the same B-properties that y has in w, then x has, in w, the same A-properties that y has in w. A globally supervenes on B iff any two possible worlds that are B-indiscernible are also A-indiscernible.

The relevant notion of indiscernibility is deﬁned as follows: For any set of properties and relations B, two worlds w and z are B-indiscernible iff there is a 1–1 correspondence between the domains of w and z, and any individual in the domain of w has the same B-properties in w as the corresponding individual from the domain of z has in z.77

One of our deﬁnitions needs a patch before we continue, since as it stands, global supervenience is not even sufﬁcient for weak supervenience, and the loophole that permits this is not, I think, intended. Let me use an example with some ﬁctional physics to bring out the problem. Suppose the world consists of elementary particles that come in a range of colors, shapes, and ﬂavors. In addition, each particle is either positively or negatively charged. It is a law of nature in this world that particles always come in pairs: for every positive particle, there is a negatively charged one that is indiscernible from it with respect to color, shape, and ﬂavor. I assume that this law is a necessary truth, perhaps because the law is constitutive of the charge properties in the sense that nothing in any possible world can have these charge properties unless the law holds,78 or perhaps because we are deﬁning supervenience relative to all nomologically possible worlds, rather than all metaphysically possible worlds. Now let the B-properties be the

76

This particular formulation comes from an excellent recent discussion of the abstract concepts of supervenience, Paull and Sider (1992: 834). It is equivalent to deﬁnitions given by Kim.

77

Paull and Sider bring time into their deﬁnition of indiscernibility (an individual's B-properties at time t in w must be the same as the corresponding individuals B-properties at t in z ). But in giving the abstract deﬁnition, I prefer to assume that, where appropriate, the temporal relations will be in the relevant set of properties and relations, and should not have separate mention. One reason is that one application of the concept of supervenience might be to a thesis about the supervenience of spatio-temporal relations on something else. It seems reasonable to think that Leibniz held such a supervenience thesis. Another reason is that the identiﬁcation of times across possible worlds might be problematic. See Paull and Sider (1992: 852).

78

See Shoemaker (1980) for a defense of a theory of properties according to which properties are explained in terms of causal powers. According to this kind of theory, the causal laws relating the properties are essential to them.

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shape, color, and ﬂavor properties, and let the A-properties be the charge properties. A-properties are not even weakly supervenient on B-properties, since even in the same world there are particles alike with respect to B-properties that differ with respect to A-properties. But A-properties do globally supervene on B properties, since for any two Bindiscernible worlds, there will be one way of mapping the individuals of one onto the individuals of the other that preserves the A-properties. To close the loophole, I suggest we give the following stronger deﬁnition of global supervenience: ﬁrst, relativize the notion of B-indiscernibility to a mapping: two worlds w and z are B-indiscernible, relative to a function of the domain of w onto the domain of z iff the function is 1–1, and each individual in the domain of w has the same B-properties in w that the corresponding individual has in z; then revise the deﬁnition of global supervenience as follows: (3′) A globally supervenes on B iff for any two worlds that are B-indiscernible relative to a mapping from the domain of one onto the domain of the other are also A-indiscernible relative to the same mapping.

Our revised deﬁnition of global supervenience does not avoid the counterexamples that have been given to the equivalence of strong and global supervenience,79 nor should it, since strong supervenience is sometimes intended to make a stronger claim. A philosopher might, for example, be a materialist who is also an internalist about intentional or experiential properties, and such a philosopher might formulate his thesis as a supervenience claim: that intentional or experiential properties of individuals are supervenient on their intrinsic physical properties. It would not be enough to say that the intentional or experiential properties of individuals globally supervene on the intrinsic physical properties of individuals, since that would be compatible with the mental properties of one individual varying with the intrinsic physical properties of others. But while the thesis that A strongly supervenes on B is not in general equivalent to the thesis that A globally supervenes on B, every global supervenience thesis (with our revised deﬁnition) is equivalent to the strong supervenience of A on a set B′, which is a certain closure of the set of B-properties—the set of properties that are deﬁnable from B-properties, using quantiﬁers, identity, and ﬁnite and inﬁnite Boolean combination.80 So a global supervenience thesis is in fact quite strong: Kim has shown that if A strongly supervenes on B, then every Aproperty is necessarily equivalent to a

79

See Petrie (1987) and Paull and Sider (1992) for discussions of counterexamples to the equivalence of strong and global supervenience.

80

See the appendix for the argument for this equivalence.

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property deﬁnable in terms of B-properties. So our result implies that it is also true that if A globally supervenes on B, then every A-property is necessarily equivalent to a property deﬁnable in terms of B-properties. If necessary equivalence is enough for property identity, then we can say that if A globally supervenes on B, the A properties all are properties deﬁnable in terms of B-properties. Of course the assumption that necessary equivalence is sufﬁcient for identity is tenable only with a very strong concept of necessity, and will be controversial even with such a concept. This is one of the things that will be at issue when we return to the elusive metaphysical questions. Whatever one says about property identity, in general, this equivalence result does seem to me to show that global supervenience is the appropriate supervenience concept for the statement of many supervenience theses. In particular, I think a materialist is committed, in virtue of his materialism, to no supervenience thesis stronger than the thesis that the mental properties globally supervene on physical properties. Consider a philosopher who accepts this global supervenience thesis but rejects the corresponding strong supervenience thesis. If this philosopher is consistent, it must be that he holds that the set of physical properties is not closed under deﬁnability. There are two reasons he might think this: (1) perhaps he thinks that certain properties deﬁnable in terms of physical properties are not themselves physical properties; or (2) perhaps it is because he has a robust conception of property according to which certain well-deﬁned attributes (if I may use the word ‘attribute’ neutrally for any way of picking out a set of individuals) do not correspond to properties of any kind, physical or not. The philosopher with the ﬁrst reason might still say that all properties are deﬁnable in terms of physical properties, since he rejects not only the strong supervenience of A (the mental properties) on B (the physical properties), but also the strong supervenience of B′ (properties deﬁnable in terms of the physical) on the physical properties. For this philosopher, the rejection of strong supervenience seems more terminological than substantive, since it is not based on any thesis about what properties exist, or are instantiated, but only on whether or not to categorize certain properties, whose deﬁnitions are uncontested, as physical. The case of the philosopher who accepts the global but not the strong supervenience thesis for the second reason is more difﬁcult. To understand her, we need to know more about the robust theory of properties. This philosopher, presumably, believes that mental properties are genuine properties, and since she accepts the global supervenience of the mental on the physical, she will recognize that for any mental property, there is a physical attribute that is necessary and sufﬁcient for it. Her view, presumably, is that these new nonphysical properties emerge from physical nonproperties—from complex combinations of physical properties and relations. This philosopher is perhaps a dualist, but her dualism seems to be independent of her rejection of strong supervenience: even if she allowed that the complex physical attributes were physical properties (and so that a strong supervenience thesis was true), she might still say that mental properties were distinct

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from the physical properties that are necessarily coinstantiated with them. The claim would be that they were new properties that emerge from the fact that the complex physical properties are realized. This philosopher is a dualist, not because she rejects strong supervenience, but because she rejects the reductionist interpretation of supervenience, whether global or strong. Jaegwon Kim has a different kind of reason for thinking that the global supervenience of the mental on the physical may not be sufﬁciently strong for materialism. The problem is that global supervenience of the mental on the physical is compatible with large and important mental differences being dependent on trivial and seemingly irrelevant physical differences. Kim asks us to imagine a possible world exactly like ours physically, except that ‘one lone hydrogen atom somewhere in deep space is slightly displaced relative to its position in this world’. Such a world ‘could be as different as you please from the actual world in any mental respect’ without violating the global supervenience thesis. This consideration leads Kim to conclude that global supervenience is too weak ‘to give us the kind of dependency relation we should demand if the mental is truly dependent on the physical’.81 Now I agree that no sensible materialist would accept the possibility of a world that differed physically from ours only in this way, while being radically different from it in the distribution of mental properties. But sensible materialists are not only materialists, they are also sensible; one should not deﬁne materialism so that there cannot be silly versions of it. It seems to me that a philosopher who held that the mental properties of human beings on earth were constituted, in part, by the precise distribution of hydrogen atoms in distant parts of space is no less a materialist because of the bizarre and unmotivated character of his materialism. If a philosopher who accepts a thesis that the mental supervenes on the physical is a dualist, it is not because his supervenience thesis is global rather than strong, but because of his intuitive interpretation of that relation. If he thinks that new and distinctive mental properties emerge, by a kind of metaphysically necessary causality, from complex physical interactions, then he is no materialist, even if his supervenience claim is a very strong, internalist one that says that mental properties supervene on the intrinsic physical properties of the creatures that have them. But if he is using the concept of supervenience to say that everything in the world is physical—that apparently nonphysical properties are just other ways of talking about the complex physical properties and relations of things, then he is a materialist, even if he says no more about just which aspects of the physical world are the ones that constitute the mental properties.82 Although I think global supervenience is strong enough for materialism, this is not to say that one shouldn't seek out stronger relations that might

81

Kim (1993: 277, 278).

82

In Paull and Sider (1992: 841–7), there is a critique of Kim's wayward atom argument.

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be useful for saying something more speciﬁc about the relations between mental and physical properties. Kim's response to his wayward atom example is to suggest a strengthening of global supervenience that requires not only that B-indiscernible worlds be A-indiscernible, but also that worlds that are very similar with respect to the distribution of B-properties be similar with respect to the distribution of A-properties. As Kim recognizes, considerable work would have to be done to make such a notion precise, and it is difﬁcult to say in advance of doing the work how plausible, and how substantive, such a thesis might be. But staying with a rough intuitive notion of similarity, it is not clear to me that a sensible materialist should expect such a thesis to be true. Why should the materialist expect there not to be mental characteristics that are, in Kim's words, ‘in general critically sensitive to minuscule physical differences’?83 In any case, whether it would be a sensible materialism or not, it does seem clear that materialism is compatible with the acceptance of a divergence of similarity of the mental from similarity of the physical.84

4. What kind of necessity? I have argued that the distinction between global supervenience and some stronger version is not a way to spell out the intuitive contrast that I sketched in section 2—supervenience as a liberal kind of reduction vs. supervenience as some kind of substantive metaphysical dependence. I want to look now at a different dimension on which supervenience concepts may be stronger or weaker: the notion of necessity relative to which concepts of weak, strong, and global supervenience are deﬁned. If supervenience is to have the force of a reductionist thesis, then it might seem that it must be deﬁned in terms of a very strong concept of necessity. How could ascriptions of A-properties be just another way of describing the reality that is described by the ascription of B-properties if the dependence of one on the other holds only in some restricted set of possible worlds—for example the set of physically or nomologically possible worlds? Even a substance dualist about mind and body might believe that the coming to be of minds was caused, as a matter of lawful but contingent fact, by physical events and circumstances. And a realist about necessary connections who was also a determinist would regard a version of David Lewis's Humean supervenience thesis, restricted to all worlds with the same causal laws as ours, as trivially true. But on the other hand, if supervenience is deﬁned in terms of an unrestricted concept of metaphysical necessity, then

83

Kim (1993: 91).

84

Presumably, ‘being mentally similar to’ would itself be a mental relation, and so the materialist will be obliged to accept that this relation is determined by the physical properties and relations of the things that stand in it. But even if this relation were deﬁnable in physical terms, two things might be mentally dissimilar while being physically similar.

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many supervenience theses will be stronger than they are intended to be. While supervenience requires the distribution of B-properties to determine the distribution of A-properties, the intuitive idea, even when understood in a reductionist spirit, was supposed to allow for the possibility that the A-properties might supervene instead on something else. In our world (according to the materialist), everything is physical, and so the mental supervenes on the physical. But in some other possible world, ectoplasm might infuse the bodies of beings with a mental life, and their mental properties might supervene on states of that nonphysical substance. Such a world might have physical objects and properties like our world, along with the extra nonphysical substances and properties, or it might be wholly nonphysical, with a wholly different set of properties on which the mental supervenes. But if things have mental, but no physical properties, in some possible world that is within the scope of the necessity concept in our deﬁnition of supervenience, then the mental will not even weakly supervene on the physical, since things with no physical properties at all, or with only negative physical properties, will all be physically indiscernible from each other, even when they may differ with respect to mental properties. Even Lewis's Humean supervenience thesis is, according to him, a contingent thesis. There are, in the actual world, no real relations (other than spatio-temporal relations) that are not supervenient on the local qualities of things, but in other possible worlds there are. (And, Lewis says, he is prepared to learn from physicists that the thesis is not even true of the actual world.)85

85

I am skeptical about whether one who accepts Lewis's general metaphysical picture ought to accept the contingency of Humean supervenience. For on his account, Humean supervenience (in contrast with a more radical thesis that might be called Leibnizian supervenience) is compatible with some irreducible relations—the spatio-temporal relations—and these relations play a crucial role in the metaphysical theory, since it is spatio-temporal relations that individuate the possible worlds. Different possible worlds can have very different systems of spatio-temporal relations—Lewis even allows that there might be worlds that are not spatio-temporal at all in any ordinary sense, but have a system of relations that is ‘analogous’ to spatio-temporal relations. Might it be that any relations will be analogous to spatio-temporal relations (or part of the system of such relations) if they are real relations, not supervenient on the arrangement of qualities? Without some criterion to distinguish real relations that are compatible with Humean supervenience (because they are spatio-temporal, or at least analogous to spatio-temporal) from those that are not, the thesis threatens to become not only necessary, but trivial, since no one will contest that all properties and relations are supervenient on arrangements of qualities, together with facts about the instantiation of those relations that are not supervenient on the arrangement of qualities. So I think the nontriviality, as well as the contingency, of Humean supervenience depends on some account of criteria for being a spatio-temporal relation. Suppose, as Lewis speculates might happen, the problems of interpretation of quantum mechanics are solved in a way that justiﬁes the claim that there are irreducible nonlocal relations. He suggests that this would give us empirical reason to reject Humean supervenience. But what if we decide instead that these relations are part of the structure of space-time? The problem here is analogous to a more familiar problem about the characterization of physicalism. Is a world with different basic properties from our world a world in which physicalism is false, or is it a world with a different physics in which the thesis of physicalism is true? See Lewis (1986a: §1.6) for a discussion of the issue.

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Lewis provides an attractive way of reconciling the intuition that some supervenience theses are contingent with the liberal reductionist account of the intuitive force of a supervenience thesis.86 He begins with the assumption that, in any possible world, there is a set of basic properties and relations—the properties that sufﬁce to determine the world. Materialism might be deﬁned as the (contingent) thesis that the physical properties are the basic properties in our world. Other worlds might have different basic properties, including properties that are ‘alien’ to our world.87 Now in terms of this notion, we can deﬁne a relative necessity concept, necessity relative to the set of all possible worlds that share the same total set of basic properties. Then the relevant global supervenience thesis will assert supervenience relative to this notion of necessity. The supervenience of the mental on the physical is then contingent because it is a contingent fact that the set of physical properties is the complete set of basic properties that distinguish between things in our world. And although it is contingent, our supervenience thesis is still reductionist in spirit, justifying the claim that the physical is, in a sense, all there is: all that appears to be something over and above the physical is just another way of talking about the physical. Now what is interesting, and disquieting, about this way of solving the problem is that the concept of supervenience is no longer what is doing the work of formulating the reductionist thesis in a way that isolates its metaphysical component. On this account, the materialist's global supervenience thesis is this: relative to all possible worlds that have the same total set of basic properties and relations as our world, the mental globally supervenes on the physical. But this thesis is a trivial consequence of the materialist thesis that was stated without the notion of supervenience: that the set of all basic properties and relations of our world is the set of physical properties and relations. What is unsettling about this is that we started with a rough intuitive idea: the idea that one set of properties was in a sense redundant—just a different way of cutting up a world that could be, in some sense to be explained, completely described in terms of the properties and relations in another set. It seemed clear that this rough idea needed to be sharpened, and the concepts of supervenience, with their precise deﬁnitions in terms of

86

See ibid.

87

David Lewis's term ‘alien property’ refers to a property that does not exist, where a property's existing is to be distinguished from its being instantiated. There may be existent properties—complex properties such as being a golden mountain—that are uninstantiated. And it is perhaps also possible that there be alien properties—properties that do not actually exist—that are nevertheless actually instantiated, paradoxical as that may sound. Of course (at least on an actualist interpretation of possible worlds) there are no alien properties, since there are no things of any kind that do not actually exist, but just as there might have been people who don't in fact exist, so there might have been properties that don't in fact exist. What does exist is the possibility of such properties.

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given sets of properties and a given necessity concept, were attempts to pin this idea down. But now we are told that to apply these newly sharpened tools in a way that allows for the contingency of the thesis, we need to deﬁne the relevant necessity concept in terms of the idea of a set of basic properties—a set that provides for a complete characterization of the world—a set, we might be inclined to say, on which all else supervenes. But if we need to take this notion for granted in applying our supervenience concept, how have we explained it? I don't mean to be suggesting that Lewis's proposal is not correct, or that it does not help to explain how supervenience theses can be both reductionist and contingent. I am just suggesting that philosophical analysis may have taken us less far from the intuition with which we began than we might have hoped. To try to get a little clearer about the contingency of supervenience I will consider Lewis's simplest and most uncontroversial example, a kind of toy model of the metaphysical relation. A dot-matrix picture has global properties—it is symmetrical, it is cluttered, and whatnot—and yet all there is to the picture is dots and nondots at each point in the matrix. The global patterns are nothing but patterns in the dots. They supervene: no two pictures could differ in their global properties without differing, somewhere, in whether there is or isn't a dot.88

But of course if we added some properties beyond those that distinguish between the actual pictures, the pictures might have different global properties even while maintaining exactly the same dot-non-dot conﬁguration. Our actual pictures, let us suppose, are monochromatic: the dots are all black, and the empty spaces all white. But suppose we add some color—some dots are red, and some green. With the addition of color, two pictures with the same dot-non-dot pattern might differ with respect to global properties such as symmetry. More generally, the same global properties that, in the case of the dot-matrix pictures, supervene on the pattern of dots will apply to things other than dot-matrix pictures, and because of the wider application of such properties, they are not deﬁnable in terms of the patterns of dots. Even if we could give a deﬁnition, in terms of dot conﬁgurations, that succeeded in distinguishing the symmetrical or cluttered pictures from those that were not, this would not deﬁne the holistic properties, which are not only holistic, but also more abstract and general than the properties on which they, in a sense, supervene. When we turn from the toy model to the actual metaphysical theses, the situation is similar: properties that we are inclined to call supervenient are properties that are more abstract, and so might apply to things even if the properties on which they seem to supervene did not. Consider abstract geometric properties such as shape. A surface of a physical object might be

88

Ibid. 14.

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hexagonal, but so might be a shadow. And if there were nonphysical properties of surfaces, they might deﬁne a hexagonal shape as well. If there could be nonphysical objects that occupied space (perhaps made of some kind of spiritual ﬂuid), then there might be things with shape properties, but no physical properties, in which case the worlds in which such objects existed would be worlds in which shape does not supervene on the physical. One might be inclined to respond that spatial properties just are physical properties, and not properties that supervene on the physical. If so, choose instead some more abstract and topic-neutral higher-order property or relationship that might be realized in a variety of different ways. It seems reasonable to think that for any two possible worlds, however different the basic properties that distinguish between things in them, there will be some properties that are abstract and general enough to distinguish between things, or patterns of things, in both of them. If this is right, then if there are any possible worlds that are not physical worlds, there will be properties that distinguish between things in our world, but that do not supervene on the physical in all metaphysically possible worlds. The general picture suggested is something like this: We distinguish between possibilities by distinguishing different ways in which individuals can be located in some logical space—a property space. But the property spaces in which we locate individuals are themselves contingent: empirical inquiry tells us not only how properties and relations are realized by individuals, but also what the properties and relations are. It is a contingent fact that physical space has a certain structure, and that things we locate in it are distinguished by such properties as mass and charge, or color and ﬂavor. So to allow for all possible worlds, we need to recognize the possibility of property spaces that are different from the one in terms of which we distinguish individuals in our world. And whatever the structure of the different possible property spaces, there will inevitably be relationships between them, and more abstract properties based on abstract structures that are common to different property spaces. (In fact, it seems reasonable to think that the only way we can form a conception of a property space different from one that distinguishes things in our world is through the way it compares and contrasts with ours.) But the more abstract properties are essentially derivative. Once you pin down the basic property space, and the location of all individuals in it, you have pinned down the world—all that is the case. This is a nice clean abstract framework for articulating a metaphysical theory—a theory about the way we locate the world in logical space, and about the structure of the particular region of it that we locate the world in. But a representation of a particular structure of such a kind—of particular property spaces and possible property spaces—is the end point of a philosophical project, and not the place where it begins. We begin with the fact that we describe the world in various overlapping and interrelated ways. We assume that the mental and linguistic acts and attitudes in which

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we group and distinguish between things are to be understood in terms of properties of and relations between the things: we distinguish between things because there are differences in the things to be distinguished. To bring some order to our understanding of the practices, we need to ask two kinds of questions: ﬁrst, how are our thoughts and linguistic expressions related to the properties of and relations between the things that those thoughts and expressions are about? Second, what are these properties and relations, and how are they related to each other? To address and distinguish the two kinds of questions, we need a framework for representing the properties and relations—a representation of what distinctions there are to be made by the mental and linguistic acts we use to make them that abstracts away from the way we represent those distinctions. But as we have seen, it is an empirical matter what distinctions there are to be made by the properties and relations that actually distinguish the things in our world, and it is an empirical matter that we mere mortals are not omniscient about. As Quine taught us some time ago (although not with these words), the metaphysician's task of describing the structure of logical space—the space of all possible worlds—is not so easily separated from the scientist's task of locating the actual world in it.

5. Supervenience in philosophical explanation and argument Some philosophers ﬁnd the very idea of supervenience to be obscure and unhelpful. Stephen Schiffer, for example, in an often quoted passage, complains that ‘invoking a special primitive metaphysical relation of supervenience to explain [for example] how non-natural moral properties were related to physical properties was just to add mystery to mystery, to cover one obscurantist move with another’.89 As Schiffer understands supervenience, it seems to be part of the idea that a supervenience claim states a ‘brute metaphysical fact’. It is clear that he has in mind a notion of supervenience that is motivated, not by the reductionist intuition, and the attempt to isolate the metaphysical component of that intuition, but rather by the idea of supervenience as some kind of substantive relation—some kind of metaphysical superglue. I am inclined to agree with Schiffer that the more metaphysically extravagant interpretation of supervenience is obscurantist, perhaps incoherent, but as I have been suggesting, the distinction between this intuitive conception and the more austere one with a reductionist motivation is elusive. Do our explorations of the abstract concept and the kind of necessity relative to which it might be deﬁned, help us make this distinction clearer? Let us cross-examine an imaginary emergentist and see if we can pin him down.

89

Schiffer (1987: 153–4).

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The emergentist view, as I understand it, is something like this: when certain conﬁgurations of purely physical events and circumstances arise, they cause certain nonphysical mental phenomena to occur, and these mental phenomena in turn have causal effects on subsequent physical events. Now suppose we ask the following counterfactual question of the philosopher who holds this view: Is there a conceivable situation that is physically like the actual world, but that cuts out the mental middleman, a situation in which the same conﬁgurations of purely physical events and circumstances arise, but mentality fails to emerge, and instead, these complex physical conﬁgurations directly cause the same subsequent physical phenomena that are in fact caused by mental phenomena? Here are two different answers to this question that the emergentist I envision might give: (1) ‘The situation you describe is conceivable, in some sense, but it is a metaphysically impossible situation—one in which the metaphysical laws connecting the mental with the physical fail to hold.’ This is an answer I regard as unintelligible, since the metaphysically possible worlds, as I understand the term, are all the possible worlds. There are descriptions that create the illusion that one has coherently described a possibility when one has not, but metaphysically impossible worlds are like nonexistent objects—there are no such things. (But hasn't Saul Kripke taught us that there are epistemological possibilities that are metaphysically impossible, such as that water is not H2O, or that Margaret Truman is not the daughter of Harry and Bess? Yes, but he has also taught us how to understand such possibilities as metaphysical possibilities, differently described. There are metaphysical possibilities in which some epistemic counterpart of Margaret Truman is not the daughter of Harry and Bess, and it is possibilities such as these that are relevant to representing someone's ignorance of Margaret's relationship to her parents.) As we have seen, one can and usually should deﬁne a supervenience concept in terms of some restricted necessity, and nothing prevents one from restricting the claim to a subset of possible worlds that satisfy some conditions that one calls ‘metaphysical laws’. But if the laws are really substantive, and so restrictive, then it will be a contingent fact that they hold. One can't strengthen the claim or signiﬁcance of such generalizations by calling them ‘metaphysical’. (2) Our emergentist might instead give this more interesting answer: ‘The situation you have described is indeed a metaphysical possibility, but it is not a counterexample to supervenience, since the physical properties of things are different in this counterfactual situation. The physical laws, and so at least some of the physical properties, must be different in a world such as you describe. It is implicit in the physical powers of physical things that when they combine in certain ways, mentality will emerge. And even if you think it does not seem right to categorize those dispositional properties as physical, it is still true that to get the possible situation you describe we must alter the physical powers of things to replace the physical effects of the mental, and that is enough to

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make our counterfactual situation physically discernible.’ If this answer makes sense, then it seems that we might have supervenience in all metaphysically possible worlds, or at least all worlds that share the same basic properties with ours, even when the mental properties are themselves basic properties, in Lewis's sense—properties that are not derivative, either by being more abstract like functional properties, or deﬁnable as complex physical properties. It is not obvious that there couldn't be possible worlds in which some basic properties are supervenient on others, relative to possible worlds sharing the same basic properties. And there need be no brute metaphysical mystery here: the emergentist might say that it is an empirical causal fact that when a certain level of complexity is reached, life, or mentality, emerges. This may be a coherent position. I am not sure, because I am not sure what it is for a property to be basic. I am inclined to think that a property is just a way of grouping individuals, and that a way of grouping individuals can be a basic property only if it is one that allows for distinctions—at least possible distinctions—between individuals that cannot be explained in some other way. If this is right, then there is something wrong with the idea of a basic but supervenient property. But if our emergentist's second answer is coherent, it is a position that the philosopher with the reductionist motive wants his supervenience thesis to exclude. It is part of what he wants to say that the supervenient properties are not among the basic properties, but are either deﬁnable or derivative by being more abstract. To state his view as a supervenience thesis, he has some work to do specifying the supervenience base, and the notion of physical indiscernibility so as to ensure that the counterfactual possibility described above is one that is both physically indiscernible from the actual world, and within the scope of the relevant necessity concept.90 The philosopher who uses supervenience with a reductionist motive does not seem obscurantist in the way that Schiffer points to, since he rejects the idea of a ‘brute metaphysical fact’, but one may still be inclined to think that a supervenience thesis, by itself, does not do very much philosophical work. In fact, I think one should think of a supervenience thesis not as a thesis that, if accepted, ends discussion and solves a problem, but as a thesis that

90

The materialist may ﬁnd this easier to do if he accepts Lewis's Humean supervenience as well as materialism. For according to this thesis, the laws and causal powers of things are themselves supervenient on regularities. The two situations we have presented the emergentist (one with intermediate mentality, one with the middleman eliminated) seem to satisfy the same physical regularities, but to differ only in the causal explanations of them, and so would seem to violate Humean supervenience. But this conclusion assumes that the basic physical properties are the same in the two worlds, and not just similar. Without some criteria for identifying properties across possible worlds, Humean supervenience may not have the teeth it seems to have. On the view of properties defended in Shoemaker (1980), according to which laws and causal powers are constitutive of properties, Humean supervenience seems to hold, but not in the way that is intended.

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sharpens a problem and directs the further discussion. Two philosophers who accept that the mental is supervenient on the physical, and who understand this in the reductionist way, may disagree sharply about what kind of supervenient property mental properties are: For example, whether they are complex properties deﬁnable (even if only inﬁnitely) in terms of the physical, or more abstract, higher-order functional properties, or some mix. But the common ground shared by philosophers who agree about the supervenience thesis is important. Consider two philosophers who agree with the Parﬁttean reductionist thesis about personal identity: the identity of persons is supervenient on the physical and mental properties of and relations between momentary states. But they disagree about the proper analysis of persons: one defends a psychological continuity criterion, while the other defends an account that puts more weight on bodily continuity. What is the nature of their disagreement? If the two philosophers really agree about the supervenience thesis and a reductionist understanding of it, and really agree about the nature of the supervenience base, then they have succeeded in separating semantic from metaphysical questions: their disagreement is purely semantic, since the force of the supervenience claim is that the facts about momentary states are all the facts—the rest is just how we choose to talk about those facts, about how the words we use are in fact related to them, or about what attitude we choose to take toward them. That does not mean that the dispute is unimportant, but it does change its character. The philosopher who is inclined to accept a certain reductive analysis of personal identity because she thinks that it gets the metaphysical facts right, is, I think, one who really accepts the ‘further fact’ view, and so who rejects the common ground. It may be that the real distinction between the supervenience theorist with a reductionist motive and the one who thinks of it as a causal or metaphysical relation is in the character of the philosophical disagreement that follows agreement about a supervenience thesis. If personal identity, or mentality, or intrinsic value, emerges from conﬁgurations of more basic properties, then the questions about just which more basic properties correlate with the supervenient properties are substantive metaphysical questions. But if there are no further facts beyond the basic facts, then we have ﬁnished doing metaphysics, and turned to something else once we have accepted the supervenience thesis, and begun discussing the more speciﬁc questions about which distinctions of the kind we agree there are there to be made are the ones that the supervenient properties make.

Appendix The claim to be proven is that the global supervenience of A on B is equivalent to the strong supervenience of A on B′, where B′ is the set of properties deﬁnable in

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terms of B properties, in an inﬁnitary language with identity, quantiﬁers, and truth-functional operators. It is obvious that strong supervenience implies global supervenience, and that the global supervenience of A on B is the same as the global supervenience of A on B′. What needs to be shown is that if A globally supervenes on B, then A strongly supervenes on B′. First, deﬁne a complete B-description of a world w as follows: if there are n members of the domain of w, the description will begin with n existential quantiﬁers. If variable x corresponds to individual a, then the description will contain a conjunct Fx for each of a's B-properties F, and a conjunct ∼Fx for each B-property that a lacks. The description will also include conjuncts x ≠ y for each pair of distinct variables x and y that are bound by the existential quantiﬁers, and a universal generalization saying that everything is one of the n things. Obviously, any two worlds that have the same complete B-description will be B-indiscernible with respect to a mapping of the domain of one onto the domain of the other. Now suppose that A globally supervenes on B. Let w and z be any two possible worlds, and a and b any two individuals from the domains of w and z, respectively, such that a has all the same B′-properties in w that b has in z. Let φ be the complete B-description of w, and let x be the variable in the description that corresponds to a. Drop from φ the quantiﬁer that binds x, and the result is an open sentence with one free variable that expresses the maximal B′ property that a has in w. Since b has the same B′-properties in z as a has in w, it follows that b has this property in z. But then the existential generalization of this open sentence, which is equivalent to φ, is true in z, and so w and z are Bindiscernible, relative to a mapping that maps a to b. So since we are assuming that A globally supervenes on B, it follows that w and z are also A-indiscernible, relative to the same mapping. So a has all the same A-properties in w that b has in z. Therefore, A strongly supervenes on B′.

Postscript added in 2002 I will add some remarks about discussions of some technical consequences of supervenience concepts in two papers that appeared since this paper was ﬁrst published.

1. Innitary languages In giving the rather casual argument in the appendix above, I did not specify the inﬁnitary language that I was using, but I was assuming a language that allowed inﬁnite quantiﬁer preﬁxes as well as inﬁnite Boolean combinations. The simple argument I gave requires such a language if it is to apply to possible worlds with inﬁnite domains. But Michael Glanzberg has shown91 that a more sophisticated argument establishes that a language that has inﬁnite Boolean combinations but only ﬁnite quantiﬁer strings will sufﬁce. To see the rough idea, note that one could say, in such a language, that there exist inﬁnitely many distinct things by conjoining the statements that say there are at least n things, for each n.

91

Glanzberg (2001). I am grateful to Michael Glanzberg for very helpful discussion and correspondence about both technical and philosophical issues about supervenience and inﬁnitary logic.

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But Glanzberg also argues that this inﬁnitary language is too powerful to yield a notion of supervenience that will do the philosophical work we want supervenience to do. He suggests that a strong supervenience thesis that takes the supervenience base to be a set of properties that is closed under deﬁnability in such a language will be too weak since the resources of the inﬁnitary language make it possible to deﬁne arbitrary properties. To get a supervenience thesis that is strong enough to be interesting, we need (he argues) some restrictions on the closure conditions that determine the relevant set of properties. If this were right, then the fact that global supervenience of A on B implies strong supervenience of A on B′ (the set of properties that is the unrestricted closure of the set B) would be of limited interest, but I don't think that the strong supervenience claim, with an unrestricted closure condition on the set of properties that is the supervenience base, is as weak as Glanzberg suggests. It is, I think, exactly as strong as we want a supervenience thesis to be. The reason I think this is that the strong supervenience of A on B′ is, as noted in the appendix, equivalent to the global supervenience of A on B. That is, the converse of the main claim shown in this appendix is also true. This follows from the following three facts, which hold for any sets of properties X, Y, and Z, and where X′ is the set of properties deﬁnable in the inﬁnitary language in terms of the X properties: 1. 2. 3.

If X strongly supervenes on Y, then X globally supervenes on Y. If X globally supervenes on Y, and Y globally supervenes on Z, then X globally supervenes on Z. X′ globally supervenes on X.

A global supervenience thesis (which does not need to mention the resources of inﬁnitary languages) is clearly not trivial, in general. It is obviously not true, in general for arbitrary sets of properties A and B, that A globally supervenes on B, and so not true, in general, that A globally or strongly supervenes on the inﬁnitary closure B′. However powerful the resources of the inﬁnitary language may be, they don't give us the power to deﬁne properties, or surrogates for properties, that distinguish between B-indiscernible possible worlds. Glanzberg's argument seems to suggest otherwise only because his formal argument assumes that a complete B-description of a possible world fully describes the possible world, but this will be true only when all properties globally supervene on the B-properties.

2. Dening global supervenience Timothy Williamson has given an argument (in the context of a criticism of a claim by Frank Jackson) that shows that global supervenience (as Jackson deﬁnes it) is not sufﬁcient for strong supervenience.92 Williamson's result may appear to conﬂict with what is shown in the appendix of this paper, but it does not. The deﬁnition of global supervenience (of the ethical on the descriptive) that Williamson is criticizing is this: (S) For all [worlds] w and w′, if w and w′ are exactly alike descriptively then they are exactly alike ethically.

92

Williamson (2001). This paper was a contribution to a book symposium on Jackson (1998).

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Here is one of Williamson's examples to show that global supervenience, in this sense, might hold even if the corresponding strong supervenience claim fails: say that a property is uniform if it is necessary that it is true either of everything or of nothing. Let the supervenience base be the set U of uniform properties. U = U′ (the inﬁnitary closure of U), since every property deﬁnable in terms of uniform properties is uniform. Now if w and w′ are alike with respect to all uniform properties, than w = w′, so any worlds alike with respect to uniform properties are alike with respect to any properties. So the set of all properties globally supervenes, in the sense deﬁned, on the uniform properties. But it won't be true that all properties strongly, or even weakly, supervene on uniform properties. Two individuals that exist in the same possible world will have all the same uniform properties, but may differ with respect to many non-uniform properties. This argument is decisive—and there are many other examples—but it exploits the loophole in the deﬁnition of global supervenience that we closed, and therefore does not conﬂict with our result. Let F be any property that applies to some but not all things in world w, and let f be any mapping of the domain of world w onto itself that maps something that is F in w to something that is not F in w. w will be U-indiscernible from itself relative to f, but not {F}-indiscernible from itself relative to f. Therefore, any set of properties including F will fail to globally supervene (in the sense we deﬁned) on U. Williamson's argument shows that the loophole is bigger than I had realized, and it raises questions about the intuitive idea behind the notion of global supervenience—about the idea of a characterization (of a possible world) that is, in some metaphysical sense, complete. Set aside, for the moment, any technical deﬁnition of global supervenience, and consider the motivating intuitive idea. Should we say that all properties globally supervene on the uniform properties? If God made the world by ﬁxing all the uniform properties of things, wouldn't he be ﬁnished? He would have ﬁxed a speciﬁc possible world. What more is needed? The theological image doesn't seem so helpful here. Consider a toy model: there are exactly three possible objects, a, b and c, and they all exist necessarily. A world is speciﬁed by saying of each object whether it is red or black. Necessarily, something is red iff not black, and every combination of colors for the three objects is possible, so there are eight possible worlds—call them w1 to w8 . Let Wi be the strongest uniform property instantiated in world wi , for each i from 1 to 8. Now God decrees that the world shall be one in which all things have W4 . Isn't he ﬁnished? We know that the actual world is w4 . If we knew which world that was (in terms of red and black), we would know what God had done. Here is a different image. Consider the conception of properties and possible worlds discussed in Chapter 4 , the quality space model. A quality space is (intuitively) complete if one would give a qualitatively complete speciﬁcation of a possible world by specifying which points in the quality space are occupied (and if there may be indiscernible individuals, how many at each point). If the A-properties globally supervene on the B-properties, then specifying the location in the B-space will sufﬁce to determine the A-properties of everything. Now consider the toy example again: let the B-space be the space of the 8 U-properties. The world w4 is the one where all three individuals are located at the W4 point. But which objects are red there?

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It is part of the intuitive picture behind the quality space model that there is a difference between qualitative properties and properties deﬁned in terms of the individuals that have them. The model represents this distinction, but it does not help to make it in application. In our toy model, if the properties red and black are, as the intuitive description suggests, qualitative properties, then the universal properties will not be purely qualitative, and so are perhaps not a suitable supervenience base. If, on the other hand, we treat them as qualitative, then the properties red and black will be referential properties, and deﬁnable in terms of the U-properties, plus the identity properties.

PART III Identity in and across Possible Worlds

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6 Counterparts and Identity (1987) 1. Introduction Philosophers who take possible worlds seriously are often divided into two camps. First there are the possibilists who hold that possible worlds and other possible objects may exist without actually existing. Other possible worlds, according to the possibilist, are concrete universes, spatially and temporally disconnected from our own, but just as real. The claim that such universes are not actual is, in effect, just the claim that we are not located in them. Second, there are the actualists who hold that nothing is real except what is actual—that is, except what exists as a part of the actual world. According to the actualist, the things that are (perhaps misleadingly) called ‘possible worlds’ are not really worlds but are properties or states of the world, or states of affairs, or propositions or sets of propositions, or perhaps set-theoretic constructions of some kind. There are many different versions of actualism; what they have in common is the thesis that possible worlds are things that can be instantiated or realized. A nonactual possible world is not a concrete object that exists in some nonactual place, but an abstract object that actually exists but is uninstantiated. A second issue that divides the friends of possible worlds concerns the relations between the individuals that exist in the different possible worlds. Just as the possible worlds theorist (possibilist or actualist) explains the claim that something might have been true as the claim that it is true in some other possible world, so this theorist explains the claim that some property might have been true of a certain individual as the claim that in some other possible world, that property is true of some individual suitably related to the actual individual. But what is the suitable relation? The straightforward answer is that the relation is identity. The reason that Daniels might have been a professional pianist is that there is a possible world in which Daniels, and not some other individual, is a professional pianist. But according to an alternative line of argument, this cannot be right, since Daniels exists only in our world—he cannot be here and some place else as well. The pianist in a counterfactual world in virtue of which Daniels might have been a professional pianist is not Daniels himself, but his counterpart, or one of them, in that other world.

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These two philosophical issues concerning possible worlds are distinct but related. It happens that David Lewis is the most articulate defender of both the possibilist line about possible worlds and the counterpart line about possible individuals.93 As a result, the most prominent arguments for counterpart theory, and against strict identity of individuals across possible worlds, are given within a possibilist framework, and some of the motivations and arguments for counterpart theory derive from possibilist assumptions. But counterpart theory has a number of quite different motivations and involves a number of different theses that need to be distinguished. What I want to explore in this paper is a version and a defense of counterpart theory that is quite different from Lewis's version. The version that I will explore is tied to actualism rather than to possibilism. The main thesis that I will, somewhat tentatively, suggest is that the actualist can coherently combine a belief in primitive thisness94 and genuine identity across possible worlds with a version of counterpart theory that permits one to make sense of contingent identity and distinctness—that is, of the claims that one thing might have been two, and that distinct things might have been identical. I am not conﬁdent that the account of counterparts and identity that I will sketch is a plausible one, but even if it ultimately fails, I think it is important to see that it can be pushed farther than many have supposed. I am conﬁdent that if the account I will explore is wrong, it is wrong for reasons quite different from those that are usually given for rejecting counterpart theory and contingent identity. Developing the account and bringing out its problems will, I think, throw some light on the interconnections between some metaphysical and semantical questions concerning possibility, predication, and identity. I will begin, in section 2, by looking at counterpart theory as it is usually conceived, distinguishing three different motivations for it, and discussing some arguments against it. Then, in section 3, I will look at the thesis of actualism and at the actualist strategy for explaining, or explaining away, merely possible individuals. In section 4, I will consider the thesis, or cluster of theses, that David Kaplan has called haecceitism.95 Here I will argue that haecceitism, properly understood, can be reconciled with a version of counterpart theory, and with the coherence of contingent identity. In section 5, I will look brieﬂy at the temporal analogy, considering some of the similarities and differences between identity through time and identity across possible worlds. Finally, in section 6, I will look quickly at some of the consequences that this account of counterparts and identity has for

93

Lewis (1968) introduced counterpart theory. See Lewis (1986a) for his most recent and most detailed defense of possibilism.

94

This term is from Adams (1979).

95

Kaplan (1975).

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the abstract semantics of quantiﬁed modal logic. The problems come, surprisingly, not with identity, which is perfectly standard, but with variable binding and quantiﬁcation.

2. Counterpart theory Let me begin with an informal sketch of the basic elements of a formal semantic analysis of quantiﬁed modal logic in its standard form. The abstract semantics is essentially the same whether it is given a possibilist or an actualist philosophical foundation. A frame or model structure for interpreting a quantiﬁed modal language consists of a set of possible worlds, each with its domain of individuals—the individuals that exist in that world. The rules for assigning semantic values to the primitive descriptive expressions of the language and for determining the values of complex expressions as a function of the values of their parts are for the most part straightforward generalizations of the rules of extensional semantics; modal semantics does for many possible worlds at once what extensional semantics does for the actual world alone. The semantic values, in extensional semantics, are extensions of various kinds: for example, individuals for singular terms, sets of individuals (subsets of the domain) for one-place predicates, truth-values for sentences. The corresponding values in modal semantics are intensions, which are identiﬁed with functions from possible worlds into extensions of the appropriate kind. So, for example, the intension of a one-place predicate is a function taking a possible world into a set of individuals (a subset of the domain of that world), and the intension of a sentence is a function from possible worlds into truth-values. The semantical rules for the various extensional operators, the quantiﬁer, and the identity predicate, are just like the extensional rules, except relativized to possible worlds. For example, the rule for negation says that a sentence ~A is true in possible world w if and only if A is false in w. The rule for the one new operator—the necessity operator—captures the familiar slogan, that necessity is truth in all possible worlds: A is true in w if and only if A is true in w′ for all possible worlds w′.96 This simple story can be modiﬁed and elaborated in various ways. The counterpart variation of the story requires three changes: it adds a constraint on the domains, adds an element to the structure, and makes some changes in the semantical rules. First, the domains of the different possible worlds are required to be disjoint. Second, a binary counterpart relation is added to the model structure. The third change—the change in

96

This is the rule for the simplest semantics for S5. In semantic theories for other systems, necessity is relativized to the worlds. A binary accessibility relation between worlds is added to the structure, and the necessity rule says that A is true in w if and only if A is true in w ′ for all w ′ that are accessible to w.

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the semantical rules—can be carried out in various ways.97 What the changes must do is to make the modal properties of objects in one possible world depend on the properties, not of the object itself, but of its counterparts in other possible worlds. Consider an open sentence àGx. The standard semantic rules say that this will be true of an individual a in a world w if and only if Gx is true of a in some possible world w′. In counterpart semantics, the rules must be changed to make àGx true of a in w if Gx is true of a counterpart of a in some world w′. Hubert Humphrey, for example, will have the property of being possibly a president of the United States by virtue of the fact that in a different possible world, a different person who is a counterpart of Humphrey was president. Obviously, the standard theory, allowing the domains of the different possible worlds to overlap and interpreting modal predicates in the straightforward way, is simpler and more natural. What are the motivations for the counterpart move? I will discuss three different motivations. The ﬁrst is tied to possibilism. The second derives from a metaphysical doctrine about the nature of individuals—a doctrine that is independent of possibilism. The third—again independent of possibilism—derives from intuitions about the contingency of identity and distinctness. First, the possibilist argument: nothing can be in two places at once. If other possible worlds are really other universes, then clearly, you and I cannot be in them if we are here in this one. People who resemble us in one way or another might be there, but we cannot be there. At least we cannot be wholly in this world and also in some other possible world. The possibilist will concede that it would be coherent to say that individuals such as you and I are extended across possible worlds, with parts—world-parts analogous to time-slices—in different possible worlds. But it would be intuitively implausible to say that we are (and always will be) only partly actual, the other parts being counterfactual. It would be coherent, but intuitively bizarre, to hold that ordinary individuals are scattered objects with parts existing in many spatially and temporally disconnected locations.98 This argument seems to me compelling, given the possibilist framework it presupposes, but it has no force at all for an actualist. For the actualist, the claim that I exist in a different possible world is not, as it seems, a claim that I am in some other place as well as here but is, instead, the claim that there is a way the world might have been, different from the way it is, such that had the world been that way, I would still have existed. A second motivation for counterpart theory derives from the metaphysical doctrine that there is nothing to a particular individual over and above the properties it has, the relations it stands in to other individuals, and the

97

I discuss two ways of modifying the rules in section 6. See also Lewis (1968) and Hazen (1979). Lewis formulates counterpart theory, not as a semantics for a modal language, but as an extensional theory with quantiﬁers ranging over possible worlds and possible individuals.

98

Lewis gives an argument like this (1983b : 21–2).

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spatial and temporal locations it occupies. There is no thisness or individual essence underlying the qualities and relations. It does not strictly follow from this metaphysical doctrine that individuals exist only in one possible world, but it does seem to follow that the relation of identity of individuals across possible worlds must be explained or analyzed in terms of qualitative similarities and differences between individuals within worlds. If things are identiﬁed across worlds, these identiﬁcations must be supervenient on some kind of counterpart relation between the worldbound parts of individuals. This metaphysical motivation is independent of the possibilist–actualist contrast. A possibilist, who opted for counterpart theory for the ﬁrst reason, might believe in irreducible thisness, rejecting the second motivation, and with it the demand that the counterpart relation be explained in qualitative terms. For this kind of counterpart theorist, primitive thisness is represented by a primitive counterpart relation. On the other hand, there is no reason why an actualist who regards other possible worlds as other ways our world might have been could not reject primitive thisness, opting for counterpart theory, not for the ﬁrst reason, but because it provides a more natural setting for the analysis of identity across possible worlds in qualitative terms. Finally, a third motivation for the counterpart move derives from intuitive examples and puzzle cases that are difﬁcult to account for on the standard account of modality. I will sketch four examples discussed in the recent philosophical literature that raise problems about identity across possible worlds. 1.

99

Some of the examples that help to motivate counterpart theory are variations on older examples used to raise problems about identity through time. Consider the notorious ship of Theseus. Over the years, the parts are gradually replaced until none of the original parts remain. Then, sometime later, the original parts are gathered up and put back together according to the original plan. We now have two ships. Which is the original? Each seems to have some claim; of each it seems reasonable to say that it clearly would have been the same as the original ship if it had not been for the other. Suppose we say that continuity is the dominant criterion of identity, and so the original ship is the one that remained aﬂoat throughout, the one that now has all new parts. Now consider this cross-world elaboration of the puzzle, devised by Hugh Chandler:99 Suppose possible world w1 is as described in the original ship of Theseus story. In possible world w2, the story is the same, except that as the old parts are gradually removed, they are not replaced. The ship is gradually dismantled, and then, sometime later, it is reconstructed. The question is, what are the relations between the ships in the two worlds—which ships are identical to which? To avoid begging any questions, I will use different names for each ship that might be thought to be distinct from any other: Let a be the original ship in w1, b the ship

See Chandler (1975).

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2.

3.

continuous with it with all new parts, and c the ship constructed, in w1, from the original parts. Let d be the original ship of w2, and e the ship constructed, in w2, from the parts of d. Now which identity statements involving these names are true? First, intraworld identities: We have assumed that a = b, and of course it is clear that b ≠ c. In w2, it seems clear that d = e; the original ship was taken apart and put back together. Next, crossworld identities: we can stipulate that a = d; the idea is to tell two alternative stories about one original ship. It also seems reasonable to say that e = c, since c and e are composed of exactly the same parts, and the history of those parts—their relations to each other at various times—is exactly the same in w1, as it is in w2. But we cannot hold all of these identity and distinctness claims at once: they imply a contradiction. Allan Gibbard tells a story about a lump of clay called ‘Lumpl’ and a statue called ‘Goliath’.100 The statue is made out of the lump, and the lump and the statue came into being, and ceased to exist, at exactly the same moments. It is reasonable to say, Gibbard argues, that in this case, the lump and the statue are identical, but it is clear that they are not necessarily identical. Consider a different possible world in which the statue is destroyed before the lump. In that world, Goliath and Lumpl are distinct. But on the standard theory, one cannot make sense of this. Consider the one thing that is (in the actual world) both Lumpl and Goliath. Is that thing in the domain of the other possible world, and if so, is it the lump or the statue that exists there? It seems reasonable to say that a complex artifact, say a car, a building, or a bicycle, might have been originally made out of slightly different parts from those it was actually made out of. If, in putting together a certain custom-made bicycle, the bicycle-makers had used a different nut, bolt, gear lever, or spoke, they would have made, not a different bicycle, but the same bicycle slightly differently. But if most or all of the parts had been different, then the bicycle constructed would have been a perhaps similar, but distinct, bicycle. If this is right, we are in trouble, for consider a sequence of possible worlds, each containing a bicycle that differs slightly in its composition from the bicycle in the preceding world, but such that the bicycle in the ﬁrst world in the sequence has no parts in common with the bicycle in the last world.101 Identity, of course, is transitive. One cannot say that each bicycle is identical to the bicycles in neighboring worlds, but not to the corresponding bicycles in distant worlds.102 The argument suggests that one

100

Gibbard (1975).

101

Chandler (1976) discusses this case. Salmon has a very detailed discussion of the case, which he calls ‘the four worlds paradox’ (1981: 229–52). See also his more recent discussion (1986). Chisholm (1967) had discussed a similar problem much earlier.

102

The form of argument may look superﬁcially like a sorites argument, and it does seem true that the constraints on cross-world identity being appealed to here are vague. But the problem is independent of vagueness. Even if the threshold were perfectly precise, the puzzle would remain.

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4.

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must either adopt an extreme form of mereologieal essentialism, requiring identity of all parts for identity of the whole, or else give up the standard account of identity across possible worlds.103 Consider the bilingual Pierre who sincerely assents, in French, to the statement ‘Londres est jolie’ while dissenting, in English, from ‘London is pretty’.104 It seems that Pierre has a false but coherent conception of the world. In the possible worlds that are the way Pierre thinks the world is, there are two distinct cities, one that is pretty and called (in French) ‘Londres’, and one that is not so pretty and is called (in English) ‘London’. Which of these cities is the city we call ‘London’? It seems reasonable to say that both of them are. Both of Pierre's beliefs are beliefs about London; when he says either ‘Londres est jolie’ or ‘London is not pretty’, he is obviously referring to London, and since he is sincere, he is expressing his beliefs. And it seems that he is successfully describing the world as he believes it to be. But, of course, the standard account will not permit us to say that both of these cities are London while maintaining that they are distinct from each other. Mistakes of identity are familiar: it is not at all uncommon to think one thing is two, or two things one. This kind of mistake creates problems for the semantics of propositional attitudes, since the standard theory does not permit us to describe them in a straightforward way.

These examples remind us what an unyielding relation identity is. The source of the puzzles seems to be that the richness and ﬂuidity of intuitions about possibilities conﬂict with the inﬂexible demands of this relation. Loosen up, says the counterpart theorist. A more adequate description of the modal phenomena can be given if we replace the restrictive cross-world identity relation with a more ﬂexible relation that permits intransitivities and asymmetries. This third motivation for the counterpart move is the one closest to the phenomena and least tied to metaphysical presuppositions. Actualists and believers in primitive thisness may still be troubled by these examples, and so may still have at least one reason to be tempted by counterpart theory. But most philosophers who are troubled by such examples have resisted the temptation to respond with the counterpart move. The following argument, made most explicitly by Alvin Plantinga105 and Nathan Salmon,106 spells out

103

The response that Chandler suggests, and that Salmon adopts in his discussion of the puzzle, is different from either of these: they argue that all the bicycles are identical, but that the more distant possible worlds in the sequence are not accessible to each other. That is, there is a possible world in which the bicycle has totally different parts from those it actually has, but this world is not possible relative to the actual world. Things cannot, of course, lack their essential properties, but according to this solution, it is possibly possible for them to lack their essential properties.

104

This case was invented by Kripke (1979).

105

See Plantinga (1973).

106

Salmon (1981: 232–8).

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one reason for thinking that counterpart theory does not really solve the problems raised by such examples. One may divide the counterpart doctrine into two parts: the ﬁrst part is the metaphysical thesis that the domains of the different possible worlds are all disjoint; possible individuals exist in at most one possible world. The second part is the semantical thesis that modal predicates should be interpreted in terms of counterparts (in the way sketched above) rather than straightforwardly in terms of the individuals themselves. If one considers the ﬁrst thesis by itself, it seems to suggest a rather extreme form of essentialism according to which nothing could have been different in any way from the way it actually is. In fact, according to this form of essentialism, none of us would have existed if anything in the world had been even slightly different. ‘If a leaf deep in the mountain fastness of the North Cascades had fallen in October 31, 1876,’ Plantinga writes, ‘the day before it actually fell, then (according to Counterpart Theory) I should have been either nonexistent or else a different person from the one I am. And surely this is false.’107 The metaphysical part of the doctrine, considered alone, does seem quite implausible. How is the addition of the semantical component supposed to help? It cannot, according to the Plantinga–Salmon argument, since it does not retract or qualify the metaphysical thesis in any way. What the second part of the doctrine does, they argue, is to reinterpret the language so as to disguise the metaphysical consequences of the doctrine. One can no longer say, in the object language the counterpart theorist sets up, that everything has all of its properties essentially, or that no thing could have been different from the way it was, but these unpalatable essentialist claims remain, in Plantinga's words, ‘the sober metaphysical truth of the matter’,108 according to counterpart theory. Nathan Salmon, in his statement of this argument, concludes that counterpart theory is, at bottom, just a particularly inﬂexible brand of essentialism.⋯The counterpart theorist can mouth the words ‘ship a might have been made from slightly different matter’, but any such pronouncement by the counterpart theorist in modal operator discourse is a verbal camouﬂage that merely postpones the inevitable. What matters is what the counterpart theorist means by these words, and more importantly, what is not meant by these words.109 I am not sure what to think of this argument, mainly because I am not sure how to disentangle the semantical and metaphysical issues. On the one hand, I am inclined to say that the argument just begs the question. The counterpart theorist, in putting forward the semantical part of the doctrine, is not simply proposing that we talk in a different way—that we introduce a ‘new and looser sens-e’ for certain modal expressions.110 Rather, the counterpart theorist is proposing an analysis of what we ordinarily say—what we

107

Plantinga (1973), as reprinted in Loux (1979: 164).

108

Ibid. 158.

109

Salmon (1981: 236).

110

Plantinga (1974: 117).

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have meant all along—when we talk about the ways things might have been. To say, as Plantinga does, that ‘the Counterpart Theorist is using that sentence [“Socrates could have been unwise”] to express a proposition different from the one the rest of us express by it’111 is simply to deny the counterpart theorist's semantical thesis. The argument is not so much an argument against the thesis as it is a rhetorical appeal to its intuitive implausibility. The counterpart theorist replies that although the theory may be surprising, it does account for the phenomena: it can give truth-values to ordinary modal claims that agree with our intuitions about those claims. The semantic thesis, and the contrasting one from the standard theory, should be judged on how well they account for the use of ordinary modal language, and not on alleged intuitions about how the theoretical terms of the theory relate to the modal language they are being used to explain.112 On the other hand, I am not entirely persuaded by this reply to the argument because I am inclined to reject the sharp contrast between the theoretical apparatus of semantics and the ordinary discourse it is used to explain. The semantical apparatus, and the theses stated in terms of it, must be understood partly in terms of ordinary modal discourse. For example, possible worlds are explained as ways things might have been, and we are urged to believe in other possible worlds simply on the basis of the intuitive plausibility of the ordinary modal claim that there are many ways things might have been. We get an intuitive grip on what it is for something to be true in a possible world by identifying it with what would be true simpliciter if that world were actual. This is, of course, to acknowledge some circularity in modal semantics. The apparatus makes clear the abstract structure of modal discourse, but it does not really provide an analysis of that discourse in terms that are understood independently of it. If this is right, then we may be entitled to take seriously our intuitions about theses stated in terms of the apparatus of semantical theory. In the case of counterpart theory, the worry is that we must use modal locutions in explaining the apparatus in a way that is inconsistent with what the apparatus says that those locutions mean. Consider a statement based on Plantinga's example mentioned above: ‘If a leaf had fallen a day earlier than it in fact fell, Socrates would still have existed.’ Intuitively, this should come out true, and it does, according to the counterpart interpretation, since the consequent is true in the relevant possible worlds by virtue of the fact that counterparts of Socrates would have existed there. But to understand what is distinctive about the counterpart move, we must also recognize that it is in some sense not really Socrates who exists in those other possible worlds. If we understand truth in a possible world as what would be true if that world were realized, then the theoretical claim that the

111

Ibid.

112

Hazen (1979) gives an argument like this. Salmon (1981: 235 n.) criticizes it.

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individual in the other possible world is not Socrates, but only a counterpart of him, is the claim that if a leaf had fallen a day earlier than it in fact fell, the individual who would have been Socrates would not have been not him but someone else. This argument is not decisive. The counterpart theorist will not accept these intuitive explanations of possible worlds and of truth in possible worlds. But without them, or some alternative, it is not clear that we know what we are talking about when we talk about possible worlds. So I am unsure how to evaluate this objection to counterpart theory in its usual form, but I will bypass the issue by defending a version of counterpart theory that is not subject to the Plantinga–Salmon argument. The version that I will suggest is motivated only by the third of the three considerations distinguished above. It will be an actualist theory, and a theory that is compatible with haecceitism, as I will interpret that doctrine. In fact, despite being a version of counterpart theory, it will make the claim that the individual who would be me if things were different really would be identical to me. Before saying how this is possible, I need to make some general remarks, ﬁrst about actualism, and then about haecceitism.

3. Actualism and merely possible individuals The actualist believes that existing and actually existing are the same thing. There exists nothing that is not actual, and this thesis should be understood not as a restrictive metaphysical thesis like materialism and nominalism about what there is in the world, but simply as a trivial consequence of the meaning of the word ‘actual’. How then, according to the actualist, can there be unactualized possibilities? The actualist explains how this is possible by distinguishing two senses of the term ‘possible world’. On the one hand one may mean by ‘possible world’ a way things might be: a property of a certain kind that the world might have, or a state it might be in. On the other hand, one might mean a world that is that way: that has that property, or is in that state. Nonactual possible worlds in the ﬁrst sense exist, and actually exist, but are unexempliﬁed. Nonactual possible worlds in the second sense do not exist at all, although they could have if things had been different. Modal semantics, in its application (which of course takes place in the actual world), is committed to the existence of possible worlds only in the ﬁrst sense.113 The actualist has a problem about possible individuals, as well as possible worlds, and needs to reconcile actualism not only with the intuition that things might have been different from the way they actually are but also with the intuition that there might have been things other than those there actually are. Modal semantics posits nonactual possible worlds; the actualist explains them as uninstantiated ways things might be. Modal semantics may

113

I defend this actualist account of possible worlds in Ch. 1 of this collection.

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also populate the domains of these possible worlds with nonactual possible individuals. How are these to be explained? The actualist needs a distinction, parallel to the distinction between a world and a state of the world, between an individual and some kind of abstract property or state of an individual that can represent it, something that can exist even when the individual itself does not. Alvin Plantinga, in a discussion of actualism and possible worlds, raises this problem and defends this kind of solution. ‘How can the actualist understand⋯“There could have been an object distinct from each object that actually exists”?⋯Easily enough; he must appeal to essences. Socrates is a contingent being; his essence, however, is not. Properties, like propositions and possible worlds, are necessary beings. If Socrates had not existed, his essence would have been unexempliﬁed, but not non-existent.’114 In the application of modal semantics, Plantinga suggests, we should regard the domains of the various possible worlds, not as sets of individuals themselves, but as sets of essences—the essences that would be exempliﬁed if that world were actual. Whatever the fate of Plantinga's particular theory of individual essences, the general point is difﬁcult to avoid. Any actualist who accepts the intuitively very plausible thesis that there might have been individuals other than those that actually exist will need to distinguish in some way between individuals in the strict sense and their representatives in the domains of the possible worlds. The commitment of an application of possible worlds semantics will be to the representatives that make up the domains. To say that there might have existed an individual with such and such properties is not to say that there does exist an individual with those properties in the domain of some possible world, but rather that there exists in the essential domain (to use Plantinga's term for the domain of essences) of some possible world a representative of an individual who is represented in that world as having such and such properties. However the details are spelled out, if we make this kind of distinction, we will need also to distinguish two questions about identity across possible worlds—questions that are easy to conﬂate if we ignore the distinction required by actualism between individuals and their individual essences or representatives. We may ask, of two ‘individuals’ drawn from the domains of two different possible worlds, whether the essences or representatives are identical, or we may ask whether the individuals represented are identical. The two questions are obviously different and might receive different answers. A particular theory of essences such as Plantinga's may have the consequence that the answers to the two questions will always be the same, but once we have made the general distinction, we can consider alternative theories that answer these two questions differently. An actualist version of counterpart theory, I want to suggest, is one such theory.

114

Plantinga (1976), as reprinted in Loux (1979: 268).

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Suppose we require that the essential domains of different possible worlds be disjoint. But the essences or representatives that make up these domains will be related by a counterpart relation.115 The intuitive explanation of the counterpart relation is roughly as follows: the relation holds between representatives a and b if and only if a and b represent the same individual. In the application of this version of counterpart theory, it will be true that if a leaf had fallen a day earlier than it did in 1876, Socrates himself would still have existed, even though the essence or whatever it is that the model theory uses to represent him in the domain of the actual world would have been unexempliﬁed. Instead, he would have instantiated a different ‘essence’. Saying this may require a nonstandard theory of essences, but it is no longer a plausible charge against this version of counterpart theory that it is ‘at bottom just a particularly inﬂexible brand of essentialism’. Still, the critic may respond, what is the point? This theory will surely be just a clumsy notational variation of the standard theory, one that uses an artiﬁcial concept of essence to say, in a slightly different way, the same things that could be said with Plantinga's original concept. Here the actualist counterpart theorist may reply in the same way that Lewis replied, in his original exposition of counterpart theory, to a similar suggestion on behalf of the standard theory: ‘But beware. Our difference is not just verbal, for I enjoy a generality he cannot match. The counterpart relation will not, in general, be an equivalence relation.’116 But, the critic is likely to protest at this point, Lewis can say this, since his counterpart relation does not really represent identity, but the actualist counterpart theorist cannot consistently use identity to explain the counterpart relation in the way suggested above and also allow a counterpart relation that is not an equivalence relation. Suppose, the critic continues, the counterpart relation holds between essences a and b, and also between essences b and c. It follows that the individual that exempliﬁes a is identical with the individual that exempliﬁes b, and that the individual that exempliﬁes b is identical with the individual that exempliﬁes c. Then, by the transitivity of identity, the individual that exempliﬁes a is identical with the individual that exempliﬁes c, and by the explanation of the counterpart relation, it follows that the counterpart relation holds between a and c. So, the critic concludes, this relation must be transitive, and a similar argument will show that it must be symmetric. If this argument were right, then it would show that the actualist counterpart move that I am suggesting would have no point. For our only motivation in making the move is to get the added ﬂexibility that will allow us to account for the various puzzle cases, and this requires a nontransitive counterpart relation. But I will argue that the argument does not

115

The label ‘essence’ is not really appropriate for the world-bound representatives of individuals, since they are not essential to the individuals that instantiate them, but I will continue to use the term.

116

Lewis (1968), as reprinted in Loux (1979: 112).

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work—that we can permit the counterpart relation to be nontransitive and nonsymmetric while using it to represent cross-world identity, where ‘identity’ really means identity. But before giving this argument, I need to make some general remarks about thisness and identity.

4. Haecceitism and absolute identity David Kaplan has given the name ‘haecceitism’ to the doctrine that it does make sense to ask—without reference to common attributes and behavior—whether this is the same individual in another possible world, that individuals can be extended in logical space (i.e. through possible worlds) in much the way we commonly regard them as extended in physical space and time, and that a common ‘thisness’ may underlie extreme dissimilarity or distinct thisness may underlie great resemblance.117 The opposite doctrine—antihaecceitism—is the doctrine I cited in section 2 above as the second motivation for counterpart theory, but I have disclaimed this motivation. The version of counterpart theory that I am defending is or may be haecceitist: the counterpart relation may be a primitive relation, irreducible to qualitative similarities and differences. The question is, can a haecceitist version of counterpart theory permit a ﬂexible counterpart relation, one that is nontransitive or nonsymmetric? There is, of course, no reason why a counterpart relation that is primitive and irreducible must be an equivalence relation. The question is whether a counterpart relation that is not an equivalence relation can represent genuine cross-world identity. How does the doctrine of haecceitism rule this out? Nathan Salmon interprets Kaplan's doctrine to be explicitly about the identity relation. ‘At least one version of haecceitism’, he suggests, ‘may be described as the view that the logic of possible world discourse includes a binary absolute concept of genuine identity between individuals in addition to its ternary world-relative concept of identity.’118 Salmon's thesis, as he develops it, is incompatible with my version of haecceitist counterpart theory, but I will argue that the actualist has no reason to accept it. Salmon suggests that we must accept his thesis if we are really to mean identity by ‘identity’—the relation that holds between x and y ‘in a world w if and only if x and y are, in an absolute sense, one and the very same thing’.119 But I will argue that this suggestion is mistaken. The relation that Salmon calls a ternary world-relative relation is as absolute as a relation of genuine identity needs to be. For an actualist, all statements, including those made by possible worlds theorists when they are talking in their semantical metalanguages, are made in and from the perspective of a possible world. The idea that there is a

117

Kaplan (1975: 722), as reprinted in Loux (1979: 217).

118

Salmon (1981: 127 n.).

119

Ibid. 224.

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perspective outside all possible worlds from which we can talk about them is a possibilist myth. Actual semantic theorists, even when they are talking about other possible worlds, speak in the actual world, and their statements are true if and only if they are true at the actual world. Identity statements are not special in this regard: true identity statements are identity statements that are true at the actual world. To say this is not to espouse any kind of relativism. Truth, from the perspective of the actual world, is absolute truth, the only real truth there is. Truth in or at other possible worlds is just what would be true if things were different. Of course, some things that an actual or possible person might say are necessary truths, and for these statements, it makes no difference whether they are evaluated from the perspective of the actual world or from the perspective of some other possible world. One might mean by an absolute property or relation a property or relation that is true in all possible worlds of whatever it is true of in any possible world. In this sense, the identity relation is absolute just in case all identities are necessary. But this is not what we usually mean when we talk about properties and relations being absolute. No one would argue against absolute simultaneity, for example, simply on the ground that simultaneity is contingent—that some simultaneous events might not have been simultaneous. Suppose we reject the assumption that there is an identity relation that is absolute in Salmon's sense. Can we still explain the intraworld or world-relative identity relation as the relation of ‘being the very same thing’, irrespective of ways of conceptualizing the things identiﬁed? There is no reason why we cannot: identity is the binary relation whose extension, in any possible world w, is the set of pairs such that d is in the domain of w.120 This is surely identity. But what about cross-world identities? How can we ask and answer questions about whether a member of the domain of one possible world is or is not identical, in the strict sense, with a member of the domain of a different world? The actualist can make sense of such questions, provided it is kept in mind that they, like any other questions, are answered from within a possible world. There is no reason why we cannot pick out an individual by virtue of the properties it has in one possible world and then talk about the properties or

120

There is a general question about how to evaluate predication statements, including identity statements, in possible worlds in which the individuals the predicate is being applied to do not exist. Is, for example, ‘Socrates is a man’ true, false, or neither in possible worlds in which Socrates does not exist at all (and has no counterpart)? I prefer modal semantic theories (whether in their standard or counterpart forms) that require the extension of a predicate in a possible world to be a subset of the domain of that world. On this decision, x = x will be false in a possible world where the value assigned to x does not exist (or has no counterparts). An alternative decision— the one that is usually made in modal semantics—would permit nonexistent things to have properties and stand in relations. On this decision, the extension of the identity relation might include in all possible worlds, whether d exists there or not.

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activities of that individual in a different possible world. Consider Nixon, the man who in fact won the 1968 presidential election; suppose he had lost. Here we refer to Nixon, in the actual world, and select a (partial) counterfactual world as a function of him. We might also describe an individual in the counterfactual world, and then locate that individual in the actual world. Consider the person who won the 1968 presidential election in the counterfactual world I have selected. Who is he? He is our very own Hubert Humphrey. That is, the person who (in the counterfactual world) won the 1968 presidential election is (in the actual world) identical to Hubert Humphrey. This is a cross-world identity statement, and it is really identity that we are attributing, an equivalence relation that obeys Leibniz's law, the strongest equivalence relation, the one that holds only between a thing and itself. We are now in a position to answer the arguments against the coherence of contingent identity. Here is one such argument: suppose it were possible for what is in fact one thing to be two distinct things. Then there will be something a that is one thing in one world, w1, and two distinct things, call them b and c, in another world, w2. Then the cross-world identity statements b = a and a = c will both be true, but the intraworld identity statement b = c will be false, and this violates the transitivity of identity. The problem with this argument becomes clear when we ask which possible world it is given in, or relative to. First, consider the argument from the point of view of w1: the two cross-world identity statements are both true: b = a and a = c. But b = c is also true in w1. That is, it is true in w1 that the individual that in w2 is b is identical with the individual that in w2 is c. So there is no violation of transitivity. Now consider the argument from the point of view of w2: b = c is clearly false here. What about b = a and a = c? What these identity statements do is identify each of b and c with the individual that in w1 is identical with a. But the description ‘the individual that in w1 is identical with a’ is, in w2, an improper description. So the identity statements are, in w2, either false, truth-valueless, or ambiguous. The fallacy of the w2 version of the argument, b = a, a = c, therefore b = c, is analogous to the fallacy in the following argument: Russell is the author of Principia Mathematica, the author of Principia Mathematica is Whitehead, therefore Russell is Whitehead. A similar answer can be given to the argument sketched in section 3 that the counterpart relation, to represent identity, must be an equivalence relation. Strictly, the intuitive explanation that relates the counterpart relation to identity is as follows: the counterpart relation holds between essence a in the domain of w1, and essence b in the domain of w2 if and only if the individual that instantiates a (in w1) is (in w2) identical with the individual that instantiates b (in w2). If the counterpart relation is nontransitive, then there will be identities true in one possible world that conﬂict with those true in another, but within any world, the identity relation will be perfectly well-behaved.

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Our defense of actualist counterpart theory and the coherence of contingent identity requires, ﬁrst, a distinction between possible individuals themselves and their essences or representatives in the domains of the various possible worlds and, second, the rejection of a world-independent concept of identity. Both, I have argued, are motivated, independently of the defense of contingent identity, by a thoroughgoing actualist conception of possible worlds and possible individuals. Since, according to actualism, there are no merely possible individuals, we need something other than possible individuals to represent the possibility that there be things other than those that actually exist. And since, according to actualism, the actual world is not one place among others but is the only place there really is, real truth is truth at the actual world. It is not, of course, that actualism requires contingent identity or world-bound essences. The examples and intuitions that motivate actualist counterpart theory are themselves controversial and might be rejected or explained away. My aim has been only to argue that one cannot refute the possibility of contingent identity simply on the basis of the semantics and logic of identity. A proper defense of the necessity of all identities must recognize it as the metaphysical thesis that it is. I will conclude with two sets of brief remarks: ﬁrst some very impressionistic comments about the analogy between identity across possible worlds and identity through time; second, some informal comments about some problems that arise in constructing a formal semantics for actualist counterpart theory.

5. Worlds and times Can one give an account of identity through time that is analogous to the account that I have sketched of identity across possible worlds—an account that permits temporary identity, the branching and merging of individuals through time? It would be nice if we could. There are plenty of puzzle cases that such an account might help to clarify. The literature on personal identity is ﬁlled with examples of one person becoming two, cases that are difﬁcult to describe in a plausible way.121 It is generally assumed in discussions of personal identity that one cannot coherently say, about such cases, that the original person literally is each of two later persons, even though the later persons are, at the later time, distinct from each other. But even if the actualist counterpart account of cross-world identity works, there are disanalogies between worlds and times that prevent a straightforward extension of the account to identity through time. This is too large an issue to

121

See, for example, the papers by Derek Parﬁt, John Perry, Sydney Shoemaker, and Bernard Williams in Perry (1975).

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discuss adequately here; my aim in this section is just to point brieﬂy at some of the relevant analogies and disanalogies. Start with a spatial analogy: just southwest of Ithaca, Route 13 and Route 96 merge. They go through town together and then divide again; 13 goes east through Cortland while 96 goes north on the west side of the lake. Might we talk of local identity, analogous to temporary and contingent identity, in such a case?122 Southwest of Ithaca, Routes 96 and 13 are distinct, but in town they are identical. We can and do talk this way sometimes, but we are also inclined to say that, strictly, Routes 13 and 96 are nowhere identical; they just share a part. What is identical is that part of Route 13 that is in the city and that part of Route 96 that is in the city. Compare this with the putative cases of contingent identity. There is a possibility that I am tempted to describe as the possibility that I might have been twins. Philosophers may disagree about whether there really is such a possibility, or about how best to describe it, but no one would say that the sober truth of the matter is that there are really two persons where I am who share a common part, the part that actually exists—that is located in the actual world. What is the difference between the spatial and the logical-spatial cases? The crucial difference is that while most of us have an actualist conception of possible worlds and possible individuals, we all hold a thesis that is analogous to possibilism about other spatial locations. The regions south and north of Ithaca where 13 and 96 go their separate ways are as real as this place here, within Ithaca. Although there are no individuals that exist only in other possible worlds, there really are things that are located only in other places—for example, that stretch of Route 13 that passes through Cortland. We do not need surrogates that are here for things and places that exist only elsewhere; our ontology accommodates the things themselves. Even if there is no worldindependent identity relation, there is, it seems plausible to say, a location-independent identity relation. If I say that America's most famous highway is U.S. Route 66, you need not ask where I am when I say this in order to assess its truth. Are other times more like other places or other possible worlds? Should we admit past and future individuals into our ontology? Is there a temporally neutral perspective—the perspective of eternity—from which objective reality is best described? These are large and elusive questions. I suspect most of us are ambivalent, shifting between a space-like and a world-like conception of time. Some of the puzzles about identity through time may derive from this shift. If you think of time as space-like, then you will think of continuant individuals—persons and physical objects—as extended through time in the same way that they are extended through space. We are the same as our

122

Kaplan (1979: 103) mentions the highway analogy.

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histories. Only a part of you exists now; other temporal parts are past, or yet to come. On this conception of an object or person, cases of splitting persons should be unproblematic. Suppose a undergoes an operation that results in two persons, b and c, each continuous with a in all the psychological and physical ways that would normally make it appropriate to say that it was the same person. The most natural thing to say, from the point of view that sees time as space-like, is that there were two persons all along, but persons with a common temporal part, the part that existed before the operation. Just as two highways pass through Ithaca together, so two persons share the same youth. If this seems implausible, I think it is because we are inclined to think of a continuant substance—person or physical object—not as something with temporal parts, like an event, but as something that is ‘all there’ in some sense at each moment, even though it is the same thing at different times. We are inclined to say this even if we have trouble explaining what it means. This inclination comes, I think, from a ‘presentist’ conception of time analogous to an actualist conception of worlds—a view according to which we are extended through time in the way we are extended through possible worlds. This conception can, I think, make sense of genuine temporary identity. From this perspective, we can coherently describe the cases of splitting persons as cases of two distinct persons who used to be identical to each other.

6. Variable binding In this concluding section, I will make some informal remarks about the problem of constructing a formal semantics for a modal quantiﬁed language that is appropriate to the actualist counterpart theory that I have been exploring. Some serious problems arise when one tries to generalize the usual semantic rules to cover the case that permits contingent identity, although they are problems about variable binding and predication and do not have to do directly with the logic or semantics of identity. The problems can be solved, but only at some cost in complexity and some loss of intuitive naturalness. I will try to say what the problems are, to identify their source, and to point to two alternative solutions.123 Variable binding is essentially a device for constructing complex predicates out of sentences. Take any sentence, remove a name, and replace it with a blank, represented by a variable. One then has what is, in effect, a predicate that is true of an individual if and only if the sentence would have been true if the name removed had named the individual. Quantiﬁcation

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There are other solutions than the ones I will discuss. See Hazen (1979) for one. Although the strategy I will recommend is different in some ways from the one Hazen has developed, it borrows some ideas from it.

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was the original motivation for the device, and in the usual formulation of quantiﬁcation theory, variable binding is tied to quantiﬁcation: it is the quantiﬁer that binds the variable. But complex predicates have uses independent of quantiﬁcation. There is no loss of expressive power, and some gain in conceptual clarity, if we separate the use of variables to construct complex predicates from the application of quantiﬁers to those predicates. One can formulate ordinary extensional quantiﬁcation theory so that the only variable binding operator is an abstraction operator taking an open sentence into a one-place predicate. In this formulation, the quantiﬁers bind no variables but are simply operators that take a predicate, simple or complex, into a sentence.124 In extensional semantics, the semantical rule for complex predicates will be something like this: the extension of (where A is any sentence) will be the set of individuals d in the domain for which A is true when x is assigned the value d. The generalization of this rule to the standard version of modal semantics is relatively straightforward. In general, in standard possible worlds semantics, the semantic values of expressions are intensions—functions from possible worlds to extensions. The semantic rules are generalized by relativizing them to possible worlds. They say what the intension of an expression is by saying what its extension is, relative to each possible world. In its standard modal version, the rule for complex predicates will then be something like this: For any world w, the extension of in w will be the set of individuals from the domain of w for which A is true in w when x is assigned the value d. But this simple generalization will not do for counterpart semantics, at least if the semantics permits individuals to have more than one counterpart in the same possible world. To see why, consider the simplest model of contingent identity: there are two possible worlds, w1 and w2. There is one individual in the domain of w1, a, and two in w2, b and c. The counterpart relation holds (in both directions) between a and b, and between a and c. Suppose further that the one-place predicate G expresses a property that is false of everything in w1 and true just of b in w2. Now consider whether a is (in w1) in the extension of the complex predicate . According to our rule, it is, if àGx is true in w1 when x takes the value a, which in turn will be true if Gx is true in w2 when x takes the value a. But a has two counterparts in w2, one of which has the property expressed by G and one of which does not, so how do we decide whether Gx is true there when x takes the value a? The problem is that although the value of G is a well-deﬁned property (function taking a possible world to a subset of the domain of that world), the property does not determine a unique propositional function (function taking an individual into a proposition, where a proposition is a function from possible worlds to

124

See Stalnaker (1977) for a discussion and defense of this way of formulating quantiﬁcation theory.

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truth-values). As a result, a complex predicate constructed with G may fail to express a determinate property. One response to the problem—not the one I will recommend—is to stipulate that d should be in the extension of in w if there is at least one way of choosing the counterparts of d in other possible worlds so that A comes out true in w when x takes the value d. This idea can be made precise by assigning to the variables, not individuals themselves, but individuating functions: functions that select one counterpart of a given individual for each world in which it has a counterpart.125 The extension of in w will then be deﬁned as the set of individuals d in the domain of w such that for at least one of d's individuating functions f, A is true in w when x takes the value f. This is perfectly coherent, but it is complicated and has intuitively and formally unpleasant consequences for the logic of predication and quantiﬁcation. For example, in our simple model, a will have the property expressed by but it will also have the property that seems to be the complement of this one, the one expressed by . But of course a will not have the contradictory property one gets by conjoining these two, . The abstraction principle that asserts the equivalence of and Ay/x for all y in the domain will be invalid, as will quantiﬁer distribution principles, which implicitly involve abstraction. Even the simple duality relations between the quantiﬁers will break down. If means that everything has the property , and means that something does, then will not be equivalent, in general, to . Our simple abstract model again illustrates this: something, namely a, satisﬁes in w1, so is true in w1. But also everything (since a is the only thing) satisﬁes in w1, so will be true in w1. The problem is that our rule has introduced a hidden existential quantiﬁer into the predicate-forming operation—a quantiﬁer over individuating functions—and this has radically distorted the logic of complex predicates and quantiﬁers. I prefer a different strategy that seems to me conceptually more natural and that has a less radical effect on the logic. What our model shows, according to the line of thought that motivates the second strategy, is that complex predicates are sometimes ambiguous or indeterminate. is true of a on one way of individuating a, false on another. This indeterminacy might be resolved by context—by selecting one set of individuating functions for the purpose of describing things—or we might just leave the predicates with fuzzy boundaries. One can develop this strategy by associating with each possibly indeterminate interpretation a set of determinate extensions of it—all the admissible126 ways of selecting counterparts so as to

125

Hintikka (1969) formulates a modal semantics in terms of individuating functions rather than a counterpart relation.

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I say every admissible way of choosing counterparts since, as Hazen (1979) has pointed out, there may be links between the counterparts of different individuals. Suppose Ronald Reagan and his daughter Maureen (or their ‘essences’) each has two counterparts in a certain possible world. There are four pairs consisting of counterparts of Ronald and Maureen, respectively, but there may be only two pairs that are counterparts of the father–daughter pair in this world.

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resolve all ambiguities. Then the supervaluation move can be used to deﬁne truth and falsity in the indeterminate model: a sentence is true if it is true on all determinate extensions, false if false on all determinate extensions, and neither if true on some and false on others.127 The logic of abstraction, quantiﬁcation, and identity will be standard on a theory of this kind, but the counterpart relation may still be nontransitive and nonsymmetric, even in determinate models, and this will give rise to some differences between the logic of the standard combined modal-quantiﬁcation theory and its counterpart variation. Chandler's case of the bicycle with parts that vary slightly from world to world, for example, can be modeled by a determinate interpretation with a counterpart relation that is nontransitive. I think this theory is worth exploring. One ﬁnal comment: what about the sentence of modal quantiﬁcation theory that says that all identities are necessary?128

It has been argued129 that this can be proved using only Leibniz's law and uncontroversial principles of quantiﬁcation theory. How does actualist counterpart theory avoid this conclusion? The answer is that it does not, by either of the two ways of doing the semantics that I have described. Both kinds of accounts will validate the statement, although for different reasons. In the ﬁrst kind of semantics, what the statement says is that for any individuals x and y, if x and y are the same, then there is at least one way of picking counterparts so that in every possible world, the counterpart of x is identical with the counterpart of y. This will of course be true even in our model of contingent identity. Note, though, that a statement that

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Van Fraassen invented the supervaluation account of semantic indeterminacy. The ﬁrst application of this strategy was to the problem of nonreferring singular terms (Van Fraassen 1966). The strategy has since been used to represent many kinds of semantic indeterminacy, including ordinary vagueness of predicates, sortal incorrectness, semantic paradoxes, indeterminate counterfactuals, and future contingent statements.

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I am ignoring an irrelevant side issue in this discussion: the issue of what to say about predication statements, including identity statements, in possible worlds in which the individuals the statements are about do not exist. (See n. 28 above.) If one requires, as I would prefer, that the extensions of all predicates in a given possible world must be subsets of the domain of that world, then x = x will be false of d in w if d does not exist in w. In this case, identities will not be necessary, but for a reason that has nothing to do with the kind of contingent identity at issue. The real question is whether identities are essential: whether if x = y, it is necessary that if x exists, x = y. If one makes the decision about predication that I recommend, the discussion should be, not about (NI), but about the qualiﬁed principle: (x )(y ) (x = y (Ex x = y ) ).

129

See, for example, Wiggins (1980: ch. 1).

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appears to be equivalent to the negation of (NI) will also be true in w, in this model:

On the second way of doing semantics, (NI) is also determinately true, even in our simple model. Obviously, every way of picking counterparts of a will pick the same counterpart for a as the one it picks for a. Because both b and c are, in w2, self-identical, x = y will be determinately true in w2 where the values of x and y are both a. There will, however, be more devious ways of expressing the fact that the model represents, in some sense, contingent identity. The inner necessitation of (NI), for example, will not be valid:

Our model is a countermodel for this principle: in w2, b and c are examples of individuals such that it is possible that they be identical, but not necessarily identical. That is, where x takes the value b and y the value c, à(x = y & à x ≠ y) will be true in w2. If there is such a thing as contingent identity in the sense actualist counterpart theory tries to say that there is, it is not easy to talk about it.130

130

I would like to thank the National Endowment for the Humanities for fellowship support, and Cornell University for time off during the period when this paper was written.

7 Vague Identity (1988) Can the identity relation be vague, or semantically indeterminate? The following argument, offered by Nathan Salmon, suggests that it cannot be: Suppose there is a pair of entities x and y ⋯such that it is vague whether they are one and the very same thing. Then the pair <x, y> is quite deﬁnitely not the same pair as <x, x>, since it is determinately true that x is one and the very same thing as itself. It follows that x and y must be distinct. But then it is not vague whether they are identical or distinct.131 This is, I think, a sound argument for something, but one may be misled about what it shows, particularly about identity across time and across possible worlds. In this paper, I will try to get clearer about just what the conclusion of the argument is: about what kinds of semantic indeterminacy it excludes, and what kinds it permits. The ﬁrst point to make is that the argument does not show, and does not pretend to show, that identity statements cannot be vague. It is clear that if there is any semantic indeterminacy in the language at all, then it will be possible to construct vague identity statements. There are at least two different kinds of cases. First, consider the statement ‘Harry's best friend is Sue’. Suppose that the relation ‘is best friend of ’ is a vague relation, and that it is semantically indeterminate whether it is Sue or George who stands in this relation to Harry. Then the deﬁnite description ‘Harry's best friend’ will be a semantically indeterminate singular term. Harry's best friend is either Sue or George, but there is no fact of the matter about which of the two it is.132 One might be tempted to think that Salmon's argument showed that this kind of indeterminacy is impossible. Following the strategy of the argument, one might reason as follows: it is determinately true that Sue is Sue, and so if it is not determinately true that Sue is Harry's best friend, then the pair

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Salmon (1981: 243). There is a similar argument in Evans (1978: 208). Evans described his argument as an argument against the coherence of the idea of vague objects in the world, but the argument itself is against semantically indeterminate identity statements. Thomason (1982) uses a supervaluation semantics to argue that Evans's argument is fallacious.

132

One could adopt a semantic account of deﬁnite descriptions according to which statements containing vague descriptions were false, rather than neither true nor false. But it would be a mistake to think that Salmon's argument shows that one must adopt such a semantic account.

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<Sue, Sue> is deﬁnitely not the same as the pair <Sue, Harry's best friend>. But if these pairs are deﬁnitely distinct, then Sue is deﬁnitely not Harry's best friend. The fallacy in this argument is in the move from the premiss that a certain relational statement is indeterminate to the conclusion that there is a determinate pair of persons such that it is indeterminate whether they stand in the relation. But of course if it is indeterminate whether Sue is Harry's best friend, then it is indeterminate which pair of persons is denoted by the expression ‘<Sue, Harry's best friend>’. Here is a different kind of example of an indeterminate identity statement, used in several places by Sydney Shoemaker.133 Two multistory structures are connected by a covered passage. Is this one building with two wings, or two connected buildings? Suppose neither the concept of building nor the linguistic practices of the users of this/these building(s) determine an answer. Jones is in room 201 on one side, while Smith is in room 395 on the other side. There is no fact of the matter about whether the building Jones is in is the same as the building Smith is in. Here the indeterminacy does not necessarily derive from a vague deﬁnite description. One might use demonstratives to pick out the building(s) without resolving the ambiguity. (Smith may wonder, ‘is this building the same as that one?’) But in this example, as in the ﬁrst one, the source of the semantic indeterminacy in the identity statement is indeterminacy about what things are being said to be identical.134

133

See, for example, n. 5 in Shoemaker's reply to Swinburne in Shoemaker and Swinburne (1984: 145).

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In the building example, the kind of semantic indeterminacy seems to be ambiguity rather than vagueness since there is a small number of alternative interpretations. But there are also cases with a continuous range of alternative interpretations that look more like cases of vagueness. Consider, for example, the concept of a mountain (cf. Quine 1960: 125 ff. and Hughes 1986). Obviously one could not say, nonarbitrarily, exactly which square inches of territory are parts of a given mountain, and which were parts of the plain or foothills surrounding it. Should we say that it is semantically indeterminate just which precise parcel of land the name ‘Mt Rainier’ refers to, or should we say that this name refers determinately to a vague individual? Some say that the latter description is confused, since vagueness is in the language, not in the world. But it is not clear to me that one description is better than the other, or what hangs on the difference. Intuitively, it does not seem unnatural to say that there are objects with vague boundaries. But if we insist that, say, Mt Rainier is a vague individual, and that the name ‘Mt Rainier’ refers determinately to this individual, we do not thereby commit ourselves to vague identities, Suppose I deﬁne a precise piece of territory whose boundaries are within the range of vagueness of the boundary of Mt Rainier. Call this piece of land ‘M’. Is it false that Mt Rainier = M, or is it indeterminate? If Mt Rainier is a vague individual, then it seems we ought to say ‘false’, since M is not a vague individual, and so cannot be the same thing. On the other hand, if we say that this identity statement is indeterminate, then it seems reasonable to say that it is not determinate whether or not ‘Mt Rainier’ refers to M.We might ask a parallel question about vagueness in the expression of properties. Are there vague properties, or just vague predicates—predicates that indeterminately express one of a range of precise properties? For example, does the predicate ‘is short’ determinately express a vague property, being short, or is it indeterminate which of a range of precise properties, such as being less than 161.3 centimeters tall, it expresses? If we say the latter, then we should say that the statement ‘the property of being short just is the property of being less than 161.3 centimeters tall’ is semantically indeterminate, rather than false.

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Some relational statements may lack a truth-value even when it is clear what things the statement relates. For example, even where it is clear who we are referring to with the name ‘Sam’, and determinate who Sam's father is, there may be no fact of the matter about whether Sam is more successful than his father, What Salmon's argument shows is that this cannot happen with identity. Once it is clear that this is all the argument purports to prove, there should be no controversy about it. Identity is a very simple relation. Its extension (relative to a domain of individuals D) is the set of pairs such that d is a member of D. If there is any question about whether a given pair of individuals is in this set, it obviously must be a question about what pair we are talking about. Salmon gives his argument in the context of a discussion of identity across possible worlds. Suppose we describe, uniquely, a possible table, that exists in some nonactual possible world, and ask whether that table is or is not identical with some particular actual table. Does Salmon's argument show that if there is only one possible table that ﬁts our description, then there must be a fact of the matter about whether or not it is one and the same table as some actual table? Or consider the related issue concerning identity across time: does the argument

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show that there must be a fact of the matter about which ship (if either) is the original ship of Theseus? These are the kinds of examples that have led philosophers to suggest that identity is in some cases vague, and it is this response to the examples that Salmon's argument aims to refute. I will consider some examples that make a prima facie case for vague identity over time, and across possible worlds, asking what Salmon's argument shows about how we must describe such examples. I will begin with a temporal example. In Philadelphia there are two prominent seafood restaurants named ‘Bookbinder's’ that carry on a rather unseemly rivalry. One calls itself ‘Bookbinder's Seafood House’ (‘The Bookbinder's Family serves classic seafood only in Center City’); I will call it ‘B1’. The other describes itself as ‘The old original Bookbinder's’ (‘There is only one’, ‘Imitated⋯never duplicated’); I will call this one ‘B2’. Each lays claim to a tradition going back to 1865 when a single restaurant named ‘Bookbinder's’ was founded. I will call this original restaurant ‘B0’. Now I don't know the historical facts; perhaps one of the two restaurants is really the original, while the other is a new restaurant started later by the descendants of the original family. But it could be that the history is somewhat tangled, with several changes in ownership and location, branches opened, buildings sold, partners or heirs dividing the property. Perhaps—and this is what I will assume—each of the two current restaurants has some legitimate claim to be that restaurant that was founded in 1865. Does Salmon's argument show that there must be facts about the histories of these two restaurants that determine which of the two is the original, or that determine that neither of the two presently existing restaurants is the original? It is clearly false that B1 = B2, and so, because of the transitivity of identity, it cannot be that both B0 = B1 and B0 = B2, but there is some temptation to say, given the historical assumptions I am making, that these latter two identity claims are semantically indeterminate. Can we reconcile this temptation with Salmon's argument? I want to suggest that we can. In deﬁning my notation for describing the example, I said that B0 is the original restaurant. There are at least two ways to take this stipulation. On the most natural way to take it, a description is used to pick out a restaurant in 1865. ‘B0’ reaches back to that time, referring directly to a certain restaurant existing then. But we might instead understand the stipulation as saying that ‘B0’ is to be the name of a certain presently existing restaurant, the one that has a certain historical property. B0 is the one of the two presently existing restaurants called ‘Bookbinder's’ that has the property, was founded in 1865. On the second way of understanding the stipulation, the example resembles the vague deﬁnite description case. ‘B0’ is an ambiguous name, since its reference was ﬁxed by an ambiguous deﬁnite description. It is indeterminate which restaurant, B1 or B2, has the historical property was founded in 1865, and so it is indeterminate whether the name ‘B0’ refers to B1 or to B2. But on the ﬁrst way of understanding the stipulation, ‘B0’ seems to have a determinate referent since (it seems) in 1865 there was only one restaurant named ‘Bookbinder's’. If a Philadelphian had said, in 1865, ‘Let's have dinner at Bookbinder's’, he would, it seems, have referred unambiguously; ‘B0’ names the restaurant that he would have named. It seems also clear that ‘B1’ and ‘B2’ are unambiguous. So, given Salmon's argument, how can it be indeterminate whether B0 = B2? The answer to this question will depend on how we understand continuant things: persons, physical objects, and institutions such as restaurants that exist through time. One kind of account is this: continuant things are fourdimensional objects, things with temporal as well as spatial parts, things that are extended in time in the same way that they are extended in space. To use the technical jargon, they perdure rather than endure. If we understand continuant things in this way, then the restaurant example will be just like the building example. When I say ‘this building’, it is indeterminate whether I refer to a larger or a smaller structure, and the indeterminacy is explained in terms of an indeterminacy in the general concept of a building. It is indeterminate whether the larger structure is one building or two, and whether the smaller structure is a whole building or merely a part of one. In the same way, there are two temporally extended restaurant-like objects, each containing a common temporal part—the part that existed in 1865 and for some time after. But it is indeterminate which of these things is a restaurant, and which is a composite of two temporal parts

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of different restaurants. For this reason, it is indeterminate which of these entities ‘B0’ refers to. It might appear that we have succeeded in referring to a determinate thing with ‘B0’ since it is determinately true (true on both ways of understanding the concept of restaurant) that there was, in 1865, exactly one restaurant in Philadelphia named ‘Bookbinder's’. Similarly, it might appear that I have referred to a determinate thing when I said ‘this building’, since on either of the two construals of the concept of building I was in exactly one building (I was not straddling two buildings). But it is clear (assuming this conception of a continuant thing) that this appearance of determinacy is an illusion. I think this is a satisfactory explanation of the indeterminacy of reference in the restaurant example, assuming that it is right to think of persons, physical objects, and restaurants as this kind of four-dimensional object. But some will protest that this is just not what such things are. They will insist that continuant things, unlike events or lives, don't have temporal parts. They exist through time, but are wholly present at each time. It is not entirely clear what this protest amounts to—some philosophers would complain that it makes no sense, since to persist through time just is to have temporal parts.135 But even if this is a dark doctrine, difﬁcult to make sense of, there is some intuitive inclination to assent to it. I don't want either to defend or to criticize the doctrine that continuant things are wholly present at each time at which they exist, nor will I try to explain what it means. But I will consider whether, if we assume that sense can be made of it, and that it is correct, we will have a harder time explaining prima-facie cases of vague identity as cases of indeterminacy of reference. The proponent of this conception of enduring objects might argue as follows: First, consider the domain of restaurants that existed in Philadelphia in 1865. There is only one named ‘Bookbinder's’. It is the one we are calling ‘B0’. Not only are there no other restaurants that are candidates to be the referent of this name, there are (on this way of understanding enduring objects) no other restaurant-like entities—entities that would be correctly called ‘restaurants’ on some different way of disambiguating the term ‘restaurant’—that are candidates to be referents of the name ‘B0’. For even if our ‘criteria of identity’ for restaurants are indeterminate, this can't affect the domain of things that are restaurants at a given time,

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David Lewis, for example, argues that the only way to make sense of the dark saying (continuant things don't have temporal parts—they persist through time, but are wholly present at each time) is to assume that its defender is using the concepts part and whole in a restricted way, to exclude temporal parts. See Lewis (1986a : 203). But this cannot be quite right, since the defender of this conception of continuant things will grant that some kinds of things—football games, wars, eras, and centuries—can have temporal parts.

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since the restaurants that exist at that time are wholly present then. So it seems that we have achieved determinate reference to a particular enduring thing. Now consider the domain of restaurants that exist in Philadelphia today. There is just one that we are calling ‘B1’ and it is clear which one it is. Again, we seem to have determinate reference. So if we accept the validity of Salmon's argument, it seems that there must be a fact of the matter whether the determinate thing B0 is or is not identical with the determinate thing B1. Against this argument, I will contend that the semantic indeterminacy may be more subtle on the assumptions we are making, but it is still there. To help bring it out, let me ﬁrst consider an argument about a related question concerning identity over time. Consider the proverbial statue and lump of clay out of which it is made. Yesterday, the statue did not exist, although the lump of clay did, so the statue cannot be the lump of clay, even today. The two things have (today) different historical properties: one has the property of having existed yesterday, while the other does not. Notice that this familiar argument does not require that we think of the statue and the lump as four-dimensional things, only parts of which exist today. Even if we insist that (in some sense to be explained) both the statue and the lump are wholly present now, the argument still shows that they must be (now) distinct. The argument does not depend on claiming that the two things have different parts; it requires only that they have different historical properties. Now consider again the restaurants. Suppose that the concept of restaurant is indeterminate in that it is indeterminate what counts as the same restaurant at different times (as a concept would be indeterminate if it were indeterminate whether it picked out statues or lumps of clay). On some ways of arbitrarily reﬁning our concept, B0 will become B1, and on others B0 will become B2. So on some disambiguations, B0 had (in 1865) temporal properties (for example, being such that it will be located in Center City in 121 years) that B0 lacked on other disambiguations. The referent of ‘B0’ will thus depend on how we disambiguate, and so will be indeterminate. I recognize that in giving this argument I am supposing things that Salmon regards as incoherent, but I don't think I am begging any questions. What is at issue is whether Salmon's argument shows that what I am supposing is incoherent. My argument is that what I am supposing commits me to indeterminacy of reference, and not to indeterminacy of identity between determinate objects. But Salmon's argument refutes only the latter commitment. Salmon's argument shows us that if we succeed in picking out entities, of any kind, a and b, there must be a fact of the matter whether a and b are one thing or two. Or to put it contrapositively, the argument shows that if it is indeterminate whether a = b, then it is indeterminate what ‘a’ refers to,

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or what ‘b’ refers to. This simple abstract argument cannot, by itself, give us reason to think that the facts, together with our conceptual resources, must decide the question whether a given identity statement is true. All it tells us is that if the facts and our concepts do not decide the question, then it is undetermined what the terms in the identity statement are referring to. Imagine someone who responded to the building example this way: ‘I am perfectly clear what buildings I am referring to: I am referring to this one, and to that one (pointing to the other structure). So, because of Salmon's argument, I conclude that our concept of a building must determine an answer to the question whether this building is that one.’ This is obviously not a reasonable response. The building case is a prima facie case of indeterminate identity, and what Salmon's argument shows is that a prima facie case of indeterminate identity just is a prima facie case of indeterminacy of reference. Our problem is to explain the source of the indeterminacy. The cases of identity over time show that the indeterminacy of reference can be of a subtle kind. Just as we can distinguish intimately related things such as an artifact and what it is made of, a person and his or her body, by distinguishing their temporal properties, so we can distinguish subtly different potential referents of indeterminate terms by distinguishing their temporal properties. But while Salmon's argument can force us to recognize such subtle indeterminacies, it cannot make a plausible case that our conceptual resources must be doing more work than they seem to be doing. I want to conclude by commenting, more brieﬂy, about what Salmon's argument has to say about prima facie cases of indeterminate identity across possible worlds. There are strategies here that parallel those available to reconcile the phenomena about identity through time with the argument, but there are also some signiﬁcant differences. Strategies that are plausible in one context may be implausible in the other. I will begin by sketching an example—the example from Saul Kripke's Naming and Necessity that provided the context for Salmon's argument—and then discuss four contrasts between the case of identity through time and the case of identity across possible worlds. Suppose we consider a particular counterfactual variation on the history of the molecules that constitute some actual table—call it T. ‘One may ask whether T would exist, in that situation, or whether a certain bunch of molecules, which in that situation would constitute a table, constitute the very same table T. ⋯[I]n some cases the answer may be indeterminate.’136 The molecules that constitute the table, at least at its beginning, must be substantially the same as those that constitute the actual table if the counterfactual table is to be the actual table, but presumably they need not be exactly the same molecules. If this is right, there will surely be borderline cases. That is, surely there will be a possible world at which there exists a

136

Kripke (1972: 50–1).

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table whose origin and constitution in that world makes it indeterminate whether or not it is numerically the same as the actual table T. How is this to be reconciled with the argument? Our thesis is that where there is indeterminacy of identity there is indeterminacy of reference, but in this kind of case, where is the indeterminacy of reference? In answering this question, we cannot follow the temporal analogy too closely; there are a number of contrasts. First, while there is some plausibility to the conception of continuant objects as four-dimensional things, with temporal parts, there is no plausibility to the corresponding conception of objects and persons as spread out across possible worlds, existing only partly in each one. On such a conception, we would have to say that only a small part of our table is actual; most of it is merely possible. If we are to distinguish potential referents of the terms we use to talk about tables, we will have to do it in terms of their contrasting modal properties, and not in terms of their contrasting parts. Second, while it is not entirely unnatural to distinguish things (such as statues and hunks of clay) solely by their historical properties, and so to distinguish potential referents in terms in this way, it is much more artiﬁcial, at least in some cases, to distinguish things solely by their modal properties.137 Consider, not Bookbinder's, but Turback's, a restaurant in Ithaca with a shorter and less checkered history: continuous management and the same location since its beginning. But of course Turback's might have had a history similar to Bookbinder's. Does this counterfactual possibility, in which there would exist restaurants that are neither determinately identical to Turback's nor determinately distinct from it, force us to say that our actual references to Turback's, in ordinary statements about it, are indeterminate? We should hope that it does not. Third, there is an option open to us in the cross-world case that does not parallel any available in the temporal cases. We can attribute the indeterminacy to the fact that we have not picked out a single possible world, but only a set of them. One might say that if specifying the identity and arrangement of the molecules in a given possible world does not determine whether the table that those molecules constitute is this very table, then it is open to us to decide whether it is or not. In so deciding, we are making a further stipulation about which possible world we choose to describe. But there are at least two problems with this strategy. First, as Salmon brings out in his discussion, we can make this move only if we reject a very plausible supervenience assumption: the assumption that the totality of facts about the molecular constituents of the world determines all the facts

137

Allan Gibbard, discussing a cross-world version of the statue–lump of clay example, allows that one may distinguish things from what they are made of by their different temporal properties, but argues that if the statue and the lump of clay coincide throughout their history, they will be contingently identical. Apparently he ﬁnds it less plausible to distinguish things by their modal properties. See Gibbard (1975).

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about physical objects. If we use this strategy to eliminate the cross-world indeterminacy, we have to distinguish not just possible worlds that are qualitatively indiscernible, but worlds that are constituted by numerically identical components arranged in exactly the same ways throughout their histories. Two such indiscernible worlds might differ only in this way: in one of them, a certain table is this table, while in the other the corresponding table (made in the same way of the same molecules) is not this table. Even if we were willing to reject the supervenience assumption, there is a second problem with this response. Presumably, the reason we are inclined to say that it is indeterminate whether the possible world we describe is one in which table T exists is that we are inclined to say that it is indeterminate whether it is possible for this table to have that origin and constitution. But if we solve the problem of indeterminacy by proliferating possibilities, we will have to conclude that it is determinately possible for the table to have that origin and constitution.138 Finally, if we are actualists, but not presentists, we must keep in mind the following contrast between the temporal and the worldly cases, a contrast that may underlie all the others. Past times are parts of reality on a par with our own time, but other possible ‘worlds’ are just alternative ways that the one world there is might have been. We can refer directly across time to a past thing by interacting with the thing as it was then, since causal relations are relations that hold across time. But reference to ‘things’ in other possible worlds is really just a way of talking about the potentialities of things in the actual world. The only things there are, of any kind, are the actual things. What it is for some actual thing to exist in the domain of some alternative possible world is for that possible world to represent that actual thing as existing, and being some particular way. Questions about whether some thing in the domain of a counterfactual world is identical to some particular actual thing are questions about whether a certain representation is a representation of that actual thing. This relation—the relation between a representation and what it represents—is not the identity relation, and it, unlike identity, may be vague even if it is clear what the relata are. Exactly how does this actualist interpretation of the possible worlds rhetoric help us to reconcile Salmon's argument with Kripke's example? Suppose that T is a determinate table, and that we have got hold of a particular possible world—call it w—that contains a single table—call it T′—with the sort of origin and composition to make it indeterminate whether it is the

138

Salmon's solution to the problem is to allow that the world at which the table with the problematic origin and constitution is this table may be an impossible world—a world that is inaccessible to the actual world. Or, perhaps the accessibility relation is vague, in which case it is indeterminate whether this world is possible or impossible (relative to the actual world). Salmon also seems to think that his solution is compatible with the supervenience assumption, since there cannot be two distinct possible worlds (relative to any world) that are indiscernible on the molecular level. See Salmon (1981: app. I).

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same table as T. So, it would seem, ‘T = T′’ is indeterminate, yet it also seems that both T and T′ have determinate reference. But ﬁrst, we must keep in mind that the question whether ‘T = T′’ is true, false, or indeterminate is the question whether it is true, false, or indeterminate in the actual world, since for the actualist, truth and falsity are the same as actual truth and falsity. So our two names, if they succeed in picking out tables, will do so in quite different ways. ‘T’ names a table unproblematically, but if ‘T′’ names a table (an actual table) and not just a table-representation, it will have to do so in virtue of some relation between a table-representation expressed by ‘T′’ and a table. The question is, does T have, in the actual world, the modal property ‘would be T′ if w were actual’? This question depends on whether the tablerepresentation, T′, which is a feature or component of the possible state of the world w, stands in a certain relation—a relation that is obviously not identity—to the table T. If it does, then ‘T′’ denotes, in the actual world, T, and so the identity statement is true. But if it is indeterminate whether T has this modal property, then the name ‘T′’ is indeterminate, in the actual world, and so the identity statement can be indeterminate without conﬂicting with Salmon's argument. ‘T′’ may appear to be determinate because it picks out a determinate table in w. But this is only to say that if w were actual, the table-representation T′ would represent a unique table.139 Identity is often confused with other relations—composition, genidentity, unity, counterparthood—and when it is, discussions of identity may be discussions of interesting metaphysical questions. But identity itself is a very simple and a very abstract relation. There are no limits on its domain of application: restaurants and rivers, nations and numbers, persons, pigs, pictures, powers, possibilities, and propositions are all things that, if they exist at all, are identical to themselves, and to nothing else. If we are not clear what we are talking about, it may be unclear whether a statement that ascribes this relation is true, but the relation itself is unproblematic and uninteresting. That some entity stands in this relation to itself says nothing

139

In a footnote commenting on this example, and the general problem of the vagueness of cross-world identity, Kripke suggested that ‘some sort of “counterpart” notion (though not with Lewis's philosophical underpinnings of resemblance, foreign country worlds, etc.), may have some utility here’ (Kripke 1972: 51, n. 18). I think this is right, and I have tried to motivate such an application of counterpart theory in Ch. 6. The focus there is on contingent identity statements rather than vague identity statements. It is important to keep in mind that the relevant counterpart relation is not a weaker relation between things that some take to be identical (like, say, the relation of composition between a substance and what it is made of). The counterpart relation holds between representations rather than between the things represented. Very roughly, the idea is this: if representation a is a counterpart of representation b, then the thing represented by a is identical with the thing represented by b. The counterpart relation can be vague, and intransitive, even though the identity relation can be neither. See also Forbes (1984) for a defense of the application of counterpart theory to these problems.

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about the nature of the entity, and so one should be suspicious of any argument that purports to get substantive metaphysical conclusions out of the logic of identity—conclusions about what kinds of things there can be in the world, or about what the things that are there must be like.140

140

In thinking about these issues, I have beneﬁted from correspondence and conversation with a number of people, including Hugh Chandler, Graeme Forbes, Christopher Hughes, Nathan Salmon, Sydney Shoemaker, and Peter van Inwagen.

8 The Interaction of Modality with Quantication and Identity (1994) 1. Introduction One might once have hoped that an adequate quantiﬁed modal logic could be obtained simply by putting propositional modal logic together with the extensional theory of quantiﬁcation and identity. One might have expected, on the one hand, that the sentences and schemata valid in the separate theories should remain valid when each was generalized by being combined with the other, and one might have hoped, on the other hand, that any new validities that depended on the interaction of modal and quantiﬁcational concepts would be derivable from the axioms and rules of the separate logics for these concepts. But it did not happen that way. The increase in expressive power gained by combining the two languages cast doubt on familiar logical principles such as Leibniz's law and existential generalization, and raised new questions about the logical status of sentences in which modality and quantiﬁcation were combined. The development of a semantics for the combined languages required decisions in response to questions not raised by either of the separate theories, for example questions about the relationship between the domains of individuals relative to which the quantiﬁers are interpreted and the domains of possible worlds relative to which the modal operators are interpreted. These questions, and the arguments about how to answer them, helped to clarify the concepts involved in both theories—the nature of variable binding, quantiﬁcation and identity, and of the possible worlds used to interpret modality. Ruth Barcan Marcus was one of the ﬁrst to explore the issues concerning the interaction of modality and quantiﬁcation, and the formulas named for her—the Barcan formula and its converse—are the most prominent examples of principles that make general claims that depend essentially on the interaction of modality and quantiﬁcation. Her discussions of the logical status of these principles, and of other principles in which modal and extensional concepts interact such as the necessity of identity, helped to clarify the conceptual foundations of quantiﬁed modal logic.141 My aim in this paper is to continue

141

See Barcan (1946), where a version of the Barcan formula is introduced, and Marcus (1963) for a discussion of the necessity of identity.

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this kind of discussion by looking at two other logical principles that combine modality with quantiﬁcation and with identity: ﬁrst, a weaker version of the converse Barcan formula, and second, the principle of the necessity, not of identity, but of distinctness. I will show, ﬁrst, that while each of these principles is validated by a very natural and very general semantic theory, they are each independent principles—not derivable in a theory that results from combining complete axiomatizations of extensional predicate logic and propositional modal logic. I will argue that there are conceptual assumptions that lie behind and help to explain the independence of these principles, and a semantics with some conceptual interest that invalidates them. To sharpen the focus on the problems that arise from the interaction of quantiﬁers with modality, I will begin by sketching and motivating the separate modules—semantics and proof theory ﬁrst for extensional quantiﬁcation theory and then for propositional modal logic—before putting them together. My aim is to try to make the generalization that results from combining them as smooth and natural as possible, and to ensure that our logics of predication, quantiﬁcation and identity do not include principles that have to be taken back when the expressive power of the language is increased. After sketching semantics and proof theory for the separate theories and putting them together, I will introduce and discuss the qualiﬁed converse Barcan formula. While it will be obvious that this principle is valid in the standard semantics, I will show that it is an independent principle by sketching a variant semantics—a version of counterpart theory—that invalidates it while validating the rest of the logic. Finally, I will look at the interaction of modality with identity, showing that the necessity of distinctness is also an independent principle, even in a theory that includes the qualiﬁed converse Barcan formula.

2. Extensional predicate logic Our extensional theory is a ﬁrst-order predicate logic with primitive singular terms and identity. The semantics is standard in most respects, but it has two features that distinguish it from more familiar formulations of predicate logic: ﬁrst, it has a variable-binding abstraction operator; second, it is a free logic, allowing that the domain may be empty, and that singular terms may fail to denote. The syntax and semantics for the language are spelled out in an appendix. I will here just make a brief comment about each of these idiosyncrasies. First, on abstraction. The only primitive variable binding operator in our language is the abstraction operator for deﬁning complex predicates. The quantiﬁers do not bind variables, but are operators on one-place predicates. This is not the usual way to formulate ﬁrst-order predicate logic, but it is a minor variation on the usual procedure that gives the same

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truth-conditions to quantiﬁed sentences, and that uses exactly the same Tarskian device: open sentences are interpreted in terms of satisfaction by a sequence rather than truth, and expressions with bound variables are interpreted in terms of satisfaction by certain variant sequences. But while the variable-binding device used in our semantics is essentially the same as the one standardly used, I think the formulation I will use gives a clearer representation of the logic of quantiﬁcation because it separates two conceptually distinct operations that are performed by variable-binding quantiﬁers: ﬁrst, the implicit formation of complex predicates from complex sentences by introducing blanks—free variables—in the sentences; second, generalization: the formation of general claims from predicates—the claims that everything in the domain, or at least one thing in the domain, satisﬁes the predicate that is implicitly represented by the open sentence. In our language, the abstraction operator makes the ﬁrst of these operations explicit, turning an open sentence into an expression that has the syntactic role as well as the semantic function of a predicate. Then the quantiﬁer has only the job of expressing generality.142 So rather than a rule for the universal quantiﬁer like this:143

we have the following two rules, which together achieve the same effect:

Second, a comment on free logic. The models for our language, like those in the classical extensional semantics, are pairs where D is a set—the domain—and ν is a function assigning values to the primitive descriptive expressions—the sentence letters, predicates, and individual constants. The only difference is that the domain D may be empty, and individual constants may lack values. That is, the valuation function ν may be a partial function, undeﬁned for some individual constants (although it must be deﬁned for all predicates and sentence letters). To interpret sentences containing nonreferring names, a semantic decision must be made. Our theory makes the simplest decision: sentences of the form Ft (or more generally of the form Rt1⋯tn) are false if t (or any of t1,⋯, tn) is undeﬁned. Some might have preferred a different decision (for example, stipulating that such

142

In Stalnaker (1977), I argued in more detail for the conceptual advantages of this way of formulating extensional predicate logic.

143

s is a function assigning values (members of the domain) to the variables, or equivalently, a sequence of members of the domain. ‘s [d /x ]’ denotes the function that is everywhere like s, except that the variable x is assigned the value d.

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sentences are neither true nor false, rather than false), but there is nothing here to argue about, so long as one avoids equivocation.144 The semantics for identity in our theory is perfectly standard: identity is the binary relation that is satisﬁed by every pair such that d is a member of the domain. But since names may fail to refer, and since predication sentences with nonreferring terms are stipulated to be false, some identity theses normally assumed to be valid will be invalid, for example, . But the universal generalization of this, , will of course be valid, since the property of being self-identical must be true of everything. Both of the idiosyncratic features of our extensional predicate logic are included in anticipation of the modal generalization in which the problems they address require attention. The abstraction operator provides the resources to express modal properties and to make scope distinctions that involve modality and predication, but not quantiﬁcation. The elimination of existential presuppositions makes room for the possibility that individuals not exist necessarily by providing for the interpretation of sentences containing singular terms that have no referent in the domain of the possible world in which they are being interpreted. But even though the theory has features that are motivated by the modal generalization, the language, logic, and semantics remain purely extensional. Here is a complete axiomatization of this version of free predicate logic: Axiom schemata:Any closed sentence that is an instance of one of the following forms is an axiom. Propositional logic: All (closed) tautologous sentences are axioms

145

144

The truth-value gap decision would require additional decisions about the interpretation of complex sentences containing sentential components that lack truth-values. This is the reason that our decision is the simpler, and more conservative one. A second alternative decision, sometimes taken in semantics for free logic, would require adding resources to the semantic structure relative to which the sentences are interpreted. This is the Meinongian decision: to add an outer domain of nonexistent individuals, or perhaps a single arbitrary virtual individual that is outside of the domain, to be the referents or referent of singular terms that do not refer to any existent thing. The nonexistent individuals or individual might or might not be in the extension of any predicate.

145

denotes the result of substituting x for all free occurrences of y in ϕ (relettering bound variables in ϕ if necessary to ensure that all new occurrences of x in are free). ‘x ’ and ‘y ’ are to be understood as schematic metavariables ranging over the variables of the object language.

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146

147

Rules:

Most of these axioms and rules will be familiar (at least if one ignores the in expressions of the form . ‘ϕ’ stands for any sentence, open or closed, ‘F’ for any one-place predicate, ‘F n’ for any n-place predicate, ‘s’ and ‘ti’ for any singular terms (individual constants or variables), ‘x’ and ‘y’ for any individual variables. One-place predicates may be simple or complex, open or closed, but one cannot treat sentences generally as predications. For example, ‘ ’ is an instance of the form Fs, but ‘ ’ is not. The identity axiom schema is thus much more restricted than Leibniz's law as usually formulated. All instances in the extensional language of the general schema, , will be theorems of the extensional logic, but they are not instances of the identity axiom schema. The validity of the general schema, unlike the validity of the identity axioms, depends on the expressive limitations of the extensional theory, and when the language is enriched, some new instances of it will not be theorems.

3. Propositional modal logic The propositional modal language is a perfectly standard one with sentence letters, truth-functional connectives, and one modal operator ‘ V’ for necessity. The semantics is the standard Kripke semantics: a model consists of a frame or model structure, , where W is a nonempty set of possible worlds and R is a binary relation (the accessibility relation) on them—and a valuation function v that assigns truth-values (1 or 0) to the sentence letters at each of the possible worlds. This modal semantics is a generalization of extensional semantics, doing for many possible worlds at once what the extensional semantics does for one world—the actual world. Since the extensional semantics assigns truth-values to sentences, the modal generalization assigns truth-values to sentences at each possible world. The same rules for the truth-functional connectives give truth-values for complex sentences

146

This axiom, necessary to tie up a small loose end, is nonredundant only for the case where F is a primitive predicate.

147

Identity theory usually needs an additional axiom—the reﬂexivity of identity, terms of identity, this principle is a theorem.

. But because of the existence axiom, and the way existence is deﬁned in

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at each possible world as a function of the truth-values at the worlds of their parts. Necessity is truth in all accessible possible worlds. That is, is true in w iff is true in all possible worlds accessible to w. ( iff for all u such that wRu) In the most general version of this semantics, no constraints are put on the accessibility relation relative to which the necessity operator is interpreted. The logic validated by this minimal semantics, K is as follows: Axiom schemata:⊢ All tautologous sentences are axioms

Rules:

4. Combining the theories The basic idea of the modal semantics provides a way to generalize any extensional theory to a modal version of that theory. Whatever the extensional semantics does to deﬁne the extensions of complex expressions as a function of the extensions of their parts, just do the same for many possible worlds at once. Whatever an extension is according to the relevant extensional theory, let an intension in the modal generalization of that theory be a function from possible worlds into extensions. So to combine our two separate theories, we need models that provide a set of possible worlds and for each world, whatever the extensional semantics provided. In our extensional semantics for predicate logic, a model is a domain of individuals and a valuation function that assigns extensions to the primitive descriptive expressions: truthvalues, members of the domain, and sets of n-tuples of members of the domain to the sentence letters, individual constants, and n-place predicates, respectively. So the models in the modal semantics should assign to each possible world a domain, and to the sentence letters, individual constants and n-place predicates, functions from possible worlds to, respectively, truth-values, members of the domain of the world, and sets of n-tuples of members of that domain. That is, a model for modal predicate logic is a quadruple, . W and R are the same as in the semantics for propositional modal logic; D is the domain function from W into sets of individuals. For is the domain of possible world w. The valuation function assigns intensions to the descriptive expressions, where an intension is a function from possible worlds into extensions, and extensions are as deﬁned in the extensional semantics. The semantic rule for the necessity operator remains exactly the

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same, and the rules for the logical expressions of the predicate logic are straightforward generalizations of the extensional rules: just add a subscript ‘w’ to the v's and D's in each rule. For example, the rule for universal generalizations is as follows:

The only place where the generalization from extensions to intensions is not perfectly straightforward is with the interpretation of open sentences in terms of an assignment function.148 In the extensional theory, the assignment function assigns values—individuals—to the variables. In the modal generalization, it should still be individuals (and not, say, functions from possible worlds into individuals) that are the values of variables, since open sentences are devices for the formation of complex predicates that express properties of individuals, and not properties of some kind of intension. So in the semantics for the modal predicate logic, the assignment function is a function from variables into possible individuals, where a possible individual is a member of the domain of some possible world. The semantic rule for the abstraction operator is then a straightforward generalization of the extensional rule, obtained as with the other rules simply by adding a subscript for the world to the v and the D:

The axiomatizations for the separate theories remain sound relative to this generalized semantics: we don't have to take anything back. But we do not get completeness for the proof theory that is the result of simply combining the rules and axiom schemata of the separate theories. It is interesting, I think, to consider why not.

5. A variation on the Barcan formula The Barcan formula and its converse are principles that express claims that involve the interaction of the universal quantiﬁer with the necessity operator.

It was for a long time unclear whether these principles were provable from unassailable logical principles, and whether they ought to be theorems

148

One might think of the situation this way: the Tarskian semantics for quantiﬁcation generalizes truth simpliciter to satisfaction (that is, to truth of a sequence of individuals, or truth relative to an assignment). Kripkean modal semantics generalizes truth simpliciter to truth at a world. The problem of semantics for quantiﬁed modal logic is to ﬁt the two generalizations together to get truth relative to an assignment at a world (or truth at a world, relative to an assignment).

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of an adequate quantiﬁed modal logic. But Kripke's semantics made clear exactly what semantic assumptions were required to validate the principles, and he diagnosed the fallacy in proofs that purported to deduce them from premisses that did not make the required assumptions.149 Both principles are valid only if one makes assumptions about the relations between the accessibility relation and the domains. Speciﬁcally, BF is valid if it is assumed that whenever , and CBF is valid if it is assumed that whenever . Neither assumption seems intuitively motivated in general, although either or both might be plausible in some particular application, or with some particular interpretation of the accessibility relation. But the following qualiﬁed version of CBF does seem to be validated without any assumptions about the relationships between the domains of the different possible worlds:

where ‘E’ is the predicate of existence (deﬁned as ). Whatever the relations between the domains, surely if in w it is necessary that everything satisﬁes , then anything that exists in w must satisfy in every accessible possible world in which that individual exists. It is a straightforward matter to show that QCBF is valid in the semantics sketched above, but it is not a theorem. To show that it is not, I will construct a variant semantics which validates the axioms and rules of the theory, but in which QCBF is invalid. After sketching the variant semantics and the counterexample in it to QCBF, I will consider whether the nonstandard semantics might have some conceptual interest beyond its use as a technical device to prove independence. The variant semantics makes a different decision at the place where the modal generalization was least natural: the interpretation of free variables and open sentences. The central idea of the modal generalization (that modal semantics does for many worlds at once whatever the extensional semantics does for one world) did not give clear directions about how to handle the interpretation of free variables in the general theory, and it put no constraints on the relationships between the individuals in the different domains. Suppose we begin by assuming that the domains are disjoint, where this is motivated not by the substantive assumption that individuals could not possibly exist while being different in any way, but instead by the assumption that the entities in the domains are not individuals themselves, but world-slices, analogous to time slices, individuals-at-a-world. Even if Socrates might have been hooknosed, and so exists and is hooknosed in some counterfactual world c, it remains true (by deﬁnition) that the entity, Socrates-as-he-isin-this-world manifests itself only in this world. Set aside for the moment your worries about whether there really are any such things

149

Kripke (1963).

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as Socrates-as-he-is-in-@, and assume that it is entities of this kind that, according to our variant semantics, populate the domains of the possible worlds. Now when we ask whether Socrates (or Socrates-as-he-is-in-@) has, in @ (the actual world), the modal property being possibly hooknosed, we still want the answer to be yes. Even though (according to the story I am trying to tell) it isn't Socrates-in-@ who is the hooknosed member of the domain of the counterfactual world c, it is still Socrates-in-@ who has, in @, the modal property of being possibly hooknosed. ‘He’ has this property in virtue of his relation to the individual—his counterpart, Socrates-in-c—who, in c, is hooknosed.150 Our variant semantics, then, assumes that the domains are disjoint, and that the modal properties of the world-bound individuals that populate the domains are determined by a counterpart function that takes a possible world into the counterpart (if any) of the individual. Our version of counterpart theory is conservative (as counterpart theories go) in the following sense: it is assumed that an individual can have at most one counterpart in any possible world.151 But the counterpart relation is not just a mirror of the identity relation. We do not assume that it is symmetric or transitive. My counterpart's counterparts need not be mine, and I need not be my counterpart's counterpart. More explicitly, we add to the semantics, along with the requirement that the domains be disjoint, a partial function f that takes possible individuals and worlds into possible individuals. The only restrictions are that if ,(every individual is its own counterpart in its own world), and that if is deﬁned, then . (Any counterpart in a world must be in the domain of that world.) Surprisingly, this variation requires only one small and localized change in the semantic rules, a change in the rule assigning values to the variables. The original rule was this:

150

Counterpart theory was invented by David Lewis, though his version of the theory differs both in intuitive interpretation and in technical detail from the one I am using here. The motivation for Lewis's theory is connected with his modal realism; the worldbound individuals that populate the domains of the possible worlds are ordinary individuals. And Lewis does not assume, as I do, that an individual may have at most one counterpart in any possible world. See Lewis (1968), and for a more philosophical discussion in the context of a defense of modal realism, Lewis (1986a: ch.4. See also Hazen (1979).For a philosophical discussion of the actualist interpretation of counterpart theory, see Ch. 6 of this book.

151

The theory can accommodate a counterpart relation that allows multiple counterparts in a single world by representing such a relation by a set of counterpart functions, and letting the semantics be indeterminate between them. If, for example, London has two counterparts, one pretty and one not, in a certain possible world, then if ‘F ’ expresses the property of being pretty, it will be semantically indeterminate whether Fx is true or false in that world, relative to the assignment of London to x. In general, sentences will be determinately true (false) if and only if they are true (false) for all admissible ways of arbitrarily resolving the indeterminacy (cf. Ch. 6, pp. 130–1).

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The corresponding rule in the variant semantics is this:

The assignment function, as before, assigns possible individuals to the variables, but the extension of a variable at a world is the counterpart of the individual that is the value of the variable. With all of the other rules, including the rule for complex predicates, remaining the same, this gets us the result we want: Socrates will have the property of being possibly hooknosed if he has a counterpart who is hooknosed in some accessible possible world. Because the change in the semantics is so small, and because it does not affect either the semantic rule for the modal operator or any of the rules that concern the relationships between extensions within a possible world, it is easy to check that all of the axioms and rules of inference of the combined modal predicate logic are valid in the variant semantics. All that remains to be done to show the independence of QCBF is to give a countermodel, in the variant semantics, for an instance of that schema. The instance of the schema to be falsiﬁed is this:

Here is the model: there two possible worlds, α and β, which are accessible to themselves and each other. and and . (That is, 3 is 1's counterpart in β, and 2 is 3's counterpart in α) , and . In α, since 1 satisﬁes Fx and 2 satisﬁes Gx, and so àGx, it follows that is true in α. In β, the only individual, 3, has a counterpart in α that satisﬁes Gx, so it satisﬁes àGx; consequently, in β also, is true. Since is true in both possible worlds, the antecedent of the sentence to be falsiﬁed, is true in α. But the consequent, , is false in α, since 1 does not satisfy the open sentence . Ex is true of 1 in β, since it has a counterpart in β, but Fx is false of 1's counterpart in β, as is àGx, since 1 has no counterpart that satisﬁes Gx. This counterpart semantics makes its technical point—showing the independence of QCBF—whether or not one thinks it has any intuitive application. But I want to suggest that it also makes a conceptual point about the status of this principle. The variant semantics brings to the surface an assumption about the relation between the modal properties of an individual in different possible worlds—an assumption implicit in the standard semantics that is not grounded in the nonmodal logic of predication, or in the modal logic of propositions, or in their combination. The counterpart semantics can be seen as a semantics that is neutral on a question that is

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answered by the standard semantics, since the standard semantics can be seen as a special case of the counterpart semantics, one that is obtained by putting constraints on the counterpart relation. Suppose we impose two additional conditions on the counterpart function:(1)

(2)

. With these conditions, it will follow that the relation that holds between an individual and its counterparts is an equivalence relation. Individuals in the standard semantics can be identiﬁed with equivalence classes of the worldbound individuals in the counterpart semantics, and world-bound individuals in the counterpart semantics can be identiﬁed with individual-world pairs, in the standard semantics. Since there is a version of the counterpart semantics that is equivalent to the standard semantics, the philosopher who makes the standard assumptions about individuals can have no complaint with the semanticist who wishes to formulate the theory in a way that is neutral on a question that is not settled by either the modal logic of propositions or by the logic of predication and quantiﬁcation—a question about the relationship between the modal properties that an individual has in different possible worlds.152 And he cannot legitimately claim that the counterpart theorist is adopting a nonstandard account of predication or quantiﬁcation, since he and the counterpart theorist share the same logic and semantics of predication and quantiﬁcation. The nonstandard conceptions of individuals and their modal properties that the counterpart semantics allows for may not be defensible, but the issue is a philosophical one that cannot be settled by logical theory.

6. Identity and distinctness The standard theory and the counterpart theory do not disagree about the semantics of identity: identity is the relation that holds between anything and itself, and not between anything and anything else. And they agree that identity is an essential relation: for any things x and y that are identical, x and y are essentially identical—identical in all possible worlds in which

152

One way to put the question in dispute, in terms of an example, is this: suppose it is agreed that in the actual world Socrates has the property of being possibly hooknosed, which is to say that there is a possible world in which he is hooknosed. Suppose we agree further that in the world in which Socrates is hooknosed, he has the modal property of being possibly ﬂatfooted. Does it follow that Socrates has, in the actual world, the modal property of being possibly ﬂatfooted—or at least of being possibly possibly ﬂatfooted? The counterpart theorist says that this does not follow without further assumptions that are not grounded in the standard interpretation of ‘possibly’, and the standard assumptions about the way predicates are formed from open sentences.

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that thing exists (or has a counterpart).153 How could it be otherwise? If x is y, then there is only one thing. Not only can't it be distinct from itself, it cannot have a counterpart in any world that is distinct from itself.154 As one would expect for a principle that is valid in the neutral counterpart semantics as well as the standard semantics, the principle of the essentiality of identity:

is provable, using only the identity axiom, the minimal propositional modal logic, and the extensional logic of predication and quantiﬁcation. But a stronger principle, the necessary essentiality of identity:

is not provable in the minimal logic, and not valid in the counterpart semantics. We can make sense, in the counterpart semantics, of a counterexample to this principle, since we can make sense of distinct individuals that might be identical (by having the same counterpart in some world). Suppose worlds α and β are each possible with respect to each other, and that two distinct things in world α, 1 and 2, have the same counterpart, 3, in world β. Then the pair satisﬁes the identity relation in world β, but since 1 exists in world α and is distinct from 2, the pair fails to satisfy in β. So there can be two (distinct) things that might be identical without being essentially identical, which falsiﬁes NEI. NEI is of course valid in the standard semantics, and it can be proved with the help of QCBF.155 But a related principle that is valid in the standard semantics (and not in the counterpart semantics), the necessity of distinctness:

cannot be proved even with the help of QCBF. To show the independence of this principle, I will use a more local semantic variation: a standard

153

The principle of the necessity of identity —fails in both the standard semantics and the counterpart semantics, but only because a thing may exist contingently, and because self-identity, like all properties, entails existence.

154

A thing might, according to the more radical counterpart theorist, have more than one counterpart in some possible world, and so might have counterparts that are distinct from each other. But if (in the actual world) , then there are not two things in the actual world, the x and the y, one with one counterpart and the other with the other. Even in the more radical theory, there will be no pair of things of which is true, but false.

155

Start with the necessitation of EI, use instances of QCBF to move the necessity sign inside the quantiﬁers, and then eliminate the Ex and Ey antecedents, using the existence axiom. (Since , by the existence axiom, follows from .

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interpretation of individuals, but a nonstandard interpretation of the identity relation. It has been noted, by Quine among others, that identity is indistinguishable from indiscernibility.156 If we interpret the identity sign, not as identity, but as indiscernibility,157 then even though distinct things might now stand in the relation expressed by the identity sign, the extensional logic of this relation remains the same. That is, the identity axiom,

, remains valid under this reinterpretation of the meaning of ‘=’. None of the other axiom schemata or rules (with one exception) include the identity sign essentially, so they are unaffected by a change in the interpretation of this predicate. The exception is the existence axiom,

which obviously remains valid when the sign is given the weaker interpretation. So all of our axioms and rules, of both the extensional predicate logic and the propositional modal logic, are validated, as is QCBF. Since EI is a theorem, it must be that the essentiality of indiscernibility is as sound a principle as the essentiality of identity; even the necessary essentiality of indiscernibility must be sound, since NEI can be proved with the help of QCBF. These principles can be seen to be valid: anything that is possibly discernible (or even possibly possibly discernible) is actually discernible, since possibly discernible things can be distinguished by their modal properties. (If a is possibly discernible from b, then a, but not b, actually has the property of being possibly discernible from b.) But the necessity of discernibility, unlike the necessity of distinctness, is not a valid principle. Discernible things are not necessarily discernible, since distinctions present in the actual world may be absent in some accessible possible world.158 Suppose there are two worlds, α and β, β accessible to α, but α not accessible to β. The fact that two individuals were discernible in

156

See, e.g. Quine (1960: 230).

157

More precisely, say that two individuals, a and b, are indiscernible in a possible world w in a model if and only if, for all assignment functions s and all one-place predicates F that have no occurrences of ‘=’ (where F may be simple or complex, open or closed), Then we replace the rule giving the meaning of the identity predicate with the following: and a is indiscernible from b in w }.

158

A counterexample to the necessity of discernibility will require a model with a nonsymmetric accessibility relation, which is what allows distinctions to be lost when one moves to an accessible world. In a semantics for S5, or any semantics that assumes the symmetry of accessibility, the necessity of discernibility will be valid, and the necessity of distinctness will be provable in the appropriate modal logic.

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α would not ensure that they were discernible in β, since what is true in α cannot affect what is true in β. Since (at least in the theory that makes the standard assumptions about the modal properties of individuals), ND is valid when ‘=’ is interpreted as identity, but invalid when it is interpreted as indiscernibility, the combination of identity theory with modality provides the resources to distinguish identity from a weaker relation that cannot be distinguished from it in a nonmodal context. Perhaps this shows that there is in some sense something modal about the concept of identity. This conclusion would not be entirely surprising, since intuitively, one is inclined to distinguish identity from indiscernibility in modal terms. Indiscernibility and discernibility, unlike identity and distinctness, are fragile relations. Distinct but indiscernible things are only accidentally indiscernible, owing this relation to the limitations of our powers, or the power of our language, to discern; and discernibility, unlike distinctness, could be lost if we lost an ability to discern, or if distinguishable things changed to become indistinguishable.

7. Summary and conclusion If we are careful in the way we formulate the extensional logic of predication, quantiﬁcation, and identity, it turns out that we can come close to the original goal of doing quantiﬁed modal logic simply by putting propositional modal logic together with extensional predicate logic and identity theory. We do not have to take anything back when we put the two theories together, but if we do the combined semantics in the usual way, we do have to add two principles that concern the interaction of modality with predication, and modality with identity. These are logical principles that are valid, but that cannot be derived from the logical principles governing the separate notions. If we add just these two principles159 we get a quantiﬁed modal logic that is complete relative to the standard semantics. The assumptions implicit in the standard semantics that account for the validity of these two principles can be identiﬁed, and we can give a semantics that does not make those assumptions, and that is at least formally coherent. In this more neutral semantics for modal predicate logic with identity, the valid sentences are exactly those derivable using the rules and axiom schemata of the separate logics.160

159

The schemata we need are generalized versions of QCBF and ND: where stands for n occurrences of .

160

Our propositional modal logic is K, and the accessibility relation is unconstrained. If our logic were instead D, T, K4, S4, S5, KB, or B, and the accessibility relation were constrained in the appropriate way, the completeness claims would still hold. But there are complete propositional modal logics whose predicate logic extensions are incomplete.

and

,

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APPENDIX This is a speciﬁcation of the language and semantics for the extensional predicate logic.

Syntax Vocabulary The vocabulary consists of three kinds of primitive descriptive expressions: sentence letters, n-place predicates for each n > 0, and individual constants (a denumerable set of each), individual variables (a denumerable set), four syncategorematic logical symbols, ‘∀’, ‘∨’, ‘~’, and ‘̂’, a two-place logical predicate, ‘=’, and parentheses for punctuation. Non-primitive logical symbols, ‘∃’, ‘∨’, ‘→’, ‘⇆’, are to be understood as abbreviations in the usual way. A singular term is either a variable or an individual constant.

Formation rules There are two kinds of complex expressions, sentences and one-place predicates, deﬁned by the following rules: If If If If If

F is an n-place predicate and are singular terms, then ϕ is a sentence, then is a sentence. ϕand Ψ are sentences, then ( ) is a sentence. F is a one-place predicate, then ∀F is a sentence. ϕ is a sentence, then is a one-place predicate.

is a sentence.

Semantics Models and assignment functions A model is a pair , where D is a set, the domain, and v is the valuation function assigning values—extensions—to the primitive descriptive expressions of the language. The domain may be empty, and the valuation function may be a partial function, assigning no values to some singular terms (though it must be fully deﬁned for all sentence letters and predicates). The extension of a sentence letter is a truth-value: 1 or 0; the extension of an n-place predicate is a set of n-tuples of members of D; the extension of an individual constant, if it has one, is a member of D. Well-formed expressions in general, including both open and closed sentences and predicatfes—receive values in a model relative to an assignment of values to the variables. The closed sentences and predicates receive the same value for all assignments of values to the variables. An assignment function, s, is a partial function from the set of individual variables into the domain. (If the domain is empty, the only assignment function will be the one that is undeﬁned for all values.) If s is an assignment function, then takes the value d.

is the assignment function that is everywhere like s, except that for x it

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159

The syncategorematic logical symbols are interpreted by the semantic rules, but there is one logical symbol that is a predicate and gets assigned an extension: the identity sign, ‘=’, is a two-place predicate whose value, for all valuation functions, is given as follows: . Since identity is a two-place predicate, uniform formation rules for atomic sentences imply that identity sentences have the form ‘ ’ but, bowing to tradition, we will abbreviate them in the usual way: ‘ ’.

Semantic rules The semantic rules extend the valuation function to give values, relative to an assignment function, to the complex expressions—one-place predicates and sentences. If v is the valuation function and s the assignment function, then vs is the function that assigns values relative to the assignment function. If x is a variable, . If φ is a primitive descriptive expression, then . The rules are as follows: Sentences: .

.

Predicates:

POSTSCRIPT ADDED IN

.

2002

Timothy Williamson has argued161 that if one adds an ‘actually’ operator to the minimal propositional logic K, then one can prove the necessity of distinctness from the necessity of identity. A version of his argument will establish an analogous result for the classical version of the system sketched above. That is, in a system that includes (1) the propositional modal logic K, (2) a complete propositional logic for an ‘actually’ operator, ‘@’, (3) the extensional logic of quantiﬁers and identity, and (4) the generalized QCBF axiom, one can prove that actually distinct things are necessarily distinct. That is, one can show the following:

.

161

Williamson (1996).

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The independence argument for the necessity of distinctness that I gave was based on these two facts: ﬁrst, that the extensional logic of identity is the same as the logic of indiscernibility, but second, that in a modal semantics without a symmetry condition on the accessibility relation, individuals might be discernible in one possible world, but indiscernible in an accessible world. When one can't ‘look back’ at a possible world, the information that distinguishes between two individuals may be lost. But the addition of the ‘actually’ operator (a second modal operator) allows one to recover the lost information, since one can always ‘look back’ at the actual world. More generally, the information about any world reachable from the actual world will be reﬂected in the actual world, and so in any other world in the model. I agree with Williamson that the independence of the necessity of distinctness (in a classical version of quantiﬁed modal logic) derives from the expressive limitations of the modal language, and does not by itself show anything about the metaphysics of identity. Williamson also gives an argument for the following more general thesis:

In our classical system, the universal generalization of this,

, will be invalid, and unprovable because of the fact that predication implies existence, and so a negation of an identity statement might be true, not because the terms refer to distinct things, but because they don't refer at all. But the version of this more general thesis, with the quantiﬁers inside the necessity operators,

, will be valid in the classical version of our semantics, even when the identity sign is interpreted as expressing the indiscernibility relation, but it will not be provable in the system with the four features described above. The problem here has nothing to do with identity; it is that quantiﬁed K + @ is one of the incomplete quantiﬁed modal logics. That is, the result of combining a complete propositional logic for K, and for @, with a complete extensional logic for quantiﬁers and identity (plus the generalized QCBF axiom) does not yield a complete logic for the corresponding semantics. And the problem does not depend on the idiosyncratic features of our particular formulation of quantiﬁcation theory—the incompleteness will carry over to more traditional versions of quantiﬁed modal logic. The problem is that the semantic constraints on the interpretation of the actuality operator have consequences for quantiﬁed sentences that are not reﬂected in the propositional logic for that operator, consequences that emerge in a theory that allows the domains of the quantiﬁer to vary from world to world. There are sentences not involving identity that are valid in the semantics, but will not be provable, such as the following:

It should also be emphasized that the kind of argument Williamson gives (even for the weaker conclusion that the necessity of distinctness holds in the actual world) will not work without the QCBF principle, or assumptions that imply it. The failure of the necessity of distinctness in the counterpart semantics does not

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depend on the expressive limitations of the modal logic (it fails, even in the S5 version of that theory). The necessity (or at least the essentiality) of identity is valid and provable in that theory, but with or without an actuality operator, the necessity of distinctness is neither. So I don't think Williamson's result threatens the general point that the necessity (or esssentiality) of identity is more central to the logic of identity than the necessity of distinctness Williamson makes a remark at the beginning of the essay in which he gives these arguments about ‘the depth to be gained in metaphysics from the constraints of orthodoxy in logic’.162 I share Williamson's respect for orthodoxy in logic, which is why my defense of counterpart theory goes to the lengths it does to show that both the logic and the semantics of identity are standard. There is also much to be gained, if we can manage it, from separating orthodoxy in logic from orthodoxy in metaphysics.

162

Ibid. 1. Williamson's paper appeared in a Festschrift for David Wiggins, and this remark is made in praise of Wiggins's work.

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PART IV Semantics, Metasemantics, and Metaphysics

9 Reference and Necessity (1997) Saul Kripke remarked, at the beginning of his lectures, Naming and Necessity, that he hoped his audience would see some connection between the two topics mentioned in his title. In those lectures Kripke defended some bold theses, some about naming that belong to semantics and the philosophy of language, others about necessity that belong to metaphysics. It is clear that the arguments for the different theses were interrelated, but it remains a matter of debate just what the connections are, both in Kripke's argumentative strategy, and in the issues themselves. Kripke and Hilary Putnam were criticized for attempting to derive metaphysical conclusions—about the essential properties of things—from premisses in the philosophy of language—about the nature of reference and the semantics of proper names. One might instead think that the direction of Kripke's arguments go the other way: that conclusions about reference and proper names were derived in part from controversial metaphysical assumptions about possible worlds and essential properties. Either way, there is reason to be puzzled: on the one hand, one might be skeptical (to borrow the metaphor that Nathan Salmon used to express his puzzlement about this) that one could, without sleight of hand, pull a metaphysical rabbit out of a linguistic hat.163 On the other hand, one might wonder why a proper understanding of the way our language happens to work should require controversial assumptions about the metaphysical nature of the world that our language talks about. My aim in this paper is to try to resolve some of this puzzlement by clarifying the relationship between theses and questions about reference and theses and questions about necessity and possibility. In the background of my discussion will be very general questions concerning how claims about the way we talk about the world relate to claims about what the world must be like, but in the foreground will be more speciﬁc questions concerning the relations between the different theses Kripke defends about individuals and their names. My main claim will be that Kripke's contribution was not to connect metaphysical and semantic issues, but to separate them: to provide a context in which questions about essences of things could be posed independently of assumptions about the semantic rules for the expressions used to refer to the things, and questions about how names refer could be addressed

163

See Salmon (1981).

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without making assumptions about the nature of the things referred to. I will argue that Kripke's theses about proper names and reference do not presuppose any metaphysical theses that ought to be controversial, though even stating those theses requires a framework that might be thought not to be metaphysically neutral. And I will argue that no metaphysical conclusions are derived from theses about reference and names, although clariﬁcation of the nature of reference helps in the rebuttals to arguments against metaphysical theses that Kripke defends. I will start (in section 1) by contrasting three kinds of questions that Kripke discusses in Naming and Necessity—two that belong to semantics and the philosophy of language, and one that belongs to metaphysics—and sketching the answers that Kripke defends, along with contrasting answers that he criticizes. Then (in section 2) I will discuss the apparatus that Kripke uses to clarify his questions—the possible worlds framework—and argue that it should be understood not as a metaphysical theory, but as a methodological framework in which alternative metaphysical and semantic theses can be stated. In sections 3–5 I will look in more detail at the arguments for the different theses, and the way the three different kinds of issues interact.

1 Questions and theses At this point my aim is just to set the stage by making some simple distinctions between questions, and stating, without much explanation or argument, some alternative answers to the questions. First there are questions of what I will call descriptive semantics. A descriptive semantic theory is a theory that says what the semantics for the language is without saying what it is about the practice of using that language that explains why that semantics is the right semantics. A descriptive semantic theory assigns semantic values to the expressions of the language, and explains how the semantic values of the complex expressions are a function of the semantic values of their parts. The term ‘semantic value’, as I am using it, is a general and neutral term for whatever it is that a semantic theory associates with the expressions of the language it interprets: the things that, according to the semantics, provide the interpretations of simple expressions, and are the arguments and values of the functions deﬁned by the compositional rules that interpret the complex expressions. If, for example, the semantic theory in question assigns senses or intensions to the names and predicates of a language, and explains the senses of complex expressions as a function of the senses or intensions of their parts, then as I am using the term, the semantic values of that semantic theory will be the senses or intensions. The particular descriptive semantic question we will be concerned with is the question, what kind of thing is the semantic value of a proper name? Second, there are questions, which I will call questions of foundational semantics, about what the facts are that give expressions their semantic

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values, or more generally, about what makes it the case that the language spoken by a particular individual or community is a language with a particular descriptive semantics. The speciﬁc question of this kind that we will focus on is the question, what is it about the situation, behavior, or mental states of a speaker that makes it the case that a particular proper name, as used by that speaker in a particular linguistic community, has the semantic value that it has? Third, there are questions about the capacities and potentialities of the things in the domain that forms the subject matter of some language; what, for example, might have been true of the things such as persons and physical objects that are the referents of some particular proper names? Kripke's answer to the ﬁrst question—the descriptive semantic question about proper names—is the Millian answer: the semantic value of a name is simply its referent. The contrasting answer that he argued against is that the semantic value of a name is a general concept that mediates between a name and its referent—a concept of the kind that might be expressed by a deﬁnite description. According to this contrasting answer, the semantic value of the name—its sense or connotation—determines a referent for the name as a function of the facts: the referent, if there is one, is the unique individual that ﬁts the concept, or perhaps the individual that best ﬁts the concept. Kripke's answer to the second question—the foundational semantic question—is that a name has the referent that it has in virtue of a causal connection of a particular kind between the use of the name and the referent; the referent is the individual that plays the right role in the causal explanation of the fact that the name is being used in the particular context in question in the way that it is being used. In the case of this question, it is less clear what the contrasting thesis is, since the question is not explicitly addressed by the philosophers Kripke is criticizing. But what seems to be suggested is that the sense of a name is determined by the abilities and dispositions of the speaker to describe or identify a certain individual. In response to the question about the capacities and potentialities of the things that we commonly refer to with names, Kripke defends the thesis that it makes sense to talk about the logical potential of an individual thing independently of how it is referred to, and that this potential is greater in certain ways, and less great in others, than some philosophers have supposed. For example, Shakespeare need not have been a playwright; he need not have written anything at all. He might have died in infancy, and been someone who we never heard of—even someone of whom all trace was lost after the seventeenth century. He might not have been called ‘Shakespeare’, by us, or by anyone. His plays, or at least plays word for word just like his plays, really could have been written by someone else of the same name. On the other hand, Shakespeare could not possibly have been anything other than a human being, and he could not possibly have had parents other than the ones that he in fact had. In contrast, others have conceded that

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Shakespeare might have lacked any one of the attributes commonly attributed to him, but argued that he could not have lacked them all. Attributes not commonly known to apply to Shakespeare, such as having the particular parents that he in fact had, are all attributes that he might have lacked. One thing I will argue is that while Kripke defends these theses about the descriptive semantics of names, the way the reference relation is determined, and the capacities and dispositions of human beings and physical objects (and I think he makes a persuasive case for each of them), his most important philosophical accomplishment is in the way he posed and clariﬁed the questions, and not in the particular answers that he gave to them. I will suggest that we might buy Kripke's philosophical insights while rejecting all of the theses—while opting for a pure Russellian description theory of ordinary names, a non-causal account of the way names get associated with their values, and in metaphysics either for an anti-essentialist thesis according to which Shakespeare might have been a lamppost or a fried egg, or for a Leibnizian theory according to which Shakespeare had even his most apparently accidental properties essentially. The positive case for the theses that Kripke defends is not novel philosophical insight and argument, but naive common sense. The philosophical work is done by diagnosing equivocations in the philosophical arguments for theses that conﬂict with naive common sense, by making the distinctions that remove the obstacles to believing what it seems intuitively most natural to believe.

2 The possible worlds framework To accept what I will argue is Kripke's main philosophical contribution, you do have to buy a framework, an apparatus that he used to sharpen and clarify the contrasting theses, both semantic and metaphysical. I won't try to claim that the apparatus is either semantically or metaphysically neutral, but I will argue that the motivation and commitments of the framework are more methodological and conceptual than they are metaphysical. Philosophers often talk as if the decision to theorize with the help of this framework is, if one takes the claims one makes while using it seriously, a speciﬁc ontological commitment to a certain kind of entity. Some philosophers reject the framework because they reject the ontological commitment that its serious use makes. One hears: ‘I don't believe in possible worlds’, as one might hear people say that they don't believe in transubstantiation, or ﬂying saucers from other planets (commitments that some philosophers believe are about as plausible as the commitment to possible worlds). I think this attitude is based on a misconception (although I have to concede that it is a misconception that some defenders of possible worlds share with the critics). It is not that it is a misconception to think that serious talk about possibilities commits one to the existence of the possibilities one claims there are, just as it is not a misconception to think that the literal use of

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quantiﬁers commits one to the existence of things that one purports to quantify over. But it is not the framework itself that makes the speciﬁc commitments, just as it is not the semantics for ﬁrst-order logic that makes any particular ontological commitment. Suppose someone were to reject the standard (extensional) semantics for ﬁrst-order logic on the ground that he did not believe in individuals, to which that semantics is ontologically committed. The proper response would be to point out that ﬁrst-order semantics is a framework for doing ontology, and not a particular thesis about what ontology is correct. Individuals are whatever there is to talk about; the semantic theory itself says nothing about what there is to talk about, and so makes no particular ontological commitments. Quine's slogan, ‘To be is to be the value of a bound variable’, is not an ontological thesis, but an attempt to promote a framework in which the ontological commitments of alternative philosophical and scientiﬁc theories can be stated without equivocation and compared. The Leibnizian slogan, ‘necessity is truth in all possible worlds’, should be understood in a similar spirit. This slogan and the possible worlds framework that it presupposes should, I think, be understood not as an attempt to provide an ontological foundation for a reduction of modal notions, but as an attempt to formulate a theoretical language in which modal discourse can be regimented, its structure revealed, equivocation diagnosed and avoided. Modal discourse—speech that involves words such as ‘may’, ‘might’, and ‘must’—is notoriously complex and problematic, providing fertile ground for ambiguities, both ambiguities of scope that arise because the semantic structure of modal statements is complicated and not simply reﬂected in surface syntax, and ambiguities that arise from alternative senses and context dependence of the modal words. Modal words interact with each other and with quantiﬁers, descriptions, temporal modiﬁers and grammatical tense, aspect, and mood in complicated ways that are difﬁcult to sort out. Philosophical puzzles about, for example, necessary connection and counterfactual dependence, reference to nonexistent things, capacities and dispositions, the ability to do otherwise, the necessity of the past and the openness of the future, will presumably not all be dissolved simply by getting clear about modal discourse, but everyone should agree that clarifying the discourse in which such problems are posed is an essential ﬁrst step. It is important to separate disagreements based on contrasting interpretations of the way the language works from disagreements about the claims that the language is being used to state. Whatever one's metaphysical beliefs about the reality that modal discourse purports to describe, one should agree that it would be nice to have a language that is free of some of the ambiguities that infect modal discourse, and in which the claims made with modal words and constructions might be paraphrased—a language that uses only parts of discourse that are relatively clear and uncontroversial (the indicative mood and quantiﬁers), but that still has the expressive power to

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make claims about what might, would, or must be true. Achieving such clariﬁcation does not require a reductive analysis of modal to nonmodal concepts, and so it is not required that a canonical language in which we do modal semantics be built on some pure, nonmodal foundation, any more than formal languages designed to clarify quantiﬁcation needed to be built on some pure, nonquantiﬁcational foundation (whatever that would be). What is needed is only the kind of opportunistic departure from ordinary language involved in the bootstrap operation that Quine called ‘regimentation’. In the kind of regimentation Quine recommends, we begin with ad hoc paraphrases to remove ambiguity, we introduce variables to facilitate cross-reference, and we adopt a syntax in which quantiﬁer scopes are reﬂected in a simple and systematic way in the order of the symbols and the placement of parentheses. ‘The artiﬁcial notation of logic’, Quine remarked, ‘is itself explained, of course, in ordinary language.’164 Similarly, the primitive resources of the possible worlds framework are explained in ordinary modal language, and the explanations will be intelligible only to one who understands at least some of that part of language. A modal skeptic who doubts that anything both meaningful and true is said in modal discourse will doubt both the value and the intelligibility of a framework in which that discourse is clariﬁed. But it may be that the source of the skepticism is in the equivocations and unclarities that the framework helps to remove. The general strategy is to ﬁnd a part of our modal discourse that seems relatively free of the particular equivocations and unclarities that infect modal discourse generally, a part that might be developed and used to clarify the rest. We look for a way of making modal claims that uses paraphrases to avoid problematic constructions, a way that uses forms of expression that may perhaps be stilted and less idiomatic than the familiar ones, but that will still be recognizable paraphrases of ordinary modal claims. The following assumption about what is, in any sense, possible points the way to one such strategy of paraphrase: if something might be true, then it might be true in some particular way. It would make no sense to afﬁrm, for example, that there might be life elsewhere in our galaxy, while denying that it is possible that there be life in any particular part of the galaxy, or that there might be life of any particular kind—animal life, or nonanimal life—elsewhere in the galaxy. If something is possible, then it is possible that it be realized in a concrete way—perhaps in many alternative ways. The possible worlds framework begins with this simple assumption, and with the assumption that, in general, statements about what may or might be true can be described in terms of the ways a possibility might be realized. The framework takes alternative speciﬁc ways that possibilities might be realized as the primitive elements out of which propositions—the things that are said to be possible, necessary, or true—are built and in terms of which the

164

Quine (1960: 159).

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modal properties of those propositions are deﬁned. The main beneﬁt of this move is that it permits one to paraphrase modal claims in an extensional language that has quantiﬁers, but no modal auxiliaries, and so in a language in which the semantic structure of the usual modal discourse can be discussed without begging controversial questions about that structure. I have been arguing for the metaphysical neutrality of the possible worlds framework, but I should emphasize that I do not mean to suggest that the use of the framework is free of ontological commitment to possibilities (ways things might be, counterfactual situations, possible states of the worlds). Regimentation clariﬁes one's commitments, but does not pretend to eliminate them. Furthermore, it must be conceded that the moves made in this regimentation of modal discourse (particularly the move that paraphrases ‘——might have been true in various particular ways’ as ‘there are various particular ways that——might have been true’) are not completely innocent. As Quine would be the ﬁrst to emphasize, no strategy of regimentation is neutral in any absolute sense: ‘The quest of a simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of ultimate categories, a limning of the most general traits of reality.’165 But it is a desideratum of any such project that it be able to accommodate and articulate a range of alternative responses to the questions and puzzles that motivated the project. I think the possible worlds framework satisﬁes this desideratum, but the real test of this claim is not in some general methodological argument, but in the fruits of the work that is done with its help.

3 What are the semantic values of names? The possible worlds framework provides the resources to state and clarify both metaphysical and semantic theses. In both cases, I want to argue, the principal conceptual beneﬁt of the apparatus is that it provides an account of a subject matter that is independent of languages used to describe that subject matter. Of course whether the subject is geology or modal metaphysics, we never get away from language—it is just too hard to say very much without using it. But just as we want to distinguish rocks from words (even if we have to use words for rocks to do it), so it is useful to distinguish possibilities from the words used to describe them. To make this distinction is not to beg any questions against the philosophical thesis that the source of all necessity is in language; a conceptual distinction does not foreclose the possibility that one thing distinguished may in the end be reduced to the other. To see that possibilities are part of the subject matter of semantics as well as of modal metaphysics one need only make the following assumptions: ﬁrst, a central function of an assertion is to convey information, and

165

Ibid. 161.

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information is conveyed by distinguishing between possibilities. Second, a principal goal of semantics is to explain how the expressions used to perform speech acts such as assertion are used to convey information—to distinguish between possibilities—and how the way complex sentences distinguish between possibilities is a function of the semantic values of their parts. To understand what is said, for example, in an utterance of ‘The ﬁrst dog born at sea was a basset hound’, one needs to know what the world would have to be like in order for what was said in that utterance to be true. These simple assumptions about the goal of semantics might be expressed in terms of truth-conditions: semantics is concerned, among other things, with the truth-conditions of statements, and the way their truth-conditions are a function of the semantic values of their parts (where semantic values are whatever they must be in order to contribute appropriately to truth-conditions). What are truth-conditions? If we are looking for an answer to this question that identiﬁes a nonlinguistic object that semantics can associate with statements, it seems natural to say that the truthconditions of a statement are the possibilities that, if realized, would make the statement true. We want a conceptual distinction between truth-conditions and any particular forms of expression in which those truth-conditions might be stated simply because it is useful to theorize about a language in a different language, and when we do so, we want to be able to talk, not just about the interlinguistic relations between the language we are theorizing about and the language we are theorizing in, but about the relation between the language we are theorizing about and the world. The task of descriptive semantics, in this framework, is to say what kinds of things the semantic values of expressions of various categories are, and to explain how the truth-conditions of sentences (or sentences in context) are a function of the semantic values of their constituents. So to give the semantic value of a proper name is to say what contribution a proper name makes to the truth-conditions of the sentences containing it, where the truth-conditions of a sentence, or a sentence in context, are represented by the set of possibilities that, if realized, would make what the sentence says in that context true. The two answers that Kripke compares—the Millian and the Fregean answers—are made precise in the following ways. (1) The semantic value of a name is simply its referent; the proposition expressed by a simple sentence containing a name is the proposition that is true in a possible world if and only if that referent has the attribute expressed by the predicate of the sentence. (2) The semantic value of a name is its sense, which is a concept that applies to at most one individual in each possible world (the kind of concept that might be expressed by a deﬁnite description). The proposition expressed by a simple sentence containing a name is the proposition that is true in a possible world if and only if the individual to which the concept expressed by the name applies in that world has the attribute expressed by the predicate of the sentence.

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Thus far, I have talked only about a question and a framework for clarifying alternative answers to it, and not about arguments in support of one or the other of the answers. The framework is neutral on the question of which of these alternatives, if either, gives a correct account of the semantics of the expressions in English and other natural languages that we identify as proper names. This seems to be an empirical question of no particular philosophical interest, a question that philosophical analysis and argument are not relevant to answering. The way in which the alternative answers are articulated in the framework does point the way to some of the empirical considerations that may be relevant to settling the issue by making clear what the consequences of those alternatives are, but it appears that no philosophical—certainly no metaphysical—issue hangs on which answer is right. Even though Kripke defended, on empirical grounds, the Millian answer, he nowhere suggested that things had to be this way. For all he argues, we might perfectly well have spoken a language with names that all referred only by having senses that determined referents. It just happens that we do not. What needed philosophical defense was not the empirical adequacy of the Millian answer, but its coherence. While Kripke did not suggest that philosophical argument could establish that the answer he favored was correct, he had to answer philosophical arguments that purported to establish that it was incorrect. John Searle, for example, argued that the view that there could be a class of logically proper names, i.e. expressions whose very meaning is the object to which they are used to refer, is false. It isn't that there just do not happen to be any such expressions: there could not be any such expressions.⋯ The view that proper names are ‘unmeaning marks’, that they have ‘denotation’ but not ‘connotation’, must be at a fundamental level wrong.166 Michael Dummett makes a similar claim: ‘there cannot be a proper name whose whole sense consists in its having a certain object as referent, without the sense determining that object as referent in some particular way.’167 These claims are puzzling, in the light of Kripke's way of posing the problem of the descriptive semantics of proper names. It appears that he showed, simply in setting up the alternatives, how to give a coherent speciﬁcation of a language containing ‘expressions whose very meaning is the object to which they are used to refer’. What kind of argument could show not only that we do not in fact speak such a language, but that we could not possibly do so? To address this question, we need to turn to the second of the two kinds of issues in the philosophy of language that Kripke is concerned with.

4 How do names get their semantic values? Why do Searle and Dummett think that we could not speak a language of the kind that Kripke described in which the semantic value of a name is

166

Searle (1969: 93).

167

Dummett (1973: 232).

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simply its referent? Searle's reason was that ‘if the utterance of the expressions communicated no descriptive content, then there could be no way of establishing a connection between the expression and the object’, no way to answer the question, ‘what makes this expression refer to that object?’168 Dummett's reason is similar: ‘an object cannot be recognized as the referent of a proper name⋯unless it has ﬁrst been singled out in some deﬁnite way.’169 In both cases, the reason for rejecting the possibility of a certain descriptive semantic thesis appeals to considerations that relate to the foundational question, which asks what it is about the capacities, customs, practices, or mental states of a speaker or community of speakers that makes it the case that an expression has the semantic value that it has. What seems to be suggested is that the hypothesis that a language has a Millian semantics poses a foundational question that cannot be given a satisfactory answer. But this is not the way either Searle or Dummett put their claims, since they do not separate the two questions, ‘what is the semantics for names (or the semantic value of a particular name) in the language we speak?’ and ‘what makes it the case that the language we speak (or a particular name in that language) has this semantics?’ Once the two questions are separated, it is difﬁcult to see what could rule out the possibility that we speak any language that has a well-deﬁned semantics. If a Millian semantics for names can be articulated, why can't a community of speakers adopt the convention to speak such a language? The assumption implicit in the rejection of the possibility of a Millian semantics is that the two questions we have separated should receive a single answer. Something like a Fregean sense should explain why a name has the particular referent it has, where this is interpreted to mean that it should explain both what it is about the capacities and attitudes of the speaker that give the name the referent it has, and also what it is that the speaker communicates or conveys in using the name. Kripke charged Frege with conﬂating these two questions: ‘Frege should be criticized for using the term “sense” in two senses. For he takes the sense of a designator to be its meaning and he also takes it to be the way its reference is determined. Identifying the two, he supposes that both are given by deﬁnite descriptions.’170 Whether Frege is responsible for making this mistake is a question of textual interpretation that I will not comment on, but it is clear, I think, that Searle is concerned with both kinds of questions, and that he takes himself to be following Frege. Searle describes his axiom of identiﬁcation, a principle that is supposed to be constitutive of singular deﬁnite reference, as ‘a generalization of Frege's dictum that every referring expression must have a sense’.171 The principle is about what must be communicated or conveyed

168

Searle (1969: 93).

169

Dummett (1973: 232).

170

Kripke (1972: 59).

171

Searle (1979: 80).

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(or at least ‘appealed to’ or ‘invoked’) in the utterance of the referring expression, but it is also an attempt to say what it is about the capacities of speakers that explains why their referring expressions have the referents they have. ‘What I am trying to get at,’ he says, ‘is how noises identify objects.’172 If we are implicitly looking for a semantic account of names that answers both questions at once, then the Millian theory that says that the semantic value of a name is simply its referent looks like a nonanswer; it seems to be denying the obvious fact that there must be something about the capacities, behavior, or mental state of the users of the name that make it the case that the name has the referent that it has. On the other hand, the conﬂation of the two questions masks the fact that the sense theory, interpreted as an answer to the question of descriptive semantics, is also a nonanswer to the foundational question. Suppose we were to accept the Fregean thesis that names have the referent that they have because they have a sense that determines a function whose value (at the actual world) is that referent. This simply raises the question, what is it about the capacities, behavior, or mental state of the users of the name that makes it the case that the name has the sense that it in fact has? Whether one is a Fregean or not, the two questions need to be distinguished, and once they are, the way is opened for answers to each that are less easily seen as possible answers to the other: the Millian answer to the descriptive question and the causal account of reference that Kripke defends as an answer to the foundational question. This latter thesis—that what makes it the case that a name has a certain individual as its referent is that the individual plays a certain role in the causal or historical explanation of the speaker's use of the name—makes no sense as an attempt to specify a semantic value, a candidate to be the meaning or sense of a name, and so it can be taken seriously only after the two questions are distinguished. Kripke and other defenders of a causal theory of reference were criticized for the vagueness of their thesis. Causal connections are ubiquitous, and it is obvious that there are a great many individuals that are causally implicated in the speaker's use of the name, but that are not by any stretch of the imagination plausible candidates to be the referent. A proper causal theory of reference would have to specify just what sort of causal connection is necessary and sufﬁcient for reference, and that is a notoriously difﬁcult demand. Kripke himself emphasized that he was presenting not a reductive analysis of reference, but only an alternative picture. To some skeptics, this sounded like an evasion. The suspicion was that any sufﬁciently speciﬁc and precise version of the causal theory would be subject to as many counterexamples as the description theory, and so that the plausibility of the positive alternative to the description theory rested on its lack of speciﬁcity. But I think this line of criticism misses the point. What is essential to the

172

Ibid. 83 n.

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alternative picture was the separation of the questions, and the distinction between two different ways in which the extension of an expression might depend on the facts: ﬁrst, what semantic value an expression has depends on the facts; second, if the semantic value is a sense, the extension of an expression with a given semantic value may depend on the facts. The philosophical work was done in making the distinctions that removed the obstacles to accepting the naive answers to the questions that were distinguished. If we ask ‘what does one have to know to understand a name?’, the naive answer is that one must know who or what it names—nothing more. (In contrast, no one would be tempted to give this answer to the analogous question, what must one know to understand a deﬁnite description.) And if we ask, how does a name come to name what it names—what, for example, makes ‘Shakespeare’ as we use it a name of the particular person Shakespeare?—I think most people would be inclined to point to an historical narrative: his family was called ‘Shakespeare’, or something like that, at the time, and knowledge of him, his plays, and his name were passed down through the generations to us. This is not a particularly exciting philosophical theory, but it doesn't seem wrong, and it does seem incompatible with the kind of answer implied by a description theory. Kripke's causal chain story is just an articulation of the naive answer, one that does not add a lot of constructive detail to it. But by separating and clarifying the questions that these naive answers are answers to, he brought out why the theoretical reasons for resisting those answers are bad reasons. The diagnosis of equivocation is rarely the end of the matter in a philosophical argument. I will sketch a line of argument for the impossibility of a Millian semantics that recognizes the distinction between the two kinds of questions. I don't think this line of argument is successful, but it is instructive to see where it takes the debate. If there is a credible defense of the thesis that a Millian language is impossible, I think it must challenge the assumption that any well-deﬁned semantics might be the semantics of a language that is used by a speaker, or realized in a speech community. Here is one way that the assumption might be challenged. First, the following seems a reasonable general constraint on the correctness of a claim that a certain semantics is the semantics for the language spoken in a certain community of speakers: if the semantics is correct, then speakers must know, at least for the most part, what, according to the semantics, they are saying. A notion of saying might allow that in some cases one succeeds in saying things using words one does not understand, but it is hard to deny, ﬁrst that if one doesn't know what one is saying, then one does not mean what one says, and second, that according to a correct account of what people say in a given speech community, speakers generally mean what they say (not in the sense that they are sincere—believe what they say—but just in the sense that what they say coincides with what they mean).

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Second, we may note that it is possible to give a determinate speciﬁcation of a semantic value without knowing what that value is, even without anyone knowing what the value is. Consider this example discussed by Gareth Evans: let ‘Julius’ be a (rigid) proper name for the person (whoever he or she was) who invented the zip.173 Then (assuming that some particular single individual invented the zip) a sentence such as ‘Julius was born in Minsk’ expresses a determinate proposition about a particular individual, but we don't know who the individual is, so we don't know what proposition it is that is expressed. We understand a description of the proposition, and we understand, and may believe, metalinguistic statements about that proposition, such as ‘What is said by “Julius was born in Minsk” is probably false.’ We can have beliefs and make assertions about the truth or falsity of whatever proposition is expressed, but (according to this line of argument) we do not thereby assert or believe that Julius was or was not born in Minsk, and we cannot do so unless we know who invented the zip. Now suppose that one could make a case that our mental relations to particular individuals are all in relevant respects like our relation to Julius—that since we can know individuals only by description—only as whoever or whatever it is that is presented to us in a certain way—we don't ever know, in the relevant sense, who or what it is that we are referring to with the names we use. Then it would seem to follow that, although we can deﬁne a language with a Millian semantics, we could never speak one, since we could not have the knowledge required to know what the sentences of such a language say. I think the ﬁrst premiss of this argument should be conceded: a semantics for the language spoken by a community of speakers cannot be right if it implies that speakers generally do not know what they are saying. It should also be conceded that according to the Millian semantics for names, as contrasted with the Fregean semantics, speakers do not know what they are saying when they use a name if they do not know who the referent of their name is. But what is it to know what one is referring to? At this point, the battleground shifts from semantics and the philosophy of language to the philosophy of mind where variations on some of the same battles are fought. Underlying the contrasting answers to the foundational question about reference (what makes it the case that a name has the referent it has?) are contrasting strategies for answering parallel foundational questions about mental states: what makes it the case that a thought—a judgment or an intention—has the content it has, or is about what it is about? The argument sketched above against the possibility of a Millian semantics for an actual language rests on the assumption that thoughts can be about particular things only by expressing general concepts that apply to those

173

Evans (1982: 31).

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individuals. If this were right, then the kind of causal chain or historical explanation story that Kripke and Keith Donnellan told to answer the foundational question about semantics would be an answer that detached the determination of the semantic values of expressions from the mental states and capacities of the users of the expressions, and so would be an answer that was vulnerable to this argument. But why should we think that thoughts, any more than names, can be about individuals only by expressing general concepts? ‘What is it’, Searle asks rhetorically in defense of his principle of identiﬁcation and his argument against the Millian theory, to mean or intend a particular object to the exclusion of all others? Some facts incline us to think that it is a movement of the soul—but can I intend just one particular object independent of any description or other form of identiﬁcation I could make of it? And if so, what makes my intention an intention directed at just that object and not at some other? Clearly the notion of what it is to intend to refer to a particular object forces us back on the notion of identiﬁcation by description.174 The suggestion implicit in these rhetorical questions is that an intention to refer to a particular individual must be explained as a behavioral capacity, the capacity to give a general description, or otherwise identify an individual who is, by ﬁtting the description or being the object identiﬁed, the object meant or intended. The only alternative, it is implied, is some kind of obscurantist intentional magic, some kind of movement of the soul. Even if Searle were right in his suggestion that intentions and other intentional states directed at particular individuals must be explained in terms of the capacities of the agent to identify the individual, this would still not give him the additional premiss needed for the argument against the possibility of a Millian semantics for names. For Searle is not arguing that we cannot have intentions and other attitudes toward particular individuals; he is only arguing for a condition that is necessary for having such intentions and attitudes. What he needs for the argument is a constraint on the content of the attitudes we can have, but what he offers instead is a constraint on the conditions under which one can have attitudes with a certain kind of content. Whatever it is that constitutes intending and having knowledge and beliefs about a particular object, ‘to the exclusion of all others’, so long as it is possible to have such intentions, knowledge, and beliefs, it will be possible to understand and speak a language with a Millian semantics. But in any case, there is no real argument for the conclusion that mental magic is the only alternative to an explanation of intentionality in terms of an agent's capacities to identify. A causal account of intentional content—an explanation that looks back to how mental states came to be rather than

174

Searle (1969: 87).

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only forward to what those states dispose the agent to do—is equally compatible with a nonobscurantist account of intentionality. A causal account of intentions and beliefs seems in fact to be presupposed by the defense of a causal account of reference given by Kripke and Donnellan, since it is argued that speakers not only can refer, but can intend to refer, to particular individuals without being able to describe or identify those individuals. Causal and noncausal accounts of how names get their reference can share the assumption that reference is determined by intentions. The causal theory of reference is causal because it assumes a causal account of the content of the intentions that determine reference. An argument of Michael Dummett's for the impossibility of a Millian semantics, like the argument I have sketched, bases this conclusion on the impossibility of a certain kind of knowledge: what Dummett calls bare knowledge of reference. Here is his characterization: ‘A bare knowledge of the reference of the name a will consist⋯in knowing, of some object, that a refers to it, where this is a complete characterization of this particular piece of knowledge.’175 I am not sure what Dummett means by a ‘particular piece of knowledge’, or what it is for a characterization of such a piece to be complete, but if we interpret Dummett's arguments in the context of the possible worlds conception of content, I think it is reasonable to identify his notion of bare knowledge of reference with knowledge of a singular proposition—the proposition that is true in a possible world if and only if a certain particular individual is the referent of the name a. An essential step in Dummett's argument for the impossibility of bare knowledge of reference is a claim that is essentially equivalent to Searle's principle of identiﬁcation: we cannot have what Dummett calls knowledgewhat—knowledge of a certain individual that it has some property F (for example, knowledge of a certain individual that it is the referent of the name a)—unless we have the capacity to describe or identify the object. More strongly, for any true knowledge-what ascription, there must be a true propositional knowledge ascription whose content is a nonsingular proposition that makes the method of identiﬁcation explicit, and that entails the knowledge-what ascription: a propositional knowledge ascription on which the knowledge-what ascription rests’.176 Now I am not persuaded that this claim is correct, but even if this much is granted, I don't think it gives one reason to reject the possibility of knowledge of singular propositions. Suppose we grant that one cannot know of some particular individual x that it is F unless for some G one identiﬁes x as the G, and knows that the G is F. Further, suppose we grant that in a particular case the claim that y knows of x that it is F rests on, and is entailed by, the claim that y knows that the G is F. What has been granted is a claim that certain conditions are necessary, and others sufﬁcient, for having knowledge of a certain kind; but nothing follows from this

175

Dummett (1991: 127).

176

Ibid. 130.

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about the content of that kind of knowledge. If ‘bare knowledge’ of some object that a refers to it is taken to mean knowledge that can exist in isolation—without knowing anything else about what a refers to, then we can grant that bare knowledge of reference is impossible, but that does not imply that knowledge of x that a refers to it is not knowledge of a particular proposition—a singular proposition—or that it is not possible to have knowledge of such propositions. We can agree with Dummett that it is a difﬁcult problem to say just what conditions must be met for one to know who or what the referent of a name a is, and that the problem is not solved simply by saying that to have such knowledgewhat is to know a singular proposition of the form ‘x is the referent of a’. But the problem is not that saying this would be wrong; it is just that specifying the content of a knowledge ascription is not the same as saying what it is for that knowledge ascription to be true. The distinctions, both on the level of speech and on the level of thought, between questions about what content is and questions about how content comes to be determined, help to open up a place in conceptual space for a causal account of reference and of intentionality generally, and provide a rebuttal to arguments for the impossibility of a Millian semantics for a realized language. They do not, of course, end the debate. Once theoretical obstacles to such accounts are removed, examples and untheoretical considerations make a strong prima facie case for the claim that some such account is correct, but as Gareth Evans reminded Kripke, ‘the deliverances of untutored linguistic intuition may have to be corrected in the light of considerations of theory.’177 I think more theoretical considerations also support causal accounts of intentionality, but that is a different part of the story. I want to turn back now to questions about the relation between reference and metaphysical necessity.

5 Names and essences Whatever the fate of the debate between them, we have a stark contrast between two pictures of the way we are related, both by speech and by thought, to particular things in the world. On one picture, we can think and talk directly about particular things in virtue of our causal interaction with those things; on the other, our mental and linguistic acts relate us to particular things only by our grasping and expressing purely qualitative concepts that may be instantiated by particular things. The question now is: do these pictures of mental and linguistic representation either presuppose or support some particular conception of the nature of the particular things that we talk and think about, or that instantiate our concepts? Speciﬁcally, does the conception of reference that Kripke argues for presuppose or

177

Evans (1982: 76).

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support the particular brand of essentialism that he defends? The two kinds of issues, I will argue, are independent. The only role of the theory of reference in Kripke's arguments for metaphysical conclusions is to help diagnose and rebut fallacious arguments that rest on a conﬂation of the two kinds of issues. One of Searle's arguments against the Millian account of proper names was that it (or at least an ‘uncritical acceptance’ of it) leads us into some ‘metaphysical traps’.178 It is suggested that this conception of proper names presupposes ‘a basic metaphysical distinction between objects and properties or aspects of objects’.179 Actually Searle's attitude toward the relation between the metaphysical and the semantic issues is not entirely clear. Does he locate the mistake in the premiss—the Millian semantics for names—or in the inference from this premiss to a metaphysical conclusion? On the one hand, we are warned against ‘the original sin of metaphysics, the attempt to read real or alleged features of language into the world’, and ‘the metaphysical mistake of deriving ontological conclusions from linguistic theses’,180 but on the other hand, the fact that the Millian account of names seems to presuppose this metaphysical distinction is part of an argument against that semantic account. It cannot be a good argument against a semantic account of proper names that someone has illegitimately drawn metaphysical conclusions from that account. So perhaps the view is that the Millian theory of names is already a covertly metaphysical thesis—that false metaphysical conclusions are validly drawn from it because the thesis is the result, rather than the occasion, for reading alleged features of language into the world. But if so, can't we separate the semantic from the metaphysical aspects of the thesis, and evaluate the semantic thesis independently of the metaphysical conclusions that are illegitimately drawn from it? If we couldn't make such a separation, then it would not be so clear that it was illegitimate to draw ontological conclusions from linguistic theses. Searle's target is the Wittgenstein of the Tractatus, and not Kripke (whose lectures were given after Searle's book was published). But Kripke does make the kind of metaphysical distinction between objects and properties that Searle rejects, and of course he also defends the account of names that Searle argues is the illegitimate source of the metaphysical distinction. I will sketch the way Kripke makes the metaphysical distinction and then argue that his metaphysical theses are compatible with the Fregean picture of mental and linguistic representation, and so do not presuppose the Millian semantics or the causal theory of reference. What is presupposed in the defense of Kripke's metaphysical conception is only that the two accounts of reference and intentionality not be conﬂated. I will conclude by considering whether there is a dependence that goes in the other direction: whether the semantic picture that Kripke defends presupposes his metaphysical theses

178

Searle (1969: 163).

179

Ibid. 164.

180

Ibid.

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about the relation between individuals and their properties. Here the issues are harder to disentangle, but I will argue that the Millian theory of names and the causal theory of reference are compatible with alternative metaphysical conceptions of individuals and their properties. There is no derivation of metaphysical conclusions from semantic premisses. What is it to make a basic distinction between objects and properties? Searle derided the metaphysical picture of an object as ‘a combination of its propertyless self and its properties’, as well as the contrasting picture of an object as nothing but ‘a heap or collection of properties’,181 but what do these pictures really come to? Kripke also scorned the same two contrasting pictures, rejecting the assumption that objects are some kind of ‘bare particulars’ or ‘propertyless substrata underlying the qualities’, as well as the claim that they are nothing but bundles of qualities, ‘whatever that may mean’.182 The possible worlds framework suggests a way to express the idea that a particular is conceptually separable from its properties without relying on the rejected picture of a bare particular. Properly understood, the issue concerns the modal properties of an individual. Intuitively, it seems clear that ordinary things might have had different properties from the ones they in fact have: Shakespeare might not have written plays, which, in the possible worlds paraphrase, is to say that there is a possible world in which Shakespeare did not write plays. This possible world is one in which the very person who actually wrote the plays we know and love exists, and did not write plays. So (assuming the modal claim is right) the property of writing plays is not essential to a particular person who has this property. The same goes for lots of other ordinary properties ascribed to ordinary persons and things, but not to all of them. Shakespeare obviously could not have been someone other than Shakespeare (although he could have been called something else), and according to Kripke he could not have been a member of a different species, or even have had different parents. Now these simple modal claims say nothing about names or reference, but in stating them I am using the proper name ‘Shakespeare’, so the content of what I am saying about counterfactual possibilities might be thought to depend on the semantics for names. If ‘Shakespeare’ were an abbreviation for a deﬁnite description as Russell argued, then the statement that Shakespeare might not have written plays, and its paraphrase, that there is a possible world in which Shakespeare did not write plays, would both be ambiguous. If, for example, ‘Shakespeare’ were an abbreviation for ‘the most famous Elizabethan playwright’, then on one interpretation the claim that Shakespeare might not have written plays would be the claim that there is a possible world in which the person who is the most famous Elizabethan playwright in that world did not write plays. This, of course, is not the claim that Kripke intended to make, and it does not seem, intuitively, that the words used to

181

Searle (1969: 163).

182

Kripke (1972: 52).

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make the claim are open to such an interpretation. The modal claims, in either their ordinary form or in their possible worlds paraphrases, do not seem ambiguous, but that is a linguistic intuition which is separable from the modal intuition about the person who is the referent, by whatever means, of the name ‘Shakespeare’, the proposition that is expressed by the other reading of the statement that the most famous Elizabethan playwright might not have written plays. Now on what I have been calling the Fregean conception of mental representation, perhaps we cannot have such modal intuitions about particular individuals since perhaps on that conception the only way we can have any thoughts at all about an individual is to have beliefs about whoever it is that is presented to us in some particular way. But this does not matter to the issue, since the metaphysical intuition can be expressed in a perfectly general way: whoever the person is who ﬁts our Shakespeare concept, that person might have been someone who didn't write plays. So the modal theses stand or fall independently of the success or failure of the defense of theses either about the semantics for proper names, or about the way our thoughts relate us to the individuals that are the referents of those names. If both the Fregean conception of reference and intentionality that Searle favors and the alternative semantic conception that he criticizes are compatible with the metaphysical distinction between particulars and their properties, what is the source of his objections to this distinction? I think they derive from a conﬂation of the two semantic conceptions. By equivocating between the two semantic theses, one can argue from semantic assumptions to a metaphysical conclusion: On the Fregean picture, there is an analytic, and so necessary, connection between the name ‘Aristotle’ and a cluster of properties, and so it is legitimate to conclude, as Searle does, that ‘it is a necessary truth that Aristotle has the logical sum [inclusive disjunction] of the properties commonly attributed to him.’183 This claim by itself implies nothing about what must be true of the person Aristotle and so raises no problems about the traditional distinction between objects and their properties. On the unequivocal Fregean picture, ‘Aristotle’ means, roughly, whoever satisﬁes the cluster; so according to this semantic hypothesis, if the person Aristotle hadn't satisﬁed the cluster, he would not have been Aristotle, but he might still have existed. It is only when one combines the Fregean premiss with the incompatible assumption that the name ‘Aristotle’ is a Millian name that one can take the next step in the argument, the inference from the claim, necessarily Aristotle satisﬁes the cluster, to the conclusion that it is necessarily true of Aristotle that he satisﬁes the cluster. (‘I wish to argue that though no single one of them is analytically true of Aristotle, their disjunction is.’184) It is only when one has the conclusion that the person Aristotle is necessarily connected with the properties used to

183

Searle (1969: 173).

184

Ibid. 169.

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identify him that one has reason for skepticism about substance, and for the claim that ‘it is misleading, if not downright false, to construe the facts which one must possess in order to refer as always facts about the object referred to, for that suggests that they are facts about some independently identiﬁed object.’185 All Kripke does to make a positive case for his modal theses about individuals is to develop the framework in which the theses can be formulated clearly and separated from theses about names and reference. The rest of the work is done simply by pointing out what seems from an intuitive point of view obviously true, once it is clear what the alternatives are. If Kripke's rhetorical style had been a little different, he might have made this point by saying that he was just assembling reminders, not putting forward theses. What philosophy does, he might have said, is simply to put everything before us.186 Not all of the metaphysical claims about individuals that Kripke defends on intuitive grounds are equally compelling. On the one hand, it seems hard to deny that we can make intuitive sense of questions about the potentialities of particular individuals, independently of the means used to refer to them. To suppose that Shakespeare never wrote plays is to envision a counterfactual situation in which Shakespeare—the man himself—wrote no plays. Other theses Kripke defends are more controversial from an intuitive point of view, particularly theses that deny that certain things are possible, or equivalently, that afﬁrm that particular things have certain essential properties. Can I coherently suppose that Shakespeare—the man himself—had different parents from the ones he in fact had, or that he was born in a different century? Kripke would argue that if we think we can suppose these things, we are confused: if we think clearly about what we are trying to suppose we will see that these are not coherent counterfactual possibilities. Not everyone will share these intuitions, even after setting aside the bad reasons for resisting them that Kripke points out. The possible worlds framework does not settle such metaphysical questions, or even tell us how they should be settled; its job is to raise them, and to make clearer what the alternative answers say. I have argued that Kripke's metaphysical theses do not presuppose his theses on reference and intentionality. What about the other direction? Does the Millian semantics for proper names or the causal account of reference and intentionality presuppose the metaphysical picture that Kripke defends? The theses about names can easily be separated from the more speciﬁc essentialist theses, but the general metaphysical issues about the identiﬁcation of individuals across possible worlds are more difﬁcult to disentangle from the thesis that names are rigid designators whose reference is established by causal interaction between the speaker and the referent.

185

Searle (1969: 93).

186

Wittgenstein (1953: §126–8).

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A rigid designator is a designator that denotes the same individual in all possible worlds; doesn't this presuppose that the same individuals can be found in different possible worlds? Consider the following anti-essentialist metaphysical picture, a version of the ‘bundle of qualities’ conception of an individual rejected by both Kripke and Searle. According to this conception, a particular individual is just the coinstantiation of a certain set of qualities. If individuals are identiﬁed across possible worlds at all, it is only in virtue of some counterpart relation which is deﬁnable in terms of the relations between the bundles of qualities coinstantiated in the different worlds. Consider ﬁrst the pure Leibnizian version of this metaphysical picture according to which particular individuals have all of their properties, including their relational properties, essentially. On this conception, not only is it a mistake to think that we can coherently suppose that Shakespeare—the person himself—had different parents, we cannot even make sense of a counterfactual possibility in which he ate a slightly different breakfast than he in fact ate on a certain morning, or even lived in a world in which slightly different events took place years after his death. The thesis that names are rigid designators is perfectly compatible with this uncompromising metaphysics, but the combination of metaphysical and semantic theses has no plausibility. It gives us the conclusion, for example, that the proposition expressed by the statement that Shakespeare wrote plays is a proposition that is true only in the actual world, and so is a proposition that entails every true proposition. Only God could know that Shakespeare wrote plays. We more limited creatures can know that ‘Shakespeare wrote plays’ expresses a true proposition, and we can know that whatever proposition it expresses, it is necessarily equivalent to the proposition expressed by ‘Elvis Presley played the guitar’, but so long as we are ignorant of any fact, we cannot know which proposition it is that these sentences express. Giving up the Millian theory of names would not resolve the problem, since there is no plausibility in the assumption that however we refer to him, Shakespeare—the man himself—could not possibly have failed to write plays, or to eat what he in fact ate for breakfast. A less uncompromising version of this metaphysical picture gives a different account of what it is for an individual to have a property essentially. According to the liberal Leibnizian,187 to say that Shakespeare—the person himself—might not have written plays is to say that a counterpart of that person in some possible world did not write plays, where the counterpart relation is reducible to some kind of qualitative similarity. The counterpart variation of the Leibnizian metaphysics of individuals is not a thesis about names—it is about the modal properties of individuals, however they are referred to. The difference between the unreconstructed Leibnizian theory and the

187

Lewis (1986a : ch.4.

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counterpart version might still be construed as a semantic rather than a metaphysical difference, but it is a difference in the way complex predicates involving modality are to be interpreted, and by itself says nothing about how names are to be understood. But the absurd consequences drawn from the combination of the Leibnizian metaphysics and the Millian account of names were about the propositions expressed by simple sentences involving nonmodal predicates. If ‘Shakespeare’ is a Millian name, then ‘Shakespeare wrote plays’ is true in a possible world only if Shakespeare himself wrote plays in that world, which means only in the actual world. The fact that we construe ‘could have written no plays’ in such a way that ‘Shakespeare could have written no plays’ is also true in (and only in) the actual world is beside the point. One might try to reconcile the Leibnizian metaphysics in its counterpart variation with a version of the Millian semantics for names by reinterpreting the concept of a rigid designator in a way that parallels the reinterpretation of modal predication. Suppose we say that a designator is quasi-rigid (relative to a possible world w) if its referent in any possible world w′ is a counterpart of some particular individual is w. Then if ‘Shakespeare’ is a quasi-rigid designator, relative to the actual world, ‘Shakespeare wrote plays’ might be true in some other possible worlds—worlds in which a counterpart of Shakespeare wrote plays. The thesis that names are quasi-rigid designators is a kind of compromise between the Millian theory and the sense theory that accounts for some of the phenomena Kripke brought to our attention, but there are problems with it. First, if (as David Lewis has argued) an individual may have more than one counterpart in the same world, then the semantic value of a name will not be determined by the individual. Suppose Shakespeare has two counterparts in some possible world, only one of whom wrote plays. Is ‘Shakespeare wrote plays’ true in that possible world or not? To answer this we need to know which of two (or more) quasi-rigid concepts is expressed by ‘Shakespeare’. Second, even if an individual has at most one counterpart in any possible world, a designator might be quasi-rigid relative to one possible world, and not relative to another, since two counterparts of the same thing (in different possible worlds) need not be counterparts of each other. Despite these problems, the basic Kripkean picture of the way the reference of names is determined might still be reconciled with this metaphysical theory. What is essential to Kripke's picture, I think, is the idea that the content of speech acts and mental attitudes may be determined as a function of particular things (and kinds) with which the speakers and thinkers interact. Whatever one's metaphysical presuppositions, it will be agreed that the way content and reference are determined by the facts will be context-dependent, and inﬂuenced by general beliefs, purposes, and assumptions. The counterpart theorist's story about the background against which reference to a particular (worldbound) individual can determine a proposition

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will be different from the story Kripke might tell, but there is nothing in the counterpart theorist's metaphysics that prevents him telling such a story. The dialectic of this last discussion shows that metaphysical and semantic issues cannot be kept completely apart for at least two reasons. First, if semantic and metaphysical theses together yield implausible consequences, it may be a matter of dispute where the source of the problem lies. Second, some metaphysical theories may force a reformulation of claims about semantics and intentionality. But the possible worlds framework helps to clarify the metaphysical alternatives, and to separate metaphysical from semantic issues so that each can be evaluated on its own terms.

10 On considering a Possible World as Actual (2001) Hell is paved with primary intensions. (English proverb)188

1. Introduction In Naming and Necessity,189 Saul Kripke presented some striking examples that convinced many philosophers that there are truths that are both necessary and a posteriori, and also truths that are both contingent and a priori. The classic examples of the former are identity statements containing proper names (Hesperus = Phosphorus) and statements about the nature of natural kinds (gold has atomic number 79). Realistic examples of the second kind of statement are harder to come by—perhaps there are none—but once one sees the idea it is easy to construct artiﬁcial examples. The most famous example is based on Gareth Evans's descriptive name ‘Julius’.190 ‘Julius’ is, by stipulation, a proper name of the person (whoever he might be) who invented the zip. So the statement ‘Julius invented the zip’ can be known a priori to be true, but since the description is used to ﬁx the reference rather than to give the meaning, of the name, the fact that Julius invented the zip is a contingent fact. Someone other than Julius (the person we in fact named) might have invented the zip, and if some else had invented it instead, it would not have been true that Julius invented the zip. The divergence of the two distinctions was surprising, but the examples are simple and relatively transparent. Kripke's exposition pointed the way to an abstract description of the phenomena that made it clear, on one level at least, what is going on. But the apparatus used to give this description can be interpreted in quite different ways, with different consequences for our understanding of the foundations of semantics, and the nature of intentionality. My concern in this paper will be with the contrast between different lessons that different philosophers think should be learned from the story Kripke told. The account of the phenomena, and of the apparatus used to

188

Slightly modiﬁed from the original. Cf. Bartlett (1955: 715a).

189

Kripke (1972).

190

Evans (1979).

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describe them, that I want to defend (and to attribute to Kripke) can be seen as a variation on, and development of, the skeptical lesson about a priori knowledge and truth taught by Quine. I will begin by sketching the two-dimensional modal analysis of the phenomena, using some of the paradigm examples of contingent a priori and necessary a posteriori truths to motivate it. Then I will distinguish two different ways of interpreting the two-dimensional apparatus and explore the contrasting consequences of the different interpretations.

2. The two-dimensional framework Let's take a closer look at Evans's story of Julius. A certain person, let us suppose, invented the zip, but we don't know who he or she was. That is, there is a fact about a particular person—that he or she invented the zip—that we do not know. But despite our ignorance, we can give this person, whoever he or she is, a name, and when we do, we acquire the semantic resources to state the fact that we do not know to be a fact. If ‘Julius’ names this unknown person, then ‘Julius invented the zip’ states the unknown fact. But we know, in virtue of our act of naming, that it is true that Julius invented the zip (or more cautiously, that if the zip was invented by some one person, it was invented by Julius), so it seems that the fact that it states is not unknown after all: in fact, it is known a priori.191 A slight variation on our example will give us a necessary a posteriori truth. Suppose I ﬁnd out who Julius is: the inventor of the zip was Whitcomb L. Judson.192 That Judson invented the zip is obviously a contingent fact that is knowable only a posteriori. Since this contingent statement is a priori equivalent to the statement that Julius is Judson, the latter statement will have the same epistemological status as the former, but since ‘Julius is Judson’ is an identity statement with two rigid designators, it is a necessary truth, and so a necessary a posteriori truth. Of course ‘Julius’ is a contrived case; real names don't work that way. But real names are like ‘Julius’ in that their reference and what is said with them depend on the facts. This is not a point based on some controversial theory of reference. On any theory of meaning or reference, it will be a contingent fact that a particular word or name has the meaning or reference that it has. It is enough to generate necessary a posteriori truths for there to be two

191

This looks like semantic sleight of hand. An historian wondering who it was who invented the zip would not be satisﬁed with Evans's answer to his question. One will be tempted to complain that we still don't know who Julius is, and so that while we know that ‘Julius invented the zip’ states a fact, we don't know what fact it states. But it is notoriously difﬁcult to say what one has to know to know who someone is.

192

Check out http://web.mit.edu/invent/www/inventorsI-Q/judson.html. It might be noted that, although I can say that I found out who invented the zip, and have told you, neither of us knows very much more about Julius than we did before. Why is knowing what his friends called him enough to know who he is, while knowing what Gareth Evans called him is not?

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different names that have the same semantic value—that make the same contribution to what is said—but that have that value in virtue of different facts. The reference of ‘Julius’ was ﬁxed by the description ‘the inventor of the zip’, while the reference of ‘Whitcomb L. Judson’ was ﬁxed in a different way. The reference of a use of ‘Hesperus’ is ﬁxed by one historical chain of references, while the reference of ‘Phosphorus’ is ﬁxed by a different one. Any identity statement with two such names will be necessarily true, but not knowable a priori, since to know that it is true one will have to know the empirical fact that the two methods of determining reference yield the same result. What lies behind the examples of both kinds is the fact that what is said depends on the facts. For our purposes, we can identify what is said—the propositional content of a statement—with the way the statement says the world is—that is, with its truth-conditions.193 And we can represent a truth-condition by the set of possible worlds in which the condition is satisﬁed, or equivalently with a function from possible worlds to truth-values. But the dependence of what is said on the facts points to an ambiguity in the notion of the truth-condition of a statement. Under what condition is ‘Julius invented the zip’ true? Speciﬁcally, would it have been true if Eli Whitney, rather than Whitcomb Judson, had invented the zip? If our question is about what is (actually) said by that statement—then the answer is ‘no’. But we can also ask about the truth-value of what the statement would have said if Whitney had invented the zip, and to this question the answer is yes. Truth-conditions, in the second sense, can also be represented by functions from possible worlds into truth-values. These ideas have been spelled out with a simple formal semantic apparatus—a

193

Perhaps there is more to the content of a statement than its truth-conditions, but it should be uncontroversial that on any account of what a proposition is (for example, on accounts that identify propositions with structures containing individuals and properties, or Fregean senses as constituents) propositions determine a truth condition, and have that truth-condition essentially. We will set aside contentious questions about propositions and focus on this one feature that all notions of proposition have in common.

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two-dimensional possible worlds semantics.194 In the one-dimensional modal semantics, we start with a language and a set of possible worlds. The language is interpreted by assigning intensions to the expressions, where an intension is a function from possible worlds to extensions of the appropriate type (individuals for singular terms, subsets of a domain for one-place predicates, truth-values for sentences, etc.). Propositions (sentence intensions) are functions from possible worlds to truth-values. The two-dimensional theory associates with each expression, not an ordinary intension, but a two-dimensional intension, which is a function from possible worlds to ordinary intensions.195 Equivalently, we can think of a two-dimensional intension as a function taking an ordered pair of possible worlds to an extension. So a two-dimensional sentence intension (a propositional concept) is a function from possible worlds to propositions, or from pairs of possible worlds to truth-values. A propositional concept can be used to deﬁne two different propositions, representing the two ways of understanding truth-conditions that we have distinguished. One (which David Chalmers calls the secondary proposition expressed by the sentence) is the value of the two-dimensional intension where the argument is the actual world. More generally, the secondary proposition expressed in possible world x is the value of the propositional concept when the argument is possible world x. This represents what is said by the sentence in the sense of the term we have been using. The other (which Chalmers calls the primary proposition) is the proposition that is true in world x if and only if the proposition that is the value of the two-dimensional intension in world x is true in world x.196 Chalmers's primary proposition is what I have called the diagonal proposition, since it is represented in a matrix expressing the two-dimensional intension by the diagonal from upper left to lower right.197 In this framework, the truth-value of a statement, relative to a given possible world, is determined in two different ways depending on which of the two propositions associated with the statement one is considering. To use the jargon ﬁrst introduced by Martin Davies and Lloyd Humberstone in their development and application of this framework, to consider the world x as actual in evaluating a statement relative to world x is to evaluate the primary or diagonal proposition associated with that statement. The alternative way of evaluating the statement, relative to world x, is to determine ﬁrst the secondary proposition that the statement expresses relative to the actual world, and then to determine the truth-value of that proposition relative to world x. Davies and Humberstone describe this as considering x as ‘the “ﬂoating” world’. Chalmers describes this procedure as ‘considering the world as counterfactual’. The distinction between considering a world as actual and considering it as counterfactual is a technical distinction within the two-dimensional framework, but it is also supposed to have some intuitive content that helps to connect the abstract apparatus to its application. To consider a possible

194

See Stalnaker (1978), Davies and Humberstone (1980).

195

As David Chalmers develops this framework, this function takes, as argument, not a possible world, but a centered possible world, where a centered world is a pair ‘consisting of a world and a center representing the viewpoint within that world of an agent using the term in question’ (Chalmers 1996: 60). Formally, we can identify a center with an individual in the domain of the world, and a time. The general idea of a centered possible world, and the terminology, comes from W. V. Quine. This variation will be important when we consider the interpretation of the apparatus, but I will ignore it for the moment.

196

That is, let f, a function taking a pair of possible worlds into a truth-value, be the two-dimensional intension associated with a sentence S. Then the secondary intension of S in world x, fx , and the primary intension of S, fp , will be deﬁned as follows: fx (y ) = f (x,y ), and fp (x ) = f (x,x ), or equivalently, fp (x ) = fx (x ).

197

In Stalnaker (1978). For further discussion of diagonal propositions see the introduction and other papers in Stalnaker (1999).

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world is to make a supposition, and the intuitive contrast is between a counterfactual supposition (for example, ‘suppose Oswald hadn't killed Kennedy’) and a supposition about what is actually true (‘suppose Oswald didn't kill Kennedy’).198 The two-dimensional framework gives a straightforward representation of the phenomena: a contingent a priori statement is represented as a statement with a contingent secondary intension, but a necessary primary intension. Necessary a posteriori statements are the reverse: they have necessary secondary intensions, but contingent primary intensions. No proposition is contingent a priori or necessary a posteriori; there are just different ways in which necessary and contingent propositions are associated with statements. But while the formal apparatus provides a perspicuous representation of the phenomena, I will argue that it leaves open some crucial questions about how the apparatus is to be interpreted, and that, properly interpreted, the two-dimensional story fails to provide a satisfactory account of a priori knowledge or truth, or an adequate account of the ways in which what is metaphysically necessary and possible may depend on the facts.

3. Interpreting the framework I will contrast two different ways of interpreting the apparatus—two ways of saying how expressions and thoughts are associated with their primary, secondary, and two-dimensional intensions. I will begin with a distinction that David Kaplan makes in the context of a discussion of the status of the mechanisms of reference hypothesized by the causal or ‘historical chain’ theory of reference for proper names. Kaplan asks whether those mechanisms are a part of the semantic theory for the language, or whether they belong to what he calls ‘metasemantics’. Semantics says what semantic values of expressions are in a given language. Metasemantics is an account of what the facts are in virtue of which expressions have the semantic values they have. ‘The crucial question’ about the causal theory of reference, Kaplan writes, seems to be: does the theory state a semantic value of proper names, or does it rather tell us the basis for determining a semantic value for proper names.⋯Those who believe that a name means something like the individual who lies at the other end of the historical chain that brought this token to me will regard the historical chain theory as a part of semantics, as giving the meaning rather than telling us how to discover it.199

198

The Oswald example, much discussed in the literature on indicative and counterfactual conditionals, was introduced in Adams (1970).

199

Kaplan (1989a : 574). Cf. Almog (1984), where ‘semantic’ is distinguished from ‘presemantic’, and Ch. 9 of this book, where descriptive semantics is contrasted with foundational semantics.

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Kaplan's distinction is related to, but not quite the same as, the distinction Kripke makes between the meaning of an expression and what ﬁxes its reference. (Kripke criticized Frege for using the term ‘sense’ in a way that conﬂates the two.) The issue is not, as it is with Kripke's distinction, about the contribution that names make to what is said by statements containing them. It is agreed that names are rigid designators, and so that the truth-conditions of propositions expressed with names depend on the individual who is the actual referent of the term. Kaplan's question is whether proper names are like indexical expressions that depend systematically on the context of use. The word ‘I’, for example, is a rigid designator: the truth-conditions of what is said in statements using that word depend on its actual referent. But it still seems clear that one gives the meaning of the word by saying how its referent is determined by the context. An account of how the referent of a use of the word depends on who is using it would be included in a semantic theory of English, and a person who knew that in English ‘I’ refers to the speaker would be said to know the meaning of the word, even if she did not know, or some occasion, who the speaker was, and so did not know what was said by the speaker on that occasion. The meaning of the word ‘I’ is what Kaplan calls a character—a function from possible contexts of use to referents. Kaplan's theory of demonstratives, with its distinction between character and content, provides a model for one interpretation of the two-dimensional apparatus—the semantic interpretation. On this way of applying the apparatus, two-dimensional intensions of expressions are characters, in Kaplan's sense: they are what a correct descriptive semantic theory for a language should associate with expressions. Just as the meaning of ‘I’ is a function that yields a referent (the speaker) as a function of context, so the meaning of the name ‘Aristotle’ is a function that yields a referent as a function of context, and just as ‘I’ may be used in different contexts with the same meaning to refer to different people (although it refers rigidly in each context), so ‘Aristotle’ might be used in different contexts with the same meaning to refer (rigidly) to different people. Similarly, on this account, ‘tiger’ might be used with the same meaning in different possible contexts to apply to members of different animal species (and perhaps to things other than animals). The meaning (character) will be a rule that says how the referent is determined by the facts about the context. Competent speakers will know the primary intension of an expression, but just as they may not know to whom the word ‘I’ refers (if they don't know the relevant contextual facts), so they may not know the secondary intension (the content) of some expression they understand, since that is a function of facts of which a competent speaker may be ignorant. The semantic interpretation of the two-dimensional framework is a considerable extension or generalization of Kaplan's theory: the idea is to treat most words of the language (including proper names and most common

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nouns) the way Kaplan's theory treats indexical pronouns. Since the phenomena that the theory purports to explain are the examples of necessary a posteriori and contingent a priori truths, the relevant expressions in all such examples will be interpreted as expressions with a variable character—a meaning that determines its contribution to content as a function of the contingent facts about the context of use.200 The contrasting interpretation—the metasemantic interpretation—begins by noting that whatever the meanings are that a semantic theory for a language associates with its expressions (or with expressions in context), the fact that the expressions have the semantic values they have will be a matter of contingent fact. There is no controversy about this—the only issue is what the facts are that make it the case that the utterances of speakers have the meanings or contents that they in fact have. But whatever these metasemantic facts are, and whatever semantic values a semantic theory associates with expressions, we can represent the way that those values depend on the facts with a function from possible worlds to semantic values. Now suppose we assume that one kind of semantic value that an expression has (on a particular occasion of use) is a (one-dimensional) intension. Then the function that represents the way that the intension of the expression depends on the facts will be a two-dimensional intension. On the metasemantic interpretation, two-dimensional intensions and so-called primary intensions of expressions are derivative from the secondary intensions that those expressions have in the different possible worlds. The content (secondary intension) of an expression may be different in two different possible worlds either because it is a contextdependent expression and the context is different in the two worlds, or because the expression has different meanings in the two worlds. A primary intension, on this interpretation, is not a kind of meaning that the expression has, but a function whose value depends on the meanings that the expression has, and the contexts in which it is used, in the different possible worlds that are the arguments of the function. The semantic interpretation assumes that the semantic facts about a language determine intensions of the two kinds that can be abstracted from those semantic facts and applied in possible worlds in which those facts do not obtain. We can take the primary intension that an expression of English has in the actual world, and consider the extension determined by that intension relative to an arbitrary possible world. The metasemantic interpretation assumes only that the semantics (plus the context) determines an

200

Those who interpret the two-dimensional framework on the model of Kaplan's theory recognize that they are extending his theory. Chalmers, after noting a correspondence between the primary/secondary intension distinction and Kaplan's character/content distinction, points to some differences: ‘Kaplan uses his account to deal with indexical and demonstrative terms like “I” and “that,” but does not extend it to deal with natural-kind terms such as “water,” as he takes “water” to pick out H2 O in all contexts’ (Chalmers 1996: 366).

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ordinary intension, so it assumes less about what can be derived from the semantics for a language. But its primary intensions are functions with a more limited domain. On the metasemantic interpretation, the values of primary intensions are determined in a straightforward way only for possible worlds containing the (token) expression. Chalmers, in his discussion of the two-dimensional framework, notes Kaplan's distinction, but says that whether a process of reference ﬁxation ‘is part of metasemantics or semantics makes little difference for my purposes; all that matters is that reference ﬁxation depends in some way on how the actual world turns out’.201 But I will argue that it does make a difference, since the question is not simply one of how to categorize a representation of how referents depend on the facts. The distinction reﬂects two different uses of the two-dimensional apparatus, both of which have a part to play in an adequate theory of speech and thought. Some issues about intentionality, and about a priori knowledge, are obscured or distorted when the two uses are conﬂated. To try to bring out the signiﬁcance of the difference between the two interpretations, I will look at some cases where the two accounts yield different results about what the primary intension is, and argue that such examples show that the metasemantic interpretation is the one that is supported by intuitions about what we are doing when we consider the world as actual. Then I will argue that whether we characterize the relevant two-dimensional and primary intensions as kinds of meaning or not has consequences for our understanding of a priori knowledge and truth, speciﬁcally for our understanding of the sense in which the primary intensions of expressions are known a priori, and of the thesis that statements knowable a priori are those whose primary intensions are necessary propositions.

4. Contrasting applications of the framework We can all agree that natural languages contain context-dependent expressions, and that an adequate descriptive semantics for such languages will make the kind of distinction between character and content that Kaplan makes in his theory of demonstratives. But we should also all agree that it is a matter of contingent fact that the expressions of natural language have the character and content that they have, and that these facts can be represented with functions from possible worlds to semantic values of the relevant kind. (If meaning is a kind of two-dimensional intension, then we will need three-dimensional intensions to represent the metasemantic facts.) Whatever the form of a correct descriptive semantics for a language, or of a descriptive account of the contents of the thoughts of some thinker, there will remain the question, what are the facts in virtue of which that descriptive account is correct?

201

Ibid. 366, n. 25.

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So two-dimensional and primary intensions for the same expression can be determined in two different ways, and the two procedures may yield different results. For an example in which they diverge, consider Joseph Almog's case202 of a twin earth where the meanings of the pronouns ‘I’ and ‘you’ are interchanged. An English speaker, Hilary Putnam, has a conversation there with his twin, Hilary Mantup. They each say to the other ‘you are charming’. Let us suppose that the two are unaware of the difference between their languages, and so that they misunderstand each other. Putnam thinks, mistakenly, that he is in a possible world w in which Mantup is speaking English. Now if the primary intension we are evaluating is based on a Kaplanian character, then when we ask what the extension of Mantup's word ‘you’ is relative to world w, we are asking what Mantup's word, with its actual meaning, would refer to in a context in which Mantup is speaking to Putnam. So it is the speaker, Mantup, that the pronoun refers to, relative to w. In contrast, if we are evaluating a primary intension determined by the metasemantic procedure, then we ask what Mantup's word, as used in w, refers to. Mantup is speaking English, and not twin-English, in world w, so the value of this primary intension of Mantup's ‘you’ (centered on Mantup in w) is the addressee Putnam. The question is, which application is appropriate for explaining the phenomena of necessary a posteriori and contingent a priori truth, and for making sense of the intuitive idea of considering a world as actual? I think it is the metasemantic interpretation that provides the basis for the intuitive content of the idea of ‘considering the world as actual’. To see this, consider another example where the semantic and metasemantic primary intension diverge. Suppose in possible world x, the word ‘tiger’ means what ‘sofa’ means in the actual world. Even if ‘tiger’ is a word whose meaning (in the actual world) is a variable character (in Kaplan's sense), it still should be uncontroversial that the meaning of ‘tiger’ in x is different from the meaning the word has in the actual world. (Perhaps it is a different word.) Now what are we being asked to do if we are asked to consider the world x as actual? We are to suppose that we discover that we are actually in world x. This may be difﬁcult to do when, as in this case, the possible world in question is very obviously counterfactual. It might help to get a better handle on the idea of considering a world as actual to imagine ourselves in a conversational context in which someone else believes, or at least doesn't disbelieve, that x is the actual world. Whatever we know or believe, we could not, without begging the question, presuppose in such a context that x is not the actual world. Now it seems clear that if x really is the actual world, then our word ‘tiger’ refers to pieces of furniture. If x is actual, then one speaks the truth when one says ‘tigers are pieces of furniture’ (assuming that, in x, ‘piece of furniture’ refers to pieces of furniture). So when we

202

Almog (1984: 479).

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evaluate ‘tigers are pieces of furniture’ in x, considered as actual, we should say that it is true. Contrived as this example is, it does seem intuitively right that if we were in a conversation with someone who was under the misapprehension that ‘tiger’ was a synonym for ‘sofa’, it would be natural to correct him by saying ‘tigers aren't pieces of furniture—they're animals.’ This remark would have a point only if it said something that was false in possible world x, since what one is trying to do in making the remark is to tell one's interlocutor that the actual world is not a world like x. But if we were to evaluate the statement according to the semantics of the actual world, then it would be true in world x. It is the primary intension of that utterance, understood on the metasemantic interpretation, that is the information we are intending to convey.

5. A priori knowledge and truth Given the two-dimensional framework, however it is interpreted, we can, if we like, simply stipulate that when we call a sentence ‘a priori’ what we are saying is that its primary intension is necessary. But whether ‘a priori’ in this technical sense has any epistemological signiﬁcance will depend on how the framework is interpreted. What does it mean to say that something is knowable a priori? One idea is that knowledge is a priori if it is knowledge that derives from a decision rather than from a discovery. As we use them, words mean (it is tempting to believe) what we intend them to mean, and we may choose to use them in a way that ensures that what we say with them is true. Consider ‘Julius’ again. ‘Julius invented the zip’ seems, intuitively, to be a truth that is knowable a priori because Evans made it true by stipulation. The decision that ﬁxed the reference of the name ensured that (if reference was ﬁxed at all) the statement would be true. But what exactly did Evans stipulate—what meaning did he give to this name? There are two ways to understand this act of reference ﬁxing that correspond to the different interpretations of the two-dimensional apparatus. Consider a formal language with a two-dimensional operator, ‘dthat’,203 which is used to construct complex singular terms of the form ‘dthat(n)’, where n is a singular term, perhaps a deﬁnite description. The semantic rule for ‘dthat’ in a two-dimensional semantics is as follows:

‘Dthat’, on this interpretation, is a rigidifying operator: it turns any singular term into a rigid designator for the thing that is the actual referent of that term. In this formal language, any sentence with the form

203

Kaplan (1978). In Kaplan (1989a ), Kaplan contrasts two different ways of understanding the word he introduced, and suggests that the one I am using here is not the one he originally had in mind.

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‘ ’ will be a logical truth, even though, if what goes in for n is a nonrigid designator, the resulting sentence will have a contingent secondary intension. We might interpret Evans to have stipulated that the name ‘Julius was to be an abbreviation for a complex singular term that has the meaning ‘dthat[the inventor of the zip]’. If this is what he did, then his stipulation makes the sentence of quasi-English ‘If any one person invented the zip, then Julius did’ an abbreviation for a logical truth. But there is an alternative way of understanding Evans's stipulation that ‘Julius’ should be a name for the inventor of the zip. On this contrasting construal, what he did was to establish a semantic link between the name ‘Julius’ and a certain person. The role of the description was to ﬁx the reference, not to be part of giving the meaning. (Kripke's distinction between meaning-giving and reference-ﬁxing descriptions acquires more complexity when rigidifying operators are incorporated into the language.) On this interpretation, the stipulation is part of the story about how the name acquired its semantic value. (Analogous to a story that an historical linguist might tell about how the word ‘villain’, which once meant something like farm servant, came to mean something like malicious person.) ‘How did Whitcomb L. Judson ever come to be called “Julius”?’ someone may someday ask. The historian answers: ‘Years ago, a philosopher, in concocting an example, gave that name to the inventor of the zip, and it later came to light that Judson was the one he had named.’ On this second way of understanding the stipulation, the a priori status of ‘Julius invented the zip’ is fragile, and not a fact about anything that could reasonably be called the meaning or intension of the sentence type. Perhaps at the moment when Evans said, ‘let “Julius” name the inventor of the zip’, his knowledge that Julius invented the zip if anyone did was a priori knowledge. Perhaps the same is true for us when we read about Evans's stipulation, and decided to use the name in the same way. But suppose someone—call him Jones—picks up the name from me without getting the full story about how Julius got his name. (‘Eli invented the cotton gin, Thomas the lightbulb, and Julius the zip,’ I tell him. Jones knows, a priori perhaps, that Julius is the person I was referring to (if I succeeded in referring) with the name ‘Julius’. Whether he knows at all that Julius invented the zip may be questioned, but it is clear that if he does know it, he knows it on my authority—the same way he knows that Eli invented the cotton gin—and not a priori. If we give the ﬁrst account of Evans's stipulation, taking the name to be an abbreviation for a complex singular term, then we must say that Jones does not understand my statement, and that when he subsequently uses this name, he means something different by it. My sense is tied to the description ‘the inventor of the zip’, while Jones's use is parasitic on mine: his sense is something like ‘dthat[the person Stalnaker was referring to with the name “Julius” on such and such an occasion]’. If we build the means by which the

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name acquired its reference into the semantic properties of the term, then the fragility of a priori knowledge becomes the fragility of meaning. But if the connection between ‘Julius’ and the invention of the zip is part of the historical story of how the name came to have the semantic properties that it has, then it is not something that a person using it with those semantic properties needs to know to be a competent user of the name. What does one have to know in order to be using the name with the semantic properties Evans gave it? If Kripke is right about reference, we don't have to know very much about a person to be able to use a name to refer to him or her, and even if we do have to know some things, there need not be anything we have to know a priori. Since the metasemantic two-dimensional intension represents all the ways in which the reference or content of an expression depend on the facts, it will not provide any nonvacuous account of a priori truth. To say that a primary proposition associated with a sentence was necessary would be to say that the sentence would express a truth whatever it meant, and that notion, of course, will have no application. The semantic interpretation of the two-dimensional apparatus assumes that semantics provides cognitively accessible two-dimensional meanings for all of its expressions—meanings that are determined by the internal states of the users of the expressions, and that the expressions have in virtue of the decisions of the speakers to speak a language with that semantics. I don't think it is plausible to think that semantics provides any such thing. Such attraction that this kind of theory has comes, I think, from the other interpretation, which models the ways that semantic values depend on the facts, but which neither depends on nor provides any account of a priori truth. But the metasemantic account can, I think, provide an explanation for the phenomena that Kripke's work brought to light. Suppose our semantics for names is a simple one-dimensional semantics: they have no semantic values other than their referents. Suppose further that the right account of what determines reference is an externalist story. Reference is established by our referential intentions, but intentions are mental states with content, and their content is determined by facts, some of which are in our environment, and of which we are often ignorant. Both O'Leary and I refer to Hesperus with ‘Hesperus’ in virtue of our intentions to refer to Hesperus, and our intentions are intentions directed at Hesperus in virtue of the role that that planet plays in the explanation of our mental states and behavior. It is a familiar story. Now suppose O'Leary and I agree that Hesperus is a planet, but he doubts whether Phosphorus is a planet. Or so he says. Or so he seems to say. How do I understand what it is that he doubts? I, or a theorist trying to characterize our discussion, might try to get clear about the issue in question by considering the possible worlds that are compatible and incompatible with our respective beliefs, and with

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various things we might say in the attempt to resolve our disagreement. But there is a problem, since O'Leary thinks there is a possible world in which Hesperus is a planet, but Phosphorus is not, while I know that there is no such possible world. Our disagreement seems to be partly semantic—about what ‘Hesperus’ and ‘Phosphorus’ are used to refer to. But we can get clear about the facts we disagree about, and about what O'Leary is saying, by considering worlds as actual. If I suppose (even though I know it isn't true) that the actual world really is as O'Leary thinks it might be, then I am supposing that Hesperus and Phosphorus really are two distinct things, and only one of them is a planet. In supposing this, I am supposing that we are in a possible world that differs both in astronomical and semantic facts from the world that I think we are in. The two kinds of facts are interconnected, and perhaps cannot be separated, but the two-dimensional apparatus allows us to represent the situation without separating them. I can consider such possible worlds ‘as actual’ without assuming that the names for the planet have underlying senses to which we have a priori access, and that determine what the names refer to in the different possible worlds. I can assume that, as the simple story says, the semantic value of a name is just its referent.

11 Conceptual Truth and Metaphysical Necessity (2003) 1. Introduction Long ago, in ancient times, before Kripke, and even before Quine, philosophers (at least empiricist philosophers) held that all necessity was verbal, or perhaps conceptual. There were matters of fact, expressed in statements that are contingent, synthetic, and knowable only a posteriori, and there were relations of ideas, expressed in statements that are necessary, analytic, and knowable a priori. The idea that there might be substantive metaphysical truths about the necessary structure of reality or the essential natures of things was thought to be a relic of an outdated, prescientiﬁc philosophy. What necessary truths there are have their source in us—in the way we choose to talk, or in the concepts with which we think about the world, and not in the reality we talk and think about. Later, Quine taught us to be skeptical of the very idea of necessity, analyticity, and a priori knowledge, but he did not question the empiricist's assumption that these notions stand or fall together. But then Kripke began pulling the different distinctions apart, arguing that there could be, and in fact are, truths that are necessary, despite the fact that they can be known only a posteriori, and also truths that are contingent, but can nevertheless be known to be true a priori. The separation of the metaphysical and epistemological distinctions might be thought to make it possible to agree with the empiricist that substantive truths about the world can be known only on the basis of empirical evidence while also allowing that there might be nontrivial metaphysical truths about the essential natures of things—statements that, despite their dependence on empirical support, are necessarily true. The empiricist remains skeptical. While it is generally agreed that Kripke's striking examples of the necessary a posteriori and the contingent a priori show something, it is controversial just what the moral of his story should be. A number of philosophers204 have argued that the facts that Kripke brought to light can be reconciled with the idea that all necessity has its

204

Most prominently, Alan Sidelle, Frank Jackson, David Chalmers. See Sidelle (1989), Jackson (1998), Chalmers (1996).

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source in our language and our ideas—it's just that the relation between our language and the world is more complicated than the traditional empiricist picture suggested. There are no irreducible necessary a posteriori truths, according to this line of argument. Such truths can be factored into a part that is necessary, but knowable a priori through conceptual analysis, and a part that can be known only a posteriori, but that is contingent. Frank Jackson and David Chalmers have used the apparatus of two-dimensional semantics to make this kind of reduction of the necessary a posteriori precise. I agree with Jackson and Chalmers that the phenomenon has its source in the relation between the way we represent the world (in both thought and language) and the world that we represent, but I think it reveals something about the nature of mental representation, and not just something about the way the languages we use happen to work. I also agree with Jackson and Chalmers that the two-dimensional semantic framework provides a useful apparatus for representing Kripke's distinctions between metaphysical and epistemological concepts, and for clarifying their status. But I remain unconvinced that the necessary a posteriori can be reduced or factored in the way they suggest, or that the two-dimensional semantic framework succeeds in dissolving the problem of the necessary a posteriori. There are at least two interpretations of the abstract two-dimensional framework, equally legitimate, but different. Neither, I will argue, provides a basis for the kind of reduction that Jackson proposes. That kind of reduction is defensible, I will argue, only if one makes implausible assumptions about how intentionality is to be explained. Before I begin let me set aside a way of explaining the phenomenon of necessary a posteriori truth that Jackson contrasts with his own, and that we can all agree is wrong. This is the view that metaphysical necessity is a restricted kind of necessity, and not necessity in the widest sense. Since we cannot know a priori, simply by grasping the concepts involved, that gold is an element with atomic number 79, we are tempted to say that even if that proposition is metaphysically necessary, it is nevertheless not conceptually necessary, and so is false in some conceptually possible worlds. On this picture, we should think of metaphysical necessity as analogous to physical or nomological necessity. The laws of nature are contingent

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truths—true in some possible worlds and false in others.205 But we can deﬁne a class of possible worlds in terms of the laws that hold in the actual world, and say that the laws, and their consequences, are necessary in a restricted sense. Nomological necessity (in possible world x) is truth in all possible worlds that have the same laws of nature as possible world x. Analogously, one might think that there are some conceptually contingent metaphysical truths—the metaphysical laws—and that metaphysical necessity is truth in all possible worlds that are compatible with the metaphysical laws. Conceptual analysis and deductive reasoning sufﬁce to tell us what is conceptually possible, but are powerless to reveal the metaphysical laws that rule out the possibilities that are conceptually coherent, but metaphysically impossible.206 Restricted necessity is a perfectly coherent notion, but to understand it, one needs to be told about the nature of the restriction. To what do the metaphysical laws owe their exalted status? How are they different from mere physical laws? Even if one could justify some distinction of levels—deeper and less deep contingent laws—it still seems that this way of drawing a distinction between conceptual and metaphysical necessity is committed to the view that mere metaphysical necessities are not really necessary. To evoke the theological metaphor, couldn't God have created any world that is logically or conceptually possible?207 The real problem with this way of thinking about what Jackson describes as ‘the now famous distinction between metaphysical and conceptual necessity’208 is that it confuses a property of the propositions that are the contents of our speech and thought with a property of the linguistic and mental representations that have those contents. The necessity or contingency of a proposition (in either a restricted or an unrestricted sense) has nothing to do with our concepts or the meanings of our words. The possibilities would have been the same even if we had never conceived of them. They are not given by or constructed out of our concepts. Rather, we make sense of a concept, and of the conceptual coherence of a thought, only by making sense of metaphysically possible situations that would, if realized, instantiate the concept, or make the thought true. Conceptual possibilities are just (metaphysical) possibilities that we can conceive of. So we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense. It is not just that the metaphysical laws rule out the possibility that gold be something other than an element with atomic number 79—it is that if we think clearly (in light of empirical facts) about what it would be for there to be gold that was not such an element, we see that there is no such possibility for any laws to rule out. But it remains to be seen what conclusions can be drawn from this about the epistemological status of our beliefs about what is and is not metaphysically possible.

205

Some philosophers would disagree, arguing that the laws of nature are metaphysically necessary, but we will ignore them for the purposes of this analogy.

206

Frank Jackson argues against this kind of distinction between two senses of necessity in Jackson (1998: 67–84). David Chalmers argues against what he calls ‘strong metaphysical necessity’ in Chalmers (1996: 136–8).

207

Cf. Chalmers (1996: 138). Chalmers poses this rhetorical question to the philosopher who thinks that zombie worlds are logically, but not metaphysically, possible.

208

Jackson (1998: 68).

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Here is my plan: I will start by outlining the basic two-dimensional framework in the abstract, and spelling out what is required to apply this framework to the phenomena of speech and thought. I will contrast two kinds of interpretation—two ways of applying the abstract two-dimensional framework—that suggest very different pictures of the phenomena that Kripke brought to light. My main aim will be to bring out the signiﬁcance of the contrast I will draw, and to show what one must assume about how the problem of intentionality is to be solved if one is to sustain the kind of general reduction of necessary a posteriori truth that Jackson and Chalmers propose.

2. The abstract framework Let me start with a remark that I hope will be obvious and uncontroversial: meanings ain't in the head. Wide contents ain't, narrow contents (if any) ain't. A-intensions, C-intensions, two-dimensional intensions—none of them are in the head. Frege said it ﬁrst: ‘Cut the pie any way you like, senses just ain't in the head.’ Of course Frege said it in German, and this is a free translation, but Putnam's famous slogan actually ﬁts Frege's anti-psychologism better than it ﬁts Putnam's and Burge's anti-individualism. The point is that intensions of any kind are abstract objects. Any of these objects—meanings, contents, intensions of various kinds—are the meanings or contents of some utterance, inscription, or mental act or state. The abstract objects are somehow associated with things that in some cases are in the head—the things that have the meanings or contents. So there are two different kinds of questions to ask about a theory of meaning, content, or intension. First, what are the objects? Second, what are the relations in virtue of which they are associated with certain linguistic and mental acts and states? Questions of the ﬁrst kind, which I will call descriptive questions, might be either general (for example, what kind of thing is the content of an assertion or a judgment—what is a proposition?) or speciﬁc (what was the content of O'Leary's utterance of ‘the cat is on the mat’?). Questions of the second kind, which I will call foundational questions, are about what it is that makes it the case that the acts and states of thinkers and talkers have contents of the kind they have; what is it, in general, that makes it the case that certain patterns of sound, marks on a page, or states of a person's brain are associated with the intensions with which they are associated? And speciﬁcally, in virtue of what did O'Leary's uttering the particular sounds he uttered constitute his saying something with the particular content that it had? The abstract two-dimensional framework gives us answers to general questions of the ﬁrst kind. To interpret the framework we need to answer questions of the second kind. It is the second kind of question that I am mainly interested in, but just so we

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are clear about what we are interpreting, I will sketch the nuts and bolts of the abstract framework, using Chalmers's terminology. There are three interrelated kinds of intensions that can be deﬁned in the abstract framework: two-dimensional intensions, primary intensions or A-intensions, and secondary or C-intensions. Each kind of intension is a function whose arguments are possible worlds (which we here take as given),209 or centered possible worlds. The values of these functions may be objects of various kinds (including people, physical objects, sets of individuals, and truth-values), but for simplicity I will talk only about sentence intensions, or intensions that take truth-values as their values. A centered world is an ordered triple consisting of a possible world, an individual in the domain of the world, and a time. A two-dimensional sentence intension is a function with two arguments, a centered world and a possible world. Its value is a truth-value. A primary sentence intension is a function with one argument, a centered world. Its value is a truth-value. A secondary sentence intension is a function with one argument, a possible world. Its value is a truth-value. A two-dimensional intension can be thought of as a function from centered worlds to secondary intensions: if I is any two-dimensional intension, then for any centered world , the secondary intension determined is the one that takes a possible world x to . Each two-dimensional intension I determines a unique associated primary intension P, deﬁned as follows:

That is the theory. It gives answers to the general descriptive questions about the natures of the different kinds of intensions that the theory posits. Now what do we do with it? The ﬁrst thing we can do is to point to answers to some of the speciﬁc descriptive questions in order to connect the framework with the phenomena that it is supposed to explain. Since it is the phenomenon of necessary a posteriori truth that we are interested in clarifying, we will look at two of Kripke's now familiar examples: gold has atomic number 79 and Cicero = Tully. According to the two-dimensional explanation of the phenomena, the necessity of these statements is constituted by the fact that the secondary intension is a necessary proposition, and their a posteriori character is constituted by the fact that the associated primary intension is a contingent proposition. So the two-dimensional intensions

209

There are, of course, lots of questions, not addressed here, about what possible worlds are. These are questions about the interpretation of the abstract theory that are for the most part orthogonal to the issues of interpretation I will be raising.

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associated with the statements will determine (relative to the actual world) the proposition that is true in all possible worlds, but relative to some other possible worlds, it will determine secondary propositions that are false, and so the primary or diagonal proposition determined will be contingent. In any possible world, it will be true that the actual stuff that we call ‘gold’ has atomic number 79 , and that is why the secondary proposition determined, relative to the actual world, is necessary. But in some possible worlds there will be a different kind of stuff that is superﬁcially like gold, and that is causally connected to speakers' uses of the word ‘gold’ in the same way that gold is connected to our use of the word in the actual world. This other kind of stuff is the referent determined by the primary intension of our word ‘gold’, relative to those other possible worlds, and since that stuff does not have atomic number 79 , the primary intension of ‘gold has atomic number 79’ is false in such worlds, and so is a contingent proposition. Similarly, the two names ‘Cicero’ and ‘Tully’ actually have the same referent, and since the identity relation holds necessarily if at all,210 the secondary proposition determined relative to the actual world is necessary. But since two different individuals might have played the roles that Cicero actually played in ﬁxing the referents of the two names, the primary or diagonal proposition will be false in some possible worlds. This is the intended result, but nothing has yet been said about the foundational questions—about what it is that associates two-dimensional intensions, and their corresponding primary and secondary propositions, with utterances and mental acts and states. These are big questions, requiring a solution to the problem of intentionality. My aim here is only to focus attention on questions of this kind, to contrast two different strategies for answering them, and to bring out the signiﬁcance of the contrast.

3. The Kaplan paradigm Here is one interpretation or application of the two-dimensional semantic theory, which I will call the Kaplan paradigm: start with the obvious fact that natural languages are highly context-dependent. The meaning of a sentence does not by itself determine the content of what, on some particular occasion, it is used to say. Meaning determines content only relative to a context. For example, the sentence ‘you will feel better in the morning’ does not by itself say anything. Just knowing what that sentence means will not sufﬁce to know what, when someone uses it, it is being used to say. One needs to know (at least) who is being addressed, and when the statement was made. In a formal semantics for a context-dependent language, the meaning of a sentence (what Kaplan calls its ‘character’) will be a function from context to content. If contexts are represented by centered worlds, and

210

Ignoring, as Kripke does, possible worlds in which Cicero does not exist.

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contents by propositions (functions from possible worlds to truth-values), then a character, in Kaplan's sense, will be a two-dimensional intension of the kind described above.211 The Kaplan paradigm is one important application of the two-dimensional semantic apparatus, but it does not by itself provide a full answer to the foundational question, and it is not in any case suitable, as it stands, to account for the phenomena we are interested in accounting for. First, Kaplan's theory is a descriptive semantics for a language, and not a theory about the interpretation of thought. The original rationale for Kaplan's distinction between character and content was that sentence meanings don't represent thoughts expressed, but only the means used to express thoughts. It is the content (the secondary intension) that is, according to Kaplan, what is said in a statement; it is the thought expressed, the information the speaker intends to communicate. According to Kaplan's semantics, when Daniels said ‘you will feel better in the morning’ to O'Leary, he expresses the (singular) proposition that O'Leary will feel better in the morning, and if Daniels doesn't know to whom he is speaking, he doesn't know what he is saying.212 But the phenomena we want to explain concern the epistemological status of what is expressed in a statement. To account for the phenomena, we need an interpretation of the framework that associates two-dimensional intensions with the mental states of the person who believes or doubts that Cicero is Tully, or that gold has atomic number 79, and not just with the sentences used to express those thoughts. The Kaplan paradigm, in its unreconstructed form, does not in any case give the right account of the standard examples. Proper names and natural kind terms are not naturally interpreted as indexical expressions. In contrast with the case of personal pronouns, there is no systematic semantic rule saying how the referents of such terms depend on the context. ‘Gold’, ‘Cicero’, and ‘Tully’ have constant character in Kaplan's theory.213 The semantics for ‘Cicero’ tells you that it names Cicero, and for ‘gold’ that it names the metal gold. So according to this application of the framework, both the secondary and the primary intensions of our necessary a posteriori truths will be necessary propositions. So the framework, interpreted this way, cannot explain why our standard examples are knowable only a posteriori.

211

See Kaplan (1989b).

212

Of course knowing to whom you are speaking (or, more generally, who someone or something is) is a complicated matter. It isn't clear exactly what Daniels has to know to know who he is talking to, or what it is to intend to express a singular proposition about that person. In some cases, one may not know, in any sense, to whom one is speaking. Suppose Dr Daniels leaves a message on his answering machine for any sick person who happens to call, saying ‘take two aspirin, and you will feel better in the morning’. Not very responsible medical practice, and not a standard use of the personal pronoun either.

213

The names may be used to name other things—I might call my cat ‘Cicero’. But this is treated, in Kaplan's account of names, like a case of ambiguity.

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To use the Kaplan paradigm to account for the phenomena we are concerned with, it needs to be extended to a theory of thought as well as language, and to be used to give a semantics that treats a much wider range of expressions as context-dependent than is usually done.214 According to what I will call the generalized Kaplan paradigm, a proper semantic theory for our language, and for the interpretation of our judgments and attitudes, will apply the character–content distinction much more widely—practically all descriptive expressions of the language will have a variable character. On the generalized Kaplan interpretation of the two-dimensional framework, it is the character of a thought (and the primary intension that it determines) that is its cognitive value. The content of your thought, when you think that gold has atomic number 79, or that Cicero is Tully, is a contingent proposition. More generally, to think that Cicero was a Roman orator, or that the price of gold is going down, is to think a descriptive thought about the persons, whoever they are, who ﬁt certain descriptions, or about whatever substance it is that plays a certain role in our lives. The rigidity of the proper names and the natural kind term is the result of what is, in effect, a generalized scope device. The two-dimensional intension for the thought determines a non-rigid description of a proposition; the secondary intension is the referent of that description. This proposition is not the content of the thinker's thought, but is determined by it, as a function of the facts. The generalized Kaplan paradigm, as I have described it so far, leaves a large question unanswered—the foundational, or metasemantic question: what is it about the minds and behavior of speakers and thinkers, or the way they are situated in the world, in virtue of which their states and acts have the two-dimensional characters that they have? I will say more about this question after sketching a different interpretation of the framework.

4. The metasemantic paradigm Suppose we begin with a causal or information-theoretic account of the intentionality of thought. The rough idea is that to believe that P is to be in a state that tends to carry the information that P, and that plays a certain role, in connection with the believer's desires, in determining her actions. The thoughts I would express with the name ‘Cicero’ are about Cicero in virtue of facts about the role of Cicero in the causal explanation of the fact that I have the thought.215 It is a big and difﬁcult question exactly how such an account should be developed in detail, but any way of developing it will give

214

Chalmers notes that he is applying the Kaplan framework in a more general way than Kaplan intended. Cf. Chalmers (1996: 365–6, n. 25).

215

This kind of account applies directly to thought, and indirectly to language. My uses of the name ‘Cicero’ refer to Cicero in virtue of my intention to refer to Cicero, and that intention is an intention to refer to Cicero in virtue of the role of the person Cicero in explaining the fact that I have that intention.

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an account of intentionality that is externalist or anti-individualist in Tyler Burge's sense: it will hold that the contents of our thoughts are determined, not just by what is going on in our heads, but also by the way we are situated in the world. The facts about the way a thinker is situated in the world that explain why his utterances and thoughts have the content that they have are not part of the content, and may not be cognitively accessible to the person. The content of my thought that Cicero was a Roman orator, on this kind of account, is simply the singular proposition that Cicero—the man himself—was a Roman orator. The facts about the way I am related to Cicero that explain why my thought has that content are not part of what I believe when I believe that Cicero was a Roman orator. Like any account of intentionality, the causal-information theoretic account is externalist in a different sense: it is not the story the thinker tells about his thoughts, but an external theorist's account of the relation between the thinker and his thoughts. The contents of thought—the information (or misinformation) that thinkers' states of mind tend to carry—are ordinary propositions, one-dimensional sentence intensions. On the metasemantic interpretation of the twodimensional framework, the second dimension is used to represent the metasemantic facts about the relations between a thinker or speaker and the contents of her thoughts or utterances. That a certain utterance or occurrent thought has a certain content is a function of the way the world is. If the world had been different in certain ways—speciﬁcally if a different person had played the role that Cicero in fact played in causing my internal mental states to be as they are—then my remark, ‘Cicero was a Roman orator’, and my internal state that in fact constitutes my thought that Cicero was a Roman orator would have had a different content. Its content would have been a singular proposition about that different person. Whatever story we tell about the facts that determine the contents of thoughts and utterances, if we assume that those contents are propositions (one-dimensional sentence intensions), then we can use a two-dimensional intension of the kind described above to represent the metasemantic facts in virtue of which particular thought and utterance tokens have the content that they have. The metasemantic paradigm is not committed to the causal/information-theoretic account of intentionality. Two-dimensional intension, interpreted this way, might be useful on any account of intentionality for describing situations in which speakers or thinkers are ignorant or mistaken about what someone is saying or thinking, since on any account of intentionality, it will be a contingent fact that utterances and mental states have the content that they have. How does the metasemantic paradigm apply to the phenomena we are interested in? Consider the person who is ignorant of the fact that gold has atomic number 79. Suppose that O'Leary thinks that gold is a mixture of tin and copper, and so isn't an element at all. (He has plans to get rich by manufacturing gold out of its much cheaper components.) Confused as

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O'Leary is, it might seem that he could have a coherent, if mistaken, conception of the world. What does he think the world is like? The world, as O'Leary conceives it, is a world that differs from the actual world both in its semantics and in its extra-semantic facts. In that possible world, the term ‘gold’ refers (rigidly) to bronze, since it is bronze that plays the role there, in both our semantic and economic lives, that gold in fact plays. So English has a different semantics in the world as O'Leary takes it to be. The two-dimensional framework, on the metasemantic interpretation, is suited for describing situations of this kind in which someone is ignorant or mistaken about semantic facts, or facts about what determines the contents of thoughts. The diagonal of the two-dimensional intension of the sentence ‘Gold is a mixture of tin and copper’, on the metasemantic interpretation, will represent the mix of semantic and factual misinformation that is a part of O'Leary's conception of the world. Does the fact that O'Leary is mistaken about semantic facts mean that he does not know what ‘gold’ means? Well, he knows that it refers to gold (and he knows of gold that it refers to it). It is just that he is mistaken about the nature of gold. Or consider the person who is ignorant of the fact that Cicero is Tully. The names (according to the semantics we are presupposing) have as their semantic values simply their referent—the same for both. But there is a different account, for each name, of how it came to have this semantic value, and so one might not realize that the two names have the same semantic value.216 Does this mean that the person who doesn't know that Cicero is Tully doesn't understand one or both of the names—doesn't know who it is that ‘Cicero’ or ‘Tully’ denotes? Perhaps in some sense (it would seem natural to say that she doesn't know that ‘Tully’ denotes Cicero), but it would not seem right to say, simply on the basis of not knowing the identity, that she was not competent with the name, or did not express beliefs about Tully with her uses of the name ‘Tully’. We might say that she knows that ‘Tully’ refers to Tully, but doesn't know that ‘Tully’ refers to Cicero. This claim would be subject to the same kind of two-dimensional analysis as the original identity statement.

5. The signicance of the contrast I have distinguished the generalized Kaplan paradigm from the metasemantic paradigm, but one might wonder whether there is really a signiﬁcant

216

Those who are as ignorant of Roman history as I am are able to say very little about exactly how the two accounts differ. Unlike the case of Hesperus and Phosphorus, or the ﬁctional case of Superman and Clark Kent, there are not contrasting descriptions that are stably associated with the names. Still, even though many of us probably acquired the name ‘Tully’ by learning that it was another name for Cicero, we can recognize the a posteriori character of the identity statement.

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difference between the two kinds of account. Does it matter whether we think of the causal chains that connect names with their referents as part of the metasemantic explanation of why those names have the semantic value they have or whether we incorporate the causal story into the semantic content of what is said with the names? Chalmers says, in defending the generalized Kaplan paradigm, that whether the ‘process of reference ﬁxation ⋯is part of metasemantics or semantics makes little difference for my purposes; all that matters is that reference ﬁxation depends in some way on how the actual world turns out.’217 But I will argue that the way we draw the semantics/metasemantics distinction does matter. The two accounts tell very different stories about necessary a posteriori truths. However one draws the distinction between semantics and metasemantics, it is important not to bypass the metasemantic question by equivocating between the two kinds of questions. Whatever descriptive semantics one defends—whether it is a direct reference theory or a version of causal descriptivism— one has to tell a story about what the facts are in virtue of which that semantics is a correct semantics for the language or states of mind in question. If one builds the causal story into the descriptive semantics, then one has said how, given a language with this descriptive semantics, the referents of names are determined by the facts. But there is a further question: how do the facts determine that the language has that semantics? One reason to emphasize the distinction between semantic and metasemantic questions is to be sure that, whatever one's semantics, this question is not overlooked. Causal descriptivism—a description theory of names that builds the causal story into the description that is the content of the name (and also incorporates a rigidifying operator to ensure that the descriptions that names abbreviate have wide scope)—is a theory that passes the metasemantic buck from names to general terms, but one still needs an account of how the general terms get their meaning—how the reference of the terms with which the causal story is told is ﬁxed. Jackson suggests at one point that there might be a language that banned the kind of reference ﬁxing that, as our actual language works, connects names (rigidly) with their referents, and says that in such a language there would be no necessary a posteriori sentences, even though the language would still have the resources ‘to say how things are in some detail’.218 The suggestion that there might be such a language makes sense on the assumption that the reference-ﬁxing devices in question are part of the descriptive content of the names. Possible languages can be given whatever semantics we want to give them, and we can certainly deﬁne a language with no fancy rigidifying operators, or other two-dimensional devices. But if the source of necessary a posteriori truth is in the relations between us and the world that give our thoughts and utterances content,

217

Chalmers (1996: 366, n. 25).

218

Jackson (2001: 621).

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then it is not so easy to avoid the phenomenon of necessary a posteriori truth. We could have a purely descriptive language that had only resources to talk about the general features of things, but how would the reference of the general terms of such a language be ﬁxed? The causal theorist of reference (as contrasted with the causal descriptive theorist) takes the kind of reference-ﬁxing illustrated with proper names as an account of how expressions in general—predicates as well as names—get their reference. If we understand reference ﬁxing this way, then we cannot ban it without banning the capacity of the language to say anything about the world at all. The metasemantic account that is appropriate to the generalized Kaplan paradigm is what David Lewis (who defends a version of such an account) calls global descriptivism.219 Lewis notes that a local description theory is simply a way of explaining one part of a language in terms of other parts—the terms in which the descriptions are given. But a global description theory is a theory that takes a speaker or thinker's whole language and theory as a description of the world. One simultaneously interprets all the terms of the language, and makes a claim about the world by asserting one's theory. Roughly, the terms refer to whatever things, properties, and relations do the best job of making the theory, or at least as much of it as one can, true. Lewis argues that global descriptivism as it stands cannot be right, since it will be impossible to explain, on an unconstrained global descriptivism, how statements could ever be false (that is Putnam's paradox). But he argues that with some additional constraints (the primitive terms of our language must refer to properties and relations that in some sense ‘carve nature at its joints’), and with causal notions and two-dimensional devices built into the language, this kind of metasemantic theory can account for the facts. I am skeptical that such a metasemantic theory can be made to work at all, but if it can, it is clear that it gives a very different account of the contents of our speech and thought than the causal information-theoretic account. The interpretation will be holistic: what someone says, and thinks, is determined by her whole theory, and will change with any changes in her whole theory. And it will be solipsistic, since the causal relations that are built into the meanings of most of our terms are relations to our own uses of terms. The meaning of my name ‘Tully’ is given in terms of the historical explanation of my uses of the name ‘Tully’, and so ‘Tully’ as I use the term will have a different meaning from ‘Tully’ as you use it. According to this kind of theory, we talk about the world only at an extremely high level of generality. It is not only that we don't refer to and think about particular individuals, as contrasted with whoever it is that ﬁts some description. We don't describe things in terms of ground-level properties and relations, but only in terms of whatever properties and relations are the ones that best ﬁt the abstract structure given by our uninterpreted theory.

219

Lewis (1984: 224).

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The defender of the generalized Kaplan paradigm might respond that the two-dimensional scope devices built into the language give us the resources to express propositions that say things more directly about the world, since the secondary propositions determined by our thoughts and utterances will be singular propositions, and propositions that predicate ground-level properties and relations. But it is the primary intensions that represent the cognitive values of our thoughts—the things that we understand when we know what we are saying and thinking. According to the generalized Kaplan paradigm, the secondary intensions of our thoughts and utterances are described but not expressed: they are uniquely determined, as a function of the facts, but not something to which we have cognitive access. Consider some examples of propositions known only by description: the content of the sentence quoted on lines 3–4 of page 26 of Frank Jackson's From Metaphysics to Ethics; the content of the ﬁrst assertion that Napoleon made to Josephine after he was crowned emperor; what she just said (referring to a person who just said something in a language one does not understand). One cannot assert such propositions by saying ‘I hereby assert the proposition that meets the following condition’, nor, when one believes that the proposition so described is true would it be right to report that one believed the proposition itself. Our relations to secondary intensions, according to the generalized Kaplan paradigm, seem like this.

6. Rejecting conceptual necessity The most important difference between the generalized Kaplan paradigm and the metasemantic interpretation is that the latter yields no account of conceptual truth—truths knowable a priori on the basis of the semantics of the language. All necessary truths, including necessary a posteriori truths, are made true by the semantics of the language—by the fact that the proposition expressed in such statements is the necessary proposition. But the twodimensional intensions, on the metasemantic interpretation, do not represent the conceptual contents, and are not the meanings of the sentences they interpret. The framework, on this interpretation, gives us no account of a priori truth. The metasemantic interpretation allows that there may be necessary a posteriori truths whose necessity cannot be reduced to or explained by conceptual truths that are knowable a priori. It is this feature of the kind of account I am defending that its critics ﬁnd most problematic. Frank Jackson argues that ‘the deeply pessimistic nature of this view is insufﬁciently realized.’ He takes it to be a consequence of the rejection of a priori, conceptual truth that we cannot ‘say how things are independently of how they actually are’,220 which he takes to imply that we cannot say at all, categorically, how things are, or might be—we can only say how things might be

220

Jackson (2001: 618).

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conditionally on facts about how they are. But what does this mean? Let me distinguish two ways of interpreting the claim that one can say how things are only conditionally on how they actually are, again drawing on the semantics/ metasemantics distinction. First, one might make a claim of this form: only on condition P does the sentence S expresses the proposition that Q. Alternatively, one might claim that sentence S expresses only a conditional proposition: it does not assert Q unconditionally, but only that if P, then Q. Making the same distinction in general, we can give two interpretations of the pessimistic view that we cannot say how things are independently of how they actually are. On the ﬁrst interpretation, the claim says that the fact that certain brain events, or sounds or marks have the propositional content that they have is dependent on facts about the actual world. If certain facts had been different, what the person in question in fact said or thought would have been different. On the second interpretation, the claim says, not that what the content is depends on the facts, but that the content is itself relational or conditional. On the ﬁrst interpretation, the claim seems undeniable (whether or not it is pessimistic). On the second interpretation, the claim is unintelligible, but I think it is only the ﬁrst interpretation that one who rejects a priori conceptual analysis is committed to. An example used by Jackson to illustrate a limited form of the pessimistic view will help to clarify the distinction I am trying to make. ‘Consider the view held by some that there is such a thing as absolute position, but all we can ever represent in thought and language are facts about the relative position of the objects in our environment. This view amounts to skepticism about our ability to say or think where something is in the absolute sense.’221 Suppose we want to show the skeptic who holds this view that he is wrong, to argue that we can represent absolute location. How do we do it? Presumably by specifying a coordinate system and a unit of measurement. For example, I might say ‘Take the centers of mass of the earth, the moon, and Mars at the moment of the birth of Isaac Newton. Let the plane of the triangle determined by these three points be the x–y plane, the center of the sun be the origin, and the line between the sun and the earth be the x axis.’ If I add that the units are a meter and a second, and specify the positive and negative directions on each axis, then we have the resources to specify the absolute locations and times of objects and events with quadruples of real numbers, at least assuming that there are absolute locations to be speciﬁed (and ignoring the possible vagueness of our speciﬁcation of the points that deﬁne the coordinate system). Jackson's skeptic may respond that this does not really allow us to say where things are absolutely, but only to say how they are related to where the sun, the earth, and Mars were at the time of Newton's birth. But it is not clear what the principled basis would be for his resistance. We cannot

221

Ibid.

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escape the fact that all of our words, and more generally all of our representational resources, are things we ﬁnd in the actual world—there is nowhere else to look for them. That our statements have the content that they have is unavoidably dependent on the way we are related to what we talk about. But that does not imply that the contents we use our words to express are dependent on the facts that determine that our words have those contents. We form a conception of the world, and of the space of all possible worlds, out of the materials we ﬁnd in the actual world. There is no other way. (It is not that we construct the possible worlds out of the materials we ﬁnd in the actual world—rather, it is that we can describe the worlds, and discriminate between them, only by using such materials.) Whether some description that purports to describe a possible situation succeeds in describing a possible situation will depend on the materials used to give the description—on the things, events, properties, and relations that we refer to in describing a putative possibility. And there is no other way to ﬁnd out about those materials than to engage in empirical investigation of the actual world. O'Leary dreams of a world in which he mixes molten tin and copper, and gets gold (not by some magic alchemic process—in the world he dreams of, the mixture simply is gold). But Daniels knows that there is no world of the kind that O'Leary dreams of, or perhaps what he knows is that the world that O'Leary dreams of isn't the way O'Leary thinks it is. It is a world that would be the way he thinks it is only if the actual world were the way he thinks it is. But how does he think the actual world is? He thinks it is a world in which gold is a mixture of tin and copper—in which gold is bronze (though he wouldn't put it that way). But there is no such world. So how do we say how it is that O'Leary thinks the world is? The problem is that the content of what we think and say inevitably depends on the facts—facts that may themselves be in dispute—and this sometimes makes it difﬁcult to describe the thoughts of people with whom we disagree—to describe the way they take the world to be. But our resources for representing the possible worlds are rich and diverse. We can usually ﬁnd ways that are not in dispute (in the particular context) for describing possible worlds that distinguish the beliefs of people who disagree. If, for example, the essential nature of copper and tin are not at issue in a discussion between Daniels and O'Leary, then we, and they, might refer to those substances in characterizing the world as O'Leary thinks it is: it is a world in which the stuff people call ‘gold’ (and that plays all the roles that Daniels and O'Leary agree that the stuff people call ‘gold’ plays) is a mixture of tin and copper. The two-dimensional framework, on the metasemantic interpretation, gives us a useful framework for characterizing such situations. It does not give us a way of describing the possible worlds that is a priori, purely conceptual, neutral in all possible contexts—that cannot be done. The best we can do is to describe the possible worlds from within the actual world, using the resources that it gives us. But that is good enough.

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PART V Subjective Possibilities

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12 Comparing Qualia across Persons (2000)

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The inverted spectrum is one of the oldest philosophical chestnuts—a puzzle that children sometimes think up for themselves. What if red things looked to you the way green things look to me, and vice versa? More generally, the hypothesis is that the qualitative character of my experiences is a permutation of the qualitative character of yours. Your experience, when presented with something of a certain color, corresponds in its intrinsic character to the experience I have when presented with something of the complementary color. If this were true, how would we tell? We would both still call red things ‘red’, and might respond to the colors of things in the world in all the same ways. The only thing that would differ is our respective inner experiences, experiences that no one is in a position to compare. Veriﬁcationists took the inverted spectrum hypothesis to be a paradigm of meaningless metaphysics. Because, they argued, no one could be in a position to test the hypothesis, even in principle, one should conclude that no sense has been given to the statements that your inner experience is the same as, or different from, mine. But veriﬁcationist arguments and Wittgensteinian skepticism about inner experience are not taken to have the force that they were once thought to have, and philosophers with a wide variety of different views about the nature of mental phenomena are now inclined to take the inverted spectrum hypothesis seriously. More generally, they are inclined to take seriously the hypothesis that there are facts about whether one person's conscious experiences of colors, tastes, and smells have the same or different qualitative character as those of another. But it is clear that such hypotheses raise problems for materialist and functionalist theories of mind, and that the account philosophers give of the relations between the phenomenal experiences of different people will have consequences for their general philosophical account of mind—on their accounts of consciousness, and of intentionality, and of the relations between them.

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Sydney Shoemaker and I were colleagues at Cornell for seventeen years. Throughout this time and since I have continued to learn from his work, and his example, what it is to be a philosopher. My debt to him will be evident from this paper, which even though it defends a view he disagrees with, draws most of its ideas and arguments from his illuminating and incisive papers on the topic. Sydney is a resourceful critic of his own views, and what I do here is mainly try to put a different spin on an argument that he has presented against his own view, an argument that I ﬁnd more persuasive than he does.

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Sydney Shoemaker is one philosopher who has taken on the burden of reconciling a broadly functionalist and materialist conception of mind with what he calls ‘the common-sense view’ of the inverted spectrum.223 My plan in this paper is to look critically at Shoemaker's articulation and defense of the common-sense view, and at the conception of the content of qualitative experience that lies behind it. I am interested both in the issue itself, and in the argumentative strategy that Shoemaker uses—a strategy that trades on the relation between intrapersonal and interpersonal comparisons of qualitative content. The dialectic of intrapersonal and interpersonal comparisons of qualia is a twoedged sword: it can be used (and is used by Shoemaker) to raise problems for the coherence of the inverted spectrum as well as to defend it. Shoemaker contrasts the common sense view that he defends with what he calls ‘the Frege–Schlick view’, a view that rejects the meaningfulness of interpersonal comparisons of the character of phenomenal experience. It is a version of this old-fashioned view that I want to defend against Shoemaker's alternative. My criticisms of the common-sense view, and defense of the Frege–Schlick alternative, will build on challenges that Shoemaker himself presents to the thesis he defends, challenges that I don't think he succeeds in meeting. Before looking at the speciﬁc issue and arguments, I will (in section 1) make some general and impressionistic remarks about what is at stake in the way one responds to this puzzle. In section 2, I will sketch the speciﬁc problem posed by the inverted spectrum for the possibility of a functionalist theory of the mind, and the account of qualia that Shoemaker thinks can reconcile functionalism about mental properties with the common-sense view of the inverted spectrum. I will look at what Shoemaker calls the intra–inner argument,224 an argument that begins with a defense of the meaningfulness of an intrapersonal spectrum inversion, and moves from this to a defense of the coherence of interpersonal qualia comparisons. In section 3, I will sketch the Frege–Schlick view, and use some analogies to try to make clear what it claims, and that it is at least a coherent view. In section 4, I consider how the Frege–Schlick view should respond to the intra–inner argument, and what this kind of view ought to say about intrapersonal comparisons over time. Finally, in section 5, I will look in some detail at a counterargument (which I call ‘Shoemaker's paradox’) that Shoemaker uses to raise a prima facie problem for the view he is defending, and at his response to it. I will argue that when Shoemaker's account of qualia is developed in response to the paradox, it loses its intuitive appeal, and its claim on the label, ‘the common-sense view’.

223

Shoemaker's most detailed discussion of the inverted spectrum is in Shoemaker (1981). See also Shoemaker (1975). There are later discussions of the issue in Shoemaker (1996).

224

Shoemaker (1996: 141). I am not sure why it is ‘intra–inner’ rather than ‘intra–inter’ since it is short for intrapersonal/interpersonal, but I will follow Shoemaker's terminology.

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1. Qualitative and intentional content Philosophers have often distinguished two components of the mind–body problem, two different distinctive features of the mind that are difﬁcult to reconcile with a materialist account of mental life. First there is the problem of intentionality—the problem of explaining how the physical states of a human being can represent the world. How can the physical states of a physical object be about something? How can they be states that are capable of being evaluated as true or false? Second, there is the problem of phenomenal experience—the task of explaining how a physical being can be in states with the kind of qualitative character that our conscious states seem to have. How is it possible to explain, in purely physical terms, ‘what it is like’ to see colors, or to experience the taste of wine, or the smell of turpentine? Different philosophers have had contrasting attitudes toward the relation between these two problems, and the two kinds of content—representational and qualitative content—used to characterize them. One strategy, best exempliﬁed in the phenomenalist tradition, takes qualitative content as more basic, and aims to explain representational content in terms of it. We project our experience onto the world, or we construct a conception of the world out of the materials provided by phenomenal experience. Phenomenalism is not a doctrine that has many adherents these days, but I think the ideas underlying it persist in some internalist accounts of intentionality. A contrasting strategy is to begin with an account of the capacity to represent, and to explain qualitative experience in terms of it. We project our conception of the world back into ourselves. Qualitative states are to be explained in terms of the way things (including our own bodies) seem or appear to be—as hedged and self-conscious versions of the way we take things to be. Uncompromising proponents of this second strategy (Fred Dretske, Gil Harman, Bill Lycan, Michael Tye) have recently argued for the thesis (dubbed ‘representationism’ by Ned Block) that phenomenal character just is a kind of representational content.225 One motivation of the second strategy is that from a functionalist or materialist point of view, the problem of intentionality seems more tractable than the problem of consciousness. Functionalist analyses of intentional states such as belief and desire are prima facie more plausible than functionalist accounts of phenomenal consciousness, since it is intuitively more natural to hold that there are conceptual connections between intentional mental states and the environmental causes and behavioral effects that they normally have. So if the two problems are tied together by an account of phenomenal character in terms of the ways our experience represents the world, the prospects for an explanation of consciousness that is compatible with materialism will be improved.

225

See Harman (1990), Dretske (1995), Lycan (1996), and Tye (1995). The label ‘representationism’ comes from Block (forthcoming).

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The puzzle of the inverted spectrum has played a prominent part in recent discussions of the relation between representational and qualitative content, since if we take spectrum inversion to be a possibility, we seem to have a case in which qualitative character and intentional content come apart. If your experience when you see a ripe tomato is (and always has been) like mine when I see an unripe pepper, and vice versa, then the same experience that in you represents the tomato as being red would, in me represent the tomato as being green. We have contrasting experiences when we look at a ripe tomato in normal conditions, but the tomato appears to be red to both of us (the representational content of our two experiences is the same). So if this hypothesis is coherent, it seems that we cannot explain the qualitative character of the visual experience in terms of the properties that things appear, to the experiencer, to have. It is not my aim in this paper to defend representationism, since I do not really understand the thesis that the representational contents of experiences ‘completely capture the phenomenal character of the experiences’.226 But I am sympathetic to the general strategy of trying to explain qualitative content in terms of representational content, and skeptical about the coherence of thought experiments such as the inverted spectrum that attempt to pull them apart. I have to grant that common sense supports the coherence of the inverted spectrum, and that one who rejects it has a compelling cognitive illusion to explain away. But I think the illusion can be explained away, and that common sense does not speak with a single voice about the comparison of qualia over time, and between different persons. While common sense may support the coherence of the inverted spectrum, I think it also supports the idea that there is a conceptual connection between the qualitative character of a person's experience and the way things seem, to that person, to be.

2. Reconciling qualia with functionalism If we assume that the inverted spectrum hypothesis makes sense, why is this a problem for a functionalist theory of mind? Functional accounts of qualia explain them in terms of a relational structure. We have certain perceptual discriminatory capacities, we are disposed to make certain judgments of similarity and difference in our experience, and to associate certain kinds of experiences with others. Discriminability is the intrapersonal criterion of identity for qualia: experiences we can't tell apart have the same qualitative character, and those we can tell apart differ in some qualitative respect. But suppose (as the inverted spectrum hypothesis does) that the relational structure has some symmetry in it. Suppose we could deﬁne a systematic permutation of types of qualitative experience that preserved all judgments

226

Block (forthcoming: 1).

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of similarity and difference, and that more generally preserved the whole relational structure. If the experiences of two different people were permuted with respect to each other in this way, then we would have functional identity (because of the symmetry) with qualitative contrast (because qualia are mapped onto qualia discriminable from them). If this is possible, it seems to imply that no functional account of qualia could be right. One response to the problem is to deny the symmetry. One may argue that even if there is some symmetry in the structure of color experience—in discriminatory capacities and judgments of similarity and difference—the whole relational structure in terms of which qualitative color experience is deﬁned is more complex, including cross-modal associations (red is hot and loud, blue is cool, etc.), and facts about the way contrasting colors interact that will not be preserved in a permutation of colors with their complements. I will follow Shoemaker in setting this response aside. All we need assume is that symmetry is at least possible for some possible creatures with qualitative experience—that whatever the case with the actual capacities of human beings for qualitative experience, there could be creatures capable of qualitative experience with a symmetrical structure—capable of permutation that preserved all the relations between qualia that are available for a plausible functionalist account of qualitative experience. Since a functionalist analysis of qualia individuates them by intrapersonal discriminatory capacities—relations between experiences that have no interpersonal analogues—one might expect a functionalist to embrace the Frege–Schlick view that rejects the intelligibility of interpersonal qualia comparisons. But Shoemaker resists this easy way out of the problem. His aim is to reconcile interpersonal qualia comparisons, and the coherence of the inverted spectrum, with a functionalist account of qualia. The strategy of reconciliation is to grant that ‘we cannot functionally deﬁne particular qualitative states’, but to argue that ‘there is a sense in which we can functionally deﬁne the class of qualitative states—we can functionally deﬁne the identity conditions for members of this class, for we can functionally deﬁne the relationships of qualitative (phenomenological) similarity and difference.’227 This kind of functional analysis will determine an equivalence relation on the physical states of the person—equivalent states will be states that are realizations of the same qualitative state. The qualitative states are then identiﬁed with their physical realizations (or with the set of functionally equivalent physical realizations). To say that a ripe tomato looks to me just like it looks to you is to say not only that we are in functionally equivalent states, but also that your qualitative state is realized physically in a way that is also one of the possible realizations of the state I am in. The main reason that Shoemaker resists the Frege–Schlick response to the problem is that he thinks that no one can plausibly deny the coherence of

227

Shoemaker (1984: 195).

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the hypothesis that there has been an intrapersonal spectrum inversion, and he thinks there is an irresistible argument from the intrapersonal case to the coherence of the interpersonal case. It is this argument, and more generally the intrapersonal/interpersonal dialectic, that will be my main concern. Shoemaker begins with a passage from Wittgenstein in which he considers a situation in which a person reports that ‘I see everything red blue today and vice versa’. In such a case, we would, Wittgenstein suggests, ‘be inclined to say that he saw red what we saw blue’. Neither veriﬁcationists nor functionalists would have any basis for rejecting the intelligibility of such a case, since the inversion is reﬂected in the behavioral dispositions and capacities of the person. But how does one move from this to the interpersonal case? The argument seems to be something like this: suppose an intrapersonal spectrum inversion is possible. Then if Fred undergoes this change while Mary does not, it cannot be that Fred's color experiences are the same as Mary's both before and after the change. Fred and Mary must be spectrum-inverted with respect to each other either before or after the change. Now it should be clear that this argument has no force against the Frege–Schlick view, since it presupposes that Fred's and Mary's color experiences are comparable, both before and after the change, which the Frege–Schlick view denies. What the argument shows is only that if it makes sense to say that two people's qualitative experiences are the same, then it must make sense to say that they are different. I don't think Shoemaker disagrees here—at one point he explicitly includes as a premiss of the intra–inner argument the assumption that ‘the relations of similarity and difference that are well-deﬁned intrasubjectively are also well-deﬁned intersubjectively (i.e.,⋯the Frege–Schlick view is false).’228 So the intra–inner argument has a narrow target: those who accept the intelligibility of the claim that our color experiences are qualitatively similar, while rejecting the intelligibility of the claim that they are qualitatively different in a behaviorally undetectable way. But the argument still has some intuitive force for those who think that, at least in the special case where two people are exactly alike, both functionally and physically, it is hard to resist the conclusion that their experiences are qualitatively identical.229 For there could be a person who was a functional and physical duplicate of Fred before his inversion, and another who was a duplicate of Fred after the inversion. (Or better, a duplicate of what Fred would become if his inversion were later followed by amnesia about the earlier experiences.) These two twins, it seems reasonable to conclude, would be spectrum-inverted with respect to each other.

228

Shoemaker (1996: 144).

229

Though I think it is the assumption that physicalism is true—that everything is globally supervenient on the physical—that supports this intuition, and not the commonsense view of qualia. I think that naive intuitions about qualia would tend to support the conceivability of a situation in which even physical duplicates might be spectruminverted.

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Shoemaker notes that Wittgenstein, in the passage cited, seems to commit himself to interpersonal comparisons, at least in some situations, for he says that in a case such as the one he described, we would ‘be inclined to say that we saw red what he saw blue’. But even a proponent of the unqualiﬁed Frege–Schlick view can make sense of the supposition that red things appear blue to someone. Before his mysterious alteration, Fred, like the rest of us, could tell what colors thing were by the way they looked. After the change, red things looked to him to be blue. Even when Fred comes to believe that it is he who has changed, and not the colors of things in the world, it remains true that red things look blue to him—that his visual system represents them as being blue. He just knows that things don't look (to him) the way they are. The Frege–Schlick view has no problem with this description of the situation since what that view rejects is only a notion of qualia that is both independent of representational content, and also comparable across persons. So I think this passage gives no reason to think that Wittgenstein is not in complete agreement with Frege and Schlick in rejecting this conception of qualia. To counter the intentionalist interpretation of the case of the intrapersonal spectrum inversion, Shoemaker elaborates the story by imagining that the subject accommodates, semantically, to the change. After a while, Fred no longer reports that red things look blue. It is not that they have changed the way they look; it's just that Fred has adjusted to the fact that that is (now) the way that red things look, and so describes that look as ‘looking red’. After the accommodation it can no longer be said that Fred's experience misrepresents the colors of things. So, it is argued, the qualitative contents that remain switched cannot be identiﬁed with the intentional content. Shoemaker also bolsters the argument by imagining that the spectrum inversion takes place gradually, in a series of partial inversions. The subject reports that ‘nearly everything looks the way it did before, but that the shades of color within a very small range have “switched places” with their complementaries.’ The partial change results in a difference in the relational structure of the person's quality space, but a sequence of such changes (accompanied by semantic accommodation) might result in a full symmetrical inversion, a situation in which the relational structure, and the discriminatory capacities and behavioral dispositions, were all as they were at the beginning. But, it is argued, we cannot plausibly say that the qualitative character of our subject's experience is the same at the end of this sequence of changes as it was at the beginning. ‘It would be ridiculous to suppose that these (ﬁnal partial inversion plus semantic accommodation to it) would, at one fell swoop, restore the character of the person's experience to what it was originally—for what the subject reports, and what her behavior would conﬁrm, is that the ﬁnal change affected the appearance of only a

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tiny fraction of the shades of color.’230 I will express some skepticism about this argument below, but ﬁrst I want to try to get clearer about exactly what the Frege–Schlick view is, and how it should respond to the story of the intrapersonal spectrum inversion.

3. The Frege–Schlick view The Frege–Schlick view is sometimes thought of as an eliminativist thesis—a thesis that denies the existence of phenomenal character, or qualia. I don't think this is quite right. The proponent of this view may say that there really are qualitative properties—it is just that the common-sense view of them distorts their nature. The common-sense view is that qualitative properties are local and intrinsic properties of experience—in fact they are the paradigm of an intrinsic property. The Frege–Schlick view holds that qualitative properties are relational—part of a purely relational structure. To try to clarify this kind of view, I will use some analogies with other purely relational conceptual structures: ﬁrst, with a relational theory of space, and second with utility theory. The kind of relational theory of space I have in mind is a simpleminded theory—more Leibnizian than Einsteinian in that it assumes the conceptual independence of space and time. This kind of theory may not be plausible, but I think it is coherent, and that the analogy with it can throw some light both on the form of the Frege–Schlick view of qualia, and on the structure of some of Shoemaker's arguments. There are, on this view, no absolute locations. One can still talk meaningfully about the spatial location of things, but this is just a framework for talking about the spatial relations between things. The framework is conventional. Of course even an absolutist about space will say that the framework with which we assign triples of numbers to spatial points is conventional—there is no nonarbitrary origin or axes. The issue between the absolutist and the relationist is whether the identiﬁcation of spatial points across time is conventional. There is no absolute motion—only change over time in the relative positions of things. Claims about the locations of things, and about motion, or change of location over time, are perfectly meaningful, according to such a theory, but such claims have to be understood in terms of a frame of reference. Now suppose someone set out to refute the relational theory, or at least to show it to be highly implausible, by using an argument analogous to Shoemaker's gradualism argument cited above. Analogous to the denial of the meaningfulness of an interpersonal spectrum inversion is the denial of the meaningfulness of the hypothesis that the entire universe was shifted in space, three feet to the left. A possible world in which everything is three feet to the left is (according to the relationist) just a conventional redescription

230

Shoemaker (1996: 144).

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of the world as it is. ‘But even the relationist must grant’, the critic argues, that this chair might be shifted three feet to the left, and then this table. If one such change is possible, there is surely no impossibility in a series of such changes that all together would amount to a shift in everything in the universe. It would be ridiculous to suppose that the last of these changes would, in one fell swoop, return everything to the way it was originally when it is obvious that the last small change affected only the location of a single object. I hope that no one will take this argument to have any force against the relationist. The effect of breaking the alleged shift into small steps is to make salient, at each stage, a certain frame of reference. The relationist can grant that, and can explain why, it would be quite unnatural to describe the ﬁrst change, or the last one, as a change in which one small thing remained ﬁxed while the rest of the universe shifts three feet to the right. But he has no reason to grant that the alternative descriptions of these changes falsiﬁes the facts, or to give up his claim that the overall effect of the sequence of hypothetical changes is to leave things exactly as they were. My second analogy—one that provides a richer parallel with the case of qualia comparison—is with Von Neumann–Morgenstern utility theory. One begins with a preference relation for a given person—an ordering of some set of alternative possibilities that represents the relative evaluation of the desirability of the alternatives. O'Leary, let us say, prefers the duck to the salmon, and the salmon to the haggis. The purely ordinal structure is extended to an interval measure by introducing uncertainty, and representing the person's preferences over lotteries that may result in better or worse outcomes. So we ask O'Leary which he would choose between the salmon and a ﬁfty–ﬁfty chance of the duck or the haggis. If he prefers the salmon, that means that the interval between the duck and the salmon is less than the interval between the salmon and the haggis. Further questions, with different probability values for the lottery, can determine exactly where the middle item falls on the scale between the best and the worst option. More generally, preferences between lotteries determine cardinal utility values for all the options in the set. But the scale is a conventional one: any linear transformation of the scale yields an equivalent scale that represents the same facts about the subject's preferences. Does it make sense to compare utility values across persons? There is an obvious analogy between the dispute between the Frege–Schlick view and the common-sense view on the one hand and controversies about the interpersonal comparison of utilities on the other. And if one took utility as a measure of pleasure, or of the felt intensity of a desire, or of the subjective satisfaction that would be brought by attaining the option in question, then perhaps the question about utility would be an example of a question about

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comparing the qualitative character of experience. But this notion of utility is not intended as a measure of the feelings of satisfaction that one would receive if the option in question were realized—of the extent to which one would enjoy the duck if one were to eat it. Nor is it intended to be a measure of the intensity of feelings one has when one contemplates one's preferences.231 If such things could be measured, there is no reason to think that this notion of utilities would correspond in the right way to one's preferences between lotteries. This concept of utility is supposed to systematize a person's motivational structure—the way her attitudes toward the alternative outcomes that might result from choices she faces or might face are disposed to affect her actions. If we can contrast intentional mental states and properties with phenomenal states and properties, it is clear that utility, on the intended interpretation, belongs on the intentional side. The questions about the possibility of interpersonal comparisons of utility in a theory that extends the Von Neumann–Morgenstern theory are complicated and interesting,232 and I think the parallels and contrasts with our issue are worth developing, but for my purposes here, I want simply to take the simple theory as an example of a theory that presents a purely relational structure, one that gives content to certain intrapersonal comparisons without providing content to interpersonal comparisons—an example that helps to clarify, by analogy, the kind of claim that the Frege–Schlick

231

At least some reasons for thinking that utilities can be compared across persons derive from the assumption that utility is a measure of an introspectible feeling. John Harsanyi, for example, writes that ‘we have direct introspective access only to our own mental processes (such as our preferences and our feelings of satisfaction and dissatisfaction) deﬁning our own utility function, but have only very indirect information about other people's mental processes. Many economists and philosophers take the view that our limited information about other people's minds renders it impossible for us to make meaningful interpersonal comparisons of utility’ (Harsanyi 1987: 128). But this is a misconception of the basis of the rejection of the meaningfulness of interpersonal comparisons. It is not that this kind of comparison is meaningless because it is too hard to get information about it. The view is rather that utility numbers are used to represent a structure of the preferences of a person, and are not intended to represent facts, available or not, about relations between persons. The critic of interpersonal comparisons views the question as like the question whether grams are bigger or smaller than centimeters. The reason we can't say is not that the facts are hidden from view.

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Those who reject the meaningfulness of interpersonal comparisons of Von Neumann–Morgenstern utility need not deny that one might extend the theory to provide for interpersonal comparisons for the purpose of making welfare judgments—comparative judgments about the value to a whole community of various alternative social arrangements. Speciﬁcally, one might calibrate utility scales in one way or another, and argue that maximizing total or average utility, calibrated in that way, should be a goal of social policy. For example, one might argue for a scale that assigned 0 to each person's least favored outcome, and 1 to each person's most favored outcome. Alternatively, one might propose that the scale should be normalized by assigning 0 to the worst outcome, and 1 to the sum of the utilities of all the alternative possible outcomes. There might be arguments for or against such principles for calibration, or interpersonal comparison, and one might be clearly better than another. But such an extension of utility theory would be based on social and political principles— assumptions about the relative claims of different individuals on available resources—and not on factual judgments about the comparative intensities of people's experiences.

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view is, and to show the coherence of the view. It would not be right to describe the utility theory as eliminativist—as denying the reality of utilities. According to the theory, there really are facts about people's preferences that are represented by utility numbers, but since the zero point and unit of the scale are arbitrary, no signiﬁcance has been given to comparisons of the utility values of different persons.233 And it would not be right to say that this theory is essentially incomplete—that there must be some kind of underlying facts that provide answers to the questions about interpersonal comparisons. There are, of course, underlying facts about the brain (and the environment) on which utility functions presumably supervene, but there is no reason to think that they will provide a basis for treating utility values as a measure of anything other than intrapersonal comparative relations. The analogies support, I think, the coherence of a purely functionalist account of qualia that takes phenomenal character seriously, but treats it as a relational feature of our experience. Such a conception of qualia need not be based on outmoded veriﬁcationist assumptions, but might be grounded in the kind of account of the identity conditions for qualia that Shoemaker gives, an account that is like the Von Neumann–Morgenstern utility theory in that it grounds the concept of qualitative character in intrapersonal relations—discriminatory capacities and judgments of similarity and difference. But the intuition that it makes sense to ask how my phenomenal experiences compare with yours is a compelling and persistent one. Even if it is coherent to reject those questions, one may think that an account of qualia that makes sense of them will better accord with our common-sense notion of qualitative character. And even if an intra–inner argument cannot refute the Frege–Schlick view, that view does have to give some account of the possibility of an intrapersonal spectrum inversion.

4. Memory and intrapersonal inversions So what does the proponent of the Frege–Schlick view—of a purely functionalist theory of qualia—say about Wittgenstein's example of the intrapersonal spectrum inversion, and more generally about intrapersonal comparisons of qualitative experience over time? Everyone should agree that intrapersonal comparisons over time essentially involve memory. One is comparing an experience one is having with what one remembers a previous experience to have been like. For the functionalist, memory is constitutive—part of the account of the identity conditions for the qualitative

233

I emphasize the point that a purely relational theory is not eliminativist because I suspect that one of Shoemaker's motivations for resisting the Frege–Schlick view is that he takes it as a view that, as he puts it, ‘quines qualia’, and he argues, against eliminativist views (such as representationism), that we need qualia to account for facts about our experience, and about secondary qualities. But I think a purely relational account of qualia can do the work that Shoemaker wants qualia to do.

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properties. If I am disposed to judge, on seeing a red tomato today, that its color looks to me exactly like it looked yesterday, then this will be the basis for saying that my qualitative color experience is the same (and that the relevant brain states I am in at the different times are realizations of the same qualitative state), provided that my memory is accurate. But one can correctly say that the memory is accurate only if the two experiences are in fact qualitatively the same. The Frege–Schlick view should be skeptical, not only about interpersonal comparisons of qualia, but also about the independence of intrapersonal comparisons and assessments of the accuracy of qualitative memories. The commonsense view would say that a memory report that the tomato looks now just like it did before is an accurate report if and only if the way it looked then really is just the way it looks now. But on the Frege–Schlick view (and on Shoemaker's view as well), the memory mechanisms that dispose the subject to make such judgments will be part of the functional theory that says what constitutes sameness or difference of qualitative experience. Shoemaker is explicit in agreeing with this point: The functional role of a quale must surely include the ways in which the instantiation at one time combines with instantiations of the same or different qualia at later times to produce certain effects—e.g. recognition or surprise. This means that the total realization of a quale will have to include the memory mechanisms by which qualia have the appropriate ‘downstream’ effects.234 One can accept the conceptual interdependence of memory and qualitative identity conditions and still be able to distinguish clear cases of memory error, or memory-tampering. But a functionalist might allow that in some cases it will be arbitrary whether one says that two different visual experiences are qualitatively the same, or that the subject is systematically misremembering one to be like the other. This perhaps conﬂicts with the common-sense view, but I think reﬂection on some examples suggests that it is not only what a functionalist should say, but is also intuitively plausible. Consider another kind of inversion, the famous case of the inverting glasses. The glasses contain lenses and mirrors that turn everything upside down. After one has worn them for a while, one begins to adjust—one reﬂexively looks up rather than down when lightning ﬂashes above, and one reports that, while things still look somewhat confusing, they are beginning to look a little more normal. And when the glasses are then removed, the subject reports, at ﬁrst, that things look upside down. It is my understanding that no one has worn these glasses continuously for very long, but suppose one micro-engineered a device that could achieve this effect in a less cumbersome and intrusive manner, and that our heroic subject was able to wear it continuously for several years. It is at least a reasonable empirical

234

Shoemaker (1996: 147).

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hypothesis that the subject would eventually adjust completely, reporting that things look completely normal, and recovering his abilities to ride a bicycle, and to hit a curve ball. And when the subject who has completely adjusted to the glasses then removes them, let us suppose, he reports that things look upside down, just as they did when he ﬁrst put the glasses on. Now should we conclude that our subject is reporting accurately? Should we say that his visual experience after the adjustment really is just like it was, qualitatively, before he ﬁrst put on the glasses, or should we conclude that he is systematically misremembering his previous experience? Perhaps the subject misremembers, or misinterprets, his phenomenal experience because of the way that, after the adjustment, his visual experiences are connected with other things, for example the way he is disposed, unreﬂectively, to respond to them. How should we tell whether this is a case of an adjustment to reversed qualia, or a case of return to the original qualia? Suppose physiological investigation reveals that various brain maps that are candidates for the core realizations of the qualitative visual experience remain inverted after the adjustment, just as they were immediately after the subject donned the glasses. Would that mean that the qualia remain inverted but that earlier qualia were misremembered because of way the adjustment changed the relations between the qualitative visual experience and other things, or should one instead say that the total realization of the qualitative experience involves all of the connections to one's responses (hand–eye coordination, etc.) that were involved in the person's adjustment to the change? On the second hypothesis, the two total physical states, with the reversed brain maps and corresponding changes elsewhere, would be alternative physical realizations of the same qualitative state. I don't think even naive common sense supports the judgment that there must be an answer to the question of which of these hypotheses is correct. Here is still another kind of inversion: suppose it were possible to rewire nerves so as to change the felt location of pains. Just after the rewiring, when you stub your left toe, you feel a pain in your right toe. But in time, let us say, you adjust. You undergo something like the kind of semantic accommodation that Shoemaker assumes in his cases of intrapersonal color reversals, but the accommodation is more than semantic since one's reﬂexes and spontaneous behavior adjust along with one's linguistic behavior. (The accommodation is more than semantic in Shoemaker's case as well, since the subject's spontaneous reactions to color experiences adjust. Are the reactive tendencies that change when one adapts to a spectrum inversion part of what constitutes the quality of visual experience, or are they just responses to it that may change without the quality of the experience changing?) It is only an empirical speculation that in the pain case one would accommodate to such a change, but suppose the subject reports, after a certain amount of time, that the pain in the left toe now actually feels like it is in the left toe, just as it did before the rewiring. We can assume that, as in the inverted glasses

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case, the adjustment was not a sudden reversal, but that there was perhaps a transition period of confusion and disorientation during which one ﬁnds it hard to locate one's pain, or to describe its felt location consistently. Might the subject be misremembering what it was like to feel a pain in the left toe? Can we separate the representational content of the pain experience—the fact that it seems to be something happening in my left toe—from the qualitative character of the experience? Or consider the intrapersonal spectrum inversion case itself: suppose physiological examination of Wittgenstein's character reveals that the explanation for his unsettling experience (‘I see everything red blue today, and vice versa’) was a disturbance located in his memory/recall system. What is happening (physiologically, in the visual system) as he perceives the world is exactly like what happened yesterday. What has changed is what is happening, physiologically, when he remembers how things looked before. Would it be right to say to Fred, when we learn this, ‘Don't worry—things don't look queer to you at all—they look perfectly normal, just the way they always looked. What's queer is the way you remember things looking yesterday. At least the qualitative character of your visual experience is, despite the way it seems to be, just the same as it was.’ I would expect Fred to reply, with some justiﬁcation, ‘I don't care what you say, the sky really does looks ﬁery red to me, and it didn't look that way yesterday. I don't mind your telling me why things look so strange—why the sky looks ﬁery red—but don't tell me I'm wrong about how things look to me.’ If Fred did reply in this way, I think he would have common sense on his side. Even from an external theoretical point of view, it might not be clear from the details about the physiology and functional organization of our spectrum-inverted character, whether to explain the switch in terms of memory error or in terms of a change in qualia. Consider the following simpleminded model of a memory mechanism, inspired by Hume's picture of ideas as pale copies of impressions. Suppose that when you have a qualitative experience—seeing red (realized, say, by the stimulation of X ﬁbers)—a record of the experience is stored (in memory location M). The mechanism for recalling the memory is for the M state to cause the X ﬁbers to be stimulated again (perhaps in a milder way than when one actually has a red experience). Now suppose (to draw on one of the kinds of cases Shoemaker discusses in his original paper on the inverted spectrum) our subject has a backup perceptual system. When the backup system kicks in, it is Y ﬁbers rather than X ﬁbers that are stimulated by seeing red. It seems that X- and Y-ﬁber stimulation are alternative realizations of the same quale, since the subject has no awareness of any change when the backup system takes over. If he is staring at a ripe tomato when the physiological change takes place, he reports no change in the way it looks. The theoretical explanation for the fact that he reports that the tomato looks the same (when the Y ﬁbers are being stimulated) as it did earlier (when the X ﬁbers

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were being stimulated) is that the memory of the earlier experience (which was caused by X-ﬁber stimulation) is recalled by stimulating the Y ﬁbers (in the pale way). Now if the qualia are really different, then this is a case of misremembering, but if they are alternative realizations of the same quale, then this is a case of accurate memory. On the common-sense view, there is a fact here that is perhaps impossible to know (since we may suppose it is physically impossible for the two states to be realized simultaneously). But it is not only veriﬁcationists who should be skeptical of this: I think a functionalist like Shoemaker should be skeptical as well. The case of the intrasubjective inverted spectrum shows that the relational structure that constitutes a quality space involves memory as well as capacities for simultaneous discrimination. Bringing memory into the functionalist account of qualia widens the intrapersonal relational structure, but does not contribute to providing a basis for interpersonal comparisons. Shoemaker will not disagree with this point; he agrees that we cannot ground interpersonal comparisons of qualia in functional analysis alone. His strategy is to explain qualia identity across persons in terms of identity of the physical properties that realize qualia. But there is a potential problem with this combination of two very different kinds of criteria for identifying qualitative properties—a problem that is brought out in an example that Shoemaker presented as a problem for his view in a postscript to his original paper on the inverted spectrum. In the next section, I will sketch the problem and Shoemaker's response to it, and say what I think it shows about what qualia must be if we are to make sense of interpersonal comparisons of them.

5. Shoemaker's paradox The paradox presents a sequence of four scenarios involving the visual experiences of a person.235 From assumptions about how qualia are identiﬁed, both within and across persons, that seem intuitively plausible, given Shoemaker's account of qualia, a contradiction is derived. Here are the stories: Case A: Alice is capable of being in either of two qualitative states (suppose they are visual experiences as different as red and green are for us). The qualia are physically realized by physical states Px and Py, respectively. Case B: Bertha is just like Alice, except that she has a backup visual system of the kind discussed above. Call the primary system (the system of case A) the α system and the backup system the β system. When the β system is active, there are two possible qualitative states realized by physical states Pz and Pw. Only one system is active at a time, and the subject does not notice the difference when the β system takes over. If Bertha was previously in state Px when looking at a ripe tomato, and is now in state Pz, she reports that things look just as they used to look. Similarly for states Py in the β system, and Pw in the β system. (No signiﬁcance should be attached to the fact that the β system is called ‘primary’. Either might have been active ﬁrst, or more often.)

235

I have told the story my own way, but the structure of the argument follows Shoemaker exactly. See Shoemaker (1984: 353–4).

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Case C: Like Alice, Clara has only one visual system, but in her case, it is the β system rather than the α system. Case D: Dorothy is like Bertha. She has two visual systems, one a backup to the other, and they are the same two α and β systems. But in Dorothy, they are differently connected. If Dorothy was in state Px before when looking at a ripe tomato, and is now in state Pz, she reports that it looks very different—the way grass used to look. (When Dorothy earlier looked at grass, she was in physical state Py, rather than Px.) In order not beg any questions about which qualia are the same and which different, I will label the qualitative properties with both the person and the physical realization state. So, for example is the quale experienced by Alice when she is in physical realization state Px. The following qualia identities seem reasonable: 1.

2.

since Alice and Bertha are in the same state, physically, at the time of the experience. It does not seem reasonable to suppose that the presence of an inactive backup system could affect the qualitative character of the experience.

3.

4.

5.

for the same reason.

since there is no introspectible difference for Bertha between being in the Px state and being in the Pz state. This looks like a clear case of alternative physical realizations of the same quale. It follows from 1–5 that

, but it seems undeniable that

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6.

since for Dorothy, there is an introspectible difference— as great as the difference between red and green—between being in the physical states Px and Pz. The source of the problem is this: Shoemaker's account of qualia relies on two different criteria of identity for qualitative properties—two different equivalence relations between physical realizations that are supposed to make them realizations of the same qualia. The functional theory provides a criterion for intrapersonal identities in terms of discriminatory capacities, and identity of physical realization properties provides a criterion for interpersonal qualia identities. One cannot assume that the two equivalence relations can be coherently put together: x might be equivalent to z and y to w in the interpersonal sense, and x equivalent to z in the intrapersonal sense, even if y and w are nonequivalent in the intrapersonal sense. The mere abstract possibility of this kind of conﬂict between two equivalence relations is not enough to raise a problem, but the story makes at least a prima facie case that the particular equivalence relations needed for a plausible development of Shoemaker's account may clash in this way. Is the story really coherent? In particular, how could the two visual systems, α and β, be ‘differently combined’ so that the correspondences between physical states are reversed? It is here that memory mechanisms become essential to the story. Recall our simpleminded model of a memory/recall system. When any of our four subjects has a visual experience (realized by states Px, Py, Pz, or Pw), a trace of the experience is stored in a memory, and later recalled by recreating (in the pale way) the appropriate physical state. So it is the memory/recall system that connects the alternative realizations of a qualitative state. Px and Pz are realizations of the same qualia (in Bertha) because x states (experienced while the α system is in effect) are later recalled (when the β system is operative) by activating a z state, and vice versa. But the situation is reversed in Dorothy. This is, as I said, only a simpleminded sketch of a mechanism, but I think it helps support the coherence of the story. I don't see any reason to think that a more complicated and realistic account of the memory and recall of experience might not also be compatible with such differences in the way memory connects experiential states at different times. There are two ways one might avoid the contradiction: one might reject identity 5, or one might reject identities 1–4. The ﬁrst response moves away from functionalism and toward a more purely physicalist account of qualia. Subjective indistinguishability (over time) is no longer taken to be a criterion of qualia identity; phenomenal experiences may systematically seem to the subject to be just the same when they are not. Spelling out this response would require deciding at what level of generality to deﬁne the physical types that are to be identiﬁed with qualitative properties, and it is not clear

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on what basis this should be done. But to avoid the kind of clash that arises in Shoemaker's paradox it may be necessary to identify qualia with very speciﬁc, ﬁnely individuated physical properties, and this might have the consequence that our qualitative experiences are much more variable and idiosyncratic than they seem to us to be. Suppose, as seems to me not empirically implausible, that the precise location in the brain of the physical events that realize perceptual experiences is somewhat variable, depending on accidents of development and experience, and that it changes over time within a single person as the brain develops, deteriorates, and interacts with the environment, without the changes being perceptible to the person. Should we say, if this were discovered to be true, that our phenomenal experiences keep changing their qualitative character in ways that we are incapable of noticing? If we did say this, I don't think we would any longer be defending the common-sense view, which should maintain some conceptual connection between the qualitative character of experience and the way things seem from the point of view of the experiencer. The second response—to reject the identities 1–4—is the response that Shoemaker defends. He argues that the addition of the backup system will affect qualitative character, since it will change the memory mechanisms that are constitutive of the identity conditions for qualia. So we should conclude that Alice's color experiences are qualitatively different from Bertha's because of the differences in ways their experiences are remembered and recalled. This response avoids the contradiction, but does it save the common-sense view? According to this response, later changes in a person's perceptual and memory system, even differences in unrealized counterfactual possibilities, can affect the qualitative character of one's experience. Compare two people who differ only in this way. Bertha has a ﬂexible brain: should the part of the brain that realizes a certain qualitative experience be damaged, another part of her brain could take over the task. Alice, on the other hand, has a less ﬂexible brain: should she suffer the brain damage, she would lose the capacity for that kind of qualitative experience. Even though the core realizations of their qualitative experience are the same, and even if the brain damage never in fact occurs in either person, it would seem that Shoemaker's response implies that their qualia would be different, because of the different connections with potential alternative realizations of the experience. This kind of difference might be purely intrapersonal: suppose Alice once had a ﬂexible brain, just like Bertha, but as she aged the potential backup system atrophied, perhaps from lack of use. The Shoemaker response seems to imply that the qualitative character of Alice's color experiences changes with the change in her brain, even though the change is inaccessible to introspection. To support his response, Shoemaker considers a version of the paradox in which all the comparisons are intrapersonal. Suppose we have a person—call her Ellen—with the same α and β systems, but in whom they are connected ﬁrst in one way (as in Bertha), then in the other (as in Dorothy).

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Since the same incoherence can be generated in a purely intrasubjective case, Shoemaker argues, it is ‘not to be avoided by retreating to the Frege–Schlick view and giving up on intersubjective qualitative comparisons’.236 But as we have seen, the purely relational account of qualia that grounds the Frege–Schlick view not only rejects interpersonal qualia identities, but also claims that intrapersonal comparisons across time may hold only relative to perhaps arbitrary assumptions about the accuracy of qualitative memories. Shoemaker's purely intrapersonal version of his paradox seems to me to add support to this kind of conclusion. Consider how things seem to Ellen through the changes she undergoes: At time t1, she sees a red tomato. By time t2 the backup system has taken over, but she reports that the tomato looks just the same. At time t3, when the two systems have been differently connected, she reports that the tomato looks exactly like it did at t2, but radically different than it looked at t1. Puzzled, she reports, ‘I know it seemed at the time (t2) that it looked just the same at it did at t1, but as I now recall it, they looked very different at those two earlier times.’ It is clear that Ellen must be misremembering something about her experiences at one time or another, but when (at t2, or at ;t3)? Need there be any facts that tell us which it is? Reﬂection on the case of Ellen—the purely intrapersonal case—makes clear that at some point, with one or another of the changes that she undergoes, something momentous will happen in Ellen's experience, something similar to what happened to the character in Wittgenstein's story. At some point, when the perceptual systems switch places either before or after the relations between her perceptual systems and memory/recall system are realigned, she will report that things that previously looked red now look green, and vice versa. At which point will that happen? Our telling of the stories does not say, since that depends on how our subject's experiences are connected to the world—on what the external stimuli are that put our subjects into the physical states that realize their qualitative experiences. We have ignored this because, while it is relevant to the intentional content of experience, the qualitative content of experience is supposed to be independent of what causes, or tends to cause, our qualitative experience. If we bring the connections with colors of things in the world into our stories of Alice through Ellen, this will break the symmetry: either Bertha or Dorothy, but not both, will undergo the intrapersonal spectrum inversion when the perceptual system switches between α and β. Which it is will depend on whether Px in α subjects is caused by the same color as the one that causes Pz states in β subjects, or by the color that causes Pw states in β subjects. Does this give us a third way of resolving the paradox by giving a reason to reject two of the identities, 1–4, but not the others? This asymmetry can resolve the paradox only if we allow the intentional content of experience

236

Shoemaker (1996: 149).

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to play a role in the individuation of qualia. And while this could provide a basis for interpersonal comparison of the quality of experience, it won't do it in a way that makes sense of the interpersonal spectrum inversion. Shoemaker's intra–inner argument began by assuming that, at least in normal cases, it makes sense to say that the qualitative content of my color experience (when I see a ripe tomato) is the same as yours. The force of the argument, and the counterintuitive character of the Frege–Schlick view, rest on the plausibility of this assumption. The assumption is plausible, but I think that is because the common-sense view of qualitative content does not separate it so sharply from intentional content. It does seem to be a common-sense view to think that the qualitative character of experience has something essential to do with the way things appear to us to be.

13 What is it like to be a Zombie? (2002)

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Zombies are creatures that are physically exactly like ordinary people, but that have no phenomenal consciousness. A zombie world is a world physically exactly like our world, but with no phenomenal consciousness at all. The sun shines in such worlds, but the lights are out in the minds of the unfortunate creatures who live in them. These beings behave just as we do, and their internal physical and functional properties are exactly the same as ours. They make judgments, and perhaps have beliefs (or at least functional analogues of beliefs: states that represent the world), but their states have no qualitative character, no ‘inside’. There is nothing it is like to be a zombie. To be really clear about what a zombie world would be, a lot more should be said about what it means for a possible world to be physically exactly like our world. Suppose for a moment that some form of mind–body dualism is true, and that physical interactions cause emergent non-physical phenomenal experience. Isn't it part of the physical character of this world that physical interactions have these effects, and wouldn't a world without them be physically different? If so, then the possibility of zombie worlds will be ruled out from the start by dualists and materialists alike. But I will assume that to say that two possible worlds are physically alike is only to say that all physical phenomena, and physical powers to produce physical phenomena, are the same. There will still be room for considerable debate about just what phenomena and properties count as physical, but even if we don't look too carefully at the extent of the domain of the physical, contenting ourselves with a rough intuitive distinction, it will still be controversial whether zombies, and zombie worlds, are possible, and the controversy has metaphysical consequences. There is a simple argument against materialism, and for a kind of dualism, that has as its central premiss the hypothesis that it is conceivable, or conceptually possible, that there be zombies. From this it is inferred that zombies (and zombie worlds) are metaphysically possible. But if there are possible worlds exactly like ours with respect to all physical

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I am grateful to Katie Balog, Daniel Dennett, Sydney Shoemaker, and the editors, Tamar Szabó Gendler and John Hawthorne for very helpful comments on a prior draft of this paper. Thanks also to audiences at Johns Hopkins University, the University of Wisconsin at Madison, the University of Illinois at Chicago, Cornell University, Stanford University, the University of Oxford, the University of North Carolina at Chapel Hill, UCLA, the Australian National University, and the University of Konstanz for stimulating discussion.

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facts in which there is no consciousness, then the facts about consciousness in our world (assuming there are such facts) are not determined by (or supervenient on) the physical facts. So materialism—the thesis that everything is supervenient on the physical—is false. Some have questioned the move from the premiss that zombies are conceivable, or conceptually possible, to the conclusion that they are metaphysically possible, and I will consider below whether there might be a gap between conceptual and metaphysical possibility, but for the moment I will assume that metaphysical possibility is possibility in the widest sense. My aim is to try to get clearer about the nature of the disagreement between those who think zombies are possible and those who think they are not. What kind of dispute is this, and what kinds of arguments are relevant to resolving it? I am interested in getting clear about this issue mainly for the light it might throw on general questions about the nature of modal claims and about the relation between metaphysical, semantic, and empirical questions. I will begin by describing the views of three ﬁctional philosophers who give unequivocal answers to the question ‘Are zombies possible?’ These characters may seem to resemble real philosophers with the same names, and I will not claim that the resemblances are coincidental, but I want to be able to oversimplify without getting into trouble, so I won't identify my characters, whom I will call ‘Dave’, ‘Patricia’, and ‘Sydney’, with any real philosophers. (It is not that the views of my characters are any less complex than those of the real philosophers on which they are based; it is just that my ﬁctional characters can't complain when I oversimplify their views.) Dave and Patricia believe that zombies are possible, while Sydney denies that they are. Although Dave and Patricia agree about the possibilities, they disagree about the facts: Patricia thinks that the world we live in is a zombie world, while Dave agrees with Sydney that the world we live in is not a zombie world. I said that Dave and Patricia disagree with Sydney about whether zombies are possible, but what sort of disagreement is this? Speciﬁcally: is it an ontological disagreement about what sorts of metaphysically possible worlds there are, or is it a semantic disagreement—a disagreement about the meanings of the words we use to describe the possible worlds? Consider the dispute between O'Leary, who insists that it is impossible for there to be a veterinarian who never served in the military, and Daniels, who thinks that not only is this possible, there actually are such people. On closer inspection, we learn that this is not really a disagreement about what possible worlds there are: O'Leary agrees with Daniels that there are animal doctors who are lifelong civilians—he just has a misconception about some words that are used to describe these people. Is our dispute between Dave and Patricia, on the one side, and Sydney, on the other, like this? (Those who have taken the lessons taught by Quine to heart may be skeptical about the distinction I am trying to make, but let's ignore them for the moment.)

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In the case of Daniels and O'Leary, a paraphrase helped to bring out that the issue was semantic rather than metaphysical. Daniels could describe the kind of world he claimed was possible without using the disputed word ‘veterinarian’, and when he did, O'Leary agreed that this was indeed a metaphysically possible world. The only issue that remained is whether a certain expression was correctly applied to describe such a possible world. One might, at that point, get out the dictionary, but O'Leary, like Humpty Dumpty, doesn't care how other people use words. He insists that ‘veterinarian’, as he uses the term, applies only to former members of the military. Once this became clear, there was nothing left to argue about. Daniels, and we, may ﬁnd O'Leary's idiosyncratic speech perverse, but we don't disagree with him either about the facts or about the possibilities. If Dave and Patricia can paraphrase their description of the world they are claiming to be possible in a way that avoids the crucial expression ‘phenomenal consciousness’, and related expressions, then we may be able to see whether their disagreement with Sydney is semantic or metaphysical. One can't expect this procedure to work in general. It is rarely easy to ﬁnd paraphrases for controversial philosophical expressions that are not equally controversial. But in this case it turns out to be surprisingly easy. Let us deﬁne a z-world as a possible world exactly like the actual world in all physical respects, and that contains nothing except what supervenes on the physical. To use the popular metaphor, a z-world is a world in which God made and arranged the physical stuff, and then stopped. He did not go on and add anything else. We have not mentioned the absence of consciousness in our characterization of this world, but both Dave and Patricia should agree that our deﬁnition gives a determinate description of the world they are claiming to be possible. At least it is as complete as their original description of the zombie world. Clearly a zombie world (if there is one) ﬁts this description, and there cannot be two discernible possible worlds ﬁtting the description, since we have speciﬁed all of its physical features, and added that there are no others. Assuming that there cannot be distinct possible worlds that are indiscernible in all respects, there is a unique z-world, so one need not say more to say what kind of possible world we are talking about. According to David Lewis, the thesis of materialism is true in our world if and only if the following condition is met: Among worlds where no natural properties alien to our world are instantiated, no two differ without differing physically; any two such worlds that are exactly alike physically are duplicates.238

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Lewis (1983c : 364). Might there be possible worlds with laws that permit the emergence of nonphysical phenomena, but only in circumstances that, because of the accidents of chance or initial conditions, never in fact arise? And if there are such possible worlds, shouldn't we say that materialism is false in them? Lewis's Humean metaphysics, according to which laws are supervenient on arrangements of particular matters of fact, excludes such possible worlds, but those who want to allow for them might want to tinker with this deﬁnition (perhaps referring not to instantiated fundamental properties, but to properties that play a role in the fundamental laws of the world). But I don't think this issue will matter for our purposes here.

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This says what it is for materialism to be true in our world. One could say more generally what it is for materialism to be true in an arbitrary possible world x by replacing ‘our world’ in Lewis's deﬁnition by ‘world x’. Materialism is the proposition that is true in those possible worlds x that satisfy Lewis's condition. If we accept this deﬁnition of the thesis of materialism, then the unique z-world is just the world meeting the following two conditions: ﬁrst, it is physically exactly like the actual world; second, materialism is true in it. So anyone who believes that materialism is true will believe that the actual world is the z-world. Sydney is a materialist, so he believes, in agreement with Patricia, that the actual world is the z-world, and so of course that the z-world is possible. So it seems that Sydney and Patricia agree both about the possibilities and about the facts. Their disagreement about whether zombie worlds are possible is, like the disagreement between Daniels and O'Leary, a semantic one. ‘I am a materialist, but not an eliminative materialist,’ says Sydney. ‘As I use the expressions “phenomenal consciousness”, “feeling”, “qualia,” etc., they all apply in the actual world, and so in the world that both Patricia and I agree is the z-world.’ So it seems that all three of our characters agree that there is a possible world of the kind that Dave and Patricia call a zombie world. The disagreement is about whether it is properly so-called. Both Sydney and Patricia are what David Chalmers has called type-A materialists: those ‘who hold that consciousness, in so far as it exists, supervenes logically on the physical, for broadly functionalist or eliminative reasons’. Chalmers would distinguish both of them from type-B materialists, who ‘accept that consciousness is not logically supervenient, holding that there is no a priori implication from the physical to the phenomenal, but maintain materialism all the same’.239 We will introduce a new character who is a type-B materialist later, but we should note now that all materialists, whatever their views about the epistemological status of materialism, will agree that the actual world is the z-world—that follows from the deﬁnition of materialism and of the z-world. So any materialist who believes that we are conscious beings (any noneliminative materialist) will deny that the z-world is a zombie world. For type-B as well as type-A materialists, the ground for claiming that the zombie world is metaphysically impossible is that the candidate possible world (the z-world) is not a zombie world. If this is right, then there is no room for a defense of materialism against the zombie argument that tries to open a gap between conceivability and possibility by claiming that there are possible worlds that are conceivable but not metaphysically possible.240 Any materialist will agree with Dave, Sydney, and

239

Chalmers (1996: 165–6).

240

Ibid. 136 ff.

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Patricia that the z-world is not only conceivable, but metaphysically possible, and there is no other world, whatever its status, that is a candidate to be a zombie world. The question is not whether a certain conceivable situation is metaphysically possible; it is whether a certain situation that is agreed to be metaphysically possible is correctly described in a certain way. We said above that Sydney and Dave agreed with each other (disagreeing with Patricia) about whether the actual world is a zombie world. It now seems that this was a case of only apparent agreement. It is like the apparent agreement between Daniels and O'Leary that Jones is a veterinarian. Daniels knows that Jones is an animal doctor who never served in the military, while O'Leary believes, falsely, that he served in the military, but is not an animal doctor. They disagree about the facts about Jones, but since they use the word ‘veterinarian’ in different ways, they agree that Jones is correctly described as a veterinarian. Their agreement in assenting to the statement ‘Jones is a veterinarian’ results from two disagreements—one semantic and one factual—that cancel each other out. The same seems to be true of the superﬁcial agreement between Dave and Sydney about the truth of the statement ‘the actual world is not a zombie world’. It is a result of disagreement about whether we live in the z-world, and about whether certain words are correctly applied to the z-world. The ﬁrst disagreement is the only substantial one. On the second question, Dave and Sydney may ﬁnd each others' choices about how to talk perverse, but when each is clear about what the other means, there is nothing to argue about. Or is there? The argument against materialism that motivated our inquiry depended crucially on the assumption that the z-world is a zombie world. The soundness of this argument cannot depend on an innocent choice about how to talk. Perhaps it is not so easy to separate the semantic question about how to describe the z-world and its alternatives from the substantive questions about what kind of world we live in. Let's look more closely at the way the z-world and its alternatives are speciﬁed. The ﬁrst thing to note is that we have deﬁned the z-world in terms of the actual world, and since our characters are not omniscient, they may disagree about what the actual world is like physically (and so about what the z-world is like). So, while it is right that in deﬁning the z-world we have speciﬁed a unique possible world (assuming we have speciﬁed a possible world at all), there will remain empirical questions about what the world we have speciﬁed is like. Here is one way that future science might go: as cognitive psychology and neuroscience develop, they, along with common-sense psychology, converge. Both ordinary concepts for describing thought, emotion, and sensation, and functional concepts developed by psychologists, tend to ﬁt together smoothly with neurophysiological concepts and categories. Introspective reports about phenomenal experience as well as cognitive categories motivated by behavioral experiments are found to correlate well with brain states

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and events revealed by new brain-imaging techniques. Call this the optimistic scenario. Alternatively, it might happen that as neuroscience learns more about the brain and develops sophisticated methods for explaining and predicting behavior, common-sense mentalistic concepts and functional psychological theory seem increasingly irrelevant and outmoded. As we learn more about the brain, it becomes harder to reconcile what we are inclined to say about our thoughts, feelings, and sensations with what science tells us to be true about what is going on in our bodies and brains. Common-sense and cognitive concepts seem increasingly unnatural. Folk psychology comes to look increasingly like a theory with false presuppositions deeply embedded in it. Call this the pessimistic scenario. Patricia is inclined to believe that the pessimistic scenario is closer to the truth, while Sydney is disposed to expect something more like the optimistic scenario to be realized, and this empirical disagreement is part of what explains their disagreement about whether the z-world is a zombie world. But it is clear that this is not the whole of the disagreement. For one thing, Dave agrees with Sydney that the optimistic scenario is more likely, but agrees with Patricia about whether the z-world is a zombie world. In addition, it is clear that Patricia and Sydney would continue to disagree about whether the z-world is a zombie world even on the hypothesis that the pessimistic scenario is correct. Sydney will grant that the pessimistic scenario is an (unlikely) empirical possibility, but he thinks that zombie worlds are not only impossible, but inconceivable. According to him, we know on conceptual grounds that phenomenal consciousness is a functional property, although just what functional property is open to further discussion, informed by consideration of both thought experiments and empirical evidence. We might well discover that, according to some particular conceptual analysis of phenomenal consciousness, there was no such thing, but that would be a compelling reason to reject the analysis as incorrect. It is not (according to Sydney) an a priori truth that we are conscious beings, but the belief that we are conscious is a datum that should play an important role in evaluating any proposed conceptual analysis. We can characterize the semantic difference between the usage of Sydney, on the one hand, and Dave and Patricia, on the other, in a general way. The issue concerns how theoretically loaded the idea of phenomenal consciousness is. Some words carry with them a lot of theoretical baggage; such a word can be correctly applied only if the theoretical presuppositions implicit in its semantics are correct. Other words are more innocent. If we discovered that we were mistaken about the fundamental nature of Fs, in the one kind of case we say that we learned that there are no Fs, while in the other kind of case we say that Fs turned out to be fundamentally different from what we thought.

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Consider water: it was once believed to be a fundamental element (perhaps the one out of which all matter is made, but at least one of four fundamental elements). Imagine a more skeptical ancient scientist who expects that future science will reveal that what we call ‘water’ is not a fundamental kind at all, but just a heterogeneous category held together by a cluster of superﬁcial properties. Separate from this empirical issue is a semantic question about what we should say if the second hypothesis turned out to be true. One view is that ‘water’ is a theoretical word—it is built into its meaning that anything correctly called ‘water’ is a fundamental element. On this semantic hypothesis, if the skeptical ancient scientist turned out to be right, then the right thing to say would be that there is no water. A contrasting semantic hypothesis is that ‘water’ is theoretically innocent. Water is the stuff we call ‘water’, whatever it turns out to be. If the facts were as the skeptic thought, then ‘water’ would turn out to be vaguer than expected, but it would still be said that the stuff we regarded as paradigms of ‘water’ is water. Of course, water turned out not to be one of the fundamental elements, but it is nevertheless regarded as a natural kind of stuff. The situation was different with the other fundamental elements, but we are still not inclined to say that there is no such thing as earth, air, and ﬁre, in contrast with what we are inclined to say about phlogiston, or what we would say about oxygen or neutrinos if the theories of which they are a part turned out to be fundamentally mistaken. It not only seems descriptively right to say that ‘water’ is a term with little theoretical baggage built into its semantics—it is also clear that such terms are necessary to facilitate discussion when there is disagreement about the nature of the stuff we ﬁnd in the world. Suppose we are having a discussion with Thales, who is defending the view that water is the fundamental element out of which everything in the world is made. ‘Water’, says Thales, is, by deﬁnition, a fundamental element. According to you crazy H2O theorists, there is no such thing as water. You may try to paper over the paradoxical character of your theory by changing meanings, calling the stuff you think ﬁlls the rivers and lakes by the name ‘water’, but what you really are committed to is the incredible claim that the world is bone dry. Isn't it just obvious that that is false? The H2O theorist may be tempted to reply in kind: ‘It is you, Thales, who are claiming that we live in a waterless world. The world as you think it is a version of Putnam's counterfactual twin earth—a world superﬁcially like ours, but with no water (we might call your fundamental element “XYZ”). But obviously we don't live on counterfactual twin earth.’ But it might be more helpful to respond instead in this way: You may talk as you like, Thales, though we might argue about whose usage is eccentric. Your decision about what to mean by the word ‘water’

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is clear enough, and we agree that if we use the word as you are using it, our account is committed to the claim, ‘there is no water in the world’. And we agree that this sounds like a crazy claim, but if you use words in eccentric ways, the simple truth may sound like a crazy claim. (To quote Berkeley's character Philonous: ‘Suppose a traveller should tell you, that in a certain country men might pass unhurt through the ﬁre; and, upon explaining himself, you found he meant by the word ﬁre that which others call water; or if he should assert there are trees which walk upon two legs, meaning men by the term trees. Would you think this reasonable?’241) We don't want to quibble about words, but we do think (quite independently of our theory about the nature of the stuff in question) that it is useful to have a word that is less theoretically loaded than your word ‘water’, or our expression ‘H2O'—a name for the stuff whose composition is under discussion. If we have such a word we can more easily frame our disagreement, which is primarily empirical, and not semantic. Granted, we can't completely separate questions about what is in the extension of a term from questions about the nature of the stuff, but at least in a speciﬁc context of disagreement, we can choose our words so as to describe clearly the issues that are in dispute. ‘Water’ seems a word that is well suited for this purpose, but whatever we call the stuff whose nature we are arguing about, it is pretty clear that we agree, in large part, about when we have a paradigm example of the stuff, and about what many of its superﬁcial properties are. The point might be put with the help of a distinction, and some terminology for it, introduced by Martin Davies and Lloyd Humberstone.242 If we consider the twin-earth world as a counterfactual world (presupposing what we H2O theorists know to be true—that water is H2O), we describe it as a world without water, and this is a correct description of that possible world. But if we describe that counterfactual world as actual—imagine ourselves in it, describing it from within—then we adopt the semantics that we (or our counterparts) use in that possible world. We grant that if Thales were right about the nature of the stuff, then he would be right that the word ‘water’ applies to the stuff with that nature. We believe that there is no water on counterfactual twin earth, but we beg the question if we assume this in a discussion with someone who thinks that we actually are in such a world. In using the two-dimensional apparatus to formulate this point, I do not mean to endorse the view that Stephen Yablo has called ‘textbook Kripkeanism’,243 according to which a word like ‘water’ has two kinds of meaning or intension, one of which is a reference-ﬁxing deﬁnition in terms of the manifest properties that we use to pick out water. Our capacity to identify

241

Berkeley (1713 1713/1979: 51).

242

Davies and Humberstone (1980).

243

See Yablo (1999), (2002). Yablo (correctly, I think) refrains from attributing this line of thought to Kripke.

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water, and the fact that we agree, in many cases, about where it is to be found make it possible for us to talk about it without talking past each other, but this does not imply that the facts about water that we agree about are implicit in the meaning of the word ‘water’, in any sense, or that we know a priori that water has the properties we use to pick it out.244 The contrast between more theoretically innocent and more theoretically loaded words is not meant to be a sharp or deep distinction of kind. There will be intermediate cases, and it may in some cases be an accident of lexicographic history whether one says, when a theory is overturned, ‘we discovered that there were no such things as Fs’ or ‘we discovered that Fs are very different from what we thought’. The important thing is not to equivocate between the two. To return to consciousness, it seems clear that Dave and Patricia are building some theoretical content into the concept of phenomenal consciousness, and the cluster of related words; that is, they are treating ‘consciousness’ more like ‘oxygen’ and ‘phlogiston’ than like ‘water’, ‘earth’, or ‘ﬁre’. Patricia will probably agree with us about this; for her, the idea of phenomenal consciousness is inseparable from an outdated false theory of the mind. But Dave may insist that, as he uses the expression, ‘phenomenal consciousness’ has a demonstrative meaning. ‘Zombies are possible,’ he might say, ‘because there might be creatures physically just like us who do not have this going on in them’ (inwardly demonstrating the property we all experience ourselves as having). But Dave does assume that there are some theoretical constraints on the kind of thing that we can be demonstrating. Speciﬁcally, he seems to assume that it follows from what we mean when we talk about consciousness that consciousness is nonphysical. For consider what happens when Dave's zombie twin judges that he himself is conscious. According to Dave, the word ‘conscious’, as used by the zombie, does not refer to some property that is salient to the zombie, as one might expect with a demonstrative. (I assume that properties can be salient to zombies: they can, for example, presumably use words like ‘she’ to refer to a most salient female in the relevant context.) Rather, the word, as used by both Dave and his zombie twin, is constrained to refer only to a property of a certain kind. ‘There is no doubt.’ Dave says, that his zombie twin, in judging that he himself is conscious, ‘is judging that he has some property over and above his structural and functional properties—a property that he calls “consciousness.” ’245 (Even the zombie (at least the zombie who is Dave's zombie twin) is judging that he has some nonphysical property.) Sydney uses the word ‘consciousness’ in a contrasting way, but a way that may also be theoretically loaded. He is an analytical functionalist, so, while

244

I discuss alternative interpretations of the two-dimensional modal apparatus in ‘On Considering a possible World as Actual’, reprinted as Ch. 10 of this volume.

245

Chalmers (1996: 180).

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Dave is insisting that it is part of the meaning of the word that consciousness is not a functional property, Sydney is insisting that it is built into the meaning of the word that it is a functional property. This semantic mismatch is not conducive to a perspicuous debate about whether we in fact live in the z-world, or in one of its alternatives. So let me introduce a new character—a materialist who tries to use words in a more theoretically neutral way. I will call her Anne. (Don't look for a real-world analogue for this character—at least not one with this name.) Anne thinks that ‘phenomenal consciousness’ and related expressions are names for, or ways of talking about, properties that we ﬁnd ourselves with, but she thinks that there is no theoretical account of the nature of these properties built into the semantics of the expressions. Perhaps they are functional properties, or physical properties. Perhaps they are irreducible nonphysical properties. Empirical inquiry will be relevant to answering the question of what kind of properties they are, though the questions are obviously highly theoretical. Thought experiments, as well as empirical experiments and observations, will be relevant to deciding what kind of properties they are. Some arguments about the nature of the properties may look like something that might be called ‘conceptual analysis’. But Anne—a good Quinean—thinks that the line between theoretically informed conceptual analysis and empirical discovery is difﬁcult to draw in a nonarbitrary way. Anne is the promised type-B materialist. Since Anne is a materialist, she agrees with Sydney and Patricia that we live in the z-world, and since she is not an eliminative materialist, she agrees with Sydney that the z-world is not a zombie world. The contrast between Sydney's and Anne's views about the semantics of the contested expressions is a subtle one. To bring it out, we need to be more explicit about the alternative to the z-world—the world that Dave thinks is actual. I argued above that it was easy to specify a unique z-world without using contested words, but this is not possible with the alternative to the z-world. And while it is common ground that there is a z-world, it is less clear whether our characters will agree that there are possible worlds of the alternative kind. We can say this much, before running into disagreement, about what such an alternative world would have to be like: an a-world is a world that is physically just like the actual world, and so just like the z-world; in addition, it has some properties not instantiated in the z-world: alien properties, in Lewis's sense—that is, properties that are alien relative to the z-world. (The ‘a’ in ‘a-world’ is for ‘alternative’, or ‘alien’, but if you are on Dave's side in this dispute, you can think of it as short for ‘actual’.) All of our characters agree that an a-world meets these conditions, and that worlds meeting these conditions are possible. But of course this is far from enough to specify the kind of possible world that Dave has in mind. We have to add that the extra properties in the a-world (call them the a-properties) are properties of conscious beings, and that they are the properties we are referring to when we talk about consciousness, experience, qualia, and so forth.

WHAT IS IT LIKE TO BE A ZOMBIE?

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It is here that Sydney will balk. I will grant that there are possible worlds like ours, but with extra nonphysical properties or substances. I will even grant that the mental/functional properties such as phenomenal consciousness that are physically realized in our world might, in some other world, be realized by alien nonphysical properties. But it has been stipulated that aworlds and the z-world are physically alike, so the functional properties that are physically realized in the z-world will be realized in exactly the same way in a corresponding a-world. Since I think expressions like ‘phenomenal consciousness’ refer, in virtue of their meaning, to such functional properties, I hold that they will refer to them, and not to the a-properties, in (or with respect to) the a-worlds. But if we set aside the purely semantic assumption that our expression ‘phenomenal consciousness’ and others like it refer (with respect to the a-world) to aproperties,246 then I will grant that a-worlds are possible, and I will agree with Dave that we, or our counterparts in the a-world, are conscious there (since I think we are conscious in the physically and functionally equivalent zworld). But I deny that the a-properties he postulates have anything to do with our consciousness in such worlds. That is, I claim that phenomenal consciousness in the a-world is independent of the a-properties, which is to say that the following counterfactual is true there: Even if none of the a-properties were instantiated, people would still be conscious, have qualitative experience; there would still be something it is like to be them. You can hypothesize all the alien properties you like, but if they don't affect our brains or our behavior, then they won't have anything to do with our minds—and they won't be anything we could know about. Dave and Sydney have reached an impasse much like that of Thales and the H2O theorist. At this point, Anne enters the discussion:We disagree about the nature of consciousness, but just as with water, we agree, for the most part, about when and where it is to be found. Talk of qualitative experience—of ‘what it is like’, and so on—is somewhat elusive, but people with very different theoretical views seem to be able to understand each other when they talk about experience, at least outside of an abstract theoretical debate. (Just as Thales and we can agree about whether there is water or vodka in the glass, so Dave and we can agree about exactly when the patient regained consciousness after the operation.) And just as it seems natural to describe the disagreement

246

Instead of stipulating that the a-properties are the ones we refer to when we talk about conscious experience, we might (Sydney suggests) more cautiously say only that the aproperties coincide with mental properties, leaving open whether they are identical to them. (My character wants to acknowledge help from comments by the real Sydney Shoemaker in formulating his views—he was careless in an earlier draft. But he insists that he remains ﬁctional; neither he nor Sydney Shoemaker should be held responsible for views expressed by the other.)

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between Thales and the H2O theorist as a dispute about the nature of water, so it seems natural to describe the disagreement between Sydney and Dave as a dispute about the nature of consciousness. Let's call the phenomenon whose nature is at issue ‘phenomenal consciousness’, without prejudging its nature. We have no a priori assurance that we can identify the subject matter of our dispute in a theory-neutral way, but let's assume provisionally that there is a property that Dave thinks is an irreducible nonphysical property and that Sydney thinks is a functional property—a property that we all agree we ﬁnd ourselves with. The property may be essentially nonphysical, or essentially physical, or neither, but since that is part of what is in dispute, we'll try to leave it open. I should say that I am not convinced that an a-world in which the inhabitants succeed in talking about properties that are epiphenomenal is really coherent, but I am setting these worries aside.247 What we will try to do is to consider both the z-world and the a-world as actual: as possible worlds that are compatible with the context in which our debate is framed. What is presupposed in the context of any discussion is only what is presumed to be the common knowledge of the participants in that discussion. In the debate between materialists and dualists, some think that we are in the z-world, and some that we are in an a-world, so both kinds of world must be included in the context. But it is common ground (since Patricia has gone home) that we are conscious. So, if you are going to take our materialism seriously, you must consider the world that we think we are in as actual, which means entertaining the possibility that our thesis is actually true. Of course you might argue that our position is incoherent— that there is no possible world of the kind we think we are in. But you grant that the z-world is possible. You think it is a zombie world, but suppose you discovered that the z-world was not only possible but actual? (God reveals to you that all there is, is supervenient on the physical.) Would you then conclude that you are a zombie—that your consciousness is an illusion? Of course not. Dave responds to Anne this way:I'm sorry, but I can't take your materialism seriously as possibly actual, since I know, simply by being conscious, that I am not in a zombie world, and I think the world that you materialists are claiming we live in is a zombie world. Let's go back to the original intuition—the one with which our argument against materialism began: that it is conceivable that there are zombies (and zombie worlds). Don't even you materialists have to admit that there is at least a prima facie plausibility to the claim that we can form a coherent conception of a world just like ours, but with the

247

See Chalmers's discussion of the paradox of phenomenal judgment in Chalmers (1996: 172–209), and Shoemaker (1999).

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inner light of consciousness extinguished? I grant that this is in part a semantic intuition—an intuition about what we mean by ‘consciousness’—but isn't it a compelling intuition nonetheless? We have to take our semantic intuitions seriously, as Berkeley's Philonous reminded us earlier in the discussion. Anne responds:I agree that we have to take semantic intuitions seriously, but my worry is that, in rejecting the coherence of our noneliminative materialism you are appealing to incompatible semantic intuitions. On the one hand, you want to insist that ‘consciousness’ bears a theoretical load—that it is part of the meaning of the term that it refers to a nonphysical property; on the other hand, you want to insist that consciousness is a property we can know we have, simply by having it. This seems to me suspicious in a way that is reminiscent of Thales's move when he noted ﬁrst that it is obvious that there is water—who but a radical skeptic could deny that there is water in the lake?—and then claimed that the H2O theorist was committed to denying this obvious fact, since ‘water’ by deﬁnition refers to a fundamental element. I agree that ‘consciousness’ is something we simply ﬁnd ourselves with, and I can't imagine being convinced by any kind of theoretical consideration that I am not conscious—that I am a zombie. Since I can imagine being convinced, on theoretical grounds, of the truth of materialism (this takes little imagination, since I am convinced of it), I conclude that the existence of consciousness is compatible with materialism. Anne continues:I will, however, concede that the intuition that zombies are conceivable has considerable intuitive force, and I think that, with the help of the two-dimensional apparatus that you are so fond of, we can accommodate it. Let's look one more time at the analogy with water: We agree that in a sense it is conceivable that water be something other than H2O, even though it is necessary that water is H2O (and so that there is no possible world in which water is something other than H2O). What is conceivable (and metaphysically possible) is that the XYZ theorist is right, and if he were right, then we would be referring to something other than H2O with the term ‘water’. The situation is symmetrical: The XYZ theorist believes that ‘water’ refers to XYZ in all possible worlds, but grants that, as he puts it, ‘if the H2O theorist were right, we would all be referring to H2O with the term “water”, rather than to water’. If the XYZ theory were true, then what he would be saying would be true, and it is conceivable that his theory is true. So much is familiar. But now consider whether it is conceivable that there should be no water in the world at all, even though H2O ﬁlls the lakes and streams, and falls from the sky on rainy days, just as it does in the world as we believe it to be? That is, try to envision a possible

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world physically and chemically exactly like ours, but with no water. This, we say, is surely impossible, but the XYZ theorist disagrees. He thinks that the world we think is actual is a world that is correctly described in this way—as a world with H2O, but no water, in the lakes and streams. (Just as we describe the XYZ world as a possible world with XYZ in the lakes and streams, but no water.) Of course the XYZ theorist is wrong, but since it is conceivable that he might be right, it is conceivable that what he says is true. It may seem a rather artiﬁcial and oversubtle exercise to use the two-dimensional modal apparatus to describe the actual world (considered as counterfactual) from the perspective of a counterfactual world (considered as actual), but if it is really an open question—a real live disagreement—which world is actual, this may be less artiﬁcial. We materialists don't believe that Dave's dualist theory is right, but we beg the question if we presuppose that he is wrong. So suppose he's right—suppose that we really are in an a-world, and that consciousness—this property we ﬁnd ourselves with—is an irreducible nonphysical property. (I'm not convinced that this is really possible, but we're granting it for the moment.) Now consider the counterfactual ‘if we didn't have this property—or any of the aproperties—we wouldn't be conscious.” More speciﬁcally, consider, ‘if we didn't have any of the a-properties, but the world were physically just as it is, then we wouldn't be conscious—we would be in a zombie world.’ I will grant (though Sydney would not) that if we were actually in an a-world, then this counterfactual would be true. If it is conceivable, and possible that we are in an a-world, then it is conceivable, in this convoluted sense, that there be zombies. If zombies are conceivable in just this sense, does that mean that zombies are metaphysically possible—that there is a zombie world? If we are in fact in an a-world, as Dave believes, then there are (counterfactual) zombie worlds. But if the materialists are right, and we live in the z-world, then there are no possible worlds correctly describable as zombie worlds. Whether or not Dave's dualism is true, if we can coherently suppose that it is true, then we can coherently suppose that zombies are possible, and so can form a coherent conception of zombies. But if this is the only sense in which zombies are conceivable, their conceivability will provide no argument against materialism, since we must assume that materialism is false to be justiﬁed in inferring that zombies are possible from the fact that they are conceivable.248 So what is it like to be a zombie? According to Anne, it is something like being H2O without being water.

248

Anne's attempt to accommodate the zombie intuition is similar to a line of argument that is developed (independently) in more detail by John Hawthorne (2002).

14 On Thomas Nagel's Objective Self (2003) I think there is something idiotic about the self, that every day you have to get up and be the same person. (Wallace Shawn)249 Thomas Nagel ﬁnds it a remarkable fact that he should be Thomas Nagel, of all people. It is not because he thinks that Thomas Nagel is a particularly remarkable person that he ﬁnds it remarkable that he is that person. Each of us, he suggests, should ﬁnd it remarkable that he or she is the person that he or she in fact is. There is a distinctively philosophical thought expressed in ﬁrst-person identity statements such as ‘I am TN’, and a philosophical problem to get clear about the content of such thoughts.250 There is, as Nagel emphasizes, work to be done to turn the intuitive puzzle, the ‘inchoate perplexity, into an articulated philosophical problem. The general problem is about how to relate a person's point of view toward him or herself and the world to a centerless conception of an objective world—the world as it is in itself—but it is not clear what needs to be said to clarify that relation. We may begin with the problem of trying to say what the content of thoughts expressed by sentences such as ‘I am TN’ is, and to say what kind of fact they state when they are true. There is a prima facie problem, since it is not clear that our conception of the world has room for such facts. ‘I seem to have on my hands a fact about the world, or about TN, which both must exist (for how things are would be incomplete without it), and cannot exist (for how things are cannot include it)’ (57). There is a familiar deﬂationary solution to this problem which Nagel calls the ‘semantic diagnosis’, and which he ﬁnds unsatisfactory. He also rejects a metaphysical or ontological solution to the problem—one that tries to account for philosophical thoughts of the form ‘I am TN’ by enriching our conception of the objective, centerless world. The intermediate view that he defends, which invokes the idea of the objective self, is somewhat elusive. I am not sure that I understand it, but I will argue that the invocation of the objective self is not necessary or helpful. We can agree that there is more

249

Interview in the New York Times Magazine, 12 Aug. 2001, p. 17.

250

See Nagel (1983) and Nagel (1986). Most of the passages I will quote come from Nagel (1986). Page numbers in parentheses after a quotation will be from that book.

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that needs to be said to clarify the place of a subjective point of view in the objective world than is said by the semantic diagnosis, but that diagnosis, properly understood, still seems to me to have the potential to give an adequate account of the contents of such thoughts, and an explanation of the sense in which our conception of the world allows for objective facts of this kind, and the sense in which it does not. My plan is this: I will begin by describing the semantic diagnosis and Nagel's reasons for ﬁnding it unsatisfactory. Second, I will sketch a metaphysical solution to the problem, and Nagel's reasons for rejecting it. Third, I will sketch the idea of the objective self, as I understand it, and say why I think it is a mistake—a response to a nonproblem. Fourth, I will take a look at the broader problem of explaining the place of subjective points of view in an objective world, trying to spell out some of the consequences of the austere view of that problem that is implied by the semantic diagnosis. Finally, I will consider whether the austere view of contextual or subjective information that I defend can account for information about the qualitative character of experience.

1. The semantic diagnosis I will put the semantic diagnosis in my own terms, and my version of it will differ in some respects from other versions of this kind of response to the problem. I will also leave out the evaluative commentary that Nagel takes the semantic diagnosis to imply. It is not part of the semantic diagnosis, as I understand it, that ‘I am TN’ is ‘devoid of signiﬁcant content’, or that the thought it expresses is ‘trivial or at any rate unremarkable’. As I will understand this response to the problem, it tries to make precise, from an external point of view, exactly what the content of statements such as ‘I am TN’ is, to say exactly under what conditions they are true. But it does not add, as Nagel does in his exposition of this response, that ﬁrst-person identity statements are ‘automatically and uninterestingly’ true under those conditions(58).251 The semantic diagnosis begins with a straightforward account of the truth-conditions of statements containing a ﬁrstperson singular pronoun: A statement of the form ‘I am F’ is true, when said or thought by XY, if and only if XY is F. In particular, ‘I am TN’ will be true, when said by XY, if and only if XY is TN. But this simple description of the conditions under which a statement of this kind is true does not answer the question, what is the content of the statement—what information does it convey? When a statement of this form is true, what kind of fact, if any, does it state? One proposal is this: if the contents of ordinary beliefs about objective facts can

251

In Nagel (1983), Perry (1977, 1979) and Lewis (1979) are cited as defenses of the semantic diagnosis.

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be represented by sets of centerless possible worlds, then the contents of self-locating beliefs can be represented by sets of centered possible worlds—possible worlds with a designated time and person or object. Since ‘I am TN’ is true if and only if it is said or thought by TN, its content will be represented by the set of centered possible worlds that have TN as their designated object. The content of ‘the execution is taking place now’ will be a set of centered worlds at which the execution in question takes place at the time that is designated as the center. Equivalently, one can think of the content of a belief as a property, since a property determines a unique set of centered worlds (those in which the designated individual has the property in the world at the designated time), and any set of centered worlds determines a unique property (the property that x has at time t in a world w if and only if the centered world is in the set.) To have a belief with a given property as its content is to ascribe that property to oneself.252 The truth-conditions ascribed to self-locating statements and beliefs by the semantic diagnosis are uncontroversial, but I don't think this account of their contents is quite right. It seems that what I believe when I believe that I am a philosopher, what I discover when I discover that my pants are on ﬁre, or what I say when I say that I live in Massachusetts, is something about myself, and something different from what someone else might believe, discover, or say about themselves. And it also seems that when TN expresses his belief about who he is by saying ‘I am TN’ and his interlocutor understands and believes him, then the information she acquires is the same information that he imparted. But she does not, of course, thereby ascribe the property of being TN to herself. So the account of content as selfascribed property, or as set of centered possible worlds identiﬁes contents that need to be distinguished, and distinguishes contents that should be identiﬁed.253 Let me see if I can do better. On the account I will sketch, what I will call contextual or subjective content is like ordinary objective content in that it is to be understood in

252

This is essentially the version of the semantic diagnosis given by David Lewis (Lewis 1979). Lewis's proposal provides a uniform account of the contents of belief, since it takes all beliefs, and not just self-locating beliefs, to have properties as their objects. He points out that objective propositions (sets of centerless worlds) will correspond to properties; to believe that φ (where φ is a proposition) is to ascribe to oneself the property of being in a world in which φ. John Perry's version of the semantic account is somewhat different. Rather than providing a distinctive kind of content for self-locating beliefs, he distinguishes belief contents (which he takes to be objective propositions) from belief states. Belief states use what Perry calls relativized propositions to classify believers: You and I have a belief state in common if we both have a belief that we might express by saying ‘I am a philosopher’. But the relativized propositions that Perry uses to deﬁne belief states correspond to the sets of centered possible worlds, or properties, that Lewis takes to be the contents of belief (Perry 1977, 1979).

253

Cf. Stalnaker (1982), where Lewis's account of indexical belief is criticized. Inconclusive second thoughts about those criticisms are expressed in the introduction to Stalnaker (1999). I am indebted to Alex Byrne for very helpful comments that have signiﬁcantly inﬂuenced my account of subjective content.

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terms of the way it distinguishes between possible worlds. What is distinctive about contextual or subjective content is that the identity of the information is essentially tied to the context of speech or thought in which the possibilities are being distinguished between. It is true in general that what is said (self-locating or not) is said in a context, against a background of shared information that includes information about the context itself. Possible worlds compatible with the context—with what the speaker takes to be the shared background information—are all possible worlds in which the speaker exists, and is saying what he is in fact saying. The main aim of the speaker is to distinguish between the possible situations compatible with that background information. Similarly, any normal believer who believes something (self-locating or not) also believes that he himself exists, and has that belief. When we say what a person believes, we are saying how that person distinguishes between a range of possibilities all of which include that believer with those beliefs. In the case where what is said or believed is objective information, we can detach the information from the context in which it is expressed, or from the situation in which it is believed. That is, we can identify the content of what was said or thought (the way it distinguishes between possible worlds) independently of the fact that it was something that was said or thought on that particular occasion. But sometimes, the information—the way a speech act or thought distinguishes between the possibilities—essentially involves the context in which it is expressed or thought, and cannot be detached from it. The point is not simply that a proposition can be about a context in which something is said or thought. A proposition about a speech act or a mental state can be an ordinary objective proposition since the proposition might be expressed in some independent context, or not expressed at all. It is, for example, an objective fact about the centerless world that TN believed, on a particular occasion, that bats navigate by sonar, or that he identiﬁed himself as TN. The point is rather that sometimes the way in which the information is expressed in a given context, or the particular way the thinker is related to the things she is thinking about are essential to the information conveyed, so that even when the same possible worlds are distinguished in some different context, it does not seem right to say that the content expressed is the same. So, for example, suppose John points to a certain ship and says ‘That is the SS Missouri’. What he said is true in all and only possible worlds in which what he was pointing at on this particular occasion was the SS Missouri. A statement made in a different context about John's act of pointing (for example, a statement made the day before that the next day, John would point to the SS Missouri in certain particular circumstances) might be true in just the same set of possible worlds, but does not seem to convey the same information. John himself might have known the day before that he would the next day be pointing to the SS

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Missouri, but he was not yet in a position to know what he would express the next day when he said ‘that is the SS Missouri’. There is no mysterious, ineffable content here: it is just that the identity conditions for contextual content include the context in which the content is expressed or thought. This kind of content is subjective in that its speciﬁcation contains information about the subject who expresses or thinks a thought with that content. We have no difﬁculty describing, from an external perspective, what that content is. And although the content is undetachable from the context in the sense that the content is deﬁned, in part, in terms of the context in which it is expressed, and cannot be expressed outside of that context, it may still be detachable from its context in a different sense: we can evaluate it independently of its context. It seems reasonable to say that what John said when he identiﬁed the SS Missouri would have been true even if he had not said or thought it.254 Does the statement ‘I am TN’ (said or thought by TN) state an objective fact, according to this kind of account of its content? If one means by ‘an objective fact’ a fact that must be included in a complete description of the world as it is in itself, then the answer (according to the semantic diagnosis) is ‘no’. Any complete description of a centerless world in which TN thinks the thought ‘I am TN’ will include the information that TN is (at some particular time) thinking this thought. But neither this proposition nor any other objective proposition can be said to be the content of TN's thought. If, however, we mean by ‘an objective fact’ a fact that is a fact independently of whether someone believes it, then the statement states an objective fact. If TN were deluded, and thought that he was SK, or if he were an amnesiac who was ignorant of who he was, the thought he in fact expresses with ‘I am TN’ would still be true. Even if, per impossibile, TN were so unphilosophical that the thought ‘I am TN’ never occurred to him, it would still be true. So in this sense, the fact that TN states when he says ‘I am TN’ is an objective fact. The semantic diagnosis thus provides a straightforward response to the paradox that ‘I seem to have on my hands a fact about the world, or about TN, which both must exist (for how things are would be incomplete without it), and cannot exist (for how things are cannot include it).’ In one sense of ‘objective fact’ there is no such fact; in a different sense, there is. Nagel's objection to the semantic diagnosis is that ‘it doesn't make the problem go away’ (59). But what is the problem that does not go away? Nagel says that an adequate solution ‘must be one which brings the subjective and objective conceptions of the world into harmony’ (57), but to know how to do this (and to know whether it has been done) one needs to

254

I recognize that this is a very rough sketch of an account of subjective or contextual content, and that much more needs to be said to make the idea clear. The kind of undetachability that I am attributing to contextual content is a matter of degree, and is itself context-dependent. Contexts might be individuated in different ways, yielding notions of contextual content that are more or less local.

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articulate the prima facie source or sources of disharmony. Nagel warns against answers to a philosophical question that ‘may seem adequate to its verbal form but that don't really meet the problem beneath the surface’ (56). One does not want to rest content with a solution to an inadequate formulation of the problem, but such a solution may be an important ﬁrst step. To take the next step, we will need a better formulation of the problem. Let me belabor the general methodological point with an analogy. Suppose a skeptic, or a person who ﬁnds skepticism a problem, articulates the problem by giving a simple-minded skeptical argument (e.g.: ‘Knowledge implies truth, so if one knows something, it cannot possibly be false. Therefore, one can know only necessary truths.’). The anti-skeptic responds with a diagnosis that identiﬁes an equivocation on the scope of the modality. The person worried about skepticism responds that the diagnosis is unsatisfactory, since it doesn't make the problem go away. The response is correct—skepticism is a deeper problem than that. But the diagnosis of the simple-minded argument is a start—equivocations on possibility may be part of what lies behind one's skeptical worries. And the diagnosis forces the person worried about skepticism to articulate a more sophisticated reason for worrying about skepticism—a more sophisticated argument for skepticism that one can then examine and respond to. The diagnosis of the simple-minded argument puts the ball back in the skeptic's court. The sophisticated skeptic, or person bothered by skepticism, has no problem articulating more interesting skeptical arguments that come closer to revealing the underlying problem. But it is often a controversial philosophical question whether there really is an underlying problem—whether a particular philosophical problem is one where ‘a trick of language produces the illusion of a question where none really exists’ (55), or whether there is some kind of deep problem beneath the surface. The fact that one ‘can feel the question apart from its verbal expression’ (55) is not enough to refute the hypothesis that the problem is at root an illusion. Some illusions are persistent—one may continue to feel their pull even after they are explained. And the fact that one continues, even after clearheaded reﬂection, to ﬁnd something surprising, or worthy of wonder or puzzlement, does not by itself imply that there is a problem to be solved or a question to be answered. We may agree that ‘amazement that the universe should have come to contain a being with the unique property of being me is a very primitive feeling’ (56), and we may judge that the feeling is an appropriate one. One wants to get clear about the source of the feeling, and about the unique property, but the fact that the feeling persists even after getting clear about those things is not necessarily a sign that an underlying problem has not been solved.255

255

I am inclined to think that the famous explanatory gap (see Levine (1983), where the term is introduced) gets much of its intuitive force from a natural and appropriate feeling of wonder that is not a reﬂection of a real question or problem. ‘How could chemical and electrical activity in the brain, however complicated, ever give rise to this (gesturing inwardly to the quality of one's experience)?’ Taken literally, as a question about how something is possible, the right response may be, ‘why should it not be possible?’ Questions about how something is possible make sense only in the context of a reason to think that it is not. Perhaps there is such a reason in this case, and so a question that requires an answer. But perhaps the inclination to ask the question should be understood simply as a reﬂection of a natural and appropriate attitude toward the character of one's experience.

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Let me hasten to add that I think there are plenty of real problems about the relation between the subjective and objective standpoints, problems that Nagel has done more than anyone else to bring out and to clarify. But there are also some illusory problems that need to be dissolved (and dissolving them helps to clarify the real problems). I want to suggest that the problem to which the objective self is a response is one of them.

2. The metaphysical response Before trying to say what Nagel's conception of the objective self is, let me say what it is not. Here is one picture, which one might be tempted by the term ‘objective self ’ to think is the view being proposed.256 There is a property that is in fact unique to TN that he calls ‘being me’ and that is distinct from the property ‘being TN’. Or perhaps there is an entity—his objective self—that TN calls ‘me’, and that is distinct from TN. It is an objective fact, by which we mean here a fact that must be included in a complete conception of a centerless possible world, that TN has this property, but this is a contingent fact. This very property might have been possessed by SK instead of TN (or, if we put the view in terms of objects rather than properties, it is a contingent fact that TN's objective self resides in him, rather than in SK). There is a possible world exactly like the actual world, except for the fact that the self properties of TN and SK are interchanged. Now it is clear that this is not Nagel's view of the objective self, and I do not want to attribute it, in this uncompromising form, to anyone else either. But it will be a useful reference point, since it represents a pure form of a certain kind of response to the problem of relating subjective and objective, a response that tries to build subjective information into the objective character of the centerless world. This kind of response may have more plausibility in more subtle variations, so it is worth spelling out exactly what is wrong with it. Here is Nagel's reason for rejecting the view just described, which I will call ‘the ontological view’:

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I think David Chalmers may have interpreted Nagel to be holding something like the ontological view that I will describe. He attributes to him, in a passing reference, the view that there is an ‘ontological gap’ reﬂected in indexical statements such as ‘I am TN’. I take Chalmers to mean by this that one's account of uncentered possible worlds must recognize a distinction between the referent of ‘I’ and the referent of ‘TN.’ See Chalmers (1996: 144).

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If we suppose ‘being me’ to be any objective property whatever of the person TN, or any relation of that person to something else, the supposition quickly collapses. We are bound to include that property or that relation in the objective conception of the world that contains TN. But as soon as it has been made an aspect of the objective TN, I can ask again, ‘Which of these persons am I?’ and the answer tells me something further. No further fact expressible without the ﬁrst person will do the trick: however complete we make the centerless conception of the world, the fact that I am TN will be omitted. (56) I think this response is essentially right, but the proponent of the ontological view may ﬁnd it a little too quick. He might respond this way: The objective property that TN refers to with the expression ‘being me’ is a property that meets these two conditions: (1) only TN in fact has it, and (2) only the person who has it has the capacity to ascribe it, since only that person can be acquainted with the property. It is part of the ontological view that each of us has exactly one of these distinctive self properties, so we must grant that anyone will be able to give a unique description of the self properties of others. But according to the ontological view, a description such as ‘TN's self property’ is a non-rigid deﬁnite description of that property. Relative to the possible world in which TN's and SK's self properties are interchanged, that description denotes a different entity, the one that is in fact SK's self property. So to apply the predicate ‘has TN's self property’ to someone is not to ascribe TN's actual self property, just as saying that something is the color of the sky (when in fact the color of the sky is blue) is not the same as saying that it is blue.257 Everyone who understands the descriptive proposition that TN has TN's self property will believe that proposition, but only TN can grasp propositions that ascribe the property itself. If TN is deluded about who he is, or an amnesiac, then even though he knows that TN has TN's self property, he will remain ignorant of the fact that TN has the property itself—the property that he calls ‘being me’. This is a fact about the objective, centerless world, and if he knows it, then he knows who he is. So (says the defender of the ontological view) it is just false that a question remains for TN (‘Which of these persons am I?’) even after he knows that it is TN who has this objective property. The strategy of this reply to Nagel's objection to the ontological view is instructive. After objectifying selves—turning self-locating properties into features of the centerless world—one tries to recapture their essentially subjective character by constraining the subject's capacity to grasp certain

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What if we rigidify the description, using the predicate ‘has TN's actual self-property’? That will allow us to formulate sentences that express the propositions that people other than TN cannot grasp. Those people can, in a sense, understand those sentences, but that won't help them to grasp the propositions. Similarly, we might put an ‘actual’ in our description of the color of the sky, so that ‘Cornﬂowers have the actual color of the sky’ expresses a proposition that is true if and only if cornﬂowers are blue. But one who does not know that the sky is blue will not know what color the statement says that cornﬂowers have.

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objective propositions. The issue shifts from metaphysics—what the world is like—to intentionality—our capacity to represent what the world is like. But the constraint on our representational capacity seems unmotivated. If self properties are simply features of things in the objective centerless world, why are they so much harder to refer to and ascribe than any other property? It seems that the otherwise gratuitous metaphysics requires, in order to do its work, an implausible account of intentionality.258 (To those who wonder why I am ﬂogging this horse: my real interest is in a parallel, to be discussed below, with the objectiﬁcation of qualia.)

3. Subjects of the centerless world The semantic diagnosis is deﬂationary in the sense that it rejects this kind of ontological response to the problem, and Nagel agrees that we need a solution to the problem that is deﬂationary in this sense. The semantic diagnosis accounts for the sense in which self-locating statements and thoughts have objective content, and for the sense in which they are contingent. What are the problems that remain, and what is the response that invokes the objective self? As I understand it, one remaining worry that concerns Nagel is something like this: We begin with the fact that each of us is capable of forming a conception of the world as it is in itself, a conception according to which each of us is just one thing among others. To think of the world in this way is to take a detached view of oneself—to see oneself as a ‘momentary blip’, an ‘insigniﬁcant speck’(61). The person who is the subject of this conception of a centerless world must detach himself from the person who is in the world being conceived—the one who is just one thing among others. How can I be both the subject of my centerless conception, and also a part of it? It seems that I must be both outside looking in, and also in there to be looked at, both essential to the centerless world, as its subject, and an inessential part of it. The objective self is the subject who is doing the looking.

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A neo-Fregean might be attracted to a variation on the ontological view that tries to objectify the content of self-locating thoughts without buying the extravagant metaphysics. It is concepts, not properties, he will say, that are grasped, apprehended, and ascribed. The property that TN calls ‘being me’ is simply the property of being TN, but the sense of the expression ‘being me’—the concept it expresses—is different from the sense of ‘being TN’. The ﬁrst-person concept that is part of TN's thought ‘I am TN’ is one that only TN can grasp. Perhaps this was Frege's view, though I would prefer to think that the remark he makes that suggests it (’everyone is presented to himself in a particular and primitive way⋯. And only [the subject] himself can grasp thoughts determined in this way’ (Frege 1919 /1956: 298) ) was an unfortunate lapse. To understand such a view, I would need to know more about what concepts are, and what it is to grasp them. And I am not sure that the metaphysics can be so easily avoided. If the thought ‘I am TN’ (thought by TN) is conceivably false (if even a logically omniscient TN might grasp the thought without knowing that it is true), then why is its falsity not a metaphysical possibility?

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The picture is this: Essentially I have no particular point of view at all, but apprehend the world as centerless. As it happens, I ordinarily view the world from a certain vantage point, using the eyes, the person, the daily life of TN as a kind of window. But the experiences and the perspective of TN with which I am directly presented are not the point of view of the true self, for the true self has no point of view and includes in its conception of the centerless world TN and his perspective among the contents of that world. It is this aspect of the self which is in question when I look at the world as a whole and ask, ‘How can TN be me? How can I be TN?’ And it is what gives the selflocating philosophical thought its peculiar content. (61) It it not clear exactly what is being proposed, beyond the articulation of a certain attitude of detachment that one may take toward oneself, since the view repudiates the ontological response that objectiﬁes the self, or self properties, in the way considered above. So even though, in a sense, TN's location within the world is essential to TN, but not to TN's objective self, this should not be understood to imply that there is a distinct entity, TN's objective self, or an objective property that is distinct from being TN. But however the response to the problem is to be understood, I am skeptical about the problem to which it is a response. Speciﬁcally, I am suspicious of the idea that the centerless conception of the world must have a subject, something that is both essential to it, as its subject, and also in some sense in the world being conceived. A subject—a center that is in the world—is part of what constitutes a subjective point of view on the world, but the idea of an objective conception is that it is abstracted from the subject who is conceiving of the world that way. There are two reasons to reject the claim that ‘any purely objective conception of the world⋯must have a subject that is in the world’. The ﬁrst is a familiar act–object ambiguity. A conception of the world might be either an act of conceiving of the world, or the content of a possible act of conceiving. Completeness or incompleteness seems to apply to a conception in the content sense, but it is acts of conceiving that must have subjects. A conception, in the content sense, is an abstract object, and does not have a subject. The same conception might be the content of different acts of conceiving, or might be the content if no such act. It is not incomplete as a result of being unconceived. But even if we are concerned with a particular act of conceiving of a centerless possible world, it is a mistake to think that its subject—the one doing the conceiving—must be in the world being conceived, somehow a part of it. It is not just that a conception of a centerless world remains silent about where in that world the world is being conceived of that way; it is rather that the conception may leave open the question whether the world is being conceived that way at all (in the world being conceived). It might be a counterfactual world that is being conceived—a conception of the world that excludes the fact that the world is being conceived of that way.

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The idea of a ‘view from nowhere’ seems to me to be an attempt to reconcile the Berkeleian assumption that in any coherent conception of a world, the act of conceiving the world that way must be in the world being conceived—with the centerless conception of the world. One adds a perspectiveless place in the world from which to view it (and an objective self to do the viewing). But the place from which the world is being conceived will always be a particular place—somewhere (though not necessarily somewhere in the world being conceived).259 In ﬁction, there is often a narrator who tells the story from within. The telling of the story takes place in the story; the ﬁction is that one of the characters is recounting fact (or sometimes telling lies). But there is nothing necessary about this device. The author might simply tell the story. In such a case, he is not pretending to tell the truth, but simply expressing propositions that describe a conception of a world, one that does not include anyone who is telling the story. Fiction of this kind is sometimes said to be written ‘from the omniscient point of view’ (which is presumably the same as the view from nowhere), but this seems to me a misdescription. One could have a story with an omniscient narrator who was a character in the story—perhaps an unobtrusive one whose place in the world is unspeciﬁed, and whose superhuman epistemic powers are unexplained. But such a character need not be postulated to make sense of a story told by someone who is not in the story.260 One has no problem with a story in which, at the end, no one is left to tell the tale. Still, we can agree with Nagel that ‘in a sense, any purely objective conception of the world is incomplete’.261 Here is the sense: if one asserts that the actual world is like this, and then gives a purely objective impersonal description, a question will always remain: where in the world is this act of describing the world taking place?262 The question must have an answer, if

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I don't want to suggest that Nagel would endorse the notorious Berkeleian doctrine. In another context he explicitly rejects it (93). And I don't want to suggest that he is ignoring the possibility of a conception of a centerless world that is counterfactual. He says: ‘So far as the content of the objective view goes, it might be of a world in which I, its subject, never have existed, and never will.’ But he goes on to say this: ‘But since the objective conception has a subject, the possibility of its presence in the world is there, and it allows me to bring the subjective and objective views together’ (64). I don't see why this follows. Why should the fact that I can conceive of a certain kind of situation imply that I might possibly be in it?

260

In a story told by someone who is not in the story, there may still be a ﬁctional narrator who is not the same as the author. The ﬁction may be that a ﬁctional character is telling a story.

261

Nagel (1983: 230),

262

The expression ‘considering a possible world as actual’ is introduced in Davies and Humberstone (1980) to make a technical distinction in a two-dimensional modal semantics, but the terminology evokes an intuitive understanding of the distinction that is connected with this point. It is a world considered as actual that requires a subject in the world who is doing the considering. See also Ch. 10 of this book.

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the assertion is true, and the answer will not be given by the objective conception, however complete.263 This kind of incompleteness is acknowledged and explained by the semantic diagnosis, which emphasizes the irreducibility of indexical or subjective information. The semantic diagnosis may be enough to explain the content of ordinary self-locating thoughts and statements—for example what TN says when he introduces himself to a job candidate at an APA interview, or what the amnesiac learns when he ﬁnds out who he is. But Nagel suggests that there is a distinctively philosophical thought that can be expressed with the words, ‘I am TN’, and he doubts that the semantic diagnosis accounts for that. But I think it is a mistake to think that there is a philosophical thought with a content that is distinct from the content of the statement in its more humdrum uses. There is, perhaps, a distinctive philosophical attitude toward, or response to, the fact or belief that one is XY, but a difference in attitude does not require a distinctive content. An analogy: one might regard the fact that a rhinoceros is about to charge, or respond to one's belief that a rhinoceros is about to charge, with either apprehension or bored indifference. One might tell someone that a rhinoceros is about to charge as a warning, or simply as a report about something interesting that will soon happen. In all of these cases, the content of the belief, warning, or report is the same. Similarly, TN may feel wonder or puzzlement at the fact that he should be the particular person (in his centerless conception of the world) that he is, but I think the fact that he feels wonder or puzzlement about is the very same fact as the fact he states when his reason for stating it is only to get himself seated for dinner when the head waiter announces that TN's table is ready. What is required by an account of the content of the statement or thought is only that it be a thought about which one might have the distinctive philosophical attitude. Neither the objective proposition that TN = TN, nor the objective proposition that TN is at a certain time identifying himself as TN is a plausible candidate for a proposition that might evoke this kind of philosophical response, but it seems to me that the subjective content identiﬁed by the semantic diagnosis is a plausible candidate, even if more needs to be said than is said by that account of content in order to explain why we have that attitude.

4. Reconciling subjective and objective conceptions The semantic diagnosis has a very limited aim: to represent, from the objective standpoint, the contents of thoughts that a subject may have about his, her, or its place in the world. While it rejects the objectiﬁcation of

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If my objective description contains enough detail, it will very probably be easy for me to locate myself in it, but the representation itself won't do the job; I have to put it together with certain subjective information about myself.

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subjective content—the ontological response to the problem—it does not, by itself, put any constraints on what needs to be included in a complete, purely objective conception of the world. It does not say what aspects of one's subjective experience are reﬂections of objective features of the world. So, for example, it leaves open questions about whether a complete account of the objective world must include irreducible mental facts, such as facts about the quality of one's experience. This account of subjective content is nevertheless an austere one: not only does it reject the objectiﬁcation of selflocating thoughts, it also rejects a more robust account of subjective content, one that includes more than information about the subject's place in the world. What is rejected is the idea that there might be an act of thought such that there was an open question about whether that thought correctly represented a certain possible situation even after we have speciﬁed all of the objective facts about that situation, and also located the act of thought itself in the situation. What would remain open, on the picture that contrasts with the austere view, are questions about the subjective facts. The austere view of subjective content assumes that a perspective on the world is no more than a perspective on the objective world. There is no realm of subjective fact—substantive facts that are facts only for me—beyond the facts about my place in the world as it is in itself, and facts that can be explained in terms of that. In insisting on this austere view of the intentional content of a subjective point of view, I am not sure whether or not I am disagreeing with Nagel. Perhaps he would say that the austere view fails to appreciate the extent to which the objective conception of reality is incomplete. He says: If we try to understand experience from an objective viewpoint that is distinct from that of the subject of the experience, then even if we continue to credit its perspectival nature, we will not be able to grasp its most speciﬁc qualities unless we can imagine them subjectively. We will not know exactly how scrambled eggs taste to a cockroach even if we develop a detailed objective phenomenology of the cockroach's sense of taste. (25) Is the point that there are subjective facts that even a complete account of the world as it is in itself necessarily leaves out, or is it that there are facts (for example, about how scrambled eggs taste to a cockroach) that we cannot possibly grasp, and so could not include in our conception of the objective world, but that are nevertheless objective facts? The austere view of subjective content is compatible with the latter interpretation. But is there really such an objective fact (about how scrambled eggs taste to a cockroach), a fact that is not only unknowable by us, but also that could be stated only in a proposition that we could not grasp or express? Presumably the cockroach could not grasp or express it either, since it lacks the conceptual powers. Perhaps the best we could do to describe such a proposition would be to say that it is one that the cockroach, if it had the

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conceptual resources to reﬂect on its experience and the linguistic resources to express its thoughts, would express by saying, as it eats scrambled eggs, ‘scrambled eggs taste like this’. But it is hard to take this counterfactual seriously. An alternative view of this fact (if there is such a fact at all) is also compatible with the austere view of subjective content. This would be to say that the fact about how scrambled eggs taste to the cockroach is unknowable by me in the same way, and in the same sense, that the fact expressed by TN when he says ‘I am TN’ is unknowable by me, or (to use a slightly closer analogy) in the same way that the fact that the execution is taking place now, or that the treasure is buried here is knowable only at the time when the execution is taking place, or at the place where the treasure is buried. For subjective facts, to know them you have to be there. What is distinctive about subjective or contextual content is that it is not separable from the subject who is thinking the thought that has that content, or at least from the context in which it is being thought. The task of reconciling subjective and objective standpoints (according to the austere view of subjective content), is to explain the facts that are recognized from a subjective point of view in terms of features of the objective world, together with facts about the subject's place in it. This requires deciding how rich our objective picture of the world must be in order to account for the fact that we, and other things in the world, can be things that have a subjective point of view—a view of the world and our place in it—of the kind that we have. This is obviously a daunting project. We can begin with the question ‘what is it to be a subject?’ Among the things to be found in the world (according to our objective conception of the world) some, but not all, are things of which it makes sense to say that they have a subjective point of view. It seems reasonable to think that there are objective differences between the subjects and other things. One task is to say what they are. Some may reject the presupposition of this question, arguing that there is no fact of the matter about what does and what does not have a subjective point of view. According to this line of thought, it may be more or less interesting or useful to think of something as a subject, but anything might be thought of this way. This kind of instrumentalist view of subjects does not seem very plausible. When a person treats certain things as other selves (for example, if he gets angry at a computer, or a golf club, for bad behavior, and punishes it), it seems right to say that the person is simply making a mistake, or succumbing to an illusion. But I also want to reject the assumption that there is a simple line to be drawn between the things that are subjects and the things that are not (things such that there is something it is like to be them, and things such that it is not like anything). It seems reasonable to think that subjecthood is complex; there are degrees and levels, and it is clear that relatively simple things can be subjects in a

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minimal sense. Anything that is a representor—anything that functions to receive, store, or transmit information—is something that has a point of view, since it may carry information both about the world as it is in itself, and about its place in the world. I don't know whether a simple robot could engage in philosophical reﬂection on the remarkable fact that it should be this particular robot, of all the things in its objective conception of the world, but whether this is a remarkable fact to it or not, I think it is a fact that the robot might know, or be ignorant of, a piece of information that it might or might not carry. (If Nagel can worry about what scrambled eggs taste like to a cockroach, I can worry about the possible philosophical reﬂections of a simple robot.) An objective account of what it is to be a minimal subject can clearly be given in functional terms, terms that are compatible with materialism. And I see no obstacle, in principle, to a functional account of richer, more robust conceptions of a subject—conceptions that require it to be a thing with more sophisticated representational capacities, or a capacity for action guided by its information and motivations, or a capacity for phenomenal consciousness. One might give an objective account of what it is to be conscious, even if the idea of phenomenal consciousness is characterized, or at least evoked, in subjective terms—in terms of there being something it is like for the thing. An objective account (whether compatible with materialism or not) won't tell one what it is like to be conscious, but this is not its aim, which is only to say what the world must be like in itself for a thing in it to be conscious. There is no pretense that in saying what it is, from the objective standpoint, to have a subjective point of view, or a subjective view of a certain kind, we are thereby recreating or simulating the subjective point of view, or that we are replacing it with the objective account. I have been discussing an external way of understanding a subject, as one kind of thing in the centerless world among others, emphasizing the contrast between this way of understanding a subject and a way that tries to see the world from the subject's point of view. But various things conspire to break down this simple contrast, and so to complicate the issue of the relation between subjective and objective standpoints. First, there is information that is subjective, in that it is essentially connected to a particular perspective on the world, but also shareable between subjects. You and I can both know, if the time or place is right, that the execution is taking place now, or that the treasure is buried here, but these are not pieces of information that we can carry away with us. A complete description of the centerless world will exclude these pieces of information in the same way and for the same reasons that it excludes the content of TN's thought when he thinks, ‘I am TN’. Even our basic example has a content that is in a sense shareable, but still essentially context-dependent. While we can understand the sense in which only TN can know that he is TN—an unmysterious sense in which this subjective information is

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private—it also seems that nothing could be easier than for TN to share this information with the rest of us—to tell the candidate in the interview, or the head waiter, that he is TN. The information that he shares with his interlocutor is public, but still not something that will be found, as such, in a complete impersonal description of the centerless world. A second complication arises from an obvious objective fact about subjects—even relatively simple ones: that they persist through time, and have memory, and so have a temporally extended point of view. My past and future points of view occupy, for me, a kind of middle ground. Should I think of my past self as like another self—a thing in the objective world among others that has a point of view—or as an extension of my present point of view? The temporally extended character of a point of view contributes to the inclination to believe that there is something that is both internal to a point of view and also in a sense objective—something that one may be right or wrong about. I can remember what it was like, or misremember, and I can anticipate what it will be like, and later learn that I was right, or wrong. Or so it seems. We may exaggerate the extent to which there is a fact of the matter about whether my past experiences match my memories of them, or whether my present experiences are the way I expected them to be.264 The middle ground occupied by my past and future selves tempts one, perhaps enables one, to think of other selves the way we think of our own past and future selves.265 It is clear that we have the ability to put ourselves in another person's shoes, to imagine being him in a certain situation the way we remember being ourselves in some past situation, or anticipate what some future situation will be like for oneself, and this is one way to treat something in the world as something with a subjective point of view.266 But how do we evaluate such acts of imagination? If I believe what is expressed in a ﬁrst-person statement (that I am RS, or TN, or Napoleon at the start of the battle of Austerlitz, or a cockroach eating scrambled eggs), then it is clear enough what it is to get it right: the person who has this belief (me) must be RS, or TN, or Napoleon at the start of the battle of Austerlitz, or a cockroach eating scrambled eggs. But when I imagine being TN, or Napoleon, or the cockroach, the content of my imagining is both subjective and counterfactual. Though it is counterfactual in that I know and presuppose that I am not in fact Napoleon, we may

264

I must confess to some sympathy with Wittgenstein's expressions of skepticism, throughout the Philosophical Investigations, about private identiﬁcations of sensations as being of the same type.

265

Sydney Shoemaker explores the relation between (cross-temporal) intrapersonal comparisons of qualitative experience and interpersonal comparisons, arguing from the intelligibility of the ﬁrst to the intelligibility of the second. See Shoemaker (1996). Shoemaker's intra–inner argument is examined critically in Ch. 12 of this book.

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There is an extensive literature discussing such acts of imagination. Williams (1973) is a seminal article. See also Velleman (1996) for an insightful discussion.

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assume that my aim is not just to imagine being in some counterfactual situation in which I am Napoleon at Austerlitz, but to imagine it as it really was for Napoleon. It is clear that, if this is my aim, I can get it wrong. Perhaps I imagine being on a black horse, looking out at the bright summer sunrise. But the horse was in fact white, it was December, and there was a dense fog. Perhaps Napoleon in fact had a headache, but I don't include that in my imagining. All will agree that we can get it wrong by getting the straightforward objective facts wrong, but might we get all that right, while still mistaking how it was for Napoleon? The austere view of subjective content implies that the answer to this question is ‘no’. The claim is not that the act of imagining being Napoleon is no more than the act of entertaining an objective proposition about Napoleon, something that might be expressed in a detailed impersonal text (perhaps with Napoleon's name highlighted to indicate that the world being considered is to be centered on him). That is obviously false. The claim is only about what it is, when one is trying to imagine things as they really were, to get it right. An act of imagining, whatever else is true of it, will have an objective propositional content. The claim is that to have imagined the situation as it really was it sufﬁces for the act of imagining to have an objective content that is true. Nor is it the claim that to get it right it sufﬁces to get the physical facts right. That would follow from the austere view of subjective content only if it were conjoined with the metaphysical doctrine of materialism. The austere view is compatible with what David Lewis calls the Hypothesis of Phenomenal Information, which is the hypothesis that besides physical information there is an irreducibly different kind of information to be had: phenomenal information. The two are independent. Two possible cases might be exactly alike physically, yet differ phenomenally. When we get physical information we narrow down the physical possibilities, and perhaps we narrow them down all the way to one, but we leave open a range of phenomenal possibilities. When we have an experience, on the other hand, we acquire phenomenal information; possibilities previously open are eliminated, and that is what it is to learn what the experience is like.267 It is clear that on the hypothesis that Lewis is articulating, phenomenal information is objective information—information that must be included in a complete representation of a centerless possible world. This hypothesis was introduced by Lewis as a possible response to Frank Jackson's puzzle about Mary, who knows all there is to know about the physics of color and the neurophysiology of color vision, but who, because she has spent her life in a black and white room, has never seen colors, and so does not know what it is like to see colors.268 The hypothesis of phenomenal information is an hypothesis about what it is that Mary does not know—what information

267

Lewis (1999: 270).

268

Jackson (1982, 1986).

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she lacks that she can acquire only by coming out of her room and seeing colors. But Lewis rejects the hypothesis, arguing that it ‘is more peculiar that it may at ﬁrst seem’.269 A richer conception of the objective world, he argues, won't, by itself, solve the problem about what Mary doesn't know. Let parapsychology be the science of all the non-physical things, properties, causal processes, laws of nature, and so forth that may be required to explain the things we do. Let us suppose that we learn ever so much parapsychology. It will make no difference. Black-and-white Mary may study all the parapsychology as well as all the psychophysics of color vision, but she still won't know what it is like.⋯If there is such a thing as phenomenal information, it isn't just independent of physical information. It's independent of every sort of information that could be served up in lessons for the inexperienced⋯. Therefore phenomenal information is not just parapsychological information, if such there be. It's something very much stranger.270 This argument against the hypothesis of phenomenal information is similar to the argument that Nagel gave against the ontological view of self-locating information. Both arguments suggest that it is futile to try to objectify a certain kind of information, since no matter how we enrich our objective conception of the world, that kind of information will be left out. In both cases, the objectiﬁer might respond to the argument by claiming that the special kind of objective information is accessible only to certain subjects, or to subjects with a certain place in the world, and is not communicable to others in the way that most objective information is communicable. In both cases, this response requires an account of intentionality—of what it is that gives thoughts their content—that explains how there can be objective content that has this special status. In the case of the information about who one is—what TN is thinking about when he reﬂects on the fact that he is TN—the semantic diagnosis seems to me to provide an account that removes any temptation to objectify the content, and so to take on both an extravagant metaphysics, and the burden of explaining our special relation to a certain kind of objective information. The case of information, or apparent information, about the qualitative character of our experience is harder, but I will conclude by considering whether phenomenal information can be understood in the same way.

5. Phenomenal information If we reject the hypothesis of phenomenal information, how do we explain what it is that Mary doesn't know about colors, or that the expert on the sensory apparatus of cockroaches doesn't know about what scrambled eggs taste like to a cockroach? Lewis rejects the hypothesis by rejecting the

269

Lewis (1999: 280).

270

Ibid. 281.

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assumption that there is any kind of information at all that Mary lacks, and acquires only when she sees colors. What she lacks is only a cluster of abilities such as the ability to imagine seeing red, and to recognize it as the same color when she sees it again. But it is not clear that one can understand the relevant abilities except in terms of some notion of the intentional content of some of the things that the abilities are abilities to do. In one sense it is easy for me to imagine what it is like for the cockroach; I can, for example, imagine that scrambled eggs taste, to it, the way vegemite tastes to me.271 If this does not count as an exercise of the ability, it must be because it doesn't get it right—because this is not, in fact, how scrambled eggs taste to a cockroach, or at least because I don't have any reason to think that it is. But if the ability in question is the ability to get it right, then it is an ability that must be explained in terms of a kind of intentional content.272 Can we explain what Mary doesn't know as subjective information, on the austere understanding of subjective information? Can we explain it as a kind of information about the subject's place in the world? I want tentatively to suggest that we can.273 Consider the following analogy: The treasure is buried under a certain cross in one of those vast battleﬁeld cemeteries with row after row of indistinguishable grave markers arranged in a symmetrical grid pattern. Mary knows, even while still in her room, which cross the treasure is buried under: it is the 143rd south and the 57th west from the northeast corner of the cemetery. But what she cannot know, until she goes to the place, is that the treasure is buried here. Even if she continued to remember the location of the treasure (143 S, 57 W) as she makes her way to the place, counting as she goes, she might still have gotten it wrong when she got there. ‘I know that it is here,’ she says, ‘but if I had miscounted, I might have thought that it was there instead, or I might have been unsure whether it was here or there.’ So what Mary knows, when she gets to the place, is distinct from the information about the objective location of the treasure. There is no mystery here, and no temptation to postulate special objective location properties, hereness and thereness, that are independent of the location properties deﬁned by the coordinates. We can explain without postulating such properties, from the external objective standpoint, what kind of possible situation Mary would have mistaken for the actual situation if she had gotten it wrong. There is a possible world that might have been compatible with Mary's knowledge in which she miscounts, as

271

Vegemite, for those who don't know, is an Australian condiment, whose distinctive taste was one of David Lewis's paradigm examples of a qualitative sensory experience—one that he was apparently ignorant of in the way that Mary was ignorant of colors. I am indebted to Daniel Stoljar for buying me a jar of the stuff (‘for the purpose of phenomenological experimentation’) on a recent visit to Australia, and so for enabling me to refer to the way vegemite tastes to me.

272

Cf. Lycan (1995).

273

Cf. Perry (1999), who responds to Jackson's knowledge argument in a similar way.

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she goes to ﬁnd the treasure, and in which the place she is demonstrating, when she says ‘the treasure is buried here’, is 143 S and 58, rather than 57, W. The information that Mary gets right, but might have gotten wrong, is subjective because we cannot abstract its content from the subject and the context. Reference to Mary and her location in the world is essential to the objective characterization of the possible situations in terms of which we describe that information. And we also cannot identify the content of Mary's belief (the one she would express by saying ‘the treasure is buried here’) with the objective proposition that Mary is (at a certain time) demonstrating the place where the treasure is buried. (That would be like identifying the content of TN's thought that he is TN with the objective proposition that TN is thinking, at a certain time t, that he is TN.) The objective proposition that Mary is at a certain time successfully demonstrating the location of the treasure is a proposition that she might have known to be true while she was still in her room. That is, she might have known before leaving her room that she would later be at the place where the treasure is buried, and that she would succeed then in demonstrating that place. It would be in a sense right, but misleading, to say that Mary, when still in her room, did not yet know what she later knows when she is in a position to say that the treasure is buried here. It would be misleading because she was not then in a position either to know or to be ignorant about whether it was here or there. Just as Mary, when still in her room, is not in a position either to know or be ignorant of the fact that the treasure is buried here (demonstrating the place), so she is not in a position to know or be ignorant that the color red looks like this (demonstrating, in memory, a certain experience). Just as we can give an objective description of what Mary would be ignorant of if she was at the site, but didn't know whether the treasure was buried here or there, so we can give an objective description of the different possible situations that would be compatible with Mary's knowledge if, after having seen the color red, she still didn't know whether this is the experience of red or of green. Here is one such description. Mary, still in her room, is told that she will be subjected to the following experiment. She will be shown either a red or a green tomato, to be chosen by the ﬂip of a coin, and she is told in great detail the exact circumstances of the two possible scenarios. So given her extensive knowledge of neurophysiology and color science, she knows that when the experiment is performed, she will be in the presence of a tomato with one of two speciﬁc light reﬂectance properties, and will be in one of two speciﬁc brain states. Both before and after the experiment is performed, there are two possible worlds compatible with Mary's knowledge—call them worlds r and g. As it happens, the red tomato is chosen, so she is in fact in possible world r. In a sense, after the experiment is performed, Mary knows what it is like to see

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red, although not under that description. ‘Now I know,’ Mary says, ‘either what it is like to see red, or what it is like to see green. I just don't know which it is, since for all I know, this experience could be the experience of seeing red, or of seeing green.’ What changed about her epistemic situation, when she was shown the tomato, is that she was then in a position to represent subjective information about this experience. We noted that we cannot identify the subjective content of Mary's knowledge (when she is at the scene in the cemetery) that the treasure is buried here with the timeless objective proposition that when she is at the scene, she succeeds in demonstrating the place where the treasure is buried. Similarly, we cannot identify the subjective content of Mary's knowledge (after she learns what color she has seen) that red looks like this with the objective, timeless proposition that after having seen red, she succeeds in identifying the experience she has with the experience of seeing red. That objective proposition is one she might have learned while still in her room. If this analogy is apt, then we can solve the problem of what Mary doesn't know without invoking the hypothesis of phenomenal information, but many will ﬁnd the analogy strained. Suppose Mary is still in her room, but we are at the location of the buried treasure. There is little inclination for us to say: ‘Even though Mary knows exactly where the treasure is buried (143 S, 57 W) she still doesn't know whether it is here or there.’ Mary may or may not know this when she gets here, but right now, it seems natural to say, she is not in a position either to know it or to be ignorant of it. In contrast, there is a strong inclination for us to say about Mary, still in her room, that even though she knows exactly what it is (physically) to see red, she does not yet know that seeing red is like this (demonstrating the experience of seeing red) and not like that (demonstrating the experience of seeing green). That is, it seems much more natural to abstract a demonstratively identiﬁed property (looking like this—the way red looks) from the demonstrative context in which it is identiﬁed—to objectify it, while still retaining some of its demonstrative character. Once we have made this move, the hypothesis of phenomenal information, with all its problems, is difﬁcult to resist. I suspect that one source of the inclination to objectify the phenomenal information in this way (at least for those of us who think of information in terms of distinctions between possibilities) is this: there is a temptation to think that if two possible situations are both epistemically possible for a certain subject, then they must be phenomenally indistinguishable to the subject. That is, we are tempted to think that we understand knowledge and ignorance of facts in terms of a prior notion of subjective indistinguishability. But a subject's ability to distinguish one experience from another—intraworld, intrapersonal distinguishability—has no clear application to the interworld case. We understand phenomenal indistinguishability in terms of scenarios like this: a person is presented with two different yellow color samples projected on a screen, perhaps in succession. Suppose they have

274

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different reﬂectance properties, that the light impinging on the retina is different, and that the brain state is different, but that the person cannot tell the difference. When the signal shifts from yellow-1 to yellow-2, the subject reports just a continuous, unchanging yellow. That is indistinguishability—an incapacity to discriminate. The temptation is to think that we can compare two possible worlds in the same way: if I were, contrary to fact, in a certain possible situation, then I wouldn't know the difference. But consider the case just described in which Mary has seen a red tomato, but is ignorant of whether it is red or green. The two possible situations we used to represent her ignorance were physically different: world r is the actual world, while in nonactual world g she is presented with a green tomato, with all the optical and physiological consequences that that would have in the actual world. (Since Mary knows all the general optical and physiological facts, these facts will hold in all worlds that are epistemically possible for her.) But it seems intuitively that these two possible worlds are phenomenally as well as physically different. If the ﬂip of the coin had been different, and Mary had been shown the green tomato instead, things would have looked very different to her. Nevertheless, she still doesn't know which of the two situations she is in. If it is assumed that epistemic alternatives must be phenomenally indistinguishable, then to account for Mary's ignorance of which color she has seen in this case, one will be required to suppose that there is a different possible world, g′ which is physically just like the world g, but phenomenally just like the world r, and if we accept that, we have bought the hypothesis of phenomenal information. But the assumption is gratuitous. There is no reason to think that it even makes sense to talk of a subject's capacity to distinguish phenomenally between alternative possible worlds. In the case where a person does not know who he is, the assumption that epistemic possibility implies phenomenal indistinguishability would require the comparison of phenomenal experience across persons as well as across possible worlds. If Rudolph Lingens does not know whether he is Rudolph Lingens or Gustav Lauben, then there must be a possible world in which Gustav Lauben's experience, at the relevant time, is exactly the way Rudolf Lingens's experience actually is at the corresponding time. Even if it is accepted that such interpersonal comparisons are intelligible, it is not clear that the assumption that epistemic possibility implies phenomenal indistinguishability can be reconciled with the kind of examples that have been used to show the irreducibility of self-locating information. David Lewis told a story of two gods, both omniscient with respect to objective information. Both gods know exactly what possible world they are in, but (he supposes) neither knows which of the two gods he himself is.274 Let us add to Lewis's story that the two gods are spectrum-inverted with respect to

274

Lewis (1979: 520–1).

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each other. (Granting for the purpose of the example that this assumption makes sense.) Red things look, to one of the gods, the way green things look to the other. Call the gods ‘Castor’ and ‘Pollux’, and call the phenomenal character of Castor's experience of red, ‘ph-red’.275 Castor knows that red things look ph-red to Castor, and ph-green to Pollux, but doesn't know whether they look ph-red or ph-green to himself, since he doesn't know whether this experience is ph-red or ph-green. If we continue to maintain that the two gods are really omniscient about the objective facts, we will have to give up the assumption that epistemic possibility implies phenomenal indistinguishability. One further twist: if we add to the story that nothing in the world is green, so that Castor, but not Pollux, has experienced ph-red, and Pollux but not Castor has experienced ph-green, then we will have to conclude that our omniscient gods are in a position something like Mary, and that they would remain in this position even if each learned which god he was. Despite their objective omniscience, there are experiences such that they don't know what it is like to have them.276

275

This inspired name for the phenomenal character of the experience of red is due to Bill Lycan.

276

I am grateful to Thomas Nagel and to Alex Byrne for illuminating comments and discussion on a previous draft of this paper.

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Index A-intension see intension, primary/secondary a posteriori/a priori 16–19, 188–200, 201–16 actualism 6–8, 63–5, 111–32, 139–43; and merely possible individuals 1203 Adams, E. 192n Adams, Robert 32–5 Almog, Joseph 192n, 196 analytic 3–4, 18, 86, 90, 183–4, 201 Anscombe, Elizabeth 21 Armstrong, David 9–10 Augustine 29–30 Barcan (Marcus), Ruth 73, 144–5 Barcan formula 144–5, 150–4 belief ; about individuals 177–9, 183; about modal reality 31–2, 40–54, 203, 215; causal/functionalist account of 179, 221; inconsistent 63, 117, 199, 210; self-locating 21–2, 253–76 Benacerraf, Paul 41–3, 46–7, 50 Blackburn, Simon 47n Block, Ned 221 Bricker, Phillip 34n Burge, Tyler 204, 208–9 centered worlds 205, 255 C-intension see intension, secondary Carnap, Rudolf 2–5, 44–8, 82 Chalmers, David 16–19, 190–2, 194n, 195, 202–6, 211–13, 239–52, 259n Chandler, Hugh 115–16, 181–2 character 193–7, 206–8 Chisholm, Roderick 116n conceptual analysis 201–203, 213–214, 244–52 content 50–4, 63–7, 171–2, 177–80, 188–200, 201–16, 219–38, 253–76 consciousness 19–22, 219–38, 239–52, 267–76; see also qualia contingent identity see identity, contingent context 39, 44–5, 193–7, 206–8, 259n counterparts 11–15, 111–32, 144–62; and actualism 12–13, 112; and essentialism 72; and identity 111, 142–3, 154; motivations for 114–17; and modal error 102; and semantics 185–7 descriptive semantics see semantic/metasemantic diagonal proposition see intensions, primary/secondary Davies, Martin 191, 246, 263n descriptivism 211–12 Donnellan, Keith 178–9 dthat 197–9 dualism 94–6, 239–40, 250–2; see also materialism; functional-

ism; physicalism Dummett, Michael 47n, 173–4, 179–80 emergentism 90, 101–4 empiricism 1–6, 48, 53, 201–2 essences 71–85, 115, 180–7, 201, 215; see also essentialism; individual (see also haecceitism) 115, 121; as counterparts 121–3 essentialism 71–85, 167–8, 201, 215, 250; see also essence; and counterpart theory 118–20; about identity and indiscernability 154–7; and philosophy of language 165, 180–7; mereological 116–17

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externalism 199–200, 208–9 Evans, Gareth 133n, 177, 180, 188–90, 197–200 Field, Hartry 44 Ford, Gerald 35 Forbes, Graeme 142n foundational semantics 166–8, 174–80, 204–6, 208–15; see also semantic/metasemantic Frege, Gottlob 174–5, 193, 204, 261n, Frege–Schlick view 220, 223–38 Fregean 174–5, 177, 181–3 functionalism 219–24, 229–30, 233, 235, 247–8; see also dualism; materialism; physicalism Gibbard, Allan 116, 140n Glanzberg, Michael 105–6 Goodman, Nelson 81 grue 78, 81 haecceitism 112, 120, 123–6 haggis 227 Harsanyi, John 228n Haugeland, John 89n Hawthorne, John 252n Hazen, Alan 114n, 119n, 128n, 130n Hellman, G. 89n Hesperus/Phosphorus 188, 190, 199–200, 210n Hintikka, Jaako 130n holism 34, 89, 99, 212 Horgan, Terence 90–1n Humberstone, Lloyd 191, 246, 263n identity 11–15, 111–32, 133–43, 144–62; a posteriori see identity, informative; contingent 11–15, 111–32, 144–62; criteria of see identity conditions; funniness about ﬁrstperson statements of 253–76; necessity of 12, 144–62, 206; and counterpart theory 11–15, 111–32. 144–62; across possible worlds 11–15, 111–32, 135, 139–41, 144–62; across time 86, 135–38; and indiscernability 222–3; informative 188, 189, 206, 210; see also Hesperus/ Phosphorus; personal 86, 88, 104; of properties 94; as supervenient 114–15, 140–1; temporary 126–8; vague 14, 133–43 identity conditions ; for qualia 222–3, 229–33, 235–6; for contents 35–6, 38, 257 impossible worlds 55–68, 102 indeterminacy 130–1, 133–43 indexicality ; of ‘actual’ 27–33, 40; of ‘now’ 30; and names 193; of non-modal knowledge and belief 43, 49; and twodimensionalism 193–4, 207; and self-locating belief 264 intensions 34, 113, 129, 149–50, 166, 246–7; A see intensions, primary/secondary; C see intensions, primary/secondary; primary/secondary 191–200, 204–8, 213; three-dimensional 195; two-dimensional 190–200, 204–10, 213 intentionalism 225; see also representationism intra-inner argument 220, 224–6, 238

inverted spectrum 219–38 Jackson, Frank 106, 201–4, 211, 213–15, 269 Judson, Whitcomb L. 189–90, 198 Julius 177, 188–90, 197, 198–9 justiﬁcation ; of modal beliefs 40–54 Kaplan, David 112, 123, 192–8, 206–8, 210–13 Kim, Jaegwon 86, 88, 90, 91, 95–6 knowledge argument see Mary

INDEX

Kripke, Saul ; and counterpart theory 142n; and essentialism 79–80, 181–5; and identity 139–42, 205; and modal semantics 148–51; and names 172–87, 198–9; and a posteriori necessities 102, 188–9, 201–2, 205; Naming and Necessity 165–8, 172–87, 188–9, 201–2; and reference ﬁxing 193, 198 Lambert, K. 76n Leibniz 25, 72, 84 Leibnizean 168, 169, 185–6, 226 Leibniz's Law 125, 131, 144, 148 Levine, J. 258–9n Lewis, David ; and counterpart theory 11, 72, 112, 114n, 122, 152n, 186; and descriptivism 212; and Humean supervenience 88, 96–101, 241n; and materialism 241–2; and impossibilities 55–68; and modal realism 6–8, 11, 25–39, 40–54, 112; and phenomenal information 269–71; and properties 9–10, 98–101, 248; philosophical methodology 31; as Quinean 5–6; and self-locating belief 255n, 274–5; and temporal parts 137n logical space ; see also possible worlds; as property space 76–85, 100; as space of possible worlds 62–3, 67, 101, 123 Lycan, William 55–68, 221 Mackie, J. L. 25, 32 Marcus, Ruth see Barcan (Marcus), Ruth Mary 269–75 materialism ; see also functionalism, physicalism; and phenomenal information 269–70; and subjectivity 267; and supervenience 86, 88, 93–6, 98; and spectrum inversion 219–20, 221–2; and zombies 239–52 meaning ; Carnapian view of 44, 47–8; causal theory of 192, 212; and character 193–4; compositionality of 64–5; and content 206–7; contingency of 189–90, 194; see also twodimensionalism; semantic/metasemantic; and essence 80; of interpersonal comparisons of qualia 219–38; location of 204; of logical connectives 58–60, 166; of names 165–87, 188, 193, 198, 212; of predicates 62; of natural kind terms 245–7; and twin earth cases 196; as twodimensional intensions 195–200, 207; of ‘zombie’ 239–52 Meinongian objects 56–7 metasemantics see semantic/metasemantic, two-dimensionalism Millian theory of names 167, 172–87 modal ; see also possible worlds; discourse, clariﬁcation of 168–71; epistemology 40–5; logic 25, 71, 111–32, 144–62and counterpart theory see counterpartsand essentialism 71–85and identity see identitypropositional 148–9and quantiﬁcation 71, 73–4, 144–62van Fraasen semantics for 76–85and variable binding 128–32; operators 58; properties 114, 140, 142, 147, 182–6; realism 25–39, 40–54; see also actualismarguments for 26

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epistemological problems with 40–54extreme vs. moderate 25–39, 40–54, 120–3, 168–9and impossible worlds 55–68as both semantic and metaphysical theses 40; reality, characterization of 50–4, 67 Moore, G. E. 90 Nagel, Thomas 253–76 Naylor, M. U. 55n necessity ; see also modal; and a priority 188–200, 201–15; conceptual 202–4, 213–15; and conventionality 66; of discernability 156; of distinctness 155, 159–61; of identity 116, 124–6, 131–2, 144–5, 155, 190, 206, 251–2; of indiscernability 156; and supervenience 91–3, 96–104; varieties of 39, 96–101, 202–4 Von Neumann–Morgenstern utility theory 227–9 new riddle of induction see grue nominalism see universals ontology 38–9, 44–9, 56, 168–71, 181 Parﬁt, Derek 88, 104 Parsons, Terence 73, 74, 78 Paull, R. 92n, 93n, 95n Perry, John 255n personal identity 86, 88, 104, 126–8 Petrie, B. 93n phenomenal information 269–71 physicalism see dualism; functionalism; materialism Plantinga, Alvin 73, 117–20, 121–2 Platonism, liberal 43–50, 54 possibility see necessity, modal possible worlds 5–8; see also actualism; modal realism; as location functions 76–85; as properties 27–39; realism about see modal realism; in analysis of modality 25, 31, 74–5, 113–14, 128–32, 144–61; reduction to propositions 33–7, 63–4 Powers, Larry 25 predicates ; abstraction 128–32, 145–8, 149–50; see also variable binding; complex 128–32, 185–6 presentism 128, 141 primary intension see intension, primary properties 9, 129–30; alien 248–50; basic distinction between objects and 181–3; as elements of propositions 37; emergent 94–5, 102–3; essential see essentialism; as functions from worlds to extensions 74–6, 129–30; historical/temporal 136–40; identity between 93–4; incompatible 62–3; intrinsic 74, 78, 81, 82–4, 226; modal see modal properties; natural 212–13, 240; necessarily coextensive 93–4; as objects of belief 255; possible individuals as 120–3; possible worlds as 27–8, 54, 111, 120; and propositional functions 74–8, 81, 129; qualitative 226–38; and quality spaces 76–85; referential 73, 75, 78; as sets of propositions 33; time-indexed 78; world-indexed 73, 75, 78, 79 propositions ; basic 37; diagonal see intension, primary/

secondary; horizontal see intension, primary/secondary; primary see

INDEX

intension, primary/secondary; reduction of possible worlds to 33–8; as sets of possible worlds 34–6, 50–4, 61–2, 74–5, 170; secondary see intension, primary/secondary; singular 179–80, 207, 209, 213 propositional concepts 16–17, 191 Putnam, Hilary 165, 196, 204, 245 Putnam's paradox 212 qualia ; see also zombies, phenomenal information; eliminativism about 226; Frege–Schlick view of see Frege–Schlick view; functionalist account of 222–3, 229; identity conditions for see identity conditions for qualia; interpersonal comparisons of , 219–38; inverted see inverted spectrum; and memory 229–38; as relational see Frege–Schlick view; and backup systems 233–8 quality space see logical space quantiﬁers ; as operators on predicates 129, 146–8; in modal logic 129, 144–61 Quine, W. V. 3–6, 44–5, 55, 56–7, 71–2, 101, 156, 169–71, 189, 201, 241, 248 Ramsey, Frank 53 reference ﬁxing 80, 188, 197–8, 212 relational theory of space 226–7 representationism 221–2; see also intentionalism rigid designators 81, 184–6, 189, 193, 197–8 rigidifying 197–8, 211 Salmon, Nathan 116n, 117–20, 123–4, 133–43, 165 Schiffer, Stephen 101, 103 Schlick, M. 2, 223–38 Searle, John 173–87 secondary intension see intension, secondary self-locating belief see belief, self-locating semantic/metasemantic 15–19, 192–200, 208–15see also foundational semantics ship of Theseus 115 Shoemaker, Sydney 20, 92n, 103n, 134, 220–38, 268n Sider, Ted 92n, 93n, 95n Stoljar, Daniel 271n Stroud, Barry 44n supervenience 10–11, 86–108, 115, 140–1, 242 temporal parts 127–8, 136–7, 140 Thompson, F. 89n time 29–30, 126–8 TN see Nagel, Thomas two-dimensionalism 16–19, 188–200, 201–16, 246–7; see also intension; semantic/metasemantic universals 9–10 utility comparisons, interpersonal 227–9 van Fraassen, Bas 76–7, 131n variable binding 128–32, 145–8 Velleman, David 268n veriﬁcationism 2–4, 48, 219, 224, 229, 233 vegemite 271; see also Stoljar, Daniel

Williamson, Timothy 106–8, 159–61 Wittgenstein, Ludwig 52–3, 181, 224–5, 229, 232, 237 world-stories 33–7 worlds, possible see possible worlds Yablo, Stephen 246 Yagisawa, T. 55n, 58n zombies 239–52

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