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WORLDS AND INDIVIDUALS, POSSIBLE AND OTHERWISE

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Worlds and Individuals, Possible and Otherwise TAKASHI YAGISAWA

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Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With ofﬁces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York # Takashi Yagisawa 2010 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2010 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Library of Congress Control Number: 2009938562 Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by MPG Books Group, Bodmin and King’s Lynn ISBN 978–0–19–957689–0 1 3 5 7 9 10 8 6 4 2

For my parents, Hidehiro and Mitsuko Yagisawa

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Preface Many times I have read or heard philosophers say at the beginning of the presentation of their work that they aimed to convince the reader or audience. I have never felt sympathetic to this way of introducing one’s work. Such philosophers seem to me to be like an artist who declares that she is trying to impress the viewer. It will be nice to produce a painting which impresses the viewer, but it should not be the declared objective of the artistic endeavor. Similarly, it will be wonderful to present philosophical work which convinces the reader or audience, but it should not be the declared aim of the academic endeavor. Or so I feel. Paul Ziff once told me that a former Harvard colleague of his had said to him that philosophers should say interesting things, to which Ziff had responded that philosophers should say true things. I sympathized with Ziff ’s former colleague, for I thought it was entirely too easy to say true things: e.g. ‘Bachelors are unmarried’, ‘If pigs ﬂy, then pigs ﬂy’, ‘3þ5¼8’. I also sympathized with Ziff, for I thought that, even though it was a little harder and subject to varying individual judgments, it was easy enough to say interesting things: e.g. ‘Leonardo da Vinci squared the circle’, ‘I am your father’. Ziff and his former colleague were both right, albeit only partially. Interestingness and truth are equally important. Philosophers should say things which are both interesting and true. When I try to say something philosophical, however, I ﬁnd truth a more difﬁcult goal to aim at than interestingness. The reason is not that it is hard to ﬁnd true propositions to articulate. The above three examples illustrate how easy it is. Rather, it is that among philosophically relevant propositions, it is hard to ﬁnd true ones, for they do not wear their truth values on their sleeves. Philosophical interestingness, on the other hand, seems to me fairly transparent, at least in the ﬁeld of metaphysics and related areas. In this book I have tried to say things which are philosophically interesting, and I dare hope some people may agree that I have succeeded to an acceptable degree. As for truth, I claim no special access to it but have tried my best not to stray too far from it. T.Y. Los Angeles 17 March 2009

Acknowledgments W. D. Hart and Colin McGinn got me started on modal logic and metaphysics. Saul Kripke and David Lewis made me delve deeper into theorizing about possible worlds and possible individuals. Nathan Salmon and William G. Lycan helped me sustain my interest in the topic and gave me unfailing encouragement. I am grateful to all of them. None of these philosophers would agree with my main thesis in the book, and some of them would disagree with it more strongly than others. In 2001, I presented a precursor thesis at a conference in Bled, Slovenia. Nobody appeared to ﬁnd my idea remotely plausible, except Anthony Dardis, who said to me privately after my presentation, ‘Takashi, I think you are right’. I found his brief remark reassuring and uplifting. I thank him for it. In 2005, Peter Momtchiloff of Oxford University Press approached me. We met at the American Philosophical Association Paciﬁc Division annual meeting in San Francisco that year. On Union Square, we talked about my writing a book on modal realism. Without the encouragement he extended to me that day, various fragments of my thought on modality might not have coalesced into a book. I thank him for his role as the catalyst. My thanks also to two anonymous referees for Oxford University Press. Most of 3.5 was originally published as ‘A New Argument Against the Existence Requirement’, Analysis 65/1 (2005): 39–42. Chapter 5 and a brief paragraph in 1.1 were originally published in a slightly different form as ‘Modal Realism with Modal Tense’, Australasian Journal of Philosophy, 86/2 (2008): 309–27; the Journal ’s website is . Sections 7.4–7.4.5 and the whole of Chapter 9 make use of a substantial portion with minor changes of my ‘A Somewhat Russellian Theory of Intensional Contexts’, Philosophical Perspectives, 11. Mind, Causation, and World, ed. J. E. Tomberlin (Cambridge, Mass., and Oxford: Blackwell, 1997): 43–82. Section 10.3.1 overlaps ‘Against Creationism in Fiction’, Philosophical Perspectives, 15. Metaphysics, ed. J. E. Tomberlin (Cambridge, Mass., and Oxford: Blackwell, 2001): 153–72. Finally, I thank my wife, Bianca Kovar, for her unfailing support and occasional Biancasims, which sound to me both whimsical and deep at the same time: for example, ‘I am a visual artist. I am one big eyeball.’ (Any resemblances between her and Bianca in some of the examples in the text are purely coincidental.)

Contents Introduction

1

1. Modal Realism 1.1. Realism and Modality 1.2. Constituent Modal Realism 1.3. Particular Mere Possibilia 1.4. Modality De Re 1.5. The De Re and the De Dicto 1.6. Non-Constituent Modal Realism 1.7. Externalism

8 8 10 12 13 16 18 20

2. Time, Space, World 2.1. Metaphysical Indices 2.2. Time 2.3. Space 2.4. Time and Space 2.5. Metaphysical Indices among Alethic Indices 2.6. Possible Worlds 2.7. Ersatz Worlds 2.8. Comparison with Lewisian Worlds

24 24 25 27 31 34 39 42 43

3. Existence 3.1. Domain Relativity 3.2. Existence at a Metaphysical Index 3.3. Existence and Reality 3.4. Existence and Predication 3.5. Argument by Iteration

49 49 53 54 55 58

4. Actuality 4.1. Actual So-Sein 4.2. Actuality, Presentness, and Hereness 4.3. Default Indices

62 62 65 70

5. Modal Realism and Modal Tense 5.1. Methodology 5.2. Background Assumptions 5.3. Tense

73 73 74 75

Contents

x

5.4. Modal Tense 5.5. Presentism and Four-Dimensionalism 5.6. Five Case Studies 5.6.1. Skyrms’s epistemic objection 5.6.2. Quine’s rhetorical query 5.6.3. Peacocke’s reductio argument 5.6.4. Van Inwagen’s ontic objection 5.6.5. Van Inwagen on actuality 5.7. Actuality of Spatiotemporally Isolated Wholes and Existence at a World 5.8. Neither ‘Stunning Advantage’ nor ‘Outrageous Falsity’

76 80 81 81 83 85 86 87 90 91

6. Transworld Individuals and their Identity 6.1. Transworld Individuals 6.2. Haecceitism 6.3. Transworld Identity 6.4. Closest-Continuer Theory 6.5. Vagueness 6.6. Density, Continuity, Causality 6.7. Unity of Consciousness 6.8. The Indiscernible 6.9. Stipulations and Counterfactuals 6.10. Over-Identiﬁcation 6.11. Overlapping Individuals 6.12. Two More Objections 6.13. Vagueness Again 6.13.1. Epistemic and nihilistic views 6.13.2. Semantic view 6.13.3. Metaphysical view 6.14. Degrees of Possibility 6.15. Ambiguity of Identity 6.16. Superblobs and Hyperblob

94 94 97 99 101 106 109 113 116 118 121 123 128 130 131 134 137 140 141 145

7. Extensionalism 7.1. Reduction 7.2. Soft Reduction 7.3. Possibility 7.4. Intensional Entities: Preliminaries 7.4.1. Name theory 7.4.2. Demonstrative theory 7.4.3. Belief sentences

147 147 150 153 157 159 164 168

xi

Contents 7.4.4. Russellian description theory 7.4.5. A modal leap

8. Impossibility 8.1. Impossible Worlds 8.2. Russell–Quine–Lewis Argument 8.3. Counterpossible Conditionals 8.4. Impossible Suppositions 8.5. Doxastic Possibility 8.6. Distinctness of the Indiscernible 8.7. Non-Compossibility of the Indiscernible 8.8. Modiﬁed Skyrms Argument 8.9. The Necessary A Posteriori 8.9.1. Misdescribing a world 8.9.2. Stipulating a world 8.9.3. Reconciliation 8.9.4. Two-dimensional interlude 8.9.5. Kripkean stipulations again 8.10. More on Alternative Metaphysical Spaces 8.11. Two-Dimensional Semantics Again 8.11.1. Not metalinguistic 8.11.2. Not about @ 8.11.3. Not pretense 9. Proposition and Belief 9.1. Reduction of Intensional Entities Again 9.2. Propositions 9.2.1 Contents other than propositions 9.3. A Challenge 9.4. Modal Russellian Theory Revised 9.5. Meaning and Expression 9.6. Iteration 9.7. Non-Descriptiveness of Names 9.8. Non-Linguistic Believers 9.9. A Frenchman in London 9.10. A Polish Musician Politician 9.11. An Imperiled Conversationalist 9.12. The De Se 9.13. Two Tubes 9.14. Belief Sentences: Summary

171 174 176 176 182 186 191 193 199 200 202 205 207 209 212 215 217 218 221 226 227 228 231 231 233 239 240 243 245 247 248 250 250 253 253 254 254 255

Contents

xii

10. Fictional Worlds 10.1. Fictional Individuals 10.2. Kripke on Unicorns and Sherlock Holmes 10.3. Fictional Names and Existence 10.3.1. Creationist argument 10.3.2. Kripke on Zeus and Hamlet 10.3.3. Desiderata 10.4. Impossibility of Fictional Individuals 10.5. Imagined-Seen Fictional Worlds

257 257 259 265 266 269 271 271 277

11. Epistemology 11.1. How Do We Know? 11.2. The Self 11.3. Intensionalism 11.4. What Perception Tells Us 11.5. Ontology

284 284 287 288 291 293

Bibliography Index

295 307

Introduction Suppose you are seated at a table in a quiet room. Your hands are resting on the table top relaxed. You think to yourself that your right hand is open. You have the clear proprioception that it is open and also the clear visual perception that it is. You touch the right hand with your left hand and feel it as being open. You ask a friend who is seated across the table and receive a conﬁrming response. You are as certain as you can be that your right hand is open. At the same time, you think that even though it is in fact open, your right hand could be clenched instead at this very moment. It is up to you whether your right hand is open or clenched. You in fact hold it open but you could have decided to clench it instead. Your right hand being open is one possibility, your right hand being clenched is another possibility, and you choose to make the ﬁrst possibility realized instead of the second. You have a very strong, almost irresistible sense that both of these states of your right hand are live possibilities. Even though one of them and not the other is in fact brought about, or actualized, both remain genuinely possible. You sense an aura of reality surrounding the unactualized possibility. This sense of reality cannot be the same as, or imply, the sense of actuality, for the clenched state of your hand is not actualized. Yet you are unable to shake the sense of reality about that state of your hand being objectively possible. This ‘robust’ sense of reality which transcends the sense of actuality provides the most immediate and intuitive motivation to pursue alethic modal realism, or modal realism for short. The version of modal realism I defend shares a certain theoretical conviction with David Lewis’s classical modal realist theory and also, superﬁcially, with antiLewisian actualist theories. It is the conviction that modal talk should be understood in terms of talk of possible worlds.1 My version of modal realism, however, sharply differs from both actualism and Lewis’s modal realism. Actualists believe that there is one and only one universe, and so do I. But they postulate all possible worlds as abstract objects existing within the universe as it 1 Lewis is a reductionist about modality but actualists are not. Lewis advocates understanding modality in terms of possible worlds (and possible individuals) in a reductionist way, but actualists advocate understanding modality in terms of possible worlds only in a pedagogical or heuristic way. I am more sympathetic to Lewis than to actualists, as the latter’s advocacy is theoretically superﬁcial. More on this shortly.

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Introduction

actually is. I, on the other hand, postulate all possible worlds not as existents (abstract or not) within the universe as it actually is but as points in modal space at each of which the universe is a certain way. This seems to me the best way to take seriously not only the idea that merely possible worlds are genuine alternatives to the actual world but also the idea that possible worlds have their own ontological status separate from the universe as it actually is. Furthermore, I respect the intuitive idea that there is nothing modally special about actuality. The way the universe actually is, including how we actually are, may be the object of our gratitude, despair, scorn, amusement, etc., but the universe’s being the way it actually is has no metaphysical upper hand over the universe’s being some other way. Actualists defy this aspect of our robust sense of modal reality by refusing to countenance anything outside the universe as it (the universe) actually is. Their view cries out loud, ‘Our actual being is special!’ Intuitively, this seems to me to be the height of metaphysical arrogance. On this score, I am sympathetic to Lewis, who, like me, does not postulate merely possible worlds as being in the universe as it actually is. At the same time, I am not sympathetic to Lewis on other scores. Lewis equates the actual world with the universe as it actually is. This blurs the distinction between the universe and the worlds. I consider the distinction to be at the heart of the realist view of alethic modality which I prefer. According to this view, there is only one universe2 and that universe could be any number of ways, and it is one way at one possible world, another way at another possible world, yet another way at yet another possible world, and so on. If we take this idea literally and robustly realistically, we should be dissatisﬁed with Lewis’s view, according to which there are many universes and each one of them is a possible world. If each possible world is a distinct universe, then the only way to make sense of the idea that this very universe could have been other than how it actually is will be by saying that there is another universe that bears a certain relation to this universe and is that other way. But this is unsatisfactory to the robust realist, for it sounds ersatzy. Why should another universe’s being a certain way be relevant to this universe’s possibly being that way? This rhetorical question echoes a common complaint against Lewis that Hubert Humphrey’s possibly having been the winner in the 1968 US presidential election should not be analyzed in terms of someone else’s (Humphrey’s counterpart’s) having been the winner. My non-standard use of the word ‘ersatzy’ is meant to point to the ironic fact that I am using the sentiment behind this complaint against Lewis, which is voiced by actualists whose theories Lewis criticizes under the label ‘ersatzist program’, to motivate a non-Lewisian realist theory of modality.

2 I do not mean to rule out what some cosmologists call ‘multiverses’ or ‘other universes’. My use of the word ‘universe’ is more inclusive than the use of the same word by such cosmologists. Those ‘other universes’ in their sense will be different parts of the one and only universe in my sense. There should be no confusion about this. They are engaged in physics, and I in metaphysics.

Introduction

3

I, like Lewis and actualists, start with the conviction that true modal claims are objectively and non-trivially true. Necessity, possibility, and actuality are central to philosophical theorizing about reality and meta-philosophical theorizing about philosophical theories. There are two mutually incompatible3 attitudes toward these modalities that we may take. One is the attitude of modal primitivism, according to which modality is primitive and not subject to analysis in more basic terms, or even to informative theoretical elucidation. This does not rule out, of course, reduction of some modalities into others: for example, impossibility is the negation of possibility. It only holds that not all modalities are reducible. Usually possibility and actuality, or necessity and actuality, are regarded as primitive, as necessity and possibility are mutually deﬁnable with the help of negation. Assume that possibility, rather than necessity, is a primitive notion. Then if you do not already grasp the notion of possibility, no conceptual tutoring will help you grasp it, any more than a thorough tutoring in the science of color perception will help a congenitally blind person know what it is like to see a color. This is known as modalism and was held by A. N. Prior. Prior’s inﬂuence has been considerable among contemporary thinkers on modality, many of whom follow him in subscribing to modalism.4 The other attitude we may take toward modalities is reductionism, according to which all modalities are reducible ultimately in non-modal terms. There are at least as many ways to uphold reductionism as there are candidate bases of reduction. There are a number of kinds of items which may be used as such a base but two stand out: essences and possible worlds. Aristotle was the ﬁrst to propose essences seriously as a base for necessity, and Kit Fine has produced considerable elaborations on the Aristotelian idea.5 Whether reduction in terms of essences constitutes reductionism rather than reversion to primitivism may well be a verbal issue, depending on what we mean by ‘modality’. If we include essences as a kind of modality, reduction of other modalities into essences is merely an intra-modal reduction, hence modality as a whole remains as primitive as essences are. If, on the other hand, we count essences as a sui generis category outside modality, this is a reduction of modality in non-modal terms. A more widespread and popular initial approach to reducing the notions of modality goes back at least to Leibniz and has been inspired more recently by the twentieth-century development of modal logic. This is the approach I shall follow. It is to understand modal notions in terms of possible worlds; actual truth is truth at the actual world, possible truth is truth at some possible world,

3 This is one example of a modal notion (incompatibility) being used in a discussion about philosophy. It is practically impossible (another modality) to do philosophy without resorting to some modal notion or other. 4 Prior 1967; Prior and Fine 1977. See also Forbes 1985 and esp. Forbes 1989. There are other modalists, too many to mention in a short note. Most actualists are modalists. 5 Fine 1994a, 1994b, 1995, 2000, 2002, 2005.

4

Introduction

and necessary truth is truth at every possible world. According to this tradition, central to any serious conception of modality is the notion of a possible world. Unfortunately, the philosophical status of this notion is obscured by those philosophers who use the phrase ‘possible world’ but intend something other than the notion of a possible world as it ﬁgures in genuine reduction of modality. Actualists are the philosophers in question. They freely use the phrase ‘possible world’ in their modal theorizing and say that the notion of a possible world is of great heuristic value in philosophical theorizing. But they deny any value in the notion of a possible world for the purposes of conceptual reduction. When we study their theories, we quickly discover that they are really modal primitivists. They use the notion of a state of affairs, a situation, a property, a proposition, or a sentence to analyze possibility and necessity.6 They call, say, a certain type of state of affairs a ‘possible world’ but this label should not be taken seriously as anything more than just that, a mere label. To specify the relevant type of state of affairs, they commit themselves to an ineliminable modal notion, such as possibility.7 To deﬁne possibility in terms of states of affairs cum possibility would be obviously circular. Those theorists know this and do not pretend to offer any conceptual reduction of possibility. But then, what is the point of their account of possibility in terms of states of affairs cum possibility masquerading as possible worlds? The answer is, as I indicated earlier, that the account serves pedagogical and heuristic purposes. When we teach the notion of possibility or necessity to novices at the beginning of a serious philosophical discussion of conceptual matters, it facilitates their comprehension if we put matters of possibility or necessity in terms of the picturesque prose of possible worlds. And when we ponder upon intricate conceptual issues involving modality ourselves, we ﬁnd it easier to think in terms of possible worlds, as the possibleworlds talk neatly systematizes modal matters for our abstract and intricate pondering. At the conclusion of the process, we can translate the results of our philosophical investigations conducted in the language of possible worlds back into the language of primitive modality. Talk of possible worlds is thus a useful fac¸on de parler. Some actualists use the notion of consistency in their non-reductive deﬁnition of a possible world. What kind of consistency is used depends on what kinds of entities are marshaled under the label ‘possible worlds’. Some use sentences, propositions, or collections of sentences or propositions. Others use properties or collections of properties. Either way, what they call a ‘possible world’ is a maximally consistent entity of the preferred kind. Consistency and possibility are closely related. Most actualists are satisﬁed with the idea that consistency 6 See Adams 1974; Armstrong 1989; Barwise and Perry 1983; Carnap 1947; Cresswell 1972; Forrest 1986; Jeffrey 1965; Jubien 1993; Lycan 1994; Menzel 1990; Plantinga 1974, 1976, 2003; Stalnaker 1976; van Inwagen 1986. 7 e.g. Plantinga 1974: 45.

Introduction

5

must be deﬁned ultimately in terms of possibility, even though some attempt to give a deﬁnition of consistency that is entirely non-modal.8 Despite the superﬁcial fac¸on de parler nature of the talk of possible worlds by actualists, I ofﬁcially count their theories among modal realist theories with respect to possible worlds. This is largely due to my desire to conform to the already established consensus among modal theorists that possible worlds are real entities according to actualists. Unlike these actualists, however, I take the notion of a possible world seriously in such a way that talk of possible worlds is not a mere fac¸on de parler and support a form of reduction of the modal notions in terms of it. The reduction is not merely pedagogical or heuristic, but conceptual. In this sense, I am as anti-actualist as Lewis is. But I differ from Lewis signiﬁcantly on the nature of possible worlds and on the extent of the reduction. Lewis proceeds in two stages in his characterization of possible worlds. First, a particular possible world is speciﬁed. It is the concrete mereological totality of you, me, and all things physically surrounding us, however spatio-temporally remote they may be from us. By deﬁnition, this totality is the actual world. Next, anything that is like this totality in important respects is said to be a possible world. This is a delicate maneuver, the success of which hinges on the choice of the important respects of similarity. Lewis initially chose spatio-temporal relatedness, but later suggested tentatively that relatedness by means of any natural relation might be a better choice. If we ignore this complication, the Lewisian deﬁnition amounts to saying that a possible world is a mereological totality of spatio-temporally related concrete individuals. I reject this Lewisian characterization of possible worlds. As I hinted earlier, on my view, possible worlds are points in modal space, which are deﬁned by modal axes. A good deal of what follows in the book is an attempt to explain what this means. I am closer to Lewis on merely possible individuals. Lewis postulates merely possible individuals as real objects, and so do I. Actualists do not, and this is why actualism falls short of being realist with respect to merely possible individuals. To be fully modal realist, a theory needs to be realist both with respect to merely possible worlds and with respect to merely possible individuals. Lewis’s theory and the theory I favor are both fully modal realist but actualist theories are not.9 Some theorists may strive to treat possible worlds and times in a parallel manner, while others may not. Among those who do, some may treat an ordinary individual as existing only at one world and only at one time, while others may treat an ordinary individual as existing at two or more worlds and at two or more 8 A model-theoretic deﬁnition of consistency is the foremost example. For some difﬁculties it faces, see Shalkowski 2004. 9 For some criticisms of actualism by philosophers other than Lewis, see Chihara 1988: 120–41; Jubien 1988; Grim 1984, 1986, 1988. Grim presses his critique further against Plantinga’s defense of actualism in Plantinga and Grim 1993.

Introduction

6

times. Among those who do not strive for a parallel treatment, some may treat an ordinary individual as existing only at one world but at two or more times, while others may treat an ordinary individual as existing at two or more worlds but only at one time. I treat an ordinary individual as existing at many worlds and at many times. I take this to be largely a matter of methodological decision. There are both arguments in favor of any of these positions and arguments against any of them. When taken in isolation, such arguments are never conclusive. I follow two methodological principles: the Constructivist Principle and the Indexist Principle. The Constructivist Principle is a general principle concerning the activity of theoretical work in philosophy. It says that it is worthwhile to take a small number of basic assumptions with some initial attractiveness, stake an overarching thesis on that basis, and elaborate it constructively. The Indexist Principle is a speciﬁc principle on how to approach the metaphysics of possible worlds and says that possible worlds should be treated as alethic indices on a par with times and places; possible worlds, like times and places, are indices of a metaphysical kind with respect to which matters of truth are relativized. These are the methodological principles underlying this book. As one needs to start somewhere and these principles provide me with my starting point, I shall not argue for them. My main task in the book is to articulate and elaborate a version of modal realism based on these principles. Modal realism is the main theme of this book, but there are two related subthemes. They are impossible worlds and intensional objects. I shall argue that we need impossible worlds for a number of reasons and that the reduction of propositions as collections of worlds is not as hopeless as many philosophers might think. As part of the discussion on the latter, I shall touch on the semantics of belief sentences. These sub-themes are, strictly speaking, detachable from the main theme of modal realism, but discussing them in conjunction with modal realism only enriches our thinking about modal reality. I would like to end the Introduction with a brief comment on a well-known fact about Lewis’s modal realism. Lewis complained that his theory was met with many ‘incredulous stares’ but few reasoned objections.10 Even after serious arguments started to come out against his theory, he noted, the incredulous stares persisted.11 It has since become almost a comically self-conscious requirement for modal theorists to mention the ‘incredulous stares’ when discussing Lewis’s theory. It seems to me rather odd that the ‘incredulous stares’ directed at Lewis’s theory have been elevated to a legendary status among philosophers when the history of philosophy is crowded with theories and proposals which go directly against common-sense opinions or are otherwise highly counter-intuitive. My general sense of what is credible and what is incredible tells me that Lewis’s modal realism is no less credible than theism, a rather prevalent doctrine 10

Lewis 1973: 86.

11

Lewis 1986: 133.

Introduction

7

throughout the history of Western philosophy.12 In fact, common sense seems quite friendly to modal realism of one sort or another. Common sense does not seem to regard merely possible objects as nothing. Common sense also appears friendly to theism, at least in some societies. In many cases, of course, common sense should be rejected after sustained careful investigations. Some of these cases of common-sense opinion are labeled with the adjective ‘folk’ in a pejorative sense, like ‘folk physics’, and others have respectable-sounding names, like ‘astrology’. Folk physics and astrology should be rejected because they conﬂict with what rational empirical inquiry tells us. Credibility of a claim is measured sometimes against common sense and sometimes against rational empirical inquiry. When measured against common sense, modal realism and theism seem to fare equally well. When measured against rational empirical inquiry, some traditional forms of theism fare as badly as astrology, while other more thoughtful versions fare better. Modal realism does not come in many different versions but the two we shall discuss, Lewis’s version and the version I prefer, fare at least as well as the thoughtful versions of theism. The ‘incredulous stares’ are gloriﬁed with respect to modal realism but not with respect to theism, not because the former is inherently more outlandish than the latter but because the politico-historical weight of the latter far exceeds that of the former. When assessed in calm detachment from politics and history, theism is seen to be at least as fantastic as modal realism. All the same, undeterred by the ‘incredulous stares’ from atheists, theists march on with passionate fervor. Like their theistic friends, modal realists are not deterred by the ‘incredulous stares’ from modal nonrealists. They stroll on with good cheer.13

12

I remember walking down the street while discussing the nature of mental states with a classmate in my ﬁrst year of undergraduate study. We had just attended a class on Donald Davidson’s theory of reasons and causes. I tried to make a philosophical point about Davidson’s theory by using an example involving a dog. My classmate immediately retorted by saying that dogs didn’t have beliefs. I expected him to go on to give an elaborate Davidsonian reason why dogs didn’t have beliefs. Instead he said, ‘Dogs are just mechanical automata. God created them that way.’ I was incredulous, much more so than when I later encountered Lewis’s modal realism for the ﬁrst time. I had to excuse myself to recover from this completely unexpected blow. There were a number of things amiss in my classmate’s assertion but I found his invocation of God at that point in our serious conceptual discussion on the nature of mind utterly astounding. To this day this remains one of my most glaring moments of philosophical incredulity. (I attended a Catholic kindergarten but did not discuss philosophy there.) 13 As will become evident later, I hold the view that God is real. This, however, is no cause for celebration for traditional theists, as I also hold that all gods are real, as are all demigods, quartergods, and Santa Claus. Cf. ‘…I am perhaps the most extreme polytheist going. If, as I suppose, a being does not have to satisfy some inconsistent description to be a god, then I take the number of the gods to be at least n2. Unlike most polytheists, however, I think of this world we live in as entirely godless’ (Lewis 1983a: p. xi n. 4).

1 Modal Realism 1 . 1 . REALISM AND MODALITY Realism concerning X is the view that X is real. The opposing view, anti-realism concerning X, is the view that X is not real. Nominalism is the standard version of anti-realism concerning Platonic objects, which asserts the conjunction of the claim that Platonic objects are not real and are therefore nothing and the claim that linguistic expressions are real and can play many of the theoretical roles Platonic objects are thought to play. Modal realism is realism concerning items invoked to elucidate alethic modality (necessity, possibility, actuality, etc.). There are two kinds of items which are invoked to elucidate modality in the possible-worlds framework: possible worlds and possible individuals. Modal realism comes in a number of varieties. Any version of modal realism, as I understand it, presupposes the possible-words analysis1 of modality: ‘Possibly P’ is true if and only if ‘P’ is true at some possible world; ‘Necessarily P’ is true if and only if ‘P’ is true at every possible world; ‘Actually P’ is true if and only if ‘P’ is true at the actual world.2 Any version of modal realism asserts that the possible worlds invoked in such an analysis are real entities. Beyond the commitment to the reality of possible worlds, the unity of modal realism disappears. So it is important to distinguish among different versions of modal realism and say which one is to be preferred. Depending on how one conceives the nature of possible worlds and possible individuals, one arrives at different versions of modal realism. Some modal realists, notably actualists, postulate possible worlds separately from possible individuals and claim that while merely possible worlds are real, merely possible individuals are not. The version of modal realism I favor postulates both merely possible worlds and merely possible individuals as real.3 1 By ‘analysis’, I mean both conceptual analysis and heuristic analysis. A heuristic analysis of a concept is not intended to reveal more primitive concepts into which the given concept is to be reduced, but to provide a handy way to facilitate the grasping and use of the concept. 2 This is the possible-worlds analysis in a nutshell. Important details, e.g. modality de re and accessibility relations, are suppressed. Different modal realists may disagree about such details. 3 How about nominalism concerning modality? A version of actualism may be considered nominalism concerning possible worlds. It says that a possible world is a maximally consistent sentence; a linguistic object plays the role of a possible world. Or, to put it in a way closer to the traditional nominalist way, talk of possible worlds should be replaced with talk of sentences. One

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But what does ‘real’ mean? I take the notion of reality to be primitive, hence I can offer no reductive analysis of it. I can offer, however, a somewhat informative running characterization of what I have in mind. To be a realist about objects of a certain kind is to hold that true statements about those objects are true in virtue of the right sort of facts involving those objects in the right sort of way. Exactly what the right sort of facts and the right sort of way are is notoriously difﬁcult to pin down, and I am not prepared to attempt to pin them down. An example should sufﬁce to indicate what is intended. To be a realist about cats and mats is to hold that, for example, the statement ‘A cat is on a mat’, if true, is true in virtue of the fact that a cat bears the ‘on’ relation to a mat. One way not to be a realist about cats and mats is to hold that the statement, if true, is true in virtue of the fact that we have a perceptual experience in which we are appeared to a-cat-is-ona-mat-ishly. Another way is to hold that the statement, if true, is true in virtue of the fact that it is logically consistent with the statements made in the Supreme Book of Truth.4 It is important to note that my running characterization does not include existence; I do not say that one is a realist about cats and mats only if one holds that cats and mats exist. I think that the question of reality is entirely separate from the question of existence and that failure to keep them separate tends to cause grave confusion, especially in modal metaphysics. Existence is not addressed in this chapter. It will be addressed in Chapter 3. The extensive parallel between temporal logic and modal logic has been widely and routinely acknowledged. This naturally raises the expectation that satisfactory metaphysical theories of temporality and modality will parallel each other accordingly. The methodologically pregnant part of this expectation encourages modal metaphysicians to look to the metaphysics of temporality for guidance. A number of prominent modal metaphysicians endorse such a general methodological outlook,5 while others refuse to be impressed by the metaphysical implications of the parallel between temporal and modal logics.6 I agree with the former group of modal metaphysicians and pursue the parallel, expanding on it and proﬁting from it as much as I can. I ﬁnd it informative to divide the various versions of modal realism into two groups. The ﬁrst group includes various versions of what I call constituent modal realism. David Lewis’s theory and his ersatzist rivals are in this group. might choose to use the label ‘modal nominalism’ for such a version of actualism and discuss it separately from the other versions of actualism, which are discussed under the label ‘modal realism’. Such a dual treatment of actualist theories would be cumbersome and pointless. I cannot think of an interesting and productive way to set up my discussion of metaphysics of possible worlds by classifying some theories as realist and others nominalist. Adherence to the traditional realism/ nominalism dichotomy is not something I particularly seek. 4 What this book is exactly may be open to debate. 5 See Kraut 1979, 1980; Adams 1986; Zalta 1987; Lycan 1994: 36; Sider 2001; Markosian 2004. 6 See Lewis 1986; Divers 2002; King 2003.

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My preferred version of modal realism belongs to the other group, non-constituent modal realism. 1. 2. CONSTITUENT MODAL REALISM In his wide-ranging book, Possible Worlds, in which Lewis’s theory is partially defended, John Divers deﬁnes what he calls realism as ‘the ontological thesis that there exists a plurality of possible worlds (of some kind or other)’.7 On this deﬁnition, what Divers calls actualist realism and Lewis calls ersatzism qualiﬁes as realism, as well as Lewis’s theory. To distinguish Lewis’s theory from actualist realism, Divers deﬁnes what he calls genuine realism as the view that ‘unrestricted ﬁrst-order existential quantiﬁcation [ranges] over a domain of individuals among which only some actually exist’.8 Genuine realism also says that a world is ‘a concrete object—an individual which is, in some sense, maximal’.9 Lewis’s theory is genuine realism but actualist theories are not. When I use the label ‘modal realism’, I do not mean realism or genuine realism in Divers’s sense. I do not approve of Divers’s use of the existential predicate, ‘there exists’, as applied to a plurality of possible worlds in his deﬁnition of realism. In order to articulate the reason why I do not approve of it, I need to say what I take to be the nature of existence, which is the topic of Chapter 3. To expound fully the reason for my resistence to Divers’s way of putting it, I need to explain what I call modal tense, which will be discussed in Chapter 5. The same goes for the often-given characterization of modal realism as the doctrine that there exist things that are not actual, i.e. that merely possible objects exist. As for genuine realism, Divers characterizes it in terms of ﬁrst-order quantiﬁcational logic. My conception of modal realism in general, as well as any particular version of modal realism, is independent of any particular logical theory. In addition, Divers tailors genuine realism closely just to ﬁt Lewis’s theory. The version of modal realism I shall defend is neither an actualist theory nor Lewis’s theory. When I speak of individuals, I mean to speak of concrete individuals. The notion of concreteness is notoriously difﬁcult to articulate precisely,10 and I have nothing special to offer to elucidate the notion. Sufﬁce it to say that you, I, tables, chairs, trees, mountains, rivers, oceans, planets, galaxies, and galactic clusters are concrete, whereas numbers, sets, and Platonic forms are not. To avoid clutter, I shall not modify the noun ‘individual’ with the adjective ‘concrete’ when I mean to speak of concrete individuals, unless it is absolutely necessary to do so. My use of the word ‘individual’ should be understood accordingly.

7

Divers 2002: 19.

8

Ibid. 21.

9

Ibid.

10

Lewis 1986: 81–6.

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If possible individuals are conceived as constituents of possible worlds—actual individuals as constituents of the actual world and merely possible individuals as constituents of merely possible worlds, either by being mereological parts of possible worlds or by bearing some other constituting relation to possible worlds—I call the resulting position individual constituent realism. David Lewis’s theory is an instance of individual constituent realism according to which possible individuals are mereological parts of possible worlds. If possible worlds are conceived as constituted not by possible individuals but by objects of some other kind, I call the position non-individual constituent realism. Some actualist theories are instances of non-individual constituent realism. They not only shun merely possible individuals, hence do not have them constitute merely possible worlds, but also do not have the actual individuals constitute worlds, actual or merely possible. But since they do have abstract objects constitute possible worlds, they are constituent realist theories. It is just that the constituents of possible worlds they postulate are not concrete individuals. Theories of this type include those which construct a possible world as a maximally consistent set of sentences, propositions, properties, situations, or states of affairs, or as some other kind of maximally consistent abstract object. If a possible world is a maximally consistent set, then it is constituted by whatever a set is constituted by.11 If a possible world is a maximally consistent abstract object of some other kind, then it is constituted by whatever an abstract object of that kind is constituted by. Either way, none of the constituents are individuals.12 It is important to note that both individual constituent realism and non-individual constituent realism are realist with respect to merely possible worlds, but only some versions of individual constituent realism are realist with respect to merely possible individuals, or mere possibilia. In this regard we should make a sharp distinction between the deﬁnition of a possible world as a maximally consistent set of situations or states of affairs and the deﬁnition of a possible world as a maximally consistent situation or state of affairs. The former is non-individual constituent realism, hence it is not realist with respect to mere possibilia. The 11 Lewis thinks that every non-empty subset of a set is a mereological part of the set. If he is right, we can say that a set is mereologically constituted by its non-empty subsets. See Lewis 1991. 12 I am assuming that no constituent of an abstract object is an individual, i.e. a concrete individual. This assumption is in conﬂict with the Russellian view that the proposition that Mont Blanc is covered with snow is an abstract object with Mont Blanc, a concrete individual, as one of its constituents. It is customary to represent the proposition that Mont Blanc is covered with snow by means of the ordered pair, <Mont Blanc, the property of being covered with snow>. Some even speak of identifying the proposition with the ordered pair. Such an identiﬁcation faces the difﬁcult problem of multiple candidates (Benacerraf ’s problem); the ordered pair, , is an equally good candidate for the identiﬁcation but one thing should not be identiﬁed with two things. Even if such an identiﬁcation is justiﬁed somehow, it does not justify the claim that Mont Blanc is a constituent of the proposition, for it does not justify the claim that a member of an ordered pair is a constituent of that pair; the standard representation, due to Kazimierz Kuratowski, of an ordered pair by a set does not encourage such a claim. I shall not pursue this issue further but shall have something to say about propositions in Chs. 7 and 9.

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latter, on the other hand, is individual constituent realism. No individuals are constituents of sets but individuals are constituents of situations and states of affairs in some sense. There is a sense in which the situation or state of affairs of Socrates being snub-nosed is constituted by Socrates and the property of being snub-nosed.13 One may decide to allow only actual individuals to constitute situations or states of affairs. If one does, the result is a version of individual constituent realism that is not realist with respect to mere possibilia. On the other hand, one may decide to allow mere possibilia, as well as actual individuals, to constitute situations or states of affairs. If one does, the result is a version of individual constituent realism that is realist with respect to mere possibilia. Such a theory will be closer to Lewis’s theory than to the theory of possible worlds as sets of situations or states of affairs in an important way. 1 .3 . PARTICULAR MERE POSSIBILIA Consider David Kaplan’s example of a particular mere possibile.14 Kaplan invites us to imagine a complete set of new automobile parts scattered around. They can be assembled into a new automobile in exactly one way, i.e. every part has to ﬁt with the other parts in just one way. The parts are in fact never assembled. But if they were assembled into an automobile, there would be one unique new individual, namely, that very automobile. This is perfectly possible. Here we have an example of not just a generic mere possibile, like a fat man in the actually vacant doorway who is distinct from all actual individuals, but a particular mere possibile. When we say, ‘that automobile’, we mean to refer to whatever would result from assembling those automobile parts in the only way they can be assembled into an automobile. Since the parts are actually existent, we are assured that the reference of our use of ‘that automobile’ is to a unique, albeit merely possible, automobile. It is not that the automobile is actually presented to us ﬁrst and we decide to use the phrase ‘that automobile’ to refer to it as so presented. We intend to be referring to whatever would result from the assembling of those automobile parts in front of us. Given the (assumed) metaphysical fact that the parts would result in one particular automobile, we in fact succeed in rigidly referring to that automobile. Every possible situation happens at some possible world. So, this happens at some possible world. The automobile, that very particular automobile, would exist at such a possible world. Take the version of actualism according to which a possible world is a maximally consistent set of 13 I do not assume that no abstract object is a constituent of a concrete individual. I do not assume that the state of affairs of Socrates being snub-nosed is an abstract object. If it is a concrete object, then the version of individual constituent realism in question has much in common with Lewis’s theory. 14 Kaplan 1973.

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propositions. It should say that there is a possible world of which a certain proposition is a member. What proposition? It cannot be a singular proposition about that automobile, for the automobile is a mere possibile and no actualist theory countenances a mere possibile. Some may say that the unassembled automobile parts collectively are an individual that is identical to the automobile which would result if the parts were assembled. If this is right, the particular automobile in question is not a mere possibile but an actual individual. It is just not actually an automobile. Such a position does not sound very plausible, but whether it is ultimately acceptable or not, there is a harder case for actualism. It is Nathan Salmon’s Noman.15 A particular human egg, E, and a particular human sperm, S, are never actually fused with each other or with anything else, but it is possible for them to be fused with each other, and if they were, they would result in a normal human being. Suppose at some possible world they are fused in a certain way and result in a particular man—call him ‘Noman’. Noman exists at that possible world. It is highly implausible to suggest that Noman, that very individual who would be a man at that possible world, also actually exists as E and S considered together. According to individual constituent realism with mere possibilia, the reality of mere possibilia follows from the core doctrine that all possible individuals are constituents of possible worlds. Since possible worlds are real (as any realist about possible worlds would claim) and any constituent of something real is real (as individual constituent realists assume), all possible individuals, including mere possibilia, are real. In particular, Kaplan’s automobile and Salmon’s Noman are real. In addition, many merely possible automobiles not made of any actually existing parts and many merely possible human beings not resulting from the fusion of any actually existing egg and sperm are also real. Even many merely possible automobiles and humans not constituted by any actually existing elementary particles are real, too. 1 . 4 . MODALITY DE RE All versions of individual constituent realism with mere possibilia are fully realist in the sense that they postulate merely possible worlds and merely possible individuals, as well as the actual world and actual individuals, as real. There is, however, a different but important sense of ‘realist theory of modality’ in which Lewis’s version is not fully realist. The issue is a familiar one and concerns not the status of merely possible worlds or mere possibilia but the analysis of modality de re. As the results of the 1968 US presidential election were announced, Hubert Humphrey could have raised his arms in triumph over Richard Nixon, even 15

Salmon 1981: 39.

14

Modal Realism

though he in fact did not. So there is a possible world, w, at which Humphrey raised his arms, even though he did not at the actual world. If one applied individual constituent realism to this picture straightforwardly, one would say that Humphrey is a constituent of w and raised his arms as a constituent of w, even though he is also a constituent of the actual world and did not raise his arms as a constituent of the actual world. But Lewis rejects this as an unacceptable case of overlap. The idea of overlap is this: to say that Humphrey raised his arms as a constituent of w and did not raise his arms as a constituent of the actual world, @,16 is like saying that the stem of the letter ‘Y’ in the ‘HOLLYWOOD’ sign in Los Angeles is entirely metal as a part of the left-bending half of the letter (consisting of the stem and the left horn) and is entirely plastic as a part of the right-bending half (consisting of the stem and the right horn). But such a situation is impossible.17 This objection may appear convincing but it can be resisted. Even if an overlap is unacceptable, Lewis’s objection is not as powerful as it may appear. Endurantism is the claim concerning temporal metaphysics that Humphrey, for example, exists wholly at every moment of his life. Lewis assumes that the view he criticizes asserts a modal analog of endurantism, namely the claim that Humphrey exists wholly at @ and also exists wholly at w. If we deny this, his objection loses its bite. The modal realist theory I favor denies it.18 As an alternative to what he considers an objectionable overlap theory, Lewis offers his famous counterpart theory. Humphrey is a constituent of only one possible world, namely @, and held his arms down simpliciter, but he bears a special relation (not identity) to some merely possible individual who is a constituent of w and who raised his arms simpliciter. The special relation is the counterpart relation, and Lewis thinks of it as a similarity relation.19 Whether it is Lewis’s counterpart relation or some other relation, the special relation is supposed to be a doubly external relation, relating Humphrey to some other possible individual who is external to Humphrey and also external to the only world of which Humphrey is a constituent, namely @.20 It is an integral part of this picture that every possible individual is a constituent of just one possible world. This avoids overlap of worlds but makes Lewis’s theory less realist in an important sense. Humphrey is said to have raised his arms at w by virtue of 16 17 18

2003.

I follow the customary use of this symbol as the name of the actual world. Lewis 1986: 199–200. For a response to Lewis which does not reject the modal analog of endurantism, see McDaniel

19 The similarity relation that is the counterpart relation is independent of the similarity relation explicitly invoked in a statement of modality. For example, I could have been more like you than myself. So at some possible world, my counterpart is more like you than myself. See Feldman 1971; Lewis 1986: 254–5. 20 Lewis suggests that we should allow a counterpart of x to be x’s worldmate (i.e. a constituent of the same world) in some cases. For example, you may count as my counterpart at the actual world under special circumstances in which it is true to say that I might have been you. See Lewis 1986: 231–2, esp. n. 22.

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bearing some external, indeed transworld, relation to some other individual who is a constituent of w and who raised his arms. Humphrey’s arm raising at w is analyzed as the arm raising by someone else at w who bears an external relation to Humphrey. Humphrey does not exist at w, hence he is not a constituent of w. Instead Humphrey has a representation at w, namely, the bearer of the external relation in question to him. Humphrey is said to be one way or another (but not existent or a constituent21) at w precisely by virtue of his representative at w being that way. On Lewis’s individual constituent realism, a possible world at which donkeys talk is a possible world which contains real talking donkeys as constituents. On an actualist non-individual constituent realism, a possible world at which donkeys talk is a possible world which contains (say) the proposition that donkeys talk. The existence of talking donkeys is represented by that proposition. In this regard, the actualist non-individual constituent realism is less realist than Lewis’s individual constituent realism, that is, the former replaces real talking donkeys postulated by the latter with a representation of the existence of talking donkeys; the representation is real but not talking donkeys. What we have seen with the Humphrey example is that Lewis’s counterpart theory replaces Humphrey at possible worlds other than the only world at which he exists (@) with his representations, his counterparts. Lewis, like his actualist rivals, resorts to representations in a crucial way. It is not really Humphrey who wins and who is a constituent part of a relevant possible world when we consider the possibility of Humphrey’s winning. This is the sense in which Lewis’s theory falls short of full realism in an important sense.22 Note that I am not merely echoing the often-expressed complaint that Lewis’s counterpart theory misconstrues the de-re-ness of modality de re by making someone other than Humphrey ﬁgure crucially in the truth conditions for non-actual possibilities about Humphrey. The complaint usually comes from actualists, but not all actualists are in a position to make the complaint. Take those actualists who deﬁne a possible world as a maximally consistent sentence or set of sentences. According to them, the truth conditions for non-actual possibilities de re involve representations instead of the res itself. An actualist who holds such a theory and who accuses Lewis of inadequacy on this score is a kettle 21 We should be careful to distinguish between the question of Humphrey being existent or a constituent at w (he is not) and the question of Humphrey being represented by his counterpart as being existent or a constituent at w (he is). 22 My reason for calling Lewis’s treatment not fully realist in an important sense has to do with my conception of what it is to be a realist about modality de re. To be a realist about objects of a certain kind is to hold that statements about those objects are true in virtue of the right sort of facts involving those objects in the right sort of way. To be a realist about the res ﬁguring in modality de re as such is to hold that statements of modality de re about the res are true in virtue of the right sort of facts involving the res in the right sort of way. The intrusion of Humphrey’s counterpart at w makes the Lewisian truth condition not fully realist in an important sense, because Humphrey’s counterpart at w is a person distinct and separate from Humphrey and ﬁgures more directly in the crucial part of the truth condition than Humphrey.

16

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calling a pot black. I group Lewis’s theory and such actualist theories together and regard them all as falling short of treating modality de re in a fully realist manner in an important sense. A fully realist treatment in an important sense of modality de re (e.g. ‘Humphrey could have won’) should lay out its truth condition as a matter involving the res (Humphrey) in a crucial way (winning), not the representation of the res in a crucial way. So, my complaint against Lewis is more general in scope than the usual complaint by actualists. Not all actualists are subject to this criticism. For example, those who hold that possible worlds are maximally consistent states of affairs, propositions, sets of states of affairs, or sets of propositions, are not. Actualists of this type explain the possibility of Humphrey’s win in terms ultimately of Humphrey himself, not his representation. A state of affairs concerning Humphrey or a singular proposition about Humphrey is a state of affairs or a proposition directly involving Humphrey in the sense that Humphrey himself, not his representation, ﬁgures in it. This, of course, does not mean that actualism of this type is completely satisfactory. It still has to face the challenges, inter alia, of giving a non-circular characterization of consistency (provided that reduction of modality is intended), accounting for possibilities about mere possibilia, and either living with the primitiveness of states of affairs or propositions, or giving non-circular characterizations of them. 1. 5 . THE DE RE AND THE DE DICTO Actualists are averse to mere possibilia. One way to reveal the non-straightforwardness resulting from their aversion is to point out how similar mere possibilia are to actual individuals, about which actualists have no qualms. Lewis employs this strategy, and I approve of it. But there is another way. It is to point out how similar mere possibilia are to non-actual possible worlds, about which actualists also have no qualms. Let me illustrate the ﬁrst way before explaining the second. (1) Aristotle is possibly polka-dotted. (1) ascribes possible polka-dottedness to Aristotle. It says of Aristotle that he is possibly polka-dotted. It is an assertion of possibility de re, where the res is Aristotle and the possibility is the possibility of being polka-dotted. The truth of an assertion of possibility is analyzed in terms of the truth at some possible world. So, to say of Aristotle that he is possibly polka-dotted is to say of Aristotle something that is true if and only if at some possible world he is polka-dotted. We say that (1) is true. So we say of Aristotle that at some possible world he is polka-dotted. Let us take as the representative of actualism the theory which deﬁnes a possible world as a maximally consistent set of propositions. Our discussion does not hinge on the idiosyncrasies of this theory not shared by the other actualist theories. This actualist theory will have us say that the singular

Modal Realism

17

proposition about Aristotle that he is polka-dotted is a member of some possible world. (2) Noman is possibly polka-dotted. (2) is very similar to (1). The only difference is a difference between ‘Noman’ and ‘Aristotle’. Prima facie this difference should not affect the general shape of the truth condition. It seems that (2) asserts concerning Noman that he is possibly polka-dotted, and that this is to assert concerning Noman something that is true if and only if at some possible world he is polka-dotted. If this is so, then the actualists should have us say that the singular proposition about Noman that he is polka-dotted is a member of some possible world. But of course, they cannot, for if they did, their theory would not be actualist. The availability of a singular proposition about a particular res presupposes the availability of the res, but Noman is not available as a res to the actualists. Their very actualism stands in the way of a smooth and uniform treatment of possibility de re. Now for the second way, consider: (3) Possibly someone is polka-dotted. (3) is dissimilar to (1). (3) does not ascribe the property of being polka-dotted to any individual. It does not make an assertion of possibility de re at all. Instead, it is customarily said to make an assertion of possibility de dicto, where the dictum is the proposition that someone is polka-dotted. The actualist truth condition is then straightforward: (3) is true if and only if the proposition that someone is polka-dotted is a member of some possible world. Note that to say that (3) makes an assertion of possibility de dicto whereas (1) makes an assertion of possibility de re is not to say that in (3) what is said to be possible is a proposition but in (1) it is an individual. To think that it does would be a gross misunderstanding of the terminology of de dicto and de re, and, of course, the actualists are free from such misunderstanding. Possibility de dicto simply is possibility of a proposition being true, whereas possibility de re is possibility of a singular proposition being true. In either case, a proposition is involved, and this is congenial to actualism. A moment’s scrutiny, however, reveals that there is more to the distinction between the de dicto and the de re. (4) Aristotle is polka-dotted. (4) expresses a singular proposition. That singular proposition not only is about Aristotle but also says of him that he is polka-dotted. We may well put this by saying that (4) says of a particular individual that the property of being polkadotted is possessed by that individual. Something very similar to what has just been said of Aristotle can be said of the dictum whose possibility is asserted in (3). (5) Someone is polka-dotted. (5) expresses a proposition. That proposition is not about any particular individual but is about things in general and says of things in general that they are such

18

Modal Realism

that someone is polka-dotted.23 We may well put this by saying that (5) says of a particular item that the property of being such that someone is polka-dotted at it is possessed by that item. The item in question is not an individual but a possible world. Which particular possible world it is depends on the context in which (5) is used or considered. If (5) is used or considered without any modal element made explicit in the discourse, it is the actual world. If (5) is used or considered with respect to an antecedently introduced and currently salient possible world, it is that world. The actualists do not hesitate to postulate a non-actual possible world at which someone is polka-dotted, so that (3) comes out true. The nonactuality of such a possible world does not deter them. Why, then, should the non-actuality of Noman deter them from postulating him? Possible worlds are possessors of monadic properties (e.g. the property of being such an x that someone is polka-dotted at x). Individuals are possessors of monadic properties. Both possible worlds and individuals are possessors of monadic properties. If one embraces non-actual possible worlds as possessors of monadic properties, one should also embrace non-actual individuals as possessors of monadic properties. The actualists would be quick to respond that the non-actual possible worlds they postulate are not non-actual possessors of properties, monadic or not. They would insist that non-actual possible worlds are actual possessors of properties. All maximally consistent sets of propositions, including all non-actual possible worlds, are actual objects, they would insist. This is where the true lack of straightforwardness of their theory is revealed. They endeavor to account for non-actual possibilities in terms of actuality. This goes against the straightforward way to treat non-actual possibilities, according to which non-actual possibilities, by their very nature of non-actuality, go beyond actuality. I say more about this in 1.7. 1 .6 . NON-CONSTITUENT MODAL REALISM Non-individual constituent realism is realist on possible worlds but not realist on mere possibilia. Individual constituent realism without overlap, such as Lewis’s theory, is realist on both possible worlds and mere possibilia but not realist in an important sense, due to its treatment of modality de re. Individual constituent realism with overlap seems incoherent, as Lewis argues.24 One question is: is there a modal realist theory that is at least as realist as individual constituent realism and also realist in an important sense? Another question is: is there a 23 Things in general in the sense similar to the ﬁrst sense in which Penelope Mackie uses the word ‘things’ in Mackie 2006: p. v, namely, the state of the universe at large. Mackie uses the phrase ‘the state of the world in general’ to elucidate her meaning but I believe my wording expresses what she has in mind more accurately. 24 But again, see McDaniel 2003.

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modal realist theory than which no other modal realist theory is more realist in any sense, i.e. is there a modal realist theory that is fully, or maximally, realist? I shall save the second question for another occasion but propose to answer the ﬁrst question in the afﬁrmative. I shall sketch a modal realist theory that is realist on possible worlds and on mere possibilia, and is also realist in an important sense, providing a non-representationist treatment of modality de re. Take Lewis’s theory. According to it, possible worlds are akin to places. Let us say that Humphrey was in Minnesota when he lost the election. Minnesota is part of North America, so he was also in North America. North America is part of Earth, so he was on Earth. Earth is part of the Milky Way, so . . . If we continue in this manner, we will come to an end point, where we reach a maximally large place in which all of us, including Humphrey, are located, and that maximally large place is our actual world, according to Lewis. (Here I am ignoring the temporal maximality for the sake of simplicity.) Non-actual possible worlds are just like our actual world: maximally large places in which their inhabitants are located. Thus in Lewis’s theory, possible worlds are like Minnesota, just fantastically larger. Minnesota is a place, and so is a possible world. A place is a concrete physical thing, and so is a possible world. The actual world is one place, and non-actual possible worlds are other places. If one has this basic conception of a possible world, it is easy to hold the view that Humphrey exists wholly at the actual world and only at the actual world. If Humphrey is wholly in Minnesota, no part of him is in any place entirely separate from Minnesota, say, California. So, if Humphrey wholly exists at the actual world, no part of him exists at any other possible world, for every possible world is entirely separate from every other possible world, according to Lewis. This forces Lewis to employ counterpart theory in order to make sense of modality de re, hence the failure of realism in an important sense results. Dispensing with possible worlds conceived as concrete physical things is an important ﬁrst step toward a deeper realist theory. Humphrey was in Minnesota, for he was (let us suppose) in Minneapolis and Minneapolis is in Minnesota. But he was in Minneapolis because he was located at a much smaller human-shaped spatial region in Minneapolis (assuming that his loss was a more or less instantaneous event during which he scarcely moved). That human-shaped spatial region does not have a conventional name, so let us give it the name ‘R’. R is not a concrete physical thing. Minneapolis could change location within Minnesota, for example, as a result of a massive earthquake or a draconian civil engineering project like the moving of the Czech town of Most during the 1960s in order to facilitate lignite mining. But R could not change its location. As a spatial region, R’s spatial location is essential to it. (Or so we assume.) The smallest spatial regions are spatial points. They have no extension, only location. I think we should conceptualize possible worlds as more like spatial regions, including spatial points. A parallel point can be made about temporal locations. Lewis’s possible worlds are spread out in time as well as in

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space. It is less easy to confuse a temporal region with an event occupying it than to confuse a spatial region with a city occupying it. Few would identify the stretch of time during which the Second World War occurred with the war itself. Nonetheless, it is important to note that temporal regions, including the smallest temporal regions, namely, moments of time, are not concrete physical things. We should model our thinking of possible worlds after our thinking of temporal regions, including moments of time, and not our thinking of individuals, events, and states of affairs occupying temporal regions. Spatial and temporal regions are constituted by smaller spatial and temporal regions, and ultimately by spatial and temporal points. Humphrey, Kaplan’s automobile, and Salmon’s Noman are not spatial or temporal regions. They are concrete individuals. They are not the kind of things that constitute spatial or temporal regions. Conceptualizing possible worlds after spatial and temporal regions means, among other things, refusing to have concrete individuals constitute possible worlds, and in general, refusing to have anything constitute possible worlds. The only exception might be a possible world being constituted by other possible worlds in a way analogous to the way in which a spatial or temporal region is constituted by other spatial or temporal regions. But possible worlds are not entirely like spatial and temporal regions, and the idea of smaller possible worlds constituting a larger possible world seems much less intelligible than the idea of smaller spatial and temporal regions constituting larger spatial and temporal regions. I do not know whether there is a way to make such an idea ultimately intelligible for possible worlds, and I prefer to avoid the issue altogether. Thus I propose to conceptualize possible worlds not after any old spatial and temporal regions but more speciﬁcally after spatial and temporal points. Spatial and temporal points have no constituents except themselves, and neither do possible worlds. 1 . 7 . EXTERNALISM Modal realism is motivated by a largely externalist semantic outlook broadly understood. Betty knows little about serious running, let alone internationallevel competitive distance running. In your living room Betty happens to glimpse at a short article on the pages of a popular sports magazine’s special issue on the greatest athletes in the world in the last century. After a cursory look at the article, she turns to you and says, ‘Abebe Bikila was a great Ethiopian runner’. You nod with agreement. Why? Because she uttered not gibberish but a grammatical English sentence with a deﬁnite meaning. Its meaning and her use of it are such that her utterance is true if and only if Abebe Bikila was a great Ethiopian runner. You understand this. You also believe that Abebe Bikila was a great Ethiopian runner. So you conclude that she said something true, hence the nod. The important part of this little story is that Betty’s utterance of the name ‘Abebe

Modal Realism

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Bikila’ refers to Abebe Bikila, the ﬁrst marathoner to repeat as Olympic champion, and not to anyone or anything else. She knows little about Bikila beyond the fact that he was a great Ethiopian runner and was called ‘Abebe Bikila’. There are other great Ethiopian runners, say Haile Gebrselassie, and she could not tell Bikila from Gebrselassie. Still her utterance of the name ‘Abebe Bilika’ refers to Bikila, not Gebrselassie. The reference of her utterance of the name is not completely determined by what is internal to her; what is internal to her does not determine any unique Ethiopian runner, let alone the right one. Whatever completes the determination of the reference is external to her. This is an example of externalism about reference.25 There is another kind of externalism, which concerns predicates. Suppose that Betty is not only uninformed about distance running but also uninformed about medical matters. After attempting a running program for ﬁtness for a short while, she complains, ‘I can’t run anymore. My thigh hurts too much. It must be arthritic.’ Her doctor corrects her, ‘Arthritis is a joint disease. You cannot be arthritic in your thigh.’ Betty knows little about being arthritic. She is certainly not able to distinguish it from a host of other medical conditions. Yet her utterance of the word ‘arthritic’ is not meaningless. She succeeds in communicating the thought that her thigh is arthritic. That is, her word ‘arthritic’ expresses the property of being arthritic. The expression of this property by her utterance of the word ‘arthritic’ is not completely determined by what is internal to her. In this sense, the expression of the property transcends what is internal to her.26 These examples of externalism are well-known examples in philosophy of language and mind. The next example of externalism is also from philosophy of language but more relevant to modal realism and of a different kind. Unlike the previous two, it is usually not discussed as a species of semantic externalism at all. But inasmuch as the semantic encompasses all that pertains to the relation between a language and what the language represents, and in particular, the relation between a linguistic expression and its intension, the next example should count as an example of semantic externalism, at least in the broad sense of the phrase. An expert paleontologist says today, ‘Dinosaurs lived 80 million years ago’. The sentence as she utters it is true at the time of utterance (today) if and only if dinosaurs lived 80 million years before today. Assume that the meaning of her sentence is completely determined by what is internal to her, that is, she has complete mastery of the meanings of the words ‘dinosaur’, ‘live’, etc., so that the kind of semantic externalism of the previous examples of ‘Abebe Bikila’ and ‘arthritic’ does not apply here. Yet another kind of semantic externalism does 25 Externalism of reference should be distinguished from externalism of content. My point here is only about determination of reference. On both of these matters, see Donnellan 1972; Kaplan 1978; Kripke 1980; Putnam 1975; Burge 1979. 26 A famous example of ‘arthritis’ is due to Burge 1979.

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Modal Realism

apply. The truth condition for her sentence does not transcend what is internal to her in the sense that its complete speciﬁcation requires no information that is not available inside her head, but the obtainment of the truth condition goes beyond not only what is internal to her but also what is internal to the circumstances relative to which the truth value of her sentence is evaluated. Her sentence is true at a time t (today) if and only if a certain situation (dinosaurs living) obtained at a different time related to t in a certain way (80 million years before t). The obtainment of the condition for her sentence’s truth today requires something that goes beyond what happens today. In this sense, the truth of her sentence transcends the circumstances of its truth-value evaluation. The phenomenon of tense is obviously responsible for this in a way that is routine and undisputed by common sense.27 It is important to note that the truth-conditional variety of externalism we are concerned with is not the same in kind as a certain familiar claim about many predicates such as ‘is an uncle’ and ‘is not alone’. In order for ‘Mel is an uncle’ or ‘Mel is not alone’ to be true, there must be something other than Mel. The truth conditions go beyond Mel. But this merely means that such predicates express extrinsic properties. Possession of an extrinsic property requires the existence of something else that bears a certain relation to the possessor, but that something else, as well as the possessor, are still internal to the circumstances of evaluation. The relevant externality of truth-conditional externalism is externality beyond the circumstances of evaluation, whereas the extrinsicness of an extrinsic property only takes us outside the possessor of the property but holds us well within the circumstances of evaluation. What is common to the three varieties of externalism is that the semantic item in question (reference, property, obtainment of truth condition) requires transcendence and is as real as what it transcends. In the ﬁrst two cases, Abebe Bikila and the property of being arthritic are as real as Betty and what is internal to her. In the third case, the obtainment of the truth condition for the paleontologist’s utterance is as real as today and what goes on today. Since the truth condition involves a past time, that past time, 80 million years before today, is as real as today. As noted before, this last case is the most relevant to modal realism. We take the paleontologist’s utterance seriously as being true today. We take it to be really true today. This commits us to the reality today of the past time, as the past time is integral to that condition of truth. Thus, taking her utterance seriously as true today commits us to the reality of a time external to today. We should note that the reality of a time external to today should be understood as the reality the time has today, not the reality the time had 80 million years ago but not any more. After all, we take her utterance seriously as being true today.

27

sense.

That is why presentism, the claim that all that is real is present, is highly contrary to common

Modal Realism

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(I touch on this point again toward the end of Chapter 5.) More generally, we may characterize externalism as follows: Let X be a certain item, P a class of properties for X to possess, and Y a certain item with respect to which X’s possession of a member of P is relativized. The determination of which member of P X possesses with respect to Y transcends the total internal facts about X and Y. The total internal facts about X and Y are the total internal facts about the composite object constituted by X and Y. They include the total internal facts about X, the total internal facts about Y, and the total relational facts involving just X and Y. Now we are in a position to state the externalist motivation for modal realism. We take certain (utterances of) modal sentences of the form ‘Not actually but possibly P’ seriously as actually true. That is, we take them to be really true at the actual world. Just as the real truth now of sentences of the form ‘Not now but in the past P’ commits us now to the reality of past times, this commits us at the actual world to the reality of non-actual possible worlds. In connection with the question of the reality of mere possibilia, we should recall that the real truth of the paleontologist’s utterance requires the real obtainment of the truth condition for the utterance, which in turn requires the reality of everything the truth condition involves. The truth condition involves not only a past time but also dinosaurs. So, dinosaurs are real. Modal realists are motivated to regard mere possibilia as real in the parallel manner.28 I hasten to add that reality does not entail existence. Dinosaurs are real but (though they existed) they do not exist. Mere possibilia are real but (though they possibly exist) they do not actually exist. Existence will be discussed in Chapter 3. 28

For more on this and impossibilia, see 8.8.

2 Time, Space, World 2 . 1. METAPHYSICAL INDICES I have suggested that modal realists should model their theory of possible worlds by regarding them as being on a par with spatial and temporal points in an important metaphysical respect, namely, alethic relativization. I subsume spatial and temporal points (as well as extended regions) and possible worlds under the common heading metaphysical indices. I shall not offer a deﬁnition of the notion metaphysical index, for I do not think the notion can be deﬁned in an informative and non-trivial yet sufﬁciently general manner. But I can give a brief explication. The main role of metaphysical indices is that of alethic relativizers, i.e. those items to which matters of truth are relativized. Let me try to convey the basic idea without resorting to the notion of truth. A metaphysical index is a metaphysical region (extended or not) at which things in general are (or were or will be) a certain way. I am seated in front of my computer and polar bears are (still) roaming on arctic ice shelves. I and the polar bears are not the only things that count when I say that things in general are a certain way. You, France, and the Golden Gate Bridge are also included, and so are the planet Earth, its constituent molecules, and many other things. All these things are a certain way now but were a certain other way a year ago, and will be yet another way a year from now. The notion metaphysical index is a generalization of this idea. It presupposes the relativity of things in general being a certain way; things in general are a certain way only relative to something or other. That something or other relative to which things in general are a certain way is a metaphysical index. France is a republic now but was not in 1777. That is, France is a republic at the temporal index that is the current temporal region, but was not at the temporal index that is 1777. In other words, the English sentence ‘France is a republic’, as I actually utter it now, is true at the temporal index, now, but not at the temporal index, 1777. I consider these three statements to be equivalent to one another and feel free to switch back and forth among them. In particular, I sometimes ﬁnd it convenient to speak in the metalinguistic mode rather than in the object-linguistic mode: for example, ‘The sentence “France is a republic” is true at time t’ rather than ‘France is a republic at time t’. What is expressed in the metalinguistic mode is a special case of things in general being a certain way at an

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index, for sentences are among the things in general and being true is among the ways things are or are not. Our focus is metaphysics, not semantics, so the metalinguistic mode of speech is a device of convenience, nothing more, and should be accepted without serious risk of misunderstanding. 2 . 2 . TIME Times include both extended temporal regions (periods of time) and temporal points (moments of time). Things in general, including me, polar bears, you, France, the Golden Gate Bridge, Earth, its constituent molecules, and so on are a certain way now. Things in general were not the same way in the past. I was walking from the parking lot to my ofﬁce at a certain past time, and not seated in front of my computer as I am now. France was once a monarchy but not now. Things in general were different at some past time than they were at another past time. Things in general will also be different at a future time from how they are or were: for example, Earth revolves around a star now but at some future time it will not. In short, things in general are (or were or will be) different at many different temporal indices. We have the most familiarity with and sensitivity to temporal indices among all metaphysical indices partly because of the prevalence of the linguistic phenomenon of tense. In English we cannot even formulate a grammatical sentence without committing ourselves to a particular grammatical tense of the main verb in most cases. When we use an expression designating a past (present or future) time, we have no choice but to use the past (present or future) tense for the matching verb, except in some isolated cases such as a command (e.g. ‘Be at the front desk at noon’). Dinosaurs roamed in the Cretaceous Period. Human beings live on Earth in the twenty-ﬁrst century. No vertebrate animal will live in the solar system in the twentymillionth century. Apart from a variety of tenses, there are also a number of temporal quantiﬁers, such as ‘sometimes’, ‘always’, ‘never’, ‘often’, ‘rarely’, etc. Earth’s moon is sometimes between Earth and the sun, i.e. at some times Earth’s moon is between Earth and the sun.1 The universe has always been expanding, i.e. at every past time (since the big bang) the universe was expanding and at the present time it still is. Human beings will never be outside the Milky Way, i.e. at no future time will human beings be outside the Milky Way. It is important to separate the signiﬁcance of the word ‘now’ from the present tense. This is common knowledge among philosophers of language but it is 1 The word ‘sometimes’ means ‘at some times’ (plural) not just ‘at some time’ (singular). ‘It sometimes rains in England’ is true at a temporal period p if and only if for some times t1, t2,…, tk in p, ‘It rains in England’ is true at t1, at t2,…, and at tk, where 1< k. For the meaning ‘at some time’, the word ‘sometime’ is more appropriate: e.g. ‘Sometime in the past London was bombed heavily’. Cf. ‘Some day all this will be yours’.

26

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worthwhile to remind ourselves. There is an obvious connection between the word ‘now’ and the present tense, of course; whenever we use ‘now’, the matching verb has to be in the present tense. (There is a use of ‘now’ which does not call for the present tense: for example, ‘She burned the last bridge she had just crossed. Now there was no turning back.’ We shall ignore this kind of use.) To appreciate the semantic difference between ‘now’ and the present tense, we need to be clear about the distinction between the time of utterance and the time of truth-value evaluation. When we say at a time t that dinosaurs roamed by uttering the sentence ‘Dinosaurs roamed’, t is the time of utterance. The sentence, so uttered, is true as evaluated at the time of utterance, t, if and only if the present-tensed sentence, ‘Dinosaurs roam’, is true as evaluated relative to some time before t. The past tense is understood in terms of the present tense and a past time of truth-value evaluation. The present-tensed sentence, ‘Dinosaurs roam’, is in fact true as evaluated at some time t’ before t, so the original pasttensed sentence is true as uttered at t and evaluated at t.2 Obviously the sentence, ‘Dinosaurs roam’, or any sentence remotely resembling it, was not uttered at t’, but this is entirely irrelevant, for evaluation does not entail utterance. Next consider the sentence ‘Jane will be taller than she is’ (where ‘she’ is coreferential with ‘Jane’), said of a growing child. Charitably interpreted, the sentence is true as so uttered. The sentence, as uttered at a time t, is true as evaluated at t if and only if the present-tensed sentence ‘Jane is taller than she is’ is true at some future time t’. But ‘Jane is taller than she is’ is not true at any time of evaluation, past, present or future, as long as the two occurrences of ‘is’ are understood to ﬂag the same time of evaluation. Since the ﬁrst occurrence of ‘is’ is the occurrence of the main verb of the sentence, it has to be evaluated with respect to the future time, t’. So the charitable interpretation of the sentence demands that the second occurrence of ‘is’ be evaluated with respect to some other time, and it is obvious that the right time of evaluation has to be the time of utterance. Our use of the word ‘now’ in this connection will leave no doubt about this: ‘Jane will be taller than she is now’ as uttered at t is true as evaluated at t if and only if the present-tensed ‘Jane is taller than she is now’ is true as evaluated at some future time t’, and the latter is the case if and only if Jane is taller at t’ than she is at t. The word ‘now’ directs us to the time of utterance irrespective of the tense of the main verb. To put it differently, the present tense ﬂags the time of evaluation, whereas ‘now’ ﬂags the time of utterance.3

2 The semantics of the past tense is a little more complicated than this, and some further details are given in 5.3. 3 The pioneering work on the semantics of ‘now’ is due to J. A. W. Kamp 1971.

Time, Space, World

27

2 . 3 . SPACE There are two key differences between temporal indices and spatial indices. Time is one-dimensional but space is (at least) three-dimensional. Natural language contains tense but lacks a spatial equivalent of tense. As far as we know, time is one-dimensional and space has three dimensions (or more). Moreover, the one dimension of time seems to have a particular direction. Our consciousness seems to track the temporal dimension naturally in one direction. Time seems to us to ﬂow, from the past to the present then on to the future.4 Causation also seems to track this same direction in time; backward causation is highly problematic. There is no corresponding directionality to space. Our consciousness does not track any spatial dimension naturally or in any speciﬁc direction. No one spatial dimension is privileged, and space does not seem to us to ﬂow in any particular direction along any particular dimension. Causation does not seem to favor any spatial direction over the others. Times, as temporal indices, are either temporal points (moments of time) or temporal intervals (periods of time), and the latter comprise multitudes of the former. Spatial indices are likewise either spatial points or spatial regions, and the latter comprise multitudes of the former. Things are a certain way at some spatial points or regions and not at others. Unlike times, however, spatial indices are easily confused with what occupy them. We may ordinarily say that things are a certain way in San Francisco but not in Los Angeles. This may tempt us to regard San Francisco and Los Angeles as spatial indices. But San Francisco is a city, not a spatial index; likewise with Los Angeles. When someone says, for example, that cable cars transport people in San Francisco, we should not understand her utterance by regarding San Francisco as a spatial index and interpreting her as saying that things are a certain way (the cable-cars-transport-people way) at that index. Instead we should regard her mentioning San Francisco as a way of specifying a spatial region and interpret her as saying that things are a certain way at that region.5 San Francisco occupies a certain (vague) spatial region at a time. Such a region has no conventional name, and the easiest way to specify it is by referring to the most obvious and easily noticed thing which occupies it, namely, San Francisco.6 A similar phenomenon occurs when a news reporter says, ‘Washington’s response to the declaration by Pyongyang was muted’. What the reporter means to say, and should be interpreted as saying, is that the United States government’s response to the declaration by the North Korean 4 In a different way of conceptualizing the ﬂow of time, time seems to ﬂow in the opposite direction, from the future to the present then on to the past. In which direction time really seems to ﬂow is not a question which concerns us. 5 Graeme Forbes does likewise (1989: 37). See his n. 22. 6 This may be thought of after the model of Quine’s deferred ostension and termed deferred reference. See Quine 1969: 39–41.

28

Time, Space, World

government was muted. The reporter speciﬁes the United States government by referring to the capital of the nation, and the North Korean government by referring to the capital of that nation. In this case, the two governments are easily speciﬁable independently of their capitals, but the names of the capitals are shorter, and the reporter risks little chance of misinterpretation, for it is common knowledge that cities do not issue declarations or respond to them but governments do.7 Things become slightly more complicated when we consider spatial indexing combined with temporal indexing by means of a period of time instead of a moment of time. Cable cars transported people in San Francisco in the year 2000. Here temporal indexing by a time period, as well as spatial indexing, is involved. (Notice how easy it is to specify the temporal index by means of a conventional designator of the period of time in question, ‘the year 2000’. Unlike the spatial case, there is no need to refer to an event or state of affairs which occupied that year.) What is the relevant spatial index? It is not the spatial region occupied by San Francisco in 2000, for there is no unique such region. San Francisco has been moving away slowly from the American continent and into the Paciﬁc Ocean. If we delineate San Francisco by means of longitudinal and latitudinal degrees at one time, the same coordinate numbers will not accurately delineate San Francisco at another, sufﬁciently distant time. When San Francisco has shifted its position a little to the west, it no longer occupies the exact spatial region it used to occupy. Also, and more dramatically, San Francisco is ﬂying through cosmic space at a phenomenal speed relative to a sufﬁciently non-local inertial frame, due to the rotation of Earth, the movement of the solar system, the rotation of the Milky Way, and so on. San Francisco keeps occupying different spatial regions of the universe in rapid succession. None of us will ever specify the same such region twice by referring to San Francisco or anything else we can readily refer to in ordinary discourse. Thus, there is no unique spatial region which San Francisco occupied throughout 2000. But there is a set of spatial regions each of which San Francisco occupied sometime during 2000. So strictly speaking, we should say that our sentence, ‘Cable cars transported people’, is true with respect to the set of spatial regions occupied by San Francisco and with respect to 2000 if and only if cable cars transported people in a sufﬁcient number of the members of the set in 2000.8 To do so, however, would be tedious and largely pointless for our purposes. Therefore, we shall forgo the strict way of speech and speak of the truth of the sentence with respect to the spatial region occupied by San Francisco instead of a set of spatial regions occupied by San Francisco. In fact, it is convenient to go even further and 7 The name ‘San Francisco’ may be used to specify the city government, rather than the spatial region, the way ‘Washington’ is used to specify the national government. ‘San Francisco issued many marriage certiﬁcates to homosexual couples’ is an example. 8 It is not entirely clear exactly what the sufﬁcient number should be. It is not implausible to suggest that it should be one.

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speak of the truth of the sentence with respect to San Francisco instead of the spatial region occupied by San Francisco, unless the distinction between a spatial region and its occupier is important to the discussion. Let such loose speech not cause any misunderstanding.9 There is no spatial analog of tense. I may say, ‘It is raining in Los Angeles and also it is raining in London’. The sentence ‘It is raining’ in this very form may easily be used to say something literally true with respect to the spatial region of utterance and also about some other spatial region. The main verb need not change its form. Nor do we need to add an extra item to the sentence or subtract some item from it. This in effect is equivalent to there being only one spatial analog of tense, namely, the analog of the present tense. The present tense ﬂags the time of evaluation as the relevant time to ﬁgure in the truth condition. Correspondingly, the evaluation of ‘It is raining’ (as uttered wherever) with respect to a spatial index (Los Angeles or London) ﬂags that same spatial index as the relevant spatial index to ﬁgure in the truth condition. For a different type of example, consider the sentence, ‘Earth is wet’. Is it true?10 It is not entirely false, as ‘The sun is wet’ is. It is not entirely true either, for the Sahara desert and Earth’s inner core are parts of Earth and are not wet. A plausible way to deal with this is to say that the sentence is true or false, depending on which part of Earth is in question. There is a parallel with the temporal case. The sentence, ‘Yesterday it was sunny in London’, may be true or false, depending on which part of yesterday is in question: for example, true at noon but false at 12:15 p.m. Using spatial indices, we say that ‘Earth is wet’ is true at (the spatial region occupied by) the Paciﬁc Ocean, and is false at (the spatial region occupied by) the Sahara desert or the inner core. Here is another example: ‘China is tropical’ is true at (the spatial region occupied by) Guangdong, for Guangdong is part of China and is tropical. ‘China is tropical’ is false at (the spatial region occupied by) Heilongjiang, for Heilongjiang is part of China and is not tropical. ‘China is tropical’ is not true at the spatial region occupied by Cuba, for even though Cuba is tropical, it is not part of China. If (the spatial regions occupied by) large spatial parts (Guangdong, Heilongjiang) of a large thing (China) can be understood as spatial indices to which ascriptions of properties to the thing are relativized, the same should hold of small spatial parts of a small thing. Take a piece of cloth that is a token of the ﬂag of Poland. ‘The piece of cloth is red’ is true at the lower half of the cloth and false at the upper half of 9 An alternative to relativizing the truth of the sentence to a set of spatial regions is to relativize it to a spatiotemporal region. It may be said to have the additional beneﬁt of conforming to the relativity theory. It also sanctions our practical decision to speak of San Francisco as if it were the relativizer of the truth of the sentence, for the city more or less precisely occupied the spatiotemporal region in 2000. See the penultimate paragraph of 2.4. 10 Do not say that it depends on what the speaker has in mind. What the speaker intends to say is one thing, and what the sentence she utters says as she utters it is another. We are concerned with the latter, not the former.

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the cloth.11 There are expressions quantifying over spatial indices. The sentence ‘The piece of cloth is red all over’, as normally understood, is true as evaluated at a spatial region R if and only if for every chromatic part (part which can be colored) x of the cloth occupying R, ‘The piece of cloth is red’ is true as evaluated at the spatial region occupied by x. ‘The piece of cloth is red all over’ is true as evaluated at the lower half of the cloth and false as evaluated at the upper half. The sentence ‘The piece of cloth is partly red’, as normally understood, is true as evaluated at R if and only if for some chromatic part x of the cloth occupying R, ‘The piece of cloth is red’ is true with respect to the spatial region occupied by x. ‘The piece of cloth is partly red’ is true as evaluated at the entire cloth and false as evaluated at the upper half of the cloth.12 There is a kind of use of the word ‘there’ which makes it the closest spatial analog of the present tense. It ﬂags the spatial region of evaluation as the relevant spatial region to ﬁgure in the truth condition of a sentence containing it. The sentence ‘Cosmic rays surge there’, in which ‘there’ is used in that particular way, is true as evaluated at a spatial region R if and only if cosmic rays surge at R. The word ‘there’ also has a different, demonstrative use, as explained in the next paragraph. There is a kind of use of the word ‘here’ which makes it the closest spatial analog of the word ‘now’. When so used, ‘here’ ﬂags the spatial region of utterance. The sentence ‘Cosmic rays surge here’, in which ‘here’ is used in that particular way, is true as uttered at a spatial region R and as evaluated at a spatial region R’ if and only if cosmic rays surge at R. But ‘here’ has another use, which makes it function as a demonstrative. Suppose that we are in Los Angeles and looking at the map of California. Pointing at the area marked ‘Lake Tahoe’, you say, ‘Here is the clearest body of fresh water in California’. Your sentence, as so uttered, is true if and only if the clearest body of fresh water in California is in the spatial region occupied by Lake Tahoe, not Los Angeles (or the spatial region of evaluation, whatever that may be). The word ‘here’ in such a use refers not to the spatial region of utterance, or the spatial region of evaluation as such, but to the spatial region demonstrated on the map. Substituting ‘there’ for ‘here’ while keeping everything else the same in this example would change nothing of relevance and provide an example of the demonstrative use of ‘there’. The word ‘now’ does not seem to have a corresponding demonstrative use. Suppose that we are looking at a chronological chart of the evolution of life on Earth. A misinformed fan of ancient reptiles says, ‘Dinosaurs are still alive now’. Her sentence, as uttered at a time t, is true at t’, for any t’, if and only if dinosaurs are still alive at t. This means, of course, that her sentence, so uttered, is false. Pointing at the area marked ‘the Cretaceous Period’ on the chart and uttering 11

It is the other way around for the ﬂag of Indonesia. ‘The piece of the cloth is partly red’ is true as evaluated at the lower half of the cloth, even though no chromatic part of the lower half of the cloth is non-red. We are not reading ‘partly red’ as meaning ‘partly red and partly not red’. 12

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the tense-adjusted sentence, ‘Dinosaurs were still alive now’, would not help her make a true utterance. The word ‘now’ in her mouth stands for the Neogene Period, the period in which her utterance occurs, if it stands for any geological period, no matter what period is clearly and unambiguously demonstrated on the chart, or in any other representational system, to accompany her utterance of it. Replacing ‘now’ with ‘then’ would make her utterance true, provided that she pointed at the right part of the chart. The word ‘now’ seems to be strictly token-reﬂexive,13 always standing for the time of utterance. The word ‘here’, on the other hand, seems to be very close in meaning to the indexical phrase ‘this place’, where the indexical word ‘this’ may function either token-reﬂexively or demonstratively.14 But consider our earlier example: ‘She burned the last bridge she had just crossed. Now there was no turning back.’ It might be argued with some plausibility that this example sentence contains an occurrence of ‘now’ that is demonstrative rather than token-reﬂexive. It does not appear to be clearly false to suggest that ‘now’ functions as ‘this time’, where ‘this’ is directed at the time of her having burned the last bridge. If ‘now’ turns out to be more like ‘here’ than not, I will happily accept it, for the parity of the two words will only buttress the parity of spatial and temporal indices. 2 . 4 . TIME AND SPACE Some might wish to point out an important dissimilarity between time and space so as to cast doubt on my grouping them together under the label ‘metaphysical indices’. They might point out that ordinary objects persist through time (exist at different times) without changing places. For example, an airplane sits on the tarmac at Heathrow Airport from midnight to noon GMT. But, they might continue, ordinary objects do not persist through space (exist at different places) without existing at different times. But this is muddled thinking. To begin with, we have distinguished spatial points and regions from places. If an airplane is parked at Heathrow from midnight to noon, it remains in one place from midnight to noon but occupies many different spatial regions in succession during those twelve hours, due to the rotation of Earth, etc. The loose talk according to which we deliberately conﬂate Heathrow and the spatial region it occupies has its place but not here. We need to stick to the strict way of speech here.

13 Hans Reichenbach (1947) coined the term ‘token-reﬂexive’. The semantic content of a tokenreﬂexive term relative to a context of utterance is an item in that context, such as the agent, place, time, etc., of the utterance. 14 I heard Steven Rieber advocate such an assimilation of ‘here’ to ‘this place’ sometime in the 1990s.

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It is not hard to respond to this, however. My opponents might well say that even if, vastly contrary to fact, Earth, the solar system, the Milky Way, etc., stood still and the airplane occupied the same spatial region from midnight to noon, the difference between time and space would remain. Let us therefore suppose that Earth, etc., indeed stood still and the airplane occupied the same spatial region during the twelve-hour period. It is true that then the airplane would persist through time without changing the spatial region it occupied while it sat at Heathrow. But this does not show that there is an asymmetry between time and space that is important for our purposes. The airplane would be at different spatial regions at the time when it sat at Heathrow at noon, for its fuselage and wings would be positioned at different spatial regions at noon. The airplane would be no less where its fuselage was than you are in the hallway when your left foot is in the hallway and the rest of your body is in the dean’s ofﬁce. You are not entirely in the hallway, for not all of your spatial parts are in the hallway, but this does not mean that you are not in the hallway. The airplane would not be entirely in the spatial region where its fuselage was, for not all parts of the airplane would be there, but this does not mean that the airplane would not be there. It might be retorted, however, that at each time when the airplane existed, all parts of the airplane would exist, whereas it is not the case that at each spatial region where the airplane existed, all parts of the airplane would exist. To this I say that we should distinguish between the spatial parts of the airplane and temporal parts of the airplane. Even though it is true that all spatial parts of the airplane would exist at each of the times of the airplane’s existence, not all temporal parts of the airplane would exist at each of the times of the airplane’s existence. Since not all spatial parts of the airplane would exist at each of the spatial regions of its existence, the parity between time and space obtains. Also, all temporal parts of the airplane during the twelve-hour period would exist at each of the spatial regions where the airplane existed, for we are assuming that the airplane would sit still during that period. Remember that, like your left foot, the fuselage of the airplane would make the airplane exist where it (the fuselage) did, so that each temporal part of the airplane would exist where the fuselage of that temporal part of the airplane existed. My opponents might persist still further. An airplane was at Heathrow at noon GMT, then ﬂew to O’Hare, and was at O’Hare at 8:00 p.m. GMT. The airplane was not at Heathrow and O’Hare at the same time. This suggests the plausible general claim that if an ordinary object changes its spatial location completely from one spatial region to another, it also changes temporal location. Since an ordinary object can certainly change its temporal location completely from one temporal period to another without changing its spatial location (e.g. the airplane sitting still for a while in a stationary universe), this points to an asymmetry between time and space, my opponents might say. But if we press them for a precise formulation of their point which makes it plausible, we discover it to be

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elusive. Take, for example, the initially promising suggestion that for any ordinary object x, any time t, any time t’, any spatial region p, and any spatial region p’, if x is at p at t and at p’ at t’ and p 6¼ p’, then t 6¼ t’, whereas it is not the case that if x is at p at t and at p’ at t’ and t 6¼ t’, then p 6¼ p’. The latter half of this formulation is plausible. The airplane was at Heathrow at 11:00 a.m. and at noon, but it had not moved an inch. (Remember that we are disregarding the rotation of Earth, etc.) But the former half is not, and the reason is familiar by now. A thing is where its part is. At noon, the airplane was at the spatial region where its fuselage was. The airplane was also at the spatial region where its wings were. And these are different spatial regions. But the plane had not moved. So it was at different spatial regions at the same time. The needed revision of this half of the formulation seems obvious. We need to exclude insufﬁciently inclusive spatial regions from being the values of ‘p’ or ‘p’’: if all spatial parts of x at t are at p, all spatial parts of x at t’ are at p’, and p 6¼ p’, then t 6¼ t’. But this is still not completely satisfactory. If p and p’ overlap, all spatial parts of x could be at p and p’ at the same time by being entirely in the overlapping area. So we need an additional revision: if all spatial parts of x at t are at p, all spatial parts of x at t’ are at p’, and p and p’ do not overlap, then t 6¼ t’. This seems plausible. But for the objection to be effective, the result of switching time and space should not be plausible. If we switch time and space, we obtain the following. If all temporal parts of x at p are at t, all temporal parts of x at p’ are at t’, and t and t’ do not overlap, then p 6¼ p’. But this is now plausible. Suppose that all temporal parts of x at p are at t. Then no temporal part of x at p is at any time outside t. So, for any time t’ that does not overlap with t, no temporal part of x at p is at t’. So, if all temporal parts of x at p’ are at t’, then p 6¼ p’.15 How about those cases in which an ordinary object shifts its position slightly, diminishes in size slightly, or grows in size slightly, so that its new position shares a common area with its old position? We want to say that even in such cases, the time of the new position must be different from the time of the old position. If all spatial parts of x at t are at p, and either some sub-spatial-region of p is occupied by some spatial part of x at t but not occupied by any spatial part of x at t’ or some spatial region not included in p is unoccupied by any spatial part of x at t but occupied by some spatial part of x at t’, then t 6¼ t’. The corresponding timespace-reversed claim is: if all temporal parts of x at p are at t, and either some subtemporal-period of t is occupied by some temporal part of x at p but not occupied by any temporal part of x at p’ or some temporal period not included in t is unoccupied by any temporal part of x at p but occupied by some temporal part of x at p’, then p 6¼ p’. This is as plausible as the non-reversed claim. Both claims are indeed consequences of Leibniz’s Law of Identity. In each case, the key

15 This argument is invalid if x has no temporal part at p’ at t’. We are assuming that x does have some temporal part at p’ at t’, naturally.

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part of the claim is, schematically put, ‘If A occupies B at z and A does not occupy B at z’, then z 6¼ z’.16 If someone objects to our treatment of temporal and spatial points and regions as separate indices on the relativistic ground that time and space are not separable, we may choose to speak of spatiotemporal points and regions as a uniﬁed type of index. We may then say, for example, that cable cars transported people at each of the spatiotemporal regions occupied by San Francisco in 2000. Other statements concerning temporal and spatial indices may be rephrased along the same lines.17 An ordinary object is not identical with its actual spatiotemporal whole, namely, the actual sum consisting of all of its spatiotemporal parts. The actual spatiotemporal sum is only a proper part of an ordinary object. The actual spatiotemporal sum is to the object what the spatial sum, or the temporal sum, is to the spatiotemporal sum. The object is larger; it has more parts not included in the actual spatiotemporal sum. Among those parts are spatiotemporal sums at other possible worlds. That is, the object has not only actual spatiotemporal parts but merely possible spatiotemporal parts as well. This does not mean that the object is identical with its spatiotemporal-possible-world whole, but a full discussion of this point must wait until Chapter 8. 2 .5 . METAPHYSICAL INDICES AMONG ALETHIC INDICES A proposition is identiﬁed as what is said. There are two kinds of sayer: sentence and speaker. Correspondingly, there are two ways to identify a proposition: as what a sentence says, and as what a speaker says. This does not mean that there are two kinds of proposition, sentence-kind and speaker-kind. All propositions are uniform in nature. One and the same proposition may be said by a sentence and said by a speaker. Propositions are the primary bearers of truth values; they are what are true or false in the most basic sense. Other bearers of truth values bear truth values in a non-basic, secondary sense. For example, a sentence has a particular truth value by virtue of the fact that it expresses a proposition which has that truth value.

16 The same situation holds for the claim covering further cases in which an ordinary object shifts positions of its parts without shifting its overall position—a` la the rotation of a completely circular object around its center—and its time-space-reversed claim. An example is a case where a disk is said to occupy the same circular gapless region by having its discrete parts occupy different discrete subregions within the circular region at different times. If all spatial parts at t of some spatial part y of x at t are at p, and some sub-region of p is either occupied by some spatial part y’ of y at t but not occupied by y’ at t’ or occupied by no spatial part of y at t but occupied by some spatial part of y at t’, then t ≠ t’. I omit a statement of the reversed claim. 17 For some classic expositions of the parity of space and time, see Williams 1951; Goodman 1951: 457–72; Taylor 1955.

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Having a particular truth value is not an intrinsic property of a proposition. It is a relational property. Items to which the truth value of a proposition is relative form a motley crew. Let us start with standard kinds of examples: (1) (2) (3) (4)

There are only three eggs. It is raining. Barbara is tall. France is hexagonal.

The truth value of what (1) says is relative to a domain of discourse. What (1) says is false relative to a domain consisting of the content of the neighborhood grocery store but true relative to a domain consisting of the content of my refrigerator. The truth value of what (2) says is relative to a place. What (2) says is true relative to San Francisco but not relative to Los Angeles. The truth value of what (3) says is relative to a comparison group. What (3) says is true relative to a group of 5-year-old children but not relative to a group of NBA players. The truth value of what (4) says is relative to a standard of precision. What (4) says is true relative to a rather loose standard of precision for shapes but not relative to a stricter standard for shapes according to which even the building housing the Department of Defense of the United States is not pentagonal.18 As these examples illustrate, relativity of truth value involves those relativizing factors which are at least as diverse as domains of discourse, places, comparison groups, and standards of precision. And the diversity extends far beyond what these standard examples suggest. Take the sentence: (5) I butter the toast. What (5) says may be true relative to this morning but false relative to this evening. There is a sentence such that what it says is true just if what (5) says is true relative to this morning but its truth does not require relativization to a time. The following is such a sentence: (6) I butter the toast this morning. Relativization to a time is unnecessary because a required temporal element is already included as part of what is said.19 Various existential quantiﬁcations in place of ‘this morning’ will yield further sentences whose truth does not require relativization to a time: for example, (7) I butter the toast sometime today. (8) I butter the toast at some time. Let us consider an example of relativization of truth to an element other than a time. What (6) says may be said to be true relative to an instrument, say a knife, 18 19

See Austin 1962: 142. I ignore subtleties of tense, which would introduce unhelpful complications.

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but false relative to another instrument, say a fork. As with the case of relativization to a time, there is a sentence such that what it says is true just if what (6) says is true relative to the knife but its truth does not require relativization to an instrument: (9) I butter the toast this morning with the knife. Various existential generalizations of (9) in place of ‘the knife’ will also yield further sentences whose truth does not require relativization to an instrument: for example, (10) I butter the toast this morning with a knife. (11) I butter the toast this morning with something. There are other kinds of element with respect to which truth may be relativized, as illustrated by the following sentences: (12) I butter the toast this morning with the knife slowly. (13) I butter the toast this morning with the knife slowly in the drawing room. (14) I butter the toast this morning with the knife slowly in the drawing room while wearing a kilt.20 As we can see from (12)–(14), the part of the sentence corresponding to a relativized element may be any number of different types of adverbial phrase. If what (12) says is true, what (9) says is true relative to the slow mode rather than relative to the fast mode. If what (13) says is true, what (12) says is true relative to being in the drawing room rather than relative to, say, being in the kitchen. If what (14) says is true, what (13) says is true relative to wearing of a kilt rather than relative to, say, wearing of a tutu. All those items, and more, are items to which truth of a proposition may be relative. Times, spatial regions, and worlds are among them. Why are times, spatial regions, and worlds picked out as metaphysical indices among all truth relativizers? What is special about them? The answer is that times, spatial regions, and worlds are features of the universe which permeate it, whereas the other truth relativizers are not. Domains of discourse, comparison groups, and standards of precision are not even features of the universe. They are logical parameters, not metaphysical indices. Places, instruments, action speeds, and sartorial modes are neither permeating features of the universe nor logical parameters. They are simply mundane non-logical relativizers of truth.

20 This sequence of sentences, (5)–(14), is fashioned after Donald Davidson’s famous example sentences in Davidson 1967. Davidson uses his sentences to illustrate the open texture of the logical structures of action sentences and argue for quantifying over events, but I use them to illustrate a different point.

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What is unique about metaphysical indices is their generality. (6) is the result of adding the time-relativizing expression ‘this morning’ to (5). Conversely, (5) is obtained from (6) by deleting the time-relativizing expression. (5) is devoid of any time-relativizing expression. Let us say that (5) is free of T-R (time-relativizing expressions). Similarly, let us say that (1) is free of D-R (domain-relativizing expressions), (2) is free of P-R (place-relativizing expressions), and so on: I-R (instrument- . . . ), A-R (action-speed- . . . ), S-R (sartorial- . . . ), W-R (world- . . . ). We may then speak of a sentence free of x-R, where ‘x’ marks the slot for substituting ‘T’, ‘D’, ‘P’, etc. For any x, if x is a metaphysical index, then truth of what is said by any sentence free of x-R is non-trivially relative to x. On the other hand, if x is a truth relativizer but not a metaphysical index, then truth of what is said by some sentence free of x-R is at best only trivially relative to x. For example, (5) is free of T-R and truth of what it says is non-trivially relative to a time; it may be true relative to one time but not relative to another. Similarly with any sentence free of T-R. (5) is also free of W-R and truth of what it says is non-trivially relative to a world; it is true relative to one possible world but not relative to another. Likewise with any sentence free of W-R. On the other hand, (3) is free of D-R but need not be relativized to a domain for truth. At best, if it is true at all, it is true relative to all domains, making the relativity trivial. (3) is also free of I-R, A-R, and S-R, but need not be relativized for truth to an instrument, action speed, or sartorial mode; any such relativization would be trivial at best. Another mark of a metaphysical index is that any relativization of predication of an individual to it amounts to predication of a part of the individual. (15) Socrates was bald. (16) The Polish ﬂag is red. (17) The sun went supernova in the year 2000. Socrates’s being bald is to be relativized to a time. (15) is true at a certain time, t, late in Socrates’s life but false at another time t’, earlier in his life. This means that Socrates as he was at t was bald but Socrates as he was at t’ was not, which is to say that Socrates at t was bald but Socrates at t’ was not, which in turn amounts to saying that Socrates’s temporal part at t (Socrates’s t-stage) was bald but his temporal part at t’ (his t’-stage) was not.21 The Polish ﬂag’s being red is to be relativized to a spatial region. (16) is true at the lower half of the ﬂag, L, but false 21 Some may think that when we are engaged in temporal-stage talk we should employ a tenseless language and say that Socrates’s t-stage is bald instead of saying that Socrates’s t-stage was bald. Those who may think this way do so perhaps because they believe that the whole point of introducing temporal stages is to free oneself from the tensed language. I do not concur with these people. I believe that when we talk about a past temporal stage of an individual and predicate a property like baldness of that stage we should use the past tense, just as when we talk about a past individual who lived and died in the past and predicate a property like baldness of him we naturally use the past tense. The point of temporal-stage talk is independent of the issue of tense. It is to cash out the effect of temporal relativization of predication in terms of temporally non-relativized predication.

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at the upper half, U. This amounts to saying that the ﬂag’s spatial part at L (the ﬂag’s L-stage) is red but its spatial part at U (the ﬂag’s U-stage) is not. The sun’s going supernova in the year 2000 is to be relativized to a possible world. (17) is true at some possible world, w, but false at another, say @. This amounts to saying that the sun’s modal part at w (the sun’s w-stage) went supernova in 2000 but its modal part at @ (the sun’s @-stage) did not. I hasten to emphasize that this mark of a metaphysical index only concerns concrete individuals. Socrates, the cloth that is a Polish ﬂag, and the sun are all concrete individuals. An obvious example of an object that is not a concrete individual and is a primary subject matter of relativization to possible worlds is a proposition. A certain property, say, truth, may be predicated of a proposition relative to one world but not relative to another, but it hardly seems to make sense to speak of the proposition’s having world-stages one of which is true and another false. For all I know there might be a way to make sense of such speech in a philosophically proﬁtable way, but I do not see it. So propositions are excluded from this consideration. Some people might say that some sentences are about non-spatial objects, such as souls, and that such sentences need not be relativized to spatial regions to be true. Others might say that some sentences are about non-spatial and nontemporal objects, such as sets, numbers, and Platonic forms, and that these sentences need not be relativized to spatial regions or times to be true. These people might be right, especially in the case of Platonic forms. But even if they are, souls, sets, numbers, and Platonic forms are notoriously difﬁcult objects to understand. All sentences about ordinary physical objects, such as rocks and ﬂowers, and books and towers (or collections of ultimate constituents of matter shaped like them22) seem to need relativization to a time and a spatial region to be true, as long as they are not also about souls, sets, numbers, Platonic forms, particular times, or spatial regions. So let us set aside souls, sets, numbers, and Platonic forms as special cases. It is important not to confuse truth-relativizers, including metaphysical indices, with contexts of utterance. Take sentence (2) as an example: (2) It is raining. What (2) says is true relative to a certain time and a certain place, and false relative to a certain time and a certain place. (We are only considering the actual world.) These truth-relativizers, times and places, themselves and their truthrelativizing role are independent of contexts of utterance. Contexts of utterance are useful contrivances of formal semantics, which was invented in the midtwentieth century, whereas times and places have been around much longer and independently of any semantic theory, formal or otherwise. Contexts of utterance are introduced primarily to distinguish the determination of the proposition 22

Cf. Heller 1990; Merricks 2003; van Inwagen 1990.

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expressed by a sentence (what the sentence says) from the determination of the truth value of the sentence.23 A context of utterance partly consists of a time (of utterance) and a place (of utterance). The idea is that, for example, the sentence (2) by itself does not say anything truth-evaluable but says different truthevaluable things when understood with respect to different contexts of utterance, and therefore the determination of the truth value of what (2) says becomes possible only after all the parameters of the context of utterance have been ﬁxed. Not everyone accepts this picture. Those who disagree hold that (2) by itself says something truth-evaluable prior to relativization to a context of utterance. If they are right, the truth value of what (2) says by itself may be determined directly relative to a time and a place, not as contextual factors but as independent relativizers of truth, without ﬁxing any parameters to be provided by a context of utterance. What (2) says by itself is just that it is raining, and this thing, which (2) says, is truth-evaluable relative to a number of truth-relativizers, such as a time, a place, a world, and so on. Here is an example. In a hurricane-watch command center located in Miami, Florida, the chief of operation looks at the computer screen displaying the current weather condition in New Orleans and says to a reporter, ‘It is raining’. Even if the reporter does not know whether the chief has Miami or New Orleans in mind, he knows what the chief said (what her sentence said as she uttered it). And that thing he knows as what the chief said is truth-evaluable. It is, say, true relative to New Orleans and false relative to Miami. The dispute between these two camps24 does not affect the metaphysical status of truth-relativizers, including the metaphysical indices, but taking the truth-relativizers seriously, and in particular incorporating the metaphysical indices into the metaphysics of the truth-evaluable, might provide the second camp some tools to solidify its position. I shall say more on this in 9.2.1. 2. 6 . POSSIBLE WORLDS Possible worlds are metaphysical indices on a par with temporal and spatial indices. They are modal indices. I doubt that the claim that possible worlds are not temporal or spatial indices requires an argument. But if it does, here is one: I took a particular route from the parking lot to my ofﬁce on campus on Tuesday. I could have taken an alternate route on campus on Tuesday. This possibility is explicated in terms of a possible world at which I took the alternate route on Tuesday. Suppose possible worlds are temporal periods. (Temporal points are ignored, as moving from the parking lot to the ofﬁce takes more than a moment. If the stance in favor of 23

Kaplan 1978, 1979b. See e.g. Bach 2001; Cappelen and Lepore 2004; Borg 2004; King and Stanley 2005; and Bach 2006, which is part of a symposium on Cappelen and Lepore 2004 in Philosophy and Phenomenological Research. 24

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analogizing worlds to temporal and spatial points in 1.6 is taken seriously, there may well be no need for an argument after all.) Then I took the alternate route on Tuesday during some temporal period. But I did not. I walked only once from the parking lot to my ofﬁce on Tuesday and it was not on the alternate route. Therefore, possible worlds are not temporal indices. Suppose possible worlds are spatial regions. (Again spatial points are ignored, and again this may mean that we need no argument after all.) Then I took the alternate route on Tuesday in some spatial region. But I did not. I walked only in a particular serpentine region from the parking lot to my ofﬁce on Tuesday and it did not include the alternate route. Therefore possible worlds are not spatial indices. Suppose possible worlds are combinations of temporal periods and spatial regions. Then I took the alternate route on Tuesday during some temporal period in some spatial region. But I did not. I walked only once and only in the serpentine region from the parking lot to my ofﬁce on Tuesday and it did not include the alternate route. Therefore, possible worlds are not temporal-cum-spatial indices. Do we need possible worlds in addition to possible occurrences? Are possible occurrences not enough? Why do we need a possible world at which I took the alternate route on Tuesday? Why is it not enough to have the possible occurrence of my taking the alternate route on Tuesday? The answer is that without possible worlds there would be modal chaos. Someone25 once said that time is nature’s way of preventing everything from happening all at once. Someone (else?) also said that space is nature’s way of preventing everything from happening all in one place. We might as well say that the multitude of possible worlds is reality’s way of preventing everything from being the case all together. Postulating possible occurrences without possible worlds would fail to prevent it. When I say that possible worlds are real, I mean that they are at least as real as temporal and spatial indices. That is, I assume that temporal and spatial indices are real and say that possible worlds are no less real than they are. I can offer no informative explication of the notion real. I consider it an absolutely basic notion in metaphysics. Reality is the comprehensive ultimate subject matter of metaphysics. Fundamental philosophical questions center around a handful of ultimate subject matters of metaphysics. Identity is one such subject matter. Causation is another. But reality is unique among ultimate subject matters of metaphysics in that any serious discussion of any ultimate subject matter of metaphysics is ultimately about reality, or some part or aspect of reality.26 It is crucially important not to confuse reality with actuality. We have noted this already but it bears repeating. All that is actual is real but not all that is real is actual. I took a particular route from the parking lot to my ofﬁce on Tuesday. My having taken that route at that time is actual and real, and my having taken the other route at that time is not actual yet equally real. The reality of my having 25 26

I am told that it was either Henri Bergson or Mark Twain. For discussion of some issues related to the basic nature of the concept reality, see Fine 2001.

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taken the other route makes it a real possibility, and the non-actuality of my having taken the other route makes it a mere possibility. To be clear about the distinction between actuality and possibility, it again helps to consider temporal and spatial indices. I am seated now but was standing a moment ago. At the present time, I am seated. At some recent past time, I was standing. The former is analogous to my having taken the route on Tuesday at the actual world, and the latter is analogous to my having taken the other route then at a non-actual possible world. The atmospheric pressure is rising here but not there. In this spatial region, the pressure is rising. In that spatial region, it is not. The former is analogous to my having taken the route on Tuesday at the actual world, and the latter is analogous to my having taken the other route then at a non-actual possible world. What happens at any of these metaphysical indices is equally real. Possible worlds are not only real but objective; at least as objective as temporal and spatial indices. Objectivity is not only to be contrasted with subjectivity but also to be understood as independence from all human activities in general. The nature of temporal points and periods is not created by human beings or dependent on what human beings do or think. Similarly with spatial points and extended regions.27 They are all objective. I say the same about possible worlds. Reality has an objective temporal dimension, objective spatial dimensions, and objective modal dimensions, independently of human beings. Reality spreads out along the temporal, spatial, and modal axes, as a matter of objective metaphysical fact. The objectivity of the possibility of my having taken the other route on Tuesday calls for the objectivity of modal indices if the latter are to ground the former, as any serious possible-worlds theory of modality should dictate. Possible worlds themselves are independent of human beings, but speciﬁcations of possible worlds are performed by us and are subject to human limitations. We have no direct access to possible worlds and need to rely on indirect means to specify them. This is analogous to the situation when we specify a set of spatial regions not directly by enumerating the spatial points in the regions but indirectly by referring to familiar places, say, San Francisco, which occupy the regions. We almost never specify a single possible world uniquely. (The obvious exception is our actual world. We manage to specify the actual world uniquely in a way analogous to the way we manage to specify the present moment—now— uniquely.28) The reason is that we almost always rely on propositional means to 27

According to Kant, time and space are imposed on things themselves by us in a deep and somewhat mysterious sense of ‘impose’. I do not deny this Kantian thesis. All I deny is that time and space are created by and dependent on our activities the way tables and chairs are. Time and space are not subject to our whim. I am inclined to take more or less what Kant is supposed to have said about the nature of time and space and say it about the nature of possible worlds. But I am not prepared to discuss it. 28 If quantum indeterminacy stands in the way of our referring to a unique totality of what actually obtains, then we cannot even specify the actual world uniquely or the actual world itself is somehow fuzzy.

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specify possible worlds and almost no proposition we can use is true at just one possible world. By referring to San Francisco as it is at a particular moment of time, we specify the set of spatial regions occupied by San Francisco at that time. By designating the proposition that donkeys talk, we specify the set of possible worlds at which donkeys talk.29 2 . 7 . ERSATZ WORLDS The actualist conceptions of a possible world are realist, for the possible worlds they postulate are real. David Lewis calls such worlds ersatz worlds, for they are mere representations of what he takes to be real possible worlds. Ersatz or not, actualists’ possible worlds are real. It is worth noting, however, that some ersatzist conceptions of a possible world do not respect the analogy with time and space. For example, take the ersatzist conception of a possible world as a maximally consistent set of (interpreted) sentences. On that conception, truth of (a proposition expressed by) a sentence at a possible world is deﬁned in set-theoretical terms: S is true at w if and only if S is a member of w. Consider the sentence ‘Pigs ﬂy’. Whether it is true at a given possible world w is solely a matter of whether it is a member of w. So, it is not a matter of whether pigs ﬂy relative to w in the same sense of ‘relative to’ in which whether ‘Pigs ﬂy’ is true at a given time (or spatial region) is a matter of whether pigs ﬂy relative to that time (or spatial region), for this latter matter is not a set-theoretical matter. By this I mean that it is not a non-derivative set-theoretical matter. Almost any matter may be made into a derivative set-theoretical matter. If some pigs ﬂy, the intersection of the set of pigs and the set of ﬂying things is non-empty. I ignore such derivative settheoretical matters. An actualist might decide to say that whether ‘Pigs ﬂy’ is true at a given time (or spatial region) is indeed a set-theoretical matter, namely, a matter of whether the sentence, ‘Pigs ﬂy’, is a member of the set of sentences true at that time (or spatial region). But if this is not to be a derivative set-theoretical matter, it should presuppose a prior notion of a sentence being true at a time (or spatial region), along the following lines. A sentence S is true at t (or p) if and only if S is a member of t (or p). This would not make sense unless times (or spatial regions) are sets of sentences, which they are not. Instead of a maximally consistent set of sentences as a possible world, an actualist might opt for a maximally consistent sentence. The truth of a given sentence S at a given world w then will not be a matter of set-theoretical 29 We speak of just three kinds of metaphysical index: temporal points and periods, spatial points and extended regions, and worlds. I do not know whether they are the only kinds of metaphysical index. Ken Akiba has proposed a novel way to understand the phenomenon of vagueness, which might be interpreted to involve a fourth kind of metaphysical index. Akiba’s indices are modelled after possible worlds but are not meant to ground alethic modalities like necessity and possibility. See Akiba 2000a.

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membership. It will instead be a matter of w’s entailment of S. This avoids talk of possible worlds as sets of sentences and is therefore an improvement. The additional notion of entailment is easily deﬁnable in terms of consistency, so no new primitive is required. Still, this version of actualism, when understood as a conceptual analysis, shares with the set-theoretical version the presumption that consistency is conceptually prior to possibility, and this makes both versions equally undesirable. Of course, as we have observed, most actualists do not regard themselves as proposing a conceptual analysis or explication when they propound their ersatzist rendition of a possible world, or when they choose the possibleworlds framework in the ﬁrst place. But if these actualists are right about the nature of what they are doing, actualism is not a serious alternative to the line of theorizing I am interested in pursuing. Thus, to keep actualism relevant to our discussion, let us continue to assume (or pretend) that it is an attempt to analyze or explicate modal notions. Other actualists characterize possible worlds as maximally consistent propositions. Still others use states of affairs or properties in lieu of propositions. I am more sympathetic to these versions of actualism than to the sentential versions but I am no more satisﬁed by them than by the sentential versions. The reason for the dissatisfaction is my reductionist drive. Propositions, properties, and relations are intensional objects, and I ﬁnd all intensional objects mysterious unless they are reduced to extensional objects. As for states of affairs, they are even less basic than properties or relations. Even if the Wittgensteinian dictum that a world is a totality of states of affairs is true and individuals, properties, and relations have reality only as constituents of states of affairs, states of affairs would have no reality without individuals, properties, and relations. Even if Socrates and snub-nosedness have no reality without being embedded in states of affairs, the state of affairs of Socrates being snub-nosed would have no reality without Socrates and snub-nosedness. 2 . 8. COMPARISON WITH LEWISIAN WORLDS David Lewis famously says: The world we live in is a very inclusive thing. Every stick and every stone you have ever seen is part of it. And so are you and I. And so are the planet Earth, the solar system, the entire Milky Way, the remote galaxies we see through telescopes, and (if there are such things) all the bits of empty space between the stars and galaxies. There is nothing so far away from us as not to be part of our world. Anything at any distance at all is to be included. Likewise the world is inclusive in time. No long-gone ancient Romans, no longgone pterodactyls, no long-gone primordial clouds of plasma are too far in the past, nor are the dead dark stars too far in the future, to be part of this same world. Maybe, as I myself think, the world is a big physical object; or maybe some parts of it are entelechies or spirits or auras or deities or other things unknown to physics. But nothing is so alien in

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kind as not to be part of our world, provided only that it does exist at some distance and direction from here, or at some time before or after or simultaneous with now.30

What he calls ‘the world we live in’ and ‘our world’ is the actual world, and there are other worlds than the actual world. On Lewis’s theory, a possible world is a mereological sum of all that is spatiotemporally related. So, different possible worlds are spatiotemporally unrelated to one another. Lewis’s conception of a world is akin to that of a place in the sense of a spatial object: ‘The worlds are something like remote planets; except that most of them are much bigger than mere planets, and they are not remote.’31 In contrast, my conception of a world is akin to that of a spatial point (or extended region at best), not something that occupies it. What Lewis describes in the ﬁrst quotation above I call the universe, or more accurately, the actual-worldstage of the universe. The universe is a vast object which extends at least spatially and temporally. You and I are part of it, and so are the remote galaxies and the ancient Romans. But the universe is not a possible world. It is instead the comprehensive subject of possibility and necessity. When we say that possibly (or necessarily) P, for any P, we are saying that the universe is possibly (or necessarily) such that P. The universe is one way at one possible world, and another way at another possible world.32 The universe extends in modal dimensions, as well as in the spatial and temporal dimensions. What Lewis calls ‘our world’ is the universe as it actually is, i.e. the universe as it is at the actual world. In Lewis’s system there are many objects like what he calls ‘our world’, and he calls them ‘possible worlds’. In my system there are many objects like the universe at the actual world, and they are the same universe at various possible worlds. That is, there are many objects like the actualworld-stage of the universe, and they are different world-stages of the same universe. Possible worlds themselves are not objects like the universe or the inhabitants of the universe. They are just such that the universe is a certain way at, or with respect to, them. The universe is a particular way at w if and only if the w-stage of the universe is that way. I regard what Lewis calls ‘possible worlds’ as modal parts of one and the same universe. The universe’s modal parts are not possible worlds, but the universe itself as it is at possible worlds, its world-stages. The universe’s spatial or temporal parts are not spatial regions or temporal regions, but the universe itself as it is at such regions. Lewis’s modal space (what he calls ‘logical space’, the collection of all Lewisian possible worlds and all possible objects existing at them) contains many concrete objects each of which is uniﬁed by spatiotemporal (or some other more general natural) relatedness and which do not together form a single possible object. My modal space (collection of all possible worlds I embrace and all objects existing at them) contains many concrete objects all of which are modal parts of one and the 30

Lewis 1986: 1. Ibid. 2. 32 I do not mean to suggest that if the universe is one way at w1 and the same way at w2, then w1 and w2 are the same world. I do not mean to deny it either. 31

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same universe. Some of them may be uniﬁed by spatiotemporal relatedness, some may be uniﬁed by some other relation, and some others may not be uniﬁed by any relation other than being part of the universe and whatever that requires. When we say that things in general could have been such that P, we are implicitly alluding to the comprehensive subject of possibility by ‘things in general’, and I am calling that comprehensive subject ‘the universe’. We may even choose to understand sentences of the forms, ‘It is actually the case that P’, ‘It is possibly the case that P’, and ‘It is necessarily the case that P’, as implicitly alluding to the universe by interpreting the so-called dummy pronoun ‘it’ as not so dummy but as pointing to the modally extended comprehensive subject of modality de dicto: ‘The universe is such at the actual word that P’, ‘The universe is such at a possible world that P’, ‘The universe is such at every possible world that P’.33 Lewis himself disavows any useful analogy between possible worlds and times, but does not disavow a useful analogy between possible worlds and places. Lewisian worlds are indeed more like places, as we noted earlier, but it is a mistake to think that there are no important dissimilarities between Lewisian worlds and places. For example, many ordinary objects are in different places at different times but no ordinary object is at different possible worlds at different times, according to Lewis. Also, ordinary objects are in different places at the same time. For example, there are wild horses in Mongolia and some of them are also in the Gobi Desert, but Mongolia and the Gobi Desert are different places. We do not need overlapping places to have examples of ordinary objects in different places at the same time, as we noted earlier with the airplane example. A wild horse is where its head is and also is where its legs are. If someone should insist that the horse is only partially where its head is (i.e. only a part of the horse is where its head is), then we should only note that, according to Lewis, ordinary objects are not even partially in different possible worlds at any time. All parts of every ordinary object are conﬁned to a single Lewisian world at all times. Furthermore, the fact that different places overlap with one another already marks a difference between places and Lewisian worlds, for no two Lewisian worlds overlap at all. On Lewis’s view, all different possible worlds are, by deﬁnition, spatio-temporally unrelated. Are any two possible worlds spatiotemporally related on my view? The short answer is ‘Yes’ but the short answer may be misleading. The space and time of one world are the same as the space and time of many other worlds. Space and time permeate many different worlds. The space and time that exist at the actual world, however, do not exist at some remote possible worlds, being replaced by alien space and time, or no space or time at all (if that is possible). Consider Jane as she is in a spatial region r at a time t at a world w1, and John as he is in r at t at a different world w2. Is Jane as she is at w1 spatiotemporally related to John as he is at w2? It depends on what is meant by ‘spatiotemporally related’. 33

This is not a proposal in semantics, let alone syntax, of natural language.

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Jane at w1 is in r at t, and so is John at w2. They are in the same region at the same time. They are also in the same universe, albeit at different modal points. In that sense they are certainly spatiotemporally related. However, Jane at w1 could not reach and touch John at w2, or anyone or anything at w2, no matter how fast or how far she travels through space and time at w1. No space-time travel by Jane at w1 would land her at any world other than w1. I do not know whether there is a sense of ‘spatiotemporally related’ which requires the possibility of touching for objects to be spatiotemporally related, at least for ordinary objects. But if there is, then in that sense Jane at w1 is not spatiotemporally related to John at w2. The claim that Jane at w1 could not touch John at w2 is a modal claim and as such it is subject to a possible-worlds analysis: Jane at w1 could not touch John at w2 if and only if at no possible world does Jane at w1 touch John at w2. But Jane at w1 only exists at w1 and John at w2 only exists at w2, and even if John may exist at w1 or Jane at w2, John at w1 is not John at w2, or Jane at w2 Jane at w1. (Such is the way we are using the locutions ‘Jane at w1’ and ‘John at w2’. The former means ‘Jane’s w1-stage’, and the latter ‘John’s w2-stage’.) So, there is no possible world at which Jane at w1 and John at w2 both exist, let alone exist in close proximity. This is a straightforward consequence of the fact that anything that exists at a certain possible world exists at that world and only at that world as a thing existing at that world. This differentiates possible worlds from the other two kinds of indices. Let us suppose that Kathy is in Helsinki and Ken is in Hanoi. To avoid unnecessary complications, we may also assume that they are in their respective cities at the same time, say, now, and at the same world, say, the actual world. Let r1 be the humanshaped spatial region occupied by the part of Helsinki where Kathy is now, and r2 the human-shaped spatial region occupied by the part of Hanoi where Ken is now. Jane at w1 is conﬁned to w1 and as such could not touch John at w2, who is conﬁned to w2. In contrast, Kathy at r1 now is conﬁned to r1 now but could touch Ken at r2 now, who is conﬁned to r2 now. Here is why. The spatial relations between r1 and r2 are contingent; assuming that the geometry of space is contingent, if the space of which r1 and r2 are part were different, the spatial relation between r1 and r2 might be different. In particular, at some possible world the space is folded in such a way that r1 and r2 are in close proximity now so that anything at r1 now touches anything at r2 now. If there is such a possible world, there is such a possible world where Kathy occupies r1 now and Ken occupies r2 now; or so we assume. Thus at some possible world Kathy at r1 now touches Ken at r2 now. That there is this difference between modal indices and spatiotemporal indices is not surprising, as we are assuming that the notion of spatiotemporal relatedness in question involves modality, namely, touchability.34

34 It is important not to confuse Kathy at r1 now with Kathy at r1 now as she is at the actual world (Kathy’s actual-world-stage). The latter is not at any possible world but the actual.

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Let us remind ourselves that Lewis’s conception of a possible world is akin to the actualist conception in one important respect. It concerns modality de re. Lewis analyzes ‘x is F at w’ in terms of x’s counterpart at w; x is F at w if and only if x’s counterpart at w is F (except when ‘F’ is a special predicate like ‘existent’). The counterpart of x at w represents x at w, and this makes representation play a crucial role in the truth conditions for modalities de re. Actualists also analyze ‘x is F at w’ in terms of x’s representation; according to the linguistic version of actualism, x is F at w if and only if the sentence ‘Æ is F’ is true at w, where ‘Æ’ refers to x. The term ‘Æ’ represents x at w, which makes representation crucial in this theory. The version of modal realism I defend differs from both Lewis’s theory and actualism in this regard. Earlier I put the difference simply as the absence of representation in its account of modality de re. Here let me put it differently. The version of modal realism I favor analyzes ‘x is F at w’ in terms of x itself, but this does not mean that the notion of representation has no place at all in this analysis. Representation is narrowly Lagadonian just if the representative is identical to the represented. Lewis calls this simply ‘Lagadonian’.35 Narrowly Lagadonian representation is self-representation. Representation is broadly Lagadonian just if the representative is identical to a part of the represented, i.e. the representative is identical to either the represented or a proper part of the represented. Broadly Lagadonian representation is representation of a whole by a part. On my version of modal realism, x is F at w if and only if x’s world-stage at w is F. A modally extended individual is represented at w by its world-stage at w. A world-stage of x at w is a modal part of x. So, the version of modal realism I favor analyzes modality de re in terms of broadly Lagadonian representation.36 This modal realist conception of modality de re is an integral part of the modal realist conception of the relation between the universe and possible worlds. Start with a particular individual, say, you, as you actually are. The broadly Lagadonian representational analysis of modality de re applies to modalities concerning you. The same applies to modalities concerning a larger plurality of individuals, say, all that are near the surface of Earth. This will continue to hold as we move up in spatial size, to the contents of the Solar System, the Milky Way, the Virgo Supercluster, and so on. Increasing the span of temporal period will not change the applicability of the broadly Lagadonian representational analysis of modality de re: the contents of the twenty-ﬁrst century, the Holocene, the Cenozoic Era, the Phanerzoic Eon, and so on. Eventually we reach the entire universe as it actually is, what Lewis calls ‘the actual world’. But this object is (or this plurality of objects as considered together are) only a proper part of a much larger whole 35

Lewis 1986: 145. If narrowly Lagadonian representation were used instead of broadly Lagadonian representation, the resulting theory would be more like a modal analog of endurantism than a modal analog of the four-dimensional-worm view. See McDaniel 2003. 36

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extending through modal space, just as your actual-world-stage is only a proper part of a much larger whole that is you extending through many possible worlds. This object has different properties at different modal indices, just as you do. The modal indices are worlds. This object, the modally extended universe, is distinct from any world, just as you, a modally extended individual, are distinct from any world.

3 Existence 3. 1 . DOMAIN RELATIVITY Things being thus-and-so is generally relative to a metaphysical index. Existence is also relative to a metaphysical index. We may speak of something’s existence at a certain time, at a certain spatial area, or at a certain possible world. Actual existence is existence at the actual world. Non-actual possible existence is existence at a non-actual possible world. It is important not to confuse reality with existence. When I say that possible worlds and mere possibilia are real, I do not mean that possible worlds and mere possibilia exist. Reality and existence are not the same; the former is absolute, while the latter is relative. As I said earlier, reality is a rock-bottom-level metaphysical notion. The word ‘reality’ is a label for the comprehensive ultimate topic of metaphysics. It is part of what I mean by ‘ultimate’ that reality is absolute and irreducible. That is why I believe that many apparent disputes about the status of reality in philosophical theorizing are not genuine disputes; they are merely verbal disputes at best. Existence, on the other hand, is neither absolute nor irreducible. In English the verb ‘exists’ naturally expresses existence, but we tend to use the idiomatic expression ‘there is’ to express existence routinely and more often than the pedantic-sounding ‘exists’. Despite this superﬁcial difference in use, the two expressions are identical in meaning; they both mean existence. Some theorists misunderstand this mundane phenomenon concerning our linguistic practice and believe that there is an important semantic difference between the two expressions. Some theorists even propose elaborate logico-metaphysical theories based on the conviction that there are things that do not exist, even though there are not things that there are not and nothing that does not exist exists.1 I agree with such theorists that it is not always contradictory to say that there are things that do not exist. But I do not agree that this is so because ‘there is’ and ‘exists’ do not mean the same. The reason why it may not be contradictory to say that there are things that do not exist is the same reason why it may not be contradictory to

1

The best-known relatively recent example is Parsons 1980.

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say that there are things that there are not, or that things that do not exist exist. Let me explain. Suppose that you check the printer in the ofﬁce, see no paper inside, and say, ‘There is no paper’. I look around the ofﬁce, see a stack of printing paper next to the ﬁle cabinet, and say, ‘There is paper’. You and I are not contradicting each other. According to the most natural way to understand our utterances, they are perfectly consistent with each other. Your utterance is understood to say that there is no paper in the printer, while my utterance is understood to say that there is paper in the ofﬁce. Even though the printer is in the ofﬁce, the ofﬁce contains much more than what is in the printer. The paper I see is outside the printer but inside the ofﬁce. Thus our utterances are both true. This illustrates spatial relativity of existence. Paper exists relative to the interior of the ofﬁce but not relative to the interior of the printer. This is relativity with respect to locations, hence relativity with respect to spatial regions. This illustrates how spatial regions work as existence relativizers. We do not need two speakers or two sentences to make the same point. Suppose that after checking the printer and saying, ‘There is no paper’, you look around and discover the stack of paper by the ﬁle cabinet. You then continue your utterance, ‘but there is paper!’ You have uttered the sentence, ‘There is no paper but there is paper’, which is true as properly understood under the supposed circumstances.2 Examples which illustrate relativity with respect to times are equally commonplace. There was paper in the printer yesterday but there is no paper in the printer today. Paper existed in the printer relative to yesterday but does not exist relative to today. Unlike the relativity to locations, the relativity to times is often marked by different tenses (‘There was paper . . . but there is not . . . ’). But this is inessential, as the time of the paper’s presence and the time of its absence may well be both in the past or both in the future. It is instructive and quite useful to cast the relativity of existence in somewhat different yet familiar logical terms. W. V. Quine famously said that to be is to be the value of a variable.3 He expressly intended this slogan to encapsulate the ontological commitment of a theory already regimented in a formal language of quantiﬁcational logic. If we want to know what objects such a theory is committed to, all we need to do is to look at the values of the variables in the theory. Variables range over a given domain, and a complete speciﬁcation of a theory by means of a quantiﬁcational language should include a speciﬁcation of a particular domain. Since every item in the domain is eligible to be the value of a variable ranging over the domain, Quine’s slogan comes to be the claim that a theory is ontologically committed to what is in the domain. This claim has been widely accepted, while some regard it as almost trivial.4 I am not concerned with evaluating Quine’s claim or discussing it any further as it was originally intended. 2 3 4

For more on this and related issues, see Yagisawa 1993. Quine 1963: 15. e.g. Haack 1978: 43–9.

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Rather, I propose to appropriate Quine’s slogan, separate it from his original intention, and reinterpret it as a claim about existence rather than about the ontological commitment of a theory. So transformed, it says that what exists is what is in the domain. Existence is thus relative to a domain. Since we are no longer concerned with the ontological commitment of a theory, the domain is up for grabs. Whatever domain may be in question, existence relative to that domain is inclusion in the domain. This domain-relativity of existence should not be considered to be a competitor to the relativity to metaphysical indices. For instance, we may easily recast the ofﬁce example in those pseudo-Quinean terms by saying that paper exists relative to the domain consisting of things in the ofﬁce but does not exist relative to the domain consisting of things in the printer. I subscribe to David Lewis’s dictum that the domain may easily shift with the pragmatic wind.5 Every use of an existence predicate is subjected to the pragmatic wind which may well shift at any moment, and therefore its proper understanding needs to be adjusted constantly according to the way the pragmatic wind happens to be blowing over it. We are now ready to see how it may not be contradictory to say that there are things that there are not, or that things that do not exist exist. One may assert, ‘There are things that there are not’, slowly and in such a way that the pragmatic wind shifts during the assertion just so to make two different domains, D1 and D2, relevant to the evaluation of the occurrence of the existence predicate in the main verb phrase of the sentence and to the evaluation of the occurrence in the relative clause, respectively. Unless D1 is empty or is a subset of D2, some item in D1 is outside D2, and if so, the asserted existence sentence, ‘There are things that there are not’, is true. Since D1 may well be non-empty and fail to be a subset of D2, the sentence is consistent. Mutatis mutandis for the sentence ‘Things that do not exist exist’. Existence is not a property but a relation: x exists in relation to a domain D if and only if x is in D. If D is a set, the in relation is the membership relation. This is the standard conception. But some may prefer to think of a domain as a mereological whole. Under such a conception, the in relation is the mereological part-of relation. Yet another conception of a domain is to regard it as a plurality. On this conception, talk of a domain consisting of certain individuals is talk of those individuals in a special, plural way. It does not involve anything other than those individuals; not the set of those individuals, the mereological sum of those individuals, or any other object that somehow results from those individuals. It involves a special way of speaking of them all at once.6 This conception has an 5 David Lewis was the ﬁrst to publicize this kind of relativity of existence claims and put it to substantial metaphysical use: ‘part of the ordinary meaning of any idiom of quantiﬁcation consists of susceptibility to restrictions; and restrictions come and go with the pragmatic wind’ (1986: 164). See also Quine 1940; Sellars 1954; Davies 1981; Neale 1990. 6 This way was investigated by George Boolos. See Boolos 1984, 1985. For a more recent overview of the matter, see McKay 2006.

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advantage over the set-theoretical and mereological conceptions (and any other conception that postulates an additional object over and above the individuals in the domain) for being the most ontologically parsimonious. I shall not choose any particular conception of a domain.7 I shall use the word ‘collection’ as a neutral term to characterize a domain. All physical objects are temporal objects; they exist at certain times. Times are metaphysical indices responsible for objects being temporal objects; times make objects temporal objects by being such that those objects exist at them. Times are makers of temporal objects, but they are not temporal objects themselves. It is improper to say of a time that it exists at a time. To say that a certain time t, for example, this very moment, exists is not to say that t exists at some time, not even at t.8 This has two implications. First, it is nonsensical to say that t always exists, where ‘always exists’ means ‘exists at every time’. Second, since t does exist, there must be a domain for the existence predicate to range over that is other than a collection of things that exist at a time. It should be a collection of times. Likewise, to say that a certain world w exists is not to say that w exists at some world, not even at w. It is nonsensical to say that w necessarily exists, where ‘necessarily exists’ means ‘exists at every world’. Since w does exist, there must be a domain other than a collection of things that exist at a world. It should be a collection of worlds. Sometimes it is said that the domain is the totality of what is being talked about, or is under discussion. I emphatically reject this. When we say under normal circumstances that talking donkeys do not exist, talking donkeys are under discussion and the domain for ‘exist’ includes only actual objects, none of which are talking donkeys. Throughout the book, I use the existence predicates and say things like ‘There is this-and-that’ and ‘Such-and-such exists’. I do not always specify the intended domain explicitly, for doing so would be tedious and unnecessary. But we should always bear in mind that every use of an existence predicate needs to be understood with respect to a certain domain, explicitly or implicitly.

7 Even though my nominalistic predilection tends to favor the last conception, I am fond of the set-theoretical conception for its familiarity and wide applicability. 8 To say so is somewhat akin to saying that liquid water is wet. Many philosophers have used ‘Water is wet’ as an example of an obvious truth about water. When I ﬁrst encountered the example, I thought it was part of a joke the punch line of which I missed. I have since become used to seeing it in the philosophical literature but am still unable to shake a semantically uneasy feeling toward it. Liquid water is what makes other things wet, but it itself is not wet. A shirt soaked in water is wet, but the water in which it is soaked is not wet. A wet shirt can be dried, but liquid water cannot be dried. Even solid water, ice, is not wet when not melting. When it is melting and sits in a pool of liquid water, it may be said to be wet. But even then, it is the ice that is said to be wet, not the liquid water surrounding it. It is never true literally to call liquid water wet.

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3. 2 . EXISTENCE AT A METAPHYSICAL INDEX Ordinary individuals typically exist at many metaphysical indices of each of the three kinds: time, space, and world. The airplane at Heathrow exists at many temporal points and periods, many spatial points and extended regions, and many possible worlds. Suppose that it exists at different times t1 and t2 (for example, yesterday and today), different spatial regions r1 and r2 (for example, where its fuselage is and where its wings are), and different possible worlds w1 and w2. The fuselage is not identical with the airplane, but the airplane is where the fuselage is, at r1. The airplane is also where the wings are, at r2, even though the wings are not identical with the airplane. The airplane is at r1 but not wholly at r1, and at r2 but not wholly at r2. The fuselage is the plane’s spatial part, and so are the wings. The airplane is at every spatial region where some spatial part of the airplane is. Similarly for times and worlds. The airplane is at t1 but not wholly at t1, and at t2 but not wholly at t2. The airplane is at every time when some temporal part of the airplane is. The airplane is at w1 but not wholly at w1, and at w2 but not wholly at w2. The airplane is at every possible world at which some modal part of the airplane is. Let us say that an object which extends over different spatial points is a trans-spatial object. Ordinary physical objects are trans-spatial objects. Trans-spatial objects exist at all spatial points or extended regions where their spatial parts exist. Transtemporal objects exist at all temporal points or periods when their temporal parts exist. And transworld objects exist at all possible worlds at which their modal parts exist. Let ‘Pavarotti0’ refer to a transworld individual, existing at various worlds, w1, w2, w3, etc. Pavarotti0 exists at w1, w2, w3, etc., by having modal parts at those possible worlds. So Pavarotti0 possibly exists and is a possible object. But some philosophers reject this.9 These philosophers tend to presume that an object exists at a possible world only if it wholly exists at that world. If we presume this, we will fail to treat metaphysicalindex-relativized existential claims in a uniform manner. For additional illustrations, consider the claim that the USA existed in 1999. The claim is obviously true even though the USA extends over time. The claim that the USA exists between the Atlantic and the Paciﬁc Oceans is true even though Hawaii is part of the USA and is not between the two oceans. The claim that Jane is in the swimming pool may be true even if Jane’s head is not in the pool. If we accept the parity of all three kinds of metaphysical index on this score, then we should conclude that Pavarotti0 exists at some possible worlds and is a possible object.10 9

e.g. Lewis 1986: 210–20; Casati and Varzi 1996. Some take this to mean that we should not accept the parity of all three kinds of metaphysical index on this score. This is an instance of the classic situation known as ‘One man’s ponens is another man’s tollens’. I justify my ponens on the basis of the initial methodological decision to tailor a theory of possible worlds after the fashion of the standard theories of temporal and spatial indices. 10

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3 . 3 . EXISTENCE AND REALITY Ned Markosian begins his article on presentism as follows: Presentism is the view that only present objects exist. According to Presentism, if we were to make an accurate list of all the things that exist—i.e., a list of all the things that our most unrestricted quantiﬁers range over—there would be not a single non-present object on the list. Thus, you and I and the Taj Mahal would be on the list, but neither Socrates nor any future grandchildren of mine would be included. And it’s not just Socrates and my future grandchildren—the same goes for any other putative object that lacks the property of being present. All such objects are unreal, according to Presentism.11

Markosian is using existence and reality interchangeably: according to presentism, all and only present objects exist, and all objects that lack the property of being present are unreal. This is not an isolated phenomenon unique to Markosian. Many philosophers readily regard existence and reality as necessarily equivalent, conceptually equivalent, or perhaps even identical. I am not one of such philosophers. I regard existence and reality as two separate non-equivalent notions. They do not even share the same adicity: existence is dyadic but reality is monadic. In this, I also disagree with some non-philosophers who regard the two notions as non-equivalent. These non-philosophers say that some non-existent things are real and give examples such as Santa Claus, who they claim is real to their small children, or Sherlock Holmes, who they claim is real to them in some sense which, I hope, is different from the sense in which Santa Claus is real to their small children. Such non-philosophers typically have an absolute notion of existence (whether something exists or not is an absolute matter, not relative to anyone or anything), whereas their notion of reality is relative (Santa is real to small children but not to mature adults, Holmes is real to avid followers of the canon but not to indifferent cursory readers). Their notion of existence is thus monadic and their notion of reality is dyadic. They have reversed the adicities of the two notions. Existence is dyadic; it is a relation between a thing and a domain. Reality is monadic; it is absolute. I do not insist that I am correct about the notions of existence and reality or that Markosian or the non-philosophers are incorrect about these notions. To some extent, the matter is stipulative. I ﬁnd using the expressions, ‘exist’, ‘existent’, ‘existence’, ‘is real’, ‘reality’, and their cognates my way to be philosophically fruitful when discussing metaphysical issues. No doubt Markosian ﬁnds his way of using those expressions useful for his philosophical purposes, and the non-philosophers ﬁnd their usage useful for their non-philosophical purposes. The issue is probably not for extended rational debate. It may well come down to a matter of somewhat arbitrary verbal decision. Yet the decision concerns a sufﬁciently fundamental part of any philosophizing that it should be made explicit and 11

Markosian 2004: 47–8.

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understood clearly, lest utterly fruitless pseudo-arguments ensue. I say the issue may be somehow a matter of arbitrary decision but I do not think it is entirely a matter of arbitrary decision. The word ‘exists’ is closely allied with the expression ‘there is’ and the latter expression is widely and routinely used in everyday discourse. So any understanding of the word ‘exists’ that obviously goes against the ordinary usage of ‘there is’ is less ﬁt for philosophical employment than an understanding that does not obviously go against the ordinary usage. The word ‘real’, on the other hand, seems to have a wide range of diverse usage. The range is so wide that it is probably not proﬁtable to focus on and scrutinize a particular usage and judge a given philosophical use according to the degree of conformity to it. The word is more ripe for purely theoretical and stipulative use than the existence predicates. Markosian characterizes presentism by speaking of ‘all the things that our most unrestricted quantiﬁers range over’. His wording is more cautious than that of some other philosophers, who would use the phrase ‘the absolutely unrestricted quantiﬁers’ or ‘the absolutely unrestricted domain for the quantiﬁers to range over’,12 but his intended meaning seems hardly distinguishable from that intended by the other philosophers. I have seen no compelling reason to believe in the absolutely unrestricted, or most unrestricted, quantiﬁers. Such quantiﬁers would range over the correspondingly absolutely unrestricted, or most unrestricted, domain. I am very skeptical of such a domain and refuse to presume that we should take seriously the idea of the absolutely unrestricted, or most unrestricted, domain. I do think that anything at all is ﬁt for being talked about. That is, we may talk about or speak of anything at all, and anything at all may be in the domain with respect to which a given existential quantiﬁer or existence predicate is to be understood. But once a particular domain is ﬁxed and in play, there is always a manner of talk that transcends that domain, thus requiring a more comprehensive domain. I think this is one of the important lessons we should learn from considerations of alethic modality, as we shall see in Chapter 8.13 3. 4. EXISTENCE AND PREDICATION ‘For the fans of NHL, this season has been a disappointing season, for there is no season.’14 This is a crisp example of how ordinary language adheres to the 12 Lewis is another cautious writer on this topic: ‘When [the ersatz modal realist] says that there are no other worlds, and no other-worldly possible individuals, he says it with his quantiﬁers wide open. He means to quantify over everything, without any restriction whatever, ignoring nothing. (And these quantiﬁers too are meant to be entirely unrestricted. I doubt that any perfect disambiguation is possible: all our idioms of quantiﬁcation alike are ﬂexible, subject to tacit restriction.…)’ (Lewis 1986: 137; his emphasis). 13 Rayo and Uzquiano 2006 contains stimulating articles on the topics of an absolutely unrestricted domain of discourse and the availability of an all-inclusive domain of inquiry. 14 Asserted by the host of the program ‘Smart Money’ on the National Public Radio, USA, on 3 Apr. 2005; his emphasis.

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principle that true predication does not require existence. It is not the case that necessarily x is thus-and-so only if x exists. The 2004–5 National Hockey League season was disappointing even though it did not exist. In fact, the season was disappointing because it did not exist. A more explicit formulation of the principle in possible-worlds terms is: it is not the case that for every possible world w, x is thus-and-so at w only if x exists at w. The season was disappointing at the actual world because it did not exist at the actual world. Socrates is dead. Death does not entail non-existence, for a tree may be dead yet stand tall in the forest, existing. But in the case of human persons, death usually results in non-existence, and Socrates is no exception. So, Socrates does not exist. Socrates is both dead and non-existent. Socrates’ being dead is compatible with his non-existence. Socrates’ being dead does not require the existence of Socrates, but it requires Socrates; it is Socrates who is dead. So, we need a way to have Socrates available without his existence in order to make sense of the true predication of death of Socrates. A follower of Alexius Meinong might say that we can have Socrates available by having him subsist, but the Meinongian concept of subsistence applies only to abstract objects and Socrates was not abstract, so this would involve Socrates transforming himself from being concrete to being abstract through death, which is hardly fathomable.15 It also invites general skepticism about subsistence, a different way of being. I think we should say that we can have Socrates available for current predication thanks to his existence at some metaphysical index. He existed at a past time at @, so he existed at two metaphysical indices, at least. This makes him available to us for predication as of now. More generally, anything existing at some metaphysical index is available for predication as of any metaphysical index. David Kaplan points out that in analogy with the fact that ‘a is F’ may be true at a time t even if ‘a’ designates an individual that does not exist at t, ‘a is F’ may be true at a world w even if ‘a’ designates an individual that does not exist at w.16 I endorse Kaplan’s point. We should be careful not to confuse this with a different, stronger claim, the claim that ‘a is F’ may be true at w even if ‘a’ does not designate any individual that exists at w. (I am assuming that ‘a’ designates at most one individual, so if it designates an individual that does not exist at w, it does not also designate another individual that does.) If ‘a’ does not designate anything that exists at w, then either (1) ‘a’ designates something that exists at some other world, or (2) ‘a’ designates something that exists at no world, or (3) ‘a’ designates nothing at all. (2) and (3) make the claim not justiﬁed by Kaplan’s analogy with time, for ‘Socrates’ does designate some individual who existed at some past time. 15 Bernard Linsky and Edward Zalta (1994, 1996) propose that concreteness and abstractness are contingent properties, so that an individual who is a human being, hence concrete, at one possible world might be an abstract object at another possible world. But even they do not endorse the view that at some possible world an individual who is a human being at some time is an abstract object at some other time. 16 Kaplan 1973: 503–5 and 1989: 498. Also, Salmon 1981: 36–40; Fine 1985: 163–8.

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One way to frame a discussion of this issue is in terms of propositions. My ofﬁcial position is that worlds are metaphysically prior to propositions. This prohibits me from speaking of propositions before laying out a more or less complete picture of worlds, strictly speaking. Loosely speaking, however, it is sometimes convenient to engage in proposition talk to communicate easily with those who prefer to couch most philosophical discussion in propositional terms. The principle of predication without existence, as couched in propositional terms, says that a singular proposition about x may be true at a world where x does not exist. A singular proposition about x may either exist and be true at a world where x does not exist, or be true at a world where it itself does not exist. These two alternatives are not equally plausible to everyone. Philosophers who think that all propositions, including singular propositions, are abstract objects and that all abstract objects are necessarily existent will defend the ﬁrst alternative. Other philosophers subscribe to the thesis that any singular proposition about x ontologically depends on x. This may be so because x is a constituent part of any singular proposition about x, or because of some other relation holding between x and any singular proposition about x that is essential to the proposition.17 Those philosophers will oppose the ﬁrst alternative. I oppose the ﬁrst alternative, too. But not for the same reason. My reason is twofold. First, the principle of predication without existence in general (that x may be thus-and-so at w without existing at w) already entails the second alternative (that a singular proposition may be true at w without existing at w) as a special case, where x is a singular proposition and F-ness is truth. The ﬁrst alternative is therefore otiose. Second, I do not think it proper to think of any proposition existing at a world. Here I cannot fully give the reason why, for it requires a full exposition of my views on the metaphysics of propositions, which I shall attempt in Chapter 7 and continue in Chapter 9. Let me just say for now that I construe propositions as collections of worlds,18 and as such, they exist in metaphysical space at large (in my proprietary sense of ‘metaphysical space’, which comprises our modal space, namely, the collection of our local possible worlds, and other alternative collections of other worlds and which is open-ended in an important sense).19

17

Plantinga 1983; Richard 1993; King 1995. For pioneering work on a similar idea for meanings, see Lewis 1970a. 18 An alternative is to construe propositions as the characteristic functions of such collections, where the characteristic function of a collection C is the function which maps any element of C to 1 (‘Yes, it is an element’) and any non-element of C to 0 (‘No, it is not an element’). Recall that I am using ‘collection’ as a blanket term for ‘set, plurality, or mereological sum’. If any one of these different ways of construal proves clearly superior to the others, I shall happily adopt it. Cf. nn. 6 and 7 above. 19 A fuller discussion of metaphysical space must wait until Ch. 8.

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3 . 5 . ARGUMENT BY ITERATION As the NHL example illustrates, the principle of predication without existence is deeply rooted in our commonsensical way of speaking. Here is one argument in support of common sense. The target of the argument is the following principle: (E) For every x, for every possible world w, x is thus-and-so at w only if x exists at w. Here is the argument against (E) in a nutshell: (Premise 1) Iterated world-indexing is redundant. (Premise 2) If iterated-world indexing is redundant, (E) is false. (Conclusion) (E) is false. To say that iterated world-indexing is redundant is to say the following: (R) For every x, for every possible world w1, for every possible world w2, x is thus-and-so at w1 at w2 if and only if x is thus-and-so at w1. The second index, w2, is idle. Before proceeding, we need to dispel doubt concerning (R). Some might doubt the intelligibility of the locution ‘x is thus-and-so at w1 at w2’. For them, ‘at w1 at w2’ hardly makes sense. But consider: (T) P is true at w1. Take Alfred Tarski’s T-schema: ‘S’ is true if and only if Q, where ‘S’ is replaced with a sentence in the object language, and ‘Q’ with its translation in the metalanguage. Tarski conceives this T-schema without regard to the relativity of truth to a world. Once we introduce the relativity, we may generalize his original T-schema to: ‘S’ is true at w2 if and only if Q at w2. Let ‘S’ be replaced with the sentence (T). Then we have: ‘P is true at w1’ is true at w2 if and only if P is true at w1 at w2. This supports the intelligibility of iterated world-indexing of truth, as in ‘P is true at w1 at w2’. Of course the replacement (T) for ‘S’ contains a truth predicate, and this might cause some to pause, for it might prompt them to think that the truth predicates come at different levels in a language hierarchy20 and should not be 20

‘The celebrated hierarchy of languages of Tarski’, as Kripke calls it (1975: 694).

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mixed together willy-nilly. If this concern is to be taken seriously, we should simply stipulate that the truth predicates are not mixed in an inappropriate way. We may do this by using subscripts: ‘P is truek at w1’ is truen at w2 if and only if P is truem at w1 at w2. We should stipulate that the relation among the levels, k, n, and m, be appropriate. Such a stipulation is certainly legitimate and is sufﬁcient for the intelligibility of iterated world-indexing.21 I shall now give two examples to illustrate the wide acceptance the ﬁrst premise enjoys. I shall then argue that the second premise is true. Saul Kripke proposed that Wittgenstein’s example, (M) The standard meter stick is one-meter long, is an example of the contingent a priori.22 Reactions to Kripke’s proposal have been mixed but one particular theoretical position is almost universally deemed untenable, namely, the position which maintains the contingency of (M) while interpreting (M) as saying that the meter stick is one-meter long at the actual world, @. The almost universally accepted reason is that if the meter stick is onemeter long at @, then for any possible world w, the meter stick is one-meter long at @ at w, and vice versa. Alvin Plantinga proposed the notion of Æ–transform.23 The Æ–transform of a property is that same property as indexed to @: for example, the Æ–transform of being a philosopher is being a philosopher at @. It is almost universally accepted that the operation of Æ–transformation produces necessity out of contingency, i.e. if a thing has a property contingently, it has the Æ–transform of that property necessarily. The widely accepted reason is that if x is F at @, then for any possible world w, x is F at @ at w, and vice versa. In both of these cases, not only has the redundancy of iterated world-indexing not been questioned but it has been so widely accepted that any discussion of a related topic has come to presuppose it automatically. Two objections come to mind against this line of reasoning. First, the fact (if it is a fact) that a claim is widely accepted does not show that the claim is true. Perhaps, the philosophers who accept it are wrong and the claim should not be accepted. This objection is well taken and I concede that I have not established the redundancy of iterated world-indexing. But my intention is not so much to establish it as to point out the proper onus of proof. Given the widespread consensus, the burden is on those who hold the contrary view to show that 21 Since we are not trying to derive a paradox or to avoid a derivation of a paradox but are only concerned with the intelligibility of a certain locution, we have no vested interest in a particular relation holding or failing to hold among the levels. 22 Kripke 1980: 54–6, 75–6. 23 Plantinga 1978. See also Plantinga 1974: 62–3, 72–3, for world-indexed properties in general.

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iterated world-indexing is not redundant. In the absence of such a counterargument, it is reasonable to maintain the redundancy claim. The second objection, due to Ben Caplan, casts doubt on my claim that the redundancy claim is in fact widely accepted.24 Those who casually assent to (R) may not have in mind (R) but (R’) instead, strictly speaking: (R’) For every x, for every possible world w1, for every possible world w2, x is thus-and-so at w1 at w2 if and only if x is thus-and-so at w1 and x exists at w2. I shall argue shortly that the second premise (‘If iterated world-indexing is redundant, (E) is false’) is plausible when (R) provides its antecedent. But if we substitute (R’) for (R), that argument becomes unavailable. The merit of Caplan’s objection is that it shifts the burden back onto me. The objection is not that a majority of philosophers in fact believe (R’) instead of (R), but that I offer no reason why they should not. An appropriate response therefore should offer such a reason, and here is one: why should the existence of the meter stick at any other world matter to its length at @? If it is one-meter long at @, then it is onemeter long at @ relative to any world, irrespective of its existence at that world. Let me put this more carefully. The standard meter stick is one-meter long at @. From this it trivially follows that for any x, x is such that the standard meter stick is one-meter long at @, irrespective of whether the standard meter stick is longer than x, is heavier than x, or exists at x. For example, the standard meter stick is not longer than you and not heavier than you, but you are such that the standard meter stick is one-meter long at @. The standard meter stick does not exist at you (it is even doubtful that it is fully intelligible to say that the stick exists at you), but you are such that the standard meter stick is one-meter long at @. Let x be a world w, and we have: w is such that the standard meter stick is one-meter long at @. That is, the standard meter stick is one-meter long at @, at w. This last move is justiﬁed by the generalization of the following move: @ is such that the standard meter stick is one-meter long, so the standard meter stick is onemeter long at @. Another way to look at this is to think of all world-relativized truths, like the truth that the meter stick is one-meter long at @, as truths belonging to modal space at large rather than to any particular world. So, from the ‘point of view’ of modal space at large, the meter stick is one-meter long at @, which means that relativization to any particular world is otiose inasmuch as the world belongs to modal space. In other words, to say that the meter stick is onemeter long at @ at w, for an arbitrary possible world w, is a slightly misleading way of saying that the meter stick is one-meter long at @ from the ‘point of view’ of modal space at large. As for Æ–transformation, Caplan argues that Plantinga himself intends the (R’)-wise interpretation of the associated truth conditions 24

Caplan 2007.

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rather than the (R)-wise interpretation. He may well be right, but the question is whether Plantinga or anyone else should so interpret them. Here I see little difference from the meter-stick case. Instead of speaking of truth of a proposition, speak of possession of a property, and the above responses will go through mutatis mutandis.25 I now argue for the second premise. Let us distance ourselves from the wellworn Nixon–Humphrey example for a change. Al Gore lost the pivotal presidential election to George W. Bush in the United States in the year 2000, but Gore could well have won it.26 Thus: (1) Gore lost at @. (2) For some possible world w, Gore won at w. Against this familiar background, consider the following consequence of (R): (RR) For every possible world w1, for every possible world w2, Gore lost at w1 at w2 if and only if Gore lost at w1. Consider also the following consequence of (E), where x is Gore and ‘x is thusand-so’ is ‘x lost at @’: (EE) For every possible world w, Gore lost at @ at w only if Gore exists at w. (RR) and (EE) jointly entail: (RE) For every possible world w, Gore lost at @ only if Gore exists at w. But (RE) is false. It is easy to see why. There is some possible world w at which Gore does not exist. Given (RE), it follows that it is not the case that Gore lost at @. This contradicts (1). Therefore, if (R) is true, (E) is false.27 25 A different opposition to my argument is mounted in McCarthy and Phillips 2006. The crux of their objection depends on a particular take on existence. This chapter makes it clear that I do not share their way of understanding existence, and given my way of understanding existence, which is coherent and not without plausibility, the core of their objection melts away. 26 Some might insist that Gore did win it, but we shall not discuss the issue. 27 There is a parallel argument against the counterpart-theoretic version of (E): (EC) For every x, for every possible world w, x is thus-and-so at w only if x’s counterpart exists at w. If x’s counterpart at w is not identical with x, x is said to be thus-and-so at w in absentia (Lewis 1986: 9–10). The corresponding counterpart-theoretic versions of (EE) and (RE) say ‘only if Gore’s counterpart exists at w’ instead of ‘only if Gore exists at w’. The rest of the argument goes through as before, provided that Gore lacks a counterpart at some possible world.

4 Actuality 4 . 1 . ACTUAL SO-SEIN The actual world according to Lewis is what he calls ‘the world we live in’ in the famous passage quoted in 2.8. Lewis also says that the actual world is ‘I and all my surroundings’.1 As noted already, it is not what I call ‘a possible world’, let alone ‘the actual world’. It is rather what I call ‘the universe as it actually is’. It is a modal part of the universe, a part of the universe at the actual world, the universe’s @-stage. Robert Stalnaker has a different disagreement with Lewis. Stalnaker says: 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 solipsism, based on a restrictive theory of what there is room for in reality, but rather on the metaphysically neutral belief that ‘the actual world’ is just another name for reality.2

Such usage of the phrase ‘the actual world’ as Stalnaker’s is wildly non-standard. It is not only contrary to Lewis’s usage but also contrary to the actualist usage, according to which the actual world is just one abstract object among many, for example, just one maximally consistent set of propositions among many maximally consistent sets of propositions. It is contrary to modal semantics, in which the actual world is just the mundane modal relativizer of truth. And it is unnecessary even for Stalnaker, for, as Stalnaker himself observes, he does not mean by the phrase anything different from what he means by the word ‘reality’. Stalnaker’s basic mistake is to think that the phrase ‘the actual world’ has an ordinary-language pre-theoretical meaning that is relevant to philosophical theorizing about possible worlds in modal metaphysics. As the ofﬁce example in Chapter 3 illustrates, ordinary non-modal utterances of existential sentences are easily and routinely understood without serious difﬁculty. This is so because the contexts surrounding such utterances tend overwhelmingly to make the relevant domain perspicuous. In everyday life we

1

Lewis 1973: 86.

2

Stalnaker 1976 in Loux 1979: 229.

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rarely need to be concerned with domains larger than the domain consisting of things in the vicinity of the surface of Earth. The relevant domain in ordinary speech is almost always vague but the vagueness almost never hinders correct and smooth communication. (Vagueness probably often helps lubricate smooth real-time communication.) Astronomers, by contrast, have to include myriad things from all corners of the universe in the domain relevant to their non-modal theoretical discourse. But even cosmologists whose work spans the whole history of the universe in its entirety need include only those things which are actually a certain way—for example, expanding, collapsing, having 300 solar masses, being a billion light-years away from Earth, etc.—in the domain relevant to their nonmodal theoretical discourse. The largest such domain, call it D, might be said to be the domain that delineates actual existence: for any x, x actually exists if and only if x exists relative to D. The actual world might then be deﬁned as the metaphysical index at which things exist if and only if they actually exist. This would have the disadvantage of being dependent on the discipline of cosmology and what cosmological objects the cosmologists are interested in. It has two undesirable consequences. First, it would automatically exclude abstract objects not relevant to cosmology from actually existing. By choosing to use the word ‘universe’ the way I have been using it, I do not intend to foreclose the actual existence of any abstract objects. Second, it would exclude quotidian objects, such as my favorite socks and your house keys. Inclusion of all other scientists in addition to the cosmologists will help cover many objects outside the interest of the cosmologists but will not guarantee full coverage. Not everything that actually exists is of theoretical interest to scientists. Alternatively, one might deﬁne the actual world as the metaphysical index at which things are a certain way if and only if they are actually that way. I favor this approach. It sidesteps existence. The actual world is deﬁned in terms of actually being a certain way—or, some might prefer to say, in terms of actual so-sein. I will not attempt to offer a deﬁnition of what it is actually to be a certain way, for I do not know how. It would be clearly circular to deﬁne ‘is actually thus-and-so’ as ‘is thus-and-so at the actual world’. I take the notion of actually being a certain way to be a basic notion, hence indeﬁnable in more basic terms. This, however, does not mean that it is mysterious. Actually being a certain way (actual so-sein) should be distinguished from being a certain way (so-sein simpliciter, or bare so-sein). It is often hard to make this distinction, as it is a customary linguistic practice of communicational economy to suppress the word ‘actually’ from explicit utterance even when actuality is distinctly intended as part of the asserted predication. This gives rise to the natural but mistaken impression that the word ‘actually’ is merely a device for emphasis without independent semantic function. For example, the complex predicate ‘actually serves a pie’ does not mean the same as ‘serves a pie’. When children play a game of make-believe, they do various things without actually doing them. By pushing a pile of mud, a child may serve a

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pie without actually serving a pie.3 The complex predicate ‘actually lived on Baker Street’ does not mean the same as ‘lived on Baker Street’. Sherlock Holmes lived on Baker Street but did not actually live there. Some might say that Holmes did actually live on Baker Street according to the stories of Sherlock Holmes by Arthur Conan Doyle. Likewise, it might be said that the child actually serves a pie according to the make-believe set-up within which she pretends to act. To say such things might sound plausible enough, but it does not refute the distinction between actually doing something and doing something. ‘Holmes actually lived on Baker Street according to the stories’ does not mean the same as ‘Holmes actually lived on Baker Street’. So, if ‘Holmes lived on Baker Street’ means the same as ‘Holmes actually lived on Baker Street according to the stories’, then ‘Holmes lived on Baker Street’ does not mean the same as ‘Holmes actually lived on Baker Street’. Therefore, the distinction between living on Baker Street and actually living on Baker Street is sustained. Likewise with the make-believe example. It is important to remember that we are not trying to establish a particular way to distinguish being a certain way from actually being a certain way. We are merely noting the distinction itself. Some might say that ‘Holmes lived on Baker Street’, as long as it is true, means the same as ‘Holmes lived on Baker Street according to the stories’ and that since ‘Holmes actually lived on Baker Street according to the stories’ is also true, there is no reason to believe in the difference between ‘lived on Baker Street’ and ‘actually lived on Baker Street’. This is a better objection but it only helps make explicit what is an implicit ambiguity of ‘actually’. In one sense, ‘actually’ functions within the scope of ‘according to the stories’. This is the sense in which whatever the stories say happens actually happens according to the stories. But there is another sense, in which ‘actually’ functions outside the scope of ‘according to the stories’ in a way analogous to the way in which ‘now’ functions outside the scope of ‘in the future’ in ‘In the future Jane will be taller than she is now’.4 This second sense is evidenced by our hesitation to agree that when we assert ‘Holmes lived on Baker Street’, we are prepared to assert ‘Holmes actually lived on Baker Street, whether according to the stories or not’. We know that the stories are ﬁction, that is, they are meant to depict non-actual events. So we think that Holmes lived on Baker Street according to the stories, and not that Holmes actually lived on Baker Street according to the stories. We should not be misled by the fact that, according to the stories, it would have been correct for Dr Watson to assert ‘Holmes actually lives on Baker Street’. ‘Actually being a certain way’ in Watson’s mouth according to the stories does not entail ‘actually being a certain way according to the stories’ in our mouth. Such is the second 3

Walton 1990. We shall return to the distinction between the two senses of ‘actually’ in 5.4. For general discussion, see Lewis 1970b : 18–20; 1983b : 22; 1986: 92–101; Hazen 1977, 1979; van Inwagen 1980; Forbes 1983; Davies 1983; Hodes 1984a, 1984b. 4

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sense of ‘actually’. Bear in mind also that ‘Holmes actually lived on Baker Street according to the stories’ means that according to the stories, Holmes actually lived on Baker Street, and not (nor does it entail) that it is actually the case that according to the stories, Holmes lived on Baker Street. More on this in the next section. It might be objected that taking actual so-sein as primitive and deﬁning the actual world in terms of it is putting the cart before the horse, for the proper order of analysis is to deﬁne actual so-sein as so-sein at the actual world and to deﬁne the actual world in terms other than actuality. I am sympathetic to the sentiment underlying this objection, which is the sentiment in favor of thorough reductionism that all modal notions should be deﬁned ultimately in terms of non-modal notions. For instance, David Lewis’s characterization of the actual world is intended to be non-modal. Sympathetic as I am, I do not believe that thorough reduction of modality is feasible. In particular, I do not believe that the notion of actuality is deﬁnable in any further terms, let alone in non-modal terms. In my opinion, many of Lewis’s detractors implicitly exploit the basic nature of the concept of actuality in advancing their objections. Some of these objections will be discussed in Chapter 5. I hasten to add that I still believe in reduction of modal notions, such as possibility and necessity. It is just that I do not believe in thorough reduction of all modal notions. 4. 2. ACTUALITY, PRESENTNESS, AND HERENESS The modal notion of actually being a certain way (actual so-sein) is on a par with the temporal notion of presently being a certain way (present so-sein).5 Consider the largest domain consisting of things in the entire universe that presently exist. One might attempt to deﬁne the present time (now) as the metaphysical index at which things exist if and only if they exist relative to that domain. Alternatively, one may deﬁne the present time in terms of present so-sein, as the metaphysical index at which things are a certain way if and only if they are presently that way. As with actuality, I choose this second way to deﬁne the present time. The notion of present so-sein is basic. We understand it and distinguish it from the general notion of being a certain way (bare so-sein). In the case of times, we have more to go on. We take times to be linearly ordered. The present time is among many times so ordered. Some times precede the present time in the ordering, and other times are preceded by the present time. The former are past times, and the latter future times. We can thus deﬁne the notion of having been a certain way (past so-sein) and the notion of being going to be a certain way (future so-sein), as being a certain way at a past time and being a certain way at a future time, respectively. 5 I am using the word ‘presently’ not in the sense of ‘at once’ or ‘without undue delay’, but in the sense of ‘at the present time’ or ‘now’.

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We may take a hint from this and treat possible worlds accordingly, albeit without a linear ordering. We may deﬁne the notion of non-actually possibly, or merely possibly, being a certain way (merely possible so-sein) as being a certain way at a possible world that is not the actual world. The order of conceptual priority will then be as follows. We start with the notions of bare so-sein and actual so-sein, as well as the general notion of a metaphysical index, of which a possible world is a special kind, a modal kind. We deﬁne the notion of the actual world in terms of the notions of a modal index and actual so-sein. We then deﬁne the notion of merely possible so-sein in terms of the notions of a possible world, the actual world, and bare so-sein. At the same time, the notion of possible so-sein is deﬁned in terms of the notions of a possible world and bare so-sein. Suppose that someone, call her ‘Victoria’, said approximately 150 years ago, ‘I am amused presently’. We will then correctly say that according to Victoria, she was amused then (at the time of her utterance). It will not be correct for us to say that according to Victoria, she was amused presently, for ‘was amused presently’ is as infelicitous as ‘was amused tomorrow’. The past tense does not go with ‘presently’ any more than with ‘tomorrow’. We need to use the present tense with ‘presently’.6 It will also not be correct for us to say that according to Victoria, she is amused presently, for Victoria was not speaking of what she would be doing at this time in the twenty-ﬁrst century. The case of ‘actually’ is similar. Suppose that the stories by Arthur Conan Doyle contain the sentence, ‘Holmes actually lives on Baker Street’. It will be incorrect for us to report that according to the stories, Holmes actually lived on Baker Street. The word ‘actually’ in our mouth points to our actual world, whereas the word ‘actually’ as it occurs in the stories does not. The parallel with times is not perfect, of course. For one thing, English is not equipped with a modal equivalent of tense, so it takes more effort to expose the inadequacy of the report in question. For another, it is less easy to put forth a modal equivalent of the distinction between ‘presently’ and ‘at the time of utterance’. The word ‘actually’ in one sense—the sense operative in this section—is analogous to ‘presently’, but what is analogous to ‘at the time of utterance’? The word ‘actually’ in the other sense noted earlier seems to qualify; I shall touch on this sense brieﬂy later in this section and shall discuss it more carefully in the next chapter. What other expression is equivalent to ‘actually’ in this sense? One should expect the right expression to have the form ‘at the possible worlds of . . . ’ but what ﬁlls the blank? It seems clear that ‘the Sherlock Holmes stories’ will do for the example at hand. We thus should make our report by saying that according to the Sherlock Holmes stories, Holmes lived on Baker Street at the worlds of the Sherlock Holmes stories. Later in Chapter 10, I shall discuss two issues concerning this. One is the plurality

6

Remember that we are using the word ‘presently’ in the sense of ‘at the present time’ or ‘now’.

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of the worlds of the Holmes stories, and the other is the omission of the word ‘possible’ before ‘world’ in ‘the worlds of the Sherlock Holmes stories’. As another way to see the incorrectness of our saying that, according to the stories, Watson said that Holmes actually lived on Baker Street, consider a hypothetical doppelga¨nger of Arthur Conan Doyle. Suppose that at the same time as Arthur Conan Doyle’s writing of the Sherlock Holmes stories, another man, call him Hartur Donan Coyle, wrote stories remarkably similar to Doyle’s Holmes stories. Indeed, suppose further, Coyle’s stories happened to be the exact word-for-word duplicate of Doyle’s stories. Doyle and Coyle did not know each other or linked to each other in any signiﬁcant way, and the duplication was a matter of sheer wild accident. Unlike Doyle, however, Coyle thought he was writing non-ﬁction. He thought of himself as (Dr Watson who was) reporting true adventures of an actual man. How he managed to persuade himself of such extravagance is unimportant. He did not have the intention of a ﬁction writer. He did not pretend, or make-believe, to make assertions. He fully intended to make assertions. He sincerely thought he was making true assertions. At times he even succeeded in making true assertions, for example (let us assume) when he wrote, ‘In the year 1878 I took my degree of Doctor of Medicine of the University of London, and proceeded to Netley to go through the course prescribed for surgeons in the Army.’ Under those circumstances, it would be correct for us to say that, according to Coyle’s stories, Watson said that Holmes actually lived on Baker Street. A temporal analogy of this would feature a new character, Pictoria, Victoria’s less lucid contemporary who uttered the same words as Victoria. Pictoria was under delusion and conceived of now, namely, this moment, which is our present moment (not hers), as her own present moment. I am unsure exactly how such a strangely deluded conception is to be managed, but assuming that she managed it, it would be correct for us to say that according to Pictoria, she is amused presently. The modal notion of actuality is thus proﬁtably compared to the temporal notion of presentness. The English language handicaps us when we wish to use an abstract noun for the parallel spatial notion. Since the word ‘here’ is the obvious analog of ‘now’, I shall simply conjure up the expression ‘hereness’ and appoint it to the task, along with ‘thereness’ to complement it. We start with the notion of being a certain way here (here so-sein) as primitively understood, and deﬁne the spatial analog of the present time or the actual world, namely, here, as the location at which things are a certain way here. It is important to note that this is not viciously circular, and the appearance to the contrary is only due to the paucity of the English vocabulary; the word ‘here’ as it occurs as part of the clause ‘things are a certain way here’ in the deﬁniens has no independent signiﬁcance, as the clause expresses a primitive notion. We then deﬁne being a certain way there (there so-sein) as being a certain way at a location other than here. We use the word ‘there’ to designate spatial regions other than here. Thus, hereness is to thereness what presentness is to pastness (or futureness), or what actuality is

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to mere possibility. Suppose that it is snowing in Lhasa but not in Los Angeles, and that you are in Lhasa and I am in Los Angeles. Referring to where you are, you say, ‘It is snowing here’. It will be incorrect for me to say that, according to you, it is snowing here. I should instead say that, according to you, it is snowing there, or more explicitly, it is snowing there in Lhasa. Some may wish to remind us at this point that ‘actually’, ‘presently’, and ‘here’ have alternative meanings other than what we have been focusing on. On the alternative meanings of these words, it would be correct for me to say, ‘According to the stories, Watson said that Holmes actually lived on Baker Street’, ‘According to Victoria, she was amused presently’,7 and ‘According to you, it is snowing here’ (while pointing to the dot on a world map representing Lhasa). That is, within the respective contexts of use, ‘actually’ in effect signiﬁes ‘at the worlds of Holmes and Watson’, ‘presently’ in effect signiﬁes ‘at the time of Victoria’s utterance’, and ‘here’ in effect signiﬁes ‘in the place represented by the dot on the map being pointed to’. These alternative readings, though not entirely homogeneous, make perfect sense.8 In fact, I shall make a crucial use of ‘actually’ understood in this way in Chapter 5. For now, however, let us simply say that we should clearly remember the noted ambiguity of these words and understand that the alternative meanings are not relevant to the main discussion in this section. Clearly, I rely heavily on the analogy between ‘actually’ on the one hand and ‘presently’ and ‘here’ on the other in explaining the notion of actuality. This is reminiscent of David Lewis’s well-known indexical theory of actuality. Lewis’s view has indeed inﬂuenced my thinking on the subject and my notion of actuality may well be called an indexical conception of actuality. However, there are a number of important differences between Lewis and myself on this matter. First, as I noted earlier, Lewis is rather hostile to the analogy between possible worlds and times. Lewis believes that ordinary individuals, such as trees, rocks, desks, and human beings, persist through time but not through modal space, that is, they exist at different times but not at different possible worlds. Each such individual is world-bound; there is exactly one possible world at which it exists. I, on the other hand, say that ordinary individuals exist at different possible worlds, as well as at different times. Second, on Lewis’s indexical theory, 7 Earlier I said that I was using ‘presently’ to mean ‘at the present time’ or ‘now’. Here I am not using the word in that sense. The closest synonym of ‘presently’ in the sense operative here may be ‘currently’. Note that this is not a linguistic point about the English language. Whether the English word ‘presently’ is ambiguous in a way parallel to ‘actually’ is beside the point. We could certainly imagine a word so ambiguous. 8 The meanings of ‘actually’ and ‘presently’ are of the same kind but not the meaning of ‘here’. The word ‘presently’ in this meaning ﬂags the time of utterance as the relevant time to be incorporated into the truth condition of the uttered sentence, and the word ‘actually’ in the relevant meaning similarly ﬂags the world of utterance. But the word ‘here’ in the relevant meaning functions more like a demonstrative rather than a pure indexical. See the penultimate paragraph in 2.3.

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when I say ‘the actual world’, I refer to the possible world at which I exist. Since I exist at exactly one possible world, on Lewis’s view, this conception of the actual world is legitimate. But on my view, I exist at many different possible worlds, so I cannot accept this conception of the actual world. Instead, as we saw, I suggest that we take the notion of things actually being a certain way as primitive and characterize the actual world as the modal index at which things are actually a certain way. Third, Lewis conceives of an ordinary individual’s existence at the actual world as that individual’s being part of the actual world. This stems from his general conception of a possible world as a concrete particular spatio-temporally9 related mereological whole. Any individual that exists at a possible world does so by being part of that world. I do not think of an individual’s existence at the actual world, or at any world, this way. I think of it in terms analogous to the way an individual exists at a given time. The individual is not part of the time. Rather, it is part of the universe as the universe exists at that time. This leads to the fourth difference between Lewis and myself. What Lewis calls the actual world, a spatio-temporally related whole, is part of what I call the universe as it actually is. If there turn out actually to be other concrete wholes spatio-temporally unrelated to what Lewis calls the actual world, they are also part of what I call the universe as it actually is. Lewis would say that there could not possibly (in some sense of ‘could not possibly’) turn out actually to be such wholes, but that if, per impossibile, such wholes turn out actually to be, then they would really be nonactual possible worlds, whereas I call them neither parts of the actual world nor non-actual possible worlds. Possible worlds, including the actual world, do not have parts. They are points in the modal space in a way analogous to the way a temporal instant is a point in the (one-dimensional) temporal space, or the way a spatial point is a point in the (at least three-dimensional) spatial (physical) space. The universe spreads out in time, space, and modal space. The universe is a certain way at a given possible world, and if the universe includes a particular ordinary individual as a part at that world, then the individual exists at that world; if not, it does not. The universe is not the possible world any more than the individual is part of the possible world. The possibility of the individual’s being a certain way is its being a certain way at a possible world, and the possibility of the universe being a certain way is the universe being a certain way at a possible world. The actuality of the individual’s being a certain way is its being a certain way at the actual world, which is its being a certain way at the modal index at which it is actually a certain way. In short, the actuality of the individual’s being a certain way is its actually being a certain way. Likewise, the actuality of the universe’s being a certain way is the universe’s actually being a certain way, which we expressed before more informally as ‘things actually being a certain way’. 9

Or in a more general natural way.

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It is almost universally assumed that relative to a particular context of utterance some indices are somehow privileged. They are known as default indices. The default temporal, spatial, and modal indices are the time of utterance, the spatial region of utterance, and the world of utterance, respectively. When a sentence is uttered without any speciﬁc indication of a particular array of indices to which the truth condition of the sentence is to be understood to be tied, default indices are supposed to come into play automatically to ﬁgure in the truth condition of the sentence. As uttered without any speciﬁc indication of a particular time by the agent, the sentence ‘It is raining in southern California’ is true if and only if it is evaluated at the time of utterance. ‘It was raining in southern California’ is true if and only if ‘It is raining in southern California’ is true as evaluated at some contextually indicated time prior to the time of utterance. ‘It will be raining in southern California’ is true if and only if ‘It is raining in southern California’ is true as evaluated at some contextually indicated time posterior to the time of utterance. And so on for the other tenses.10 Spatial and modal cases are similar. Usually, when we say, ‘It is raining now’, without indicating any spatial region as the relevant spatial index, our sentence is true if and only if it is true as evaluated at the default spatial location, namely, the (relatively compact) spatial region of utterance. When we say, ‘Donkeys aren’t talking in Grand Canyon now’, without indicating any possible world(s) as the relevant index (indices), our sentence is true if and only if it is true as evaluated at the default modal index, the actual world. In addition, it is almost universally assumed that sometimes, or even often, sentences are in fact uttered without any speciﬁc indications of the relevant indices. That is, it is almost universally taken for granted that sometimes or often default indices do ﬁgure in the truth conditions of uttered sentences by default, i.e. as they are supposed to as default indices. I do not accept this picture of the time, spatial region, and world of utterance. I do not believe that there is such a thing as a default index, which is supposed to be a special or privileged index that steps in by default as the index for truth relativization for a given uttered sentence when nothing in the circumstances surrounding the utterance indicates a particular index of the kind in question. It is not that I believe there is a better mechanism than that of a default index which kicks in whenever nothing about the utterance indicates a particular index. Rather, I believe that there is almost never a case in which nothing about the utterance indicates any particular index and in which the sentence so uttered has

10 These truth conditions are the most straightforward for these tenses, but there are sentences and contexts of utterance which call for other, subtler truth conditions.

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a truth condition whose slots reserved for the metaphysical indices are ﬁlled.11 Take a spatial case for example. When we look up at the sky and say, ‘It is raining now’, in an everyday situation, we are normally and correctly understood to be saying that it is raining in the vicinity of our utterance. This is so not because the spatial region of the utterance has some special status among all spatial regions even though nothing about the context of utterance indicates any particular spatial region as the spatial index that ﬁgures in the truth condition. The fact that the speaker looks up and perhaps even points to the sky when making the utterance is an indication, indeed a very strong indication, of the intended spatial region for the truth condition of the uttered sentence. Of course, the speaker may not point to the sky, or even look up, when uttering the sentence. Even when the speaker stares straight ahead without looking up, moves few body parts intentionally, and utters the sentence in a ﬂat tone, something about the context of utterance gives away a speciﬁc spatial index as relevant. The inertia for relevance from the preceding parts of the entire discourse in which the utterance is embedded usually gives a clear enough indication as to which spatial region is in question. In many everyday situations the relevant spatial region is the vicinity of the utterance or some other salient location carried over from the earlier stages of the discourse. If the sentence is uttered out of the blue without any preceding discourse which it is supposed to continue, then it is the speaker’s intention that should determine what spatial index is to ﬁgure in the truth condition. If the speaker has no such intention at all, or has an insufﬁciently strong or speciﬁc such intention, then the sentence, as so uttered, has no truth condition whose slot for the spatial index is ﬁlled. No spatial index ﬁgures in the truth condition by default. Likewise, no modal index ﬁgures in truth conditions by default. The world of utterance is not a default modal index. It does ﬁgure in the truth conditions of many sentences, but that is because the contexts of utterance of these sentences point to it as the relevant modal index. When we casually say outside philosophy classes, ‘No donkey in Grand Canyon talks’, the sentence as we say it should be understood to be true if and only if no donkey in Grand Canyon talks at the actual world. This is so not because, even though nothing whatever about the circumstances surrounding our utterance gives the slightest indication of which modal index is in question, the actual world has such a special status among all worlds that it gets into the truth condition by default. Rather, it is because the ordinary circumstances surrounding our utterance, including the speaker’s intention, make the actual world the relevant world. This is exactly as expected, 11 The relative clause ‘whose slots reserved for the metaphysical indices are ﬁlled’ is included as a gesture to accommodate the position that ‘It is raining now’ has a truth condition that is devoid of any spatial index. Such a truth condition does not require a spatial index. In a similar vein, it may also be held that ‘It is raining here’ has a truth condition that is devoid of any temporal index. Since these truth conditions do not call for the idea of a default index, there is no reason why I should oppose them here. For discussion of related issues, see Bach 2001; Borg 2004; Cappelen and Lepore 2004.

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for ordinarily outside philosophy classes we are naturally more concerned with the goings-on at the actual world than the goings-on at non-actual worlds when speaking without modally charged expressions, such as ‘possibly’, ‘necessarily’, ‘could’, ‘would’, etc. I am not suggesting that whenever we use the sentence ‘No donkey in Grand Canyon talks’ in a context which appears to determine no candidate possible world(s) as the relevant modal index (indices), the appearance is wrong and the context does determine such a candidate. We may say: ‘No donkey in Grand Canyon talks. What I have just said is actually true, but it could possibly be false.’ When we say this, our utterance of ‘No donkey in Grand Canyon talks’ should not be understood to have a truth condition that is tied to a particular possible world. The sentence should be understood to say something that is world-neutral and is true at the actual world but false at some possible world. But if an uttered sentence is to have a truth condition that is not world-neutral, the determination of the relevant possible world(s) to ﬁgure in the truth condition is by some speciﬁc contextual means, and not by the mysterious mechanism of the ‘default’ indexing.

5 Modal Realism and Modal Tense 5 . 1 . METHODOLOGY In this chapter I shall discuss our reliance on the parallel between times and possible worlds in a more self-conscious and explicit way. It will be convenient to use the phrase ‘modal realism’ in such a restricted way as to exclude actualism. Thus let us say that Lewis’s theory and the theory I endorse are modal realist theories but actualism is not. The crux of the chapter is an argument that if the methodology of the fans of the parallel is adopted to implement a certain way of theoretical locution, which involves what I call modal tense, then modal realists will reap beneﬁts. I take the moral of this argument to be that, as modal realists, we should adopt the methodology and be modal tensers. To be a modal tenser is to adopt a certain kind of theoretical locution. But it is not merely a matter of using certain words. Words express concepts. To accept a certain kind of locution and not others commits one to accepting a certain kind of concepts and not others. So being a modal tenser has conceptual implications. The repercussions of being a modal tenser do not stop there. Concepts carve out reality, and different kinds of concepts carve out reality differently. This has ontological implications. There will be little point in being a modal tenser if we can designate and quantify over all important modal facts adequately in modaltenseless terms. It will be detrimental to be a modal tenser if some important modal facts can be designated or quantiﬁed over adequately only in modaltenseless terms. Thus, in accepting the position of a modal tenser, we are committed to the ontological position that some important modal facts are modal-tensed facts, i.e. they can be designated or quantiﬁed over adequately only in modal-tensed terms, and that no important modal facts are modaltenseless facts, i.e. none of them are such that they can be designated or quantiﬁed over adequately only in modal-tenseless terms.1

1 This leaves it open whether some important modal facts are neither modal-tensed facts nor modal-tenseless facts. Some such facts might be able to be designated or quantiﬁed over adequately both in modal-tensed terms and in modal-tenseless terms, while others might be able to be designated or quantiﬁed over adequately neither in modal-tensed terms nor in modal-tenseless terms; the latter facts would defy expressive completeness of our modal language, with or without modal tense.

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To illustrate the usefulness of being a modal tenser, I shall consider ﬁve independent objections to modal realism and argue that if modal realists adopt the modal-tensing way of theoretical locution, they will be able to respond to the objections in a uniform fashion. As those objections are logically independent of one another and differently motivated, the uniformity with which modal realists can counter them gives the modal-tensing way of theoretical locution a high degree of theoretical utility. Since David Lewis’s version is the best known version of modal realism by far, four of the ﬁve objections examined are directed against Lewis’s theory; the ﬁfth objection (Peacocke’s) has a wider scope. The point of our exercise is not to defend Lewis’s version of modal realism in particular but to show that objections against Lewis’s theory can be neutralized in such a way as to beneﬁt modal realists generally. 5 . 2. BACKGROUND ASSUMPTIONS One of the basic temporal logico-metaphysical tenets we shall assume is that the common temporal operators, like lexical temporal modiﬁers such as ‘always’ and ‘sometimes’, quantify over times. In addition, there are sub-lexical temporal modiﬁers, namely, tenses. We shall assume that tenses are modiﬁers of verbs and form an integral part of our temporal discourse. I take this assumption to be uncontroversial to everyone except serious de-tensers, who insist that tenses are theoretically dispensable.2 Even the most ardent fan of the parallel between times and possible worlds would concede that there are some obvious disanalogies. As we have already noted, it is highly plausible to think that there is a natural linear arrangement of times, whereas it is not at all plausible to suggest that there is any linear arrangement of possible worlds, let alone a natural one. Also, there seems to be a natural directionality in this linear arrangement of times. Time seems to ﬂow. This may be an illusion on our part, but if it is, it is a very powerful and almost irresistible illusion. In contrast, in the absence of any natural linear arrangement of possible worlds, it is senseless to speak of any appearance of natural directionality for possible worlds.3 I propose that modal realists should take tenses seriously as temporal modiﬁers of verbs and introduce their modal analogs—modal tenses. There are many 2 Bertrand Russell says, ‘The occurrence of tense in verbs is an exceedingly annoying vulgarity due to our preoccupation with practical affairs’ (1956a : 248). 3 The topic of ordering possible worlds has not received much attention and remains unexplored, so perhaps we should not rush to the judgment that there is no natural ordering of possible worlds at all, even though it is safe to rule out a linear ordering. In the absence of any concrete proposal of a natural ordering of possible worlds, however, I shall operate on the working assumption that there is no such ordering.

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tenses in English, but owing to the lack of natural linear ordering of possible worlds, we can afford to ignore most of them. For example, the contrast between the past tense and the future tense is lost in the case of modal tense. Also, it is uncertain that the contrast between a simple tense (for example, simple past) and its complex cousins (past progressive, past perfect, etc.) has a modal analog.4 We shall therefore focus only on the simple present tense and the simple past tense. 5. 3 . TENSE Let us quickly review the semantics of the two tenses. The present-tensed form of a verb should be clearly distinguished from the tenseless, inﬁnitive form. The present-tensed sentence ‘Bart is a child’ is true as evaluated at a time t if and only if Bart is a child at t. The present tense ﬂags the time of evaluation as the relevant time to ﬁgure in the truth condition.5 The inﬁnitive form ‘Bart be a child’, on the other hand, is tenseless and hence fails to ﬂag any time, relative to the time of evaluation, as the relevant time to ﬁgure in the truth condition. So, ‘Bart be a child’ as evaluated at any time lacks a truth condition. The present tense is essential and ineliminable in the deﬁnitions of all tenses, unless we postulate an artiﬁcial grammatical element to usurp the role of the present tense or decide to do away with tenses altogether. A sentence with a present-tensed main verb should also be clearly distinguished from the same sentence with the adverb ‘now’ added. ‘Bart is a child’ does not always have the same truth condition as ‘Bart is a child now’. The former sentence has a truth condition which is sensitive to the time of evaluation, te, whereas the truth condition for the latter sentence is sensitive not to te but to the time of utterance, tu. ‘Bart is a child now’ is true as uttered at tu and evaluated at te if and only if ‘Bart is a child’ is true as uttered at tu and evaluated at tu; te is irrelevant to its truth condition (unless it is identical to tu).6 The present tense in natural language packs considerably more complications than sketched here.7 The past tense is to be understood in terms of the present tense and has its own complications. ‘Bart ate breakfast’ may have two different truth conditions, depending on whether there is some set of times, T (for example, the set of times constituting yesterday), such that all members of T are before te, not all times before te are members of T, and T is appropriately salient in the context of utterance. If there is, then the sentence is true as uttered at tu and evaluated at te if 4 I am inclined to think that the modal analogs of some such complex tenses can be made intelligible. 5 An example from Gottlob Frege illustrates a use of the present tense in which the time of evaluation is linked to the temporal word in whose scope the tensed verb occurs: ‘When the Sun is in the tropic of Cancer, the longest day in the northern hemisphere occurs’ (1892, reprinted in 1970: 72). 6 See Kamp 1971. 7 See Kuhn 1989.

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and only if ‘Bart eats breakfast’ is true as uttered at tu and evaluated at some time in T (for example, ‘Bart eats breakfast’ is true as uttered at the present time and evaluated at some time yesterday, which is the case if and only if Bart ate breakfast yesterday). If there is not, then the sentence is true as uttered at tu and evaluated at te if and only if ‘Bart eats breakfast’ is true as uttered at tu and as evaluated at some time before te.8 In contrast, ‘Sometime in the past, Bart ate breakfast’ only has the second truth condition. So does ‘Bart once ate breakfast’. Expressions like ‘sometime in the past’ and ‘once’ (in the relevant sense) may sometimes be suppressed on the surface. This complicates the task of interpreting past-tensed sentences. When the past tense occurs with an explicit mention of a particular past time, the mentioned time determines T. The expression ‘1964’ in the sentence ‘Bart was a child in 1964’ determines the year 1964 to be the sole member of T. (The uttered sentence and its features are considered part of the context of utterance. Remember also that intervals of time, as well as moments of time, are times.) So, the sentence is true as uttered at tu and evaluated at te if and only if 1964 is before te and ‘Bart is a child’ is true as uttered at tu and evaluated at 1964. 5. 4 . MODAL TENSE Let us review the two senses of ‘actually’ we noted in Chapter 4. I weigh less than 200 pounds but could have weighed 200 pounds. So I could have weighed more than I actually do. The adverb ‘actually’ in this sense is analogous to ‘now’; cf. ‘I used to weigh more than I do now’. Actuality in this sense is actuality in the rigid sense. ‘I actually weigh X pounds’ with the rigid sense of ‘actually’ is true as uttered at a possible world wu and evaluated at a possible world we if and only if ‘I weigh X pounds’ is true as uttered at wu and evaluated at wu; we is irrelevant to its truth condition (unless it is identical to wu). At the same time, I may also speak truthfully in the following way: I do not actually weigh 200 pounds, but there is nothing necessary about what I actually weigh and I could have actually weighed 200 pounds. The adverb ‘actually’ in this sense is not analogous to ‘now’ and does not express actuality in the rigid sense. It expresses actuality in the non-rigid sense. ‘I actually weigh X pounds’ with the non-rigid sense of ‘actually’ is true as uttered at wu and evaluated at we if and only if ‘I weigh X pounds’ is true as uttered at wu and evaluated at we; we retains its relevance. The temporal adverb ‘currently’ may be said to have a sense which is analogous to this non-rigid sense of ‘actually’: cf. ‘Monarchy was current in France in 1777 but not now’. The modal analog of the simple present tense may be expressed by the adverb ‘actually’ in the non-rigid sense. Let us call it the ‘simple actuality modal tense’, or the actuality tense. We have no separate modal tense corresponding to the rigid 8

For further discussion, see Partee 1973.

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sense of ‘actually’, any more than we have a special tense corresponding to ‘now’ that is separate from the present tense. The modal analog of the simple past tense is the simple non-actual possibility modal tense, or the mere-possibility tense. There would be no point in precisely mimicking the temporal case by devising an elaborate system of morphological transformations of verbs from the inﬁnitive forms to modal-tensed forms. It will serve our purposes adequately if we use the simple subscripts, ‘a’ and ‘p’, for the actuality tense and the mere-possibility tense, respectively. For example, the sentence, ‘Boris is actually an accountant’, where ‘actually’ is read non-rigidly, will be replaced with ‘Boris isa an accountant’. We may retain the non-rigid adverb ‘actually’ for emphasis if we wish: ‘Boris isa actually an accountant’. This will not change the truth condition. ‘Boris could have been an artist’ will be replaced with ‘Boris isp an artist’. Let us consider the mere-possibility tense ﬁrst. As with the simple past tense, two cases need to be distinguished: (i) there is a set W of possible worlds such that we is not a member of W, not all possible worlds other than we are members of W, and W is appropriately salient in the context of utterance, and (ii) there is no such set W. If (i) is the case, the sentence ‘Boris isp an accountant’ is true as uttered at wu and evaluated at we if and only if ‘Boris isa an accountant’ is true as uttered at wu and evaluated at some member of W. If (ii) is the case, it is true if and only if ‘Boris isa an accountant’ is true as uttered at wu and evaluated at some possible world other than we. It is easy to see how (ii) may apply. Take a temporal case ﬁrst for comparison: ‘Boris is not an accountant but sometime in the past Boris was an accountant’ is true as uttered at tu and evaluated at te if and only if ‘Boris is not an accountant’ is true as uttered at tu and evaluated at te and ‘Boris is an accountant’ is true as uttered at tu and evaluated at some time before te. Likewise, ‘Boris isa not an accountant but possibly Boris isp an accountant’ is true as uttered at wu and evaluated at we if and only if ‘Boris isa not an accountant’ is true as uttered at wu and evaluated at we and ‘Boris isa an accountant’ is true as uttered at wu and evaluated at some possible world other than we. In many important cases the world of utterance wu is the actual world. So we shall henceforth assume that the actual world is the world of utterance, and drop any explicit mention of the world of utterance unless absolutely necessary. A typical case to which (i) applies involves restricted possibility. For example, the context of utterance may make it the case that ‘Boris isp an accountant’ is true as evaluated at @ if and only if Boris is an accountant at not just any non-actual possible world but one at which Boris gets all he wants. In such a case, W only includes those worlds at which Boris gets all he wants.9 9 In general W will almost always contain many members, whereas in the temporal case T may well contain just one member, e.g. the year 1964. Hardly any humanly possible context of utterance is so detailed as to determine a single possible world as the sole member of the salient set W. Almost all humanly possible contextual determinations of W proceed propositionally. No matter how much information the propositions in question may carry, they will almost never carry enough information to determine a unique possible world.

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The actuality tense is straightforward. ‘Boris isa an accountant’ is true as it is evaluated at we if and only if Boris is an accountant at we. ‘Boris isa actually an accountant’ (with ‘actually’ rigid) is true as it is evaluated at we if and only if Boris is an accountant at @. Like tense, modal tense needs to be incorporated not only into the object language but also into the metalanguage for complete theoretical rigor. Insistence on complete theoretical rigor, however, is not always wise. If we are not allowed to suppress modal tense in our metalanguage, the preceding paragraph will have to be modiﬁed as follows: The actuality tense isa straightforward. ‘Boris isa an accountant’ isa true as it isa evaluated at we if and only if (i) Boris isa an accountant at we if we isa @, and (ii) Boris isp an accountant at we if we isa not @. ‘Boris isa actually an accountant’ (with ‘actually’ rigid) isa true as it isa evaluated at we if and only if Boris isa an accountant at @.10 Such a modal-tensed metalanguage is an overkill. To avoid unnecessary and potentially annoying proliferation of subscripts, we shall suppress modal tense whenever doing so is unlikely to cause serious misunderstanding. Pastness excludes (rigid) presentness in the sense that for any time t, t is a past time only if t is not the present time (now). But of course this does not mean that ‘Boris was an accountant’ entails ‘Boris is not an accountant now’. The ﬁrst sentence does not entail the second. The modal case is analogous. Mere possibility excludes (rigid) actuality in the sense that, for any possible world w, w is a merely possible world only if w is not the actual world. But this does not mean that ‘Boris isp an accountant’ entails ‘Boris isa not an accountant at the actual world’. The ﬁrst sentence does not entail the second. This should dissuade us from blindly accepting the claim that English already contains the mere-possibility tense, namely, the subjunctive construction. It might be suggested that in such compound sentences as ‘If Boris were an accountant, Boris would be meticulous’ and ‘I wish Boris were an accountant’, the component sentence ‘Boris were an accountant’ is the surface form of ‘Boris isp an accountant’. Such a claim should not be uncritically accepted, for it is not implausible to suggest that ‘Boris were an accountant’ implies that Boris is not an accountant at the actual world.11 One way to understand the proposal of modal tense is this. Consider the sentence ‘Boris is merely possibly an accountant’. In order to reveal its logical structure, one needs to relate the modal words ‘merely possibly’ to the rest of the sentence appropriately. There are three different ways to do this. The ﬁrst way is 10 There is more to be said about the use of the actuality tense in ‘isa true’, ‘isa evaluated’, and ‘isa (not) @’. For some related but limited discussion, see 5.8. 11 Frege e.g. thinks that the subjunctive construction implies non-actuality. He says of the sentence ‘If iron were less dense than water, it would ﬂoat on water’ that it expresses two thoughts: that iron is not less dense than water and that something ﬂoats on water if it is less dense than water (1970: 77).

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to group the modal words as part of the predicate: ‘Boris is merely-possibly-anaccountant’. One may then explicate what it is to be merely-possibly-an-accountant. All possible-worlds theorists will say that x is merely-possibly-an-accountant only if x is an accountant at some non-actual possible world. This partial explication in turn is subject to a number of different further explications, some realist and others not. The second way is to group the modal words as part of the subject term: ‘Merely-possible-Boris is an accountant’. One may then say more about what kind of individual merely-possible-Boris is. David Lewis’s counterpart theory may be understood to be an instance of this. The third way is the way of my proposal. It is to group the modal words as part of the copula: ‘Boris is-merely-possibly an accountant’. I propose that we should understand such a modally modiﬁed copula in a way analogous to the way we already understand the interaction of the copula with temporal modiﬁers. Consider the sentence ‘Boris is an accountant in 1999’ (where ‘is’ is understood tenseneutrally, or in the historical present sense). The analog of the ﬁrst way reads this as ‘Boris is an-accountant-in-1999’, the analog of the second way reads it as ‘Boris-in-1999 is an accountant’, and the analog of the third way reads it as ‘Boris is-in-1999 an accountant’. The expression ‘is-in-1999’ when uttered after 1999 should assume the surface form ‘was-in-1999’. I focus on this feature of the past tense. A realist understanding of the temporally modiﬁed copula ‘was-in-1999’ is commonplace and intuitive. My proposal is that we should take advantage of it to defend the mere-possibility tense.12 The case of the actuality tense is straightforward. Colin McGinn offers a seemingly similar idea under the label ‘the copula modiﬁer theory’.13 He contrasts the copula modiﬁer theory with the predicate modiﬁer theory David Wiggins proposes14 and says, ‘Thus, according to the copula modiﬁer theory, we do not work with an ontology of modal properties, rather, we take the stock of non-modal properties and think of them as possessed in different modes.’15 There is much in McGinn’s proposal that I agree with, but there are some important points of difference. McGinn says, ‘If I just say, “Socrates is a man”, I do not commit myself to the mode of instantiation involved—the copula is modally neutral here—but the instantiation itself is always either necessary or contingent.’16 I differ. If I just say, ‘Socrates is a man’, I usually commit myself to the actuality-tensed understanding of the copula. I also do not understand why he says ‘the instantiation itself is always either necessary or contingent’. Another difference between us is that I work within the possible-worlds framework, whereas McGinn rejects the framework: 12 I thank Uriah Kriegel for prompting me to put my proposal this way. Cf. Lewis 1986: 202–9; Haslanger 1989: 7–8; Johnston 1987: 122–5. 13 McGinn 2000: 74–83. 14 Wiggins 1976. 15 McGinn 2000: 77. 16 Ibid. 80–1.

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‘modality belongs to a special ontological category: it consists neither in objects (unlike the possible worlds theory) nor in properties (unlike the idea of modal properties that goes with the predicate modiﬁer view), but rather in items I have called modes’.17 It is, however, unclear how deep this last difference is. McGinn clearly intends to reject any peculiarly modal metaphysics but it is unclear that he succeeds. The issue crucially depends on the status of the items he calls modes. If modes are ways in which things possess properties, then it might be argued that modes are abstract objects of a peculiarly modal kind, just as Robert Stalnaker argues that possible worlds are ways things might have been and as such they are sui generis abstract objects. 5. 5. PRESENTISM AND FOUR-DIMENSIONALISM Actualism has a temporal analog, namely, presentism, which is the view that reality consists of what is now (as opposed to what was or what will be) and nothing else. The present tense of the verbs should be taken very seriously. Actualism and presentism are varieties of chauvinism. Actualists are chauvinistic about the actual, and presentists are chauvinistic about the present. The straightforward temporal non-chauvinism is four-dimensionalism, which says that past and future individuals, events, etc., are as real as the present ones.18 From the perspective of four-dimensionalists, we may as well pretend to adopt the God’seye point of view from outside time and speak by using only present-tensed verbs in something like the historical present sense. Thus at a certain time t, instead of saying, ‘Dinosaurs existed long time ago but they do not exist now’, we may pretend to step outside time and say, ‘Dinosaurs exist. They are temporally located at times long before t but not at t.’ Such a hypothetical viewpoint and slightly awkward-sounding English constructions help emphasize the ontological parity of all temporal things, past, present, and future. Modal realism, being the modal analog of four-dimensionalism, embraces an equally metaphysically egalitarian perspective on possible worlds and possible individuals. Therefore it might naturally be expected to allow, and even encourage, the hypothetical stepping out of the conﬁnes of the actual world and using the modal actuality tense universally in the way analogous to the fourdimensionalists’ use of (something like) the historical present tense. Actualism, on the other hand, embraces a decidedly chauvinist attitude toward the actual world and actual individuals as metaphysically privileged and therefore might be expected to insist on the importance of all modal tenses, including the merepossibility tense, to mark the ontological difference between the actual and the 17

Ibid. 83; his emphasis. This is four-dimensionalism in the broad sense. See Rea 2003. In the next chapter the phrase ‘four-dimensionalism’ will be used in a narrower sense. 18

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merely possible. For example, actualists would be expected to say that mute donkeys existp and exista, talking donkeys existp but do not exista , and so on.19 Thus, it strongly appears as if the divide between actualism and modal realism neatly corresponds to the divide between taking all modal tenses equally seriously on the one hand and de-emphasizing the variety of modal tense and getting on with just the actuality tense in the modal version of (something like) the historical present sense on the other hand. I claim, however, that contrary to this appearance, the variety of modal tense is in fact modal realists’ friend. Modal realists are best advised to take all modal tenses, including the mere-possibility tense, very seriously and resist all modal-tenseless languages in serious discussion of modal metaphysics and epistemology. As we noted earlier, the adoption of the modal-tensed locution will commit modal realists to a certain way to carve reality, which will enable them to shield modal realism from metaphysical and epistemological objections. In particular, modal realists will be able to formulate a uniform way to respond to a number of important objections at one fell swoop. 5 . 6 . FIVE CASE STUDIES

5.6.1. Skyrms’s epistemic objection According to modal realism, talking donkeys are real though not actual. They are as ﬂesh-and-blood as the actual mute donkeys that carry hikers in Grand Canyon. If so, we should be in a position in principle to know their existence by the same empirical means—call it ‘M’—by which we come to know the existence of the mute donkeys in Grand Canyon. But we are not in such a position; at best we are in a position to know about them by means of our modal intuition or sophisticated philosophical argumentation. Therefore, talking donkeys are not real. This is Brian Skyrms’s epistemic argument against modal realism in a nutshell.20 David Lewis responds by assuming that the empirical/non-empirical distinction for justiﬁcation matches the contingent/necessary distinction for truth.21 Without going into the details of Lewis’s response, let us simply note that modal realists should not be required to rely on such a controversial assumption in order to

19 M. J. Cresswell (2006) argues that presentism and four-dimensionalism (which he calls ‘eternalism’) are logically inter-translatable both at the object-language level and at the metalanguage level. If Cresswell is right, some might interpret his result as showing that the disagreement between presentists and four-dimensionalists is illusory, hence by analogy the difference between actualism and modal realism is illusory. That would be a mistake. Cresswell’s result, assuming it is correct, shows no such thing and has no such implication. As Cresswell himself repeatedly says, it instead shows that the dispute between presentists and four-dimensionalists cannot be solved by logic alone. The implication of this for us is at best that the difference between actualism and modal realism goes beyond logic. 20 Skyrms 1976: 326. 21 Lewis 1986: 112.

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respond to Skyrms. Adoption of modal tense will enable modal realists to give a different response which makes no such assumption. Skyrms’s objection fails when it moves from the ﬂesh-and-bloodness of talking donkeys to their knowability by M. The invalidity of this move is masked by the way Skyrms plays fast and loose in his reasoning, and when we reformulate the move more carefully and explicitly in modal-tensed terms, the error becomes clear. When modal realists say that talking donkeys are ﬂesh-and-blood, they mean not that talking donkeys area ﬂesh-and-blood but that talking donkeys arep ﬂesh-and-blood. Skyrms’s objection claims that we area not in a position to knowa about talkingp donkeysp by M. (The predicate ‘is a talking donkey’ is a surface form of ‘is a donkey and talks’. The noun phrase ‘talking donkeys’ should be understood as shorthand for ‘individuals that are donkeys and that talk’. Thus, the modal-tensed phrase ‘talkingp donkeysp’ should be understood as shorthand for ‘individuals that arep donkeys and that talkp’. The mere-possibility tense should not be understood as a modiﬁer of nouns.) So if the objection is to be understood as properly directed at modal realists, it should be understood as assuming that if talkingp donkeysp arep ﬂesh-and-blood, then we area in a position to knowa about talkingp donkeysp by M. But this assumption is implausible. We have no reason to believe that M is such that we area in a position to use it to knowa about individuals that arep ﬂesh-and-blood. The apparent contrary impression is a direct result of conﬂating this implausible assumption with the claim that M is such that we area in a position to use it to knowa about individuals that area ﬂesh-and-blood. This conﬂation is masked by the absence of modal tense in the language Skyrms uses, and is parallel to the conﬂation of the implausible claim that the introspection—call it ‘N’—by which I know about myself as I am now is such that I am in a position to use it to know about myself as I was twenty years ago, with the claim that N is such that I am in a position to use it to know about myself as I am now. The second claim is trivially plausible, whereas the ﬁrst claim is not plausible at all. The conﬂation is unlikely to occur in the temporal case because English demands the correct use of tense. To put the matter slightly differently, we are unable to ﬁnd merely possible talking donkeys by M for the reason analogous to the reason why we are unable to ﬁnd live dinosaurs now. Live dinosaurs existed (in the past) but they do not exist (now). Analogously, talking donkeys existp (at merely possible worlds) but they do not exista (at the actual world). And this difference has epistemic repercussions, just as the difference between the past and the present does. The assumption underlying Skyrms’s objection might alternatively be understood to be the following claim. If talkingp donkeysp arep ﬂesh-and-blood, then we area in a position to knowp (as opposed to knowinga) about the talkingp donkeysp by M. When understood this way, the assumption is plausible but poses no threat to modal realism, for the consequent of the conditional is plausible. We area indeed actually such that for some non-actual possible world w, we and talking donkeys existp at w and we knowp about them by M at w.

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5.6.2. Quine’s rhetorical query Take W. V. Quine’s famous rhetorical query: how many possible fat men are in the (actually vacant) doorway?22 Quine does not expect an answer, as he thinks it is unanswerable. Quine’s query in fact lacks sufﬁcient speciﬁcity mainly due to the absence of modal tense, and once enough speciﬁcity is supplied it is perfectly answerable. If someone asked a ball-player out of the blue, ‘How many hits did you have?’ it would not be a well-asked question, as the past tense would cover many games and seasons, and the context would be too impoverished to make any of them separately or collectively salient. So the appropriate response would be to ask for a more speciﬁc version of the question by saying something like, ‘Which particular game(s) or season(s) do you have in mind?’ The initial impression of unanswerability is explained as being the result of the lack of speciﬁcity in the initial formulation of the question rather than the mysterious, hence objectionable, nature of hits. Quine’s query should be treated in a similar manner, with the aid of modal tense. The obvious element to be subjected to modal tensing is the main verb ‘are’ in the predicate ‘are in the doorway’, but there is another readily noticeable element for modal tensing. Clearly, Quine is asking how many possible individuals who are fat men are in the doorway. This simple rephrasing of the query reveals a second occurrence of the verb ‘are’ in the relative clause.23 Suppose we speak of exactly three possible worlds, the actual world @, a non-actual world w1, and another non-actual world w2, and exactly three possible individuals, x, y, and z, for each of these worlds, and assume that nothing else exists in modal space. Consider x, y, and z at one world to be either identical to or the counterpart24 of x, y, and z, respectively, at any other world. Suppose also the following: (i) at @, x and y area fat men and not in the doorway, whereas z isa not a fat man and not in the doorway; (ii) at w1, x isp a fat man and in the doorway, z isp a fat man and not in the doorway, and y isp not a fat man and isp in the doorway; (iii) at w2, x and z arep fat men and not in the doorway, whereas y isp a fat man and in the doorway. Given this simple picture, among the available readings of Quine’s query are the following: (Q1) How many possible individuals who area fat men area in the doorway? (Q2) How many possible individuals who arep fat men area in the doorway? (Q3.1) How many possible individuals who area fat men arep in the doorway at w1? (Q3.2) How many possible individuals who area fat men arep in the doorway at w2? 22

Quine 1963: 4. Further paraphrasing would reveal more occurrences of ‘are’. Among them would be one in ‘individuals who are possible’. This would raise an interesting issue of modal-tensing the possibility predicate, but I shall not pursue it. 24 Modal-tensing is not incompatible with counterpart theory. My aim here is not to defend non-counterpart-theoretic modal realism exclusively. 23

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(Q4.1) How many possible individuals who arep fat men at w2 arep in the doorway at w1? (Q4.2) How many possible individuals who arep fat men at w2 arep in the doorway at w2? Are the context and the manner in which Quine makes his query sufﬁciently clear to make any particular possible world stand out? If we assume that Quine is interested only in @, then his query is (Q1) and the answer is obviously ‘Zero’, for no actual fat men area in the doorway at @. But it is unlikely that Quine is asking (Q1). (Q2) receives the same easy answer, as the doorway isa unoccupied at @ by any non-actual man, fat or otherwise. A moment’s examination will tell us that the answers to the other questions are ‘One’, ‘One’, ‘Two’, and ‘One’ in that order. (For (Q4.1), note that y isp a fat man at w2 and in the doorway at w1, even though y isp not a fat man at w1.) We may easily generate many more speciﬁc versions of Quine’s query, but in each case the resulting speciﬁc query will have a deﬁnite answer. Therefore, Quine’s query loses its rhetorical force. If Quine’s query is meant to ask for the total number of individuals who arep fat men at some possible world or other and arep in the doorway at some possible world or other, the answer is ‘Inﬁnite’. This is Terence Parsons’s answer.25 The use of modal tense enables us to see that this version of Quine’s query is but one among many others which are systematically generated. Richard Routley is more sensitive than Parsons to the different ways the query might be understood.26 After pointing out the de re / de dicto distinction and disregarding the attribute of fatness, Routley distinguishes the following questions: (R1)

How many merely possible (non-actual) men are in that actual doorway? (R2) How many men are possibly in that doorway? (R2.1) Of what number n of men is it true that for those n men it is possible that they are in that doorway (together)? (R2.2) Of what number of men is it true that it is possible that those men are in that doorway? (R3) What is the largest number of men that can possibly be in that doorway?27 Routley thinks that (R1) is the only correct way to understand Quine’s query28 and that the correct answer is ‘Zero’.29 Clearly, he means ‘area in that actual doorway’ by ‘are in that actual doorway’. He also says, ‘It is logically possible that 25 26 27 28 29

Parsons 1980: 20. Routley 1982: 159–63. Ibid. 160–1; my numbering. Ibid. 161 n. 13. Ibid. 159.

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many fat men are in the doorway, but it would be quite invalid to infer that many possible fat men are in the doorway’.30 (R1)–(R3) are all more or less reasonable readings of Quine’s query but my disambiguation in terms of modal tense is more systematic and subsumes them as special cases.

5.6.3. Peacocke’s reductio argument Christopher Peacocke invites us to consider the following statements: (A) A merely possible human being is not a physical object. (B) Anything which is not a physical object is necessarily not a physical object. (C) A merely possible human being could exist and be a human being. (D) Necessarily, any human being is a physical object. Each of these statements seems intuitively plausible. On modal realism, merely possible human beings are as real as actual human beings. Let a be such a merely possible human being. Consider the following formalized versions of (A)–(D): (A1) (B1) (C1) (D1)

Pa 8x(Px &Px) ^(Ea & Ha)31 &8x(Hx Px)

Modal realists should endorse (A1)–(D1), according to Peacocke, but (A1)–(D1) are jointly inconsistent; for (A1) and (B1) entail that &Pa but (C1) and (D1) entail that ^Pa. This is Peacocke’s argument against modal realism.32 If Peacocke is right, then while (A)–(D) are intuitively plausible, (A1)–(D1) lead to a contradiction. So we should not accept (A1)–(D1) as satisfactory formalizations of (A)–(D). Peacocke proposes to reject (C1) and replace it with the following radically different alternative: (C2) ^∃z(Rzuv & Hz), where u is a particular actual human egg, v is a particular actual human sperm, and necessarily anything that bears R to u and v is a unique human being arising from them. It is assumed that nothing actually bears R to u and v. This rather elaborate maneuver to avoid the contradiction is unnecessary, for Peacocke’s argument does not work. (A1) and (B1) are ambiguous with respect to modal tense. The ambiguity stems from the use of the verb ‘is’ as it occurs once in (A) and twice in (B). 30

Ibid. 161. (A1) and (C1) are stronger than (A) and (C), respectively, but my discussion does not exploit this fact. 32 Peacocke 2002: 505. 31

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Obviously the main verb of (B), the second occurrence of ‘is’, should be understood as actuality-tensed, for it occurs within the scope of ‘necessarily’ as part of the necessitation of non-physicality. (Cf. the main verb ‘is’ in ‘Anything which is not a physical object is always not a physical object’—understood as a completely general statement about all things past, present, and future—which occurs within the scope of ‘always’ and should be present-tensed.) The predicate letters in (C1) and (D1) should also be understood likewise. The other two occurrences of ‘is’ do not lie within the scope of a modal operator, so they may have either of the two modal tenses. Since these two occurrences of ‘is’ are clearly intended to be understood uniformly in the argument, there are only two cases to consider. First, take the actuality-tensed reading: (Ai) (Bi) (Ci) (Di)

Pa a 8x(Pa x &Pa x) ^(Ea a & Ha a) &8x(Ha x Pa x)

The same contradiction (supplemented with the actuality tense) is derivable as before but this time it is not worrisome, for (Bi) is a clear target for rejection. One way not to be physical at a world is not to exist at that world. Any merely possible physical object is such that it does not exista, existsp, and isp a physical object at any possible world at which it existsp. So, any merely possible physical object x is such that x isa not physical and isp physical, i.e. ‘Pa x &Px’ is false. Therefore, (Bi) is false. Next, consider the mere-possibility-tensed reading: (Aii) (Bii) (Ci) (Di)

Pp a 8x(Pp x &Pa x) ^(Ea a & Ha a) &8x(Ha x Pa x)

The same contradiction is still derivable but is again unproblematic, for this time (Aii) is false. Remember that a is supposed to be a merely possible human being. So a existsp and isp a human being, hence a physical object, at any possible world at which a existsp. Therefore, ‘Pp a’ is true.

5.6.4. Van Inwagen’s ontic objection There could have been a million-carat diamond. So there is a possible world at which there is a million-carat diamond, which means, according to David Lewis’s modal realism, that there is a million-carat diamond in the absolutely unrestricted sense of the existence predicate ‘there is’. But there is no such diamond in the same sense of ‘there is’. Therefore, Lewis’s modal realism is false.

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This is Peter van Inwagen’s objection to Lewis’s modal realism.33 Lewis draws a clear distinction between absolutely unrestricted use and restricted use of the existence predicate, and van Inwagen follows Lewis. William Lycan says that drawing this distinction the way Lewis does gives Lewis’s theory a ‘stunning advantage’ over Meinongians, yet at the same time confers ‘outrageous falsity’ upon it.34 Van Inwagen’s objection is an attempt to point out the ‘outrageous falsity’. Whether or not Lewis needs to countenance an absolutely unrestricted existence predicate, not every modal realist needs to. My advice to modal realists is to eschew commitment to the absolutely unrestricted sense of ‘there is’ and formulate their position by means of modal tense instead. They should say that there isp a million-carat diamond. It is plausible that there isa no million-carat diamond, but whether there isp a million-carat diamond is a separate matter, and van Inwagen does not clearly distinguish these two matters. It is important to note that, even though some may propose to deﬁne the absolutely unrestricted sense of the existence predicate ‘there is’ in terms of the two modal tenses as ‘either there isa or there isp’, modal realists need not so deﬁne it. It remains an open question whether modal realists need other modal tenses than the two we have discussed and, if they do, whether any of them goes beyond these two, that is, whether there is a modal tense—let us signify it by the subscript ‘m’—such that there ism an object which neither isa nor isp. In the next section we will see a modest application of this new modal tensing subscript. A more audacious application would countenance entities going beyond our modal space and might be called extended modal realism. Extended modal realism might be said to be extremely far-fetched and lack whatever plausibility possessed by non-extended modal realism. But whether extended modal realism is initially plausible or not is beside the point. What is relevant to the consideration of a new modal tensing subscript is that modal realism is compatible with extended modal realism and that modal realists are not committed qua modal realists to the deﬁnability of the absolutely unrestricted existence predicate in terms of a combination of modal tenses. (A version of extended modal realism will be defended in Chapter 8. No new modal-tensing subscript will be used explicitly but could easily be imagined to be present as appropriate.)

5.6.5. Van Inwagen on actuality In the course of examining various theses about the meaning of the phrase ‘the actual world’ van Inwagen comes to the following claim: (a) ‘The actual world’ means ‘the world we inhabit’.35

33

van Inwagen 1986: 221–2.

34

Lycan 1994: 25–9.

35

van Inwagen 1980: 178.

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He rejects (a) in a short paragraph, as follows: What does ‘the world we inhabit’ mean? This phrase can mean only ‘the world we exist in’. And this latter phrase is a necessarily improper description (like ‘the volume of space we are within’ or ‘the odd prime’). This is the case since each of us might have been at least a bit different and each of us, therefore, exists in more than one possible world.36

He spends an additional equally short paragraph to dismiss counterpart theory. Modal realists could certainly agree with van Inwagen’s observation that the phrase ‘the world we inhabit (exist in or at)’ is necessarily improper. Van Inwagen takes this to be an objection against (a). Since he regards (a) to be a central claim of modal realism, he takes this to be an objection against modal realism. I do not claim that modal realists are committed to (a) or that they are not. For the sake of argument, I shall simply assume that the falsity of (a) would be a serious blow to some modal realists, including but not limited to Lewis. My claim is that adoption of modal tense will help those modal realists who wish to defend (a) in the face of van Inwagen’s objection. To begin with, it is instructive to note that van Inwagen says that the impropriety of the phrase in question is like the impropriety of such phrases as ‘the volume of space we are within’ and ‘the odd prime’. The latter phrases are improper because each univocally expresses a property possessed by many. This is certainly one common way for a phrase to be improper but there is another equally common way. It is ambiguity. Adopting modal tense, proponents of (a) can say that the phrase in question is ambiguous between ‘inhabita’ and ‘inhabitp’. It is clear that any proponent of (a) would want it to be understood in the ﬁrst sense. When so understood, van Inwagen’s charge of impropriety does not apply to (a) any longer. Even though we inhabitp many worlds, we inhabita only one world. If one understands (a) as saying that ‘the actual world’ means ‘the world we inhabita’, one commits oneself to understanding actuality of a world in terms of what it is for us to inhabita a world. One should then not understand inhabitinga a world in terms of actuality of a world, on pain of vicious circularity. This is where a further objection against (a) may be made. It may go as follows. The word ‘inhabita’ means ‘inhabit the actual world’, where ‘actual’ is understood in the non-rigid sense. So, one cannot avoid understanding inhabitinga a world in terms of actuality of a world in the non-rigid sense. Thus, if (a) is meant to be a speciﬁcation of the meaning of the phrase ‘the actual world’ in the non-rigid sense of ‘actual’, adoption of modal tense does not help prevent (a) from being circular. If, on the other hand, ‘actual’ in (a) is meant to be understood in the rigid sense, the circularity does not ensue. But in that case, ‘the actual world’ designates @ rigidly, so (a) should be put in a clearer way, such as the following:

36

van Inwagen 1980: 179.

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(a’) ‘@’ means ‘the world we inhabita’. The lack of circularity is obvious here, but now the claim is false. The simple rigid designator ‘@’ designates the world we inhabita but, given the mismatch between its rigidity and the non-rigidity of ‘inhabita’, ‘@’ does not mean ‘the world we inhabita’. (Cf. the simple rigid designator ‘now’ designates the time we exist at, but it does not mean ‘the time we exist at’.) This objection will be convincing provided that we grant its starting point. But the starting point need not be granted and proponents of modal tense should surely reject it. To claim that ‘inhabita’ means ‘inhabit the actual world’ (where ‘actual’ is non-rigid) is to accept the use of the verb ‘inhabit’ without modaltensing, and this is what proponents of modal tense should not do. The actuality tense in ‘inhabita’ is ineliminable. Modal realists should say that ‘inhabita’ means ‘inhabita’, period. When charged that it is uninformative, they should deny the existence of an informative deﬁnition. They should insist that the actuality tense is primitive, just as presentists would insist that the present tense is primitive. If asked how we are supposed to grasp the meaning of any actuality-tensed verb in contrast to the mere-possibility-tensed form of the verb, they should say that we are supposed to grasp it in a way analogous to the way we grasp the meaning of a present-tensed verb in contrast to the past- or future-tensed form of the same verb. This may or may not satisfy van Inwagen, but it shows that there is a modal realist way to save (a) from his objection. Phillip Bricker defends the ‘Leibnizian Realism’, which is the combination of two theses: (1) David Lewis’s modal realism minus his ‘relativist’ theory of actuality, and (2) the claim that actuality is ‘an absolute property that marks a distinction in ontological status’.37 Leibnizian realists do not reject the indexical analysis of the concept of actuality Lewis offers but contend that the property of actuality is absolute. Thus, according to Leibnizians, the indexical concept of actuality determines the absolute property of actuality. Strictly speaking, modal realism with modal tense is neutral on the dispute between Lewisians and Leibnizians on actuality, for the equal reality of what isa and what isp does not entail their complete ontological parity. But it would not be surprising to see a modal-tensing realist take the anti-Leibnizian stance, perhaps along the following lines: Lewisians and Leibnizians agree that the concept of actuality is indexical. Take the arch-indexical word ‘I’. The concept of I-ness (selfness) is indexical, and I would say—and everyone except solipsists and egotists would concur (in a delicate appropriately indexical-sensitive manner)—that the property of being I myself marks no special ontological status. Presentness is like that. The concept of presentness is indexical and the property of being present marks no special ontological status. Likewise, the concept of actuality is indexical and the property of being actual, understood in terms of the actuality tense, marks no special 37

Bricker 2006.

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ontological status. Such an anti-Leibnizian position, though not entailed by modal-tensing realism, would not be without initial attractiveness. Indeed, it is the position of the version of modal realism I endorse. 5. 7 . ACTUALITY OF SPATIOTEMPORALLY ISOLATED WHOLES AND EXISTENCE AT A WORLD There is a sixth objection. It is commonly objected against Lewis’s theory that if there are spatiotemporally isolated merelogical wholes, then the universe as it actually is includes spatiotemporally isolated parts. That is, the objection says that if a multiplicity of what Lewis calls ‘possible worlds’ turn out to exist, then it will only show that actuality is richer than we thought. Can Lewis’s theory be defended from this objection by means of modal tense? A potential defense may proceed along the following lines: A merely possible world isp a spatiotemporally isolated whole. There arep many of them. This has no implication about there beinga spatiotemporally isolated wholes at the actual world. Since Lewis himself is no fan of drawing an analogy between possible worlds and times, he would probably not approve of any such defense. But if a Lewisian modal realist should have no qualms about adopting the modal-tense talk, the above line of defense will be available to her.38 I do not approve of this line of defense of modal realism, as I reject the claim that a possible world is a spatiotemporally isolated whole in any sense, modal-tensed or not. I also reject the claim that there arep merely possible worlds, i.e. that merely possible worlds existp. Things which existp existp at merely possible worlds. So, if a merely possible world w existsp, w existsp at a merely possible world. But it is nonsensical to say that a world exists (existsa or existsp) at a world (actual or merely possible). Existence of a world is not relative to worlds.39 It is nonsensical to say that the year 1964 existed in 1964, or in 964 or in any other past year. In 1964 the year was 1964, i.e. 1964 was the year in 1964, but this does not entail that 1964 existed in 1964. It might be pointed out that it is not only not nonsensical but true to say that 1964 existed in the twentieth century. But this does not go against my position. It is still nonsensical to say that the twentieth century existed in the twentieth century. Remember that possible worlds are points in modal space and hence are

38 Lewis’s insistence on using the unrestricted sense of ‘exist’ when he claims that non-actual possible worlds exist also would prevent him from giving his approval to such a defense of his theory. So the hypothetical modal-tensing Lewisian will need to be prepared to part company with Lewis on this score as well. 39 In a non-vacuous sense. In the vacuous sense, everything about a world is relative to worlds, even matters which themselves are relative to worlds.

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analogous to points in temporal space, namely, moments. It is nonsensical to say that a moment exists (or existed or will exist) at a moment. The nonsensicalness of a possible world’s existence at a possible world is parallel. (Note that here we have another example of true predication without existence.40 It is not true that a merely possible world w existsp at w but it is true that w isp a world at w (isp possible at w, isp self-identical at w, etc.).) But we surely do wish to say that possible worlds exist in some sense. After all, our ontology includes them. Providing an appropriate domain for the existence claim is not a problem; simply have an appropriately large collection of possible worlds. But how should we modal-tense a claim of existence of a possible world with respect to such a collection? Neither the actuality tense nor the mere-possibility tense will do, for each of them ﬂags an individual possible world rather than a collection of possible worlds. In the case of time, the standard tenses perform a double duty; the year 1964 existed in the twentieth century, today exists (in) this week, and the year 11964 will exist in the hundred-twentieth century (cf. Mt Everest existed in the twentieth century, Earth exists this week, and the Milky Way will exist in the hundred-twentieth century). We could let our modal tenses perform a similar double duty, but I think that would be a mistake. The existence of a sheet of paper at a possible world is not analogous to the existence of the sheet in a pile of sheets. The latter is existence with respect to a domain, whereas the former is existence with respect to a metaphysical index. Of course, things which exist at a world may form a domain, with respect to which a further existence claim may be made, but the formation of such a domain presupposes the notion of existence at a world. We need a third modal index. We might choose to use the subscript we introduced in the last section, ‘m’, for this special purpose. We would then be in a position to say that a possible world existsm in modal space at large. We may also be able to make statements of other forms: for example, that a particular world, w, ism thus-and-so in modal space, that some world ism thus-and-so in modal space, that particular worlds, w1 and w2, arem related in such-and-such a way in modal space, and some worlds arem related in such-and-such a way in modal space.41 5. 8. NEITHER ‘STUNNING ADVANTAGE’ NOR ‘OUTRAGEOUS FALSITY’ Some might object to the proposal of modal tensing by saying that it is merely a proposal of a neologism and is therefore superﬁcial and frivolous. To say that talking donkeys existp, for example, is just another way of saying that talking 40

I discussed this issue in a different way and more broadly in 3.4 and 3.5. We might wish to propose an analogous reform in the temporal case by inventing a new tense speciﬁcally for existence claims for times. Mimicking the subscript format of modal tense and using ‘t’ as the chosen letter, we might say that 1964 and 1968 existt in the 20th century, the morning and evening of today existt (in) this week, and 11964 and 11968 existt in the 120th century. 41

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donkeys exist at some merely possible world, they might say, and adopting modal-tensed talk changes nothing of substance. Such an objection is understandable but misses a crucial point of the proposal. As we noted earlier, Lewis’s use of the modal-tenseless language is essential to what Lycan calls the ‘stunning advantage’ over Meinongians and the ‘outrageous falsity’ of his theory. According to Lewis, talking donkeys exist in the same sense in which the mute donkeys of Grand Canyon exist. The difference between the two groups of donkeys is their location (in modal space). We readily and correctly understand the modally neutral senses of ‘exists’, ‘is a donkey’, ‘talks’, etc. They are the ordinary senses of the words. If this is so, Lewis’s quantiﬁcation over the merely possible is not only intelligible but something we already understand readily. This is the ‘stunning advantage’ over Meinongians Lycan has in mind. At the same time, this prompts Lewis’s detractors to point out that talking donkeys have a radically different epistemic status for us (Skyrms) or that in the ordinary sense of ‘exist’ we readily understand, talking donkeys simply do not exist (van Inwagen). I reject the claim that there are ordinary senses of verbs that are modally neutral. I claim instead that we ordinarily and readily understand the modaltensed senses of verbs.42 This is key to the way the ﬁve objections to modal realism are handled. No modal realist who did not insist on modal tense could legitimately mimic our moves. Modal tensing does give away the ‘stunning advantage’ over Meinongians, but not entirely. Tensed verbs are perfectly intelligible. My proposal is that modaltensed verbs are analogously intelligible, whereas the Meinongians supposedly postulate a mysterious realm of reality separate from the familiar realm of reality without informative explanation.43 Modal realists maintain that merely possible objects are real. How should we read ‘are real’ here? By my own light, the verb phrase must have a deﬁnite modal tense. Is it ‘area real’ or ‘arep real’? Actualists would be happy to say that talking donkeys arep real just as much as presentists would be happy to say that dinosaurs were real. To distance themselves from actualists, modal realists therefore must say that merely possible objects not only arep real but also area real. Furthermore, they should perhaps also say that all merely possible objects, as well as actual objects, area real and arep real at every possible world. Some might ask the following question in connection with Skyrms’s objection to modal realism: if talkingp donkeysp not only arep real but also area real, then why can’t we knowa about them by empirical means? Those who ask this question misunderstand the epistemic relevance of reality. Reality is all-inclusive 42 A modal-tenseless sense is at best an artiﬁcial product manufactured out of modal-tensed senses by means of disjunction in a way analogous to the way the four-dimensionalist tenseless sense of ‘is’ may be construed by a presentist to be the disjunction of ‘is’ (in the present tense), ‘was’, and ‘will be’. 43 For Meinong’s metaphysical theory, see Meinong 1960; Findlay 1963.

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and encompasses individuals susceptible to empirical means and individuals not so susceptible. It is not reality but the ﬂesh-and-bloodness of talkingp donkeysp that makes them prima facie susceptible to empirical means. If talkingp donkeysp area ﬂesh-and-blood, then we should be able to knowa about them by empirical means, it appears. In a sense this is indeed the case, but it is an innocuous sense. The mute donkeys in Grand Canyon as they are at the actual world are such that it is possible for them to be talking donkeys. So at some possible world they are talking donkeys. So, these donkeysa area ﬂesh-and-blood and arep talkingp donkeysp. But of course, we are able to, and do, knowa about these donkeys as they are at the actual world. This is the sense in which talkingp donkeysp area ﬂesh-and-blood and we are able to, and do, knowa about them by empirical means. This involves no mystery or problem speciﬁcally for modal realism. On the other hand, it is possible for there to be donkeys that do not exist (as donkeys or as some other kind of individuals) at the actual world and that talk. Because they area not actual, we are not able to knowa about such donkeys by empirical means. For the same reason, they area not ﬂesh-and-blood. So, such talkingp donkeysp area not ﬂesh-and-blood. Modal tense is not a gimmick. It is a mistake to think that ‘There arep talkingp donkeysp’ is a gimmicky way to say the same thing as ‘There are talking donkeys at a merely possible world’. Strictly speaking, modal realists should regard the latter sentence as not fully articulate and refrain from using it. They should instead stick to the former sentence. The mere-possibility tense is deﬁnable in terms of the actuality tense. Other modal tenses, if there are any, should also be so deﬁnable. But the actuality tense is not deﬁnable in modal-tense-neural terms. In this sense, modal tense is ineliminable. Modal realists are better off as modal tensers. This, of course, does not mean that no modal theorist opposed to modal realism can beneﬁt from modal tensing. But our discussion at least shows that modal tensing will afford modal realists a more effective way to counter objections. I suspect that there are modal tenses other than the simple actuality and merepossibility tenses. Modal realists should uncover and investigate them all and use them to formulate, elaborate, and defend their theory. Furthermore, taking modal tense seriously is only part of a larger methodological strategy. Following the parallel between worlds and times in a bold yet careful way will give modal realists a powerful framework in which to construct a full theory.

6 Transworld Individuals and their Identity 6 . 1 . TRANSWORLD INDIVIDUALS Mark Heller offers an argument for four-dimensionalism, the claim that physical objects are four-dimensional spatiotemporal worms.1 I propose to adapt it to serve our modal realist purposes. The argument I offer starts where Heller’s argument ends, that is, I begin by assuming that physical objects extend in space and time, and argue that they extend also in modal space. Heller starts with ﬁve claims which he calls ‘unpleasant alternatives’. He argues that denying all ﬁve unpleasant alternatives while accepting three-dimensional enduring objects would lead to a contradiction. He then offers four-dimensionalism as a way to reject three-dimensional enduring objects. So, the upshot of his argument is that if we wish to avoid the ﬁve unpleasant alternatives, we should accept fourdimensional perduring objects rather than accepting three-dimensional enduring objects.2 For the purpose of our argument, I shall recast the ﬂow of Heller’s argument in a more straightforward way, moving from premises to the ﬁnal conclusion via intermediate lemmas. The logical structure remains faithful to Heller’s original. What follows is not a reconstruction of Heller’s argument, but a different argument inspired by Heller’s argument. Heller himself would not accept it3 and that is his loss, I say. Let us start by following Heller by speaking of his body. (A) Heller’s body exists. Call Heller’s body ‘Body’. By (A), Body exists. We are assuming that physical objects extend in space and time. So, Body extends in space and time. Body as it actually is is a mereological whole extending in four dimensions––a four-dimensional worm––at the actual world. Consider a proper part of that worm which includes all of Body except Heller’s left hand during the last year of his life, and

1 This is four-dimensionalism in a sense narrower than the sense in which we used the term in 5.5. 2 Heller 1990: 3–4, 19–20. Heller borrows the idea for the argument from van Inwagen 1981: 123–37. See also Geach 1962: s. 110. 3 Heller 1990: 72 is a passage to that effect.

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call it ‘Body-minus’. Any macro proper part of an existing physical object also exists, so (B) A physical object exists in the space and time that we would typically say is exactly occupied by all of Heller as he actually is other than his left hand during the last year of his life. By (B), Body-minus exists. Heller’s left hand is not actually cut off but (C) It is possible for Heller to lose his left hand one year prior to the end of his life. Consider some possible world w at which his left hand is cut off one year prior to his death. Body-minus would not be affected by the loss of the left hand. So (1) The thing that, at @, is Body-minus ¼ the thing that, at w, is Bodyminus. Since including a left hand in the last year of its existence is not an essential property of Heller’s body, Body exists at w: (2) The thing that, at w, is Body ¼ the thing that, at @, is Body. Now, Body as it is at @ is larger than Body-minus is at @. So (3) The thing that, at @, is Body-minus 6¼ the thing that, at @, is Body. But of course, (D) Identity is an equivalence relation. From (1)–(3) and (D), it follows that (4) The thing that, at w, is Body-minus 6¼ the thing that, at w, is Body. But at w, Body occupies exactly the same space and time as Body-minus. So, if the thing that, at w, is Body-minus and the thing that, at w, is Body are fourdimensional objects, then two physical objects of the same kind (namely, human body) occupy exactly the same space and time at the same possible world.4 But, as the four-dimensional version of the Lockean claim would say,

4 Graeme Forbes suggests that such two physical objects as Body and Body-minus are different in kind on the grounds that one is a human body but the other is a human body minus a proper part of it (Forbes 1987: 143). This suggestion does not undermine the argument. Consider a proper part of that four-dimensional whole which includes all of Body as it actually is except Heller’s right hand during the last year of his life, and call it ‘Body-minus-right’. Consider a proper part of that fourdimensional whole which includes all of Body-minus except Heller’s right hand during the last year of his life, and call it ‘Body-minus-right-minus’. Run the argument as before with Body-minus-right and Body-minus-right-minus replacing Body and Body-minus, respectively. The new argument is as strong as the original and the two physical objects in question are clearly of the same kind even by Forbes’s standards.

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(E) No two four-dimensional objects of the same kind occupy exactly the same space and time at the same possible world. Hence, the thing that, at w, is Body-minus and the thing that, at w, is Body are not four-dimensional objects. Obviously, they are not three-, two-, one-, or zerodimensional objects. Therefore, they are ﬁveþ-dimensional objects, i.e. they extend in modal space. (I say ‘ﬁveþ-dimensional’ instead of ‘ﬁve-dimensional’, for modal space is not linear, so the modal dimensions number two or more, though it is not clear exactly how many.) The one physical object which occupies exactly the same space and time as Body (and Body-minus) at w is a common modal part of two different modally extended objects, namely, Body and Body-minus. As Heller reports concerning his own argument, Judith Jarvis Thomson denies (E) (or its three-dimensional version), Peter van Inwagen denies (A) and (B), Roderick Chisholm denies (C) (or more speciﬁcally, he denies that any physical object can undergo a loss of parts), and Peter Geach denies (D).5 David Lewis would reject (1) in favor of the counterpart-theoretic rendering of the possibility de re implicit in (C). He would also reject (2) for the same counterpart-theoretic reason. Heller says of the claim ‘that physical objects spread out across possible worlds in the same way that they spread out across space’ that ‘(a)lthough this is not an unheard of philosophical thesis, it is not one that I wish to be committed to’.6 Heller holds the view that every four-dimensional object has its four-dimensional boundaries essentially, so he would reject (2). But if Body is among ordinary physical objects we normally think actually exist, then since such objects could lose a small part without losing identity, Body could lose a left hand without losing its identity. Heller is aware of this and as a result he rejects the claim that ordinary physical objects we normally think actually exist really actually exist. This part of his theoretical position follows van Inwagen’s. I think we should include this van Inwagen–Heller view among those ‘unpleasant alternatives’ which should be avoided. Each of the four philosophers Heller mentions, Thomson, van Inwagen, Chisholm, and Geach, rejects some thesis Heller accepts. According to Heller, rejecting these theses would constitute the acceptance of unpleasant alternatives. Since he sees no way of avoiding the unpleasant alternatives except by rejecting three-dimensionalism, Heller appropriately states, ‘It is incumbent upon me, then, to offer a reasonable alternative to the three-dimensional view of physical objects’. He proceeds to give his well-known four-dimensionalist view of physical objects. In this Hellerian spirit, I shall proceed to elaborate on the ﬁveþdimensionalist view.

5 6

Thomson 1983; van Inwagen 1981; Chisholm 1973; Geach 1967. Heller 1990: 72.

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6 . 2 . HAECCEITISM We name, predicate properties and relations of, and quantify over ordinary physical objects. Those objects extend in physical space and time and in modal space. The idea is expressed concisely by David Kaplan: The doctrine that holds 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 being extended in physical space and time, and that a common ‘thisness’ may underlie extreme dissimilarity or distinct thisnesses may underlie great resemblance, I call Haecceitism.7

The point of this passage as a whole, however, is a characterization of haecceitism. As usually understood, haecceitism is a doctrine separate from and independent of modal realism.8 The usual conception of haecceitism is captured more or less by the second half of Kaplan’s characterization but not by the ﬁrst half, which captures ﬁveþ-dimensionalism. Interestingly, Kaplan goes on to say, The opposite view, Anti-Haecceitism, holds that for entities of distinct possible worlds there is no notion of transworld being . . . there is no metaphysical reality of sameness or difference which underlies the clothes.

Anti-haecceitism as so characterized is not the negation of haecceitism as characterized by Kaplan. The complexity of the relation between Kaplan’s haecceitism and anti-haecceitism becomes evident when he says, Although the Anti-haecceitist may seem to assert that no possible individual exists in more than one possible world, that view is properly reserved for the Haecceitist who holds to an unusually rigid brand of metaphysical determinism.

To spell out exactly what Kaplan’s conceptions of haecceitism and anti-haecceitism amount to is an exercise in which we shall not engage. Sufﬁce it to say for our purposes that we side with the majority of theorists in separating haecceitism, as captured roughly by the second half of Kaplan’s characterization in the ﬁrst quoted passage above, and regarding it as largely independent of detailed theorizing about possible worlds. What Kaplan speaks of as ‘thisness’ should best be understood as the property of being a particular individual object as being given in such a way as to be able to be demonstrated by ostension, for example, by a pointing index ﬁnger accompanied by a proclamation ‘this K’, where ‘K’ is replaced with an appropriate kind term, or a sortal term in David Wiggins’s 7

Kaplan 1975: 723; Loux: 1979: 217. Some explicitly endorse haecceitism, some explicitly reject haecceitism, and others assume one attitude or the other toward haecceistism more or less implicitly: e.g. Robert Adams, an ersatzist, explicitly accepts haecceitism (1979) and David Lewis (1986: 220–48) explicitly rejects it. 8

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sense.9 Despite the original Latin meaning of the word ‘haecceitism’, I ﬁnd it misleadingly loaded to use the expression ‘thisness’ in any part of the characterization of haecceitism as I understand the notion. I ﬁnd David Lewis’s characterization appropriately sterile (i.e. clean and free of potentially harmful extraneous elements), so I shall adopt it: if two worlds differ in what they represent de re concerning some individual, but do not differ qualitatively in any way, I shall call that a haecceitistic difference. Haecceitism, as I propose to use the word, is the doctrine that there are at least some cases of haecceitistic difference between worlds. Anti-haecceitism is the doctrine that there are none.10

Modal realism is compatible with haecceitism and with anti-haecceitism. The version of modal realism I advocate is anti-haecceitist. David Kaplan speaks of his ‘Jules Verne-o-scope’, which is a modal telescope enabling us to peep in at goings-on at non-actual worlds.11 Suppose we borrowed his Jules Verne-oscope and peeped in.12 As we looked through it, we might be stimulated into deep philosophizing and the following thought might occur to us: We are looking through Kaplan’s Jules Verne-o-scope and seeing a man be born, grow up, live his life, and die in qualitatively exactly the same way as Richard M. Nixon actually did. If we ask ourselves whether this man is or isn’t Nixon, we will be asking a question that is ill deﬁned. Unlike traditional telescopes astronomers use, the Jules Verne-o-scope has no natural connection to the goings-on at worlds it presents to the viewer that grounds uniqueness, and no non-natural connection between the Jules Verne-o-scope and the goings-on at worlds can ground uniqueness. Many different worlds ﬁt the same purely qualitative appearance coming through the Jules Vernes-o-scope. At some of these worlds the man appearing exactly Nixony is Nixon, and at others the man appearing exactly Nixony isn’t Nixon. A better-deﬁned question we should ask ourselves is what makes the exactly Nixony man at some of the peeped-in worlds Nixon and what makes the exactly Nixony man at some of the peeped-in worlds not Nixon.

Such a thought, when properly understood, assumes haecceitism. Suppose that there are many possible worlds which are qualitatively indistinguishable from the actual world and at which a man looks and behaves throughout his life exactly as Nixon does at the actual world and is also otherwise qualitatively the same as Nixon at the actual world. The thought in question assumes that some of these qualitative duplicates of the actual Nixon are Nixon and others are not. This is haecceitism, and I deny it. That is, I hold that all qualitative duplicates of the actual Nixon at all possible worlds the goings-on at which are qualitative duplicates of those at the actual world are Nixon. 9

Wiggins 1980. Lewis 1986: 221. 11 Kaplan 1979a: 93, 99. 12 This, of course, is metaphysically impossible. At the same time, we know what we are supposing and what is appropriate to say on that supposition and what is not. This indicates that the contents of our thinking transcend the metaphysically possible. For more on this, see Ch. 8. 10

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There is yet another conception of haecceitism. Nathan Salmon says, Haecceitism holds that it is perfectly legitimate when introducing a possible world for consideration and discussion, to specify the world explicitly in terms of facts directly concerning particular individuals, designating those individuals directly by name if one chooses to.13

According to this conception, haecceitism is not about transworld identity at all but about our speciﬁcation of possible worlds. It says that it is ‘perfectly legitimate’ to specify possible worlds by saying something like this: ‘Take Al Gore. Let us consider a possible world at which he won the 2000 U.S. presidential election.’ More generally, it sanctions the following type of speciﬁcation of possible worlds: ‘Take Æ. Let us consider a possible world at which it/she/he (Æ) is thus-and-so’, where ‘Æ’ is to be replaced with a directly referring term. Whether or not this exactly captures what Salmon intends, let us call this conception of haecceitism ‘Salmon’s conception’. I do not accept haecceitism under Salmon’s conception but accept something similar. The matter of ‘stipulating’ possible worlds will be discussed in 6.9, and further related issues will be discussed in Chapter 8. 6. 3 . TRANSWORLD IDENTITY Quine famously said that if objects lack a clear criterion of identity, then they should not be admitted into a respectable ontological theory (‘No entity without identity’), and that merely possible objects lack a criterion of identity (they are ‘disorderly elements’).14 Some philosophers have objected to Quine’s stern ontological stance by pointing out that it is acceptable only if actual objects do not lack a criterion of identity but that actual objects lack a criterion of identity,15 while others have extended Quine’s ontological sternness to argue that a respectable ontological theory should admit only those objects which have precise boundaries, excluding all (or most) ordinary objects.16 I fall somewhere between the two groups of philosophers reacting to Quine. I think that actual objects do not lack a criterion of identity and that ordinary objects with imprecise boundaries have a place in a respectable ontological theory. The key idea is that although a respectable ontological theory should demand a criterion of identity for every object it admits, an identity criterion which allows vagueness is identity criterion enough.17

13 14 15 16 17

Salmon 1996: 204. Quine 1963. e.g. Parsons 1987; Jubien 1996. e.g. Heller 1990; van Inwagen 1990; Merricks 2003. But see 6.13.3.

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When I speak of an identity criterion, I mean a criterion of identity through metaphysical indices of a particular kind. Such a criterion is best understood as a criterion for unifying metaphysical-indexical parts into a whole object which is extended in the metaphysical dimensions of that kind. For example, what Kurt Lewin called ‘gen-identity’18 is a case in point, where the metaphysical dimension in question is temporal. In order to craft a transworld identity criterion, we shall follow the spatial and temporal identity criteria. Let us ﬁrst ﬁx our attention on the universe as it actually is at a particular time. It is a temporally frozen universe at @. Take an earthworm and its particular disc-shaped spatial cross segment. Then take a different disc-shaped spatial cross segment of an earthworm. What is the condition under which the ﬁrst segment and the second segment are segments of one and the same earthworm? The current consensus among philosophers, to the extent to which there is a consensus on such a matter, is that the segments are of the same earthworm if and only if they are connected by a chain of segments of an earthworm in the following sense: there is a connected sequence of disc-shaped regions of space such that the ﬁrst region is occupied by the ﬁrst segment, the last region is occupied by the second segment, and every other region is occupied by a cross segment of an earthworm. The temporal case is similar. One temporal segment, or stage, of an earthworm and another temporal stage of an earthworm are temporal stages of the same four-dimensional whole of a persisting earthworm if and only if they are connected by a chain of temporal stages of an earthworm. (Some may say in addition that adjacent temporal stages should be related by causation. This issue will be addressed later.) A complication arises when such a chain bifurcates in one direction of time or the other. These are so-called ﬁssion and fusion cases. One moment an ordinary earthworm is crawling on the ground. The next moment two exact duplicates of the original earthworm are crawling on the ground in such a way that if only one of them were there, we would not hesitate to say that it would be identical to the original earthworm. This is an example of ﬁssion. Illustrations of ﬁssion cases are often accompanied by fancy science-ﬁction details. For example, an advanced machine may be said to scan an individual’s molecular composition, decompose the individual into the constituent molecules, duplicate the molecules, scramble the original and duplicate molecules, and reassemble those molecules into two qualitatively indistinguishable individuals. Each of the original molecules is placed in the same place within a new body as it was in the original body, and each duplicate molecule is placed in the same place within a new body as the corresponding original molecule is within its new body. We may further assume that the molecular continuity between the original and one of the emerging individuals is of the same degree and quality as the molecular continuity between the original and the other emerging individual. It is hard to identify one of the 18

As reported in Kaplan 1979a: 93.

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emerging individuals with the original over the other, and we cannot identify both of them with the original, on pain of committing ourselves to the implausible claim that the two emerging individuals constitute one spatially scattered individual that is identical with the original,19 or to the even more implausible claim that the two emerging individuals, which occupy different locations at the same time, are identical to each other. If we identify neither of the emerging individuals with the original, we are deeming the original individual to have gone out of existence. But this appears unacceptable, given that if there were only one of the emerging individuals, we would readily identify that individual with the original. What should we do? Fusion reverses the temporal direction of ﬁssion. Two qualitatively indistinguishable individuals are decomposed into molecules, which are then randomly mixed up and one half of the mixed whole is assembled into an individual that is qualitatively indistinguishable to each of the original individuals. Is the emerging individual identical to one of the original individuals? If so, which one? If not, why not? 6. 4 . CLOSEST-CONTINUER THEORY A uniﬁed way to answer these questions is given by the closest-continuer theory: for any temporal stage at t2 x of a temporally persisting individual at time t1 and any temporal stage at t1 y of a temporally persisting individual at time t2, x and y are temporal stages of the same temporally persisting individual if and only if there is a sufﬁciently tight chain of temporal stages of a temporally persisting individual between x and y and there is no tighter connected chain of temporal stages of a temporally persisting individual between x and some temporal stage of a temporally persisting individual other than y or between y and some temporal stage of a temporally persisting individual other than x.20

According to the closet-continuer theory, the cases of ﬁssion and fusion are cases of non-identity. Neither of the two emerging individuals equally close to the original individual in the ﬁssion case is identical with the original individual. The original individual ceases to be and two new individuals come to be. Likewise in the fusion case; the two original individuals cease to be and one new individual comes to be. Provided that the chain between x and y is tight enough, the presence of an equal competitor to y crucially affects the identity between the worm x is part

19 I do not pursue this scenario, because I think it is implausible to say that the worm remains one yet becomes scattered in space in such a way that it appears to be two distinct worms, not because I think it is metaphysically impossible. It may well be a worthwhile project for some purposes to develop such a scenario. 20 Though not the ﬁrst to propose a version of closest-continuer theory of identity, Robert Nozick presents a more or less deﬁnitive version and its defense (1981: 27–70). Also see Shoemaker 1979.

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of and the worm y is part of. If there is an equal competitor, the worms are not identical, but if there is not, they are. These consequences of the closest-continuer theory are not implausible. They are certainly not less plausible than the consequences of other serious theories of identity. These consequences do not satisfy all philosophers,21 but very few metaphysical theories yield non-trivial consequences which satisfy all philosophers. Extending the original closest-continuer theory, which was only intended for transtemporal identity, to trans-spatial identity requires care. (Robert Nozick, a prominent proponent of the closest-continuer view, incorporates causation into his theory. We shall suppress this aspect of the original closet-continuer idea. More on causation later.) Call the portion of my left little ﬁnger from the base to the third joint ‘L’, and the portion of the ﬁnger from the third joint to the end ‘F’. Consider a small spatial region which is occupied by my left little ﬁnger now and which is slightly thicker than the ﬁnger itself. Call the subregion of this spatial region occupied by L ‘S1’, and the subregion occupied by F ‘S2’. If I have a normal ﬁnger, the closest spatial continuer of L in S2 is F; S2 is also occupied by some air molecules but they are not closer to L than F is, nor is the sum of F and those air molecules. So F is part of the same little ﬁnger as L. This is the normal case. Now suppose that I have an abnormal left hand. In particular, suppose that F is thinner than in the above normal case. Also, suppose that a very thin structure, P, protrudes from L and occupies (most of) the rest of S2 unoccupied by F. P lacks enough nerves running through it to be subject to voluntary movement. In such a case, F is a closer continuer of L than P is in S2, and there is nothing closer, so again F is part of the same little ﬁnger as L. Although P is not part of the same little ﬁnger as L, it is an appendage to the little ﬁnger of which L is part. Now suppose a different case: F is attached to L at an angle from the vertical, and P is attached to L at the same angle on the opposite side from F and is indistinguishable from F in shape, size, color, anatomy, and function. P is as good a continuer of L as F is. So neither is the closest continuer of L. Thus if we adhere to the closest-continuer theory, we will have to say that the little ﬁnger of which L is part ceases to be at the third joint and two shorter little ﬁngers take over. That is, I have three little ﬁngers, two on top of the ﬁrst one. I do not ﬁnd this consequence of the closest-continuer theory as applied to trans-spatial identity utterly implausible but admit that it sounds odd. It may sound better to say that in the imagined case I have one little ﬁnger which branches off into two short tips. If so, then we should revise the closest-continuer theory to accommodate it. An obvious way to do so is by recognizing the difference between temporal and spatial cases and saying that while two separate temporal stages 21 e.g. Peter van Inwagen (1990: 12) lists the following thesis as one of his ten ‘convictions’, or ‘constraints’: ‘If object A is at place x at t1, and if object B is at place y at t2 , then nothing besides the causal processes or chains of events that connect what is going on at x at t1 with what is going on at y at t2 is relevant to the question whether A and B are the same object.’

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at time t of a temporally persisting individual like a worm or a ﬁnger may not be temporal stages at t of the same temporally persisting individual, two separate spatial parts at spatial region s of a spatially extended individual like a worm or a ﬁnger may be spatial parts at s of the same spatially extended individual. Thus, we may drop the uniqueness condition from the closest-continuer theory in the case of trans-spatial identity.22 And if we do, a moment’s reﬂection should also prompt us to drop the stringent closeness condition as well; P should count as part of the ﬁnger even if it were slightly less similar to L than F. Notice that these spatial cases must involve (extended) spatial regions. If we are only allowed to speak of spatial points and not regions, we cannot construct these cases. A similar situation does not hold for times; consideration of the closest-continuer theory may be conducted equally well either with moments of time or with periods of time. Possible worlds are more like spatial points or temporal moments than spatial regions or temporal periods; they lack modal extension. For this reason, we shall follow transtemporal identity as our model more closely than transspatial identity when considering transworld identity. Earlier, in Chapter 1, I mentioned semantic externalism to motivate modal realism and gave the following general abstract schema of externalism: Let X be a certain item, P a class of properties for X to possess, and Y a certain item with respect to which X’s possession of a member of P is relativized. The determination of which member of P X possesses with respect to Y transcends the total internal facts about X and Y. The closest-continuer theory of identity conforms to this schema, so it is externalist. The determination of whether temporal stages x and y are parts of the same persisting individual, i.e. whether x possesses the property (or relation) of being part of the same persistent individual as with respect to y, is partly a matter of whether there is a rival continuer other than y, hence it transcends the total internal facts about x and y. Adoption of the closest-continuer theory of identity will thus bring motivational unity to modal realism. In both spatial and temporal cases, the notion of a chain of segments presupposes a privileged arrangement of spatial regions and temporal periods. Regions and periods are arranged in a certain privileged, or natural, way along the three-dimensional ordering for space and one-dimensional ordering for time. Identity over regions and periods is then analyzed in terms of the ancestral of the similarity relation between stages at these regions and periods. (For identity over space, there is often a further complication of functional cohesion.) In the case of possible worlds, the situation appears signiﬁcantly different. Unlike space or

22 If the scenario mentioned in n. 19 can be made respectable, trans-spatial identity and transtemporal identity may be treated with more uniformity after all.

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time, there appears to be no natural arrangement of possible worlds.23 If so, there is no natural arrangement of modal stages of individuals. So there appears to be no non-arbitrary measure of the length of the chain of similarity connecting one modal stage at one possible world to another modal stage at another possible world. Take an actual earthworm which grows in length rapidly right after birth, grows at a progressively slower pace until the midpoint of its lifespan, and then shrinks (due to constant nibbling predation by its enemy perhaps) at a progressively faster pace until it vanishes at the end of its life. The four-dimensional totality of the earthworm’s spatial and temporal segments will be a thin oval hyperdisc; it will not be a smooth hyperdisc, for the earthworm wiggles. (If we pretend that space is two-dimensional, then the three-dimensional totality of the earthworm’s spatial and temporal segments will be a thin, non-smooth oval disc.) This hyperdisc-shaped four-dimensional worm is the modal segment, or modal stage, of the earthworm at the actual world. The earthworm extends in modal space. So it has other modal stages at other possible worlds. Some of these modal stages are thicker oval hyperdiscs, some are longer oval hyperdiscs, and others are entirely differently shaped. The earthworm is the modal-dimensional hyperworm24 consisting of all of those modal stages. Modality, unlike time, is not one-dimensional and objects which extend modally generally have irregular multidimensional shapes. Other earthworms are other modal-dimensional hyperworms consisting of other modal stages. One modal stage of an earthworm and another modal stage of an earthworm are modal stages of the same modaldimensional hyperworm if and only if they are connected by a sufﬁciently tight chain of modal stages of an earthworm and are each other’s closest continuer. This parallels the cases of spatial and temporal criteria of identity exactly, provided that we can make sense of the connectedness. But, as we noted, it appears that, unlike spatial and temporal connectedness, modal connectedness cannot be based on any privileged arrangement of possible worlds. Spatial points are above or below, to the left or right of, or in front of or behind, other spatial points, relative to a given spatial perspective. Times are even neater; every temporal moment is either before or after another temporal moment. By comparison, possible worlds appear to lack any natural arrangement among them; they certainly appear to lack any natural one-dimensional, two-dimensional, or three-dimensional arrangement. Fortunately, the appearance of a total lack of ordering of any privileged sort is illusory. One of many lessons we should learn from David Lewis’s fruitful 23 There might appear to be more hope for a privileged or natural arrangement of aggregates of possible worlds, especially if those aggregates form equivalence classes under propositional necessary equivalence (in some suitable sense of necessity). But even then, modal space may be divided into aggregates of possible worlds in many different ways and these ways themselves will have to be arranged in a privileged or natural way. 24 So-called not because it is an earthworm but because it is a modal analog of a fourdimensional worm.

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exploration of modal space (which he calls ‘logical space’) is the theoretical versatility of the similarity relation between possible worlds. Lewis elevated the similarity relation to form the core of his theory of counterfactual conditionals. Our current theoretical focus is elsewhere. We shall use similarity to order possible worlds to set up the background against which transworld identity is to be understood. I hasten to add that we shall not attempt to order possible worlds linearly. Such an attempt would be a fruitless endeavor, and our ﬁveþdimensionalist version of modal realism does not require it. At this point, let us note that Lewis’s other use of similarity, in his counterpart theory, is not what we should emulate. There are ﬁve reasons. First, our need for similarity in our theory is signiﬁcantly different from Lewis’s in his counterpart theory. Lewis uses similarity in his counterpart theory to account for modality de re. Since modality de re concerns an individual (res), he needs the similarity relation to hold between an individual and a counterpart individual. We, on the other hand, need similarity to ground some privileged arrangement of possible worlds. So, we want similarity to hold between possible worlds, not between modal stages of an individual. Second, our strategy is to establish a privileged arrangement of possible worlds ﬁrst and then on that basis make sense of the notion of a continuer of a given modal stage of an individual, and ultimately transworld identity. Starting ﬁrst with the notion of similarity between modal stages of an individual would get in the way of this order of account. Third, we need similarity to hold between a possible world at which a relevant modal stage exists and another possible world at which no modal stage similar to the ﬁrst one exists. This is so because we need to be able to make sense of a gap in a given sequence of possible worlds where the transworld continuation of a transworld individual is interrupted; compare how the temporal continuation of a temporally persisting individual may be interrupted at a particular time. Fourth, transworld identity cannot be grounded in an arrangement of worlds that is based solely on similarity between modal stages of individuals. Consider, for example, a biological individual. Transworld identity of such an individual may well be dependent not only on the similarity between modal stages of a biological individual but also on the similarity between evolutionary histories of modal stages of a biological individual, where the evolutionary history of a modal stage of a biological individual is not part of that stage. (Some might say that whether a modal stage of a biological individual is similar to another such stage at a different world depends on the evolutionary-historical properties of the stages. But once we allow extrinsic properties, it is a short path to allowing properties of the form ‘being such that P’ in general, and once we allow those properties, the distinction between similarity between modal stages of an individual and similarity between possible worlds is lost.) Fifth, similarity between counterparts is sensitive to the contextual factors surrounding the modal discourse. A Nixony man at one world may serve as Nixon’s counterpart at that world for the purpose of securing the truth of one possibility claim, while another Nixony man at the

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same world may serve as Nixon’s counterpart at that world for the purpose of securing the truth of a different possibility claim. But we need our similarity relation between worlds to be a context-independent relation. Lewis’s similarity relation between worlds is tailored to suit the purpose it is intended to serve, namely, grounding the truth conditions for counterfactual conditionals. It is the right similarity relation to use for our purposes, for if the universe were only slightly different from how it actually is––say with respect to a relative position of two alpha particles in the Delta Quadrant of the universe––all things would still be very much as they actually are, and we can form a chain of worlds from the actual world incrementally by means of one slight difference at a time. There are many such chains from one world to another world, and that is why worlds are not ordered linearly. In the evaluation of a counterfactual conditional, the matter of which antecedent-verifying world counts as more similar to the actual world than which other antecedent-verifying world for the purpose of the evaluation is in general sensitive to contextual factors. But this does not mean that the matter of which world is more similar to which world independently of such an evaluation is also sensitive to contextual factors. To specify how exactly all possible worlds are to be arranged in the order of similarity is too large a task to be undertaken here, and in any case I would not know how to do it. Fortunately, Lewis helps us with a rough sketch, according to which the similarity relation in question ‘must be governed by the following system of weighs or priorities. (5) It is of the ﬁrst importance to avoid big, widespread, diverse violations of law. (6) It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails. (7) It is of the third importance to avoid even small, localized, simple violations of law. (8) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly.’25 6. 5. VAGUENESS Take identity over space. Consider any mountain on the surface of Earth. It is connected to any other mountain on the surface of Earth by physical continuity. Assuming that mountains are spatially spread objects, someone might make the extraordinary suggestion that there is only one mountain, the super-mountain, on the surface of Earth, of which every bit of protrusion we customarily call a 25 Lewis 1979a: 47–8, numbering adjusted. For an outline of how Lewis arrives at this system, see 8.3.

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mountain is a locally prominent spatial segment. Such a suggestion would be coherent but not credible. It should be countered by the claim that the fact that a mountain is spatially spread out does not mean that it includes as its part everything spatially connected to it. A mountain ceases to be at some point in the spatial spread. Of course, there is no saying exactly where it ceases to be, as the matter is notoriously vague. But our task is not to solve the problem of vagueness. We should simply take note of the presence of vagueness and learn to live with it. Common sense does. Let x be a modal stage of an ordinary object at the actual world and y be a modal stage of an ordinary object at another possible world. Suppose that x and y are connected by an appropriate chain of worlds. This does not guarantee that the extent of the modal spread of the ordinary transworld object, X, of which x is the actual-world modal stage should include y. X may cease to be, somewhere along the chain before the world of y. And this ceasing to be of X may be a vague matter. There is a disanalogy between (modal stages of ) mountains and ordinary transworld objects. A mountain has a natural end point, its summit. The summit is part of the mountain if anything is. But there is no corresponding end point in a transworld object, even of an ordinary kind. Any modal stage is as good a starting point (candidate end point) for the identiﬁcation of the transworld object as any other. This means that the identiﬁcation of a transworld object must be locally constrained. We naturally identify ordinary objects as transworld objects with certain vague modal boundaries by starting with their actual-world-stages. For example, we ﬁrst point to a particular actual-world-stage of a table, and then identify the transworld object of which it is a stage by tracking modal stages at different non-actual worlds based on the actual-world-stage. The actual-worldstage functions as the end point (analogous to the summit of a mountain), and stages at different worlds are judged to be stages of the same transworld table or not according to their relation to the end point. The connectedness of a chain of worlds should be understood in terms of similarity. It is a little more difﬁcult to understand than the connectedness of a chain of temporal moments, but not much more. Imagine a scene captured in a cinema still made from a cell of a ﬁlm. Next imagine the scene captured in a still made from the next adjacent cell, then imagine the scene from the cell next to that, and so on. Such a series of imaginings is a good way to conceive of a chain of scenes at different temporal moments, and the conceived chain is the chain of the moments of those scenes. Is the chain of those moments connected? Not in the sense of containing every moment during the shooting of the sequence of the scenes, for there are far fewer cells of the ﬁlm than there are moments of time during the shooting. It is not possible to ﬁlm a scene for every moment between the two moments corresponding to a given pair of adjacent cells. But the chain is indeed connected in the sense that for any moment between the two moments corresponding to any adjacent pair of cells, the scene at that moment is fairly accurately recoverable by interpolation. To apply this idea to possible worlds,

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imagine two possible worlds, w1 and w2, which are very similar to each other overall and also speciﬁcally with respect to the w1-stage x of a human being and the w2-stage y of a human being. These worlds correspond to the moments of the scenes depicted in two adjacent cells, and x and y correspond to the temporal stages of an individual ﬁguring in the scenes depicted in the two respective cells. Let us say that x and y are almost qualitatively identical; the main difference between them is the positioning of a particular small body part, say, a hair. At w1 the tip of x’s hair is at 77 degrees to the north from the base of the hair, and at w2 the tip of y’s hair is at 78 degrees. There are inﬁnitely many degrees between 77 and 78, so there are inﬁnitely many possible worlds between w1 and w2 when judged in accordance with the similarity measure with respect to x and y while keeping the rest of the worlds qualitatively unchanged,26 and they can be ordered by means of the same similarity measure. Whether or not there are the same number of possible worlds between w1 and w2 in this ordering as there are moments between the two moments corresponding to an adjacent pair of cells of ﬁlm, the analogy is strong enough for our purposes. Consider the chain of possible worlds consisting of w1, w2, and all the interpolated worlds in between in the right order. It is a chain of possible worlds. The chain may be extended in either direction, beyond w1 or beyond w2, yielding a longer connected chain of possible worlds. Against this background of a connected chain of possible worlds, we shall characterize transworld identity along the lines of the closest-continuer theory. It is worth noting that the relation of being the closest continuer is not symmetric. Modal fusion–ﬁssion cases give obvious counterexamples, but there is another counterexample which does not involve twin worldmates. Consider a self-sustaining mid-sized inanimate object O and a small speck of dust S. Take a possible world, w8, at which O exists and nothing else (other than O’s proper parts) does, and another possible world, w9, at which O and S exist and nothing else (other than their proper parts) does. Assume that the w8-stage of O and the w9-stage of O are very similar to each other. The closest continuer at w8 of the mereological sum of the w9-stage of O and the w9-stage of S is the w8-stage of O. But the closest continuer at w9 of the w8-stage of O is not the mereological sum in question, but its proper part, namely, the w9-stage of O. If we deny that the mereological sum is a modal stage at w9, we can block this reasoning against symmetry, but I see no point in doing so. Stacking arbitrary non-symmetric relations will not produce symmetry, and the ancestral of the closest-continuer relation is not symmetric, but the modal analog of gen-identity is symmetric. So, if the closest-continuer theory is to be acceptable, it must require the ancestral of 26 We are assuming that the tip of x’s or y’s hair exactly occupies a point and that there are inﬁnitely many points between the 77-degree point and the 78-degree point. This corresponds to the presumption that there are inﬁnitely many temporal moments between the times of the scenes depicted in the two adjacent ﬁlm cells. If, contrary to the presumption, there are only ﬁnitely many moments, then we will revise the assumption and say more realistically that the tip of the hair occupies an extended region of space. For more on this and related issues, see the next section.

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the closest-continuer relation in both directions. This is especially important for transworld identity, which, unlike transtemporal identity, involves metaphysical indices which are not ordered linearly, hence not ordered linearly with directionality. (Nozick’s notion of a continuer is rich enough to incorporate directionality. See the next section on causation.) Thus, we have the following criterion of transworld identity: A modal stage x at a possible world w1 and a modal stage y at a different possible world w2 are parts of the same modally extended object of a kind K if and only if there is a chain of possible worlds from w1 to w2 ordered by the overall similarity relation such that x and some modal stage, xþ1, at the next world in the chain are sufﬁciently similar to each other in relevant respects and are each other’s closest continuer at their respective worlds, xþ1 and some modal stage, xþ2, at the next world in the chain are sufﬁciently similar to each other in relevant respects and are each other’s closest continuer at their respective worlds, . . . , and xþn and some modal stage, xþnþ1 ¼ y, at the next world, w2, in the chain are sufﬁciently similar to each other in relevant respects and are each other’s closest continuer at their respective worlds, where the sufﬁcient similarity, relevant respects, and closeness are relative to the kind K. 6 . 6 . DENSITY, CONTINUITY, CAUSALITY The foregoing criterion of transworld identity might at ﬁrst appear unsatisfactory, for it might appear to rule out transworld identity supported by a chain of similar possible worlds a segment of which is such that for any two worlds in the segment there is a world between them. Let us call such a segment dense, and a chain containing a dense segment somewhere dense. In a dense segment of a chain, there is no such thing as the next world (or even a next world) to a given world. So the above criterion simply does not apply to a somewhere-dense chain, but surely, if transworld identity can be supported by a nowhere-dense chain of worlds (i.e. a chain with no dense segment), it should be supported by a somewhere-dense chain. Suppose that at w11 a nitrogen atom swerves by Nixon along a particular path P at a time t, that at w12 a nitrogen atom swerves by Nixon along a path parallel to but ten micrometers away from P at t, and that w11 and w12 are indistinguishable otherwise (except what is entailed by the mentioned difference). Assume that this is a good supposition, i.e. that the identity of Nixon through w11 and w12 is sustainable (and so is the identity of P), without presuming any sub-chain of worlds bridging the gap between w11 and w12 by interpolation. Now consider such a sub-chain bridging the gap. There is a world, w11.5, between w11 and w12 in the chain, at which a nitrogen molecule swerves by Nixon along a path parallel to but ﬁve micrometers away from P at t. There is another world, w11.25, between w11 and w11.5 in the chain, at which a nitrogen

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molecule swerves by Nixon along a path parallel to but two and a half micrometers away from P at t. There is yet another world, w11.125, . . . And so on. Such a sub-chain of worlds would not diminish the support for the transworld identity of Nixon from w11 to w12. On the contrary, it would increase the support, if anything. If we are willing to count the Nixony modal stage at w11 and the Nixony modal stage at w12 as two modal stages of Nixon, a transworld individual, on the grounds that they are each other’s closest continuer, then for any two intervening worlds, wm and wn, between w11 and w12, the Nixony modal stage at wm and the Nixony modal stage at wn should count as modal stages of Nixon, a transworld individual, because these two Nixony stages are not less close to each other or less close to the Nixony modal stages at w11 and at w12 than the latter two Nixony modal stages are to each other. Also, it is plausible to say that if a particular case of transworld identity is supported by a somewhere-dense chain of possible worlds, then it is also supported by a chain of possible worlds which is nowhere dense. It is plausible that in the dense chain from w11 to w12 supportive of transworld identity there is an interval measure, M, such that the similarity gap between any two worlds within M is negligible for transworld identity, i.e. the relevant modal stages at two such worlds are clearly stages of the same transworld individual. Thus, there is no need for a special coverage of somewhere-dense chains of possible worlds in our criterion of transworld identity. The set of rational numbers between 1 and 2 as customarily ordered is dense; for any two of them there is another one between them. But the set has gaps, for the ordered set of real numbers between 1 and 2 is larger. We say that the set of such real numbers is continuous. What should we say about a continuous chain of worlds under similarity connecting w1 and w2 with respect to x and y? Nothing new. The continuity of the chain in this sense adds nothing importantly new. Instead of imagining space to be dense so that a nitrogen molecule (or an even smaller particle) can swerve in as many ways as there are rational numbers, imagine space to be continuous so that it can swerve in as many ways as there are real numbers. Such a chain would support the identity of the transworld individual at least as well as a somewhere-dense chain. More importantly, if a particular case of transworld identity is supported by a continuous chain, it is plausible to infer that it is supported by a somewhere-dense chain, hence also by a nowhere-dense chain. Discussion of identity over time does not typically deal with issues of density or continuity of time. This is mainly because of the involvement of causation. Nozick says: To say that something is a continuer of x is not merely to say its properties are qualitatively the same as x’s, or resemble them. Rather it is to say they grow out of x’s properties, are causally produced by them, are to be explained by x’s earlier having had its properties, and so forth.27 27

Nozick 1981: 35.

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For a temporal stage y to be a continuer, let alone the closest continuer, of an earlier temporal stage x, the relevant properties which link y to x must be ‘causally produced’ by x’s properties. This causal connection between x and y swamps the consideration concerning the discreteness, density, or continuity of the chain of temporal stages between them. Whether the chain is discrete, dense, or continuous, if there is an appropriate causal connection between x and y, y is x’s continuer. An analogous thing cannot be said of the modal case, for obviously there is no causal connection between a modal stage at one world and a modal stage at another world; transworld causation is an absurdity. This threatens our methodology. If causation plays a crucial role in transtemporal identity but no role at all in transworld identity, should this not be taken seriously as a strong warning sign against those who wish to craft the condition of transworld identity by learning from the case of transtemporal identity? Yes, it should if the antecedent of the above conditional is true. But the antecedent is not true. Most discussants of identity through time follow Nozick on the role of causation, but I do not. Nozick makes a short parenthetical remark after the above passage: Indeed, even the notion of spatiotemporal continuity is not to be explained merely as something that when photographed would produce continuous ﬁlm footage with no gaps; for we can imagine a substitution of one thing for another that would not break ﬁlm continuity. The later temporal stages also must be causally dependent (in an appropriate way) on the earlier ones. The condition that something is a continuer incorporates such causal dependence.

In a note attached to the middle of this passage, Nozick says: In classroom lectures in the fall of 1977, I used the example of two machines, a disappearing machine and a producing machine, where there is independent evidence of how each operates separately; when operated together, suitably synchronized, one makes an object disappear while another produces an exact duplicate in the same place. . . . thus showing that ﬁlmstrip continuity is not sufﬁcient for ‘same object’ . . . 28

Nozick thinks that his thought experiment involving a disappearing machine and a producing machine ‘shows that ﬁlmstrip continuity is not sufﬁcient for “same object”’. But I think it instead shows that causation is not necessary for ‘same object’. Turning to theology, Nozick says: If this causal component indeed is needed, it raises problems for theological views that hold God maintains everything in continued existence, where this includes all causal connections. How does He distinguish continuing an old thing from producing a new one, qualitatively identical, without any ﬁlmstrip ‘break’?29

God can distinguish anything worth distinguishing (and more), whether or not we can fathom how it is done. Suppose God continues an old thing in the way which 28 29

Ibid. 655–6 n. 7. Nozick mentions Shoemaker 1969, 1979. Ibid. 35 n.*.

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Nozick’s causal theory requires. Then Nozick will say that identity through time is maintained. Suppose, on the other hand, God produces a new thing every moment, replacing the old thing each time. If God does this by examining the properties of the old thing and more or less duplicating those properties in the new thing directly, then there is a causal connection between the old thing and the new thing which will please Nozick––let us assume––so in such a case Nozick will again say that identity through time is maintained. But what if God replaces the old with the new without regard to the properties of the old in such a way that there is no causal connection (of the appropriately direct kind) between the two and yet the old and the new turn out appropriately similar? For this to happen at every moment of time would be fantastic indeed, but we are speaking of God and God is the most fantastic of all. Of course, God is entirely dispensable for our purposes. Suppose that the old simply disappear spontaneously, while the new appear spontaneously in the appropriate (non-causal) relation to the old. It seems fairly clear to me that such a scenario is one according to which identity through time is maintained but there is no causal connection between earlier temporal stages and later ones; it would be a situation in which an ordinary transtemporal individual, say Nixon, is composed of appropriately lined-up temporal stages which are not causally related. It seems to me more plausible to say that in such a situation Nixon would exist through time but causation would fail to work the way we think it actually does, than to say that in such a situation Nixon would not exist through time at all. (This kind of consideration should make us pause before accepting any of the customary causal theories: causal theory of memory, causal theory of perception, causal theory of action, causal theory of knowledge, causal theory of meaning, causal theory of reference, etc.30) The closest-continuerhood under what Nozick calls ‘ﬁlmstrip continuity’ is sufﬁcient for transtemporal identity. Likewise for transworld identity.31

30 There is theoretical room for the view that, even if instantaneous temporal stages of Nixon are not causally related, events involving Nixon which are temporally extended to occupy periods of time of non-zero duration may be causally related. Such a view attempts to maintain the compatibility of the presence of causal relatedness of temporal segments of non-zero thickness with the absence of causal relatedness of temporal segments of zero thickness. Such a view is not logically incoherent, but since temporal segments of non-zero thickness are made up of temporal segments of zero thickness, if the latter are not causally related, it is hard to see how the former can be causally related. The onus is on the defenders of such a view to spell out how. 31 I borrow Nozick’s closest-continuer theory of identity but without his causal theory for my own purposes. Most followers of Nozick on identity accept his causal theory. So I need to justify my rejection of his causal theory while accepting the rest of his closest-continuer theory. I do so by providing an alternative to his causal-theoretical way of understanding the closest-continuer theory. Those who are wed to the causal theory would not be convinced by my move, but my aim is not to convince them but to provide coherent grounding for a closest-continuer theory independently of the causal theory.

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6. 7 . UNITY OF CONSCIOUSNESS Another challenge to transworld identity comes from consideration of the so-called unity of consciousness. Identity of a conscious individual, such as a normal mature human being, appears to depend on how the individual’s conscious experiences hang together. Take perception, for example. Suppose I consciously perceive a toy cymbal-playing monkey. I see it, hear it, touch it, and smell it. (I refrain from using the ﬁfth sense.) My perception of the toy by vision is uniﬁed in the sense that the experience of seeing each visible part of the toy occurs not as an isolated episode but as an integral part of a naturally organized whole which constitutes one coherent picture of an object. The toy itself is seen as a meaningful part of a larger scenery, my visual perception of which is uniﬁed in my consciousness. My conscious perception of the toy by each of the other senses similarly exhibits unity. Furthermore, the perceptual experiences arising from the four different senses themselves form a uniﬁed coherent whole in my consciousness. An opponent of transworld identity might say that the total experience I have at a particular time t at the actual world is not uniﬁed in my consciousness with any experience a modal stage of a conscious individual has at t at any world other than the actual world, so that no modal stage of a conscious individual at any merely possible world is part of me. In order to ﬁgure how properly to respond to this objection, we should start with an unsatisfactory but instructive response. It is unsatisfactory to respond by saying (i) that if the objection shows that I have no modal part except my actual self, then it also shows that I have no spatial part except my brain (or whatever part or parts of the brain responsible for my perceptual experience), but (ii) that I do have many other spatial parts than the brain. My liver, for example, does not participate in the unity of perceptual consciousness or any other kind of consciousness because it does not perceive and is not conscious in any way.32 The unsatisfactoriness of this response is twofold. First, it is open for the objector to bite the bullet and accept that I do not have any spatial part other than the brain. Such a position distinguishes me from the rest of my body and says that I am a proper part of my body, namely, the brain. If my body except the brain is destroyed while the brain is put in a vat in the usual science-ﬁction way to sustain it, my body is gone but I am not gone; I survive as a brain in the vat. The plausibility of this familiar thought experiment undermines the response. Second, and more importantly, this response presupposes a false analogy. It presupposes that when considering unity of consciousness, transworld identity should be understood in analogy with trans-spatial identity. The liver 32 This is not uncontroversial. Some might say that my liver is conscious even though there is no easy way to gauge its consciousness or compare its consciousness to ours. See Chalmers 1996: 152–3, 293–301; Strawson 2006. Even if my liver is conscious, however, its consciousness remains un-uniﬁed with mine while the liver is part of me.

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example shows that this is a silly presupposition to make. The right presupposition we should make is that, when considering unity of consciousness, transworld identity should be understood in analogy with transtemporal identity. When so understood, transworld personal identity may be treated in the broadly Lockean way. John Locke and his followers have taught us the importance of memory, among other psychological continuities over time, for transtemporal personal identity. There was exactly one person sitting and typing at the work station in ST 530 on campus ﬁve minutes ago. I remember sitting and typing at the work station in ST 530 on campus ﬁve minutes ago. This makes the person and me one and the same. The content of the person’s conscious experience is incorporated into my current consciousness via the act of recollection. The temporal stage of me ﬁve minutes ago and the temporal stage of me now are thus brought under one uniﬁed consciousness, and this unity of consciousness is crucial to the identity of the person ﬁve minutes ago and me now. I could have stood just outside ST 530 ﬁve minutes ago instead of sitting and typing at the work station inside. So there is a possible world, w, at which I stood outside ST 530 ﬁve minutes ago. At w, my modal stage had a certain conscious experience while standing outside ST 530 ﬁve minutes ago. At w, my modal stage now remembers that experience, and at the actual world my actual-world-stage remembers what my earlier stage experienced ﬁve minutes ago as he sat and typed. But my actual-world-stage does not remember the experience of my w-stage; nor does my w-stage remember the experience of my actual-world-stage. There is nothing special about the interval of ﬁve minutes in this line of reasoning. For any past moment of time t, however close it may be to the present moment, my actual-world-stage does not remember the experience my w-stage had at t; nor does my w-stage remember the experience my actual-world-stage had at t. The two modal stages do not exhibit unity of consciousness through memory. How can they then be parts of the same conscious individual? To answer this question, we need to dissociate memory from causation.33 For all we know, we might well persist through time by being constituted by temporal stages which are created instantaneously and destroyed shortly thereafter in such a way that later stages are not caused by earlier stages. Such a scenario would not change the fact that we do remember our past experiences.34 So, memory is independent of causation. Under the same causation-less scenario, we would still persist through time as conscious individuals and whatever unity of consciousness required for it would be there. Customary discussion about how 33 Causal theories have been proposed for perception and memory. But there is an important difference between memory and perception. In the case of memory, the unity of consciousness which concerns us is a unity between what is remembered (the past experience) and the current remembrance experience. In the case of perception, the unity of consciousness which concerns us is not a unity between what is perceived (the object of perception) and the current perceptual experience, but a unity within the perceptual experience itself. 34 See the last paragraph of 6.6.

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best to distinguish the right causal connection between the past experience and the present state of recollection from the wrong, or deviant, causal connections should be recast in terms of the question of how to distinguish the right chain of temporal stages from the deviant chains. That aspect of the phenomenon of memory which is responsible for the unity of consciousness in question is something other than causal. But what aspect of memory is responsible? When all causal considerations are eliminated, as long as we are truly said to remember our past experiences, thus ruling out the non-causal substitutes for deviant causal chains, there is little left except for similarity of content separated by an appropriate chain that ﬁts the bill. Your consciousness exhibits unity over time by means of your memory of the past experiences, and what uniﬁes your consciousness at the present time and your consciousness at an appropriate past time is not that the latter (or the latter’s happening) caused the former (or the former’s happening) but that the content of the memory available to the former matches the content of the experience of the latter while the former and the latter are at the opposite ends of an appropriate chain of temporal stages of consciousness. The match is a matter of degree, of course, and is usually less than perfect even in the case of the most recent and vivid memory. Usually, the farther removed into the past the remembered experience is, the less perfect the match is. For many past conscious experiences, there is hardly any match at all. Such cases largely coincide with those cases which we would describe as cases of the absence of memory. Between your present consciousness and your consciousness at a time at which you had conscious experience you now do not remember, there is no unity, but there is a chain of your temporal stages connecting the two such that each adjacent pair of stages exhibits the unity of consciousness. I can intuit my phenomenal mental states in the immediate past and immediate future fairly well. Similarly, I can intuit my phenomenal mental states in the immediately close worlds fairly well. We certainly do not remember experiences we did not in fact have in the past. Suppose that you had a total experience E at a past time t at a possible world w and a total experience E’ at the same time t at a different possible world w’, and that at w you now remember E and at w’ you now remember E’. It is tempting to reason as follows. Since w and w’ are different worlds, E and E’ are different experiences; so you do not now remember E’ at w; so your consciousness now at w is not uniﬁed with your consciousness at t at w’, even though your consciousness now at w is uniﬁed with your consciousness at t at w. If this line of reasoning is acceptable, then since it is generalizable with respect to t to make the time interval for the memory to span as short as we want, the unity of consciousness as underwritten by memory cannot be sustained to bolster transworld identity of a conscious individual. But it is easy to see that the line of reasoning is faulty. The crucial move is the one which goes from ‘E and E’ occur at different worlds’ to ‘E and E’ are different (non-identical) experiences’. This move presupposes the falsity of a generalized version of the transworld identity thesis, which says that

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not only individual objects but also individual phenomena, such as states of affairs, events, and experiences, are also transworld beings. We are trying to make reasonable sense of transworld identity for individuals like you and me, and we have no good reason for not expecting the same sense to be made of other individual beings like experiences; you and I could be otherwise than we actually are, and in exactly the same sense our experiences could be otherwise than they actually are. So we should insist that E and E’ may well be the same experience and that their transworld identity is to be sanctioned in the same way as the transworld identity of any individual. Assuming that E ¼ E’, since at w you remember E, at w you remember E’. Is this sufﬁcient for blocking the above line of reasoning? Some might say ‘No’. At w you remember E, namely E’, as you had it at t at w, whereas at w’ you remember E’ as you had it at t at w’. Assuming that E, namely E’, took place slightly differently at w and at w’ and that your recollections are correspondingly discriminating, the content of what you remember at w when you remember E, namely E’, is slightly different from the content of what you remember at w’ when you remember E’. So, the relation between your memory at w of E, namely E’, as it occurred at t at w’ is not as tight as the relation between your memory at w of E, namely E’, as it occurred at t at w. Such a retort appears convincing, yet it only works if w and w’ are dissimilar enough to allow some difference between the contents of what you remember at w and what you remember at w’. E at w and E’ at w’ may be so slightly different that the difference does not survive the act of remembering, i.e. that the contents of your memory at the two worlds are the same: for example, E at w involved an itch barely above your left elbow, while E’ at w’ involved an itch barely below your left elbow, so that both at w and at w’ you remember the itch to have been squarely on your left elbow. So, if w and w’ are similar enough to allow this sort of situation, then the relation between your memory at w of E, namely E’, as it occurred at t at w’ is made as tight as the relation between your memory at w of E, namely E’, as it occurred at t at w. It is still tempting to resort to causation, but for the reasons we noted, we should resist the temptation. Once we secure sufﬁciently close worlds like w and w’, we can construct a chain of worlds between not so close worlds in such a way that each adjacent pair of worlds in the chain are sufﬁciently close. Therefore, it now looks as if what stands in our way is plain prejudice against transworld uniﬁcation of consciousness as opposed to intra-world uniﬁcation, and once the prejudice is removed, the considerations concerning the unity of consciousness afforded by memory should be seen not to mar transworld identity of a conscious individual. 6 . 8 . THE INDISCERNIBLE Consider Max Black’s world. At Black’s world, there are two concrete objects (and their parts) and nothing else, and the two objects are entirely indistinguishable from each other. Think of the two objects as mirror images of each other and

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occupying two mirror-image regions.35 Some of those who are strong advocates of Leibniz’s principle of identity of the indiscernible might say that there could not possibly be such a pair of objects and that Black’s world is an impossible world. If they are right, Black’s world presents no problem for our criterion of transworld identity. If they are wrong, however, our criterion is threatened. We shall, therefore, expect the worst and assume that Black’s world is metaphysically possible. As they are, the two objects are in fact indiscernible. But they are concrete objects existing in space and time, and are subject to change. Even though they actually do not change at Black’s world, it is metaphysically possible for one of them to change slightly. So, at some metaphysically possible world, say w17, one of the objects changes a little over the course of its existence, while the other remains as it is at Black’s world. Let us say that the change consists in the object’s surface becoming dented slightly. We need not worry about the mechanism by which such a change should occur, for we are assuming no particular laws of nature governing Black’s world. (If we have to say something, we might say that the dent appears as a result of highly unlikely quantum ﬂuctuations, or alternatively, we might just say that it appears by a minor miracle.) Let us call the two indiscernible modal stages of the transworld objects at Black’s world ‘B1’ and ‘B2’, the modal stage of the object at w17 which gets dented ‘D’, and the other, unchanged modal stage of the other object at w17 ‘U’. There is a chain of possible worlds from Black’s world to w17 which bolsters U being the closest continuer of B1. But the chain bolsters U being the closest continuer of B2 equally well. In other words, looking at the chain in the other direction, neither B1 nor B2 is the closest continuer of U. So, our criterion of transworld identity does not allow us to say that B1 and U are modal stages of the same transworld individual or that B2 and U are. Thus, we cannot say of either one of the two objects from Black’s world that it is unchanged at w17. Worse. There is no chain of worlds from Black’s world to w17 which bolsters D being the closest continuer of B1 or B2; for U is always closer. Thus, we cannot say of either one of the two objects from Black’s world that it is changed at w17. But, as we decided initially, it is intuitively clear that it is possible for one of the objects at Black’s world to remain unchanged and the other to change. Therefore, our criterion for transworld identity is unacceptable. This is a problem. Some might suggest that we should deny the possibility of either object’s changing at all; if they are indiscernible at some possible world, then they are indiscernible at every possible world at which they exist. This suggestion would be unhelpful. First, it is simply implausible. Why could a physical object not be different from how it is? Being the sole worldmate of an indiscernible twin should not change the contingency of how a physical object is. Second, the suggestion leaves the problem essentially untouched. A part of the problem is that our criterion 35

Black 1952.

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does not allow us to say that U and B1 are modal stages of the same transworld individual or that U and B2 are. That is, we cannot allow the same object existing both at Black’s world and at w17 at all, let alone existing at those worlds in exactly the same way. Therefore, the suggestion is reduced to little more than the banality that the two objects are indiscernible at Black’s world. If we are desperate enough, we might decide to reject the initial assumption that Black’s world is a metaphysically possible world. But that would be a drastic move and should be considered the very last resort. One could always decide to accept haecceitism, of course, but that would be the end of our criterion of transworld identity. Others might suggest that we rely on Kripke’s idea of stipulation and simply stipulate that we speak of one particular modal stage, as opposed to the other. This would not help us here at all. (We shall return to Kripke’s idea in the next section.) To the extent to which it is legitimate for us to call one of the two indiscernible modal stages ‘B1’ and the other ‘B2’, we implicitly performed such a stipulation, but this does not change the fact that neither B1 nor B2 is the closest continuer of U. Also, it would be useless to stipulate that we speak of one particular modal stage, as opposed to the other, as the closest continuer of U. B1 and B2 have the same claim to being the closest continuer of U, hence neither is, as a matter of pure metaphysics. This would make Black’s world a metaphysically impossible world if we performed the recommended stipulation. Fortunately, there is a solution. As long as we consider one object at a time, we are doomed. But we do not have to consider one object at a time. In fact, when we try to consider just one of the two indiscernible objects without considering the other, we ﬁnd it difﬁcult to say which one of the two we are considering. We certainly cannot pick one as opposed to the other by perceptual imagination, and moving away from perceptual imagination to purely conceptual consideration does not help much. In any case, instead of speaking of one object and then the other, we should speak of the pair at once. The pair exists at Black’s world as an indiscernible pair, and exists at w17 as a discernible pair. In order to support the transworld identity of the pair, our criterion requires that there be a chain of possible worlds such that the modal stage of the pair (which is the pair of the modal stages) at Black’s world and the modal stage of the pair at w17 must be each other’s closest continuer. And there is indeed such a chain. The chain will not tell us which of the two objects is dented at w17, but this is not a problem for us, who refuse to speak of one object at a time but instead stick to speaking of the pair as a pair. We can still say that one of the pair is dented at w17 and the other is not. 6. 9 . STIPULATIONS AND COUNTERFACTUALS The task of providing the criterion of transworld identity is the task of laying out the conditions under which one modal stage at one world and another modal stage at another world are modal parts of the same transworld individual. It is not

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intended to tell us how we should recognize a familiar individual, say, Richard Nixon, at a possible world which is speciﬁed purely qualitatively. (To specify a possible world purely qualitatively is to specify purely qualitatively how the universe is at that world.) Modal realists regard possible worlds as fully real independently of what we do to them or how we think of them. Possible worlds may be speciﬁed purely qualitatively, and they may be speciﬁed otherwise. One way to do the latter is to specify them by mentioning a particular individual and what might happen to that individual. Thus, I agree with Kripke when he says: ‘There is no reason why we cannot stipulate that, in talking about what would have happened to Nixon in a certain counterfactual situation, we are talking about what would have happened to him.’36 Even though I say less on haecceitism and allow more theoretical room for the transworld identity criterion, I am in agreement with Salmon in his following interpretation of Kripke’s passage: . . . possible worlds are no different from anything else that might come under discussion. Suppose I say, ‘Some cities have monuments made of marble,’ as a prelude to saying something about some or all such cities. It would be silly (at best) for someone to object that while there are indeed marble monuments in this city (the city we are in), I must justify my claim that the monuments in the other cities I have in mind are really made of marble––instead of, say, some other material that was fashioned to look the way marble looks around here. I am discussing cities with marble monuments. I do not have to specify the relevant class of cities purely qualitatively and then provide a criterion for intercity identity of material. I simply select the class of cities that I wish to discuss by specifying that they have monuments made of . . . , well, marble.37

Salmon’s analogy also underscores the appropriateness of the modal realist interpretation of Kripke’s idea of stipulation. What is stipulated is the topic of our discussion; it is to be cities with marble monuments. The stipulation makes those cities come into focus in our discussion, but it does not make them come into being. The cities are not constructed out of stipulations, whatever that might mean. The cities with marble monuments are out there prior to and independently of our stipulation. The stipulation merely establishes a certain relation, being the topic of discussion by, between them and us. Likewise, when we stipulate a` la Kripke that we shall talk about possible worlds at which Nixon lost the election to Humphrey, we do not construct such worlds by means of making the stipulation, whatever that might mean. The worlds are out there in modal space prior to and independently of the stipulation.38

36

Kripke 1980: 44; his emphasis. Salmon 1996: 210; his emphasis. I tend to think that whether something is made of marble would be part of a purely qualitative speciﬁcation of that thing, but this point does not affect the main thrust of the passage. 38 Salmon himself would not accept the version of modal realism I endorse. He is an ersatzist and envisions the independently pre-existing possible worlds as a kind of abstract objects like stories, or scenarios. 37

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Suppose I say to you, ‘Consider those possible worlds at which Nixon lost the election to Humphrey’, thereby stipulating that the topic of our discussion is to be those possible worlds at which Nixon lost the election to Humphrey. Suppose I go on to say, ‘At those worlds a reptile lost the election to an amphibian’. You will be likely to be puzzled. Why? Because you will be likely to presume that the possible worlds I stipulated to be the topic of our discussion are not worlds at which Nixon is a reptile and Humphrey is an amphibian. But why will you be likely to presume such a thing? In making my stipulation I said nothing about reptiles or amphibians, a fortiori, I said nothing to rule out the possibility of Nixon being a reptile and Humphrey being an amphibian. Our criterion of transworld identity can readily explain why you will be likely to presume that such a possibility is ruled out of consideration. Transworld identity is based on similarity through a chain of worlds. We know that Nixon and Humphrey at the actual world were human beings and not a reptile or an amphibian. My stipulation puts forth those possible worlds at which Humphrey defeated Nixon. You know that Humphrey did not defeat Nixon, so you know to move away from the actual world. You, however, do not move to an arbitrary possible world at which Humphrey defeated Nixon, but instead to a possible world at which Humphrey defeated Nixon and at which other things are pretty much the same as at the actual world. That is, you know not to indulge in gratuitous departure from actuality. This is so because you (implicitly) know that the stipulated identity of Nixon and Humphrey over the actual and other worlds is to be grounded in similarity with respect to Nixon and Humphrey between those worlds. Even a fairly modest gratuitous departure will be automatically blocked. If, instead of saying ‘At those worlds a reptile lost the election to an amphibian’, I say, ‘At those worlds a Minnesotan lost the election to a Californian’, you will as likely be puzzled. The fact that Nixon was a Californian and Humphrey was a Minnesotan should not be automatically revised to reach the worlds of our discussion. If I want us to consider those possible worlds at which Nixon was a Minnesotan, Humphrey was a Californian, and Nixon lost the election to Humphrey, then I had better say so explicitly. On the other hand, whatever is entailed by the reversal of the election result, given the laws of metaphysics, physics, psychology, and the United States, will be automatically presumed to be the case at the worlds of our discussion without any explicit stipulation to that effect by me. That is because such a presumption will maximize the degree of similarity. The way the Kripkean speciﬁcation of a topic by means of a stipulated transworld identity in fact works is thus evidence for our criterion of transworld identity. Similar evidence comes from the widely held theory of counterfactual conditionals by Stalnaker and Lewis.39 Since the differences between Stalnaker’s proposal and Lewis’s do not concern us, we shall speak simply of Stalnaker’s 39

Stalnaker 1968 and Lewis 1973.

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theory, which is simpler than Lewis’s. According to this theory, any counterfactual conditional of the form ‘If it were the case that P, then it would be the case that Q’ is true if and only if Q at the closest possible world at which P. Gratuitous departures not sanctioned by what is explicit in the counterfactual antecedent are banned. This needs explanation. If the counterfactual antecedent mentions a particular individual, the explanation by means of our criterion of transworld identity is the same as for the case of Kripke’s stipulation. If, however, the counterfactual antecedent does not mention any particular individual, such an explanation cannot be given. Still, the universe as a whole might be thought of as one enormous ur-individual (whether entirely concrete or not entirely concrete), to which our criterion of transworld identity also applies. Then the explanation parallels the previous case. Of course, in this case the ordering of modal stages of the universe, which is done by means of similarity, automatically assures similarity of those modal stages at those worlds. So there is a sense in which the criterion of transworld identity is satisﬁed trivially. But this does not trivialize the explanation of why gratuitous departure from the antecedent is disallowed. We shall have more to say about counterfactual conditionals later. 6.10. OVER-IDENTIFICATION Transworld identity closely mimics transtemporal identity by design. But apparently, unlike the latter, the former is subject to an objection made famous by Roderick Chisholm.40 Consider a modal stage x at a possible world w1 and a modal stage y at another possible world w2 such that there is a chain of possible worlds under similarity from w1 to w2, and x and y are each other’s ancestral closest continuer, i.e. the ancestral of the closest-continuer relation holds between x and y in both directions in the chain. It seems that by our criterion of transworld identity, x and y must be modal stages of the same modally extended object. But x and y might be such that there is good reason not to accept the verdict that they are modal parts of the same individual. Chisholm invites us to consider not just one modal stage but a pair of modal stages that are worldmates. For example, consider Adolf Hitler as he was at the actual world, or Hitler’s @-stage, and Joseph Stalin’s @-stage.41 Also, consider Hitler’s w-stage, for some non-actual possible world w, and Stalin’s w-stage. Let us assume that at w, things are the same as at @ except that a few molecules in the Delta Quadrant of the universe wavered slightly differently a moment before Stalin’s death in the Alpha Quadrant (and whatever is logically and nomologically entailed by the different waverings). There is a chain of possible worlds under similarity from @ to w such that Hitler at @ and Stalin at w are each other’s ancestral closest continuer. To see 40

Chisholm 1967.

41

These are my examples, not Chisholm’s.

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that there is indeed such a chain, start with Hitler and Stalin at @ and imagine a slightly different world at which the two men are very slightly changed in each other’s direction in appearance, behavior, personality, molecular composition, biological history, etc. Then imagine another world at which they are very slightly changed further in each other’s direction. Continue imagining a sequence of worlds through which Hitler as he was at @ is transformed little by little into what Stalin was at @, while at the same time Stalin as he was at @ is transformed little by little into what Hitler was at @. Hitler at those worlds in the sequence becomes progressively indistinguishable from Stalin at @, and Stalin at those worlds from Hitler at @. The world w ﬁgures at the very end of this sequence of worlds, and is such that Hitler at w is the most indistinguishable from Stalin at @ in the sequence, and Stalin at w from Hitler at @. On the other hand, if we compare @ and w directly without intervening worlds, Hitler at w is indistinguishable from Hitler at @, and Stalin at w from Stalin at @. (We are assuming that the different molecular waverings in the Delta Quadrant were small and distant enough to be ignored for the comparisons.) It then seems that by our criterion, Hitler’s @-stage and Stalin’s w-stage are modal stages of one and the same transworld individual, Stalin’s @-stage and Hitler’s w-stage are modal stages of one and the same transworld individual, Hitler’s w-stage and Hitler’s @-stage are modal stages of one and the same transworld individual, and Stalin’s w-stage and Stalin’s @-stage are modal stages of one and the same transworld individual. Thus it appears that by our criterion Hitler and Stalin are one and the same transworld individual. Since Hitler and Stalin are clearly distinct individuals, it seems that either they are not transworld individuals or our criterion of transworld identity is unacceptable. Since we are committed to ordinary individuals being transworld individuals, this threatens our criterion.42 This is the problem of over-identiﬁcation. It is important to appreciate the implausibility of identifying Hitler and Stalin as one and the same transworld individual against the background commitment that ordinary individuals are transworld individuals. The identiﬁcation has the consequence that Hitler and Stalin are one and the same person, and this person has two very distinct modal stages at @, at w, and at every other world in the chain. The two stages fought each other at @, at w, and at many other worlds. This is bad enough, but consider Franklin Delano Roosevelt instead of Stalin. By 42

Chisholm would not put the argument this way. Instead he would say that by our criterion Hitler and Stalin could have switched but that they could not have switched. My version of the Chisholmian argument has stronger force against our criterion than his original version. To argue against the possible switch, Chisholm would need to resort to the principle of the necessity of identity: for any x and y, if x = y, then necessarily x = y. Kripke famously argues for it in (1980: 3–5, 97–105, 107–10, 114 n., 128–38, 140–55). It is a consequence of this principle that distinctness is necessary. For any x and y, if x ≠ y, then necessarily x ≠ y. Hitler is distinct from Stalin, so by the necessity of distinctness, Hitler could not have been Stalin. My version of the Chisholmian argument does not rely on such a principle.

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mimicking the reasoning we have gone through, we can say that our criterion of transworld identity seems to have the consequence that Hitler and Roosevelt are one and the same person. Since the relation ‘being one and the same person as’ is an equivalence relation, Hitler, Stalin, and Roosevelt are one and the same person. Likewise, Winston Churchill is also the same person as they are (he is). So is Benito Mussolini. And Hideki Tojo, and . . . The situation seems even worse. It seems that any two concrete modal stages at any two possible worlds are modal stages of one and the same transworld individual. The richness of modal space guarantees the richness of chains of possible worlds. There is a chain of possible worlds under similarity from any possible world to any other possible world appropriately linking any concrete modal stage at one world to any concrete modal stage at the other world. Some such chains are short and straightforward: for example, those linking Stalin at @ immediately to Stalin at w. Others are long and convoluted: for example, those linking Stalin at @ to a poached egg at w4591. This appears intolerable. 6 . 1 1 . OVERLAPPING INDIVIDUALS I accept that Stalin’s @-stage and the poached egg’s w4591-stage are modal stages of one and the same transworld individual. This, however, does not commit me to the claim that those stages are modal stages of one and the same transworld person or transworld egg, or that Stalin could have been a poached egg. The personhood of this transworld individual is lost somewhere in the chain of worlds from @ to w4591, though it is hard to say exactly where. Stalin-ness is also lost somewhere in the chain, perhaps at the same time as personhood is lost, perhaps not. Furthermore, egg-ness is lost somewhere in the same chain, traced in the reverse direction; again, it is hard to say exactly where. There is one transworld individual spanning from Stalin at @ through the chain to the egg at w4591, but the ready-made sortal concepts like personhood and egg-ness are not adequate to cover this transworld individual in its entirety. Neither is the individual concept, Stalin-ness. We have no adequate word in natural language for it. We may invent a new word, say, ‘pergg’ or ‘eggerson’, just for the purpose but it would be of limited usefulness. A proper part of this strange transworld individual overlaps a familiar transworld individual, Stalin, who has modal stages at various worlds, including @, and overlaps another familiar transworld individual, the poached egg, which has modal stages at various worlds, including w4591. When we ask ourselves whether Stalin could have been a poached egg, we are not asking merely whether there is a way to transform Stalin’s @-stage into a modal stage of a poached egg through modal space, perhaps by a long complicated imaginary method involving molecular removal, addition, and manipulation. Even if there is such a method, the answer to our question will not automatically be in the afﬁrmative. What we are asking is whether Stalin could have been a poached egg

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while remaining Stalin. Remaining Stalin may well involve retaining his personhood, memory, consciousness, animateness, or some combination of such traits. Since none of these traits appears to be had by any poached egg we know, the question strikes us as absurd, or at least it strikes us as absurdly easy to answer in the negative. Stalin and the poached egg do not seem to overlap each other in modal space. I accept that Hitler’s @-stage and Stalin’s w-stage are modal stages of one and the same transworld individual. I accept that any two modal stages at any two possible worlds are modal stages of one and the same transworld individual. This, however, does not commit me to the claim that Hitler’s @-stage and Stalin’s wstage are modal stages of the transworld individual that is Hitler or the transworld individual that is Stalin, or that Hitler could have been Stalin. There is a transworld individual consisting of Hitler’s @-stage, Stalin’s w-stage, and all the relevant modal stages at the intervening worlds in the relevant chain, but that transworld individual is not Hitler or Stalin, although it overlaps Hitler and overlaps Stalin. Unlike the Stalin–poached-egg case, the relevantly narrow sortals, such as ‘person’, ‘human being’, and ‘man’, are never lost in the chain of worlds. A temporal analogy is helpful here. Starting at a certain time t1, Hitler in Berlin is transformed into a qualitative duplicate of Stalin, while at the same time Stalin in Moscow is transformed into a qualitative duplicate of Hitler. Suppose further that the two transformations are executed by means of gradual molecular swap. At t1, one molecule from Hitler is swapped with one molecule from the corresponding part of Stalin. After as many swaps as there are molecules in their bodies, the two transformations are completed at time t2.43 The result is that the four-dimensional whole in Berlin starting with Hitler at t1 and ending with the transform at t2 is not a temporal segment of Hitler. Hitler overlaps this fourdimensional whole in the neighborhood of the beginning temporal period (toward t1) but not in the neighborhood of the end (toward t2). It is Stalin who overlaps the four-dimensional whole toward that end. If your intuition is not immediately moved in this direction, imagine the swap to take place at lightning speed so that there is little doubt that Hitler and Stalin are transported to each other’s respective original locations by molecular travel. Modal overlap is as straightforward as temporal overlap. Take the case of Hitler’s @-stage, his w-stage, and all the relevant modal stages at the intervening worlds in some short chain. The transworld individual consisting of these modal stages is a proper modal segment of the transworld individual who is Hitler. The transworld individual extends beyond those worlds in the chain. Let us consider a larger modal segment of Hitler which involves just as many possible worlds as in the original chain from Hitler at @ to Stalin at w but which involves modal stages that are only peripherally different from one another: for example, one modal 43 For simplicity, let us assume that the molecular constitutions of the two men were so as to allow this maneuver.

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stage’s left little ﬁngernail is a micrometer longer than another’s. This does not destroy Hitler-ness of the transworld whole. The question is: what is the difference between the original Hitler–Stalin whole and this Hitler–Hitler whole that preserves Hitler-ness in the latter but not in the former? My short answer is, ‘The length of the chain’. The notion of ‘length’ I have in mind is no ordinary notion. Clearly, counting the number of intervening worlds will not do, for, by assumption, the two chains contain the same number of worlds. Take a particular cubic-centimeter spatial part, P, of the surface crust of Earth located 7 meters away from the tip of Mt Everest and safely considered as part of Mt Everest. Compare a chain of overlapping spatial parts, each a cubic centimeter in volume, stretching from the tip of Mt Everest to P straightforwardly near the surface of Earth and another chain of overlapping spatial parts, each a cubic centimeter in volume, stretching from the tip of Mt Everest to the tip of Mt Kilimanjaro straightforwardly near the surface of Earth. The notion of ‘length’ I have in mind is such that the second chain is ‘too long’ to ground the spatially extended object as one mountain, whereas the ﬁrst chain is not. The second chain is longer than the ﬁrst, but the ‘length’ is not just a matter of the number of spatial parts in the chain. The second chain extends into the vague spatial boundaries of Mt Everest, goes past them, enters the vague spatial boundaries of Mt Kilimanjaro, and goes past them, whereas the ﬁrst chain does nothing of the sort, staying well within the close proximity of the summit of Mt Everest. Using the modal analogy of this notion of ‘length’, I say that the chain of possible worlds connecting Hitler at @ with Hitler at w straightforwardly is ‘short’ enough to underwrite the claim that Hitler at @ and Hitler at w are modal stages of a familiar person, namely, Hitler, but the chain of possible worlds connecting Hitler at @ with Stalin at w is too ‘long’ to underwrite the claim that Hitler at @ and Stalin at w are modal stages of a familiar person, Hitler or Stalin or anyone else. Hitler at @ and Stalin at w are too ‘distant’ from each other qualitatively–– given the proximity (a high degree of similarity) between the two worlds––to count as modal stages of the same person, Hitler or Stalin (or anyone else). The ‘long’ chain of worlds from @ to w which underlies the uniﬁcation of Hitler at @ and Stalin at w as modal stages of the same transworld individual is too convoluted to support Hitler-ness or Stalin-ness of the transworld individual. If we were to view the ﬁveþ-dimensional motion picture which started with a shot of Hitler at @, took us through his gradual but constant transformation at the intervening worlds toward qualitative parity with Stalin at w, and ended with a shot of Stalin at w, then we would see how much change were involved not only with Hitler–Stalin but also with the surrounding neighborhood (roughly, the situations and events near the surface of Earth in the nineteenth and twentieth centuries). Hitler at @ and Stalin at w are fairly dissimilar, while @ and w are very similar. This mismatch in similarity between the Hitler–Stalin pair and the @–w pair is a mark of the loss of certain familiar individualities, such as

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Hitler-ness and Stalin-ness. Another way to look at this is by reminding ourselves that at w there is Hitler who is indistinguishable from Hitler at @. There is a ‘short’ chain of worlds from @ to w with respect to Hitler at @ and Hitler at w, just as there is such a chain from @ to w with respect to Stalin at @ and Stalin at w. Hitler at @ and Hitler at w are world-stages of the same transworld individual who is Hitler. Likewise with Stalin. Why are we not theoretically committed to the claim that Hitler could have been Stalin? As in the Stalin–poached-egg case, in order for Hitler to have been Stalin, Hitler needs to have been Stalin while remaining Hitler. But we have seen that Stalin at w is not a modal stage of Hitler. There are, however, two dissimilarities between this case and the Stalin–poached-egg case. In this case, unlike the Stalin–poached-egg case, one common relevant high-level sortal, personhood (or humanness) applicable to the two individuals, is retained throughout the chain of worlds, as we noted before. This prompts a further consideration on this case. When we say ‘Stalin at @’, ‘Stalin at w’, or ‘Hitler at @’, we mean to speak of Stalin’s modal stage at @, Stalin’s modal stage at w, or Hitler’s modal stage at @. But when we say ‘Stalin’ or ‘Hitler’, we speak not of any particular modal stage but of the transworld individual who is Stalin or the transworld individual who is Hitler. So the question whether Hitler could have been Stalin is a question about the transworld individual who is Hitler and the transworld individual who is Stalin, and asks whether the former could have been the latter. Compare this question with a more mundane question about the two transworld individuals. Could Hitler have met Stalin? The answer is ‘Yes’ if and only if Hitler met Stalin at some possible world, i.e. Hitler’s modal stage at some possible world met Stalin’s modal stage at the same possible world. Since there is some such possible world, the answer to the question is ‘Yes’. If we follow this model, we should say that the answer to ‘Could Hitler have been Stalin?’ is ‘Yes’ if and only if Hitler was Stalin at some possible world, i.e. Hitler’s modal stage at some possible world was Stalin’s modal stage at the same possible world. This condition obtains if and only if the transworld individual who is Hitler and the transworld individual who is Stalin share a common modal stage at some possible world (i.e. if and only if they are ﬁveþ-dimensional siamese twins). Imagine a world, w’, which is Stalin–Hitler neutral. That is, at w’, no individual is more similar to Stalin at @ than to Hitler at @, and no individual is more similar to Hitler at @ than to Stalin at @. In addition, assume that at w’ there is exactly one person who is even remotely similar to either Stalin or Hitler. This human being at w’ is more similar to either of them than any other individual at w’ is. Let us call this human ‘Statler’. Statler at w’ is equally similar (and equally dissimilar) to Stalin at @ and Hitler at @. There is an appropriate chain of possible worlds leading from Hitler at @ to Statler at w’. There is also an appropriate chain of possible worlds leading from Stalin at @ to Statler at w’. These two chains are of equal ‘length’. So, if Statler at w’ is a modal stage of the

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transworld individual who is Stalin, then he is a modal stage of the transworld individual who is Hitler. This is a modal analog of the fusion or ﬁssion case in identity through time (depending on the direction in the chain we follow). If identity through modal space works like identity through time, as we are assuming, then since fusion and ﬁssion block identity through time, Statler at w’ is not a modal stage of Stalin or of Hitler.44 So, unlike the mundane question ‘Could Hitler have met Stalin?’ the answer to the question at hand ‘Could Hitler have been Stalin?’ is ‘No’. (I think that we may regard this reasoning as providing a justiﬁcation for the thesis of the necessity of identity. That is, our intuitive judgment on identity in fusion and ﬁssion cases ultimately grounds the necessity of identity via the important conceptual parity between temporality and modality.45) Note that this does not mean that Stalin and Hitler could not have been halfway like each other’s respective actual selves. It only means that Stalin and Hitler do not share a common modal stage at any possible world. When there is parity in ‘length’ between the appropriate chains of worlds to ground the identity of familiar transworld individuals, as the Statler case illustrates, neither claim of transworld identity is true. A philosopher who is Statler’s worldmate at w’ might well reason similarly at w’, starting with Statler at w’ and imagining a possible world w* at which two persons exist each of whom is halfway similar to Statler at w’. Such a philosopher should conclude at w’ that neither of these two persons at w* is a modal stage of the transworld individual who is Statler. The reasoning should be exactly parallel to ours above. Note here that the two persons at w* need not be dissimilar. They may be as similar to each other as one wishes. As long as they are distinct persons at w*, they should not be deemed to be modal stages of Statler. I can think of a different reading of the question ‘Could Hitler have been Stalin?’ which does not follow the common understanding of the mundane question ‘Could Hitler have met Stalin?’ On this reading, the question asks whether the transworld individual who is Hitler and the transworld individual who is Stalin are the same transworld individual at some possible world, i.e. 44 Strictly speaking, it is sufﬁcient to deny either that Statler at w’ is a modal stage of Stalin or that Statler at w’ is a modal stage of Hitler. We need not deny both. But these two disjuncts have exactly the same plausibility, i.e. exactly the same implausibility, so denying one of them without denying the other is arbitrary and ill founded. 45 See Nozick 1981: 656–9 n. 9. Nozick discusses the consequences of his closest-continuer theory for the thesis of necessity of identity. He tentatively concludes, ‘It certainly appears that some counterexample should emerge, even to Kripke’s speciﬁc claim, from closest-continuer considerations’ (659). It seems to me, however, that Nozick is hampered by not taking modal dimensions seriously as analogous to the temporal dimension. If he did, he would realize that the rigid designators ﬂanking the identity sign in his example sentence, ‘ROBERT NOZICK = RN’, which he tentatively judges to be contingently false in the set-up he discusses, designated two different transworld individuals and therefore the sentence were necessarily false. (ROBERT NOZICK and RN do not have a common world-stage at the actual world but have the post-t1 stage in common at the world of case 3 in Nozick’s set-up.)

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whether at some possible world there is a transworld individual in his entirety (with all of his modal stages present at it) who is the transworld individual, Hitler, and is the transworld individual, Stalin. When interpreted this way, it is an absurd question, for it is absurd to think of a transworld individual (like Hitler or Stalin) as existing at a single possible world in his entirety. ‘Transworld’ means ‘spread over different worlds’––at least as far as it concerns individuals like Hitler and Stalin. I am not necessarily committed to the claim that it is impossible for Hitler and Stalin to have switched places. If ‘switching places’ means that Hitler and Stalin switch their qualitative properties completely, then I am committed to the claim that it is impossible for them to have ‘switched places’, for such switching entails haecceitism, a doctrine I reject. But ‘switching places’ usually means switching only some select qualitative properties. For example, the following situation would count as ‘switching places’: Hitler was born in the place Stalin was actually born, was raised as Stalin was actually raised, became the leader of the USSR as Stalin actually did, and led the country during the Second World War, while Stalin was born in the place Hitler was actually born, was raised as Hitler was actually raised, became the leader of Germany as Hitler actually did, and led the country during the Second World War. I am not committed to the impossibility of such a situation. There is a ‘short’ chain of possible worlds from the actual world to a world at which the birth places of the two men are switched. It is then easy to see that there is a further connected ‘short’ chain of possible worlds leading to a possible world at which Hitler led more or less Stalin’s actual life, and vice versa. 6 . 1 2 . TWO MORE OBJECTIONS Penelope Mackie offers three arguments against the closest-continuer theory of transworld identity.46 The ﬁrst argument borrows from Graeme Forbes’s reduplication argument,47 the second argument is parasitic on the ﬁrst argument, and the third argument involves Nathan Salmon’s ‘Four Worlds Paradox’.48 I shall reconstruct Mackie’s ﬁrst argument, which is spread over many pages, as follows: Suppose that no oak tree is identical with the acorn from which it grows. Assume for reductio the closest-continuer theory of transworld identity. Consider worlds w1–w4 such that: at w1, an oak tree O1 grows from an acorn a1 in a place p1 and nothing grows in a place p2, which is totally distinct from p1; at w2, an oak tree O2 grows from an acorn a2, which is 46 47 48

Mackie 2006: 47–78, esp. 47–51, 72–8 Forbes 1985: 138–45; also 1986, 2002. Salmon 1981: 229–52.

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totally distinct from a1, in p1 and nothing grows in p2; at w3, nothing grows in p1 and an oak tree O3 grows from a1 in p2; at w4, an oak tree O4 grows from a2 in p1 and an oak tree O5 grows from a1 in p2. The four worlds do not differ in any gratuitous way. At w2, the closest continuer of O1 at w1 is O2. So O2 ¼ O1. At w3, the closest continuer of O1 at w1 is O3. So O3 ¼ O1. At w4, the closest continuer of O2 at w2 is O4 and the closest continuer of O3 at w3 is O5. So O4 ¼ O2 and O5 ¼ O3. Hence O4 ¼ O1 and O5 ¼ O1. Therefore O4 ¼ O5. But clearly O4 ¼ 6 O5. A contradiction. Forbes himself, who is no fan of the closest-continuer theory, regards his own argument as counting not against the closest-continuer theory but against the joint metaphysical possibility of the four worlds. The lesson he draws from the argument is that it is metaphysically impossible for an oak tree to grow from any acorn distinct from the acorn it in fact grows from, and more generally, that the actual propagules of a biological individual are essential to that individual. This interpretation of Mackie’s argument shields the closest-continuer theory successfully.49 Since Mackie’s second argument loses force completely after her ﬁrst argument is successfully resisted, I shall skip it altogether. For her third argument, we need to look at Salmon’s ‘Four Worlds Paradox’, which I shall sketch as follows: At a world w1, an artifact x1 is constructed out of k-many parts, p1, p2, . . . , pk, according to the design plan D. At a different world w2, an artifact x2 is constructed out of k-many parts, p1, p2, . . . , pk-1, pkþ1, according to D. At a third world w3, an artifact x3 is constructed out of k-many parts, p1, p2, . . . , pk-1, pkþ1, according to D. At a fourth world w4, an artifact x4 is constructed out of k-many parts, p1, p2, . . . , pk-2, pkþ1, pkþ2. The four worlds do not differ gratuitously. Suppose that artifacts constructed out of k-many parts according to D could have been constructed out of (k-1)-many of those parts with the remaining part replaced with a new part but not out of (k-2)-many of those parts with the remaining two parts replaced with two new parts. Assume for reductio the closest-continuer theory. The artifacts x1 and x2 are each other’s closest-continuer, so x1 ¼ x2. The 49 Mackie says, ‘it is an assumption of the discussion that the best-candidate theorist of transworld identity says that the tree at p1 in w2 satisﬁes the conditions for identity with O1 in w1, and so does the tree at p2 in (the distinct world) w3’ (2006: 75). But I am suggesting that closestcontinuer theorists (best-candidate theorists) should reject such an assumption, following Forbes’s original intention. Mackie’s own discussion does not seem to make any such assumption speciﬁcally at any point, either. This is curious. After a brief comment on Forbes’s denial of the metaphysical possibility of w2, Mackie explicitly shifts her discussion toward Forbes’s wider claim that the propagules of a biological individual are not only essential to that individual but also metaphysically impossible for any other biological individual to have, i.e. that having those propagules is an essential property of the individual. The rest of her discussion up to the quoted passage proceeds along the shifted lines. It is difﬁcult to see the reason why she says, ‘it is an assumption of the discussion’.

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The ﬁveþ-dimensional view, which embraces modal-dimensional hyperworms, or modal worms, provides us with a proper response to this argument when fortiﬁed with consideration of vagueness. Imagine a modal worm (transworld individual) of which x2 (at w2) and x3 (at w3) are modal stages. These stages are very close to each other in the worm. Farther on the x2 side away from x3 is x1 (at w1), and farther on the x3 side away from x2 is x4 (at w4). Embracing vagueness means rejecting the assumption in the argument that a one-part difference preserves identity but a two-part difference does not. Such an assumption presupposes a deﬁnite cut-off point and is contrary to the intuitive view of vagueness, according to which it is indeterminate where the boundaries of ordinary objects lie. If ordinary objects are modal worms, then on the intuitive view of vagueness, it is indeterminate where the boundaries of the modal worm in question of which x2 (at w2) and x3 (at w3) are modal parts lie. On the intuitive view of vagueness, modal stages like x1 (at w1) and x4 (at w4) should be regarded as being located toward the opposing ends of the penumbral area of the indeterminate boundaries. 6. 1 3. VAGUENESS AGAIN There is more to say about why the ‘length’ of the ‘long’ chain of worlds from @ to w should stand in the way of Hitler-ness (or Stalin-ness) of the Hitler–Stalin transworld individual. Let us return to the spatial analogy. (We shall take great care not to be misled by the points of disanalogy between spatial and modal indices noted earlier.) Mt Everest is spatially extended. How far out are its spatial parts spread? Certainly a cubic-meter tip of the summit is part of Mt Everest but a cubic-meter tip of the summit of Mt Kilimanjaro is not. So Mt Everest must 50 The obvious relativizations to worlds are omitted: e.g. x1 at w1 and x2 at w2 are each other’s closest-continuer. Mackie’s version merges w2 and w3 and identiﬁes x2 and x3 by stipulation. She speaks of ships, following Salmon, and assumes k = 3 for convenience. She then puts her objection to the closest-continuer theory as follows: ‘there are puzzles…: for example, my version of the “Four Worlds Paradox” in Section 3.5 above, in which the problem involved two ships in different worlds both of which were candidates for identiﬁcation with a single ship in another world. If there are puzzles of this form, we must conclude that the “extrinsic determination” proposal is not equipped to provide a solution to the full range of the relevant puzzles…’ (Mackie 2006: 78, her emphasis). Her objection is that the proposal is illequipped to answer the puzzling question: of x1 and x4, which is identical with x2 (x3)? My sketch of Salmon’s argument is a reductio argument against the closestcontinuer theory, and therefore has a narrower target and is stronger.

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run out of its spatial parts somewhere in between. But where? This is a difﬁcult question to answer. Many agree that it is a vague matter. Some say that the vagueness merely indicates a limitation inherent in epistemic access to the universe by human beings (or perhaps, by just about any possible subject of epistemic access) and in reality there are unknowable precise spatial boundaries delineating Mt Everest from the rest of Earth. Some say that the vagueness is not a feature of the universe and Mt Everest, which would be vague if existent, does not exist. Others say that the vagueness is a matter of semantic indecision on our part in the face of a series of objects with precise boundaries and, in particular, we are undecided about which of the many precisely bounded objects to call ‘Mt Everest’. Still others say that vagueness is an ineliminable feature of the universe, and in particular, that ‘Mt Everest’ refers to exactly one existing object and that object is a vague object. Notice that the ﬁrst three positions embrace some kind of limitation on our part vis-a`-vis reality. The ﬁrst says that we are epistemically limited, the second says that we are mistaken about the existence of ordinary objects, and the third says that we are semantically limited. The fourth is the only view that does not fault us. It is perhaps the closest to the commonsensical view. Let us discuss these positions in turn.

6.13.1. Epistemic and nihilistic views The ﬁrst, epistemic view of vagueness says that there are ordinary objects but there are no such things as vague objects, i.e. there are no objects which are vague in themselves. All objects have precise boundaries. The designators for ordinary objects designate objects unambiguously, and the precise boundaries of ordinary objects, like the precise boundaries of any object, are unknowable. Thus, ‘Mt Everest’ refers to a single precise existing object, whose precise boundaries are unknowable. In fact, according to the epistemic view, there could not possibly be vague objects, i.e. vague objects are impossible. Let us examine two representative arguments for it. Suppose that Mt Everest––call it ‘E’––is a spatially vague object. Take a tiny stone which lies within its vague spatial boundaries. Consider E minus that stone, that is, Mt Everest as it is with all of its vague boundaries except that the stone is disregarded, and call it ‘E-1’. One argument goes as follows: If Mt Everest is a vague object, then it is vague whether E ¼ E-1 but it is not vague whether E-1 ¼ E-1. (10) If it is vague whether E ¼ E-1 but it is not vague whether E-1 ¼ E-1, then E-1 deﬁnitely has a property E lacks (namely, the property of being such that it is not vague whether it ¼ E-1). (11) If E-1 deﬁnitely has a property E lacks, then deﬁnitely E 6¼ E-1 (by Leibniz’s law of identity). (12) If deﬁnitely E 6¼ E-1, then it is not vague whether E ¼ E-1.

(9)

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132 From (9)–(12),

(13) If Mt Everest is a vague object, then it is vague whether E ¼ E-1 and it is not vague whether E ¼ E-1. The consequent of (13) is a contradiction. Therefore, the antecedent of (13) is false, i.e. (14) Mt Everest is not a vague object.51 If successful, this argument would show that any possible object that is a putative candidate as a vague object is not a vague object. The argument is valid and the premises (10)–(12) are compelling. But premise (9) is dubious. If Mt Everest is a vague object, E has vague boundaries, within which the stone in question lies. But if so, disregarding the stone will result in slightly different vague boundaries. So, E-1 has vague boundaries which are different from the vague boundaries E has. So E-1 deﬁnitely has a property E lacks (namely, the property of having those particular vague boundaries). Hence by Leibniz’s law, deﬁnitely E 6¼ E-1. Therefore, if Mt Everest is a vague object, then deﬁnitely E 6¼ E-1. (9) is false. I think that the advocates of the above argument misunderstand the nature of vague objects. I think that they believe the following. In order for an object to be a vague object, its identity condition must be vague, and in order for an object’s identity condition to be vague, some identity statement about it, such as ‘E ¼ E-1’ above, must be vague. The second conjunct here is false. An object, O, may have a vague identity condition without having any statement of the form ‘O ¼ Y’ vague. Any such statement is deﬁnitely true if Y has exactly the same vague identity condition as O, and deﬁnitely false if Y does not.52 The second argument is a temporal version. Instead of comparing E and E-1 as existing at the same time, start with E existing at a time t1 with all of its parts including the vague spatial boundaries. At a later time t2 a small grain of rock is removed from the top of E. A removal of one small grain does not destroy E. At a still later time t3 another small grain is removed from the top. And so on. Eventually E will be no more. This is the classical sorites argument. (15) If Mt Everest is a vague object, then a removal of a small grain from the top of E will result in E. (16) At t1, a small grain is removed from the top of E, resulting in E1. (17) At t2, a small grain is removed from the top of E1, resulting in E2. . . . 51 Gareth Evans and Nathan Salmon proposed essentially this argument independently. See Evans 1978; Salmon 1981: 243–6; 1984a; 1986b: 110–14. Also Williamson 2003: 707–8. 52 Ken Akiba makes a similar point (2000b).

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(15þK) At tk, a small grain is removed from the top of Ek-1, resulting in Ek (where k exceeds the number of grains which lie in either E or E’s vague spatial boundaries). So, (16þK) If Mt Everest is a vague object, then E ¼ E1 ¼ E2 ¼ . . . ¼ Ek, hence E ¼ Ek. But since Ek is what is left after the removal of all grains in E and E’s vague spatial boundaries, (17þK) E 6¼ Ek. Therefore, (18þK) Mt Everest is not a vague object. Our response to this argument is similar to our response to the ﬁrst argument. Just as the ﬁrst argument dealt with vague spatial boundaries, this argument deals with vague temporal boundaries. And just as we said that the disregarded stone in the ﬁrst argument was in the vague spatial boundaries, we say that some of the removed grains in this argument are in the vague temporal boundaries. (15) should be rejected, for it is no more plausible than its spatial analog, which recursively implies that (if Mt Everest is a vague object, then) if we start from the top of E and descend very gradually by one grain at a time, then every time we make our minuscule descent, we land on E, and this spatial analog should be rejected. The latter should be rejected because we will eventually start landing on the vague spatial boundaries of E, and landing on vague spatial boundaries of E does not entail landing on E––or perhaps we should say, does not deﬁnitely entail landing on E. Vague boundaries, spatial or temporal, are exactly that–– vague. Some principles of reasoning applicable to non-vague matters simply do not apply to cases involving vague boundaries. Exactly what alternative principles do apply is an intriguing question and there have been different proposals, but we shall not pursue this issue, as it would take us too far aﬁeld. We shall simply assume that the method of supervaluation is useful for some of our purposes; see 6.13.2. There are other arguments against objective, or metaphysical, vagueness.53 If one of them is sound, there are no vague objects, in which case a key presumption in our discussion of transworld identity appears false. Fortunately, as surprising as such a result will be, it will not affect our discussion of transworld identity seriously. We set up our discussion of transworld identity on the assumption that ordinary objects are vague objects, and we so assumed because it is a plausible

53 A particularly inﬂuential one among them is the step argument, due to Mark Heller in Heller 1990, 1996, 2000.

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assumption in seeming agreement with common sense. But if the assumption is false, it will be easy to recast our discussion so as to avoid the assumption. Doing so by adopting the epistemic view of vagueness will in fact simplify our discussion considerably. According to the epistemic view, the spatial, temporal, and modal boundaries of ordinary objects are precise and unknowable. In a chain of possible worlds starting with a particular world, w, and ordered by similarity, certain modal stages at those worlds which lie within a certain precise distance from w in the chain will make up one transworld individual of a given kind, but the modal stages at all further worlds will not make up that transworld individual. We need not attempt to say what that distance is or how it is precisely to be determined, for the epistemic theory says that it is unknowable. Chisholm’s problem does not arise, for an inordinately ‘long’ chain of possible worlds, like the one from @ to w which we discussed with respect to Hitler at @ and Stalin at w, is sure to contain an unknowable cutting-point of transworld identity so that the modal stages at the two end worlds, like Hitler’s @-stage and Stalin’s w-stage, are not parts of the same transworld person. A close cousin of the epistemic view will simplify our discussion of transworld identity even further. It is the nihilistic view. It says that there are no vague objects, that the designators for ordinary objects are not ambiguous, and that ordinary objects are vague objects. This entails that there are no ordinary objects.54 Thus, there is no such object as Mt Everest. Instead there are many mountain-shaped objects with precise boundaries in the vicinity of where we ordinarily judge Mt Everest to be. Modal boundaries are no different. There is no such thing as a modal worm with vague modal boundaries; there are only modal worms with precise modal boundaries. For any distance d from w in the chain of possible worlds starting with w, the collection of the relevant modal stages at those worlds lying within d in the chain make up a precise modal worm. Transworld identity could not be simpler. Chisholm’s problem obviously does not arise.

6.13.2. Semantic view Another view against metaphysical vagueness says that reality is precise in itself and the appearance of vague objects is created by semantic imprecision or indecision. On this semantic view, there is not one object which is Mt Everest and which is a vague object. Instead, there are fantastically many precise objects any one of which is as good a candidate as any other for being the referent of the expression ‘Mt Everest’. If we say that ‘Mt Everest’ is a singular term and therefore insist that it must have a single unique referent or else no referent at all, then we may decide that it has no referent. That will be a radical version of 54 See Heller 1990; van Inwagen 1990; Merricks 2003. Van Inwagen does not deny the existence of ordinary living things.

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the semantic view. According to a more moderate version, ‘Mt Everest’ is simply fantastically ambiguous in its reference, and we only need to understand our discourse involving it in the supervaluationist way,55 or else be careful and explicit about which particular precise object is understood to be its referent when we speak of its semantic properties and relations. The radical version is radically revisionary and to that extent implausible, whereas the moderate version has considerable initial plausibility. The Evans–Salmon argument––(9)–(14) in 6.13.1—can be reinterpreted as an argument against the semantic view of vagueness. Change the ﬁrst premise to: (90 ) If ‘E’ is semantically vague, then it is vague whether E ¼ E-1 but it is not vague whether E-1 ¼ E-1. (10) through (12) will go through as before, but (13) and (14) should be changed accordingly: (130 ) If ‘E’ is semantically vague, then it is vague whether E ¼ E-1 and it is not vague whether E ¼ E-1. The consequent of (130 ) is a contradiction. Therefore, the antecedent of (130 ) is false, i.e. (140 ) ‘E’ is not semantically vague. We objected to the previous argument by rejecting its premise (9). Here again, it is the ﬁrst premise, (90 ), that is suspect. If ‘E’ is semantically vague, then any sentence containing ‘E’ (as used, not mentioned) is equally semantically vague, so in particular, ‘E ¼ E-1’ is equally semantically vague. That is, ‘E ¼ E-1’ may mean any of the following: EÆ ¼ EÆ-1; E ¼ E-1; Eª ¼ Eª-1; and so on, where each of ‘EÆ’, ‘E’, ‘Eª’, etc., is semantically precise and refers to the referent of a particular disambiguation, or precisiﬁcation, of ‘Mt Everest’. At least one of those referents fails to contain the stone which is in question in creating E-1 from E. Let us assume that EÆ is such a referent. Since EÆ fails to contain the stone, EÆ-1 is the same object as EÆ. So on that precisiﬁcation, ‘E ¼ E-1’ is true. Likewise for any precisiﬁcation of ‘E’ whose referent fails to contain the stone. All other precisiﬁcations will make ‘E ¼ E-1’ false. So, assuming supervaluation, it is neither true nor false that E ¼ E-1. This reasoning is deﬁnite. Thus, it is not vague whether E ¼ E-1. Therefore, (90 ) should be rejected. There is an apparently easy way to ﬁx the argument in response to this objection. It is to replace (90 ) and (10) respectively with the following: (900 ) If ‘E’ is semantically vague, then it is neither true nor false that E ¼ E-1 but it is true that E-1 ¼ E-1.

55

The method of supervaluation is due to B. C. van Fraassen 1966.

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Transworld Individuals and their Identity (100 ) If it is neither true nor false that E ¼ E-1 but it is true that E-1 ¼ E-1, then E-1 deﬁnitely has a property E lacks (namely, the property of being such that it is true that it ¼ E-1).

This appears to restore the truth of the ﬁrst premise of the argument while preserving validity. The cost, however, is the shift from the original (10) to (100 ), and this causes a problem. (100 ) is a crucial part of the revised argument, which still relies on Leibniz’s law. This means that (100 ) needs to have the following form: ‘If P, then a particular object x is thus-and-so and a particular object y is not thus-and-so’. That is, it needs to say in its consequent something about one object x in particular and some contradictory thing about one object y in particular. The problem is that according to the semantic view of vagueness, when we use an apparent singular term, we do not refer to any one object in particular. So when we use ‘E’ or ‘E-1’, no one object in particular is such that we refer to it. Therefore, (100 ) is unﬁt to be used in combination with Leibniz’s law. A different way to see essentially the same point is to apply supervaluation to (100 ). On those precisiﬁcations which assign to ‘E’ a referent which contains the stone, the consequent of (100 ) is true, but on those precisiﬁcations which assign to ‘E’ a referent which does not contain the stone, the consequent is false. Since we are assuming that the antecedent of (100 ) is true under supervaluation (otherwise (900 ) would lose relevance), this shows that (100 ) is neither true nor false. Therefore soundness is not attained. The sorites argument can also be reinterpreted to be directed at the semantic view. Its ﬁrst premise will be: (150 ) If ‘E’ is semantically vague, then a removal of a small grain from the top of E will result in E. This premise is even more suspect than the ﬁrst premise in the original sorites argument. Removing a grain from a precise object containing the grain will result in a different precise object. Since the grain comes from the top of the mountain instead of the vague boundary area, the resulting precise object is a different object from the initial precise referent of ‘E’ according to any precisiﬁcation. So (150 ) is false on any precisiﬁcation of ‘E’. If the argument is modiﬁed so that the grain is from the vague boundary area, then we can object to the argument by pointing out that there is some precisiﬁcation of ‘E’, let us say it is ‘E’, such that a removal of the grain from E will not result in E but in a slightly smaller precise object, hence (150 ) is not true. We shall not examine other arguments against the semantic view, for the two arguments above provide us with a sufﬁcient overview of what is involved in assessment of the view. For our purposes, the semantic view is not a serious obstacle. It does not present any additional difﬁculty to transworld identity. The semantic view removes the topic of vagueness from metaphysics and relocates it in semantics. It leaves objects themselves precise, as the epistemic view does,

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while making the word–object relation ambiguous. Since our focus is on objects, and not on words, our discussion of transworld identity need not be seriously affected even if the semantic view proves to be correct. Either all mention of vagueness should be deleted from our discussion of transworld identity of objects, or metaphysical vagueness should be replaced with semantic vagueness. If the former, our task is not compromised but simpliﬁed. The situation will be similar to the one under the supposition that the epistemic view is correct. If the latter, our task becomes a little more complicated but still fairly straightforward. The discussion couched in terms of metaphysical vagueness can easily be transformed into the corresponding discussion re-couched in terms of semantic vagueness. Instead of speaking of a vague criterion of identity for x, speak of a semantically vague designator for x, and adjust the rest of the discussion accordingly, and we will have a coherent picture of transworld identity of ordinary objects. Some might say in critique of the semantic view that the ambiguity of the word–object relation makes objects themselves vague, for objects lack independent being separately from bearing (the converse of) the word–object relation. I am not conﬁdent that I entirely understand such a critique, but if the critique is correct, then, it seems, the semantic view of vagueness is internally incoherent. But if so, this will make it unnecessary for us to attend to the semantic view, thus simplifying our endeavor. By not adopting the epistemic or nihilistic view, we make the task of spelling out the criterion for transworld identity more complicated. Any fan of transworld identity who is willing to accept either of these views is welcome to make the commitment to the correspondingly simpler criterion for transworld identity at the cost of bearing the burden of defending the view of vagueness in question. I do not wish to presuppose any view of vagueness that would make the task of spelling out the criterion of transworld identity too easy. I also do not wish to mount an unnecessary challenge, while discussing modal metaphysics, against our intuitive opinions about ordinary objects which have overwhelming initial appeal. The opinion that ordinary objects are vague objects in the sense of having vague boundaries is such an opinion. If I can uphold it in a philosophically serious way, I will. But I have my doubts, as revealed in the next section. The next best thing is the semantic view, which largely preserves our intuitive opinion of the vagueness of objects by means of ambiguous designators.

6.13.3. Metaphysical view The view that ordinary objects are themselves vague objects (have vague boundaries) is perhaps the most commonsensical view of vagueness. At the same time, it is less articulate than the semantic view, for it is not clear exactly what it is for an object to be a vague object (have vague boundaries). In this section we brieﬂy examine an argument with a conclusion unpalatable to anyone who accepts this

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metaphysical vagueness view. The semantic view has the resources to resist the argument, whereas the metaphysical view does not. This provides us with some reason to favor the semantic view over the metaphysical view. Nathan Salmon argues that there is a sharp cut-off point in the amount of matter of which an artifact could be made originally. If the argument is sound, the commonsensical take on the vagueness of the constitution of an artifact is mistaken. But there is a simple way to resist the argument. The argument goes as follows: . . . the number of molecules in the original matter of table a is n. Suppose that at time t1, n distinct tables, a1, a2, . . . , an, each qualitatively identical to a, are constructed from exactly n molecules apiece. At a later time t2 , each table is completely dismantled. At a still later time t3, n tables, a10 , a20 , . . . , an0 , are constructed according to the same plan in the following way: a10 is formed from all of the original molecules of a1 except for the replacement of one molecule by a qualitative duplicate; a20 is formed from all of the original molecules of a2 except for the replacement of two molecules by qualitative duplicates of each; and so on, up to an0 , which is formed from entirely new matter. Clearly a1 ¼ a10 whereas an ¼ 6 an0 . In fact, the construction of the second sequence of tables may be such that, for any i, if ai ¼ ai0 , then ai-1 ¼ ai-10 , and if ai ¼ 6 ai0 , then aiþ1 6¼ aiþ10 . By the proof of the determinacy of identity, for any i, it is either determinately true that ai ¼ ai0 , or else it is determinately true that ai ¼ 6 ai0 . Therefore, there must be some precise amount of different matter that ﬁrst passes the threshold for the amount of different matter possible in the reconstruction of table a, i.e. there must be some m such that am ¼ 6 am0 but 0 am-1 = am-1 . On certain natural assumptions, this yields an excellent reason for supposing that in the sequence of hunks of matter h1, h2 , . . . , hn, there is a hunk hm that is the ﬁrst to pass the threshold for the amount of different original matter possible in the construction of table a, i.e. that this threshold also consists in a precise cut-off point.56 Some might object to Salmon’s assertion that clearly a1 = a10 on the grounds that a1 ceases to exist at t2. The idea is that once a table ceases to exist, it cannot restart to exist at a later time. This idea is not completely without merit but we shall not pursue it. Rather, we should focus on Salmon’s claim that for any i, it is either determinately true that ai = ai0 or determinately true that ai 6¼ ai0 . We can resist this claim by adopting the four-dimensionalist view, in particular the ontology of ordinary objects as four-dimensional worms, and combining it with the semantic view of vagueness. From the perspective of the four-dimensional worm view, the claims that ai = ai0 and that ai 6¼ ai0 are ambiguous, because the terms ‘ai’ and ‘ai0 ’ are ambiguous. The referent of such a term is either a temporal stage or a four-dimensional worm. If it is a temporal stage, ‘ai 6¼ ai0 ’ is deﬁnitely true for 56

Salmon 1986b : 113.

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any i––for every temporal stage is conﬁned to just one time––hence it is deﬁnitely false that a1 = a10 . But if it is a four-dimensional worm, ‘ai = ai0 ’ is either deﬁnitely true or deﬁnitely false, depending on whether ‘ai’ and ‘ai0 ’ deﬁnitely refer to the same worm or deﬁnitely refer to different worms. It is easy for the holder of the semantic view of vagueness to say that the terms neither deﬁnitely refer to the same worm nor deﬁnitely refer to different worms, for according to the semantic view, each term is governed by the semantic indecision as to which of many worms it is to refer. Whether a term refers to a particular precise worm as opposed to another precise worm is simply undecided. Note that we are not challenging the determinacy of identity: for any four-dimensional worm x and any four-dimensional worm y, either determinately x ¼ y or determinately x 6¼ y; for any temporal stage x and any temporal stage y, either determinately x ¼ y or determinately x 6¼ y. The holder of the metaphysical view, on the other hand, has trouble resisting Salmon’s argument. Let us take the simplest way for a table to be a vague object: being constituted by a number of molecules but not by any particular number of molecules. The metaphysical vagueness theorist might deny the very ﬁrst move in Salmon’s argument and say that there is no particular number n such that the number of molecules in the original matter of table a is n. This would block Salmon’s argument as presented. Modifying Salmon’s argument slightly, however, would shift the pressure back onto the metaphysical vagueness theorist. Suppose that the number of molecules in the matter of table a is vague. Let us be charitable and say that the number is at most 2n. If this is not charitable enough, pick an even larger number as a reasonable upper bound. Run Salmon’s argument with 2n, or the chosen larger number, in lieu of the original n. The modiﬁed argument will go through as before. The metaphysical vagueness theorist might resist the assumption that the number of molecules in the original matter of table a has an upperbound. But the metaphysical vagueness of the table does not warrant such resistance. Even if we ignore the kind of vagueness which arises not from the indeﬁniteness of the number of constituting molecules but from the indeﬁniteness of the constituting molecules among a ﬁxed number of candidate molecules, it is quite unreasonable to insist that for any number, an ordinary table is vaguely constituted by more than that number of molecules. It is quite unreasonable to insist that the number of molecules which vaguely constitute my kitchen table exceeds, say, the number of molecules in the Milky Way. Considerations of other ways for a table to be a vague object are left to the reader. There is no other obvious way for the metaphysical vagueness theorist to counter Salmon’s argument. For any vague object x and any vague object y, either they are vague in exactly the same way in all respects, in which case deﬁnitely x ¼ y, or they are not vague in exactly the same way in all respects, in which case deﬁnitely x 6¼ y. There might be an unobvious way for the metaphysical vagueness theorist to resist Salmon’s argument, but the onus is on her to produce it.

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6. 14 . DEGREES OF POSSIBILITY The challenge Chisholm brought to our attention is a variant of the sorites problem. Any satisfactory solution to the sorites problem should provide us with a way to meet Chisholm’s challenge. Many-valued logic solves the sorites problem. So, many-valued logic provides us with a way to meet Chisholm’s challenge. Guided by this idea, Graeme Forbes offers an intriguing response to Chisholm’s challenge.57 He starts by giving an outline of the standard fuzzy logic, due to J. A. Goguen,58 in which we have continuum-many truth values represented by the closed interval [0, 1] and the standard many-valued-logical deﬁnitions of logical operators. Forbes then applies this machinery to modality. He does so by ﬁrst observing that there is a philosophical difﬁculty concerning the coherence of the notion of the degree of satisfaction by an object of the predicate ‘is identical with Æ’: In the standard semantics for S5, transworld heirlines for objects are given by real crossworld identities in the model, and thus the only object which satisﬁes ‘ = Æ’ at a world is Æ. So if there can be degrees of satisfaction of ‘ = Æ’ at a world w, then it looks as if there must be degrees of being identical to Æ at worlds. Yet the notion of degrees of identity is incoherent. We saw that the idea that a predicate F is a predicate of degree is justiﬁed by the admissibility of the comparative form ‘x is more F than y’, but it would be quite hopeless to try to make literal sense of ‘x is more identical to Æ than is y’, and we will not waste space in the attempt.59

Forbes then proposes that we turn to David Lewis’s counterpart relation, for it is grounded in cross-world similarity, which naturally admits degrees. Forbes thus gives Chisholm’s challenge a formulation which is explicitly a version of the sorites couched in terms of a vague (relational) predicate and is therefore subject to the standard fuzzy-logical treatment. I ﬁnd Forbes’s response to Chisholm’s challenge satisfactory in spirit. I agree with Forbes that Chisholm’s challenge is a sorites problem and the fuzzy-logical solution is a good solution. But I disagree with Forbes when he turns away from transworld identity to Lewis’s counterpart theory. My disagreement with him is rooted in a difference in our fundamental metaphysical outlook. When he discusses––and dismisses––transworld identity, Forbes’s reasoning stays entirely within the standard Lewisian tradition, according to which an object exists wholly at each of the worlds at which it exists. He thus ignores the idea of a transworld object as a modal worm, an entity with proper modal parts existing at different worlds as its modal stages. This is so despite the fact that he uses David

57

Forbes 1985: 160–90.

58

Goguen 1969.

59

Forbes 1985: 177.

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Kaplan’s technical term ‘transworld heir lines’. Kaplan explains his use of the term: Although I will continue to speak of identiﬁcation, there are reasons, to which I will return, for claiming that the Bobby Dylan in G is not strictly identical with our Bobby Dylan but related to him in a way something like descendant to ancestor, what Kurt Lewin called gen-identity. So I call the task of locating individuals in other worlds the problem of determining transworld heir lines.60

A transworld heir line uniﬁes different modal stages into a single transworld individual in a way analogous to the way gen-identity uniﬁes different temporal stages into a single temporally persisting individual. This is the idea we have been following all along. The failure to take this seriously forces Forbes to declare his opposition to the thesis of necessity of identity, for the counterparttheoretic translation of the thesis is false. Forbes hints that the plausibility of Saul Kripke’s original arguments in favor of the thesis is due to the restricted range of the arguments, namely, one including only objects such as people and planets. He then says that if Kripke’s arguments are extended to other kinds of objects, such as artifacts, they lose their intuitive plausibility. According to Forbes, the crucial difference between objects like people and planets on the one hand and other kinds of objects like artifacts on the other is that ‘the notion of part has no very natural application’61 to the former. I ﬁnd this contrast between two kinds of object puzzling. The notion of part seems clearly applicable to people and planets. Forbes does not elaborate on this matter, so we shall not pursue it further. Discard Lewisian counterparts from Forbes’s machinery and include modal stages of transworld individuals in their place, and the result is something a modal realist of the type I endorse can accept. This is the sense in which I approve of Forbes’s way in spirit. 6. 15 . AMBIGUITY OF IDENTITY Even when, instead of speaking of two individuals of the same kind like Hitler and Stalin, we speak of two individuals of different kinds, the basic picture should remain the same. Let us say that at a possible world w6 there are a clay statue of a human ﬁgure, call it ‘Golly’, and a separate lump of clay, call it ‘Lumpy’, which is amorphous and not meant to be a statue at all. Let us mimic the Hitler–Stalin–Statler scenario and say that at w7 there is an individual, call it ‘Gollumpy’, which is a statue made of lump of clay and is qualitatively halfway between Golly and Lumpy just as Statler is halfway between Stalin and

60

Kaplan 1979a: 93–4; his emphases.

61

Forbes 1985: 179.

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Hitler.62 Unlike Hitler and Stalin, who belong to the same restricted kind, namely, person (or human), Golly and Lumpy belong to different restricted kinds, namely, statue and lump of clay. It might seem unproblematic to identify Golly at w6 and Gollumpy at w7 as modal stages of the same statue (i.e. to identify the transworld individual that is Golly with the transworld individual that is Gollumpy as one and the same statue), while identifying Lumpy at w6 and Gollumpy at w7 as modal stages of the same lump of clay (i.e. identifying the transworld individual that is Lumpy with the transworld individual that is Gollumpy as one and the same lump of clay). But we need to be cautious. To start with, we should not ignore the thesis of relative identity, the thesis that every truth-evaluable identity statement is of the form ‘x is the same K as y’, where ‘K’ is an appropriate sortal term.63 According to the thesis of relative identity, it is true to say that Golly is the same statue as Gollumpy and that Gollumpy is the same lump of clay as Lumpy, but it is not truth-evaluable to say that Golly is the same as Gollumpy or that Gollumpy is the same as Lumpy. The transitivity of identity is to be understood in the correspondingly relative manner: if x is the same K as y and y is the same K as z, then x is the same K as z. The following trans-sortal version is to be denied: if x is the same K1 as y and y is the same K2 as z, then x is the same K1 (or K2) as z, where K1 6¼ K2. Since Golly need not be the same lump of clay as Gollumpy and Gollumpy need not be the same statue as Lumpy, the transitivity of relative identity is not ﬂouted. But the following line of thought may cause us to pause. There seems to be an appropriate sortal term covering Golly, Gollumpy, and Lumpy. Every statue is a physical object, and so is every lump of clay. So, Golly, Gollumpy, and Lumpy are all physical objects. If Golly is the same physical object as Gollumpy and Gollumpy is the same physical object as Lumpy, then by the transitivity of relative identity, Golly is the same physical object as Lumpy. But Golly and Lumpy are two distinct physical objects, as they have distinct modal stages at w6. Thus, the Statler-like problem seems unavoidable after all. It seems that either Golly and Gollumpy are not the same physical object or Gollumpy and Lumpy are not the same physical object. Some might ﬁnd it tempting to object to this line of thought as follows. Assume w7 to be the actual world and w6 to be a non-actual possible world. If Gollumpy and Lumpy are not the same physical object, then Gollumpy is not just actually not squashed into an amorphous lump of clay at w7 but it could not possibly be so squashed; for we can make w6 as close as we wish to w7 in such a way that if any modal stage at any possible world is an amorphous lump of clay

62 This example is fashioned after the famous example by Allan Gibbard 1975. Roughly, Gibbard uses the name ‘Goliath’ for the statue that Gollumpy is, and the name ‘Lumpl’ for the lump of clay that Gollumpy is or is constituted by. 63 Geach 1962, 1967; Wiggins 1980.

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and is a modal stage of the same physical object as Gollumpy, the w6-stage of Lumpy is. So, Gollumpy and Lumpy must be the same physical object. Such an objection, however, would be too hasty. It is untrue that we can make w6 as close as we wish to w7, for w6 needs to have Golly as well as Lumpy exist at it. Many possible worlds have Lumpy exist at them but not Golly, and many of them are closer to w7 than w6 is. So, as is likely, if Gollumpy has a modal stage at such a world which is an amorphous lump of clay, then the possibility of Gollumpy being squashed into an amorphous lump of clay is sustained. A more serious objection concerns the status of physical-objecthood. It is not plausible to assume that there is a uniﬁed condition of identity for all physical objects. In particular, it is not plausible to assume that there is such a condition covering both clay statues and lumps of clay. Squashing them into amorphous lumps would destroy most clay statues,64 but not lumps of clay. This may seem to indicate that ‘physical object’ is not an appropriate sortal term. So the above line of thought, which assumes that it is an appropriate sortal term, is unacceptable. This objection, however, contains a crucial mistake. When we say that squashing a clay statue into an amorphous lump would destroy it, we do not mean that squashing it would make the physical object that is the clay statue cease to exist. The object which was a statue would still exist after being squashed. It is just that it would not be a statue anymore.65 A physical object may be a statue at some time and a non-statue at another time. Imagine that a statue is squashed and someone asks us, ‘Where did the statue go?’ We reply, ‘It is here’, standing by the amorphous lump and pointing at it. This exchange is open to two systematically different interpretations. The ﬁrst interpretation says that the question asks for the location of the statue as standing as a statue and that our reply says that the statue stands as a statue where we point at. So understood, our reply is false, as nothing stands there as a statue. But the second interpretation of the exchange says that the question asks for the location of the physical object that was the statue before the squashing and that our reply says that that physical object is where we point at. So understood, our reply is true. We may even add to our reply by saying, ‘This was the statue’. This means that ‘statue’ is a phase sortal66 for physical objects. A girl grows up to be a woman. The grown woman is not a girl but is the same human being as the girl. This shows that ‘girl’ is a natural phase sortal for human beings. Likewise, a statue may cease to be a statue while remaining the same physical object as the statue. The modal case is analogous. A statue could be squashed into an amorphous lump, thus ceasing to be a statue, hence ceasing to be the same statue, yet remain the same physical object.

64 65 66

Some conceptual art pieces consisting of clay statues might not be so destroyed. Unless it is a conceptual art piece. See Wiggins 1980.

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Gollumpy at w7 is a statue and is a lump of clay. The statue and the lump of clay are identical; or more precisely, the transworld object Gollumpy has a modal stage at w7 which is a statue and has a modal stage at w7 which is a lump of clay, and those stages are identical. The different ranges of allowable variations in arrangement of matter mark out two different conditions of application for the two sortal terms, ‘statue’ and ‘lump of clay’. When we follow the sortal ‘statue’, we trace one modal worm to Golly at w6, whereas when we follow the sortal ‘lump of clay’, we trace another modal worm to Lumpy at w6. ‘Statue’ and ‘lump of clay’ are phase sortals relative to ‘physical object’; a physical object may be a statue or a lump of clay at one time and something else at another. ‘Statue’ is also a phase sortal relative to ‘lump of clay’; a lump of clay may be a statue at one time and something else at another time. ‘Lump of clay’ is not usually a phase sortal relative to ‘statue’; a statue usually may not be a lump of clay at one time and something else at another time. If a statue is a sophisticated kinetic statue made of clay with a separate moving lump which by design coalesces with the rest of the statue only to separate itself from the rest again (and perhaps then coalesces again, only to be separated again, and so on), then the statue is one lump of clay (the coalesced whole) at one time and not one lump of clay but two lumps of clay (the separate moving part and the rest of the statue) at another time. The two terms are also modal phase sortals relative to ‘physical object’; a physical object may be a statue or a lump of clay at one possible world but something else at another. ‘Statue’ is a modal phase sortal relative to ‘lump of clay’, and ‘lump of clay’ is not usually a modal phase sortal relative to ‘statue’. Kripke proposes the necessity of composition: a physical object composed of some stuff is necessarily composed of that stuff.67 A clay statue is composed of clay. Given the necessity of composition, the clay statue is composed of clay at every possible world at which it exists. So, it is not the case that the clay statue is a lump of clay at one possible world but a lump of something else at another.68 This may well explain the fact that ‘statue’ is a phase sortal relative to ‘lump of clay’. (Kripke proposes another thesis, namely, the thesis of the necessity of origin. If a statue originates in a particular lump of clay, it necessarily originates in that lump. If we accept the claim that Golly at w6 and Gollumpy at w7 are modal stages of the same statue, then we need to reject this thesis, unless we accept the claim that Golly at w6 and Gollumpy at w7 have the same origin.) A similar explanation of the fact that ‘statue’ is a phase sortal relative to ‘physical object’ may naturally be forthcoming from the even more widely embraced claim that a statue which is a physical object is necessarily a physical object.69

67

Kripke 1980. Unless it is a philosophically sophisticated conceptual art piece. 69 Some argue that being concrete, let alone being a physical object, is an accidental property of objects. See Linsky and Zalta 1994, 1996. 68

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6.16. SUPERBLOBS AND HYPERBLOB For any two modal stages x and y at any two possible worlds w1 and w2, there is a chain of possible worlds under similarity from w1 to w2 which upholds the presence of a modal worm of which x and y are modal stages. Almost all such modal worms lack designation by any expression in any human natural language, but this is not surprising, given the limitations of human natural languages. For any modal stage z at any possible world w3, which is different from w2 and w1, there is a modal worm of which y at w2 and z at w3 are modal stages. This means that there is a modal worm of which x at w1, y at w2, and z at w3 are modal stages; simply string together the chain of worlds from w1 to w2 and the chain of worlds from w2 to w3 to form a ‘longer’ chain of worlds from w1 to w3. If the ﬁrst chain and the second chain deal in two different sortals (like ‘man’ and ‘woman’), then let the third ‘longer’ chain deal in a subsuming sortal (like ‘human’). This assumes that for any two sortals each of which applies to some modal stage at some possible world, there is a subsuming sortal. This assumption is plausible; in many cases ‘physical object’ will do as the subsuming sortal, and in some of those cases in which it will not, some other correspondingly general sortal, like ‘Cartesian ego’ or ‘abstract object’, will do. In other cases in which neither of those natural general sortals will do, simply resort to the disjunction of original sortals to be subsumed (for example, ‘statue or lump of clay’70). Thus, any modal stage x at any possible world is a modal stage of some modal worm that has a modal stage at every possible world, except at an (the?) empty world; call such a modal worm x’s superblob. Similarly, any modal worm X of any modal extension is part of some modal worm that has a modal stage at every possible world, except at an empty world; call such a modal worm X’s superblob. Superblobs necessarily exist, for they have a modal stage at every possible world, except at an empty world, which we shall ignore henceforth. Nixon’s superblob necessarily exists, but Nixon does not necessarily exist. This is so because Nixon is a proper part of his superblob. Nixon is to his superblob what a boy is to the human being he is. A boy does not exist at all times at which the human being he is does. Notice that even though for every boy there is just one human being who he is, we do not assume that Nixon has a unique superblob. In general, any modal stage at any possible world has one or more superblobs. A modal worm which has exactly one modal stage at every possible world is a superblob. But it is easy to realize that all such superblobs are proper parts of an even more fantastic transworld being. Many superblobs overlap many other superblobs, i.e. they have common modal stages with many other superblobs. Consider the totality of all superblobs. All modal stages at all possible worlds are 70 Or even ‘human being or abstract object’ if Linsky and Zalta are right. I do not claim that the resulting disjunctive term is a genuine sortal, and I do not need to.

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modal stages of this single transworld being. Call it the Hyperblob.71 The presence of the Hyperblob may seem to go against the intuitive judgment that, even if we are modally extended, you and I are still two distinct and separate individuals. But to think this way is to misunderstand the Hyperblob. The Hyperblob has many proper parts, some of which are modal stages and others are extended transworld individuals, and some of these parts are as distinct and separate from one another as anything could be. Notice that the Hyperblob is neither a human being, nor a person, nor a donkey, nor a tree, nor a desk, nor . . . No single word or short phrase succeeds in characterizing the Hyperblob correctly. You and I are certainly distinct and separate, but distinct and separate as human beings, as persons, as animals, and as physical objects (or as Cartesian egos if that is what we are). We are also distinct and separate parts of the Hyperblob. The fact that a single object has you and me as its parts does not mean that you and I are not distinct or separate from each other. Also, the presence of the Hyperblob does not support the modal analog of time travel in which an individual travels to a different time and confronts herself indigenous to that time. I am part of the Hyperblob and so are you. But this does not mean that when I confront you at some world, I am confronting myself at that world. It only means that when I confront you, that part of the Hyperblob which is me is confronting that part of the Hyperblob which is you. 71 Terence Horgan and Matjaz Potic (2000, 2002) endorse something like an intra-world version of the Hyperblob.

7 Extensionalism 7 . 1 . REDUCTION One major difference between David Lewis’s realism and actualism is that Lewis’s theory is reductionist but all actualist theories are non-reductionist. Early Lewis intended a full reduction of modal discourse into counterpart theory, which does not employ any modal notion and is completely extensional. A common, and sometimes unstated theme which underlies many objections to this version of Lewis’s modal realism is that the ingredients of this theory, namely, the notions of a concrete object, a set of concrete objects, and a mereological sum of concrete objects, lack modal import and are not sufﬁcient to build modal notions out of. A typical objection of this kind is sometimes formulated as a rhetorical question: how is it assured that all Lewisian possible worlds are indeed possible and that all possibilities are indeed realized at Lewisian possible worlds? John Divers boldly attempts to take a stand on Lewis’s behalf, saying that Lewis’s theory is supposed to be truly reductive and as such it should not contain blatantly modal notions at the rock-bottom level.1 But the objection does seem powerful. Lewis’s theoretical primitives do seem to fall short of fully grounding genuine non-actual possibilities concerning concrete individuals. Interestingly, the general type of theoretical inadequacy of which this potential defect of Lewis’s theory is a special case was clearly noticed by Lewis himself in someone else’s proposal on a different topic. Lewis gave a graduate seminar in philosophy of science at Princeton University in 1978–9. A student in that seminar, David Johnson, presented an elaborate theory of inductive justiﬁcation. After a round of comments from the other students on various technical details of the proposal and replies from Johnson, Lewis stepped in and simply said that the proposal was suspect because its primitive notions were too impoverished to ground a satisfactory conceptual analysis of inductive justiﬁcation. His sweeping critique may or may not have been fair to Johnson’s proposal but it silenced all students in the seminar, including Johnson. The basic idea of the objection against Lewis’s own theory of modality is the same. His primitive notions are too impoverished to ground a satisfactory analysis of modal discourse. William 1

Divers 2002: 106–21.

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Lycan’s well-known complaint that Lewis offers no theoretical basis for claiming that Lewisian non-actual possible worlds are indeed non-actual and possible rather than actual or impossible2 is but one example of the line of criticism analogous to Lewis’s own critique of Johnson’s proposal in his seminar.3 Apart from this general objection concerning conceptual analysis, Lewis was aware of a serious technical difﬁculty in his reductive project early on. He noted that, according to his schemata for translating sentences of quantiﬁed modal logic into counterpart-theoretic sentences, some undesirable consequences appeared unavoidable: It may disturb us that the translation of 8x□∃y(x ¼ y) (everything actual necessarily exists) comes out true even if something actual lacks a counterpart in some world.4

Lewis considered alternative translation schemata he attributed to David Kaplan. They avoid the above difﬁculty but create one of their own. According to Kaplan’s suggestion, the sentence which says that something actual is possibly non-self-identical comes out true, or else everything actual has a counterpart in every world, which amounts to the necessary existence of every actual thing. Lewis reacted to this by saying, ‘Out of the frying pan, into the ﬁre’, and declared that his own original translation schemata were preferable. Later, Lewis switched his position and advocated replacement of quantiﬁed-modal-logical discourse by counterpart-theoretic discourse rather than a reduction of the former into the latter: What is the correct counterpart-theoretic interpretation of the modal formulas of the standard language of quantiﬁed modal logic?—Who cares? We can make them mean whatever we like. We are their master. We needn’t be faithful to the meanings we learned at mother’s knee—because we didn’t. If this language of boxes and diamonds proves to be a clumsy instrument for talking about matters of essence and potentiality, let it go hang. Use the resources of modal realism directly to say what it would mean for Humphrey to be essentially human, or to exist contingently.5

This shift of position lessens the burden on Lewis’s theory, which no longer carries any theoretical obligations tied to the language of quantiﬁed modal logic. The theory is to be judged solely on the basis of whether it adequately captures our ordinary modal discourse. It remains to be determined whether his move away from reduction of quantiﬁed modal logic serves Lewis’s theory well ultimately. In any case, whether via reduction of quantiﬁed modal logic or via replacement of it, counterpart-theoretic talk is supposed to elucidate ordinary modal talk conceptually. Since counterpart-theoretic talk is designed to be free of

2 3 4 5

Lycan 1979. Johnson learnt his lesson well and later published (1991). Lewis 1983c: 31. Lewis 1986: 12–13; his emphasis.

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modal idiom, Lewis’s theory, if successful as a conceptual analytic endeavor, banishes modal notions from the fundamental level of metaphysical theorizing. Actualist theories, by contrast, do not attempt to reduce quantiﬁed-modallogical talk or ordinary modal talk into non-modal talk and certainly do not attempt to replace the former with the latter, even though they are meant to be theories of possible worlds. This may be compared to the outlook adopted by most philosophers of logic concerning truth values. Gottlob Frege took truth values seriously as entities and thought of them as the referents of sentences,6 but most contemporary philosophers of logic seem to regard talk of truth values as no more than a convenient facilitator for setting up semantics. Take an elementary example: equivalence. Without truth values, one may deﬁne equivalence as follows: two sentences are equivalent if and only if either they are both true or they are both false. With truth values, one can say that two sentences are equivalent if and only if they share a truth value. This simpliﬁes the deﬁnition, albeit only slightly. The more complicated a semantic notion is, the more extensive the beneﬁt of simpliﬁcation is in deﬁning it. It also gives the deﬁnition more generality; it no longer assumes that there are only two truth values. Most defenders of actualism regard talk of possible worlds similarly. The party line of actualism is that the notion of possibility (or necessity) is primitive and there is little we can do to analyze it conceptually, and that the actualist account of possible truth as truth at a possible world, where a possible world is a maximally consistent representational object of some kind or other, is meant merely as a heuristically or pedagogically useful tool in philosophizing about modality and other important subjects. Here it is usually assumed that consistency is to be understood ultimately in terms of possibility. Some might reject this assumption (and offer a purely proof-theoretic construal of consistency, for example), but I am unaware of any concrete proposal that construes consistency as non-modal, or at least not resting ultimately on possibility, in such a way that it is ﬁt to underwrite the notion of possibility. So we shall not discuss this issue further.7 I am not entirely unsympathetic to the anti-reductionist sentiment of the actualists. At the same time, I am sympathetic to Lewis’s zeal for seeking a theoretical analysis of the notion of possibility in more basic terms. Lewis goes astray, in my view, when he refuses the methodological stance of taking the analogy of worlds with times seriously. His counterpart theory is a glaring result of this methodological decision; each ordinary object exists at different times but is bound to just one possible world. Along with the spatiotemporal-relatedness criterion for the unity of a possible world, counterpart theory is at the heart of Lewis’s proposal and one of the main reasons for its unsatisfactoriness. My proposal is to offer the theoretical identiﬁcation of possible worlds as 6

Frege 1892. See Shalkowski (1994) and Ballarin (2004, 2005) for criticisms of attempts to reduce possibility. Theodore Sider counters Shalkowski’s criticism of Lewis (Sider 2003: 196–7). 7

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metaphysical indices of the modal kind, while not offering any theoretical analysis of what it is for a metaphysical index to be of the modal kind, as opposed to the temporal kind or the spatial kind. Thus I am a soft reductionist. The notion of a possible world is not primitive but the notion of a modal index is. More precisely, the modal part of the notion of a modal index is primitive. Even though I do not offer any conceptual analysis of it, I have much to say about the notion of a modal index. Almost all of what I have to say about the notion stems from my core methodological decision to take the analogy between worlds and times (and spatial indices) as seriously as I can. The discussion in the rest of this chapter should make it clear that I am less interested in semantic reduction of modal idioms in terms of non-modal idioms than in metaphysical reduction of modal facts to facts of modal dimensions. My project is not so much to offer a theory of the meanings of ‘possible’, ‘necessary’, ‘actual’, and other modal expressions or to offer thoroughly reductive analyses of the concepts, possibility, necessity, actuality, etc., as to sketch a metaphysical picture according to which modal facts are just as real and objective as temporal (and spatial) facts. 7. 2 . SOFT REDUCTION My proposal is less reductive than Lewis’s theory but more reductive than actualism. To see the latter point clearly, let us consider temporality. What is past? What is present? What is future? The A-theory of time blatantly presupposes temporality by using the notions, past, present, and future, rather than explicating them in other terms. The B-theory with the added element now, on the other hand, explicates them in more basic terms, namely, temporal points and a linear ordering of them (the ‘earlier than’ relation), along with the special temporal point, now. What is past is what is earlier than now, what is present is what is now, and what is future is what now is earlier than. Such a version of B-theory does not reduce temporal talk completely, as it presupposes temporal points as such. But it is more reductive than the A-theory, for it reduces the temporal notions, past, present, and future, into more basic, albeit still temporal, notions. My proposal treats modality similarly. It reduces the modal notions, possibility and necessity, into a more basic notion, albeit still modal. If we conceptualize a temporal analog of actualism in a different way and compare it with my view of times as temporal indices, it will help further clarify the contrast between actualist ersatzism on possible worlds and my proposal of possible worlds as modal indices. Take the version of ersatzism according to which a possible world is a maximally consistent set of propositions. The corresponding ersatzist theory of times deﬁnes a time as a set of all and only propositions that are true at that time. Times are deﬁned as sets of propositions. In order to specify which propositions are the members of the set a given time is

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deﬁned to be, one needs to start with the time and pick those propositions which are true at it. This means that there is an element of circularity in this deﬁnition of a time. It would be a mistake to dismiss this circularity by claiming that it is no more vicious than the deﬁnition of a proposition as a set of possible worlds by philosophers such as Lewis and Stalnaker.8 It is customary to say that Lewis and Stalnaker deﬁne any given proposition as the set of all and only those possible worlds at which the proposition is true. Thus, in order to specify which possible worlds are the members of the set a given proposition is deﬁned to be, one needs to start with the proposition and pick those possible worlds at which it is true. This customary way of articulating the proposal is harmless. The crux of the proposal is simply this: all propositions are sets of possible worlds and all sets of possible worlds are propositions. This means that any particular proposition is a particular set of possible worlds and any particular set of possible worlds is a particular proposition.9 There is no circularity in this deﬁnition. The same cannot be said about the deﬁnition of times as sets of propositions, for clearly not every set of propositions is a time. Some set of propositions corresponds to no time, that is, some set of propositions is such that at no time are all and only members of the set true. So the reduction in question of times to sets of propositions involves a circular deﬁnition. At the same time, just as most modal ersatzists are unfazed by the analogous circularity in their deﬁnition of a possible world, most temporal ersatzists would be unfazed by this circularity. We should note in passing that even though both modal and temporal varieties of ersatzism contain circularity, they differ in the way a particular metaphysical index is speciﬁed. To consider any possible world, we must start propositionally. We say, ‘Consider a possible world at which P1, P2, . . . , and Pk’, where ‘Pj’ (1 j k) is a sentence expressing a proposition and {P1, P2, . . . , Pk} is presumed consistent.10 We are supposed to consider a possible world at which all those enumerated propositions are true. There are always many possible worlds at which such enumerated propositions are all true, for our human limitations inevitably prevent such propositions from forming a maximally consistent set. In order to consider any one particular possible world among many others, we need to consider a particular maximally consistent extension of the consistent set comprising those enumerated propositions. Any such extension will give us one particular possible world (or so we shall assume). In the case of temporal ersatzism, however, we may well start with a single proposition and succeed in specifying a particular time without forming any extension of the 8

Stalnaker 1984. I am ignoring propositions de se, if there are such things. They would have to be identiﬁed not with sets of possible worlds but with sets of centered possible worlds, where a centered possible world is a possible world along with a particular individual at that world (as the self ). See Lewis 1979b. 10 Here and elsewhere, we play fast and loose with the use/mention distinction to avoid tedium. I trust no serious misunderstanding will result. 9

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singleton set of that proposition that has an appropriate maximality property. Any single one of a large number of propositions will do. For example, we may say, ‘Consider the time when you turned 3 years old’. Assuming that you turned 3 years old only once, a temporal ersatzist may deﬁne that time as the set which includes the proposition that you turned 3 years old and which is appropriately maximal. The assurance that you did once turn 3 years old is enough to specify a particular time, whereas the assurance that {P1, P2, . . . , Pk} is consistent is not enough to specify a particular possible world. Unlike temporal ersatzists, I am a reductionist about times. I say that times are metaphysical indices of the temporal kind, that is, temporal indices. I am a soft reductionist, for I take the notion of a temporal index as primitive. More speciﬁcally, I take the temporal part of the notion of a temporal index as primitive. I can say that a temporal index is a point or interval on the temporal axis, but this is hardly informative for hard-reductionist purposes. I do not offer a deﬁnition of a particular time. I simply say that a particular time is a particular temporal index. So my position does not contain the kind of circularity found in temporal ersatzism. If there is any circularity in my position, it is the use of the notion of temporality in the phrase ‘temporal index’. I take the notion to be primitive. The notion is an adjectival notion, expressed by the adjective ‘temporal’, and as such is not the same as the nominal notion of a time, expressed by the noun ‘time’. I do not subscribe to the analysis of the notion of being temporal as ‘pertaining to times’. If I did, my reduction of times to temporal indices would be viciously circular. Correspondingly, my proposal about possible worlds is soft reductionist and does not contain the kind of circularity found in modal ersatzism. If there is any circularity in my proposal, it is the use of the notion of modality in the phrase ‘modal index’. As with the temporal case, I take this notion to be primitive. I do not accept the analysis of the notion of being modal as applied to metaphysical indices as ‘pertaining to possible worlds’ or ‘pertaining to possibility’, or ‘pertaining to alethic modality’. If I did, my reduction of possible worlds or possibility to modal indices would be viciously circular. I separate the notion of a possible world from the notion of a world. Among metaphysical indices, I discern three basic kinds, temporal, spatial, and modal. The modal indices are worlds. My position is that each of these three notions is primitive. The notion of possibility of a world is not primitive, but it is not deﬁned in terms of modal notions other than the notion of a world—more on this in the next section. This shields my soft reductionism from the charge of vicious circularity. Early Lewis’s hard reduction of possible worlds may be said in effect to construe them as metaphysical indices of the spatiotemporal-individual kind. According to it, possible worlds are individuals, four-dimensional maximally spatiotemporally related individuals. As I see it, some of the objections against Lewis’s theory exploit this aspect of his theory. If possible worlds are just spatiotemporal individuals, albeit maximally large ones, what is or is not the

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case at such an individual does not seem relevant to what is or is not possible. More speciﬁc objections concerning merely possible individuals, like the ones by Skyrms and by van Inwagen, which were examined in Chapter 5, also seem to be aimed at this basic aspect of Lewis’s theory. I, on the other hand, do not treat possible worlds as spatiotemporal-individual indices. Possible worlds are not individuals, so they are not spatiotemporal-individual indices. Early Lewis’s reductionist drive blinded him from recognizing the sui generis nature of possible worlds as metaphysical indices of a modal kind. 7 .3 . POSSIBILITY Worlds are metaphysical indices of the modal kind. The notion of a possible world is not primitive; it is to be deﬁned in terms of the notion of a world and other notions. The question then is what makes a world a possible world. To answer it, we need to start by noting that possibility is not a property of a world, but a relation between worlds. A world w1 is possible relative to a world w2 if and only if w1 is accessible from w2. The relation of accessibility may be regarded as primitive in a purely formal set-up, but ours is not a purely formal set-up. The most intuitive and customary way to understand accessibility is by considering so-called restricted necessities. It starts with the idea that there is one kind of necessity that is absolutely unrestricted. This kind of necessity is sometimes called ‘logical necessity’, sometimes ‘conceptual necessity’, and sometimes ‘metaphysical necessity’. These labels are sometimes thought to be coextensive, sometimes not. Whatever it is called, the absolute necessity is necessity under a universal accessibility relation; every world is accessible from every world. Every world is possible relative to every world. Being a possible world coincides with being a world. Nothing new is added to being a possible world over and above being a world. Some kinds of necessity, however, are not absolute. Assume that the laws of nature are not absolutely necessarily true, i.e. at some world the laws of nature holding at the actual world are false. Nomological necessity then provides us with an example of a kind of necessity that is not absolute. It is the necessity intended when we say that, given the way the laws of nature in fact are, it is necessarily the case that such-and-such holds. What is said to be necessary in this sense is said to be the case not at every world but at every world accessible from the actual world, where the accessibility relation is not universal but restricted; some but not all worlds are accessible from a given world. A world w1 is accessible from a world w2 in this sense if and only if all laws of nature true at w2 are true at w1. Abstracting away the reference to nature, we obtain the following general understanding of accessibility, which in turn will result in the corresponding general characterization of restricted necessity: a world w1 is accessible from a world w2 if and only if all laws of kind K true at w2 are true at w1. Vary the kind

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K, and we obtain a variety of accessibility, hence the corresponding variety of possibility. We should note four points concerning this picture. First, it is not uncommonly held that nomological necessity coincides with metaphysical necessity. If such a view is correct, and also if metaphysical necessity is unrestricted necessity, then the laws of nature hold at every world and the relevant accessibility relation is a universal relation. In using nomological necessity as an example to illustrate restricted necessity, we are obviously assuming that this is not the case. But even if our assumption is false, the general point about restricted necessity and its corresponding accessibility relation still holds nonvacuously as long as there is at least one kind K other than the nomological. Second, the possibility of a world is explicated in terms of accessibility, which in turn is explicated in terms of laws. This precludes an informative explication of the concept of a law in terms of the possibility of a world. This would be bad news if a modal way of explicating the concept of a law were the only way. By adopting the direction of explication we have just seen, we are committed to some other way of explicating the concept of a law, or else we will have to say that the concept is primitive. The literature on the concept of a law is vast and complicated, and I am afraid we should leave the topic with this very brief and sketchy note. Third, the notion of a law can be generalized away. We explicated nomological necessity by stating in effect that it is necessarily the case that, given that the laws of nature are thus-and-so, such-and-such holds. Any fact or facts of matter may take the place of the laws of nature in this statement: it is necessarily the case that, given that P, such-and-such holds. Here P may be any fact or conjunction of facts.11 This gives rise to a very large number of restricted possibilities. When we are engaged in modal discourse, our word ‘possible’ may express any one of this very large number of restricted possibilities. Which particular restricted possibility it expresses will depend on the P that is relevant to our discourse. The richer the factual content of P is, the more restricted is the accessibility, hence the easier it is for the necessity to hold, i.e. the harder it is for the contrary possibility to hold. When speaking of possibilities within human muscular power, for example, we may say correctly that it is possible for us to tear up the cardboard box used as a ballot box in a certain small local election and expose the ballots. This is so because at some world the election takes place and we tear up the ballot box and expose the ballots without exceeding the limits of human muscular power. Any such world is accessible from the actual world in the operative sense, hence any such world is a possible world in the relevant sense of ‘possible’ in the circumstances. The P here speciﬁes how much power human muscles are capable of generating (i.e. it speciﬁes the upper limits of human muscular power), and any world is accessible from the actual world if and only if P 11

Remember not to mind the use/mention conﬂation.

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holds at that world. But when our concern shifts away from what is permitted by the human muscular power and is directed speciﬁcally toward what is permitted by the election rules, the same behavior of tearing up the ballot box and exposing the ballots must be said to be not possible. This is so because at no world do we tear up the ballot box and expose the ballots without violating the election rules which are in force at the actual world. No such world is accessible from the actual world in this new operative sense, hence no such world is a possible world in the corresponding new sense of ‘possible’ in the circumstances. The P here speciﬁes the actual election rules, and any world at which they are violated is inaccessible from the actual world.12 Fourth, as we saw, the idea of restricted necessity usually goes hand in hand with the idea of unrestricted necessity, or absolute necessity. I reject the idea of absolute necessity while accepting the idea of restricted necessity. In my view, all necessities are restricted necessities. My reasons are twofold. The ﬁrst reason is that there is no need to embrace the idea of absolute necessity. We have worlds and various accessibility relations between them. Understanding various kinds of necessity and possibility in terms of them automatically gives us what is normally called absolutely unrestricted necessity, whether it is logical necessity, conceptual necessity, or metaphysical necessity. W1 is logically accessible from w2 if and only if all laws of logic true at w2 are true at w1. W1 is conceptually accessible from w2 if and only if all laws governing the concepts true at w2 are true at w1. W1 is metaphysically accessible from w2 if and only if all laws of metaphysics true at w2 are true at w1. Even if it should turn out that the laws of logic, concepts, or metaphysics do indeed permeate modal space or the entire collection of absolutely all worlds, we do not need the notion of an absolutely unrestricted necessity. Even if the logical (conceptual, or metaphysical) accessibility relation should turn out to be a universal relation, holding between any world and any world, and even if we do not know that fact, we will still have a perfectly good grasp of the notion of logical (conceptual, or metaphysical) necessity by understanding it in terms of the logical (conceptual, or metaphysical) accessibility relation between worlds. The second and more important reason is that logical, conceptual, and metaphysical necessities are not absolutely unrestricted, i.e. for some appropriate understanding of ‘every world’, the logical, conceptual, and metaphysical accessibility relations do not hold between every world and every world. The phrase ‘appropriate understanding of “every world”’ hints at my commitment to transcending the collection of all logically, conceptually, or metaphysically possible worlds. Full discussion of this matter has to wait until Chapter 8. There is one special consideration concerning metaphysical possibility which does not apply to other kinds of possibility. Our general conception of possibility 12

See Kratzer 1977. Also Barwise 1997: 495–6.

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of a kind K is such that w’ is K-accessible from w if and only if at w’ the K-laws true at w are true. This general conception applies to metaphysical possibility just as it does to any other kind of possibility, but unlike the other kinds of possibility, metaphysical possibility forces a special understanding of the truth of a law at a world. Take a typical candidate metaphysical law, say, necessity of origin: every individual metaphysically necessarily has whatever origin it has. Let us assume that it is a genuine metaphysical law. So if an individual x originates from y at w, then at every world metaphysically accessible from w, x originates from y. Consider four worlds, w1–w4. Suppose that x1 originates from y1 at w1, x2 from y2 at w2, x3 from y3 at w3, and x4 from y4 at w4. Suppose also that x1 ¼ x2, y1 ¼ y2, x3 ¼ x4, and y3 ¼ y4. Suppose further that x1 ¼ x3, hence x1 ¼ x2 ¼ x3 ¼ x4. So far, the law of necessity of origin is not violated. But now suppose in addition that y1 6¼ y3, hence y1 6¼ y4, y2 6¼ y3, and y2 6¼ y4. Then if the law of necessity of origin is to hold at w1, w2 may be metaphysically accessible from w1 but w3 and w4 should not be; the same is true when we switch ‘w1’ and ‘w2’. (So, not all laws of metaphysics true at w1—or at w2—are true at w3 or at w4.) If the law is to hold at w3, w4 may be metaphysically accessible from w3 but w1 and w2 should not be; the same is true when we switch ‘w3’ and ‘w4’. In either case, {w1, w2} and {w3, w4} may each be a pair of mutually metaphysically accessible worlds, but the result of adding a world from either pair to the other pair should not be a collection of mutually metaphysically accessible worlds. So if the law is to hold at a world from either pair, not all metaphysical laws holding at that world hold at either world from the other pair. If w1 is @ and the law holds at @, then w2 may be (metaphysically accessible from @, hence) a metaphysically possible world but w3 and w4 are (metaphysically inaccessible from @, hence) metaphysically impossible worlds. If none of w1–w4 is @, none of x1–x4 and y1– y4 is actual, and the metaphysical laws at @ hold at each of the four worlds, then each of the four worlds is metaphysically accessible from @, but w1 and w2 are metaphysically inaccessible from w3 and w4, and vice versa. Thus, metaphysical accessibility is not connected (in the logician’s sense), hence it is not an equivalence relation. This is unsurprising, given the transworld nature of the metaphysical law of necessity of origin. Other putative metaphysical laws are also transworld: for example, necessity of constitution, necessity of identity. A typical feature of a transworld law is that it is a law of some form of necessity or possibility. Necessity is not just a transworld affair but also a universal affair; necessarily P if and only if at all worlds P. The domain for the universal quantiﬁer, ‘all’, may vary. In our example, w1 and w2 belong to one such domain relevant to the law of necessity of origin, while w3 and w4 belong to another such domain. As for possibility, we should speak of the corresponding existential affair. Therefore, it is useful to think of metaphysical laws in general not as holding at one world or another individually but as holding within such a domain as a whole collectively. Within a given domain, metaphysical accessibility may then be resurrected as an equivalence relation.

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7. 4. INTENSIONAL ENTITIES: PRELIMINARIES I am a soft reductionist concerning modality, but when it comes to reductions of intensional objects, such as propositions, properties, and relations, I am a reductionist of a less soft variety. Like Lewis (and to a lesser extent Stalnaker), I count the ability to offer hard reductionist accounts of such intensional objects as a major virtue of a modal realist theory. According to Lewis, common sense regards propositions and properties in rather schematic terms, as whatever entities that fulﬁll more or less platitudinal conceptual roles, and the philosopher’s task is to provide appropriate ﬁllers of these roles. Plantinga, who objects to Lewis’s reduction of propositions and properties, does not reject this characterization of the philosophical task entirely but doubts that Lewis’s speciﬁcation of the roles common sense associates with propositions and properties are sufﬁciently rich to capture commonsensical opinions about them: Do we have only those roles Lewis speaks of, so that it is up to theory to say what ﬁlls them? Or do we also know something about the sorts of things that occupy them––e.g., that no proposition is the unit set of a donkey, or any larger sets of donkeys, or indeed any set at all?13

Plantinga’s point is that common sense is already committed to the view that, for example, propositions are not sets. This seems clearly mistaken. Common sense seems clearly not to include any opinion dealing in the concept of a set, which after all is a highly theoretical concept. The closest concept common sense has to the concept of a set is the concept of a physical aggregate, but it is obviously a different concept. The notion of a proposition is perhaps a little more familiar to common sense than that of a set, if not precisely under that label. It is the notion of what is true (or false), what is said, what is thought, or what is believed—i.e. the object, or content, of truth (or falsity), saying, thinking, and believing. This is still rather thin, leaving plenty of room for theoretical ﬂeshing out. Plantinga’s own characterization of a proposition is not quite right. He says: Propositions are claims or assertions : they attribute or predicate properties to or of objects; they represent reality or some part of it as having a certain character. A proposition is the sort of thing according to which things are or stand a certain way.14

To say that propositions are assertions is to conﬂate propositions with speech acts. One may specify a propositional content without asserting the content as true (or false, for that matter). This casts a small doubt on the reliability of Plantinga’s grasp of what is included in the commonsensical platitudes about propositions. Perhaps, by ‘assertions’ Plantinga only means ‘contents of assertions’, or ‘what is asserted’. 13

Plantinga 2003: 217.

14

Ibid. 193; his emphases.

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If so, I will withdraw my accusation that he conﬂates propositions with speech acts, but will still say that it is rather misleading to say ‘assertions’ instead of ‘what is asserted’ in a discussion concerning the nature of propositions. The rest of the quoted passage conveys an apparently less implausible idea, i.e. that propositions are representations of how things are. It may sound plausible to say that all propositions are representations.15 But we should be careful not to confuse contents of assertions with representations of reality. When we assert that such-and-such is the case, the content of our assertion is that such-and-such is the case. A representation of reality is whatever thing according to which such-and-such is the case. But a proposition is not a thing according to which such-and-such is the case. Instead it is that such-andsuch is the case. That is, a proposition is not a representation with a certain content but it is a content.16 Common sense does not appear to regard propositions, properties, and relations as forming a uniﬁed group as far as their logical properties are concerned. This is perhaps due to a relative lack of interest in serious logic by common sense. Contemporary formal logic, however, treats sentences, one-place predicates, and many-place predicates in one uniform manner. Logic treats them all as predicates, with sentences being zero-place predicates, or alternatively, it treats them all as sentences, with predicates being one- or many-place open sentences. The difference between these two alternative ways is unimportant for our purposes. What is important is the uniformity of treatment by logic. Inspired by this uniform treatment, we shall seek a uniform metaphysical treatment of propositions, properties, and relations, even though common sense does not appear to regard them as forming a uniﬁed group as far as their metaphysical properties are concerned. This latter fact is perhaps due to a relative lack of interest in serious metaphysics by common sense. Consider the following sentence schemata: (1) The proposition that P is thus-and-so. (2) The property of being Q is thus-and-so. (3) The relation of being R is thus-and-so. The following are particular instances: 15 This, of course, does not mean that it may sound plausible to say that all representations are propositions. Common sense distinguishes many representations from propositions. Realistic paintings, photographs, maps, and ﬁlms are representations of how things are but are not propositions. These examples point to the inadequacy of saying that a proposition is the sort of thing according to which things are or stand in a certain way, while intending to give a sufﬁcient condition for being a proposition. 16 One might choose to speak of a proposition as representing itself. Then one might be able to say both that a proposition is a content and that a proposition is a representation of a content. But there seems to be little point in doing so. Plantinga might be interpreted as offering two inequivalent characterizations of a proposition: as a representation of reality and as a thing according to which things are a certain way. The notion of a representation of reality might be understood in some way independent of the notion of a thing according to which things are a certain way. If so, it might turn out acceptable to say that a proposition is a representation of reality after all. I take no position on this issue.

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(4) The proposition that snow is white is true. (5) The property of being round is instantiated. (6) The relation of being a father of is asymmetric. The following sentences and their corresponding sentence schemata are stylistic variants of (5)/(2) and (6)/(3), respectively: (7) The property roundness is instantiated. (8) The relation fatherhood is asymmetric.17 Sentences of the forms (1)–(3) are canonical forms of discourse about propositions, properties, and relations. There are other slightly different forms of discourse about properties and relations, for example, (7) and (8). Yet, it remains the case that, given any predicate, using its gerundive form in the manner indicated in (2) and (3) always gives us an expression for the property or relation the predicate expresses. Let us start with (1) and its concrete instances like (4). Our goal is to sketch a metaphysical theory of propositions. To do so, we begin with the natural assumption that the subject term ‘the proposition that snow is white’ in (4) designates a proposition, and ask the following question: (*) What is the mechanism underlying the determination of the designatum of the subject term ‘the proposition that snow is white’ in (4)? Our hope is that the correct answer to this semantic question will lead us to the correct metaphysical theory of propositions. We shall approach this question ﬁrst by asking a closely related question: (#) What is the logical structure of (4)? We shall examine two popular answers to (#), rejecting both, and observe that an independently well-entrenched theory gives us a natural and plausible answer to (#). We shall then see that on that basis a certain logical apparatus which is independently motivated affords us a satisfactory answer to (*). Finally, we shall apply the result to a particularly recalcitrant kind of sentential context, namely, belief context. Only the ﬁrst half of this project is pursued in this chapter. The rest will have to wait until Chapter 9.

7.4.1. Name theory It is customary to say that ‘that’-clauses like the one in (4), namely, (9) that snow is white, 17 There is no obvious variant of (4)a` la (7) and (8). The best we can do is to have some artiﬁcial construction like ‘The proposition snow-is-white is true’. English suffers from the lack of an abstract noun, as opposed to a ‘that’-clause, to take the place of ‘snow-is-white’.

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are (proper) names of propositions. Correspondingly, though it is not as often said, strings like ‘(of ) being round’ in (5) and ‘(of ) being a father of ’ in (6) may be said to be names of properties and relations, respectively.18 If this sounds a little strained, we may rephrase (5) and (6) as (7) and (8) and speak of ‘roundness’ and ‘fatherhood’, and other similar strings with appropriate sufﬁxes, as names of properties and relations. If (9) is a name of a proposition, then (4) is analogous to (10) The planet Mars is dry. ‘Mars’ is the name of a planet,19 and (10) says nothing more or less than (11) Mars, which is a planet, is dry. Since linguistic analysis of relative clauses is not our main concern, let us stipulate for convenience that (11) has the logical structure (12) Mars is a planet & Mars is dry. This stipulation may not please linguists but pleasing them is not our aim. Likewise, let us say that if (9) is a name of a proposition, (4) says nothing more or less than (13) That snow is white, which is a proposition, is true, and that the logical structure of (13) is (14) That snow is white is a proposition & that snow is white is true. If (9) is a name of a proposition, then I am content to say that the logical structure of (4) is the logical structure of (14). The only remaining part of the logical structure of (14) to be unpacked is (the two occurrences of ) the ‘that’-clause, namely, (9). According to some theorists, all names are devoid of any semantically signiﬁcant structure. On such a view, if (9) is a name, the fact that words like ‘snow’ and ‘white’ occur in (9) as they do has no semantic signiﬁcance for the determination of the reference of (9). But it is evident that (9) should not be regarded as devoid of a semantically relevant structure, for it is evident that it contains semantically relevant parts, namely, ‘snow’, ‘is’, and ‘white’. The difference in reference between (9) and, say, (15) that grass is green 18 The fact that the word ‘of ’, unlike the word ‘that’ for propositions, usually drops out seems to be a quirk of English. I know at least one natural language in which there seems to be a perfect symmetry between propositional talk on the one hand and property and relation talk on the other in this regard. 19 Disregard ‘Mars’ as a name of a Roman god, or of anything else other than the fourth planet of the solar system.

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stems entirely from a semantic difference between (16) Snow is white and (17) Grass is green. Thus, a plausible version of the Name Theory should read the relevant structure into (9). This means that if all names are devoid of any semantically signiﬁcant structure, then there is no plausible version of the Name Theory that construes (9) as a name. Since I in fact do not think it best to construe (9) as a name, this does not disturb me. But in making the case against the Name Theory, we can do better than relying on the supposition that all names are devoid of any semantically signiﬁcant structure. The simplest, and probably the best, way to read the relevant structure into (9) within the Name Theory is to regard ‘that’ in (9) as a name-forming sentential operator. The operator view presupposes a certain well-behaved relation between a sentence and a proposition. Let us call that relation expression. Then, for any sentence S and any proposition P, the result of applying ‘that’ to S refers to P if and only if S expresses P.20 But what is expression? Without an adequate articulation of the expression relation, the theory would remain incomplete. How a sentence manages to be associated to a proposition seems as much a question in need of an answer as how a ‘that’-clause manages to stand for a proposition. One idea for an answer is to say that the sentence ‘Fa’ expresses the proposition P if and only if the property expressed by the predicate ‘F’ and the entity referred to by the term ‘a’ constitute P. This sounds plausible, until we notice two problems. First, the idea relies on the notion of expression. This is not viciously circular, for the expression relation it relies on is the one between a predicate and a property, not between a sentence and a proposition. Nonetheless, this is worrisome. If we do not have an adequate articulation of the expression relation between a predicate and a property, we are hardly better off. What property does the predicate ‘is white’ express? Notice that this is along the lines of the kind of question the Name Theory prompts when applied to sentences of the form (2). Just as it considers ‘that’ in (1) as a sentential operator, the Name Theory considers the gerund formation in (2) and (3) as a predicative operator, resulting in a name of a property or a relation, and says that, for example, ‘being white’ is a name referring to the property ‘is white’ expresses. But what property is that? Given the parity 20 See e.g. Soames 1989: 585. There four assumptions are listed, one of which says, ‘The expression dthe proposition that Pe is a directly referential singular term that refers to the proposition expressed by P. ‘Soames says of the four assumptions, ‘Indeed, I am willing to accept them.’ For a similar view differently expressed, see Salmon 1986a: 169 n. 4: ‘One should think of the “that”-operator as analogous to quotation marks, and of a “that”-term dthat Se as analogous to a quotation name, only referring to the information content of S rather than S itself.’

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between propositions and properties (and relations) as intensional objects, whatever is the right answer to this question should have the corresponding right answer for propositional expression. In fact, there is an obvious answer in this case. It is to say that the predicate ‘is white’ expresses the property of being white. This is the most straightforward correct answer. Correspondingly, the most straightforward correct answer to the question ‘What proposition does (16) express?’ is that it expresses the proposition that snow is white. Evidently this does not help the Name Theory, for we are back to the starting point, (9), the canonical notation for the proposition. Second, the relation of constitution is equally in need of articulation. A standard thing to say is that an entity e and a property p constitute a proposition P if and only if P is the result of predication of p of e. But this only prompts a further question: what is predication? The most straightforward correct answer is that the result of predicating the property of being white of snow is the proposition that snow is white, and this again unhelpfully throws us back to the starting point. Another popular thing to say is that e and p constitute P if and only if P is an ordered pair of e and p. But this way of articulating constitution is not without serious difﬁculty. There seems to be no theoretical reason to prefer the ordered pair <e, p> to a different ordered pair as the proposition constituted by e and p. But one thing cannot be identical with two things. So, it seems that neither pair is identical with the proposition. This is reminiscent of the problem Paul Benacerraf pointed out for identiﬁcation of numbers with sets: if one way to construct numbers as sets is satisfactory, many others are; no theoretically disciplined method is available for singling out exactly one way; but nothing, not even a number, can be two things; therefore, none of these ways is the correct way.21 Again, the most straightforward correct answer to the question ‘What proposition do snow and the property of being white constitute?’ is that it is the proposition that snow is white. We seem unable to shake ourselves free from the canonical notation. There is a good reason for this. We are constantly pulled back to the clause (9) because it is the canonical notation for the proposition the embedded sentence (16) expresses. Propositional expression should be articulated in terms of propositional designation by means of clauses of the form (9), not the other way around. We have one more proposal concerning the expression relation to examine. Mark Richard proposes an interesting idea. It makes propositional expression a matter of quasi-iconic representation. Let’s suppose that propositions are structured, and that the structure of a proposition is isomorphic with the structure of a sentence that expresses it, or at least with one straightforwardly determined by such, say by ‘pruning’ branches in a phrase structure tree. In fact, let’s identify propositional structures with phrase structure trees. And let’s

21 Benacerraf 1965. For an application of Benacerraf ’s problem to structured propositions, see Bealer 1993, 2004; Moore 1999; Jubien 2001.

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assume that propositions are assigned to sentences by moving ‘from the bottom up’ on their structures. We can identify the constituents of a proposition with what wind up annotating tree nodes when the assignment of content is ﬁnished. And the proposition a sentence expresses thus turns out to be the result of stripping expressions and labels like ‘NP’ and ‘VP’ from a sentence (which is itself an annotated phrase structure marker) and replacing the labels with propositional constituents.22

The structure of a sentence itself exhibits the structure of the proposition it expresses. In this sense, the sentence is a quasi-icon of the proposition. Let us say that the procedure sketched above for arriving at propositions from sentences determines a unique proposition for each sentence. The proposal then says that a sentence expresses the proposition which the above procedure determines for it. Is this a satisfactory articulation of propositional expression? I am afraid not. To begin with, we should be clear about exactly what entity the procedure determines for (16). Call the entity determined for (16) ‘Freddy’. What exactly is Freddy supposed to be? Call the annotated tree obtained from the phrase structure tree for (16) by the above procedure ‘Arb’. Is Freddy a proper part of Arb, for example, the part which annotates the top node of Arb? Or is Freddy Arb in its entirety? The correct answer is the latter. What annotates the top node of Arb is something X such that the result of a ‘functional application’23 of the annotation corresponding to ‘is white’ to the annotation corresponding to ‘snow’ gives the value of X. Freddy and Arb are identical, according to the proposal. But this seems to generate a difﬁculty. Given that (16) expresses exactly one proposition,24 the proposal assumes that (16) has exactly one annotated structured object, namely, Arb. But a tree is not the only such object. Phrase structure grammar does not assign (16) a unique structured syntactic object. There are at least two ways it may be done. One way is to assign a syntactic tree. Such a tree will be converted to Arb by the above procedure. But another equally acceptable way in phrase structure grammar is to assign (16) a linear syntactic structure, using grouping devices like brackets and parentheses. All information encoded in the tree can be encoded in it, and vice versa. Such a linear annotated syntactic structure will be converted to an equally linear annotated structure, call it ‘Lin’, by the above procedure. Lin is not Arb; one is linear, while the other is twodimensional. Of course, Lin and Arb are equivalent in some strong sense. But equivalence is not identity. Freddy, which is one, cannot be two. Which is Freddy, Arb or Lin? Neither has an edge over the other. So, it seems, Freddy is neither. This is the Benacerraf problem all over again. There is yet another problem. The proposal entails that no two sentences with different phrase structures express the same proposition. But the following two 22 Richard 1993: 211. See also Richard 1992. Richard cleverly appropriates the core idea of structuralist possible-world semanticists: see Carnap 1947; Lewis 1970a ; Cresswell 1985. 23 Richard 1993: 212. 24 Understand (16) relative to a time and perhaps also to a spatial location, if necessary.

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sentences, which have different phrase structures, seem to express exactly the same proposition: (18) Sisters are related. (19) Female siblings are related. The problem is deeper than examples like this pair indicate. The proposal entails that any two sentences from different natural languages expressing the same proposition have an identical phrase structure. There are certainly many pairs of sentences from different natural languages expressing the same proposition. Therefore, each such pair of sentences must have one identical phrase structure. Thus, the proposal leads to a rather strong form of linguistic universalism with respect to phrase structure grammar. To see how implausible such linguistic universalism is, consider the following French sentence: (20) La neige est blanche. (20) expresses the same proposition in French as (16) does in English, but its phrase structure contains extra parts which have no counterparts in the phrase structure of (16), namely, the node for the determiner ‘la’ and accompanying branches and nodes. This is but one tame example. Comparisons of languages from more distant language groups will produce more dramatic examples. This is not the end of trouble for the Name Theory. It faces a formidable difﬁculty when applied to belief sentences. But it is time to move on to the next theory. We shall return to the Name Theory and belief sentences later.

7.4.2. Demonstrative theory Suppose we say that the logical structure of (4) The proposition that snow is white is true is the same as the logical structure of (14) That snow is white is a proposition & that snow is white is true. We are agreeing with the Name Theory so far. But suppose we then say that (9) that snow is white in (4) is not a name but a demonstrative pronoun ‘that’ followed immediately by what is directly demonstrated, which in turn determines the reference of ‘that’. We now have a different theory, the Demonstrative Theory. The basic idea is that a ‘that’-clause is not a single uniﬁed string but two strings, functioning separately. The logical structure of (4) is said to be something like the following: (40 ) That [snow is white] is a proposition & that [snow is white] is true, where the two occurrences of

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(16) Snow is white in brackets are not part of the main sentence surrounding them but more like side remarks. Since obviously the two occurrences of (16) in (40 ) are artiﬁcially created from a single occurrence of (16) in (4) and the two occurrences of ‘that’ in (40 ) are meant to be coreferential, we can clean up the clutter and awkwardness of (40 ) to obtain (4d) That1 is a proposition & that1 is true: snow is white. This obviously mimics Donald Davidson’s paratactic theory of indirect discourse.25 (16) is merely exhibited in (4d) and this fact is indicated by the colon, or the brackets in the case of (40 ). The subscripts indicate the coreferentiality of the two occurrences of ‘that’. But what do they refer to? Remember David Kaplan’s lesson on demonstrative reference. Meaning does not sufﬁce; we need to bring in a context of utterance. The meaning of (4d) alone is insufﬁcient for determining what ‘that1’ in (4d) refers to. The context in which (4d) is uttered has a crucial role to play. It may provide a certain object as something demonstrated. In a standard context of utterance for (4d), the sentence following the colon is naturally expected to be the demonstrated object. This, however, does not automatically make that sentence the referent of ‘that1’, for in a standard context, charity may well prevail in such a way that the ﬁrst conjunct of (4d) is not to be falsiﬁed. Since the demonstrated object is clearly not a proposition but a sentence, it is not to be the referent of ‘that1’ in such a context. The demonstrated sentence is not itself the referent but does play a crucial role in determining the referent. Suppose I see myself portrayed in a photograph. I point to the photograph and say, ‘That is (identical with) me’. Charity demands that the demonstrative ‘that’ in my utterance be interpreted as referring not to the photograph, the demonstrated object, but to the person portrayed in the photograph. When Quine points to his fuel gauge and says, ‘That is empty’, charity demands that his ‘that’ be interpreted as referring not to the gauge, the demonstrated object, but to the fuel tank connected to the gauge. This familiar type of demonstrative reference is deferred reference.26 The referent is something to which the demonstrated object bears a certain recognizable relation. In the case of (4d), ‘that1’ refers to the proposition to which the sentence following the colon bears a certain relation. The relation may vary from context to context, just like any other contextually sensitive aspect of discourse. But in a standard context, the relation in question is that of expression; for any proposition P, ‘that1’ refers to P if and only if the sentence following the colon expresses P. Whenever a sentence is uttered in a 25 See Davison 1968. The most striking difference between Davidson’s analysis and (4d) is that the former makes ‘that1’ refer to an utterance but the latter makes it refer to a proposition. Davidson later softened his anti-proposition stance considerably. In Davidson 1991: 209, he says, ‘Since utterances, sentences and propositions are so closely related, the chances are if one choice will serve, the others can be made to serve.’ 26 After ‘deferred ostension’ in Quine 1969.

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standard context, the proposition which (the utterance of ) the sentence expresses (in that context) naturally gets associated to that utterance of the sentence. In being able to understand what it is to interpret arbitrary such utterances in a language, competent linguistic subjects are able to understand what it is to associate such a proposition to such an utterance in a standard context. Implicit knowledge of the expression relation underlies such an ability. William Lycan (1972, 1985), and Steven Boe¨r and Lycan (1986) echoing Lycan, also propose a Davidsonian analysis with something very similar to deferred reference.27 On their analysis, ‘that1’ refers to the set of all and only Snow is whites, namely, the set of all and only sentence-tokens equivalent—in a certain appropriate sense of ‘equivalent’—to the token of (16) in a given utterance of (4). Like Davidson,28 they try expressly to avoid reference to propositions in their analysis.29 Before criticizing the Demonstrative Theory, we should note three brief points. First, (4) is analyzed as two separate sentences, as (4d). Question: the truth value of which of the two sentences is to be the truth value of the analysandum? The answer is obvious: the sentence preceding the colon. Second, the fact that in English one and the same word, ‘that’, is used as a demonstrative pronoun and also as a subordinate-clause forming operator has no philosophical signiﬁcance; it is a sheer coincidence.30 To see this clearly, take (5) The property of being round is instantiated, which should be subject to the same type of analysis as (4). Its analysis on the Demonstrative Theory is (5d) That1 is a property & that1 is instantiated: being round. (5) does not contain the word ‘that’, even though (5d) contains ‘that1’. This indicates that the fact that (4) contains ‘that’ on the surface level is of little importance. Third, Stephen Schiffer gives a number of good objections against Davidson’s analysis, and Mark Richard offers a number of good objections against Boe¨r and Lycan’s analysis.31 The Demonstrative Theory, however, differs 27

They stick to Quine’s terminology ‘deferred ostension’. I doubt propositions can be ostended, so I shall continue to speak of deferred reference instead of deferred ostension so that I will not beg any important question, even though Lycan and Boe¨r and Lycan would ﬁnd my distinction pointless in this context because they think we should not speak of propositions anyway. 28 But see n. 25 above for Davidson’s softening. 29 See Lycan 1972, 1985; Boe¨r and Lycan 1986: 50–2. The dot quotes are a common-noun forming operator, due to Wilfrid Sellars. 30 Davidson’s resort to the Oxford English Dictionary on this score is misplaced in a philosophical article. Stephen Schiffer makes a mocking criticism out of this fact (1987: 125). Davidson deserves the criticism, but it should not be held against a Davidsonian theory which is not motivated by this irrelevant linguistic accident. 31 See Schiffer 1987: 122–37; Richard 1990: 87–102. See also Blackburn 1975; Arnaud 1976; McDowell 1980; Platts 1979.

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from Davidson’s original analysis, Lycan’s modiﬁed Davidsonian analysis, and Boe¨r and Lycan’s follow-up on Lycan’s analysis signiﬁcantly enough to be free from those objections. This, of course, does not mean that the Demonstrative Theory is satisfactory. The relation a photograph bears to what it portrays is different from the relation a gauge bears to what it gauges. This shows that in general the relation which mediates deferred reference may vary widely from context to context. This points to a very important difference between the Demonstrative Theory and the Name Theory. According to the operator version of the Name Theory, the relation between the sentence in the ‘that’-clause and the proposition to which the ‘that’clause refers is ﬁxed once and for all by the semantics of the operator ‘that’. The absence of such inﬂexibility helps the Demonstrative Theory perform better than the Name Theory in some important cases.32 Ironically, the very ﬂexibility which helps the Demonstrative Theory also haunts it. As a demonstrative pronoun, the word ‘that’ shifts its reference from context to context, and its reference is determined by contextually perspicuous or contextually understood parameters. Suppose I utter (4) to you. As I utter it, I hold up a carrot in front of your eyes and do everything within my power to attract your undivided attention to the carrot, and succeed. If I am uttering a sentence with a hidden demonstrative in its logical structure, as the Demonstrative Theory says, then since the carrot is the unique obvious demonstratum, the context of my utterance clearly determines the referent of that demonstrative to be the carrot, or (should deferred reference occur) some entity that bears a contextually obvious relation to the carrot. Hence my utterance will be true on the Demonstrative Theory if and only if the carrot, or (in case of deferred reference) the entity that bears the contextually obvious relation to the carrot, is a proposition and is true. This is not the right truth condition for my utterance. No matter how strongly the context may present the carrot as the demonstratum for any potential occurrence of the demonstrative ‘that’ in that context, the carrot remains utterly irrelevant to the truth condition of my utterance of (4). The Demonstrative Theory is incapable of explaining why. Getting a hint from the case of sortal variables, one might say that the demonstrative in question is a sortal demonstrative. Just as a variable may only range over a particular sort of things, a demonstrative may only refer to a particular sort of thing. The sort relevant to our discussion is proposition. Since a carrot is not a proposition, the demonstrative in question does not refer to it. There are two problems with this defense of the Demonstrative Theory. First, if I clearly, emphatically, and exclusively demonstrate a chair and say to you, ‘This man is a spy’, the most natural reaction for you is puzzlement, even if there happens to be a man perspicuously standing next to the chair. The man is the most salient candidate for the reference of my utterance of ‘this man’, but my 32

Such cases include belief sentences. See Lycan 1972, 1985; Boe¨r and Lycan 1986.

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demonstration clearly, distinctly, and uniquely singles out the chair. The least implausible thing to say in such a case is that my utterance of ‘this man’ refers to the chair. The ‘this’-part of the demonstrative phrase outweighs the ‘man’-part, as it were. The situation does not change if I say instead, ‘This is a spy’, where ‘this’ is a sortal demonstrative with the sort man associated with it. Similarly with the carrot example with a sortal demonstrative with the sort proposition associated with it. The second problem is that it is not at all obviously impossible that there should be some proposition that is more conspicuously demonstrated in a way relevant to demonstrative reference than the proposition expressed by the sentence in the ‘that’-clause. If such a context of utterance is possible, then the conspicuously demonstrated proposition will replace the carrot in the original counterexample as the spoiler, and the sortal move will buy nothing. In a desperate attempt to rescue the Demonstrative Theory, one might suggest that we radically alter the role of the colon in (4d) in such a way as to guarantee that ‘that1’ refers to the proposition expressed by the sentence occurring after the colon, no matter what else may be clearly, distinctly, and uniquely demonstrated in the context. Such a move might well do the trick. But it would be a trick. It would be no longer accurate to call the resulting theory a demonstrative theory, for ‘that1’ in (4d) would cease to function in the way in which a demonstrative pronoun is supposed to. In important respects, the resulting theory would instead be very much like the third theory, which I shall present in 7.4.4.

7.4.3. Belief sentences Consider the following instances of (1): (21) The proposition that bookmakers are sleazy is believed by Bianca. (22) The proposition that bookies are sleazy is believed by Bianca. Suppose that Bianca is a native and competent speaker of English, and in particular, she has a complete grasp of the meanings of the words ‘bookmaker’ and ‘bookie’. Let us agree that the words ‘bookmaker’ and ‘bookie’ are synonymous in English. Yet since she took a course in philosophy, Bianca has come to doubt their synonymy, without losing her grasp of their meanings. Even though she is unable to indicate how their meanings might differ, or give a counterexample to their synonymy herself, she is convinced that a sufﬁciently clever analytic philosopher would be able to articulate the difference or construct a counterexample. As a result, she thinks that the following two sentences have different truth conditions: (23) Bookmakers are sleazy. (24) Bookies are sleazy. Let us suppose that Bianca sincerely assents to (23) upon clear-headed reﬂection but sincerely dissents from (24) upon clear-headed reﬂection. The exact reason

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why she does so is unimportant. What is important is that she thinks (23) is true but (24) is not, while understanding the two sentences correctly.33 The following two-part disquotational principle has considerable intuitive plausibility: (DQ1) If a competent English speaker X who correctly and fully understands an English sentence ‘S’ sincerely assents to ‘S’ as a result of a clear-headed reﬂection, then X believes that S. (DQ2) If a competent English speaker X who correctly and fully understands an English sentence ‘S’ sincerely dissents from ‘S’ as a result of a clearheaded reﬂection, then it is not the case that X believes that S. Here the schematic letter ‘S’ should be replaced with an English sentence which lacks indexical or pronominal devices or ambiguities.34 It is understood that X assents to or dissents from ‘S’ while understanding it correctly and fully. I agree with Nathan Salmon when he says of (DQ1), at least some version of this disquotational principle is unobjectionable . . . What makes the principle self-evident is that it is a corollary of the traditional conception of belief as inward assent to a proposition. Sincere, reﬂective, outward assent (qua speech act) to a fully understood sentence is an overt manifestation of sincere, reﬂective, inward assent (qua cognitive disposition or attitude) to a fully grasped proposition.35

This is only in support of (DQ1), but I think parallel support for (DQ2) has equal force. What I have in mind in support of (DQ2) is the result of replacing ‘belief ’ and ‘assent to’ with ‘non-belief ’ and ‘dissent from’, respectively, in the quoted passage above. Salmon himself would not approve of (DQ2) at all.36 But apart from an already ﬁrmly held theoretical axe to grind, the pre-theoretical intuitive appeal of the two parts of the DQ principle seems to be equal. A theoretical position which embraces both parts of the DQ principle is certainly worth exploring.37 Given this, we say that (25) is true and (26) false: (25) Bianca believes that bookmakers are sleazy. (26) Bianca believes that bookies are sleazy. Let us assume that these colloquial sentences are mere stylistic variants of (21) and (22).38 We also assume that belief, as expressed in (25) and (26), is a dyadic 33

I owe the idea behind this example directly to Rieber 1992. See Kripke 1979. Salmon 1986a: 129–30. 36 e.g. Salmon 1986a, 1995. 37 Salmon’s position, which is shared by some other philosophers, is internally coherent and fairly well spelt out but has some intuitively implausible-sounding consequences. What I am suggesting in the text is that we explore an alternative position which may be devoid of some of the virtues of Salmon’s position but is free of its unfortunate consequences. 38 I do not mean to imply that this assumption is philosophically innocent. (21) and (22) clearly exhibit prima facie commitment to propositions, whereas (25) and (26) do not. The assumption is merely an easy way to facilitate another assumption, the one that follows in the text immediately, 34 35

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relation between a believer and a proposition. The surface structure and apparent logical behavior of belief sentences strongly indicate the truth of this assumption.39 So, if we can avoid violating this assumption, we should. It is hard to see how the Name Theory by itself can allow us to maintain these two assumptions. The logical structures of (21)/(25) and (22)/(26) according to (the operator version of ) the Name Theory are as follows: (21n) That-(bookmakers are sleazy) is a proposition & Bianca believes that-(bookmakers are sleazy). (22n) That-(bookies are sleazy) is a proposition & Bianca believes that(bookies are sleazy). If the names ‘that-(bookmakers are sleazy)’ and ‘that-(bookies are sleazy)’ refer to the same proposition, then, given the assumption that belief is a dyadic relation between a believer and a proposition, (21n) and (22n) have the same truth value. But this contradicts the assumption that (25) is true but (26) is not. Yet there is nothing in the resources of the Name Theory to block the coreferentiality of the two names. At best, the Name Theory needs substantial supplementation in order to help us maintain the two assumptions in question. Does the Demonstrative Theory fare better? It is unclear. The logical structures of (21)/(25) and (22)/(26) according to the Demonstrative Theory are as follows: (21d) That1 is a proposition & Bianca believes that1: bookmakers are sleazy. (22d) That2 is a proposition & Bianca believes that2: bookies are sleazy. In a standard context, ‘that1’ in (21d) refers to the proposition expressed by the sentence following the colon, namely, (23), and ‘that1’ in (22d) refers to the proposition expressed by the sentence following the colon, namely, (24). This leads to the same difﬁculty as before. But this just shows that the context, C1, in which (25) is true and (26) false is not standard; in C1 the relation between (23) and the proposition referred to by ‘that1’ in (21d) is not expression, or the namely, the assumption that belief is a dyadic relation between a believer and a proposition. The underlying idea is obviously a general one which encompasses sentences with other verbs. This might appear to make the idea problematic. For example, take ‘That snow is white is remembered by Bianca’ and ‘The proposition that snow is white is remembered by Bianca’, or their active-voice versions, ‘Bianca remembers that snow is white’ and ‘Bianca remembers the proposition that snow is white’. In either pair, the two sentences do not seem equivalent (share the same truth condition). If they are not equivalent, the assumption in question should be rejected. Another pair of sentences of the same kind is ‘Bianca fears that snow is white’ and ‘Bianca fears the proposition that snow is white’, and there are many other pairs like these two. Michael McKinsey (1999) takes this to show that belief is not a dyadic relation between a believer and a proposition. Kent Bach (1997) argues in a similar way. Jeffrey C. King (2002) meticulously and successfully defends the dyadic-relation view of belief (remembering, fearing, etc.) from such objections. 39 See e.g. Richard 1983: 425–52; Salmon 1995: s. IV.

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relation between (24) and the proposition referred to by ‘that2’ in (22d) is not expression. If the Demonstrative Theorist stops here, the upholding of the two assumptions in question will be superﬁcial. To give substance to the upholding, a satisfactory answer needs to be given to the question ‘What relation holds between the sentences and the propositions in C1?’ It is unclear how the answer should go. One might say that it is the relation R such that R(x, y) if and only if Bianca takes x to express y.40 Since Bianca is a competent linguistic subject, she understands what it is to interpret an utterance of a sentence in a standard context. So, she has implicit knowledge of the expression relation. Thus the relation R is well deﬁned. In addition, Bianca fully understands (23) and (24). So, there is a particular proposition P1 such that Bianca takes (23) to express P1, and a particular proposition P2 such that Bianca takes (24) to express P2. Therefore, one might say, in C1 ‘that1’ in (21d) refers to P1 and ‘that2’ in (22d) refers to P2. Now, Bianca’s full competence in English suggests the identity of P1 and P2. But this in conjunction with the two assumptions in question leads to a contradiction, as before. If Demonstrative Theorists wish to maintain that Bianca’s full competence in English is compatible with the distinctness of P1 and P2, then they need to spell out how such compatibility is to be attained in sufﬁcient detail. A major part of such an endeavor will be to say exactly what propositions P1 and P2 are. Thus it seems that, like the Name Theory, the Demonstrative Theory also needs substantial outside help.

7.4.4. Russellian description theory So far, we have followed the customary view of ‘that’-clauses that they are, or contain, referring terms, either names or demonstrative pronouns. It is time to part with this view and explore an alternative. If we take an innocent look at the sentence (4) The proposition that snow is white is true, we immediately notice that its subject term contains the determiner ‘the’; the term is a deﬁnite description. And we already have a well-entrenched theory of deﬁnite descriptions, namely, Bertrand Russell’s theory.41 Why not apply it to (4)? This is the most straightforward approach to (4) and, I claim, the most promising. The question (#) is answered quite differently on this approach.

40 For other belief sentences, R may be different. If e.g. the believer does not understand English (the language of the belief sentence), it may be something like the following: R(x, y) if and only if for some sentence S in the belief subject’s language which translates x, the subject takes S to express y. It is perfectly legitimate to let R shift like this from context to context, given the context sensitivity of demonstrative reference. 41 Russell 1905.

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On Russell’s theory of descriptions, ‘the’-phrases are not referring terms and (4) is not a singular statement about a particular proposition. Instead, (4) has a logical structure of the following gross form: (400 ) (∃!x)Ax & (x)(Ax Fx). What is the internal structure of the predicate ‘A’?42 Whatever goes into ‘A’ must correspond to the sub-string in (4), ‘proposition that snow is white’. One thing that is immediately evident is that ‘Ax’ must be a conjunction one conjunct of which means ‘x is a proposition’. So, let us say that ‘Ax’ has the form ‘Ox & Bx’, where ‘Ox’ means ‘x is a proposition’. The important question then is: what does ‘Bx’ mean? Notice that the answer will be easy for sentences like the following: (27) The proposition which ‘Snow is white’ expresses in English is true. (28) The proposition which Jack stated is true. The answer for (27) will be that ‘Bx’ means ‘“Snow is white” expresses x in English’, and the answer for (28) will be that ‘Bx’ means ‘Jack stated x’. (4) is importantly different from (27) and (28). Unlike them, (4) does not lay down a condition for picking out a unique denotation of the description in terms of a relatively straightforward relation, such as expression or stating, and a relatively straightforward object or objects, such as a sentence and a language, or a person. Instead, (4) uses a ‘that’-clause. To ﬁgure out ‘Bx’ for (4) is to ﬁgure out the role of the sentence embedded in the ‘that’-clause, namely, (16) Snow is white. That is, our question (#) is now split: (#1) What is the syntactic role of (16) in the logical structure of (4)? (#2) What is the semantic role of (16) in the determination of the denotation of the ‘the’-phrase in (4)? The answer to (#2) is rather obvious. Whatever else might be going on in the analysis, it should make the ‘the’-phrase in (4) and the proposition expressed by (16) be related to each other in such a way that the former denotes the latter. (Remember the lesson of the carrot example against the Demonstrative Theory.) An easy way to do this would be to make ‘Bx’ say in effect that (16) expresses x, but such a move would involve mentioning of (16), an undesirable linguistic ascent.43 We need some other way to implement this answer to (#2). How can we

42 (400 ) is a form of the logical structure of (4). This means, in particular, that I am not assuming that ‘A’ is an atomic predicate. Otherwise, the following discussion in the text would be unintelligible. 43 Proposals of linguistic ascent have been made by, among others, Carnap 1947: §§ 13–15; Cargile 1972; Bach 1987; Richard 1990. For the undesirability of such linguistic ascent, see Church 1950, 1954; Taschek 1990; Soames 1994: 264–70; Salmon 2001.

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answer (#1) in such a way as to accomplish the desired result without linguistic ascent? Four ways come to mind. The ﬁrst way analyzes ‘Bx’ as (29) x ¼ that-(snow is white), where ‘that-( )’ is a sentential operator, yielding a name of the proposition the sentence expresses (in the language understood from the context). The second way analyzes ‘Bx’ as (30) x ¼ that [snow is white], where ‘that’ is meant to refer to the proposition expressed by the sentence in the brackets (in the language understood from the context). Evidently, these two analyses mimic the Name Theory and the Demonstrative Theory, respectively. Only the fact that the Russellian Theory analyzes (4) as a conjunction of a unique existential sentence and a universal sentence distinguishes them from the two previously rejected theories. A moment’s reﬂection will quickly show, however, that these analyses inherit the difﬁculties of the two rejected theories. We shall therefore dismiss them as unsatisfactory. The third analysis of ‘Bx’ is radically different from the ﬁrst two; it does not smuggle any referring term back into ‘Bx’. It is supported by the conception of propositions as primary objects of thought, and claims that a sentence expresses a proposition by laying out the content that is thought when the proposition is thought. Thus, it analyzes ‘Bx’ as (31) x is thought if and only if it is thought that snow is white.44 This avoids linguistic ascent and is free from the difﬁculties plaguing the ﬁrst two analyses. But it is obviously unsatisfactory. The very object of analysis, the ‘that’clause, reappears in (31), and there is no way to eliminate it within the object-ofthought conception of propositions. We are thus left with the fourth analysis, which is supported by the conception of propositions as primary bearers of truth values. The basic idea is that a sentence expresses a proposition by spelling out its truth condition. Thus, it analyzes ‘Bx’ as (32) x is true if and only if snow is white. Fully spelled out, (4) receives the following analysis on this truth-bearer conception of propositions: (4t) (∃!x)(x is a proposition & (x is true if and only if snow is white)) & (x) ((x is a proposition & (x is true if and only if snow is white)) x is true). 44 Or, to make thinking explicitly relational, (y)(y thinks x if and only if y thinks that snow is white).

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If we read ‘if and only if ’ as material equivalence, (4t) is false; for obviously, under that reading of ‘if and only if ’, there are inﬁnitely many propositions that are true if and only if snow is white, for example, the proposition that grass is green. Since we want (4) true—or at least do not want (4) false simply because no unique proposition is such that as a matter of material equivalence it is true if and only if snow is white—we need a reading of ‘if and only if ’ stronger than material equivalence. Such a reading clearly has to be at least as strong as metaphysically necessary equivalence. But is it strong enough? Evidently not. Inﬁnitely many propositions are still such that they are true if and only if snow is white, under this reading of ‘if and only if ’: for example, the proposition that snow is white and 1þ1 ¼ 2.

7.4.5. A modal leap Is there any kind of necessity such that if we read ‘if and only if ’ in accordance with that kind of necessity, then there is exactly one proposition x such that x is true if and only if snow is white? How about conceptual necessity? Could two different propositions be such that they are true if and only if snow is white, where ‘if and only if ’ is read as expressing conceptually necessary equivalence? It appears not. For example, it is not the case that as a matter of conceptual necessity, the proposition that snow is white and 1þ1 ¼ 2 is true if and only if snow is white. A mere conception of the proposition is insufﬁcient for concluding that the proposition is true if snow is white; the metaphysical necessity of the proposition that 1þ1 ¼ 2 does not help here.45 It appears that conceptually necessary equivalence is sufﬁciently strong. Indeed, it appears to have exactly the right strength. But this sounds too good to be true. We need to be careful. What does it mean to say that a proposition x is true if and only if snow is white, under this reading of ‘if and only if ’? What else could it mean but that our conception of x is precisely such that in all conceivable circumstances under that conception, either x is true and snow is white or x is false and snow is not white? What conception of x is that? The answer, of course, is that it is the conception of x as the proposition that snow is white. We observed before that the clause (9) that snow is white is a canonical notation for the proposition in question. What makes it canonical is the very fact that we conceive of this proposition primarily as the proposition that snow is white. This prompts caution. We should be cautious not to understand ‘if and only if ’ in (4t) under the current reading in terms of the very 45 I choose the proposition that 1+1 = 2 because it is an obvious choice for metaphysical necessity. But if you think it is also conceptually necessary, simply shift to a proposition which is metaphysically necessary but not conceptually necessary. Saul Kripke has convincingly argued for the existence of such propositions in Kripke 1980: 253–355.

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conception of x which directly veriﬁes the equivalence. In other words, we should not understand (4t) as a disguised form of the following: (4c) (∃!x)(x is the proposition that snow is white) & (x)(x is the proposition that snow is white x is true). This obviously throws (4) back into (4t). The deﬁnite description is not eliminated. Little is accomplished. What we need is a non-circular way to unpack ‘x is true if and only if snow is white’ under a sufﬁciently strong but not circularitythreatening reading of ‘if and only if ’, i.e. a way which does not presuppose the conception of x as the proposition that snow is white.46 One might suspect that the project is hopeless, for any kind of necessity ﬁt for the task would be ultimately understandable only in terms of the locution ‘x is the proposition that snow is white’ and therefore would not avoid circularity. I am not entirely unsympathetic. However, I think it is premature to abandon hope. I believe that there is one promising kind of necessary equivalence which is sufﬁciently strong and yet understandable without giving rise to vicious circularity. Further discussion of this matter has to wait until Chapter 9. 46 Notice in this connection that ‘x is true if and only if snow is white’ should not be read as ‘x is true if and only if the proposition that snow is white is true’ (or ‘x is true if and only if the proposition that snow is white holds’ or ‘x is true if and only if the proposition that snow is white is the case’, etc.). Obviously, any such reading would be equally unhelpful.

8 Impossibility 8 . 1 . IMPOSSIBLE WORLDS Worlds are metaphysical indices of the modal kind. All possible worlds are worlds but not all worlds are possible worlds. Some worlds are not possible worlds, that is, they are impossible worlds. An impossible world is a world at which an impossibility obtains. Once we take note of the fact that possibility comes in many varieties, we realize that impossibility must also come in the corresponding varieties and that we can informatively speak of impossible worlds in many different non-trivial ways. Only when we clearly recapitulate the systematic way in which varieties of possibility arise, will we see clearly that impossibility is but a natural by-product of possibility.1 To make full sense of this, we need to remind ourselves of the fact, discussed in 7.3, that possibility is relative to what is sometimes known as the ‘available information’.2 An impossible world is a world at which a proposition that is impossible to be true is true. Some impossible worlds are worlds at which a logical impossibility, for example, a proposition expressed by a sentence of the form ‘P and not-P’, is true. These are logically impossible worlds. Some impossible worlds are worlds at which a metaphysical impossibility, for example, the de re proposition concerning this table—which is actually made of wood—that it is made of ice, is true.3 These are metaphysically impossible worlds. There are other kinds of impossibility, each corresponding to a kind of possibility, and they give rise to their own distinct kinds of impossible worlds. A publicly known atheist cannot win presidency in the United States. Given the overwhelming majority sentiment about the importance of religion in the United States, it is impossible for a publicly known atheist to win presidency. On the other hand, a publicly known atheist can win presidency in the United States. Given the laws pertaining to the presidential election in the United States, which do not discriminate against atheism, it is possible for a known atheist to win presidency. There is no conﬂict between these two trains of thought, even though the ﬁrst 1 William Lycan thinks that the way in which varieties of possibility arise is not systematic at all. See Lycan 1994: 171–8. Whether the way is systematic or not does not affect our discussion of impossibility. 2 Barwise 1997: 495–6. 3 We are assuming the Kripkean thesis of the metaphysical necessity of constitution.

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appears to deny the very possibility the second afﬁrms. Their compatibility is due to the relativity of possibility. An election to presidency of a publicly known atheist is impossible relative to the prevailing majority sentiment about religion but possible relative to the laws pertaining to the election. We regiment this relativity by means of the accessibility relation between worlds, as we saw in Chapter 7. ‘Possibly a publicly known atheist wins presidency in the US’ is true at @ if and only if ‘A publicly known atheist wins presidency in the US’ is true at some world w accessible from @. If the accessibility relation is deﬁned so as to make w accessible from @ if and only if the prevailing religious sentiment of the US population at w is the same as that at @ (and the sentiment of the US population plays the same role at w in determining the election results as it does at @), then the sentence asserting the possibility is false at @. If the accessibility relation is deﬁned so as to make w accessible from @ if and only if the US laws pertaining to the presidential election at w are the same as those at @, then the sentence asserting the possibility is true at @. We may say that legally it is possible for a publicly known atheist to win presidency but popular-religioussentiment-wise it is not. Examples of other varieties of possibility abound, as we noted before. Generally, ‘It is K-possible that P’ is true at w1 if and only if for some w2, all K-relevant facts (particular or general) that obtain at w1 obtain at w2 and ‘P’ is true at w2. Although K-relevant facts may be any facts at all, the familiar K-relevant facts are laws of one kind or another. If the K-relevant facts are laws of nature, the K-possibility is nomological possibility. If the K-relevant facts are laws of mathematics, the K-possibility is mathematical possibility. If the K-relevant facts are laws of logic, the K-possibility is logical possibility. And so on. In each case, those worlds which bear the accessibility relation in question to @ are K-possible worlds and those which do not are K-impossible worlds. When philosophers discuss impossible worlds, they usually do not have in mind K-impossible worlds where the K-relevant facts are of a highly restricted kind. When philosophers accept possible worlds but refuse impossible worlds while discussing modal metaphysics, they usually do not intend to refuse, say, legally impossible worlds, for example, those worlds at which the laws pertaining to the US presidential election fail to hold. At the same time, they usually do not have in mind overly comprehensive K-possibility, such as logical or conceptual possibility. Here is an example from the writings of Brie Gertler: While ‘water ¼ H2O’ is a necessary a posteriori, ‘metaphysical’ truth, it is not a conceptual truth, since ‘water ¼ XYZ’ is conceivable. The epistemic difference between conceptual and metaphysical possibility derives from the fact that metaphysical possibilities depend on actual world facts, while conceptual possibilities do not. But metaphysical possibility constrains every possible world.4

Here, Gertler contrasts metaphysical possibility with conceptual possibility and observes in effect that a world is a possible world only if it is metaphysically 4

Gertler 2002: s. vi.

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possible. ‘Water ¼ XYZ’ is conceptually possible (i.e. the concepts water, identity, and XYZ alone do not guarantee the falsity of ‘Water ¼ XYZ’) but not metaphysically possible, so a world at which water is XYZ is not a possible world. Conceptual possibility outruns metaphysical possibility, hence it includes impossible worlds.5 In this regard, conceptual possibility is like logical possibility. As long as ‘bachelor’ and ‘married’ are taken as atomic predicates, the sentence ‘Some bachelor is married’ is logically possible to be true but it is not metaphysically possible to be true. It is metaphysical possibility that is in question when philosophers discuss possible worlds without speciﬁc restricting phrase (‘K’) and also when they discuss the theoretical respectability of impossible worlds. This is as it should be, but at the same time, I think we will do well to remember that conceptual and logical possibilities are no less legitimate notions of possibility. Epistemic and doxastic possibilities are also equally legitimate notions of possibility which outstrip metaphysical possibility. In this spirit, I object to Gertler’s (and many other philosophers’) unqualiﬁed use of the word ‘possible’. If we mean to speak of metaphysically possible worlds, we should say ‘metaphysically possible worlds’, not just ‘possible worlds’. Likewise for any other kind of possibility. There is no such thing as the bare possibility of a world; the possibility of a world is always K-possibility for some K.6 The following claims are also plausible: (P1) All worlds are possible in some sense, i.e. K-possible for some K. (P2) For any K, some worlds are K-impossible. (P3) For any K, there is another kind of possibility, K’, such that some worlds are K-impossible but K’-possible. (P1) says that all worlds are possible worlds without saying that they are possible worlds in one uniﬁed sense of ‘possible’. (P2) says that any sense of ‘possible’ is accompanied by some world that is not possible in that sense; impossibility is ubiquitous. (P3) says that any sense of ‘possible’ is superseded by a wider sense of ‘possible’. (P1)–(P3) are not independent of one another: for example, (P3) entails (P2). There may be other claims which should be added to this list.

5

Gertler follows the customary two-dimensionalist talk and says that ‘metaphysical possibilities depend on actual world facts, while conceptual possibilities do not’. This is a false distinction. If we take care to be cautious in observing the use/mention distinction (for a change), we will see that the dependency on actual world facts does not distinguish between metaphysical and conceptual possibilities. Likewise with the English sentence ‘Water is XYZ’. Whether the proposition this sentence in fact expresses, given the actual world facts, is conceptually possible or not, again, does not depend on actual world facts. One source of confusion is that conceptual possibility, unlike metaphysical possibility, is more readily susceptible to metalinguistic understanding. It is easy to understand the conceptual possibility at issue as an attribute of the sentence ‘Water is XYZ’ rather than as an attribute of the proposition it expresses. For the most recent sustained critique of twodimensionalism, see Soames 2004. 6 It might be said that in some deep sense, for some K, it is K-possible that some world is a barepossible world. We are not ready to discuss this issue.

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In motivating his ontology of possible worlds, David Lewis originally started with the idea of a way things could be, identifying a possible world with such a way. But this presupposes possibility (‘could’), so it cannot be taken as a serious deﬁnition of the concept of a possible world.7 I suggest that we start with the idea of a way for things to be, and postulate worlds as modal indices at which things are various ways, rather than identifying worlds with these ways themselves. We should then say that for each type of K-relevant facts, some of these worlds are K-possible and the others are K-impossible. For each K, K-impossible worlds should be conceptually as uncontroversial as K-possible worlds. Unfortunately, impossible worlds are controversial when understood in terms of sufﬁciently strong K-relevant facts, such as the laws of mathematics, metaphysics, or logic. Let us say that Humphrey’s being a poached egg is metaphysically impossible. What are we considering when we consider Humphrey as a poached egg (in saying that it is metaphysically impossible)? It might be tempting simply to retrace our discussion of transworld identity: Consider Mt Everest as it actually is. At @, Everest spreads out over Earth’s crust. To what extent it spreads is a vague matter. As we gradually move away from the peak of Everest, it gradually becomes less plausible to say that we are on Everest. When we reach Australia, it is utterly implausible to say that we are on Everest, even though Australia is geographically continuous with Everest. The implausibility will remain no matter what path on Earth’s crust we take from the peak of Everest to Australia. Analogously, any chain (under similarity) of metaphysically possible worlds connecting Humphrey’s @-stage and the stage of a poached egg at a remote metaphysically possible world is too ‘long’ for the two world-stages to belong to the same modal worm under a reasonably restrictive sortal (say ‘person’ or ‘animate object’) under which Humphrey’s @-stage falls, and this means that at no metaphysically possible world is Humphrey’s world-stage a poached egg. But clearly this will not do. It does not allow any place for Humphrey as a poached egg. There is no room in this picture of modal space for the content of the thought that Humphrey is a poached egg, for at no world in this picture is it the case that Humphrey is a poached egg. When we entertain the thought that Humphrey is a poached egg, we are considering a world at which Humphrey is a poached egg. But since it is metaphysically impossible (we are assuming) that Humphrey is a poached egg, we will not have such a world as long as we conﬁne our attention to metaphysically possible worlds. It does not help to say that when 7

Stalnaker accuses Lewis of conﬂating ways, which are abstract objects if they are objects at all, with Lewisian possible worlds, which are concrete objects. Worlds in my sense are certainly not concrete objects but they are not abstract objects either, any more than moments of time are abstract objects. I take moments of time to be real but I am non-committal about whether they are non-concrete objects of some kind. If they are, I will be happy to accept that worlds in my sense are also non-concrete objects of some kind. If not, moments of time are real but not objects, and I will say the same about worlds. Underlying my realism is the notion of reality. I take worlds to be as real as moments or periods of time. I assume that moments and periods of time are real, but I do not assume that they are objects.

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we consider that Humphrey is a poached egg, what we are considering is the absence of a metaphysically possible world at which Humphrey has a poachedegg stage. If we say this, then we should also say that when we consider that Humphrey is sizzling bacon, we are considering the absence of a metaphysically possible world at which Humphrey has a sizzling-bacon stage. But even though the two absences are the same in the sense that the same totality of metaphysically possible worlds grounds them both equally, they are different in the sense that one is the absence involving Humphrey’s being a poached egg and the other is the absence involving Humphrey’s being sizzling bacon. Since the objects (contents) of consideration are correspondingly different, we need to go beyond the totality of metaphysically possible worlds. The difference is analogous to the difference between looking for Pierre in the cafe and looking for Wellington in the cafe; it is the same cafe but the two absent men are different. At some world, Humphrey has a stage which is a poached egg. When we consider that Humphrey is a poached egg (and judge it to be metaphysically impossible), we are considering such a world (and judging it to be a metaphysically impossible world). When we consider that Humphrey is sizzling bacon, we are considering a world at which Humphrey has a stage which is sizzling bacon. Not all worlds at which Humphrey has a poached-egg stage are worlds at which he has a sizzlingbacon stage. All these worlds are metaphysically impossible worlds. Some metaphysically impossible worlds are logically impossible worlds, while others are not. At every logically impossible world, at least one actual logical truth is false; that is what makes it a logically impossible world. Among logically impossible worlds, some are closed under the classical logical rules of inference, while others are not. The most familiar logically impossible world is the one which is closed under all classical logical inference rules and therefore at which all propositions are true. But it is only one of many logically impossible worlds. Some other logically impossible worlds are closed under some non-classical rules of inference, while others are not closed under any inference rules at our disposal. Logically impossible worlds of this last kind are such that we cannot rely on any logical inference rules to ﬁnd out what propositions are true at them. In this sense they are logically inscrutable worlds. Lewis’s ontology includes what he calls ‘impossible objects’, which are transworld mereological sums. Lewis’s acceptance of the principle of unrestricted mereological summation (that for any objects x and y, the mereological sum of x and y is an object) commits him to such objects. Lewis calls them ‘impossible objects’ on the grounds that not all parts of such an object exist at one common metaphysically possible world. Every part of them exists at a metaphysically possible world, i.e. no part of them goes beyond the totality of metaphysically possible worlds, but this is not sufﬁcient for Lewis to call them ‘metaphysically possible objects’. According to our use of the phrase ‘metaphysically possible object’, however, the fact that these objects have parts at metaphysically possible worlds is sufﬁcient to make them metaphysically possible objects. Here is a spatial analogy. The Four Corners is the geographical point in the United States where the

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states of Arizona, New Mexico, Utah, and Colorado meet. If you lie ﬂat spreadeagled at the Four Corners in such a way that each of the four states has some part of your body in it, you will be in each of the four states simultaneously but not entirely in one state. You will be entirely in the United States. Think of the United States as metaphysical space (or Lewis’s logical space) and each state as a metaphysically possible world. Being a metaphysically possible object in Lewis’s sense is analogous to being entirely within one state, so that the spread-eagled person over the Four Corners is analogous to a metaphysically impossible object in Lewis’s sense. In our sense, such a person is analogous to being perfectly metaphysically possible, for she has parts in some states. Being a metaphysically possible object for Lewis is like being entirely in one state, but it is a mistake to think that for us, being a metaphysically possible object is like being entirely in the United States. Humphrey is a poached egg at a metaphysically impossible world. So he has a modal stage at a metaphysically impossible world. So not all of his modal parts are at metaphysically possible worlds. But this does not make him a metaphysically impossible object. His having modal parts at some metaphysically possible worlds is sufﬁcient for his being a metaphysically possible object. Another analogy is temporal. You and I are temporal objects, not because all of our parts exist at one time but because our parts exist at some time or other. The analogy is not perfect, however. I shall not claim that some of our parts exist at some temporal indices that are not metaphysically temporal, whatever ‘metaphysically temporal’ might mean. Temporal indices are more structured than modal indices in being arranged in a natural linear order but are less structured than modal indices in not being subject to a temporal analog of the possible/ impossible distinction. Due to this latter feature, I doubt that we could make sense of what I have just called ‘not metaphysically temporal’ temporal indices. In Chapter 5, I speculated that we may need modal tenses other than the actuality tense and the mere-possibility tense. In view of the discussion above, it is clear that by ‘the mere-possibility tense’ I meant ‘the mere-metaphysical-possibility tense’. It is then quite natural to suggest that we need a third modal tense, the metaphysicalimpossibility tense. Using the subscript ‘i’, we may say that at some metaphysically impossible worlds, water isi XYZ, and at others, Humphrey isi a poached egg. Some might ask why it is metaphysical impossibility, and not any other K-possibility, that deserves its own special modal tense. They might in fact complain that it is not clear that by ‘the mere-possibility tense’ we meant ‘the mere-metaphysical-possibility tense’ rather than ‘the mere-K-possibility tense’ for some other K after all. To this I say that even though in principle we may introduce a different mere-possibility tense corresponding to K-possibility for each K, mere-metaphysical-possibility particularly deserves its own modal tense because of its comprehensiveness. K-possibilities for most other Ks are parochial. Legal possibility is conﬁned to the society governed by the particular laws in question. Doxastic possibility is speciﬁc to the believer in question. Human possibility does not cover non-human life forms.

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Physical possibility leaves out non-physical possibilia and worlds at which different physical laws obtain. Mathematical possibility covers only the mathematical. Even logical possibility is constrained by the language in which modal matters are expressed. ‘Bianca’s older sister is not older than Bianca’ is not logically possible but its translation into a language in which the best translation of ‘older sister’ is a simple, primitive word, L, so that the translation is in effect ‘Bianca’s L is not older than Bianca’, is logically possible.8 Metaphysical possibility is free from all these constraints and limitations. There is a deep sense, not easy to articulate, in which metaphysical possibility demarcates what is objectively and universally important in metaphysics. As we decided in Chapter 5, for the sake of avoiding a potentially annoying proliferation of subscripts, we shall continue to suppress the modal tenses, including ‘i’, unless absolutely necessary. 8 .2 . RUSSELL–QUINE–LEWIS ARGUMENT Russell defends what he calls the ‘robust sense of reality’ against Meinong’s theory of objects, which countenances a golden mountain and a round square. Russell charges that, since everything square is such that it is not round, Meinong is trapped in the contradiction that something (a round square) is round and is not round.9 Quine follows Russell’s footsteps in endorsing an argument against merely possible objects when he says that (i) if we accept merely possible objects like Pegasus, we must accept impossible objects like the round square cupola on Berkeley College, (ii) if we accept the round square cupola on Berkeley College, we must assert a contradiction, hence (iii) we should not accept merely possible objects.10 Lewis, who sharply disagrees with Russell and Quine on possible objects, seizes the crux of the Russell–Quine argument against impossible objects and uses it to argue against logically impossible worlds.11 When appropriately regimented and supplemented, it goes something like the following. Suppose, for reductio, that (1) Some world w is a logically impossible world. Then,

8 I am assuming that matters of logical possibility and impossibility pertain primarily to sentences. This goes against the overall grain of our discussion, but I make the assumption here and elsewhere in an attempt to make the clearest sense of logical possibility and impossibility. If we must insist on speaking of propositions as opposed to sentences (where we do not understand propositions as structured objects a` la sentences), then we might decide to refrain from discussing logical possibility and impossibility altogether. But fortunately we will be able to capture the difference between being an older sister and being an L (cf. being a vixen and being a female fox) without assuming linguistic ascent; see Ch. 9. 9 Russell 1905. 10 Quine 1963: 4–5. 11 Lewis 1986: 7 n. 3.

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(2) There is a logical contradiction that is true at w. Let such a contradiction be schematically represented as ‘P and not-P’. That is, (3) P and not-P, at w. So, (4) P at w, and not-P at w. But, (5) If not-P at w, then it is not the case that P at w. So, (6) P at w, and it is not the case that P at w. So, (7) At the actual world the following is the case: P at w, and it is not the case that P at w. So, (8) The actual world is a world at which a logical contradiction is true. But, (9) The actual world is not a world at which a logical contradiction is true. (8) and (9) contradict. Therefore, (10) No world is a logically impossible world. I added the steps from (6) through (9), involving the actual world, which are needed for validity and which seem to me to be faithful to the spirit of Russell’s original argument and also implicit in Lewis’s argument. No actualist accepts merely logically possible objects or logically impossible objects but some actualists accept logically impossible worlds. One such actualist is Lycan. He explicitly considers Lewis’s argument and rejects it by rejecting, in effect, the premise (5).12 Lycan says that to assert (5) is simply to beg the question. I am sympathetic to Lycan.13 I also think that 12 Lycan 1994: 40. See Lycan and Shapiro 1986 for a formalized actualist theory with impossible worlds. 13 However, Lycan’s rejection of (5) goes against the analogy between logically impossible worlds and times; cf. the penultimate paragraph in the previous section. From ‘Jane was not a student at t’ we can have ‘It is not the case that Jane was a student at t’, whereas Lycan would forbid us to move from ‘Jane isi not a student at w’ to ‘It isa not the case that Jane isi a student at w’, where w is a logically impossible world. It is interesting to remember that Lewis is more explicitly hostile to the analogy between worlds and times than Lycan, to say the least.

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the step from (3) to (4) is equally question-begging. We should not expect all logically impossible worlds to behave in accordance with all laws of logic. At a logically impossible world, a conjunction might be true without both conjuncts being true. Quine might object by saying that when we use the word ‘conjunction’ this way, we are changing the subject matter. But we are not. We know logic and when we say, ‘Consider a world at which a conjunction is true without the truth of both conjuncts’, we sincerely, clearly, and distinctly intend to speak of conjunction. That is why we say that such a world is a logically impossible world. Some reject (9), that is, some accept that a logical contradiction is true at the actual world. If we take this stance, we can easily reject the argument. But the stance is radical, for it invalidates a host of other totally unrelated arguments. The cost of adopting the stance is too high, and if we can avoid it, we should.14 Logical space comprises all and only logically possible worlds. The phrase ‘logical space’ is used in different ways by different people, and in particular, it is used by some to include all and only metaphysically possible worlds and what exists at them. To avoid unnecessary confusion, we simply stipulate that we shall use the phrase ‘logical space’ in such a way that logical space includes all and only logically possible worlds and what exists at them, and if we need to speak of the realm consisting of all and only metaphysically possible worlds and what exists at them, we shall say ‘metaphysical space’.15 The logic that governs every world in logical space is the same. So, alternative logics characterize alternative logical spaces. Let us assume that the logic governing logical space—that is, the local logical space which includes @—is classic. For example, for any logically possible world w: ‘P and Q’ is true at w iff ‘P’ is true at w and ‘Q’ is true at w; ‘P or Q’ is true at w iff ‘P’ is true at w or ‘Q’ is true at w; ‘Not-P’ is true at w iff ‘P’ is not true at w. The Russell–Quine–Lewis argument relies on logical facts such as these concerning truth functions and uses customary rules of inference from (3) through (6), thereby presupposing that logically impossible worlds are in logical space. One obvious way to make this presupposition explicit is to add the following to the argument as an additional crucial premise: ‘W is in logical space’. We should reject the argument by rejecting this premise. We should say that w is outside logical space. More carefully put, if w belongs to any logical space at all, it belongs to a logical space different from the logical space to which @ belongs. 14 We might not be able to avoid it. If we cannot, so much the better for our purpose of rejecting the argument. But then, we will need to take extreme care to avoid using some powerful methods of argumentation, like reductio ad absurdum. See dialethism: e.g. Priest 1987; Priest et al. 1989. 15 We may stipulate the analogous uses for phrases like ‘nomological space’, ‘mathematical space’, ‘conceptual space’, etc.

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Here is another, similar argument against logically impossible worlds. Let w be a logically impossible world at which something is a certain way and is not that way. (11) Æ is ç at w. (12) Æ is not ç at w. (13) For any x, if Æ is not ç at x, then it is not the case that Æ is ç at x. From (12) and (13), (14) It is not the case that Æ is ç at w. (11) and (14) contradict. What is wrong with this argument is that (13) is false if the variable ‘x’ ranges over logically impossible worlds. Here is a subtler argument: (15) Æ is ç at w. So, (16) Æ is ç-at-w. But, (17) Æ is not ç at w. So, (18) Æ is not ç-at-w. (16) and (18) contradict. World-indexed properties such as being ç-at-w16 are as legitimate as time-indexed properties such as being ç-at-t. From ‘Jane was not ç at t’ we can have ‘Jane is not such that she was ç at t’: for example, read ‘ç’ as ‘a student’. Against this argument, I say that we should block the move from (17) to (18) by rejecting (19) in favor of (20) when ‘x’ ranges over logically impossible worlds: (19) For any x, if Æ is not ç at x, then Æ is not ç-at-x. (20) For any x, if Æ is not ç at x, then Æ is not-ç-at-x. That Æ is ç-at-w and that Æ is not-ç-at-w do not contradict each other, i.e. together they do not instantiate ‘P & not-P’. This follows the basic idea behind Lycan’s response to Lewis. That we can do something does not mean that we should do it. We can include logically impossible worlds in our ontology, but should we do so? Merely logically possible worlds are extravagant enough, one might think, let alone logically impossible worlds, especially when conceived realistically in the way I recommend. There 16

Plantinga’s Æ–transforms are a particular case. See 3.5.

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are a few considerations which speak in favor of including logically impossible worlds—and metaphysically impossible worlds in general—and the basic idea behind these considerations is the same as Lewis’s own for justifying the postulation of metaphysically merely possible worlds: doing so will allow us to reap theoretical beneﬁts and be worth the cost.17 8 . 3 . COUNTERPOSSIBLE CONDITIONALS As we noted brieﬂy before, one powerful application of the possible-worlds framework is semantics for counterfactual conditionals, as devised by Stalnaker and reﬁned by Lewis. Stalnaker assumes that for any possible world w and any proposition p that may ﬁgure in a non-trivial counterfactual conditional, there is a unique metaphysically possible world at which p is true and which is closer to w than is any other metaphysically possible world at which p is true. On Stalnaker’s semantics, a counterfactual conditional ‘If it were the case that P, then it would be the case that Q’ is true (at w) if and only if Q at the closest (to w) metaphysically possible world at which P. Lewis rejects not only Stalnaker’s assumption that there is always a unique closest antecedent-verifying metaphysically possible world but also the weaker claim that there is always at least one such metaphysically possible world. On Lewis’s semantics, ‘If it were the case that P, then it would be the case that Q’ is true (at w) if and only if either P at no metaphysically possible world or some metaphysically possible world at which P and Q is closer (to w) than is any metaphysically possible world at which P and not-Q. Lewis’s version is a more general theory which subsumes Stalnaker’s pioneering work as a special case. So I shall refer to Lewis’s version as the Stalnaker–Lewis semantics. The Stalnaker–Lewis semantics handles many previously controversial counterfactual conditionals well and has become something like the orthodox theory of counterfactual conditionals. It, however, is notoriously problematic for counterpossible conditionals, i.e. conditionals with metaphysically impossible antecedents. The Stalnaker–Lewis semantics clearly has the consequence that all counterpossible conditionals are (vacuously) true. But consider, for example: (21) (22) (23) (24) (25) (26)

If P and not-P, then Q. If 2 þ 2 6¼ 4, then Q. If knowledge were justiﬁed true belief, then Q. If knowledge were not justiﬁed true belief, then Q. If determinism precluded free will, then Q. If determinism did not preclude free will, then Q.

17 For some of the arguments for metaphysically impossible worlds, see Chandler 1976; Lycan 1979; Parsons 1980; Salmon 1981: 229–52; 1984b, 1986b, 1989; Naylor 1986; Yagisawa 1988; Zalta 1988.

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It appears satisfactory to say that (21) and (22) are true, no matter what proposition ‘P’ and ‘Q’ may express, for it appears that anything follows from a logical or mathematical falsity. We shall not challenge this appearance. But how about (23)–(26)? (23) has a conceptual claim in epistemology as its antecedent, and (24) has its negation as its antecedent. (25) has a metaphysical claim about determinism and freedom as its antecedent, and (26) has its negation as its antecedent. Such conceptual claims and metaphysical claims necessarily have the truth values they have if they have truth values at all. So, either (23) or (24) is a counterpossible conditional, and either (25) or (26) is a counterpossible conditional. For each of the counterpossible conditionals, suppose we understand ‘Q’ to express whatever implausible consequence of the claim made in the antecedent: for example, ‘Edmund Gettier would be right’ for ‘Q’ in (23). We will then wish to say that those counterpossible conditionals are false. But the Stalnaker–Lewis semantics stands in our way, for it deems all of (23)–(26) as true, irrespective of the substitution we make for ‘Q’. It is hard to see how other proposed analyses of counterfactual conditionals can handle counterpossible conditionals adequately. For example, no proposal that essentially involves a causal relation, or any natural relation, in the truth condition is adequate for counterpossible conditionals. David Sanford’s suggestion that we rely on a general notion of dependence is plausible as far as it goes18 but unhelpful here, for we don’t have a well-developed theory of a general notion of dependence. Also, we need to be clear about particular cases of dependence to formulate such a theory, and in the above assortment of examples, we have a heterogeneous group of kinds of dependence (mathematical, logical, conceptual, metaphysical). The most straightforward way to deal with this situation is to preserve the attractive core of the Stalnaker–Lewis semantics and simply extend the notion of a world by including metaphysically impossible worlds in addition to metaphysically possible worlds. The extended Stalnaker semantics, for example, says that ‘If it were the case that P, then it would be the case that Q’ is true if and only if Q at the closest metaphysically possible or impossible world at which P. The extension of Lewis’s semantics is correspondingly straightforward.19 It might be suggested that a particular type of apparent counterpossible conditionals should be granted a special treatment which avoids the construing 18

Sanford 1989. Gillian Russell writes: ‘if it turns out, surprisingly, that in fact there were only ﬁfteen possible worlds, and in each of these worlds the morning star and the evening star are the same object, then you would…say that in every possible world the morning star is the evening star, and hence say that it is necessary that the morning star is the evening star and that the English sentence the morning star is the evening star expresses a necessary truth’ (Russell 2008: 39). Her counterpossible conditional ‘[I]f there were only ﬁfteen possible worlds…, then…’ raises an additional issue. Any metaphysically impossible world at which this antecedent is true must mimic metaphysical space, i.e. it must mimic a collection of metaphysically possible worlds. Or else, the extended Stalnaker–Lewis semantics needs to be modiﬁed to allow the antecedent to have a truth value with respect to alternative metaphysical spaces. We shall discuss such matters later. 19

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of them as counterpossible conditionals. Take the type of counterfactual conditional, ‘If I were you, I would ç’. I am not you. Assuming metaphysical necessity of non-identity, the antecedent of this conditional is metaphysically impossible, so this is a counterpossible conditional. Lewis analyzes this conditional to be true (at the actual world) if and only if some metaphysically possible world at which I am in your actual predicament and ç is closer to the actual world than is any metaphysically possible world at which I am in your actual predicament and do not ç. This makes the sentence have the same truth condition as an importantly different sentence, namely, ‘If I were in your predicament, I would ç’, which is no longer a counterpossible conditional. This treatment obliterates the distinction between ‘identical to you’ and ‘in your predicament’. As a semantic account, it is unsatisfactory. At best it captures only one typical use of the locution ‘If I were you, . . . ’, but it does not capture the semantics of the locution. Most speakers may well use this locution to mean what is captured by Lewis’s proposed truth condition, but speaker’s meaning need not correspond to sentence’s meaning. Even fairly widespread speaker’s meaning need not. Semantics is not pragmatics. ‘I were you’ is clearly the subjunctive form of ‘I am you’, and the latter is clearly a sentence of identity. Some might say that the locution ‘If I were you, . . . ’ is a frozen, idiomatic expression with the meaning to the effect of Lewis’s truth condition. If that is right, then the locution is not subject to any systematic semantics for counterfactual conditionals, let alone counterpossible conditionals. We therefore assume that it is not idiomatic. We also have an independent reason for making this assumption. Suppose there are exactly eight people (all sophisticated philosophers) on a desert island, including you and me, and a boat. The boat will ﬂoat with seven of us in it but will sink with eight. Observing this fact, I say, ‘If I were you, I would be one of only seven. But I am not you, so I am one of eight. Too bad.’ The meaning of the ﬁrst sentence is clear and Lewis’s proposed truth condition is clearly inappropriate. The appropriate reading of the sentence needs to incorporate envisioning of the truth of ‘I am you’ as a sentence of numerical identity, and this makes the conditional clearly a counterpossible conditional. Jeffrey Goodman considers the suggestion of extending the Stalnaker–Lewis semantics to counterpossible conditionals and raises a problem.20 Goodman invites us to consider the following two counterpossible conditionals: (27) If snow were white and non-white, then snow would be white. (28) If snow were white and non-white, then snow would be non-white. These are both intuitively true (at @) conditionals. This poses a problem to the extended Stalnaker–Lewis semantics, according to Goodman. Let us call a metaphysically impossible world at which snow is white and non-white, snow 20

Goodman 2004.

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is white, and snow is not non-white a white world. And let us call an impossible world at which snow is white and non-white, snow is non-white, and snow is not white a non-white world. Either some white world is closer (to @) than any nonwhite world, or some non-white world is closer (to @) than any white world, or neither of these is the case. If the ﬁrst is the case, the extended Stalnaker– Lewis semantics says that (27) is true and (28) is false. If the second is the case, the extended Stalnaker–Lewis semantics says that (28) is true and (27) is false. If neither is the case, the extended Stalnaker–Lewis semantics says that neither (27) nor (28) is true.21 Therefore, the extended Stalnaker–Lewis semantics says that (27) and (28) are not both true, which is contrary to the intuitive judgment. Assuming that the intuitive judgment does say that (27) and (28) are both true, it seems to me that the extended Stalnaker–Lewis semantics can be defended from Goodman’s objection. Call a metaphysically impossible world at which snow is white and non-white, snow is white, and snow is non-white a white-non-white world. It is plausible to suggest that a white-non-white world is closer than any white world or any non-white world. If this suggestion is accepted, the extended Stalnaker–Lewis semantics says that both (27) and (28) are true. Goodman reports that Earl Conee made this suggestion. Goodman’s response is to say that a white-world is closer than any white-non-white world. His reason for saying so is that snow is not non-white at a white-world, whereas snow is non-white at a white-non-white world. Since snow is not non-white at the actual world, a white-world is closer to the actual world than any white-nonwhite world. Goodman also says that the logical inference, which holds at the actual world, from a conjunction to each conjunct should be given a lower weight in determining similarity to the actual world than the speciﬁc matter of fact like snow being white. His reason for saying so is that the antecedent of (27) and (28) already violates classical logic: Retaining logical similarity properly comes second in our thinking here because we already know we must make some incredible logical leaps just to entertain the situations we are asked to entertain (speciﬁcally, the leap of admitting a situation in which there is a true contradiction).22

I think that the methodological situation here for the extended Stalnaker–Lewis semanticist is analogous to that in which Lewis ﬁnds himself in the face of objections of a similar kind to his original semantic theory, most notably an objection from Kit Fine. Fine’s objection consists in an example counterfactual conditional whose intuitive truth value differs from the truth value Lewis’s theory confers on it under a certain plausible-sounding understanding of the similarity 21 The situation is a little more complicated, allowing talk of truth-value indeterminacy. See Goodman 2004: nn. 47 and 48. 22 Ibid. 62.

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relation between metaphysically possible worlds. Lewis’s response is to propose to use the intuitive truth value of Fine’s counterfactual as a datum to determine the details of the similarity relation between metaphysically possible worlds. In effect, Lewis rejects the plausible-sounding understanding of the similarity relation Fine’s objection relies on, and instead tailors the similarity relation just so as to make Fine’s counterfactual have the truth value it intuitively should. Likewise, I think, those of us who wish to defend the extended Stalnaker–Lewis semantics along the lines of Conee’s suggestion should use Goodman’s (27) and (28) to tailor the similarity relation between metaphysically impossible worlds just so as to make them turn out true. The net effect of this strategy is that the similarity relation between metaphysically impossible worlds is such that a whitenon-white world is deemed closer than any white world or non-white world. More generally, logical similarity is considered weightier than similarity in particular matters of fact. As Goodman says, ‘we must make some incredible logical leaps’ just to fathom the antecedent of (27) and (28), but this does not mean that we should disregard logical matters when judging comparative closeness of metaphysically impossible worlds to the actual world. Fathoming what is the case at a world is one thing, comparing two or more worlds in terms of similarity is quite another; the former deals with intra-world affairs, while the latter is an inter-world affair. Note that this is in line with the system of weights Lewis proposes in response to Fine’s example, according to which avoiding ‘big, widespread, diverse violations of law’ outweighs maximizing ‘the spatio-temporal region throughout which perfect match of particular fact prevails’.23 Goodman’s positive suggestion is to ‘retain a closest possible or impossible worlds account of counterfactuals . . . but ignore (in a sense) the impossible worlds that judge explicit contradictions to be true’.24 The idea is to focus on metaphysically impossible but logically possible worlds (for example, ones at which Humphrey is a poached egg). But this will leave counterfactuals with a logically impossible antecedent unaccounted for. Since Goodman himself relies on the intuitive truth of such counterfactuals, namely, (27) and (28), in his critique of the extended Stalnaker–Lewis semantics, this is unsatisfactory. (Notice that intuitively (27) and (28) are non-vacuously true.) A comprehensive account of all counterpossibles will be preferable to a limited account of only some of them. And we can have a comprehensive account if we follow the methodology Lewis uses to deal with Fine’s example.

23 Ibid., n. 17 at the end of 6.3 for reference. Goodman acknowledges that his objection depends on the pre-Fine closeness intuitions. It is unclear what Goodman thinks is wrong with applying the move here which Lewis uses to respond to Fine. Ibid., n. 51. 24 Ibid. 63; his emphasis.

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8 .4 . IMPOSSIBLE SUPPOSITIONS The non-triviality of reductio ad absurdum must be explained, and metaphysically impossible worlds can provide a straightforward explanation. Suppose that p is a metaphysically necessarily true proposition. We may try to prove p’s truth by assuming p’s falsity and deriving an absurdity from it (in conjunction with other, obviously true propositions perhaps). We will be successful if the proof consists of deductively valid steps, ending with an absurdity. It is standard to understand deductive validity as follows: an argument is deductively valid if and only if it is not metaphysically possible for the premises to be true and the conclusion false.25 So, according to the standard way of understanding deductive validity, any step from premises one of which is metaphysically necessarily false to any conclusion is (vacuously) deductively valid. So, according to the standard way of understanding deductive validity, every reductio argument to prove a metaphysically necessarily true proposition must be successful as long as its intermediate conclusion, the reduced absurdity, is obviously false. This trivializes the reductio method. According to Daniel Nolan, this shows that each step in an acceptable reductio argument must be not only deductively valid but obviously deductively valid.26 I do not think this is satisfactory. As the example of a proverbial mathematics professor who declares a convoluted proof obvious after checking its complicated steps at length illustrates, obviousness of deductive validity is a subjective matter, whereas the non-triviality of reductio ad absurdum is an objective matter. What we need is an objective conception of deductive validity according to which not everything follows from a necessarily false premise. Metaphysically impossible worlds allow us such a conception. Instead of saying that an argument is deductively valid if and only if the conclusion is true at every metaphysically possible world at which the premises are true, we may say that an argument is deductively valid if and only if the conclusion is true at every world, metaphysically possible or not, which meets a certain condition C and at which the premises are true. For any premises and any conclusion, there is always a metaphysically impossible world at which the premises are true and the conclusion false, hence the need for the condition C, which is allowed to vary from one reductio argument to another. Intuitively, the condition C encapsulates the assumed inference rules and constrains the logical deviation of metaphysically impossible worlds. Another, related area in which metaphysically impossible worlds are called for involves discourse which includes a supposition of the truth of a metaphysically 25 For formal logical purposes, one might wish to say ‘logically possible’ instead of ‘metaphysically possible’, but we are not concerned with formal logic. 26 Nolan 1997: 538–9.

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necessarily false proposition but which does not aim to establish the falsity of the supposition by reductio. When Hilary Putnam famously introduced his Twin Earth thought experiment by saying, ‘For the purpose of the following scienceﬁction examples, we shall suppose that somewhere in the galaxy there is a planet we shall call Twin Earth. Twin Earth is very much like Earth . . . ’,27 he did not make the supposition of the existence of Twin Earth as a target for rejection by reductio. He explicitly admitted that the supposition was a ﬁction (science ﬁction), although—let us assume—it was not a metaphysically impossible ﬁction. The point of his supposition lay elsewhere; it was to argue for certain theses concerning meaning and psychological state. Those readers of Putnam’s passage who understand it correctly would not reject his arguments for the theses simply on the grounds that they are based on a false supposition. The set-up like Putnam’s for thought experimentation is common in philosophy. Sometimes, as in the case of Putnam’s, the set-up is metaphysically possible. Other times, it is not. But whether the set-up is metaphysically possible or impossible, the structure of argument is the same; the conclusion should not be rejected simply on the grounds that the assumed set-up is false or metaphysically necessarily false. Here is an example of a philosophical discussion based on a metaphysically impossible supposition, by Terence Parsons: Whether there are functions that can serve as the denotata of operators that yield the same results as the underlying event approach depends on the theory of meaning that is presupposed and on additional assumptions about the available choice of verb meanings. For example, if meanings are taken to be intensions, as these are normally understood within possible worlds theory, and if no restrictions are placed on the range of possible verb meanings, then there are possible intensions for verbs and modiﬁers such that in some cases no function works as I described. Suppose two quite different kinds of event, say stabbings and kickings, are always performed simultaneously in every possible world. Suppose, however, that some stabbings are violent when the contemporaneous kickings are not. Then the property of being a v and a w such that v stabs w would be the very same property as the property of being a v and a w such that v kicks w. And, since ‘violently’ stands for a function, it would have to map both these properties to the same property (since they are not two properties, but only one). And this would require that anyone who stabs someone violently also kicks that person violently, which should not follow. It is not true of course that kickings and stabbings coincide in all possible worlds, and a genuine example is hard to come by.28

Parsons starts by assuming that stabbings and kickings are always performed simultaneously at every metaphysically possible world, and argues from that assumption to the conclusion that anyone who stabs someone violently also kicks that person violently, which he says should not follow. His aim is not to argue against the obviously false thesis that stabbings and kickings, or other two similarly quite different kinds of events, are always performed simultaneously at 27

Putnam 1975: 223.

28

Parsons 1990: 57.

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every metaphysically possible world. Rather, it is to argue that under certain assumptions no function can serve as the denotation of the operator of the kind in question. Parsons acknowledges that his assumption that kickings and stabbings coincide at all metaphysically possible worlds is false, which makes his example not ‘genuine’. Not only is his assumption false but it is metaphysically necessarily false. Despite this defect in his assumption, Parsons’s example succeeds in helping him make his point concerning semantics of events.29 As in the case of reductio ad absurdum, some straightforward arguments based on a metaphysically necessarily false premise are valid, and others invalid; if an argument is valid, the conclusion is bolstered, and otherwise it is not. We would be hard pressed to make sense of this distinction without the revision of the deﬁnition of validity along the lines suggested earlier which involve metaphysically impossible worlds. 8 . 5. DOXASTIC POSSIBILITY Another motivation for postulating metaphysically impossible worlds comes from Stalnaker’s view on belief, much of which he shares with Lewis. Stalnaker claims that believing is eliminating possibilities. Believing is locating one’s actual world in metaphysical (or logical) space. To believe a proposition is to narrow down the class of possible worlds to which one’s actual world belongs, by eliminating some possible worlds as not one’s actual world. To believe that P is to eliminate all those possible worlds at which it is not the case that P. If this Stalnakerian view is correct generally, then to believe that water is XYZ is to eliminate all those metaphysically possible worlds at which water is not XYZ. But, at all metaphysically possible worlds, water is not XYZ, assuming that water is actually not XYZ and that the molecular structure of water is its essence. So the elimination eliminates all metaphysically possible worlds. This will leave us with no world at all if all worlds are metaphysically possible. But one does not fail to believe when one believes that water is XYZ. So there must remain a non-empty class of worlds to which one takes one’s actual world to belong, after the elimination of all metaphysically possible worlds. The worlds belonging to such a class are metaphysically impossible worlds.30 29 Here is another example: ‘Suppose…that it is actually impossible that the bright light in the sky in the morning is anything other than the bright light in the sky in the evening, so that there was no context of introduction which would result in Hesperus or Phosphorus referring to anything other than Venus’ (Russell 2008: 80; her emphases). Other examples abound in the philosophical literature. 30 Stalnaker is no fan of metaphysically impossible worlds himself and would not accept everything said in this paragraph. My point is that one may motivate the postulation of metaphysically impossible worlds by starting with Stalnaker’s view on what it is to believe a proposition. Stalnaker’s own view on beliefs whose contents are metaphysically impossible makes rather heavy use of metalinguistic propositions. See Stalnaker 1984.

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We may take Stalnaker’s idea and use it not just to motivate metaphysically impossible worlds but also to argue for them, on the assumption that there are metaphysically possible worlds. One such argument may start as follows: Bianca is a talented graduate student in philosophy. She has studied modal metaphysics and learnt much about David Lewis’s theory of metaphysically possible worlds and their inhabitants. She ﬁnds Lewis’s arguments persuasive and has come to believe much of Lewis’s theory as true. At the same time, she has learnt, among other things, that Lewis is non-committal about the question whether there are non-modally qualitatively identical but numerically distinct metaphysically possible worlds. For worlds to be non-modally qualitatively identical is for them to have exactly the same non-modal purely qualitative propositions (as opposed to modal propositions or singular propositions) true at them. Bianca thinks hard about the question and ﬁnally decides that there must be a fact of the matter one way or the other but she does not know how to determine which is the case. That is, Bianca believes that either there are non-modally qualitatively identical but numerically distinct Lewisian possible worlds or there are not, but she does not believe that there are and does not believe that there are not. Since Bianca believes that all metaphysically possible worlds are Lewisian possible worlds and all Lewisian possible worlds are metaphysically possible worlds, this means that Bianca believes that either there are non-modally qualitatively identical but numerically distinct metaphysically possible worlds or there are not, but that she does not believe that there are and does not believe that there are not. This is a perfectly understandable doxastic situation. Lewis ﬁnds himself in that same doxastic situation, and perhaps so do some others. A satisfactory account of Bianca’s doxastic situation leads us beyond metaphysical space, i.e. beyond metaphysically possible worlds, to metaphysically impossible worlds. Bianca is in a state of doxastic indecision, and doxastic indecision is a kind of modality. Bianca is undecided about which of the two alternative and mutually exclusive claims to believe; one claim might be true but the other also might be true, she says to herself. How should we understand the modality indicated by the word ‘might’ here? It is important at this point to become clear about beliefs about oneself, or beliefs de se, as Lewis calls them,31 for doxastic indecision is indecision between competing beliefs de se. Take John Perry’s famous example.32 Lingens is inside a vast library and does not know if he is on the second ﬂoor of the library or on the third ﬂoor. Lingens believes of himself that he is either on the second ﬂoor or on the third ﬂoor, but does not believe of himself that he is on the second ﬂoor, and does not believe of himself that he is on the third ﬂoor. 31 32

Lewis 1979b. See also Castan˜eda 1967, 1968; Perry 1979; Kaplan 1989. Perry 1979.

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Couched in the terminology of possible-worlds metaphysics, which we are assuming, this means that there are two possible worlds w1 and w2 such that Lingens is on the second ﬂoor of the library at w1, Lingens is on the third ﬂoor of the library at w2, and Lingens is unable to distinguish himself at @ from himself at w1 or from himself at w2 (though he can distinguish between the latter two); i.e. Lingens is undecided about whether his own actual world, @, is w1 or w2. The notion of being unable to distinguish is a modal notion and is analyzable in terms of sameness of appearance. For Lingens to be unable to distinguish himself at @ from himself at a world w is for things to appear to Lingens at @ in exactly the same way as they do to him at w. Lingens’s situation may generally be formulated as follows: (E) For any subject S at @, for any sentences P and Q which S understands at @, P and Q are doxastically undecided alternatives for S at @ if and only if there are doxastically possible worlds w1 and w2 such that (i) P is true for S at w1, Q is false for S at w1, and the universe appears to S at @ in exactly the same way as it appears to S at w1, and (ii) Q is true for S at w2, P is false for S at w2, and the universe appears to S at @ in exactly the same way as it appears to S at w2. Before explaining the notion of a sentence’s being true or false for a subject at a world, let me ﬁrst say that I propose (E) in the spirit of the advice Lewis offers to those who, instead of taking properties as objects of attitudes as he does, ‘would favor sentential objects’ or ‘sentential meanings’: ‘[D]o not limit yourself to complete, closed, nonindexical sentences or meanings. Be prepared to use predicates, open sentences, indexical sentences, or meanings thereof—something that can be taken to express properties rather than propositions.’33 (I follow Lewis’s advice not because I take sentential objects as objects of attitudes but because it is easier for our purposes at hand to speak of sentences than of propositions or properties.) Thus, the sentences, P and Q, may well contain indexical expressions, in particular, the ﬁrst-person singular indexical pronoun ‘I’ (‘me’, ‘my’, ‘mine’). (For simplicity, we are assuming that S is a monolingual English speaker.) A sentence with ‘I’ is true for S at w if and only if it is true at w when all occurrences of ‘I’ in the sentence are evaluated as referring to S. It is easy to grasp what is meant by this when we consider a few examples. Let P be the sentence, ‘The capital city of my nation is covered with snow’. Then P is true for S at w if and only if at w the capital city of S’s nation is covered with snow. Let P be ‘Three planets circle the star in the star system I inhabit’. Then P is true for S at w if and only if at w the star system S inhabits contains a unique star and three planets circling it. Let P be ‘There area talking donkeys at the world at which I exista’. Then P is true for S at w if and only if at w S existsa and there area talking donkeys. (We ignore sentences which contain no ﬁrst-person singular indexical pronoun.) To describe Bianca’s doxastic situation, we let P be ‘There arem non-modally qualitatively identical but numerically distinct metaphysically possible worlds in the metaphysical space to which the world at which I exista belongsm’ and Q be 33

Lewis 1979b: 150.

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its negation, ‘There arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds in the metaphysical space to which the world at which I exista belongsm’.34 Let us abbreviate ‘the metaphysical space to which the world at which X existsa belongsm’ as ‘X’sa metaphysical space’. P and Q are doxastically undecided alternatives for Bianca. It follows from the above deﬁnition of doxastically undecided alternativeness and what it is for P or Q to be true for Bianca at a world, that (i) at some doxastically possible world w1 there arem non-modally qualitatively identical but numerically distinct metaphysically possible worlds in Bianca’sa metaphysical space, and the universe appears to Bianca at @ in exactly the same way as it appears to Bianca at w1, and (ii) at some doxastically possible world w2 there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds in Bianca’sa metaphysical space, and the universe appears to Bianca at @ in exactly the same way as it appears to Bianca at w2. From (i) it follows that at w1, Bianca exists and hera metaphysical space, M1, is such that in it there arem non-modally qualitatively identical but numerically distinct metaphysically possible worlds. From (ii) it follows that at w2, Bianca exists and hera metaphysical space, M2, is such that in it there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds. Before continuing further, notice that in introducing M1 and M2, we implicitly assume that every doxastically possible world existsm in some metaphysical space. This seems like an innocuous assumption, but if an argument is needed for it, we may offer something like the following: One important point of introducing worlds into one’s modal ontology is to ground the notion of possibility of various kinds. To do so, we need to have a multiplicity of worlds which are related to one another by appropriately varied accessibility relations. So, for any given kind of possibility, if it is genuinely a kind of possibility, then for any given world w, we need to have some other world to which w bears the accessibility relation of the appropriate variety. The largest collection of worlds which includes w and over which the accessibility relation appropriate for metaphysical possibility is deﬁned is the metaphysical space to which w belongs. To say that a world exists in a metaphysical space is to say that it belongs to the metaphysical space. Assume for reductio that w1 and w2 arem both metaphysically possible worlds. Then, since all metaphysically possible worlds belongm to a single metaphysical space (namely, what Lewis and his followers call ‘logical space’), w1 and w2 belongm to that single metaphysical space, hence M1 ¼ M2. So, in M1, namely, M2, there arem non-modally qualitatively identical but numerically distinct metaphysically possible worlds and there arem not non-modally qualitatively 34

The modal-tense indicator subscript ‘m’ was introduced in 5.6 and applied in 5.7. The use here follows that in 5.7. The evaluation of ‘α ism φ’ in a metaphysical space works in a way parallel to the evaluation of ‘α isa φ’ at a world.

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identical but numerically distinct metaphysically possible worlds. But such a metaphysical space is not one to which metaphysically possible worlds belongm. So, w1 and w2 arem not both metaphysically possible worlds. A contradiction. Therefore, w1 and w2 arem not both metaphysically possible worlds. At least one of them is a metaphysically impossible world.35 Let us consider a few objections. Objection 1: From (ii) it follows that at w2, there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds in Bianca’s metaphysical space. But this is to say that either some metaphysical space is Bianca’s and in it there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds, or no metaphysical space is Bianca’s. If this second disjunct holds, then we are not entitled to proceed further in the argument. Reply 1: When we say that at w2, there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds in Bianca’s metaphysical space, we mean to say that Bianca exists at w2 and in the metaphysical space to which w2 belongsm there arem not non-modally qualitatively identical but numerically distinct metaphysically possible worlds. If w2 ism a metaphysically possible world, it belongsm to a metaphysical space. Objection 2: We do not need alternative metaphysical spaces to make sense of Bianca’s doxastic situation. We only need alternative metaphysically possible worlds. Instead of M1, M2, and the worlds which belong to them, we may speak of w1, w2, and the world-like parts of the universe’s w1-stage and w2-stage. We may say that the universe’s w1-stage contains non-modally qualitatively identical but numerically distinct world-like parts, whereas its w2-stage does not. If this is somehow contrary to the conception of a world as structureless, so much the worse for that conception. Reply 2: That changes the subject. What Bianca is undecided about concerns metaphysically possible worlds, not world-like parts of the universe’s metaphysicallypossible-world-stages. 35 Some might think that it is incoherent to say that a world ism a metaphysically impossible world. The reason, they might say, is that the modal tense signaled by the subscript ‘m’ requires that a world w ism thus-and-so in a metaphysical space M only if w existsm in M, but since all worlds existingm in M arem metaphysically accessible from one another, w ism a metaphysically impossible world in M only if w ism a metaphysically possible world in M, which is contradictory. This reasoning is faulty. Consider the analogous case of the actuality tense, signaled by the subscript ‘a’. We might be tempted to say that the actuality tense is such that an individual x isa thus-and-so at a world w only if x existsa at w. It would be usually correct to say so, but not always. It depends on the ‘thus-and-so’. Consider the statement that x isa non-existent at w. It is not correct to say that x isa non-existent at w only if x existsa at w; for otherwise, nothing would be non-existent at any metaphysically possible world. Another such example of ‘thus-and-so’ is non-actuality. It is not correct to say that x isa non-actual at w only if x existsa at w; for otherwise, nothing would be nonactual and non-existent at any metaphysically possible world. (This is so whether the actuality in question is rigid or non-rigid.) Analogously, it is not correct to say that w ism an impossible world in M only if w existsm in M.

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Follow-up Objection 2: (E) is misinterpreted when P and Q are themselves about possible worlds or metaphysical spaces. To say that the sentence ‘There are nonmodally qualitatively identical but numerically distinct metaphysically possible worlds in my metaphysical space’ is true for Bianca at w1 is not to say that Bianca exists at w1 and there are non-modally qualitatively identical but numerically distinct metaphysically possible worlds in the metaphysical space to which w1 belongs, but to say that Bianca exists at w1 and there are non-modally qualitatively identical but numerically distinct metaphysically-possible-world-like parts of the universe’s w1stage. We only need to have the universe’s w1-stage rich enough to contain metaphysically-possible-world-like parts. Correspondingly for w2; we only need to have the universe’s w2-stage fail to contain metaphysically-possible-world-like parts which are non-modally qualitatively identical but numerically distinct. We can handle Bianca’s situation within our familiar metaphysical space without going beyond it. Follow-up Reply 2: First, (E) is meant as a perfectly general principle, and the suggestion that we treat sentences about metaphysically possible worlds or metaphysical spaces in a separate and special way is not independently motivated. Second, just as the idea of a time-like part of the universe’s temporal stage is suspect, the idea of a world-like part of the universe’s modal stage is suspect; remember that a world is a modal index akin to a temporal moment. To think otherwise is to be trapped in the Lewisian conception of a possible world, or worse, an ersatz conception. Even within the Lewisian framework, the suggestion will not work. Every part of a Lewisian possible world is spatiotemporally related to every other part. So, if a Lewisian possible world is to play the role of a counterpart of Lewisian logical space, it must be possible that every part of Lewisian logical space be spatiotemporally related to every other part. But if so, since Lewisian logical space is nothing but the totality of Lewisian possible worlds, it is possible that every Lewisian possible world be spatiotemporally related to every other Lewisian possible world, which is plainly false in Lewis’s metaphysics. A related point is that, even though the notion of a counterpart of a Lewisian possible world might appear intelligible, a world-like proper part of a Lewisian possible world cannot be a counterpart of a Lewisian possible world. Suppose that z is a world-like proper part of a Lewisian possible world w and is a counterpart of another Lewisian possible world w’. Then z is spatiotemporally related to the rest of w. So, w’ has a counterpart z that is spatiotemporally related to something outside itself (z). So, it is possible for w’ to be spatiotemporally related to something outside itself. But such a possibility is precluded by the Lewisian deﬁnition of a possible world as something that is uniﬁed by spatiotemporal relatedness. Objection 3: Bianca faces doxastic indecision concerning a metaphysically necessary matter. Her situation should be treated in the same way as anyone else’s who wonders about any other metaphysically necessary matter. Given the set-up of metaphysically possible worlds, the best we can do is somehow to see any such situation as involving a metalinguistic issue. For example, to wonder whether 1313 þ 2 is a prime is to wonder whether ‘1313 þ 2’ designates a prime, or alternatively, it is to wonder whether ‘1313 þ 2 is a prime’ is a true sentence.

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Reply 3: Bianca might as well wonder whether modal reality is Lewisian or Plantingan and remain undecided as to which is the case. Surely, such a doxastic situation is more serious than mere metalinguistic quandary.36 8 . 6. DISTINCTNESS OF THE INDISCERNIBLE The above argument from Bianca’s doxastic indecision to the existence of a metaphysically impossible world belonging to an alternative metaphysical space produces an interesting corollary. The account of Bianca’s situation by means of (E) gives us two worlds, w1 and w2. But every world belongs to some metaphysical space. M1 and M2 are the metaphysical spaces to which w1 and w2 belong, respectively. In M1, there are non-modally qualitatively identical but numerically distinct worlds. Therefore, some worlds in some metaphysical space are nonmodally qualitatively identical but numerically distinct. So, from the supposition that Bianca wonders whether there are non-modally qualitatively identical but numerically distinct possible worlds, we have reached the conclusion that some worlds are indeed non-modally qualitatively identical but numerically distinct. This might seem like a trick. How can a mere presence of a doxastic indecision yield a particular resolution of that indecision? The answer is that it does not, and there is no trick involved in the reasoning. (We are assuming that Bianca actually exists and we speak of the @-stage of Bianca when we say that Bianca wondersa.37) What Bianca wonders is whether there are non-modally qualitatively identical but numerically distinct metaphysically possible worlds, but the corollary in question is that there are non-modally qualitatively identical but numerically distinct worlds. One of w1 and w2 ism a metaphysically impossible world, hence the worlds belonging to M1 or the worlds belonging to M2 arem metaphysically impossible worlds.38 So we are not entitled to the claim that there arem non-modally qualitatively identical but numerically distinct metaphysically possible worlds. If Bianca had wondered whether there arem non-modally qualitatively identical but numerically distinct worlds, whether metaphysically possible or impossible, then the analog of the argument would yield the conclusion that there arem in some metaphysical space. But in that case, the analog of the argument would in effect concern collections of alternative metaphysical spaces, and its conclusion would not be particularly surprising. 36

For the classic metalinguistic construal of attitude contexts, see Carnap 1947. For the classic rebuttal, see Church 1950. For more on this and related issues, see Mates 1950; Putnam 1954; Church 1954; Sellars 1955; Burge 1977, 1978; Stalnaker 1984; Yagisawa 1984; Salmon 1986a, 2001; Richard 1990; Fiengo and May 2006. 37 If Bianca does not actually exist, then the supposition that Bianca actually exists (where actuality is understood rigidly) provides us with another argument for metaphysically impossible worlds. We shall consider this when we discuss two-dimensional semantics in 8.9.4 and 8.11. 38 We are assuming that if w and w’ belong to the same metaphysical space and w ism a metaphysically possible world, then w’ ism a metaphysically possible world. This means, of course, that if w and w’ belong to the same metaphysical space and w ism a metaphysically impossible world, then w’ ism a metaphysically impossible world.

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The argument cannot be generalized to yield the conclusion that there are distinct non-modally qualitatively identical world-stages of numerically distinct transworld individuals. M1 contains at least one pair of non-modally qualitatively identical but numerically distinct worlds. Let Larry1 be a world-stage of a transworld individual at one of such a pair of worlds, and Larry2 be Larry1’s non-modal qualitative duplicate at the other world of the pair. Do we have here an example of two world-stages of transworld individuals who are non-modally qualitatively identical but numerically distinct? No. We have not established that Larry1 and Larry2 are not world-stages of the same transworld individual. Is there a way to establish it? The criterion of transworld identity we put forth in Chapter 6 not only does not help us do so but on the contrary it pushes us in the opposite direction. Larry1 is the closest continuer at w1 of Larry2, and Larry2 is the closest continuer at w2 of Larry1. So, on the criterion of transworld identity we have, Larry1 and Larry2 are world-stages of the same transworld individual. This has an obvious consequence. Since the pair {Larry1, Larry2} is an arbitrary pair of nonmodally qualitatively identical world-stages at w1 and w2, what holds for the pair holds for every such pair of world-stages at w1 and w2. So, any such pair is a pair of world-stages of the same transworld individual. 8. 7. NON-COMPOSSIBILITY OF THE INDISCERNIBLE There is an interesting feature of the Bianca argument which might appear initially puzzling. We assumed that Bianca is a graduate student. Let us modify this and assume that Bianca knows much more than any graduate student does; Bianca knows all non-modal facts about her world, i.e. the @-stage of Bianca knowsa all non-modal facts about @. She knows every particular matter of fact and every nomological connection obtaining at her world. She, however, does not know modal facts, such as what worlds are metaphysically possible worlds— i.e. what worlds are metaphysically accessible from her world @—and what world-stages her worldmates have at other metaphysically possible worlds.39 In other words, she knows all and only about her own world as considered in isolation from all other metaphysically possible worlds; she is omniscient about her own actuality but not about metaphysical possibilities. Despite this dramatic difference, this new Bianca is like the original Bianca in one crucial respect; she wonders and is undecided about whether there are nonmodally qualitatively identical but numerically distinct metaphysically possible worlds. The original Bianca argument in the last section will go through as before with new Bianca. As before, the universe appears to her at @ in exactly the same way as it appears to her at w1, the universe appears to her at @ in exactly 39 We are assuming that knowledge of all nomological matters does not cover all metaphysical possibilities any more than knowledge of the US constitution does.

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the same way as it appears to her at w2, and either w1 or w2 is a metaphysically impossible world. But new Bianca is omniscient about @ (in the sense explained). So, the universe appears to new Bianca at @ exactly as it in fact is at @. That is, how the universe appears to new Bianca at @ is how it is at @. So, the universe appears to her at w1 in exactly the same way—call that way ‘Y’—as it is at @, and it appears to her at w2 in exactly the same way, Y, as it is at @. Now suppose that there is nothing misleading to her about Y and nothing hidden from her about the universe at w1 or at w2.40 Then Y is the way the universe is at w1 and at w2, as well as at @. This means not just that w1 and w2 are indistinguishable to Bianca from @ but that they are indistinguishable simpliciter from @. Since the rest of the argument goes as before, either w1 or w2 is a metaphysically impossible world. So, there are two worlds, namely, either @ and w1 or @ and w2, which are non-modally qualitatively identical but one of which is a metaphysically possible world while the other is a metaphysically impossible world. Therefore, if there is nothing misleading to new Bianca about Y and nothing hidden from her about the universe at w1 or at w2, then whether a world is a metaphysically possible world or a metaphysically impossible world is not a matter of what is non-modal and true at it. This is interesting, for it might appear to go against our notions of a metaphysically possible world and a metaphysically impossible world; a world is metaphysically possible if and only if the laws of metaphysics are true at it. Our notions might appear to tell us that the possibility or impossibility of a world is a matter intrinsic to the world. But when we remind ourselves of the nature of the laws of metaphysics, we realize that this is not so. The laws of metaphysics include, inter alia, modal laws, which deal in relations among worlds, among world-stages (of transworld individuals), and among worlds and world-stages. For such a law to be true at a world is for that world to stand in some relation to some other worlds or some world-stages. Thus, it does not ﬂout our notions of a metaphysically possible world and a metaphysically impossible world to hold that if Y does not mislead new Bianca and the universe hides nothing from her at w1 or at w2, the metaphysical possibility or impossibility of a world is not a matter intrinsic to the world. Once we get the hang of the above line of reasoning, it is not difﬁcult to invent other similar arguments for the conclusion that some worlds are non-modally intrinsically indistinguishable but not metaphysically compossible (not metaphysically accessible from each other). Here is just one example. For some very large number N, new Bianca thinks that the total number of possible worlds ism either N or 2N but she is undecided which. The argument goes much as before to conclude that some worlds, w11 and w12, are such that the universe appears to her at w11 to be a certain way Y and appears to her at w12 to be the same way Y, where Y is the way the universe is at @. The metaphysical space M11, to which w11 belongs, contains N-many worlds and the metaphysical space M12, to which w12 belongs, contains 40 This is not a superﬂuous assumption, for new Bianca might be omniscient despite the way the universe appears to her. The assumption says that that is not the case.

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2N-many worlds. Either w11 or w12 ism a metaphysically impossible world. So, again, if Y does not mislead her and the universe hides nothing from her at w11 or at w12, some worlds are non-modally intrinsically indistinguishable but not metaphysically compossible. 8 .8 . MODIFIED SKYRMS ARGUMENT I advocate a modal dimensionalist view, according to which modality is a matter pertaining to additional dimensions, like the spatial and temporal dimensions, along which the universe spreads. The modal dimensions are more complicated than the spatial and temporal dimensions. I assumed as much in the preceding arguments involving Bianca, but it may be instructive to make the assumption more explicit and expand on it. The crucial point is that the common thrust of our arguments pushes us in the general direction of expanding the realm of metaphysical indices. Considerations of counterfactual conditionals with merely possible antecedents, merely possible suppositions, and doxastic possibility which does not infringe on metaphysical possibility move us to postulate modal axes in addition to the spatial and temporal axes. Likewise, considerations of counterpossible conditionals, impossible suppositions, and doxastic possibility not constrained by metaphysical possibility should move us to postulate extra modal axes in addition to the spatial, temporal, and original modal axes. The extra modal axes cannot be among the original modal axes, for two reasons. First, the extra modal axes accommodate metaphysically impossible worlds, whereas the original modal axes accommodate only metaphysically possible worlds. This is consonant with our refusal to accept metaphysical possibility as unrestricted possibility. Let us consider physical possibility as a contrasting example. Starting with the collection of all metaphysically possible worlds, we obtain physically possible worlds by imposing the restriction on the collection that the actual laws of physics hold; all and only those worlds in the collection at which those laws hold are physically possible worlds. The rest of the worlds in the collection are physically impossible worlds. We do not obtain metaphysically possible worlds in the same way, by imposing a restriction on the collection; for the collection includes all and only metaphysically possible worlds. Thus, metaphysically impossible worlds are not worlds left in the collection after we disregard all and only metaphysically possible worlds; no world is so left. So, we need extra modal axes going beyond the original modal axes to accommodate metaphysically impossible worlds. Some might wonder why we should delineate the original modal axes by means of metaphysical possibility to begin with. The reason is that, though not unrestricted, metaphysical possibility is not just another restricted possibility. The sphere of metaphysical possibility is somehow privileged. (I say this as I speak at @. Some of my other worldly stages at worlds metaphysically inaccessible from @ would assertively utter those same words with the same meaning.) If some properties are said to give rise to natural kinds

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because they cut nature at its joints, metaphysical possibility may be said to give rise to a metaphysical kind because it cuts modal reality at its joints. At this point, my proposal becomes highly speculative. My metaphysical sense tells me that locating metaphysically impossible worlds on extra axes, rather than on the original axes, is the most promising way to cut modal reality. Second, the extra modal axes are supposed to provide alternatives to the original modal axes. This is consonant with externalism of truth conditions, as explained in 1.7. If we think of the metaphysically possible worlds as lying in the metaphysical space deﬁned by the original modal axes as worlds of a privileged metaphysical kind as just suggested, we should think of the metaphysically impossible worlds as lying in some alternative metaphysical space deﬁned by the extra modal axes.41 There is a more general argument for postulating metaphysically impossible worlds. Brian Skyrms sketches a version of it42 and David Lewis reports Skyrms’s sketch: Skyrms conjures up the specter of a regress from a plurality of worlds to a plurality of grand worlds to a plurality of yet grander worlds . . . The regress works by cycling around three assumptions: (1) that ‘reality’ is the totality of everything, (2) that reality might have been different, and (3) that possible difference is to be understood in terms of a plurality of alternatives. I reply that (1) and (2) aren’t both right. Which one is wrong depends on whether we choose to take ‘reality’ as a blanket term for everything, or as yet another word for the this-worldly part of everything. That choice may be left unmade.43

Although I am sympathetic to the general sentiment underlying the argument Skyrms sketches as reported by Lewis, I do not endorse the argument. Like Lewis, I accept (3) and think that (1) and (2) are not both right. Unlike Lewis, however, I doubt that it is open to us to choose to take ‘reality’ so as to make (1) true, for I doubt that the phrase ‘the totality of everything’ is meaningful as intended.44 The word ‘everything’ is a word of universal quantiﬁcation and as such its interpretation is relative to the domain over which it ranges. In (1) ‘everything’ is clearly intended to range over a unique all-inclusive domain that is not restricted in any way at all. I do not think such a domain is available. Thus, I reject (1) as meaningless. The basic idea behind the argument Skyrms sketches, however, is salvageable. It should be regimented along the following lines: (10 ) Metaphysical space is the totality of all metaphysically possible worlds. (20 ) Metaphysical space might have been different. 41 I thus disagree with John Divers, who reduces locutions of the forms, ‘L is possibly φ’ and ‘L is necessarily φ’, where ‘L’ stands for logical space, to ‘L is φ’. According to Divers, possibility talk and necessity talk about L are nothing more than non-modal factual talk. According to me, they are genuinely modal—or genuinely ‘u¨ber modal’ or ‘extra modal’ or ‘meta-modal’—and call for the postulation of alternatives to L. 42 Skyrms 1976: 331–2. 43 Lewis 1986: 100–1 n. 1. 44 I am not the only one to have this doubt. See e.g. Grim 1991. Also recall our discussion in 3.3.

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This is a particular instance of a more general argument form which is required for the regress argument Skyrms has in mind. Metaphysical possibility is but one of many kinds of possibility, and there is no one kind of possibility that embraces all worlds. For any kind of possibility K, the totality of K-possible worlds (which we may call K-space) could possibly be otherwise. The ‘possibly’ here points to a different kind of possibility, K’, giving rise to K’-possible worlds. The totality of K’-possible worlds (which we may call K’-space) could possibly be otherwise, pointing to yet another kind of possibility K’’ and giving rise to K’’-possible worlds. And so on. Thus, the general form of the Skyrmsian argument is as follows: For any K, (I) K-space is the totality of all K-possible worlds. (II) K-space might have been different. (III) Possible difference is to be understood in terms of a plurality of alternatives. It might be objected that some K has a special status and is all-embracing. It might be suggested that the doxastic is such. The idea is that for sufﬁciently inclusive K, such as the metaphysical or the logical, the sense of ‘might have been’ in (II) is captured only by the doxastic. Certainly, the idea continues, if we take K to be the doxastic, the possibility (II) deals in has to be doxastic in kind as well. Any totality of worlds could be believed to be otherwise; there is no substitute for ‘be believed to’ here. Consider the following sentence with a gap: Any totality of worlds could . . . be otherwise. If we ﬁll the gap with ‘metaphysically possibly’, the result is false. If we ﬁll it with ‘logically possibly’, the result is false. The only ﬁller that makes it true is ‘doxastically possibly’ (‘be believed to’). This idea of the hegemony of doxa should be rejected. First, if ‘be believed to’ should work as a ﬁller of the gap, then ‘be conceived to’ or ‘be thought to’ will also work. So we do not need doxastic possibility for the task. Second and more importantly, it would be incoherent to say that (i) the totality of doxastically possible worlds could be believed to be otherwise and (ii) the possible difference is to be understood in terms of a plurality of alternatives. The kind of possibility in question according to which the totality of doxastically possible worlds could be believed to be otherwise is not itself doxastic possibility, on pain of paradox. It is instead metadoxastic possibility. It is like doxastic possibility except that it concerns alternatives to all doxastic possibilities. There is no reason to stop with meta-doxastic possibility. There will be meta-meta-doxastic possibility, meta-meta-metadoxastic possibility, and so on. Replacing talk of doxastic possibility with talk

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of conceivability or thinkability will not alter the big picture. We will need to distinguish levels of conceivability or thinkability: the ground level, the metalevel, the meta-meta-level, and so on. Skyrms is arguing against modal realism, embodied in (3), by reductio. He thinks that the regress is absurd. I do not. I think the regress is unavoidable and should be embraced by any modal realist. The system of modal spaces (K-spaces, for different Ks) is hierarchical and complicated. I confess that I do not understand it completely. Lack of complete understanding, however, is not the same as absurdity. It is impetus for further investigation. 8 . 9. THE NECESSARY A POSTERIORI Consider the following version of a well-known argument for the claim that no metaphysically necessarily true proposition is a posteriori: (29) If P is metaphysically necessarily true, then P is true at every metaphysically possible world. (30) Every conceivable world is a metaphysically possible world. (31) If P is true at every metaphysically possible world, then P is true at every conceivable world. (32) If P is true at every conceivable world, then P can be known to be true a priori. (33) If P can be known to be true a priori, then P is not a posteriori. (34) If P is metaphysically necessarily true, then P is not a posteriori. (31) follows from (30), and (34) follows from (29), (31), (32), and (33). The argument is thus valid, but many philosophers consider it unsuccessful. They do not think the premises are entirely true and therefore deny the soundness of the argument. I agree with them. Some of these philosophers reject (31), and others (32). I reject (31), not (32). (30) entails (31). So I am committed to rejecting (30). Such a position is not new.45 But the correct understanding of this position has been hindered by a confusion about the lessons of the two famous ideas Kripke proposed concerning our practice of conceiving a world. We need to clear the confusion and place the rejection of (30) in the proper perspective. Only then can the rejection be adequately assessed. If a proposition is actually false, then it is metaphysically possible for it to be false; actuality entails metaphysical possibility. But if a proposition is not actually false, it may or may not be metaphysically possible for it to be false. One way to try to see that it is metaphysically possible for a particular true proposition to be false might be said to be to conceive a world at which it is false; conceiving might 45

See e.g. Hill and McLaughlin 1999.

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be said to be a road to non-actual metaphysical possibility. (I am not suggesting that conceiving might be said to be a road that is certain to lead to non-actual metaphysical possibility. See the next section.46) (I myself do not believe that conceiving has any weight for establishing metaphysical possibility. This will become clear shortly.) Let P be the proposition that Hesperus is Phosphorus. Alternatively, we may let P be the proposition that water is H2O. Either choice will do in what follows. P is actually true, so it is not actually false. Is P metaphysically possibly false? Many thought so prior to Kripke’s Naming and Necessity. Their more or less implicit reasoning was to assume (29)–(33) and argue further as follows: (35) (36) (37) (38) (39)

P is a posteriori. P cannot be known to be true a priori. P is false at some conceivable world. P is false at some metaphysically possible world. P is not metaphysically necessarily true.

(33) and (35) entail (36), (32) and (36) entail (37), (31) and (37) entail (38), and (29) and (38) entail (39), all by modus tollens. Alternatively, since (29)–(33) entail (34), we may simply say that (34) and (35) entail (39). By rejecting (32), Kripke breaks this chain of reasoning, and in particular, he blocks the path to (37). But intuitively (37) appears true; it appears that it is conceivable that Hesperus is not Phosphorus, and that it is conceivable that water is not H2O. Were astronomers not conceiving some such world before the discovery of the identity of Hesperus and Phosphorus with Venus when pondering over the 46 We need to distinguish conceivedness from conceivability. The former may be said to be a fallible epistemic tool for non-actual metaphysical possibility, whereas the latter has a conceptual link to a priority, as articulated in (32). It is obvious that conceivedness has no conceptual link to a priority along the lines of (32), for ‘P is true at every conceived world’ obviously does not entail ‘P can be known to be true a priori ’ (it does not even entail ‘P can be known to be true’), and few have claimed that it does. Conceivability, on the other hand, is routinely assumed to have deep epistemic importance. But ironically, when clearly distinguished from conceivedness, conceivability is not particularly useful in modal epistemology, because of its very modal nature. In order for conceivability to have any epistemic use that goes beyond piggybacking on conceivedness, we should be able to realize, for something that we do not actually but could metaphysically possibly conceive, that we could possibly conceive it. Suppose that P is false, is not conceived by us to be true, but is metaphysically possible to be true. Under those circumstances, if we are to see that it is conceivable that P is true, then for some proposition Q, (i) Q entails that it is conceived by us that P is true, (ii) Q is not true, and (iii) we need to see that Q is metaphysically possibly true. But this is just another case of a proposition which is not true and which we need to see to be metaphysically possibly true. At this point, we either resort to conceivedness or stick with conceivability. If the former, we may as well start with conceivedness at the outset (by actually conceiving P to be true), bypassing conceivability altogether. If the latter, then for yet another proposition R, (i) R entails that it is conceived by us that Q is metaphysically possibly true, (ii) R is not true, (iii) we need to see that R is metaphysically possible to be true. We will then be faced with the choice of going with conceivedness or conceivability all over again, concerning R. Unless we opt for conceivedness at some point in this series, we will not be able to stop the series and see that it is metaphysically possible for P to be true.

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identity of Hesperus and Phosphorus? Were chemists not conceiving some such world before the discovery of the atomic structure of water when pondering over the nature of water? The answer to such a question is intuitively overwhelmingly in the afﬁrmative. Kripke needs somehow to explain away this intuitively very strong appearance of the truth of (37). This is where he introduces the idea of misdescribing a world.

8.9.1. Misdescribing a world Even those who think that conceiving is a road to non-actual metaphysical possibility will not deny that it is not always a smooth road. Nor will they deny that the road is not guaranteed to lead to the destination. Suppose that you reason as follows: ‘I conceive that P. What I conceive is metaphysically possible. So it is metaphysically possible that P.’ You may or may not be right. There are a number of ways in which you may go wrong. For example, you may be wrong in thinking that what you conceive is metaphysically possible; your conceiving may outstrip metaphysical possibility. Or you may be wrong in thinking that you conceive that P; you may indeed conceive something but it is not that P that you conceive. We focus on this second way of going astray in this section. It is Kripke who brought its importance to our attention. He uses it to defend a number of modal claims. Take his thesis of the necessity of identity, for example. People pre-theoretically tend to think that even though Hesperus and Phosphorus are identical, it is metaphysically possible for Hesperus and Phosphorus to be distinct (‘Hesperus and Phosphorus could possibly have been distinct’), for they think that they readily conceive a metaphysically possible world at which Hesperus and Phosphorus are distinct. Kripke says this is a mistake and points out that when people think they are conceiving a metaphysically possible world at which Hesperus and Phosphorus are distinct, they are indeed succeeding in conceiving a metaphysically possible world but whatever metaphysically possible world they are conceiving is not one at which Hesperus and Phosphorus are distinct but one at which some pair other than the pair {Hesperus, Phosphorus} has the overall appearance of the pair {Hesperus, Phosphorus} and is a pair of distinct objects. Such a pair of distinct objects is an epistemic counterpart of the pair {Hesperus, Phosphorus}. According to Kripke, if people are genuinely conceiving a metaphysically possible world at which Hesperus and Phosphorus are a certain way, then it is a metaphysically possible world at which Hesperus and Phosphorus are not distinct. People readily confuse themselves, on Kripke’s account, by conceiving a metaphysically possible world at which some epistemic counterparts of Hesperus and Phosphorus which are distinct from each other are a certain way and thinking that this shows the metaphysical possibility of the distinctness of Hesperus and Phosphorus. It is important to note that Kripke’s denial of the distinctness of Hesperus and Phosphorus at whatever metaphysically possible

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world people are conceiving is grounded in a certain ﬁrm pre-theoretical intuition. The intuition is the modal intuition that given the actual identity of Hesperus and Phosphorus, they could not metaphysically possibly be distinct. If they could not metaphysically possibly be distinct, then at no metaphysically possible world are they distinct. According to Kripke, this pre-theoretical modal intuition wins over the other pre-theoretical intuition people tend to profess to have about conceiving, namely, the intuition that they succeed in conceiving that Hesperus and Phosphorus are distinct. This intuition, when combined with the thesis that whatever is conceived is metaphysically possible, supports the metaphysical possibility of the distinctness of Hesperus and Phosphorus. This mistake, on Kripke’s diagnosis, stems from a confusion about the semantic status of the two names ‘Hesperus’ and ‘Phosphorus’. They are non-descriptive rigid designators but are easily mistaken to be descriptive and non-rigid. Let us switch to the other example. In defending his thesis that it is metaphysically necessary that water is H2O, Kripke says that when people pre-theoretically think they are conceiving a metaphysically possible world at which water is XYZ (and not H2O), they are successfully conceiving a metaphysically possible world but whatever metaphysically possible world they are conceiving is not one at which water is XYZ but one at which something other than water—some epistemic counterpart of water—has the macro-properties of water and is XYZ. As before, Kripke’s denial of water being XYZ at whatever metaphysically possible world people are conceiving is grounded in the competing superior intuition that, given that water is in fact H2O, it could not metaphysically possibly be XYZ. The intuition is superior, according to Kripke, for it is semantically better informed about the rigidity of ‘water’ and ‘H2O’. If water could not metaphysically possibly be XYZ, then at no metaphysically possible world is it XYZ. Schematically, the truth according to Kripke about the situations like the Hesperus-Phosphorus case and the water-H2O case is characterized by the following claims: (40) X thinks that she is conceiving a metaphysically possible world at which P.47 (41) X is conceiving a metaphysically possible world. (42) At no metaphysically possible world, P. (43) X is not conceiving a metaphysically possible world at which P. (44) X is conceiving a metaphysically possible world at which Q. (40) attributes to X, a typical holder of the pre-theoretical intuitions, two opinions:

47 We are assuming the most charitable reading of ‘thinks’ here. We are assuming that in thinking, X is clear-headed, fully focused, not self-deceiving, etc.

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(A) that she is conceiving a metaphysically possible world; (B) that whatever metaphysically possible world she is conceiving is one at which P.48 (B) depends on (A) in the sense that if (A) is false, (B) is at best vacuous. (A), however, does not depend on (B). (A) may be true without (B) being true, and Kripke’s position is that this is indeed the case; (A) is true and (B) false. (42) provides the key reason for holding that (B) is false and is itself based on a semantically informed intuition. X misdescribes the metaphysically possible world she is conceiving. It is not a metaphysically possible world at which P but is a metaphysically possible world at which Q, where Q involves an epistemic counterpart or counterparts of the object(s)/stuff involved in P.49

8.9.2. Stipulating a world Kripke has also given us another way of looking at modal matters, which yields a different picture from the one presented in the preceding section. The two pictures are in tension. When we conceive a world, certain matters are up to us, while others are not. It is not up to us to do something metaphysically impossible for us to do. So, it is not up to us to do the following two things at once: to conceive a world at which P is true, and to refrain from conceiving a world at which P is true. It is also not up to us to conceive a world at which P is true, while P is true at no world we can conceive. On the other hand, there are many things which are up to us when conceiving a world, and one of them is singled out by Kripke for special emphasis. Assume that P is a singular proposition about a particular individual and is expressed by a sentence of the form ‘Æ is ç’, where our use of ‘Æ’ refers to the individual in question rigidly. Then according to Kripke, what is up to us when we conceive a world is the de-re-ness concerning Æ; it is up to us that it is Æ that we are conceiving to be ç at whatever world we are conceiving. It is a consequence of this that, whatever world we are conceiving, it is Æ, rather than some other individual (for example, an epistemic counterpart of Æ), that is ç at that world. The usual way to put this is to say that we stipulate that it is Æ that is ç at whatever world we are conceiving, rather than discovering it.50 Take Æ to be Hesperus and being ç to be being farther away from the sun than Earth is. Then according to this stipulation view of conceiving a world, when people who are competent users of the proper name ‘Hesperus’ think they are conceiving a world at which Hesperus is farther away from the sun than Earth is by saying to 48

Assume that she knows she is not conceiving any other kind of world. Many followers of Kripke have repeated this line of thought. One of the more recent examples is Daniel Stoljar: ‘Is it likewise imaginable that water is not H2O? I think not. As Kripke argued, it is not at all clear that we can imagine water not being H2O’ (Stoljar 2006: 13; his emphasis). 50 We discussed this in another context in 6.9. 49

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themselves, ‘Hesperus is farther away from the sun than Earth is’, they succeed in conceiving a world at which it is Hesperus rather than something else—say Mars—that is farther away from the sun than Earth is. Kripke’s insight is that the success of such a de re conception is guaranteed by stipulation, rather than being discovered by close scrutiny of the qualitative characteristics of the objects at the conceived world. In effect, the conceiver’s sincerely saying to herself, ‘Hesperus is . . . ’, with all her linguistic competence with the name intact and in force, guarantees that it is Hesperus that is being conceived as being thus-and-so. What goes for ‘Hesperus’ goes for ‘Phosphorus’. Someone with linguistic competence with both of these proper names but with limited knowledge of astronomy may say to herself, ‘Suppose Hesperus is distinct from Phosphorus’, and think that she is conceiving a world at which Hesperus is distinct from Phosphorus. According to the stipulation view, she succeeds in conceiving a world at which Hesperus and Phosphorus are such that they are distinct from each other, by stipulation. Since, as we saw in the last section, our superior intuition tells us that Hesperus and Phosphorus are such that they could not metaphysically possibly be distinct from each other, she does not succeed in conceiving a metaphysically possible world at which Hesperus and Phosphorus are such that they are distinct from each other. From this it follows that if, as the stipulation view says, she does succeed in conceiving a world at which Hesperus and Phosphorus are such that they are distinct from each other, then she must be conceiving a world which is not a metaphysically possible world. Whatever world she succeeds in conceiving is a metaphysically impossible world. The case of water being H2O is similar, except that we have natural-kind terms instead of proper names of individuals. In saying to herself, ‘Suppose water is not H2O’, someone who has linguistic competence with ‘water’ and ‘H2O’ thinks she is conceiving a world at which water and H2O are such that the former is not the latter. On the stipulation view, she is successful in conceiving a world at which water and H2O are such that the former is not the latter. But water is H2O (if it exists) at every metaphysically possible world, according to our superior intuition. So, whatever world she succeeds in conceiving is a metaphysically impossible world.51 When we stipulate that it is Æ that is ç at whatever world we are conceiving, we are also stipulating that it is ç that Æ is at whatever world we are conceiving. It is as much up to us to stipulate that it is ç-ness that we are concerned with as it is up to us to stipulate that it is Æ that we are concerned with. Here are two reasons to support this view. First, there is an easy way to reach the property of being distinct from Phosphorus once we reach Hesperus to begin with. Suppose we reach Hesperus. Then, since reaching Phosphorus by stipulation is as easy as 51 Hilary Putnam has endorsed this line of thought: ‘it is conceivable that water isn’t H2O. It is conceivable but it isn’t possible! Conceivability is no proof of possibility’ (1973: 79). More recently, Scott Soames (2005) expressed his sympathy with the same line of thought.

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reaching Hesperus by stipulation, we reach Phosphorus. From there it is easy to reach the property of being Phosphorus, and once we reach that property, its negation is a small easy step away. Second, ‘Æ’ need not be a singular term. The natural-kind term ‘water’ may or may not be a singular term. Even if it is not a singular term, we seem to be able to reach water by stipulation as well as we can reach Hesperus by stipulation. But once we reach water, it is easy to reach the property of being water and the property of being a sample of water. And if we can reach one general property like that (i.e. a property which is not of the form ‘being identical with such-and-such an individual’), there seems no reason why we can’t reach other similar general properties. This is not conﬁned to the properties expressed by means of natural-kind terms. Let ‘Æ’ be ‘a pencil’ and ‘ç’ be ‘a prime minister’, for example. Someone might think that she is conceiving that a pencil is a prime minister. If, as a result of this, she is genuinely conceiving a world at which a pencil is a prime minister, and if no pencil is a prime minister at any metaphysically possible world, then she is conceiving a metaphysically impossible world. This brings out the insigniﬁcance of the distinction between ‘Æ’ and ‘ç’. Non-metalinguistically put, this means that it is not just what individual(s) the conceiver is conceiving but also any other part (as it were) of what is conceived that is subject to stipulation. In other words, the identity of the content of what is conceived in its entirety (as it were) is subject to stipulation. But we need to be careful here. If the stipulation view is correct in this general way, then why can’t we just stipulate that it is a metaphysically possible world, rather than a metaphysically impossible world, that we are conceiving? The answer is that the stipulation view does not extend to the modal properties of what is conceived; the content of what one conceives is subject to one’s stipulation, for one is free to choose which content to conceive, but the modal properties of what one conceives are not, for one is not free to choose which modal properties what one chooses to conceive is to have. This does not mean that one cannot conceive the truth of a proposition whose content deals in modality, for example, the proposition that water is not metaphysically necessarily H2O. What is not up to one is whether in doing so one is conceiving a metaphysically possible world at which (or a local metaphysical space in which52) water is not metaphysically necessarily H2O. The situation is schematically characterized as follows: (45) Concerning Æ, X thinks that she is conceiving a metaphysically possible world at which it is ç. (46) Concerning Æ, X is conceiving a world at which it is ç. (47) Concerning Æ, at no metaphysically possible world, is it ç. (48) X is conceiving a metaphysically impossible world.

52

See 8.5–7 and 8.10.

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The stipulative nature of whatever world X is conceiving is supposed to yield (46) from (45). This schematic characterization, (45)–(48), is at odds with the earlier schematic characterization, (40)–(44). Compare ‘P’ in (40)–(44) to ‘it (Æ) is ç’ in (45)–(48). We see that (41) and (48) are in conﬂict. In the earlier case, the integrity of the content (P) is sacriﬁced to preserve the metaphysical possibility of the conceived world, whereas in the current case, the metaphysical possibility of the conceived world is sacriﬁced to preserve the integrity of the content (Æ is ç). In both cases, X’s success in conceiving some world is preserved.

8.9.3. Reconciliation Kripke does not confront this tension explicitly but seems to be inclined to defend the misdescription view of the conceived content over the stipulation view of de re conceiving whenever the two come into conﬂict. The stipulation view allows us to stipulate that we conceive of an individual that it is thus-and-so, where the individual is actually not thus-and-so. One way to make sure that we have de re access to the individual for our conceiving is to have the individual available for ostension and use a demonstrative pronoun to refer to it. This is a more direct way to secure de re access to the individual than relying on the use of a proper name without the availability of the individual for ostension. Even when de re access to the individual is secured by means of ostension, however, Kripke seems to favor the misdescription view over the stipulation view. Here is a representative passage: In the case of this table, [original footnote: Of course I was pointing to a wooden table in the room.] we may not know what block of wood the table came from. Now could this table have been made from a completely different block of wood . . . ? . . . though we can imagine making a table out of another block of wood . . . identical in appearance with this one, and though we could have put it in this very position in the room, it seems to me that this is not to imagine this table as made of wood . . . , but rather it is to imagine another table, resembling this one in all external details, made of another block of wood . . . 53

According to Kripke, we cannot imagine that table—the table he was pointing to—to be made from a completely different block of wood, no matter how hard we may try. This is a repudiation of the stipulation that the content of our imagination be that that table is made from a completely different block of wood. Why does Kripke undermine the stipulation view he argues for so eagerly elsewhere in the same book? The reason is not hard to see. There is an implicit but crucial constraint that is operative in all of his discussion of modality. It is our modal intuition about metaphysical possibility. Whatever else we may be doing in conceiving a situation involving that table, we are supposed to be conceiving a world which is deemed metaphysical possible by our modal intuition. This 53

Kripke 1980: 113–14; his emphasis.

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constraint restricts the content of what we are conceiving. If we appear to conceive that that table is made from a completely different block of wood, the appearance has to yield to an alternative construal of the content of the conception, because the truth of such a content is not ﬁt for a metaphysically possible world according to our modal intuition. Since it is uncontroversial that we are conceiving something,54 the only way to make sense of what we are doing is to say that what we are conceiving has a different content. The easiest way to do so is to say that we are conceiving that a different table resembling that table is made from a completely different block of wood. According to Kripke, our modal intuition underlies all our discussions concerning matters modal and operates as the arch-constraint on them. We may stipulate that it is Humphrey that we are conceiving as being the winner, or that it is the property of being the winner that we are conceiving as being possessed by Humphrey. We are allowed to do this because our modal intuition does not stand in the way of such a stipulation. We may not stipulate that it is Humphrey that we are conceiving as being a poached egg, or that it is the property of being a poached egg that we are conceiving as being possessed by Humphrey. Our modal intuition stands in the way of such a stipulation. Thus, the general Kripkean picture is this: we may stipulate a particular individual or property as our subject matter in our conceiving if and only if our modal intuition does not stand in the way. If our modal intuition says that Æ is metaphysically possibly ç, then we are free to stipulate that we conceive of Æ that it is ç, i.e. we are free to conceive a metaphysically possible world at which Æ is ç. If our modal intuition says that Æ is not metaphysically possibly ç, then no matter how hard we may try, we will not succeed in conceiving, by stipulation or otherwise, a metaphysically possible world at which Æ is ç. But in many such cases, we nonetheless succeed in conceiving a metaphysically possible world. Since it is not a metaphysically possible world at which Æ is ç (for example, Hesperus is distinct from Phosphorus), it is a metaphysically possible world at which some other situation holds, say, is ç (for example, Mars appears in such-and-such a position in the sky at dusk and is distinct from Phosphorus). Once we see that this is what is happening when Kripke overrides the stipulation view in favor of the misdescription view, it is easy to see that there is also an element of arbitrariness in this whole situation. Even given that we should respect our modal intuition as much as Kripke does and allow it to operate as an important constraint on our conceiving of worlds, the last step in the above summary of the Kripkean reasoning is without justiﬁcation. That is, it remains unjustiﬁed to require that we should uphold the metaphysical possibility of the conceived world at the expense of the presumed content. Such a move is 54 There is theoretical room for the suggestion that we are not conceiving anything, or more accurately, there is no content to our conceiving. I know of no concrete proposal along those lines and am inclined to believe the theoretical room to be so small as to be negligible.

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simply a manifestation of a bias in favor of the misdescription view over the stipulation view, which is further rooted in a deeper bias in favor of the metaphysically possible over the metaphysically impossible. An alternative is to uphold the presumed content at the expense of the metaphysical possibility of the conceived world. That is, instead of saying that what is conceived is a metaphysically possible world at which is ç, say that what is conceived is a metaphysically impossible world at which Æ is ç. This alternative is no less justiﬁed and no less viable than the Kripkean way and has as much right to be taken seriously. In general, when we naively engage ourselves in an act of conceiving a counterfactual situation, we may have a choice of abiding by one or the other of two constraints: the constraint that what we conceive is to be metaphysically possible, and the constraint that the content of what we conceive is to be what we originally think it is. We may choose to abide by the ﬁrst constraint and say that we are really conceiving a situation alternative to the original and involving an epistemic counterpart of the original res, or we may choose to abide by the second constraint and say that we are indeed conceiving the situation we originally thought we were conceiving, which turns out to be a metaphysically impossible situation. This might be said to reveal a deeper sense of what is up to us as a matter of stipulation; we may stipulate which of the two constraints is operative and which is not. The two constraints, however, may not be on a par with each other. Our pre-theoretical modal intuition does not favor the misdescription view over the stipulation view. The stipulation view does not ﬂout our pre-theoretical intuition.55 And the fact that the stipulation view, unlike the misdescription view, does not charge us with making a mistake in describing the content of what we are conceiving but instead preserves the apparent content of our conceiving makes the stipulation view more advantageous. One obvious unfortunate consequence of this for Kripke’s purposes in Naming and Necessity is that his argument against the mind–body identity theory is weakened. When we apparently imagine that water is not H2O, we may indeed be imagining about water that it is not H2O—rather than imagining about an epistemic counterpart of water that it is not H2O—despite the fact that it is metaphysically impossible for water not to be H2O. Likewise, when we apparently imagine that pain is not C-ﬁber ﬁring, we may indeed be imagining that pain is not C-ﬁber ﬁring, despite the fact that it is metaphysically impossible for pain not to be C-ﬁber ﬁring.

55 John Divers, after echoing Kripke’s point that David ‘Kaplan makes a mistake in holding that facts about transworld identity must be discovered rather than stipulated’, says that even though we can stipulate that we speak of Socrates when we make de re predications of the form ‘Socrates is F at a world w’, we ‘do not thereby make it the case, nor do [we] come to know, that such a world is a possible world ’ (Divers 2002: 273). This is a sentiment with which I sympathize.

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8.9.4. Two-dimensional interlude The mock Hegelian mini-dialectic above has a minor complication, which is due to two-dimensional semantics. We shall take a closer look at two-dimensional semantics later, but for now an abbreviated characterization of its core tenet should sufﬁce. The two-dimensional semantic view concerning the necessary a posteriori may be summarized as follows. The microstructure of water is to be known a posteriori, if known at all. This means that competing alternative microstructures of water are conceivable.56 So, (C) Some world at which water is H2O is conceivable, and some world at which water is XYZ is conceivable. A posteriori investigations reveal the microstructure of water, and the result might turn out to be that: (D) Either (1) water is H2O at the actual world, or (2) water is XYZ at the actual world, or (3) water does not have a uniform microstructure at the actual world, a` la jade, and is, say, half H2O and half XYZ. Suppose (1) is the case. Then water is H2O and all worlds at which water is XYZ are metaphysically impossible worlds. If (C) is true, some world at which water is XYZ is conceivable. So, if (C) is true, some conceivable world is a metaphysically impossible world. But, on two-dimensionalism, whatever is conceivable is metaphysically possible. Therefore, (C) is false. In particular, when we think that we conceive a world at which water is XYZ, we are really conceiving a world at which the watery stuff—i.e. the stuff that is colorless, is odorless, is thirst-quenching, ﬁlls lakes, rivers, and oceans, and falls from the sky as rain, etc.—is XYZ. At the same time, two-dimensionalists crucially say that (C) is ambiguous and the reasoning just given applies to (C) only under one interpretation. The ambiguity arises from the ambiguity of a particular expression in (C), namely, the term ‘water’. The interpretation of ‘water’ in question is the Kripkean interpretation, which makes it a non-descriptive rigid natural-kind term. Under the other interpretation, ‘water’ is semantically equivalent to ‘the watery stuff ’, which makes the term descriptive and non-rigid. Under this second interpretation, (C) is true. Again, whatever is conceivable is metaphysically possible. So, when we conceive that water in this sense—i.e. the watery stuff—is XYZ, we are conceiving a metaphysically possible world.57 56 Two-dimensionalists speak of conceivability instead of conceiving. This is forced on them by their own insistence on linking a posteriority with conceivable alternative hypotheses; it would be obviously indefensible to link a posteriority with conceived alternative hypotheses. As we noted earlier in n. 46, it is conceiving rather than conceivability that guides us on matters of possibility. Fortunately, this issue will not affect our discussion. 57 According to some two-dimensionalists, one does not conceive a world unless one conceives it clearly and distinctly. What this amounts to is explained in Chalmers 2002.

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Suppose (2) is the case. Then water is XYZ and all worlds at which water is H2O are metaphysically impossible. If (C) is true, some world at which water is H2O is conceivable. So, if (C) is true, some conceivable world is a metaphysically impossible world. But whatever is conceivable is possible. Therefore, (C) is false. But again, according to two-dimensionalism, this is so only in the ﬁrst of the two senses of ‘water’; (C) is true in the second sense. When we think we are conceiving a world at which water is H2O, we are really conceiving a world at which the watery stuff is H2O and we are conceiving a metaphysically possible world. Suppose (3) is the case. Then some water is H2O and some water is XYZ, and water as such lacks any essential microstructure. So the two kinds of conceivable worlds reported in (C) are both metaphysically possible worlds. This scenario does not include metaphysically impossible worlds, undermines the ﬁrst sense of ‘water’, and gives strong support for the synonymy of ‘water’ and ‘the watery stuff ’. This two-dimensionalist picture systematically and without further justiﬁcation favors the constraint of metaphysical possibility at the expense of the constraint of content stipulation. Once we realize this and contemplate the alternative, we come to the following way of systematically favoring the other constraint. Suppose (1) is the case. Then water is H2O and all worlds at which water is XYZ are metaphysically impossible worlds. If (C) is true, some world at which water is XYZ is conceivable. (C) speciﬁes the content of what is conceivable accurately. Therefore, some conceivable world is a metaphysically impossible world. No ambiguity is postulated for (C). The reasoning is exactly parallel under the supposition that (2) is the case. The scenario (3) again does not raise any new issue with metaphysically impossible worlds. Thus, we see that we may perfectly well choose to embrace metaphysically impossible worlds, whether in the face of the Kripkean picture or in the face of the two-dimensionalist picture. Let us remind ourselves that in many cases this is clearly the right choice to make. The reductio ad absurdum reasoning is a good example where the priority of the constraint of content stipulation should be sustained: ‘Suppose that some bachelor is married. Call any such bachelor B. B is a bachelor who is married, i.e. B is a bachelor and B is married. Since B is a bachelor, B is unmarried. So, B is married and is unmarried, which is absurd. Therefore no bachelor is married.’ When we make the initial supposition for reductio, we are conceiving that some bachelor is married. The constraint of content stipulation must be in effect, for otherwise, the content of the supposition is not guaranteed to be the opposite of the conclusion to be established, and the integrity of the reductio reasoning demands such a guarantee. David Chalmers, a leading advocate of two-dimensionalism, famously argues for the conceivability of a zombie world, and from that to the logical possibility of a zombie world, and from that to property dualism. To the objection that conceivability does not entail logical possibility, Chalmers responds that it does as a matter of deﬁnition. Chalmers deﬁnes ‘Logically possibly P’ to mean that it is conceivable that P. To the objection that logical possibility of a zombie world

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does not entail property dualism, Chalmers responds by appealing to the philosophical need for logically possible worlds in grounding the semantics for counterfactual conditionals and providing the contents of our propositional attitudes.58 We shall not discuss extensively how responsive Chalmers is to the objections. Instead we note that his response to the ﬁrst objection is rendered ineffective precisely due to the conﬂation—by deﬁnition!—of conceivability and logical possibility. The worlds used by Stalnaker and Lewis in their semantics for counterfactual conditionals include not just conceivable worlds and they also do not include all conceivable worlds. As for providing the contents of propositional attitudes, we certainly need conceivable worlds, but that is because they are as unconstrained by metaphysical and logical laws as our attitudes are allowed to be. If this is made implausible by Chalmers’s deﬁnition of the phrase ‘logically possible’, that is because the deﬁnition is a purely stipulative deﬁnition disconnected from the use of ‘logically possible’ by most modal metaphysicians. Unlike Kripke’s argument against identity theory, which invites us to imagine a mental state without the corresponding physical state, Chalmers’s argument against materialism invites us to imagine a physical state without the corresponding mental state. Despite this difference, Chalmers’s argument is as vulnerable as Kripke’s.59 Josh Parsons defends the claim that physical objects ‘entend ’, i.e. ﬁll space by being wholly located at each of several places, by holding that some things extend in space without having spatial parts. To the objection that it is metaphysically impossible that something should extend without having parts, Parsons responds by saying that it is conceived by him and some other metaphysicians—hence it is conceivable—that some things extend without having parts.60 This is basically the same mistake as the one Chalmers makes. That Parsons, or anyone else, conceives that P does not entail—nor does it offer conclusive, or even overwhelming, evidence in favor of—the metaphysical possibility of P. If it did, anyone with any possibility claim could bolster his own claim by making and discussing the claim, for making and discussing a claim involves conceiving the claim.

8.9.5. Kripkean stipulations again Suppose that we stipulate in the Kripkean spirit to consider a world w at which Hitler, that very man, is exactly half like his actual self and half like Stalin’s @-stage and at which nobody is more like Hitler’s @-stage or Stalin’s @-stage. In Chapter 6 we called such a man at w ‘Statler’. The stipulation identiﬁes Statler as Hitler. So identiﬁed, Hitler is a metaphysically impossible man. The reason is 58

Chalmers 1999. Chalmers seems to muddy the water by suggesting that there is something wrong with drawing the distinction between possibility and impossibility or the distinction between conceivability and inconceivability ‘at the level of worlds’. See his response in Chalmers 1999 to Hill and McLaughlin 1999. 60 Parsons 2000: 406. 59

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that whereas the identiﬁcation is to be underwritten by some sufﬁciently short chain of worlds under similarity connecting Hitler’s @-stage to Statler’s w-stage, there is an equally short chain of worlds under similarity connecting Stalin’s @-stage to Statler’s w-stage, which underwrites the identiﬁcation of Statler as Stalin rather than as Hitler. If Hitler, whose identity is underwritten by the ﬁrst chain, is a metaphysically possible man, then so is Stalin, whose identity is underwritten by the second chain. Then Hitler and Stalin could metaphysically possibly be identical. But given their actual distinctness, they could not metaphysically possibly be identical (assuming metaphysical necessity of identity). Therefore, Hitler as identiﬁed in our stipulation is a metaphysically impossible man. Similarly, Stalin as identiﬁed in the parallel fashion would be a metaphysically impossible man. But there appears to be something wrong here, for w seems like a perfectly metaphysically possible world as we initially described it by using the neutral name ‘Statler’ in Chapter 6. Either the Kripean stipulation that at w Hitler exists and is half like his actual self and half like Stalin’s @-stage and nobody is more like Hitler’s @-stage or Stalin’s @-stage is somehow faulty, or w is metaphysically impossible. If we respect the legitimacy and the force of the stipulation and consider the stipulation to be effective exactly as it is made, then we have no choice but to say that w is metaphysically impossible despite appearance. If, on the other hand, we are sufﬁciently impressed with the appearance and consider w to be a metaphysically possible world, then we have no choice but to say that the Kripkean stipulation is not effective exactly as it is made. In the latter case, the most plausible thing to say is that Statler is not Hitler, i.e. w is not a world at which Hitler is half like his actual self and half like Stalin’s @-stage and at which nobody is more like Hitler’s @-stage or Stalin’s @-stage. Rather, at w some man is half like Hitler’s @-stage and half like Stalin’s @-stage and nobody is more like Hitler’s @-stage or Stalin’s @stage. That man is neither Hitler nor Stalin. To the extent to which it is plausible to say this, we are limited in saying whatever we like in issuing a Kripkean stipulation of a metaphysically possible world. 8.10. MORE ON ALTERNATIVE METAPHYSICAL SPACES David Braddon-Mitchell and Frank Jackson say that there are two ways in which we may think about Twin Earth; either as a distant planet at the actual world or as a planet at a non-actual metaphysically possible world. They then say, ‘We will suppose that it is somewhere else in our world’, opting for the ﬁrst disjunct. Later in the same work they say, ‘Twin Earth does not actually exist’, denying the ﬁrst disjunct.61 They appear to be contradicting themselves in making these two 61

Braddon-Mitchell and Jackson 1996: 65–6, 75.

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pronouncements, the ﬁrst of which is a supposition and the second an assertion. If their assertion is true, then Twin Earth is not a distant planet at the actual world, and we should think of it as a planet at a non-actual metaphysically possible world. Assuming that Braddon-Mitchell and Jackson did not change their minds about the status of Twin Earth between the two pronouncements ten pages apart, is there any way to make their position consistent? This may sound like a frivolous question. Whether these authors are consistent on this issue hardly matters to their discussion in their book, and even if it somehow did, its consequences in the overall scheme of things in their book would be unlikely to be signiﬁcant. I ask this question not because the apparent inconsistency is of high importance in evaluating their work but because I think it helps us reveal a certain natural and almost irresistible way to think about metaphysical space and actuality which is antithetical to the standard way but which I think is the right way. The answer to the question is afﬁrmative, and by coming to grips with the way the afﬁrmative answer can be sustained, we will have yet another peek at alternative metaphysical spaces from a slightly different and perhaps a little more revealing angle. (49) Twin Earth actually exists. (50) Twin Earth does not actually exist. Supposing the truth of (49) while being committed to the truth of (50) is consistent. The standard way to maintain this is the easy way. It is to understand the actuality involved in (49) non-rigidly62 with an implicit existential quantiﬁcation over metaphysically possible worlds and the actuality involved in (50) rigidly. The supposition (49) will then be equivalent to the supposition that Twin Earth existsa at some metaphysically possible world, which is consistent with (50), which will mean that Twin Earth does not exista at @. But this is too easy. The more interesting interpretation of the question presupposes the understanding of the actuality involved in both (49) and (50) as uniformly rigid. Thus: (490 ) Twin Earth existsa at @. (500 ) Twin Earth does not exista at @. Is it consistent to assert (500 ) while supposing the truth of (490 )? I think it is indeed consistent. It is perfectly consistent to think that I have in fact swallowed a sugar pill but entertain the thought (for the sake of amusement) that I have in fact swallowed a hallucinogenic pill. Likewise, it is consistent to assert that Twin Earth does not exist at @ but suppose (for the sake of argument) that it does. What is interesting about this is that in order to make sense of the supposition of the truth of (490 ) in the presence of the commitment to the truth of (500 ), we need to envision metaphysically impossible worlds. Compare this case with a

62

As we did in 5.4 when we introduced the actuality modal tense.

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corresponding temporal case. Let us suppose that Earl and Pearl were born as twins, Earl died years ago, and Pearl now misses him. (51) Twin Earl lives now. (52) Twin Earl does not live now. Pearl asserts (52) but likes to daydream under the supposition of the truth of (51). There is nothing inconsistent about what Pearl does. When Pearl supposes that Twin Earl lives now, the content of her supposition is the proposition that Twin Earl lives now. The proposition is not true and Pearl knows it. So when Pearl makes her supposition, she is considering a non-actual world which she knows to be nonactual and at which the temporal index now is such that Twin Earl lives at it. The verbatim analog for the case of (490 ) and (500 ) is to say that when Braddon-Mitchell and Jackson make the supposition (490 ), they are considering a non-actual world which they know to be non-actual and at which the modal index @ is such that Twin Earth exists at it. To make sense of this, we need to make sense of what it is for a non-actual world to be such that Twin Earth exists at @. Since in our metaphysical space, Twin Earth does not exist at @ (as we assume), we need an alternative metaphysical space, a metaphysical space in which Twin Earth exists at @. For any such metaphysical space M, it is true to say of any world w in M that w ism such that Twin Earth exists at @ in M. When Braddon-Mitchell and Jackson suppose the truth of (490 ) while asserting (500 ), they are considering a non-local metaphysical space in which @ ism such that Twin Earth exists at @. This construal of their supposition teaches us that @ is not only among the metaphysically possible worlds in our local metaphysical space but also among worlds in different metaphysical spaces. @ is such that in some such non-local metaphysical space, Twin Earth exists at it. This is not unintelligible if we take the temporal analogy to heart and understand it along the lines of the present time t being such that, at a non-actual world, Twin Earl lives at t. One and the same time has different things happen at it at different worlds. One and the same world has different things obtain at it in different metaphysical spaces. To suppose the truth of (490 ) while being committed to the truth of (500 ) is to locate, under the mode of supposition, our local metaphysical space (non-rigidly understood) among those metaphysical spaces which are such that in them @ ism such that Twin Earth exists at it. Some might object that @, or any particular world, cannot be the subject of supposition de re. It is true that @ is not an individual, any more than a temporal moment is an individual. But @ is not nothing. It has being. It is subject to our conceiving, thinking, and reasoning. It is not at all surprising that our power of cogitation transcends individuals. Some might say that what is true at a world is essential to that world, i.e. that if P is true at w, then it is metaphysically necessary that P is true at w. If this is so, then the analogy with times is imperfect. What is true at a time t is not essential to t; it is metaphysically possible for 1968 to have been such that Humphrey won in it. I shall not argue that the analogy is perfect, for even if it is imperfect, the

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main thrust of our reasoning is intact. Metaphysical impossibility does not stand in the way of supposition-making. Even if (490 ) is metaphysically impossible, we may suppose its truth, just as well as we may start a reductio with a metaphysically necessary conclusion by supposing its negation. It is not hard to see that we cannot stop with alternative metaphysical spaces but must continue on, postulating alternative collections of metaphysical spaces, alternative collections of those collections, and so on. As with Skyrms’s regress, I do not consider this absurd. Regresses are not unfamiliar in metaphysics or epistemology. In the case of modal metaphysics, we are only beginning to glimpse the initial bit of a vast regressing series. 8 . 11 . TWO-DIMENSIONAL SEMANTICS AGAIN Two-dimensional semantics is foremost a thesis about linguistic meanings. It is a natural heir to the original intensionalist theory of meanings, according to which linguistic meanings are intensions, i.e. functions from possible worlds to extensions at those possible worlds. The original intensionalist theory is a onedimensional theory in the sense that intensions are mappings from worlds to extensions. By contrast, two-dimensionalism uses functions which are mappings from world-pairs to extensions. Two-dimensionalism has been attracting serious attention and increasing recognition in recent years. I claim that two-dimensionalism needs metaphysically impossible worlds. To understand two-dimensionalism, we need to start with Hilary Putnam’s thesis on meaning.63 After refusing to endorse any theory of what linguistic meanings of natural-kind terms are, Putnam makes a proposal about what it is to explain such meanings. Putnam’s insight is to shift our attention from the question of what kind of objects meanings are to the question of what is involved in the act of explaining meanings to those who do not know them—what he calls meaningexplanation.64 What constitutes the core of any meaning-explanation is a stereotype. A stereotype of X is a conventional idea, which may be inaccurate, of what X looks like or acts like or is like. Putnam suggests that such a conventional idea is associated with each natural-kind term and plays a crucial role in the meaning-explanation for the term.65 The stereotype of water is something like the following: ‘colorless, odorless, tasteless, drinkable liquid which falls from the sky as rain, ﬁlls oceans, rivers, and lakes, and pours out of faucets’.66 To explain the meaning of the term ‘water’, according to Putnam, we are supposed to produce a sample water clearly exhibiting the stereotypical features of water. We then say, pointing to the sample, 63 64 65 66

Putnam 1975: 229–35. Ibid. 230. Ibid. 249–50. The customary abbreviation for this long noun phrase is ‘watery stuff ’. See 8.9.4.

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‘All and only samples that are samples of the same liquid as this are samples of water’. If we produce an atypical sample of water and make the same proclamation, our meaning-explanation will be defective in an important way. The sense in which such a meaning-explanation will be defective is the sense in which knowledge of the meaning of ‘water’ involves knowledge of the stereotype of water. The same-liquid relation mentioned in the meaning-explanation is a theoretical relation of physical science, which may not be transparent to ordinary users of English but which plays a decisive role in determining the extension of ‘water’. Production of a sample of stereotypical water is an integral part of the Putnamian explanation of the meaning of ‘water’ and supports the indexical reference to the sample (‘the same liquid as this’) as being essential to the meaning-explanation. This is what Putnam calls the hidden indexicality of meaning. The stereotype of water does not determine the same-liquid relation. The chemical structure of water does; for any x, x is the same liquid as this sample if and only if x has the same chemical structure as this sample. For all we, competent speakers of English, know as competent speakers of English, the chemical structure of water may be anything at all. Linguistic competence at most requires us to know the stereotype of water. So, our knowledge of the stereotype of water is compatible with any one of the myriad ways the chemical structure of water might actually turn out to be. If it actually turns out to be one way, then the extension of ‘water’ is determined in terms of that particular chemical structure; for any x, x is a sample of water if and only if x has that particular chemical structure. Since the chemical structure of water is not an accidental feature of water, it is metaphysically necessarily the case that every sample of water has that same particular chemical structure. Two-dimensionalists take up Putnam’s meaning-explanation and push it further. Unlike Putnam, two-dimensionalists are eager to reintroduce meanings as entities, in particular, as functions to extensions. They believe that the lesson of Putnam’s hidden indexicality and the accompanying complications in meaningexplanation, like the invocation of the same-liquid relation for ‘water’, is that we should not aim for functions from worlds to extensions but instead aim for functions from ordered pairs of worlds to extensions. If all (or sufﬁciently many sufﬁciently important) stereotypical samples of water actually turn out to have a particular common chemical structure, then metaphysically necessarily, all samples of water have that chemical structure. If all (or sufﬁciently many sufﬁciently important) stereotypical samples of water actually turn out to have a different common chemical structure, then metaphysically necessarily, all samples of water have that different chemical structure. Thus, how the actual stereotypical samples of water turn out to be determines the intension of ‘water’. Two-dimensionalists consider this as warranting the reiﬁcation of the meaning of ‘water’ as a function which maps an ordered pair of worlds, <w1, w2>, to a set of samples at w2, where w1 is the world the actual world turns out to be, and w2 is a world in the domain of the intension according to the traditional one-dimensional

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semantics.67 We are not concerned with assessing the ultimate merits and demerits of two-dimensional semantics. We are instead interested in clarifying the modal metaphysical commitment it has. Before doing so, however, it is instructive to note one improvement twodimensionalism makes over Putnam’s view. Putnam famously argues that ‘Cats are animals’ is not analytic.68 He invites us to imagine that the individuals we have been calling ‘cats’ turn out to be robots controlled by space aliens from Mars. He then asks us to say whether under those imagined circumstances we would assert ‘There are no cats’ or we would assert ‘Cats are robots’. He expects us to say that we would assert ‘Cats are robots’ rather than ‘There are no cats’. I think he is right about this. He concludes from this that ‘Cats are animals’ is not analytic. I am inclined to agree with him on this as well but that is not important, as analyticity is not our focus of attention. Putnam draws another conclusion from the same thought experiment, namely, the conclusion that it is not metaphysically necessary that cats are animals. I, like many others, think this is a mistake. The reason is that his thought experiment is about what we would say if actuality turned out to be other than what (we assume) it in fact is. But falsity somewhere along this dimension of worlds (candidates for actuality) does not conﬂict with the metaphysical necessity of the proposition in question, for the latter is a matter of truth everywhere along the other dimension of metaphysically possible worlds as in intensions (as traditionally conceived). Two-dimensionalists are clear about this distinction, as they would readily acknowledge the metaphysical necessity of the proposition that cats are animals (assuming that stereotypical cats are actually animals), while at the same time claiming that if stereotypical cats turned out actually to be Martian robots then it would be metaphysically necessary that cats were robots, not animals. At the actual world, the universe is a certain deﬁnite way (except for microscopic quantum ﬂuctuations and matters of vagueness). In particular, either (every sample of ) stereotypical water has a certain deﬁnite chemical structure, which we shall designate schematically as ABC, or it is not the case that (every sample of ) stereotypical water has the chemical structure ABC. Suppose that stereotypical water actually has the chemical structure ABC. Note that we are not supposing that we know, or even believe, that stereotypical water has the chemical structure ABC, but only that it does have that structure. Two-dimensionalists invite us to consider various scenarios according to which the universe at the actual world is various ways concerning the chemical structure of stereotypical water. In one of the scenarios, stereotypical water has the chemical structure ABC at the actual world. Since we are supposing that stereotypical water does have this chemical structure actually, this scenario is the true scenario. 67 For the pioneering work on two-dimensionalism, see Davies and Humberstone 1980 and Stalnaker 1978, 1981, 1987. For an overview, see Chalmers 2006. 68 Putnam 1962.

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In other scenarios, stereotypical water does not have this chemical structure but has a different chemical structure (or does not have any chemical structure common to all samples) at the actual world. All these scenarios are false scenarios. Consider one such scenario, S, in which the actual world is a world at which stereotypical water exists and (every sample of) it has a chemical structure other than ABC. Let us assume with Putnam that the chemical structure of stuff like water is essential to the stuff. Since we are operating under the supposition that stereotypical water has the chemical structure ABC at the actual world, this means that it is metaphysically necessarily the case that stereotypical water has the chemical structure ABC. So, any world at which stereotypical water exists and has a chemical structure other than ABC is a metaphysically impossible world. Therefore, S is a scenario in which the actual world is a metaphysically impossible world. If, on the other hand, we suppose that stereotypical water actually has the chemical structure other than ABC, then the scenario which says that at the actual world stereotypical water exists and has the chemical structure ABC is a scenario in which the actual world is a metaphysically impossible world. Either way, in some scenario, the actual world is a metaphysically impossible world. (The third option, which says that at the actual world no chemical structure is sufﬁciently common to sufﬁciently many samples of stereotypical water, introduces a complication along the lines of the case of ‘jade’. The complication, however, is tangential to our concern and may be safely ignored here.) According to two-dimensionalists, knowledge of the linguistic meaning of ‘water’ involves knowledge of the intension of ‘water’ relative to the Putnamian explanation of the meaning of ‘water’ under each of the various scenarios concerning the stereotypical water and the actual world. This means that, according to two-dimensionalists, knowledge of the linguistic meaning of ‘water’ involves knowledge concerning metaphysically impossible worlds. Some might object to our reasoning as follows: According to two-dimensionalism, to say that stereotypical water actually has a certain particular chemical structure is simply to say that the colorless, odorless, tasteless, drinkable liquid which falls from the sky as rain, ﬁlls oceans, rivers, and lakes, and pours out of faucets actually has that structure. Now suppose that stereotypical water actually has the chemical structure ABC. This is to suppose that the colorless, odorless, . . . liquid . . . actually has the chemical structure ABC. It does not follow from this supposition that the colorless, odorless, . . . liquid . . . (if it exists) has the chemical structure ABC at every metaphysically possible world. This is so because the colorless, odorless, . . . liquid . . . is not the same natural stuff at some metaphysically possible worlds as it is at the actual world, and at such worlds the liquid would have a different chemical structure. But if so, it also does not follow from the same initial supposition that water (if it exists) has the chemical structure ABC at every metaphysically possible world. Thus, this crucial step in your reasoning is blocked.

This objection is confused and misconstrues two-dimensionalism. According to two-dimensionalism, if stereotypical water actually has a certain particular

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chemical structure (which is common to sufﬁciently many samples of stereotypical water), then water has that chemical structure and the structure is essential to water, i.e. water has that structure at all metaphysically possible worlds. It is true that from the supposition that stereotypical water actually has the chemical structure ABC, it does not follow that the colorless, odorless, . . . liquid . . . (if it exists) has the chemical structure ABC at every metaphysically possible world. But this fact is irrelevant. What is relevant is the next move in the objection, which is supposed to take us from this fact to the claim that from the same supposition, it also does not follow that water (if it exists) has the chemical structure ABC at every metaphysically possible world. This is a faulty move. To think otherwise is to confuse two-dimensionalism with the simple-minded descriptivism about the word ‘water’. Someone under that confusion would think that to say that the colorless, odorless, . . . liquid . . . (if it exists) has the chemical structure ABC at every metaphysically possible world is equivalent to saying that water (if it exists) has the chemical structure ABC at every metaphysically possible world, hence that the move is warranted. Two-dimensionalism does not equate ‘water’ and ‘the colorless, odorless . . . liquid . . . ’ in meaning in this simplistic way. It instead says that whatever chemical structure the colorless, odorless . . . liquid . . . actually has determines what chemical structure water has (if it exists) at every metaphysically possible world. Therefore, on two-dimensionalism, from the supposition that the colorless, odorless . . . liquid . . . actually has ABC, it does follow that water has ABC (if it exists) at every metaphysically possible world. Another objection to our reasoning might say that instead of showing that two-dimensionalism is committed to metaphysically impossible worlds, our reasoning only shows that some of the worlds two-dimensionalism is committed to are misdescribed: Assume that at the actual world, the colorless, odorless . . . liquid . . . actually has ABC. Assume also that we do not know this fact. Suppose that we say to ourselves, ‘It is metaphysically possible that water does not have ABC’. Then, according to Chalmers,69 what we say is true. But under the current assumptions, water does have ABC, hence it is not metaphysically possible that water does not have ABC, if ‘water’ is understood in terms of what Chalmers calls its ‘secondary intension’—that is, as a rigid designator in Kripke’s sense. So, for Chalmers, ‘water’ in our sentence should be understood in terms of what he calls its ‘primary intension’—that is, as a designator with a certain meaning such that when we say to ourselves, ‘It is metaphysically possible that water does not have ABC’, what we are saying is tantamount to ‘It is metaphysically possible that the colorless, odorless . . . liquid . . . does not have ABC’. When so understood, what we say to ourselves is true.

It is clear that this objection has no effect against our reasoning. If we reinterpret the word ‘water’ just so as to make the sentence ‘It is metaphysically possible that 69

Chalmers 1996: 134.

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water does not have ABC’ come out true under the current assumptions, then of course the sentence is true. But the question at hand is whether the sentence is true before any reinterpretation, and the question is answered negatively by the Putnam–Kripkean reasoning. The objector might complain that it is a distortion to call the interpretation in terms of the primary intension a reinterpretation, for that interpretation is as legitimate an interpretation of ‘water’ as the interpretation in terms of the secondary intension. To this I say that Putnam and Kripke have already argued effectively against such a position as a position in semantics. To point to the truth of the sentence ‘It is possible that water does not have ABC’ under the current assumptions will not save the objection, for we can uphold the truth of this sentence by understanding ‘possible’ in terms of epistemic possibility, and not metaphysical possibility, and then give an account of epistemic possibility by means of metaphysically impossible worlds. If the objector should press on by saying that the sentence is true under the assumptions even when ‘possible’ is understood in terms of metaphysical possibility, then I, along with Kripke, will deny it. I agree with the two-dimensionalists that, for example, ‘Hammie believes that Hesperus is Phosphorus’ and ‘Hammie believes that Hesperus is Hesperus’ could diverge in truth value. I also agree with them that the proper names ‘Hesperus’ and ‘Phosphorus’ are rigid designators in the Kripkean sense. I, however, disagree with them when they think that there is a non-Kripkean sense in which the names are somehow descriptive. Where the two-dimensionalists postulate two semantic contents to explain the possibility of divergence in truth value of the two belief sentences, I stick to the classic, Kripkean semantic content and yet claim that I can explain the possibility of divergence in truth value.70 Thus if I am right, a major motivation for two-dimensionalism is undermined.

8.11.1. Not metalinguistic It is easy to misunderstand two-dimensionalism, and one way to misunderstand it would undermine the claim that two-dimensionalism needs metaphysically impossible worlds. But since the undermining of the claim depends on misunderstanding, the claim remains unscathed. The misunderstanding consists in misconstruing alternative scenarios concerning the actual world metalinguistically. One scenario says that at the actual world stereotypical water is H2O, while another scenario says that at the actual world stereotypical water is XYZ. It is a mistake to understand these scenarios metalinguistically and think that in the ﬁrst scenario at the actual world the word ‘water’ applies to H2O and that in the second scenario at the actual world the word ‘water’ applies to XYZ. If one makes this mistake, it is easy 70

See Ch. 9.

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to resist the claim that two-dimensionalism is committed to metaphysically impossible worlds. The applicability of the word ‘water’ to H2O or to XYZ depends on the language to which it belongs, and that is subject to change from world to world without violating any metaphysical law. So, on the mistaken understanding, neither scenario makes the actual world a metaphysically impossible world. But the mistake is a mistake. Anyone who makes it fails to appreciate the fact that the scenarios are supposed to be about how stereotypical water is at the actual world, not about how the word ‘water’ is used at the actual world.71

8.11.2. Not about @ Another way to misunderstand two-dimensionalism would support the claim that two-dimensionalism needs metaphysically impossible worlds, but the support is illusory. I would like to welcome every support for the claim but not an illusory one. Take the two scenarios again: the scenario that at the actual world stereotypical water is H2O, and the scenario that at the actual world stereotypical water is XYZ. The misunderstanding this time consists in mistaking these scenarios to be de re, where the res is the actual world, @. According to the misunderstanding: The ﬁrst scenario says of @ that stereotypical water is H2O at it, and the second scenario says of @ that stereotypical water is XYZ at it. Suppose that stereotypical water is H2O, not XYZ, at @. Then our local metaphysical space is such that it is not the case that stereotypical water is XYZ at @ in it. So, every metaphysically possible world is such that it is not the case that stereotypical water is XYZ at @. So, no metaphysically possible world is such that stereotypical water is XYZ at @. Clearly, if @ is such that stereotypical water is XYZ at it, then it is such that stereotypical water is XYZ at @. So, if @ is such that stereotypical water is XYZ at it, then it is a metaphysically impossible world. But the second scenario says of @ that stereotypical water is XYZ at it. Therefore, @ in the second scenario is a metaphysically impossible world.72 Suppose, on the other hand, that stereotypical water is XYZ, not H2O, at @. Then an exactly parallel reasoning leads to the conclusion that @ in the ﬁrst scenario is a metaphysically impossible world. Therefore, the complete two-dimensionalist set-up requires some scenario in which @ is a metaphysically impossible world.

Note the difference between this line of reasoning and the reasoning in 8.10 concerning the passages from Braddon-Mitchell and Jackson. Here the conclusion is the metaphysical impossibility of @ in a scenario within two-dimensionalism, whereas in 8.10 we argued for alternative metaphysical spaces. In 8.10 we 71

On this point, see Chalmers 2006, esp. 2.2, where he discusses Stalnaker’s diagonal propositions. This reasoning also shows that the second scenario is a metaphysically impossible scenario, but this is not surprising. 72

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maintained the legitimacy of making suppositions de re about @. Here also we should say that there is nothing wrong with making suppositions de re about @. What is mistaken is to understand the two-dimensionalist scenarios as saying something de re about @. In order to see why this is a mistake, and also to see how the above erroneous reasoning based on this mistake differs from our earlier reasoning for the conclusion that two-dimensional semantics is committed to metaphysically impossible worlds, let us turn to what Chalmers says. Speaking, in effect, of how we should understand various scenarios concerning how the actual world turns out to be, Chalmers uses the notion of epistemic possibility and says: For any possible world W, it is epistemically possible that W is actual; or at least, it is epistemically possible that a world qualitatively identical to W is actual. (More precisely: it is epistemically possible that D is the case, where D is a complete qualitative characterization of W. . . . )73

What is important is his parenthetical remark. Take the second scenario, which says that stereotypical water is XYZ at the actual world. According to the ‘more precise’ explanation by Chalmers of the epistemic possibility concerning how the actual world turns out to be, for the epistemically possible scenario to say that stereotypical water is XYZ at the actual world is for it simply to say that it is the case that stereotypical water is XYZ, or even more simply, it is to say that stereotypical water is XYZ. It is clear from the quoted passage that here ‘stereotypical water is XYZ’ means that stereotypical water isa actually XYZ (or, actually stereotypical water isa XYZ), where ‘actually’ is understood in the non-rigid sense. This is crucial. Reference to @ drops out of this ‘more precise’ understanding of the scenarios, and the notion of what isa actually the case (with the non-rigid ‘actually’) comes to the fore. The mistaken understanding of the scenarios considers different scenarios as telling different stories about a particular world, namely, @. The correct understanding considers different scenarios as locating actuality at different worlds, or more concretely put, as locating our actual selves, or actual-world-stages (not @-stages but actual stages in the non-rigid sense of ‘actual’), at different worlds. Our earlier reasoning was to the effect that some scenarios locate our actual selves (with ‘actual’ non-rigid) at metaphysically impossible worlds.

8.11.3. Not pretense Pretending, like believing, involves metaphysically possible worlds and impossible worlds. But there is a line of argument involving pretense which commits the same kind of error as the above and therefore should not be accepted. The error does not involve two-dimensionalism quite as directly as the above error but its connection to two-dimensionalistic thinking should be clear:

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Impossibility Consider Gareth Evans’s ‘Julius’.74 Evans deﬁnes this name as a name of the inventor of the zipper. We are supposed to understand that Evans bears no relevant causal-historical relation to the inventor of the zipper but that Evans is introducing the name ‘Julius’ purely by description; whoever happens to be the inventor of the zipper is to be the referent of ‘Julius’. Evans makes provocative philosophical points by means of this example. Whether these points are tenable is not our concern. What is interesting for our purposes is the fact that the name ‘Julius’, as so deﬁned by Evans, actually fails to refer to anyone. It certainly does not refer to Mr Yoshida of YKK (Yoshida Kogyo Kabushikigaisha). Mr Yoshida may be the founder of the largest manufacturer of zippers in the world but did not invent the zipper. More importantly, the history of the zipper is a little complicated and ofﬁcially no one person is credited with the accomplishment of having invented the zipper. Instead, two people, Whitcomb Judson and Gideon Sundback, are recognized as the co-inventors of the zipper. Since the main determiner ‘the’ in the deﬁnite description ‘the inventor of the zipper’ as Evans uses it to deﬁne ‘Julius’ is supposed to carry the uniqueness implication, ‘Julius’ must refer to one unique inventor of the zipper if it refers at all. Thus, Evans’s ‘Julius’ lacks referent. Philosophers, however, shrug this off when evaluating the philosophical discussion Evans puts forth by means of his inventive deﬁnition of ‘Julius’. This is as it should be, but how can we take Evans’s philosophical discussion using ‘Julius’ seriously while at the same time knowing that ‘Julius’ lacks referent? The answer is ‘By pretending’. We ignore the fact that there is no unique person who invented the zipper as a mere inconvenient nuisance and pretend that it is not so. We pretend that exactly one person did invent the zipper and ‘Julius’ refers to that person, just as Evans intended. We speak as if ‘Julius’ actually turned out to refer to a unique person. This enables us to discuss Evans’s philosophical work smoothly and economically without undue distraction. This is philosophically productive, and is by no means unique to Evans’s example. We adopt convenient and harmless pretense whenever it helps us facilitate discussion or make a point. Here is an example at a somewhat lower level of conceptual sophistication than Evans’s. In teaching her introductory logic class, Bianca often pretends that every human being is either deﬁnitely male or deﬁnitely female and is not both, in order to drive home to her students the difference between a universally quantiﬁed disjunction and a disjunction of universal quantiﬁcations. When we go along with Evans’s presumption of the uniqueness of the inventor of the zipper or Bianca’s presumption of the bivalent deﬁniteness of the sex of each human, we are not considering a non-actual possible world. We 74

Evans 1982: 31–2.

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Impossibility are still considering the actual world, @. We pretend that @ is other than how (we presume) it in fact is. When we pretend, we still locate ourselves at @. It is just that we do not locate ourselves at @ as it in fact is but instead locate ourselves at @ as it is according to the pretense. Since it is metaphysically impossible for @ to be other than it in fact is, at no metaphysically possible world is @ as it is according to the pretense. This means that we locate ourselves at a metaphysically impossible world.

This line of reasoning commits the same error as the one we exposed in the reasoning examined in the last section. Pretense does not involve any attitude de re about @. Pretense is pretended locating of the actual self in metaphysical space in the non-rigid sense of ‘actual’. If the locating is earnest instead of pretended, it is believing, as we have learnt from Lewis and Stalnaker. Of course, we may pretend something to be the case, where that something is metaphysically impossible. A metaphysically impossible world will get involved then, but that is because of the metaphysical impossibility of the content of the pretense, not because it is a pretense. Pretense as such has nothing essential to do with metaphysically impossible worlds.

9 Proposition and Belief 9 .1 . REDUCTION OF INTENSIONAL ENTITIES AGAIN In Chapter 7, we started our discussion of intensional entities. Now it is time to continue that discussion. Let us brieﬂy remind ourselves where we stand. The deﬁnition of properties as collections of actual individuals famously fail, as the cordate–renate example illustrates; all and only actual individuals that are cordate are renate but being cordate and being renate are not the same property. Expanding them to include all metaphysically possible individuals is the natural remedy offered by David Lewis. But such a deﬁnition fails for essentially the same reason, namely, lack of sufﬁcient discriminatory power. Lewis offers a twopronged approach in the face of this difﬁculty; some times when we speak of properties we speak of collections of metaphysically possible individuals, and other times when we speak of properties we speak of structured entities sharing their structures with the linguistic expressions expressing them. The structuralist half of his proposal is subject to the Benacerraf problem: too many equally qualiﬁed candidates. This problem seems insurmountable as long as we conﬁne our attention to the metaphysically possible. It is also unclear what it is to possess a given property according to the structuralist proposal. My proposal is to explore the strategy of including the metaphysically impossible as well as the metaphysically possible while adhering to the original non-structuralist idea.1 Before resuming our discussion from Chapter 7, it is beneﬁcial to be clear about the basic tenet we are going to develop. It is not satisfactory simply to say that a property F is the collection of all and only world-stages of individuals, metaphysically possible and metaphysically impossible, that possess F or to say 1 There is no tension between this proposal of mine, which is in accordance with Lewis’s basic idea, and my critique of Lewis’s counterpart theory. The broadly Lewisian extensionalism, supplemented with (metaphysically) impossible worlds and (metaphysical) impossibilia, respects the right sort of truth conditions for statements about propositions, properties, and relations. A merely possible person who is similar to Humphrey and who inhabits a non-actual Lewisian possible world is clearly not Humphrey. But it is not clearly the case that the collection of all possible and impossible square things is not the property of being square. The Lewisian reduction of intensional entities is motivated by respect for economy of objects, whereas the Lewisian reduction of modality de re to counterpart theory is not. In fact, the latter proliferates objects; in order to account for Humphrey’s possibly being the winner, it postulates some person distinct and separate from Humphrey.

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that a proposition P is the collection of all and only worlds, metaphysically possible and metaphysically impossible, at which P is true. The reason is that at some metaphysically impossible worlds, a world-stage of an individual possesses F and does not possess F, or in the case of propositions, a proposition P is true and is not true. Every such metaphysically impossible stage of an individual belongs and does not belong to the collection for F, and every such metaphysically impossible world belongs and does not belong to the collection for P.2 (Henceforth, we shall conﬁne our attention to propositions only. Our treatment of properties and relations will be the same mutatis mutandis.) So the collection is a metaphysically impossible object. Since this reasoning applies to every proposition, every proposition is a metaphysically impossible object, according to this simple proposal. This is unsatisfactory. We might try to identify a proposition P with the pair {C1, C2} of collections of worlds, metaphysically possible and metaphysically impossible, where C1 is the truth collection (P is true at any world in C1 and any world at which P is true is in C1), and C2 is the non-truth collection (P is not true at any world in C2 and any world at which P is not true is in C2). This will do as long as there are just two truth values which are related to each other via negation in the classical way: P is true if P is not false, P is false if P is not true, P is not true if P is false, and P is not false if P is true. But it will not do if there are three or more truth values or the truth values are not related via negation in the classical way. We need a more generalized conception. Assume that there are exactly k-many truth values, V1, V2, . . . , Vk, and that there are n-many proprietary ways for a proposition, as a primary bearer of truth values, to be related to each of these truth values. One such way is possession (for example, P has V1) and another is lack (for example, P does not have V1). I shall not speculate about the other ways, but the idea is to allow room for any non-standard proprietary way in which a proposition may be related to a truth value qua primary bearer of truth values. For a given proposition P, consider the appropriate (k n)-tuple of collections of worlds, {C11, C12, . . . , C1n, C21, C22, . . . , C2n, . . . , Ck1, Ck2, . . . , Ckn}, where Cxy (1xk, 1yn) is such that P is related to Vx in the y-th way at any world in Cxy and any world at which P is so related is in Cxy. We shall identify P with this tuple.3 The values of k and n, especially that of k, may be inﬁnite.

2 There is a second, unrelated reason. It is that world-stages of individuals have some properties at some times but not at others. I was a boy once but not anymore. So, the elements in the collection which is to be identiﬁed with the property of being a boy should be at least as ﬁne-grained as temporal stages of world-stages of individuals. A moment’s reﬂection on spatially variable properties will also show the need for spatial stages (parts) of world-stages of individuals. We shall ignore such complications and concentrate on world-stages exclusively. 3 Likewise for properties and relations, for which we should speak of k-many ‘possession values’ and ‘standing-in values’, respectively, instead of truth values. Andy Egan (2004) argues that we should identify a property with the function from worlds to possessors of the property at those worlds, rather than with the collection of the possessors. I have no objection to following his recommendation if doing so will serve us better.

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Some might object that we are still stuck with metaphysically impossible collections, for at some metaphysically impossible world P is related to some Vx in the y-th way and is not related to it in that way, and any such world does and does not belong to Cxy. Such an objection would be based on a misunderstanding. Let us say that at a metaphysically impossible world w, P is related to the truth value ‘True’ in the possession way and is not related to the same truth value in that way. All this means according to our set-up as intended is that at w, P is true and is not true. Since P is true, P gets into, say, C11. Since P is not true, P also gets into a different collection, say, C12. Neither collection is metaphysically impossible. It is important to note that C11 is such that P is true at any world in C11 and any world at which P is true is in C11, rather than such that any world at which P is true is in C11 and any world at which P is not true is outside C11. Correspondingly, C12 is such that P is not true at any world in C12 and any world at which P is not true is in C12, rather than such that any world at which P is not true is in C12 and any world at which P is not not true—i.e., is true—is outside C12. 9 . 2 . PROPOSITIONS Let us now pick up where we left off in Chapter 7. Our example was (1) The proposition that snow is white is true. Our Russellian analysis schema for (1) was (2) (∃!x)(Ox & Bx) & (x)((Ox & Bx)Fx), where ‘Ox’ and ‘Fx’ are to mean that x is a proposition and that x is true, respectively. In Chapter 7 we left the question ‘What is “Bx” to mean?’ unanswered. Let us start by introducing additional quantiﬁcation, over worlds. Read ‘Bx’ as (3) (w)(x is true at w snow is white at w), where the variable ‘w’ ranges over worlds and ‘’ means material equivalence. If we simply let ‘w’ range over metaphysically possible worlds, we are stuck with the standard problem of conﬂating metaphysically equivalent propositions, such as the propositions expressed by ‘Snow is white’ and ‘Snow is white and 1þ1 ¼ 2’. We need to have ‘w’ range over more than metaphysically possible worlds, i.e. over metaphysically possible worlds and some metaphysically impossible worlds. The obvious idea is that if we let the right metaphysically impossible worlds into the range of ‘w’, the proposition expressed by ‘Snow is white and 1þ1 ¼ 2’ will be adequately excluded; at some metaphysically impossible world w, snow is white but it is not the case that snow is white and 1þ1 ¼ 2. So for some w, the proposition expressed by

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is true at w but the proposition expressed by (4a) Snow is white and 1þ1 ¼ 2 is not true at w. The two propositions are thus adequately distinguished. Unfortunately, there are many more propositions which need to be distinguished from the proposition (4) expresses. Consider (4b) Snow is white and 1þ1þ1 ¼ 3. In order to distinguish the proposition expressed by (4) from the proposition expressed by (4b), we need a metaphysically impossible world w such that at w, snow is white but it is not the case that snow is white and 1þ1þ1 ¼ 3. Since at some metaphysically impossible world at which snow is white, 1þ1 6¼ 2 but 1þ1þ1 ¼ 3 (or 1þ1þ1 6¼ 3 but 1þ1 ¼ 2), there is no guarantee that the worlds we pick to weed out the proposition expressed by (4a) will also weed out the proposition expressed by (4b) (or the other way around). It is apparent from these examples that picking some metaphysically impossible worlds while leaving out others will not distinguish the proposition expressed by (4) from all other propositions metaphysically equivalent to it. The safest choice therefore seems to be to pick all metaphysically impossible worlds, leaving out none. Include in the range of ‘w’ all metaphysically impossible worlds, in addition to all metaphysically possible worlds. (I hasten to add that by making this choice for the range of ‘w’ we are not committing ourselves to the view that it is necessary to include all metaphysically impossible worlds in the range of ‘w’ in order to distinguish every proposition from every other metaphysically equivalent proposition. For instance, a metaphysically impossible world at which all propositions have the same truth value(s) and lack the same truth value(s)4 is useless for the purpose of distinguishing any two propositions.) The resulting net effect of the equivalence in (3) is sufﬁciently strong. Some might say it is too strong. At some metaphysically impossible world w, snow is white and snow is not white. So, at w, the proposition expressed by (4) is true and the proposition expressed by (4) is false. Thus, they might continue, if the proposition expressed by (4a) or (4b) is adequately distinguished from the proposition expressed by (4) by the above maneuver, then the proposition expressed by (4) is adequately distinguished from the proposition expressed by (4) by the same maneuver. But no proposition should be distinguished, adequately or not, from itself. Therefore, they might conclude, the proposal is self-refuting. This objection, however, is confused. What is at issue is how to secure the result that exactly one proposition satisﬁes (3). The proposal in question is to secure this result by regarding ‘w’ in (3) as ranging over all metaphysically 4

Or more accurately, all propositions stand in the same relation(s) to all truth values.

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possible worlds and all metaphysically impossible worlds. Call those worlds at which no proposition is true and false normal. Worlds at which some proposition is true and false are abnormal. If we let the range of ‘w’ include all abnormal worlds, as the proposal implies, then the proposition satisfying (3) is true and false at some world in the range of ‘w’. But this does not ﬂout the uniqueness of the proposition satisfying (3) or drive a wedge between that proposition and itself. It is expected that the proposition in question is true and false at some world in the range of ‘w’, namely, some abnormal impossible world. Any proposition is true and false at some abnormal impossible world.5 The notion of normalcy may be understood in terms of the notion of propositional identity; w is normal if and only if for any proposition P and any proposition Q, if P is true at w and Q is false at w, then P 6¼ Q. Therefore, if the notion of propositional identity were to be understood in terms of the notion of normalcy, we would have a problem of circularity. But the proposal in question does not deﬁne propositional identity in terms of normalcy. Its deﬁnition of propositional identity is quite simple; for any proposition P and any proposition Q, P ¼ Q if and only if P and Q have the same truth value(s) and lack the same truth value(s)6 at all (metaphysically possible and metaphysically impossible) worlds. So it is sufﬁcient for the non-identity of the proposition that snow is white and the proposition that snow is white and 1þ1 ¼ 2 that at some metaphysically impossible world the former has the truth value ‘True’ and no other truth value, whereas the latter has the truth value ‘False’ and no other truth value. At the same time, the proposition that snow is white is identical with the proposition that snow is white, because at every metaphysically possible or metaphysically impossible world at which the former has (lacks) a certain truth value, the latter has (lacks) that same truth value, and vice versa. In particular, any metaphysically impossible world at which the former (the proposition that snow is white) has ‘True’ and the latter (the proposition that snow is white) has ‘False’ is a world at which snow is white and snow is not white, so it is a world at which the former has ‘False’ and the latter has ‘True’, therefore it is a world at which the former has ‘True’ and ‘False’ and the latter has ‘False’ and ‘True’. That is, such a world is one at which the former and the latter have the same truth values. Some might say that if we include all metaphysically impossible worlds in the range of ‘w’, no proposition at all will satisfy (3). The reason, the objection might go, is that for any proposition, there is a metaphysically impossible world at which that proposition is true and snow is not white; therefore, for any x, there is at least one world for which the biconditional in (3) fails. To see why this 5 The objection makes the assumption that if at w snow is not white, then the proposition expressed by ‘Snow is white’ is false at w. This assumption might be subject to challenge. It might be said that ‘At w, snow is not white’ only entails that the proposition expressed by ‘Snow is not white’ is true at w, and does not entail that the proposition expressed by ‘Snow is white’ is false at w. I do not pursue this line in the text. 6 Again, more accurately, if and only if P and Q stand in the same relation(s) to all truth values.

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objection does not work, remember that the very conception of a proposition as a truth-value bearer has it that the proposition that snow is white is true precisely at those worlds at which snow is white. This is so whether a given world is a metaphysically possible world or not. So, among metaphysically impossible worlds, the proposition that snow is white is true at precisely those worlds at which snow is white. So, at any metaphysically impossible world at which the proposition that snow is white is true, snow is white. Of course, at some metaphysically impossible worlds, the proposition that snow is white is true and snow is not white. But this only means that at such worlds snow is white and snow is not white, and this merely shows that such worlds are abnormal. The underlying idea for the primary-truth-value-bearer conception of propositions we have relied on so far is that the essence, or nature, of a proposition is precisely that it stands in a proprietary relation—such as possession or lack—to every truth value at every world (inherently, rather than as a result of bearing a relation to something else that stands in such a proprietary relation to a truth value). This is the backbone of our earlier identiﬁcation of a proposition with the appropriate (kn)-tuple of collections of worlds, {C11, C12, . . . , C1n, C21, C22, . . . , C2n, . . . , Ck1, Ck2, . . . , Ckn}. Suppose that there are exactly three distinct truth values, ‘True’, ‘False’, and ‘Value-Three’ (possession of which exactly amounts to being neither true nor false), and that there are exactly two proprietary ways a proposition may be relevantly related to each of them— having and not having. At a given metaphysically impossible world, a proposition may be such that it has ‘True’, does not have ‘False’, and has ‘Value-Three’, for example. There is nothing self-refuting about this. It just means that (3) should be understood charitably as follows: (3t) (w)((x has ‘True’ at w snow is white at w) & (x has ‘False’ at w snow is not white at w) & (x has ‘Value-Three’ at w (it is not the case that snow is white at w & it is not the case that snow is not white at w))). If we wish to speak of other distinct truth values or of other distinct proprietary ways of propositional relation to the truth values, the charitable interpretation of (3) should be extended further along the lines of (3t) in an obvious manner. In order to avoid excess verbosity, we shall continue to write formulations like (3) rather than their more accurate renditions along the lines of (3t). Some might wonder what justiﬁes the claim that metaphysically possible and metaphysically impossible worlds will sufﬁce to tell all distinct propositions apart. How do we know that there are not two distinct propositions which stand in exactly the same proprietary relations to all truth values at all metaphysically possible and metaphysically impossible worlds? I do not know exactly how to answer such a question but can offer two comments. First, the reason why we know that metaphysically possible worlds alone do not sufﬁce is that we have fairly clear examples of different propositions with the same truth values at all metaphysically possible worlds: for example, the propositions expressed by (4)

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and (4a). By contrast, we have no similarly clear examples showing the insufﬁciency of metaphysically possible and metaphysically impossible worlds. Second, every world is either a metaphysically possible world or not a metaphysically possible world (or a boundary world, should the matter turn out vague somehow). And metaphysically impossible worlds are those worlds which are not metaphysically possible worlds. So, metaphysically possible worlds and metaphysically impossible worlds (plus boundary worlds, in case of vagueness) exhaust all worlds. Therefore, one would need to go beyond the truth-value-bearer conception of propositions as I have elaborated it (or beyond the conception of worlds as alethic indices of the modal kind) to cast a serious doubt on the claim that metaphysically possible and metaphysically impossible worlds will sufﬁce for telling all distinct propositions apart.7 There is a different worry. It concerns the cardinality of the collection of worlds. David Lewis reports the following paradox, which he credits to David Kaplan: (1k) Suppose that the cardinality of the set of possible worlds is N. (2k) Each subset of this set is a proposition, namely the proposition which would be expressed by a sentence which was true with respect to precisely the worlds in that subset. (3k) There are 2N such propositions, and 2N is strictly greater than N. (4k) Consider some man and time. For each proposition, it is possible that he should have been thinking a thought at that time whose content would be speciﬁable by a sentence expressing that proposition; and that this should have been his only thought at that time. (5k) So there is a distinct possible situation corresponding to each such proposition. (6k) So there are at least 2N possible worlds, contradicting the assumption with which we began.8 Lewis attempts to extricate himself from this paradox by maintaining that not every set of possible worlds might possibly give the content of someone’s 7 One small and separate objection against any theory that purports to reduce propositions to worlds should be mentioned. We touched on it earlier but it is worthwhile to confront it here again. The objection says that any such theory is circular, because a metaphysically possible or impossible world at which, say, water is H2O cannot be speciﬁed independently of the proposition that water is H2O. This is not a good objection. If it were a good objection, then by parity of reasoning, it would be a good objection against the theory which identiﬁes a statue with its constituent molecules to say that the collection of molecules in question can be speciﬁed only as those molecules constituting the statue. But such an objection is not a good objection. In both cases, a matter of metaphysics is conﬂated with a matter of epistemology, or more accurately, with a matter of speciﬁcation. The target of objection is not a claim about our speciﬁcation of propositions, but a metaphysical claim about propositions themselves, and as such, it is immune to the objection. 8 Lewis 1986: 104–5, the numbering altered with the addition of the letter ‘k’ and the letter ‘K’ in the original replaced with the letter ‘N’. Lewis says he learnt it from Kaplan c.1975. See also Davies 1981: 262.

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thought, thus denying (4k). This may or may not work ultimately, but that is not our concern. Even if the move serves him well, it is not available to us, for unlike Lewis, we take propositions to be appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds. We are subject to the following variant of Kaplan’s paradox as Lewis is to the above original: (1k’) Suppose that the cardinality of the collection of metaphysically possible and metaphysically impossible worlds is N. (2k’) Each appropriate (kn)-tuple of sub-collections of this collection is a proposition. (3k’) There are (2N)kn such propositions, and (2N)kn is strictly greater than N. (4k’) Consider some man and time. For each proposition, it is metaphysically possible or metaphysically impossible that he should have been thinking a thought at that time whose content was that proposition; and that this should have been his only thought at that time. (5k’) So there is a distinct metaphysically possible or metaphysically impossible situation corresponding to each such proposition. (6k’) So there are at least (2N)kn metaphysically possible and metaphysically impossible worlds, contradicting the assumption with which we began. Unlike Lewis, we do not seem to be able to extricate ourselves out of this paradox by denying (4k’), for we obviously cannot deny that a given situation is either metaphysically possible or metaphysically impossible. This paradox does refute the sweeping identiﬁcation of all propositions with appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds, where ‘all’ is understood in the absolutely unrestricted sense. As we saw in Chapter 3, however, I reject the absolutely unrestricted sense of a quantifying expression. My proposal of the identiﬁcation of propositions as appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds must therefore be understood as being offered with an important caveat: it is not meant to apply to all propositions at once in the absolutely unrestricted sense of ‘all’. It is improper to speak of the collection of all propositions in the absolutely unrestricted sense of ‘all’. We may not suppose the cardinality of such a collection to be anything at all. The way to block such a supposition in the argument above is to reject the conjunction of (1k’)–(4k’). This is sufﬁcient for avoiding the paradox, and we may stop here. But I offer to speculate on how a restriction on ‘all’ might proceed so as to enable us to speak of propositions not in the sweepingly unrestricted way but in a controlled and systematic way. Some propositions have contents which are non-modal and nonintentional (not involving contentful psychological states). Identify those propositions with appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds. Call the totality of those appropriate

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(kn)-tuples T1. Some propositions have contents which are modal, involving the local metaphysical space but nothing beyond, and are non-intentional. Identify those propositions with appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds. Call the totality of those appropriate (kn)-tuples T2. Other propositions have contents which are modal, involving the local and other metaphysical spaces but nothing beyond the local group of metaphysical spaces, and are non-intentional. Identify those propositions with appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds, and call the totality of those appropriate (kn)-tuples T3. Some propositions have contents which are non-modal and intentional. Identify those propositions with appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds, and call the totality of those appropriate (kn)-tuples T4. And so on. These different types of propositions should not be mixed together into a common batch. T1, T2, T3, T4, etc., should not be fused together into one whole collection of all appropriate (kn)-tuples of collections of metaphysically possible and metaphysically impossible worlds.

9.2.1. Contents other than propositions The basic idea that a proposition is an appropriate tuple of collections of worlds might be expanded to give rise to a more generalized notion of the content of a sentence, the content of a psychological state, etc. A world is one kind of metaphysical index. A temporal period or instant is another kind of metaphysical index, and a spatial region or point is yet another. If we hold our methodological stance ﬁrmly and push the parity of these three kinds of metaphysical index as far as we can, we may propose that, along with collections of modal indices, collections of temporal indices and collections of spatial indices are ﬁt to ﬁgure in the contents of sentences, the contents of psychological states, etc. We may press even further and suggest that collections of pairs or triples of different kinds of metaphysical indices are also so ﬁt. Take the sentence ‘It is raining’ as an example. As we saw in 2.5, some theorists claim that this sentence expresses a thinkable content prior to contextualization, in particular, prior to being understood with respect to any particular place of a context of utterance. We can accommodate this claim in a natural way by identifying such a content with an appropriate tuple of collections of spatial indices. Let us take an earlier example and say that the chief at the hurricane-watch command center in Miami says ‘It is raining’ at a particular time t. Let us assume that the time t and the actual world @ are the relevant temporal and modal indices with respect to which the chief ’s sentence is to be evaluated but that no relevant spatial index is indicated. Under those circumstances, according to the theorists in question, the chief ’s sentence expresses (or has) some deﬁnite content the truth value of which varies from one spatial index to another; the content is true relative to Miami if and only if it is raining in Miami at t at @, and the content is true relative to New Orleans if and

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only if it is raining in New Orleans at t at @. The content in question is not a proposition, an appropriate tuple of collections of modal indices, but it is an appropriate tuple of collections of another kind of alethic indices, namely, spatial indices. Alternatively, the chief ’s sentence may be relevantly associated with @ and a particular spatial region, say New Orleans, but not with any particular time. Under such alternative circumstances of understanding the chief ’s sentence, it may be understood to express a different content, which is to be evaluated for truth value relative to a time; for any time t, the content is true relative to t if and only if it is raining at t in New Orleans at @. In such a case, the content of the sentence is an appropriate tuple of collections of times. If neither a particular time nor a particular spatial region is relevantly associated with the chief ’s sentence but @ is, then the content of the chief ’s sentence is an appropriate tuple of collections of appropriate pairs of a time and a spatial region. If a time is associated but neither a spatial region nor a world is, then the content is an appropriate tuple of collections of appropriate pairs of a spatial region and a world. If neither a time, a spatial region, nor a world is associated, the content is an appropriate tuple of collections of appropriate triples of them. We may decide to call these various contents which are not propositions whatever we like: for example, ‘space-neutral contents’, ‘time-neutral contents’, ‘space-time-worldneutral contents’, ‘proto propositions’, ‘proposition radicals’, or whatever. What may be called a ‘world-neutral content’ is a proposition, a content whose truth value shifts just from world to world. If we wish, we may proliferate types of content by extending this treatment to the other kinds of truth relativizer. Recall the examples in 2.5: (1) (‘There are only three eggs’)–(14) (‘I butter the toast this morning with the knife slowly in the drawing room while wearing a kilt’). 9 . 3 . A CHALLENGE Let us return to the example of Bianca: (5) (6) (7) (8)

The proposition that bookmakers are sleazy is believed by Bianca. The proposition that bookies are sleazy is believed by Bianca. Bianca believes that bookmakers are sleazy. Bianca believes that bookies are sleazy.

(5) is the regimented version of the more colloquial (7), and (6) of (8). According to the current proposal of modal Russellianism, the logical structures of (5)/(7) and (6)/(8) are as follows, respectively: (5r) (∃!x)(x is a proposition & (w)(x is true at w bookmakers are sleazy at w)) & (x)((x is a proposition & (w)(x is true at w bookmakers are sleazy at w)) Bianca believes x).

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(6r) (∃!x)(x is a proposition & (w)(x is true at w bookies are sleazy at w)) & (x)((x is a proposition & (w)(x is true at w bookies are sleazy at w)) Bianca believes x).9 Assume that belief is a relation to a proposition and that (5) is true but (6) false. Then in order to avoid a contradiction, we need the deﬁnite descriptions (5rd) the proposition that bookmakers are sleazy and (6rd) the proposition that bookies are sleazy to denote different propositions. The challenge is to secure this without violating the principle that synonyms make the same semantic contribution to the determination of the propositions expressed by the sentences in which they occur (except in direct quotational and similar specialized contexts). While considering the Name Theory and the Demonstrative Theory, we noted that, given this principle on synonyms, it was compelling that the following sentences expressed the same proposition: (9) Bookmakers are sleazy. (10) Bookies are sleazy. We also observed that the two theories in question lacked adequate resources to counter this compelling point. As a result, we did not resist and assumed that (9) and (10) expressed the same proposition. Moreover, we imposed the desideratum for any adequate theory of (5) and (6) that (5rd) and (6rd) should denote the propositions (9) and (10) express, respectively. So, if we are to hold our current proposal up to the same standard of scrutiny as the two previous theories without having to reject the proposal, we need to deny that (5rd) and (6rd) denote the same proposition within the sentential contexts of (5) and (6), which in turn will commit us to denying that (9) and (10) express the same proposition within the same sentential contexts. And this is only the beginning. We rejected the previous two theories on the basis that neither contained any otherwise plausible mechanism in their analyses that gave any reason for denying the identity of the propositions denoted by (5rd) and (6rd) without violating the principle on synonyms. Such a denial by the Name Theory was theoretically ad hoc, and the way the Demonstrative Theory managed the denial led to an unacceptable consequence (the carrot case). Can our current proposal sustain the denial in a way that is neither ad hoc nor otherwise unacceptable? Unfortunately, it cannot. Our current proposal allows (5rd) and (6rd) to denote different propositions, but this is so only because it allows 9 Remember that (5r) and (6r) are to be understood charitably along the lines illustrated by (3t) for (3). All subsequent formulations we shall discuss should also be understood equally charitably.

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as it occurs, twice, in (5r) and (6rw) (w)(x is true at w bookies are sleazy at w) as it occurs, twice, in (6r) to be satisﬁed by different propositions. Call a world a Bianca world if at that world everything is exactly in accordance with Bianca’s belief system. At every Bianca world bookmakers are sleazy but bookies are not.10 If Bianca disbelieves that Earth is ﬂat, then at every Bianca world Earth is not ﬂat. If Bianca neither believes nor disbelieves Goldbach’s Conjecture, then at every Bianca world Goldbach’s Conjecture is neither true nor false. Given that it is metaphysically necessary that all and only bookmakers are bookies, every Bianca world is a metaphysically impossible world; for Bianca does not believe that all and only bookmakers are bookies. Since according to our current proposal, the range of ‘w’ in (5rw) and (6rw) includes not just metaphysically possible worlds but also all11 metaphysically impossible worlds, it includes Bianca worlds. So, for some w in the range, the proposition which satisﬁes (5rw) is true at w and the proposition which satisﬁes (6rw) is not true at w. So these propositions are different propositions.12 So far so good. However, our current proposal does not respect the principle on synonyms. As we noted, the principle makes it compelling that (5rd) and (6rd) denote the same proposition. Our current proposal says that different propositions satisfy (5rw) and (6rw) as they occur in (5r) and (6r). But (5rd) denotes a proposition P if and only if P satisﬁes (5rw) as it occurs in (5r), and (6rd) denotes a proposition P if and only if P satisﬁes (6rw) as it occurs in (6r). This itself does not make our current proposal ﬂout the principle quite yet. The reason why the principle on synonyms makes the identity of the denotations of (5rd) and (6rd) compelling is that the principle entails that, given the synonymy of the two words, (i) ‘bookmakers’ and ‘bookies’ make the same semantic contribution to the determination of the propositions satisfying (5rw) and (6rw), respectively, while independently it appears that (ii) if (i), then (5rd) and (6rd) denote the same proposition. So, if a theory can deny (ii) without denying (i), the principle is not ﬂouted. Sadly, our current proposal cannot do so. If (i) is accepted, then since our current proposal makes the rest of (5rw) and the rest of (6rw) rich enough to assure full individuation of the satisfying propositions, no room is left for us to maneuver to avoid accepting (ii). 10

I am not interested in settling the question of how many Bianca worlds there are. I use the locutions ‘every Bianca world’ and ‘Bianca worlds’ to convey generality. If there is only one Bianca world, they are equivalent to ‘the Bianca world’. 11 ‘All’ not in the absolutely unrestricted sense but still in an appropriately comprehensive sense. 12 Bianca worlds, at which not all and only bookmakers are bookies, are not the only kind of metaphysically impossible worlds at which bookmakers are sleazy but bookies are not. Another such kind of metaphysically impossible worlds are those at which all and only bookmakers are bookies but bookmakers are sleazy while bookies are not. Bianca worlds ﬂout the metaphysical necessity of analytic coextensiveness, whereas the latter kind of worlds ﬂout the indiscernibility of the identical.

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9 .4 . MODAL RUSSELLIAN THEORY REVISED This is not the end of modal Russellianism, however. We can deny (ii) while accepting (i) within modal Russellianism.13 The crucial move is to deny that the semantic contribution is all the contribution to the determination of the proposition. Even though ‘bookmakers’ and ‘bookies’ have the same semantic contribution, (5rd) and (6rd), as they occur in (5) and (6) in the set-up scenario concerning Bianca, denote different propositions. The extent of the semantic contribution is captured by the notion of a semantically regular world, that is, a world which violates no semantically sanctioned truths. A few examples should sufﬁce to illustrate the notion of a semantically sanctioned truth: the truth that bachelors are male, the truth that vixens are foxes, the truth that nightmares are dreams, the truth that walking is moving, the truth that all and only bookmakers are bookies, the truth that what is F and G is F, etc. Every such truth is metaphysically necessary.14 Every semantically irregular world is a metaphysically impossible world. (But not every metaphysically necessary truth is sanctioned semantically: for example, the truths that 5þ7 ¼ 12, that water is H2O, that a table is not made of a hunk of matter completely different from the hunk of matter it is actually made of, etc. So, not every semantically regular world is a metaphysically possible world.15) One might decide to leave the notion of semantic regularity primitive, offering nothing further than an intuitive illustration by means of a few examples of semantically sanctioned truths like the ones above. But we can do a little better if we are prepared to accept the notion of conceptual possibility; w is semantically regular if and only if w is conceptually possible. That is, w is semantically regular 13

Scott Soames (2002, esp. 204–40) also proposes that the sameness of the semantic contributions made by linguistic expressions does not entail the sameness of what is asserted by normal assertive utterances of the sentences which differ from each other at most with respect to these expressions. See n. 23 below. Soames does not endorse modal Russellianism. 14 This means that the notion of a semantically sanctioned truth is not the same as the notion of an analytic truth. The meaning of the word ‘I’ is such that it is true that I am the agent in the context of utterance. But it is not metaphysically necessarily true that I am the agent in the context of utterance. 15 Semantically irregular worlds help us weaken an argument in favor of the structuredproposition view. Let us assume that the two sentences, ‘Bachelors are neurotic’ and ‘Unmarried adult males are neurotic’, are synonymous but express different propositions in an appropriately set-up context. The structured-proposition view can accommodate this easily, as the two sentences have different syntactic structures, which results in the corresponding difference in the structured propositions the sentences express. But since appropriate tuples of collections are not (appropriately) structured, a similar accommodation is not available to those who hold that propositions are appropriate tuples of collections. Thus we seem stuck. The inclusion of semantically irregular worlds changes this. If the two sentences express different propositions, then the propositions they express are two different appropriate tuples of collections of worlds. Since the two sentences are synonymous, they are on a par with each other true-value-wise at exactly the same semantically regular worlds. But this only shows that at least one of the collections in the two appropriate tuples of collections of worlds includes some semantically irregular worlds.

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if and only if every proposition true at w is conceptually possibly true.16 The notion of conceptual possibility here should be distinguished from the notion of conceivability. What is conceptually possible is, intuitively speaking, what is allowed by the concepts: for example, being non-aggressive is allowed by the concept of vixenhood, but being a non-fox is not. Conceivability is more generous. It is conceivable that some vixen is not a fox. We have just conceived it. Do not complain that it is unacceptable to say that what is conceptually possible is what is allowed by the concepts because ‘allowed’ is itself a modal notion, to be deﬁned in terms of possibility. The point of introducing conceptual possibility at this point is to illustrate an alternative to taking semantical regularity as primitive, not to reduce modality. To say that ‘bookmakers’ and ‘bookies’ make the same semantic contribution to the determination of the propositions satisfying (5rw) and (6rw) amounts to saying that exactly the same semantically regular worlds ﬁgure in exactly the same way in the proposition satisfying (5rw) as in the proposition satisfying (6rw). Two worlds ﬁgure in exactly the same way in a proposition if and only if the proposition stands in exactly the same proprietary relations to all truth values at these worlds. But this does not guarantee that exactly the same worlds ﬁgure in exactly the same way in the proposition satisfying (5rw) as in the proposition satisfying (6rw). The revision of modal Russellianism I propose consists in denying that ‘bookmakers’ and ‘bookies’ make the same overall contribution to the determination of the propositions satisfying (5rw) and (6rw). That is, it says that not exactly the same worlds ﬁgure in exactly the same way in the proposition satisfying (5rw) as in the proposition satisfying (6rw). In particular, some metaphysically impossible worlds that are semantically irregular ﬁgure differently in the two propositions. One might ask what contribution other than the semantic contribution words may make to the determination of the propositions expressed by sentences in which they occur. One answer is ‘the syntactic’. But since our examples, ‘bookmakers’ and ‘bookies’, do not have different syntactic roles in their respective embedding sentences, this answer, though correct, is of little help to us. Another answer is ‘the orthographic’. The two words are spelt differently and that difference makes the difference in the determination of the propositions. This way lie various versions of the metalinguistic analysis, which says that Bianca’s belief that bookmakers are sleazy is a belief somehow about the word ‘bookmakers’ and she lacks the corresponding belief about the word ‘bookies’.17 I am skeptical of the metalinguistic analysis as a general theory of attitude sentences and am prepared to argue against it, but this is not the place. I shall simply 16 Of course, some might object to this on the grounds that the direction of deﬁnition should be reversed and conceptual possibility should be deﬁned in terms of semantic regularity. It seems to me, however, that such a position rests uneasily on the vulnerable assumption of the priority of the linguistic over the conceptual. 17 See Ch. 7 n. 43 for reference.

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assume that if we can get by without linguistic ascent required by the metalinguistic analysis, so much the better.18 I do not know what to say informatively about the extra-semantic contribution words may make to the determination of the propositions in belief and other attitude sentences, but I think the intuitive evidence is strong that there must be some such contribution. The contents of our beliefs and other attitudes are more ﬁne-grained than what the semantics of our words can capture. It is important to note that according to my use of the phrase ‘semantic contribution’, the proposition expressed by (9) as it occurs in (5)/(7) is not completely determined by the semantic contributions of all words contained in (9) (plus the syntactic way the words are combined). The proposition (9) expresses (within the context of (5)/(7)) transcends the semantic contributions of all words contained in (9). This is important to bear in mind, for there is a fairly standard use of the phrase ‘semantic content’, or ‘semantically encoded content’, according to which the proposition (9) expresses is its semantic content, or semantically encoded content.19 In my usage, what (9) expresses is a proposition, i.e. a primary bearer of truth values. So, the totality of the semantic contributions of the words contained in (9) does not determine the truthevaluable content of (9). For any English sentence S and any proposition P, S expresses P if and only if the result of plugging S into the blank slot in the schema ‘the proposition that ( )’ denotes P. The term resulting from such a plugging of a sentence is to be understood as a deﬁnite description in the Russellian way we have been following. 9. 5 . MEANING AND EXPRESSION Our revised proposal holds that meaning does not determine proposition even relative to a context of utterance. There is a prima facie difﬁculty with such a position. Consider: (11) (12) (13) (14)

‘Bookmakers are sleazy’ means that bookmakers are sleazy. ‘Bookies are sleazy’ means that bookies are sleazy. ‘Bookmakers are sleazy’ expresses (says) that bookmakers are sleazy. ‘Bookies are sleazy’ expresses (says) that bookies are sleazy.

Our revised proposal says that, relative to an appropriate context (for example, the context of reporting Bianca’s beliefs), the sentences (9) Bookmakers are sleazy 18 For a particularly well-developed metalinguistic theory of belief, see Richard 1990. For a devastating critique of Richard’s proposal, see Soames 1994: 264–70; 2002: 147–203. 19 e.g. see Salmon 1986a for such a use.

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mean the same but they do not express the same proposition. That is, assuming that (11)–(14) are true, the ‘that’-clauses in (11) and (12) designate the same thing but the ‘that’-clauses in (13) and (14) do not. It follows that either the ‘that’-clauses in (11) and (13) do not designate the same thing or the ‘that’clauses in (12) and (14) do not designate the same thing. But how can this be, given the assumption that (11)–(14) are all understood relative to one and the same context? The apparent force of this rhetorical question stems from the myopic comprehension of the ‘that’-clauses in (11)–(14). Take (11) and (13), for example. They both contain the same ‘that’-clause. How can that ‘that’-clause fail to designate the same thing (relative to the same context)? Here is how. Remember that under the assumption that expression is a relation between a sentence and a proposition (relative to a context), we read (13) as a stylistic variant of (15) ‘Bookmakers are sleazy’ expresses the proposition that bookmakers are sleazy. Likewise, under the assumption that the verb ‘to mean’ in (11) expresses a relation between a sentence and what is meant, namely, a meaning (relative to a context),20 we should read (11) as a stylistic variant of (a slightly awkward but more accurate) (16) ‘Bookmakers are sleazy’ means the meaning that bookmakers are sleazy. I think we should say that the deﬁnite description in (15) denotes a certain proposition P and the deﬁnite description in (16) denotes a certain meaning M. We can then understand the designation of a ‘that’-clause in terms of the denotation of the deﬁnite description which contains the ‘that’-clause; the ‘that’clause in (15) designates P, and the ‘that’-clause in (16) designates M. Since propositions are not meanings, the two ‘that’-clauses designate different things. The same ‘that’-clause functions differently when embedded in (15) and (16). In (15) it helps determine a proposition, and in (16) a meaning. Compare this with a case of sub-sentential strings. Words have meanings and some of them also express properties: (17) ‘Dog’ means dog. (18) ‘Dog’ expresses being a dog.

20 The unfortunate linguistic accident that, unlike ‘expression’ and ‘proposition’, English has the same word, ‘meaning’, for the relation and the second relatum of the relation, should not confuse us.

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Here there is not even the slightest hint of parity between (17) and (18) even on the surface. Without italicization, or some other special device (such as quotation marks), (17) might well be considered ill formed or at best a borderline case. Even if (17) were well formed and true with the last word occurring unitalicized and bare in it (‘Dog’ means dog), the counterpart of (18) would be not quite well formed and certainly not true (‘Dog’ expresses dog). It does not help to switch to an obviously well-formed sentence, (180 ) ‘Dog’ expresses doghood, which is equally removed from (17) on the surface. (17) and (18) should be read as less articulate versions of: (19) ‘Dog’ means the meaning dog. (20) ‘Dog’ expresses the property of being a dog. The word ‘dog’ is functioning differently at the end of (19) from at the end of (20). In (19) it helps determine a meaning, while in (20) it helps determine a property. A fuller version of (180 ), (1800 ) ‘Dog’ expresses the property doghood, gives another illustration that ‘dog’ as it occurs as part of the word ‘doghood’ helps determine a property, rather than a meaning. The situation with ‘that’clauses is entirely parallel, if not linguistically as obvious. 9 . 6 . ITERATION Benson Mates famously uses iterated belief sentences to argue against salva veritate substitutivity of synonyms.21 Our revised proposal gives a straightforward treatment of iterated belief sentences which supports Mates. The sentences (21) and (22) get the logical structures partially revealed in (21r) and (22r): (21) Ben believes that Bianca believes that bookmakers are sleazy. (22) Ben believes that Bianca believes that bookies are sleazy. (21r) (∃!x)[x is a proposition & (w)(x is true at w at w Bianca believes that bookmakers are sleazy)] & (x){ . . . Ben believes x}. (22r) (∃!x)[x is a proposition & (w)(x is true at w at w Bianca believes that bookies are sleazy)] & (x){ . . . Ben believes x}. The blank slots in (21r) and (22r) are to be ﬁlled with ‘[x is a proposition & (w)(x is true at w at w Bianca believes that bookmakers are sleazy)]’ and ‘[x is a proposition & (w)(x is true at w at w Bianca believes that bookies are sleazy)] ’, 21

See Mates 1950.

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respectively. The ‘that’-clauses in (21r) and (22r) are to be analyzed away in an obvious manner. For example, (21r) will be as follows when fully spelt out: (21r’) (∃!x)[x is a proposition & (w){x is true at w ((∃!y)[y is a proposition & (w’)(y is true at w’ at w’ bookmakers are sleazy)] & (y)[{y is a proposition & (w’)(y is true at w’ at w’ bookmakers are sleazy)} Bianca believes y at w])}] & (x){[x is a proposition & (w){x is true at w ((∃!y)[y is a proposition & (w’)(y is true at w’ at w’ bookmakers are sleazy)] & (y)[{y is a proposition & (w’)(y is true at w’ at w’ bookmakers are sleazy)} Bianca believes y at w])}] Ben believes x}. Likewise for (22r). Despite their complexity, (21r’) and the corresponding (22r’) should make it clear that nothing fundamentally new is involved in the iterated belief sentences beyond what was involved in the earlier belief sentences concerning Bianca. 9 .7 . NON-DESCRIPTIVENESS OF NAMES What we have said about synonymous general terms, like ‘bookmakers’ and ‘bookies’, applies equally to coreferential proper names. Charles is also known as Kit. That is, he has two names, ‘Charles’ and ‘Kit’. Becky is a competent user of these two names as the names of the man in a way parallel to the way in which Bianca is a competent user of ‘bookmakers’ and ‘bookies’ in our earlier example. Becky thinks the man is cute when she thinks of him as Charles, but does not when she thinks of him as Kit. I leave the details of how this may be so to the imagination of the reader. We say that the ﬁrst sentence below is true but the second is not: (23) Becky believes that Charles is cute. (24) Becky believes that Kit is cute. If we combine the principle on synonymy we discussed earlier with the assumption that coreferential names are synonymous, it follows that coreferential names make the same semantic contribution to the determination of propositions by sentences in which they occur. Clearly Becky’s situation is importantly similar to Bianca’s when understood this way. Let us say that ‘Charles’ and ‘Kit’ are synonymous because they are coreferential. The two names make the same semantic contribution to the determination of a proposition. The logical structures of (23) and (24) are: (23r) (∃!x)(x is a proposition & (w)(x is true at w Charles is cute at w)) & (x)((x is a proposition & (w)(x is true at w Charles is cute at w)) Becky believes x). (24r) (∃!x)(x is a proposition & (w)(x is true at w Kit is cute at w)) & (x) ((x is a proposition & (w)(x is true at w Kit is cure at w)) Becky believes x).

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If a proposition satisﬁes (23rw) (w)(x is true at w Charles is cute at w) as it occurs in (23r), with the range of ‘w’ only including semantically regular worlds, then that same proposition also satisﬁes (24rw) (w)(x is true at w Kit is cute at w) as it occurs in (24r), with the range of ‘w’ only including semantically regular worlds. Such a proposition may be denoted by ‘the proposition that Charles is cute’ and also by ‘the proposition that Kit is cute’. This respects the parity of ‘Charles’ and ‘Kit’ in their semantic contribution as they occur in (23) and (24). If we include semantically irregular worlds, however, the difference between the two names in their overall contribution to the determination of the proposition in the relevant context becomes manifest. At some semantically irregular world, Charles is cute and Kit is not. The two descriptions, ‘the proposition that Charles is cute’ and ‘the proposition that Kit is cute’, denote different propositions which differ in truth value at some such worlds. After laying out the problem faced by the proponents of the position he favors concerning propositional attitude ascriptions, Scott Soames says: Thus we are left with a dilemma. On the one hand, we may accept the alleged datum that typically, when sentences differ only in the substitution of one proper name for another, it is possible to assert and believe the proposition semantically expressed by one of the sentences without asserting and believing the proposition semantically expressed by the other. If we do this, then we must give some positive account of propositions and propositional attitudes that explains how this is possible. This problem is exceedingly difﬁcult if, as Kripke seems to have shown, proper names do not have descriptive semantic contents. On the other hand, we may reject the alleged datum and identify the semantic contents of names with their referents. If we do this, we will be led to maintain that sentences which differ only in the substitution of coreferential names semantically express the same propositions, and that attitude ascriptions involving such sentences are truth-conditionally equivalent.22

Soames opts for the second horn of his dilemma with a signiﬁcant twist.23 We opt for the ﬁrst horn with an equally signiﬁcant twist of our own; we drop ‘semantically’ from ‘semantically expressed’.24 Soames suggests that the lack of descriptive semantic contents by proper names stands against the ﬁrst horn. With the resources afforded by metaphysically impossible worlds, we do not need descriptive contents for names in order to seize the ﬁrst horn. 22

Soames 2002: 14. Soames holds the following two views simultaneously: (i) ‘that the semantic contents of most linguistically simple names are just their referents’, and (ii) that substitution of two linguistically simple names in attitude ascriptions ‘can affect the truth value of what is asserted by normal assertive utterances of the ascriptions’ (2002: 214). He packs much into his conception of assertion. 24 This does not mean that we fail to draw a distinction between sentential expression of a proposition and speaker expression of a proposition. The latter is not our concern at all. 23

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9 . 8. NON-LINGUISTIC BELIEVERS Gaah is an alien creature whose behavior strongly suggests a certain degree of intellectual sophistication. We want to ﬁgure out its psychology from the total physical, chemical, and non-intentionally described behavioral evidence that we can amass. In particular, we do not assume that Gaah is a language user.25 After spending a reasonable amount of time collecting relevant evidence, we afﬁrm (25) and deny (26): (25) Gaah believes that Phosphorus is visible in the morning. (26) Gaah believes that Hesperus is visible in the morning. Let us assume that ‘Phosphorus’ and ‘Hesperus’ are synonymous and make the same semantic contribution to the determination of a proposition. The logical structures of (25) and (26) are: (25r) (∃!x)(x is a proposition & (w)(x is true at w Phosphorus is visible in the morning at w)) & (x)((x is a proposition & (w)(x is true at w Phosphorus is visible in the morning at w)) Gaah believes x). (26r) (∃!x)(x is a proposition & (w)(x is true at w Hesperus is visible in the morning at w)) & (x)((x is a proposition & (w)(x is true at w Hesperus is visible in the morning at w)) Gaah believes x). It is easy to see that this case is perfectly parallel to the case of Becky, a language user, in the last section. Revised modal Russellianism does not treat sentences ascribing belief to creatures who are not language users (or not assumed to be language users) in any way special. 9 . 9 . A FRENCHMAN IN LONDON Saul Kripke tells his famous story about Pierre.26 Pierre sincerely assents to (27) Londres est jolie in Paris as a monolingual French speaker after looking at attractive picture postcards depicting London, England. Relying on the French version of the ﬁrst leg of the disquotational principle, (DQ1), from Chapter 7 (7.4.3) plus the obvious translation, we afﬁrm (28) Pierre believes that London is pretty. Let C1 be the context in which we afﬁrm (28). The logical structure of (28) is 25 We may think of this as the initial part of the endeavor of a radical interpreter, as characterized by David Lewis (1974). 26 Kripke 1979.

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(28r) (∃!x)(x is a proposition & (w)(x is true at w London is pretty)) & (x)((x is a proposition & (w)(x is true at w London is pretty)) Pierre believes x). Pierre then goes to London, England, learns English by the direct method (without dictionary or interpreter), and sincerely dissents from (29) London is pretty. Relying on the second leg of the disquotational principle, (DQ2), we deny (30) Pierre believes that London is pretty. Let C2 be the context in which we deny (30). The logical structure of (30) is (30r) (∃!x)(x is a proposition & (w)(x is true at w London is pretty)) & (x)((x is a proposition & (w)(x is true at w London is pretty)) Pierre believes x). (28) and (30) appear to be exactly the same English sentence. On a superﬁcial level, they are. But they are considered in different contexts, C1 and C2, and as a result elicit different reactions from us (afﬁrmation and denial). So, (28) should be understood to be a sentence as embedded in C1, and (30) a sentence as embedded in C2. Correspondingly with (28r) and (30r). Let us assume that ‘London’ as it occurs in (28) embedded in C1 makes the same semantic contribution to the propositional determination as does ‘London’ as it occurs in (30) embedded in C2. If a proposition satisﬁes (28rw) (w)(x is true at w London is pretty at w) as it occurs in (28r) embedded in C1, with the range of ‘w’ only including semantically regular worlds, then that same proposition also satisﬁes (30rw) (w)(x is true at w London is pretty at w) as it occurs in (30r) embedded in C2, with the range of ‘w’ only including semantically regular worlds. This respects the parity in semantic contribution of the two occurrences of ‘London’. If we expand the range of ‘w’ to include semantically irregular worlds, however, things change. It is an important aspect of C1 that the reason for our afﬁrmation of (28) is Pierre’s assent to (27). It is crucial that we read ‘London’ as it occurs in (28) as we afﬁrm the sentence in C1, to be a faithful translation of ‘Londres’ as it occurs in (27) as Pierre assents to that sentence in Paris. By ‘a faithful translation’, I mean whatever translation that is good enough to support the correct application of the disquotational principle. We will therefore attach a subscript to ‘London’ in the logical structure of (28) as we afﬁrm it in C1 to indicate a faithful translation of ‘Londres’ in (27) as Pierre assents to it, i.e. as in the context in which Pierre assents to it:

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Likewise, in view of the crucial role played by Pierre’s dissent from (29) in London in justifying our denial of (30), we attach a different subscript to ‘London’ in the logical structure of (30) as we deny it in C2 to indicate a faithful translation of ‘London’ in (29) as Pierre dissents from it, i.e. as in the context in which he dissents from it: (30r0 ) (∃!x)(x is a proposition & (w)(x is true at w London2 is pretty)) & (x)((x is a proposition & (w)(x is true at w London2 is pretty)) Pierre believes x). C1 and C2 are importantly different and their difference results in the different verdicts on (28) and (30) by us. So, it would be improper to assume that the two subscripts are interchangeable or that ‘London1’ and London2’ make exactly the same overall contribution to the determination of the propositions by sentences in which they occur. Thus, the appearance that (28r) and (30r) do not differ from each other at all apart from the embedding contexts (C1 and C2) cannot be upheld. We should understand them as less articulate versions of (28r0 ) and (30r0 ), where the subscripts are important but were previously suppressed or invisible. At some metaphysically impossible worlds, London1 is pretty but London2 is not. The proposition Pierre believes and the proposition he disbelieves differ in truth value at such worlds. Of course, London1 and London2 are one and the same city. This makes the Pierre case somewhat analogous to the Becky case. When Kripke says that we are at a loss as to what to say about the truth value of the sentence ‘Pierre believes that London is pretty’ and that this is a puzzle about belief independently of any particular theory of proper names, I agree. But when he raises the suspicion that the Pierre case might force the theoretical framework of propositions to collapse, I do not concur. I think that the propositional framework can handle the Pierre case adequately. The set-up of the Pierre story makes it clear that Pierre encounters London (via picture postcards while in Paris) as a pretty city and later encounters London directly (by being in it) as an ugly city, without giving either encounter an upper hand over the other, as it were, concerning the determination of his overall (all-things-considered) attitude toward the city. This makes the context of Kripke’s famous query about Pierre, ‘Does he or does he not believe the proposition that London is pretty? ’ indecisive in determining the denotation of ‘the proposition that London is pretty’, and speciﬁcally, schizophrenic between the two subscripted names. As a result, we are at a loss how exactly to understand ‘London’ in his query so as to evaluate the truth value of ‘Pierre believes that London is pretty’ in the context of the query. Kripke’s query is not sufﬁciently articulate to deserve a short deﬁnitive answer.

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9 .1 0 . A POLISH MUSICIAN POLITICIAN Kripke puts forth another ingenious example case which appears equally puzzling.27 During a discussion of various Polish musicians, an English speaker—let it be our Bianca—assents to (31) Paderewski was a great musician. So, relying on (DQ1), we afﬁrm (32) Bianca believes that Paderewski was a great musician. During a different discussion of various Polish politicians, Bianca dissents from (31). So, relying on (DQ2), we deny (33) Bianca believes that Paderewski was a great musician. One and the same Paderewski is in fact in question. The logical structure of (32) as we afﬁrm it and the logical structure of (33) as we deny it contain ‘Paderewski1’ and ‘Paderewski2’, respectively, which are faithful translations of ‘Paderewski’ in (31) as Bianca assents to it and ‘Paderewski’ in (31) as Bianca dissents from it, respectively. Unlike the Pierre case, this case involves only one natural language, English. Like the Pierre case, it involves transition from English without subscripts to English with subscripts. The rest of the story parallels the Pierre case. 9. 1 1. AN IMPERILED CONVERSATIONALIST Another interesting story is told by Mark Richard.28 Maria is talking to Bianca on the telephone. Maria does not think the person she is talking to on the phone is in danger. Maria is also watching Bianca from across the street. Maria thinks the person she is watching across the street is in danger. Obviously, Maria does not realize that she is talking to the same person as the one she is watching. Pointing across the street, Maria afﬁrms to herself, (34) I believe that she is in danger. Then, speaking into the phone, Maria denies (35) I believe that you are in danger. The logical structures of (34) and (35) are, respectively:

27 28

Ibid. Nathan Salmon’s (1986a) example of the befuddled Elmer is a variant. Richard 1983; 1990: 117–18. The names of the conversationalists are not from Richard.

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(34r) (∃!x)(x is a proposition & (w)(x is true at w she1 is in danger)) & (x)((x is a proposition & (w)(x is true at w she1 is in danger)) I believe x). (35r) (∃!x)(x is a proposition & (w)(x is true at w you2 are in danger)) & (x)((x is a proposition & (w)(x is true at w you2 are is in danger)) I believe x). Here the subscripts indicate the anaphoric relation between pronouns. In the context of Maria’s afﬁrmation of (34), ‘she1’ and ‘I’ in (34r) refer to Bianca and Maria, respectively. In the context of Maria’s denial of (35), ‘you2’ and ‘I’ refer to Bianca and Maria, respectively. The rest of the story parallels the Becky case, with contextual relativization explicitly added for the indexical pronouns. 9 . 1 2 . THE DE SE The same as above, except that Maria is not on the phone, that she is simply watching a person across the street, and that the person she is watching is herself (reﬂected on an unnoticed mirror in the store window). As before, Maria afﬁrms (34) to herself. Also to herself, Maria denies (36) I believe that I am in danger. This is parallel to the previous case, even though ‘she’ in (34) refers to Maria as she afﬁrms (34) and (36) contains ‘I’ spoken by Maria. So, (34) and (36) are not equivalent. Revised modal Russellianism does not treat belief de se in an importantly special way. Whatever is special about belief de se has to come from the unpacking of how Maria comes to believe or disbelieve a particular proposition like the one expressed by ‘I am in danger’ in (36) in the context of her denial of the sentence, not from some special element postulated by an analysis tailormade just for de se belief sentences.29 9 . 13 . TWO TUBES David Austin tells a story which involves demonstratives.30 Dave is simultaneously looking at a colored patch through a tube with his right eye, calling the patch by the demonstrative pronoun ‘this’, and a colored patch through another tube with his left eye, calling the patch by the pronoun ‘that’. What he calls ‘this’ and what he calls ‘that’ are in fact one and the same patch but he does not realize it. Talking to himself, he afﬁrms (37) and (38) but denies (39): 29 30

Lewis 1979b and Chisholm 1981 give belief de se a special status. Austin 1990: 20–5.

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(37) I believe this is red. (38) I believe that is red. (39) I believe this is that.31 Given the way the reference of each demonstrative in these sentences is meant to be determined, this might appear to make Dave an irrational believer. The logical structures of the sentences, again supplemented with explicit subscripts, are as follows: (37r) (∃!x)(x is a proposition & (w)(x is true at w this1 is red at w) & ((x is a proposition & (w)(x is true at w this1 is red at w)) I believe x); (38r) (∃!x)(x is a proposition & (w)(x is true at w that2 is red at w) & ((x is a proposition & (w)(x is true at w that2 is red at w)) I believe x); (39r) (∃!x)(x is a proposition & (w)(x is true at w this1 is that2 at w) & ((x is a proposition & (w)(x is true at w this1 is that2 at w)) I believe x). Let us say that Dave worlds are worlds at which the proposition expressed by (40) in the context of Dave’s afﬁrmation of (37) is true, and the proposition expressed by (41) in the context of his afﬁrmation of (38) is true, but the proposition expressed by (42) in the context of his denial of (39) is false: (40) This is red. (41) That is red. (42) This is that. Given the coreferentiality of ‘this’ and ‘that’ and the rigidity of demonstrative pronouns, Dave worlds are metaphysically impossible worlds, and ‘the proposition that this is red’ denotes in the context of his afﬁrmation of (37) a different proposition from the one ‘the proposition that that is red’ denotes in the context of his afﬁrmation of (38); these propositions differ in truth value at Dave worlds. So, Dave can coherently disbelieve the proposition denoted by ‘the proposition that this is that’ in the context of his denial of (39). Thus, despite initial appearance, Dave’s rationality as a believer is saved. 9 . 1 4 . BELIEF SENTENCES: SUMMARY Our discussion of belief sentences consistently construes ‘S believes that P’ as ‘The proposition that P is believed by S’ and assumes that belief is a relation between S and the proposition denoted by ‘the proposition that P’. On this basis, 31 We are also assuming that Dave afﬁrms (37) and (38) without ‘I believe’ but denies (39) without ‘I believe’, i.e. that Dave afﬁrms (40) and (41) but denies (42).

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we explain how apparently puzzling belief ascriptions are not really puzzling without denying any of the important philosophical theses which are independently attractive. We also avoid introducing a tertium quid–like a ‘mode of presentation’–to mediate the dyadic belief relation. This reduces our theoretical baggage. Thus, the dialectical situation is this: accept Russell’s theory of descriptions for canonical descriptions of propositions, in conjunction with talk of metaphysically possible and metaphysically impossible worlds, and we can obtain a powerful theory of propositional discourse with a straightforward sub-theory on belief ascriptions. Let us summarize some important results such a sub-theory upholds: (A) The treatment of belief sentences is subsumed under a general treatment of sentences of the form ‘The proposition that P is ’. (B) The treatment of sentences of the form ‘The proposition that P is ’ is subsumed under a general Russellian treatment of deﬁnite descriptions. (C) ‘S believes that P’ is not made to entail any metalinguistic sentence about ‘P’. (D) Belief is a dyadic relation between a believer and a proposition. (E) Propositions are not assumed to be structured entities. (F) Synonyms occurring within ‘P’ in ‘S believes that P’ make the same semantic contribution to the determination of the proposition S is said to believe. (G) Coreferential names occurring within ‘P’ in ‘S believes that P’ make the same semantic contribution to the determination of the proposition S is said to believe. (H) Intuitive judgments about the truth values of belief sentences are upheld. (I) The disquotational principle is upheld. (J) Customary translations are respected. For example, the proposition expressed by ‘Snow is white’ is the same as the proposition expressed by ‘La neige est blanche’ (cf. the notion of faithful translation in the Pierre case).32 (K) Fregean senses are not invoked. (L) Modes of presentation are not invoked. (M) Mentalese is not invoked. As far as I know, no other coherent theory of belief ascription supports all of the above. Also as a bonus, our revised proposal yields an adequate deﬁnition of the expression relation (see the end of 9.4). All this makes the revised modal Russellian proposal attractive.

32

Richard is compelled to cast doubt on this to save his theory. See Richard 1990: 170.

10 Fictional Worlds 1 0. 1. FICTIONAL INDIVIDUALS According to David Braun, our ordinary pre-theoretical intuitions concerning ﬁctional individuals are confused and inconsistent. He says: Consider (31). (31). There is no Sherlock Holmes. Sherlock Holmes does not exist. Sherlock Holmes is just a ﬁctional character. (31) seems true, when we do not think about it too hard. But, on reﬂection, it appears to be contradictory. If the third conjunct of (31) is true, then there is such a thing as Sherlock Holmes, and so the ﬁrst conjunct is false. So is the second conjunct, assuming (contrary to Meinongians) that everything that there is exists. Thus, ordinary, pre-theoretical intuition appears to be incoherent. And ordinary intuition does not give any consistent guide as to which beliefs we should give up. Nevertheless, many theorists think that ordinary speakers who have the typical initial intuitions about (31) must be right about something. . . . For instance, on one theory ‘Sherlock Holmes’ is ambiguous between the non-referring ‘Holmes1’ and the referring ‘Holmes2’, and (31) is true if ‘Holmes1’ replaces the ﬁrst two occurrences of ‘Holmes’ and ‘Holmes2’ replaces the third. Other theorists say that (31) semantically expresses a contradictory proposition, but speakers who utter (31) intend to pragmatically convey some other, more complicated, proposition that really is true (according to the theorist’s favorite philosophical theory). . . . None of these hypotheses is plausible. There is little or nothing in speakers’ thoughts and intentions that indicates that the name ‘Holmes’ is ambiguous in their mouths. There is little or no evidence that speakers who utter (31) intend to convey some complicated proposition that is true under some favored philosophical theory. Most ordinary speakers just do not reﬂect enough to notice that there are problems with sentences like (31). . . . Most ordinary speakers’ beliefs about ﬁction really are (deep down) confused and inconsistent.1

1

Braun 2005: 612–13; his emphasis.

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The contradictory appearance of (31) is genuine, as Braun succinctly explains. The usual theoretical attempts to rescue (31) as non-contradictory are implausible, just as Braun says. I also agree with Braun that ordinary speakers are not sufﬁciently reﬂective to notice the apparent contradictoriness of (31). But I sharply disagree with Braun when he says that the ordinary pre-theoretical judgment, expressed as (31), is really confused and inconsistent. I think (31) is perfectly consistent when properly understood, and most ordinary speakers intuitively understand it properly. Braun is right when he says, ‘If the third conjunct of (31) is true, then there is such a thing as Sherlock Holmes’, but he is wrong when he continues, ‘and so the ﬁrst conjunct is false’. What the ﬁrst conjunct of (31) says, when charitably interpreted, is that there actually is no Sherlock Holmes. The truth of the third conjunct does not require that there actually be such a thing as Sherlock Holmes. In fact, actually being ﬁctional entails not actually being existent. But true predication requires the reality of what the predication is of. Thus, if the third conjunct of (31) is true, then there is such a thing as Sherlock Holmes in reality at large. Here the range of the existence predicate ‘there is’ includes things existing only at non-actual worlds. The shiftiness in the range of existence predicates is independently motivated, as we noted in Chapter 3, and ordinary speakers intuitively grasp it. This simple and straightforward understanding of (31) saves it from inconsistency. Ordinary speakers may not be able to articulate their intuitive understanding of (31) this way themselves, but it would be too hasty and uncharitable to dismiss their intuition as inconsistent. Braun’s own position on sentences which he believes contain empty names is to treat them as expressing gappy propositions. Braun believes that ‘Sherlock Holmes is a detective’ is such a sentence and expresses a gappy proposition, represented by the ordered pair, 5( ), being a detective >, where ‘( )’ marks an unoccupied gap. The sentence ‘Hercule Poirot is a detective’ also expresses a gappy proposition, represented by 5( ), being a detective>, the same ordered pair. Braun’s position therefore commits him to the view that the two sentences, ‘Sherlock Holmes is a detective’ and ‘Hercule Poirot is a detective’ express the same proposition. Braun acknowledges and accepts this. But surely, believing that Sherlock Holmes is a detective has a different inferential and behavioral potential from believing that Hercule Poirot is a detective: for example, the former, but not the latter, tends to dispose the believer to infer that an Englishman is a detective and tends to dispose the believer to answer the question ‘Is Sherlock Holmes a detective?’ in the afﬁrmative. Braun is aware of this challenge and meets it by claiming that the difference between the two believings consists in the manner in which the believer believes the one gappy proposition in question. The sentence ‘S believes that Sherlock Holmes is a detective’ conveys that S believes the proposition in one way, the Sherlock-Holmesy way, whereas the sentence ‘S believes that Hercule Poirot is a detective’ conveys that S believes the proposition in a different way, the Hercule-Poirotique way. This difference traces

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back to the corresponding difference in the manner in which the two sentences express the same gappy proposition. Braun’s position is the most straightforward non-modal way to uphold the direct reference view—the view that there is nothing to the semantic value of a proper name than its referent—in print to date. It is simple and elegant. There are two problems with it, however. First, it is unclear what a gappy proposition is. If we take Braun’s words literally, a gappy proposition is a proposition with a gap in it. But a proposition is not like a mouthful of teeth and we are hard-pressed to make sense of a gap in a proposition. Is Braun committed to the ontology of gaps as genuine objects? If so, how are they individuated and what are their identity conditions?2 If not, why not? Second, Braun’s account of the difference between the two beliefs above makes the difference a matter of the manner in which the content of belief is believed, but it seems intuitively compelling to think that the difference is in the content itself. It is intuitive to say that someone who believes that Sherlock Holmes is a detective infers that an Englishman is a detective and says ‘Yes’ to ‘Is Sherlock Holmes a detective?’ because of what she believes, not because of how she believes it. Braun cannot uphold this intuitive judgment and therefore needs to tell a less intuitive and more complicated functionalist story about belief. Of course, Braun’s treatment of empty names exactly parallels the standard treatment of distinct but coreferential names by prominent direct reference theorists.3 Braun would claim that this strengthens his treatment of empty names. I, however, would apply modus tollens instead of his tacit modus ponens and claim that this weakens the standard treatment of empty names by the prominent direct reference theorists.4 10 .2 . KRIPKE ON UNICORNS AND SHERLOCK HOLMES What kind of entity is Sherlock Holmes? In 1963, Saul Kripke wrote, ‘Holmes does not exist, but in other states of affairs, he would have existed’.5 Later in 1970, in his celebrated lectures Naming and Necessity, he said that it was erroneous to think that the ﬁctional name ‘Holmes’ named a particular nonactual possible individual and advocated the view that Holmes was not possible.6 Later still in his John Locke Lectures in 1973, he argued for the claim that ﬁctional individuals like Holmes actually exist. These three views on ﬁctional individuals are incompatible with one another and yet each has some initial 2 3 4 5 6

On the nature and ontology of holes, see Lewis and Lewis 1970; Casati and Varzi 1994. See Braun 1998, 2002. For a better direct-reference theoretical treatment, see the previous chapter. Kripke 1963: 65. Kripke 1980: 158.

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plausibility. It would be a proﬁtable scholarly exercise to trace and examine Kripke’s change of views over the decade in question, but we shall not attempt it. My sympathy is with his view in Naming and Necessity: Holmes is neither an actual individual nor a metaphysically possible individual; Holmes is a metaphysically impossible individual. My reason for favoring such a view, however, is quite different from Kripke’s and will be discussed in 10.4. Here let us examine Kripke’s arguments critically. In Naming and Necessity, before turning to Holmes, Kripke discusses unicorns and gives two arguments against their metaphysical possibility. Let us examine his arguments about unicorns ﬁrst and then the corresponding arguments about Holmes. (As for his John Locke Lectures,7 we shall brieﬂy discuss one argument advanced in them for the actual existence of ﬁctional individuals after discussing van Inwagen’s argument for the same claim, in the next section.) The passage on unicorns goes as follows: if we suppose, as I do, that the unicorns of the myth were supposed to be a particular species, but that the myth provides insufﬁcient information about their internal structure to determine a unique species, then there is no actual or possible species of which we can say that it would have been the species of unicorns. . . . the mere discovery of animals with the properties attributed to unicorns in the myth would by no means show that these were the animals the myth was about: . . . we must also establish a historical connection that shows that the myth is about these animals.8

It is arguable that in this passage Kripke intends to be advancing only one argument. If so, the argument has two separable parts, and it seems to me proﬁtable for us to separate the two parts explicitly as two independent arguments. In any case, the point of our discussion is not Kripke scholarship but assessment of interesting arguments for the metaphysical impossibility of ﬁctional individuals. In that spirit, let us extract two arguments from the above passage. The ﬁrst argument may be regimented as follows: (1) If unicorns are metaphysically possible, then they are a particular species. (2) If unicorns are a particular species, then they have a common internal structure which determines a unique species. (3) The myth does not give enough information about the internal structure of unicorns to determine a unique species. (4) If the myth does not give enough information about the internal structure of unicorns to determine a unique species, then unicorns do not have a common internal structure which determines a unique species. 7 They remain unpublished and are available only for in situ use in the Philosophy Faculty Library at Oxford University. 8 Kripke 1980: 157; his emphasis.

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Therefore, (5) Unicorns are not metaphysically possible. (1) is the initial assumption which Kripke makes without argument. (2) encapsulates a naive view of species. It is naive because it ignores evolutionary historical properties. Two different animal species might have the same internal structure but be distinguished from each other as different species due to different evolutionary histories. This defect in (2) is not serious, for the myth gives no more information about the evolutionary history of unicorns than about their internal structure. Thus (2) and (3) may easily be read to have appropriately enriched contents and remain plausible. (4), as appropriately modiﬁed, is justiﬁed by the assumption that unicorns do not actually exist and that the myth is the only source of information about unicorns not just epistemically but metaphysically. Unicorns are exactly what the myth says they are. Since the myth does not say enough to pin down a unique species, nothing grounds the claim that unicorns are a particular species. One way to resist this argument is by saying that Kripke is overly presumptuous in assuming that unicorns are a species according to the myth. This is not a promising way. I suspect that Kripke’s assumption is probably false but it matters little whether it is. Even if it is in fact false, we can easily imagine a myth which is just like the one Kripke speaks of but which explicitly states that unicorns are an animal species, and understand Kripke’s argument as being directed to that imagined myth. So we might as well assume that the imagined myth is the actual myth. The rest of his argument will proceed as convincingly as before. Another way to resist Kripke’s argument is by claiming that even though the myth purports to depict an animal species, it simply fails to do so. The myth merely depicts a kind of animal; nothing more, nothing less. Here ‘kind’ does not mean natural kind. It means kind in the sense that, say, domesticated mammals are a kind of animal, as distinguished from undomesticated mammals. The unicorns the myth depicts are a kind of animal, namely, the kind as characterized in the myth, where the characterization does not include any internal structure or evolutionary history. Many metaphysically possible animals of different species fall under that kind. This seems to be a more plausible way to think of unicorns than Kripke’s way and is certainly more in accordance with the pre-theoretical understanding we tend to have of unicorns. One may go a step further and say that the unicorns the myth depicts are not only a kind of animal but a kind of animal species. The myth does not give a unique natural kind but a kind—or type—of natural kind. The type in question is roughly the horse-like-and-horn-in-the-forehead type. I would be happy with this way of resisting Kripke’s argument if I were convinced that the myth should be allowed to be wrong about such a central issue concerning what it depicts. The myth explicitly says that unicorns are a single animal species, or so we are assuming. Who are we to say that the myth is just wrong about this? It should be up to the myth what it depicts. The myth speaks of unicorns as a single species

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(we assume), so unicorns—as depicted in the myth—are a single species if anything. This is the principle of charity we should apply to any myth or ﬁctional story. My disagreement with Kripke’s argument is with (4). I claim that despite the failure on the part of the myth in providing enough information, unicorns do have a common internal structure (along with a common evolutionary history) which determines a unique species but that the internal structure in question is such that the species is metaphysically impossible. I shall not argue the point. Instead, I shall let our discussion concerning Sherlock Holmes later illuminate how we should proceed with the case of unicorns in a parallel manner. The second argument may be put as follows: (6) Metaphysically possible animals are unicorns only if the myth is about them. (7) The myth is about certain animals only if there is a historical connection (of the right kind) between the myth and these animals. (8) There is no historical connection (of the right kind) between the myth and any metaphysically possible animals, even those metaphysically possible animals which possess the properties the myth attributes to unicorns. Therefore, (9) No metaphysically possible animals are unicorns. (6) is justiﬁed by our intuitive judgment that unicorns are, if anything at all, the animals the myth speaks about. The historical connection (of the right kind) in (7) is akin to the historical chain connecting an utterance of a proper name to its referent, according to the causal-historical ‘picture’ of reference Kripke champions. The myth bears no such connection either to actual animals—for otherwise, it would not be a myth—or to merely metaphysically possible animals—for the actual myth bears no historical connection (of the right kind) to anything merely metaphysically possible. The obvious crux of this argument is the notion of aboutness and it is this notion that makes the argument vulnerable. As already noted, we originally acquire the idea of a unicorn from the myth; unicorns are the animals we read about in the myth. Outside the myth, we have nowhere to turn to for our idea of what a unicorn is. This is why (6) is plausible. That is, underlying the plausibility of (6) is our ﬁrm presumption that unicorns are the animals the myth speaks of, i.e. that the myth is about unicorns. But this presumption ﬂies in the face of the claim that a historical connection (of the right kind) is necessary for aboutness. If, on the other hand, we are determined to uphold the claim of the necessity of historical connectedness (of the right kind) for aboutness, then the plausibility of (6) is undermined. Thus, it is difﬁcult to uphold (6) and (7) at the same time. In the following passage, we discern two arguments against the metaphysical possibility of Holmes which are parallel to the ones concerning unicorns:

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I hold similar views regarding ﬁctional names. The mere discovery that there was indeed a detective with exploits like those of Sherlock Holmes would not show that Conan Doyle was writing about this man; it is theoretically possible, though in practice fantastically unlikely, that Doyle was writing pure ﬁction with only a coincidental resemblance to the actual man. (See the characteristic disclaimer: ‘The characters in this work are ﬁctional, and any resemblance to anyone, living or dead, is purely coincidental.’) Similarly, I hold the metaphysical view that, granted that there is no Sherlock Holmes, one cannot say of any possible person that he would have been Sherlock Holmes, had he existed. Several distinct possible people, and even actual ones such as Darwin or Jack the Ripper, might have performed the exploits of Holmes, but there is none of whom we can say that he would have been Holmes had he performed these exploits. For if so, which one?9

Corresponding to the ﬁrst argument on unicorns is the argument embedded in the latter half of the above passage, mentioning Darwin and Jack the Ripper. Unlike in the argument on unicorns, Kripke does not speak of the internal structure of Holmes, but it is clear that what is at issue is whatever property or properties of Holmes that will determine an individual uniquely and necessarily as Holmes in a way analogous to the way in which an internal structure, such as the genetic structure, may do for an animal species (when combined with evolutionary historical properties). It is unclear whether some genetic structural property or properties will sufﬁce to determine an individual man uniquely and necessarily. So let us simply say that some properties of a certain type or types will determine an individual man like Holmes uniquely and necessarily. Let us call such properties determinant of Holmes in particular Holmes-determining properties. The ﬁrst argument may then be regimented as follows: (10) If Holmes is metaphysically possible, then he is a particular man. (11) If Holmes is a particular man, then he has Holmes-determining properties. (12) Doyle’s Holmes stories do not specify Holmes-determining properties. (13) If Doyle’s Holmes stories do not specify Holmes-determining properties, then Holmes does not have Holmes-determining properties. Therefore, (14) Holmes is not metaphysically possible. (13) is justiﬁed by the assumption that Holmes does not actually exist and that Doyle’s Holmes stories are the only source of information about Holmes, not just epistemically but metaphysically. It would be even more difﬁcult than in the case of unicorns to maintain against (10) that Holmes is not a particular metaphysically possible man but a kind of metaphysically possible man, a kind under which many different metaphysically possible men fall. The reason is evident in the linguistic fact that unlike ‘unicorn’, which is a common noun, 9

Ibid. 157–8; his emphasis.

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‘Sherlock Holmes’ is a proper name (or so it strongly appears). Doyle’s stories depict Holmes as one particular man and it would be difﬁcult to fathom how the stories can be wrong about that. Difﬁcult but not impossible. I am somewhat sympathetic to the position that, like unicorns, Holmes is a kind. Doyle’s stories depict adventures not of any particular man, metaphysically possible or not, but of a kind of man.10 Sympathetic as I am to this position, I wish to avoid its implication, which is that ‘Sherlock Holmes’ is not a proper name of a man, i.e. that ‘Sherlock Holmes is a man’ is not true in any sense of ‘is a man’ (as opposed to ‘is a kind of man’).11 I assume that it is important to avoid this implication. The reason, as before, is the principle of charity for myths and ﬁctional stories. If Doyle’s stories say Holmes is a particular man, then Holmes—as depicted in the stories—is a particular man.12 If I am wrong and it is not important, then I will be happy with the position that Holmes is a kind of man. Assuming that it is important to uphold that Holmes is a particular man, however, my view is that (13) should be rejected. Even though the stories do not specify Holmes-determining properties, Holmes has Holmes-determining properties, but those properties are such that they make Holmes metaphysically impossible. The second argument may be put as follows: (15) Any metaphysically possible man is Holmes only if Doyle’s Holmes stories are about him. (16) Doyle’s Holmes stories are about a certain man only if there is a historical connection (of the right kind) between the stories and the man. (17) There is no historical connection (of the right kind) between the stories and any man, even any metaphysically possible man who possesses the properties the stories attribute to Holmes. Therefore, (18) No metaphysically possible man is Holmes. What we said about (6) and (7) applies to (15) and (16) mutatis mutandis. The notion of aboutness plays a crucial role in this argument and makes the argument vulnerable in the same way as before. To add what we said before, let us observe that Kripke himself has taught us that a uniquely satisﬁed purely qualitative description may be used to ﬁx the reference of a proper name without providing a 10

For a forceful discussion along those lines, see Currie 1990: 127–81. Here I include both the traditional predicative sense of ‘is’ and the Mally–Zalta ‘encoding’ sense of ‘is’. See Zalta (1988: 15–37; 2000) for the notion of encoding and its application to ﬁction. 12 Here, the Mally–Zalta encoding sense of ‘is’ does not do full justice to the stories, for the stories do not depict Holmes as being a particular man in the encoding sense of ‘being’. Zalta might say that, knowing that the stories are stories, we (as opposed to the ﬁctional author of the stories) should speak in the encoding sense when we say ‘Holmes is a particular man’. I take it that such a response would still be a weakening of the principle of charity. Zalta, of course, might then say so much the worse for the principle of charity. 11

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synonym for it.13 Such reference ﬁxing may ground aboutness. If so, a historical connection is unnecessary for aboutness after all. 1 0. 3 . FICTIONAL NAMES AND EXISTENCE There is a plausible principle concerning the expression of a proposition by a sentence containing a proper name. Let S be any sentence of the form Æ is , where Æ is a proper name. The principle says, (P) S expresses a proposition if and only if S expresses the singular proposition which is about the referent of Æ and the property expressed by and which is to the effect that the ﬁrst possesses the second.14 One objection to (P) uses names of ﬁctional individuals and relies on the following auxiliary hypothesis: (H) For any proper name Æ, for any predicate , if the referent of Æ does not actually exist, then it is not the case that the sentence S expresses any singular proposition about the referent of Æ. Consider: (19) Sherlock Holmes is a detective. The objection goes as follows: The referent of ‘Sherlock Holmes’ is a ﬁctional individual. Since ﬁctional individuals are merely ﬁctional by deﬁnition, they do not actually exist. So, the referent of ‘Sherlock Holmes’ does not actually exist. So by (H), it is not the case that (19) expresses any singular proposition about the referent of ‘Sherlock Holmes’. So by (P), (19) does not express a proposition. But (19) does express a proposition, perhaps even a true one. Therefore, we should reject (P).

Notice that we cannot skirt this objection by insisting that (19) does not express a proposition, that when we apparently think (19) expresses a proposition, we are mistaking (19) for (20) In the Holmes stories, Sherlock Holmes is a detective, and that (20) expresses a proposition. The reason why this will not allow us to avoid the objection is that the following auxiliary principle is plausible: (C) If S does not express a proposition, then the result of attaching a sentential operator to S does not express a proposition.15 13

David Kaplan’s ‘dthat’ operator is based on a similar idea. See Kaplan 1978. We are again being loose with the use/mention distinction. We also speak of ‘’ instead of ‘is ’ as a predicate. 15 Something similar to this principle is defended by Gareth Evans (1982: ch. 10). 14

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The plausibility of (C) is guaranteed by the compositionality of propositional expression. I do not believe that the objection is good, however. There is a seemingly rather popular defense of (P) in the face of this objection. I shall consider this defense of (P) and reject it. I shall then list a number of desiderata for a satisfactory semantic theory for names of ﬁctional individuals, sketch such a theory meeting the desiderata, and conclude that (P) is acceptable after all.

10.3.1. Creationist argument The seemingly popular defense of (P) is to claim that ﬁctional characters do actually exist. If one takes this view, (H) is irrelevant to the appraisal of (P) in view of (19). But how is one then to understand the notion of a ﬁctional individual? The answer is that, on this view, a ﬁctional individual is an actually existing thing that has been created in a special way, roughly, by a ﬁction writer’s ﬁction-writing endeavor (plus, perhaps, ﬁction readers’ reading of the resulting ﬁction). One virtue of this view is that it makes it literally true to say that Doyle created Holmes, where the meaning of ‘created’ is such that if x created y, then y came into existence. Another virtue is that it makes it literally true to say things like the following: There are characters in some nineteenth-century novels who are presented with a greater wealth of physical detail than is any character in any eighteenth-century novel. This sentence is taken from Peter van Inwagen’s writings.16 He argues that sentences like this are theoretical sentences of literary criticism and as such they should be regarded as postulating theoretical entities of literary criticism, namely, ﬁctional individuals. He says that just as we should believe in the actual existence of such theoretical entities of physics as electrons and protons, we should believe in the actual existence of such theoretical entities of literary criticism as Holmes and Hamlet. This is an interesting argument for the actual existence of ﬁctional individuals, but there are a number of problems with it. First, if Holmes actually exists, Doyle must have brought Holmes into existence by writing the Holmes stories. But since Doyle did not bring into existence a human being by writing the Holmes stories, Sherlock Holmes is not a human being. Nor is Holmes a dog, a cat, a tree, a chair, or anything else concrete. So, Holmes must be an abstract object. But being abstract does not help make Holmes any easier for Doyle to have brought into existence. There are many abstract objects Doyle might be said to have ‘created’ by writing the Holmes stories: for example, sentences, paragraphs, chapters, and stories. I am not speaking of tokens of linguistic expressions he produced on sheets of paper, but types of such expressions. I think we should 16

van Inwagen 1977: 302; 1983: 73.

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avoid saying that Doyle created these abstract linguistic objects but should say instead that he was the ﬁrst to write down their tokens. But I will not press this point, for even if Doyle could be said literally to have created such abstract linguistic objects, the ﬁctional individuals in his stories are different. They are not types of expression tokens. Their alleged creation remains mysterious. In Chapter 4 (4.2) we introduced Hartur Donan Coyle, a deeply deluded contemporary of Arthur Conan Doyle. Completely independently of Doyle, Coyle wrote a series of stories which happened to repeat Doyle’s Holmes stories verbatim. Unlike Doyle, Coyle intended his stories to be non-ﬁction and believed he was reporting facts. He believed himself to be Dr Watson, recording the adventures of his friend faithfully. It seems obvious that Coyle did not write ﬁction (in the sense of ‘write ﬁction’ in which Doyle wrote ﬁction). He wrote non-ﬁction which happened to be grossly false. Since he did not write ﬁction, he did not write ﬁction which featured a ﬁctional individual. So he did not create any ﬁctional individual. What did Doyle do but Coyle did not that was responsible for the former’s creation of the abstract object Holmes? Notice that as often as we say that an author has ‘created’ certain ﬁctional characters, ﬁctional plots, etc., we also say instead that an author has ‘thought of ’ such characters, plots, etc., before anyone else, or that an author has ‘come up with’ them ﬁrst. Such locutions as ‘thinking of . . . before anyone else’ and ‘coming up with . . . ﬁrst’ carry no implication that the characters, plots, etc., are brought into existence by the author. In gymnastics, moves are named after the gymnasts who performed them ﬁrst in competition: for example, the Tsukahara, the Yerchenko, the Liukin. In each case, the type of move in question existed before the gymnast performed a token of it for the ﬁrst time. The gymnast may be said to have ‘invented’ or ‘created’ the move in the sense of producing its token in competition before anybody else. I suggest that we understand ‘creation’ in the production of ﬁction in a similar fashion. The second problem is that some ‘theoretical’ utterances by literary critics are falsiﬁed if ﬁctional individuals are abstract. The above example from van Inwagen itself is suggestive. Notice that the relative pronoun ‘who’ in it signals that the characters in the nineteenth-century novels in question are human, or at least animate, and certainly not abstract. For a less subtle example, we may modify van Inwagen’s sentence only slightly: There are female characters in some nineteenth-century novels who are presented with a greater wealth of physical detail than is any character in any eighteenth-century novel. The noun phrase ‘female characters’ means ‘characters who are female’. Surely those who, with van Inwagen, regard ﬁctional characters as actually existing abstract objects would have no special reason to claim that ordinary English expressions used in literary criticism have special non-standard meanings.17 But 17

Except Zalta.

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then, the above sentence would commit us to the actual existence of ﬁctional characters who are female. No abstract objects are female. So the sentence is false, or else those ﬁctional characters are not abstract. Here is a related challenge to the claim that ﬁctional individuals are abstract objects created by their authors. If the claim is true, then the Holmes stories are massively false stories about the created abstract object Sherlock Holmes, since they are about Holmes and they predicate of Holmes many properties Holmes, an abstract object, does not possess. How then is reference to Holmes established? There seems to be no known mechanism of reference that applies. Edward Zalta’s theory that the abstract object Holmes ‘encodes’ the properties attributed to it in the stories seems to be the most promising line to pursue, but it strains to account for the discrepancy between the ‘encoding’ of those properties by Holmes and the predication of the properties in the traditional sense in the stories.18 Amie L. Thomasson points out that Zalta’s theory is unable to account for ﬁctional stories about non-ﬁctional individuals (for example, Napoleon in War and Peace) because non-ﬁctional individuals cannot encode properties.19 The third problem is that van Inwagen overvalues the ontological seriousness of literary criticism. Physics is a serious attempt to learn what actually exists and what properties and relations actually existing things have. That is why every theory in physics carries an ontological commitment. Literary criticism, on the other hand, is not a serious attempt to learn what actually exists. Its main concerns lie elsewhere, however important they may be. It is a mistake to take literary criticism with the same ontological seriousness as physics, or any other science. The fourth problem is that if ﬁctional individuals actually exist, then it is false to say that they do not, but it is in fact true to say that Sherlock Holmes does not actually exist. Our robust sense of actuality says that there is actually no Sherlock Holmes, or any other ﬁctional individual. Some might point out that since on my view, reality includes Sherlock Holmes, it is disingenuous for me to appropriate and adapt Bertrand Russell’s famous phrase ‘robust sense (of reality)’. In response, I would say that Russell was not particularly concerned with alethic modal metaphysical issues and that when he said ‘reality’ he probably did not clearly distinguish what he meant from what we now call actuality. But if I am wrong about what Russell really meant, then I will simply admit that I am making a non-Russellian use of the Russellian phrase and say that I do so because I think it is a dramatic way to make my point. The ﬁfth problem is that actual existence of ﬁctional individuals is not necessary for understanding the truth conditions of sentences asserting their relations to actually existing individuals. Let us discuss three typical such sentences. First, ‘Jane is taller than Sherlock Holmes’ should be understood as saying 18

See Zalta 1988: 123–9.

19

See Thomasson 1999: 104.

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that Jane is taller than Sherlock Holmes is in the stories, which is the case if and only if Jane is tall to a certain degree d (or alternatively, Jane has a certain height h), Sherlock Holmes is tall to a certain degree d’ (Sherlock Holmes has a certain height h’) in the story, and d is greater than d’ (h is greater than h’). Second, the truth of ‘Some Scotland Yard ofﬁcers admire Sherlock Holmes’ does not require the existence of Sherlock Holmes. The predicate ‘admire’ allows a non-existent direct object. Cf. ‘Some Oxford philosophers admire Aristotle now’. Third, when a sentence contains a main verb which is transitive and requires the existence of the direct object, the sentence is clearly false if the name purporting to designate the direct object is a ﬁctional name: ‘Some Scotland Yard ofﬁcers shook hands with Sherlock Holmes’; ‘Jane kissed Sherlock Holmes’. Cf. ‘Some Oxford philosophers walked with Aristotle yesterday’. The sixth problem concerns motivation. The abstractness of Holmes would make (19) false. But remember that it is the intuitive truth of (19) that underlies our intuition that (19) expresses a proposition. So, this view undermines our motivation to defend (P) in view of sentences like (19).20

10.3.2. Kripke on Zeus and Hamlet In his John Locke Lectures, Kripke offers a number of arguments for the claim that ﬁctional individuals actually exist. Let us examine one of them. It may be called the argument by contrast. He offers two versions of it. One involves the name ‘Moloch’, and the other the name ‘Gonzaga’. The Old Testament appears to say that the Jews worshiped a pagan god called ‘Moloch’. According to the two most prevailing theories about the Old Testament, there is no pagan god called ‘Moloch’ but the name was either the result of misvocalizing a Hebrew word for ‘king’ or the name of a kind of sacriﬁce. If either theory is right, then there is no god Moloch that the Jews worshiped. In contrast, ancient Greeks worshiped Zeus. That is, there is a god, Zeus, that ancient Greeks worshiped. There is an ontological difference between Moloch and Zeus, and that is actual existence. The second version of the argument by contrast concerns Hamlet and Gonzaga. Gonzaga is a character in a play within the play Hamlet. There is no such ﬁctional individual as Gonzaga. In contrast, there is such a ﬁctional individual as Hamlet. Again, the difference between them is ontological; Hamlet actually exists but Gonzaga does not. The problem with either version of the argument by contrast is that it proliferates different kinds of actual existence. When people, including Kripke, say that Moloch was not a pagan god or that the Jews did not worship Moloch, they are speaking of Moloch, just as the ancient Greeks were speaking of Zeus. They are not speaking of any other putative god or putative object of worship. 20 I say more on the arguments by van Inwagen and other creationists for the actual existence of ﬁctional individuals in Yagisawa 2001.

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They are speaking of a particular putative god, namely, Moloch. That is, a particular putative god, Moloch, is such that they are speaking of him (her, it?). By contrast, nobody is bothering to speak of a putative god Cholom. (‘Cholom’ is a nonsense word I just made up.) There is no such putative god Cholom. There is an ontological difference between Moloch and Cholom and that difference is actual existence, one may say mimicking Kripke’s move. The kind of actual existence, which Moloch has and Cholom lacks, cannot be the same kind of actual existence as the actual existence Moloch lacks but Zeus has. So this is a different kind of actual existence. Likewise with Gonzaga. When people, including Kripke, say that Gonzaga is not a real ﬁctional individual, they are speaking of Gonzaga. They are not speaking of any other putative ﬁctional individual. They are speaking of a particular putative ﬁctional individual, namely, Gonzaga. That is, a particular putative ﬁctional individual, Gonzaga, is such that they are speaking of him (it?). By contrast, nobody is bothering to speak of a putative ﬁctional individual Agaznog. (‘Agaznog’ is a nonsense word I just made up.) There is no such putative ﬁctional individual as Agaznog. There is an ontological difference between Gonzaga and Agaznog and that difference is actual existence. The kind of actual existence in question cannot be the same kind of actual existence as the actual existence Gonzaga lacks but Hamlet has. So this is a different kind of actual existence. To argue for a third kind of actual existence will require slightly more imagination but nothing fundamentally different. This shows that Kripke’s line of reasoning will lead to a proliferation of kinds of actual existence. This gives us good reason for rejecting Kripke’s claim that the contrast between Zeus and Moloch, or between Hamlet and Gonzaga, is ontological (pertaining to actual existence). There is another objection to the argument by contrast. If the argument is successful, then it can be used against the actual existence of Zeus or Hamlet. The ancient Greeks worshiped Zeus and computer nerds worship Bill Gates (at least some of them do). But there is a difference between the two, and the difference is ontological. The ancient Greeks worshiped some individual who they thought actually existed but did not, whereas the nerds worship some individual who they think actually exists and does. The ancient Greeks were wrong in believing in the actual existence of Zeus, whereas the nerds are right in believing in the actual existence of Bill Gates. There is no such individual as Zeus, but there is such an individual as Bill Gates. Likewise with Hamlet. If you go to Denmark and check the historical records of the country, you will not ﬁnd Hamlet as one of its princes in the past. But if you go to England and check the historical records of the country, you will ﬁnd, say, Albert as one of its princes in the past. Albert actually existed; Hamlet did not. (One might also object to Kripke that his argument, if successful, would make it too easy to prove the existence of God: some people worship God but it is not the case that some people worship Moloch; so God exists and Moloch does not; therefore God exists.)

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10.3.3. Desiderata I do not consider these objections to be insurmountable. But I do consider them to provide sufﬁcient justiﬁcation for looking elsewhere for a satisfactory account of ﬁctional individuals. I shall assume that, ceteris paribus, any theory satisfying all of the following desiderata is preferable to any theory not satisfying all of them: (I) It should treat ﬁctional individuals as not actually existent. (II) It should maintain proper names of ﬁctional individuals as directly referential. (III) It should allow predications of story-speciﬁed properties of ﬁctional individuals to be literally true (in the traditional sense rather than, say, Mally–Zalta’s ‘encoding’ sense): for example, Sherlock Holmes was indeed a detective. (IV) It should treat inter-ﬁctional discourse straightforwardly: for example, ‘Commander Data (of Star Trek the Next Generation) admires Holmes’. (V) It should treat discourse about relations between ﬁctional individuals and items outside ﬁction straightforwardly: for example, ‘Some ofﬁcers at Scotland Yard admire Holmes’. We have discussed (I).21 (II) stems from the desirability of theoretical unity. Proper names of actual individuals are directly referential, and names of ﬁctional individuals should not be treated differently if we can help it. I shall say a little more on direct reference shortly. (III)–(V) are intuitively attractive features of any account. My proposal is to satisfy (I)–(V) by means of the distinction between actual existence and non-actual existence. Existence is relativized to worlds (as well as to domains). Actual individuals exist at the actual world (as well as at some nonactual worlds) and non-actual individuals exist at non-actual worlds (but not at the actual world). You and I are actual individuals, whereas Holmes, Hamlet, and other ﬁctional individuals are non-actual individuals. Their non-actuality is part of what makes them ﬁctional; the rest of what makes them ﬁctional is that they are referred to by means of ﬁctional names or quantiﬁed over by means of ﬁctional quantiﬁers. 10 .4 . IMPOSSIBILITY OF FICTIONAL INDIVIDUALS The proper name ‘Hesperus’ has some description along the lines of ‘the ﬁrst heavenly body visible at dusk at such-and-such a location at such-and-such a time 21 One view that honors (I) is Meinongianism. It is not my view, for it denies the equivalence between ‘There is X’ and ‘X exists’ and it also makes it puzzling why we exist while Holmes does not. Another view that honors (I) is Kendall Walton’s ‘make-believe’ view. It is not my view, but it is not incompatible with my view. See the last note in this chapter.

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of the year’ associated with it. Such a description is not semantically equivalent to, or synonymous with, the name but ﬁxes the reference for the name. So claims Kripke. He argues for this claim extensively in Naming and Necessity. His arguments have convinced many philosophers, although some remain skeptical. We shall simply assume that Kripke is right.22 I propose to apply Kripke’s idea of ﬁxing the reference to ﬁctional names like ‘Sherlock Holmes’. Whereas on Kripke’s proposal the description associated with a name whose referent actually exists ﬁxes the reference at the actual world without being a synonym for the name, I propose that the description associated with a name whose referent does not actually exist ﬁxes the reference at world(s) sufﬁciently close to the actual world without being a synonym for the name. To pursue this idea, let us begin by asking ourselves the question, ‘Assuming that actually there is nobody who ﬁts the total description Doyle gives of Holmes in his Holmes stories, if there had been a unique such man, would he be Sherlock Holmes?’ Kripke’s answer is ‘No’. I doubt that our intuition obviously prefers this answer. Kripke offers two reasons against the afﬁrmative answer. His ﬁrst reason is that even if there had been such a man, Doyle would not have been writing about him. Even if Kripke is right on this, it does not follow that even if there had been such a man, Doyle’s stories would not have been about him. The aboutness of the stories may well be independent of the aboutness of the author’s intention or the author’s act of writing; the stories may well be about X even if the author did not intend to be writing about X and even if the author’s act of writing of the stories was not about X. I think it legitimate for us to insist that the complete (or nearly complete) ﬁt with the Holmes description in the stories should make the man in question the individual the stories would have been about, because it is the best way to uphold the judgment that such a man would be Sherlock Holmes, a judgment our intuition does not obviously oppose. In fact, I daresay our intuition embraces the judgment that such a man would be Holmes more strongly than it embraces Kripke’s claim that the stories would not have been about such a man.23

22 Two-dimensional semanticists do not completely agree with Kripke. This is not the place to discuss their disagreement. 23 Kripke’s choice of Sherlock Holmes as an example ﬁctional individual for discussion is a curious one, given the theoretical position he wishes to maintain. Doyle’s Holmes stories are written in the ﬁrst-person singular, from the perspective of Holmes’s associate, Dr Watson. Writing of the stories by Dr Watson is part of what is depicted, or at least obviously implied, by the stories themselves. So any world at which the stories are true as written is a world at which Dr Watson writes them as true. At any such world, the author of the stories writes about the unique person who satisﬁes the Holmes description. This challenges Kripke’s contention that the author of the stories would not be writing about anyone in particular. It is true that Doyle might not be Dr Watson even at such a world, but Doyle ﬁgures importantly in our reasoning on Holmes not because he is Doyle but because he is the author of the Holmes stories. Kripke could have avoided this complication by choosing a different ﬁctional individual whose exploits are told in the more traditional detached third-person way. We shall not discuss the repercussions of the technique Doyle uses in his telling of

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Kripke expresses his second reason for giving the negative answer by saying, ‘there is none of whom we can say that he would have been Holmes had he performed these exploits. For if so, which one?’ The point of his rhetorical question is that there is no fact of the matter as to which particular one of many different metaphysically possible men at different respective metaphysically possible worlds ﬁtting the Holmes description would be Holmes, beating out all the others. This is a good point and I agree with it. But it does not warrant giving the negative answer he gives. The question, we should recall, is the counterfactual conditional question whether if there had been a unique man ﬁtting the Holmes description, he would have been Holmes. Suppose there are exactly three metaphysically possible worlds which are the closest to the actual world and at which the Holmes stories are true. At the ﬁrst world the Holmes description is uniquely true of a man, let us call him a, at the second world the description is uniquely true of another man b, and at the third world it is uniquely true of yet another man c. Kripke’s rhetorical question ‘Which one?’ is easily answerable. At the ﬁrst world it is a, at the second world it is b, and at the third world it is c. This is sufﬁcient for the afﬁrmative answer to the counterfactual conditional question. What is more interesting about Kripke’s point expressed in his rhetorical question is that it points to the metaphysical impossibility of Holmes. The metaphysical impossibility of Holmes is a consequence of the fact (we assume) that Holmes is a, b, and c at the ﬁrst, second, and third worlds, respectively. The three worlds are equally close to the actual world, so they are fairly close to one another, and the world-stages of a, b, and c at those respective worlds are one another’s closest continuers (or so we can easily assume). Our criterion of transworld identity therefore yields that Holmes is a transworld human being whose world-stages at those worlds are the stages of a, b, and c, respectively. But ex hypothesi, a, b, and c are different transworld human beings; we may even assume that they are, say, Charles Darwin, Jack the Ripper, and Lewis Carroll. Any transworld individual human being whose world-stages at those worlds are those of a, b, and c, respectively, violates metaphysical laws. To see this, take necessity of origin as an example metaphysical law. Suppose that Darwin, Jack the Ripper, and Lewis Carroll actually originated in the zygotes x, y, and z, respectively. By necessity of origin, they also originated in x, y, and z, respectively at their three respective worlds. Any transworld human being whose world-stages are the stages of Darwin, Jack the Ripper, and Lewis Carroll at the three worlds in question, respectively, is a human being who originated in x, y, and z at those worlds, respectively. So any such transworld human being is one who originated in different zygotes at different worlds. But this violates the metaphysical necessity of origin. It is futile to suggest that a, b, and c may come from the same zygote at

the Holmes stories any further, as our main focus is not so much on the subtleties in philosophy of ﬁction as on the metaphysical status of ﬁctional individuals within the framework of modal realism.

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the respective worlds, for if they do, then by necessity of origin, a, b, and c must be the same human being, which is contrary to the initial supposition. What if there is exactly one metaphysically possible world which is the closest to the actual world and at which the Holmes stories are true? In that highly unlikely event, Kripke’s rhetorical question ‘Which one?’ will be without force, for there will be only one candidate. A more likely scenario is that for every metaphysically possible world at which a unique man ﬁts the Holmes description, some other metaphysically possible world at which a unique man ﬁts the Holmes description is closer to the actual world. If there is such a sequence of closer and closer worlds at which a unique man ﬁts the Holmes description, what should we say about the metaphysical status of Holmes? If we trace along such a sequence of worlds from the far end toward the actual world, we should pass ﬁrst through worlds barely similar enough to the actual world to have a unique man ﬁt the Holmes description at them, and then through worlds increasingly closer to the actual world. If the man ﬁtting the Holmes description is deemed to be the same metaphysically possible man at all worlds in the sequence on independent grounds, say it is Darwin, then Holmes should be identiﬁed as the metaphysically possible transworld individual whose world-stages at those worlds are the worldstages of Darwin. If different men ﬁt the Holmes description at different worlds in the sequence, then the case is analogous to the case of a, b, and c above and Holmes is a metaphysically impossible transworld individual. So far we have assumed that there is only one sequence of closer and closer worlds at which a unique man ﬁts the Holmes description. Now suppose that there are two or more such sequences. Any two worlds from different sequences are incomparable in their closeness to the actual world. This complication does not change the situation fundamentally. If one and the same metaphysically possible man ﬁts the Holmes description at all sufﬁciently close worlds in all sequences, then he is Holmes at those worlds. If not, Holmes is the metaphysically impossible transworld individual whose world-stages at the sufﬁciently close worlds in the sequences ﬁt the Holmes description. It seems clear that this last scenario, according to which different individuals uniquely ﬁt the Holmes description at sufﬁciently close worlds in many sequences of closer and closer metaphysically possible worlds to the actual world, is the most plausible scenario. Thus it seems that Holmes is a metaphysically impossible transworld individual. Let us examine this issue a little more closely. Set aside all of the oft-mentioned ‘inconsistencies’ in the Holmes stories, such as those concerning the location of Dr Watson’s war wound and Russell’s viper’s ability of concertina movement up a bell-rope,24 the less-oft-mentioned ones, and the unnoticed ones. All the Holmes worlds sufﬁciently close to the actual world are then metaphysically well behaved and practically indistinguishable from the actual world except for 24

On the latter, see Gans 1970: 93, reported and discussed in Lewis 1978: 271.

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the Holmes-related facts, and the world-stage (of a transworld individual) at each such world who uniquely ﬁts the Holmes description at that world is as metaphysically well behaved as any world-stage at the actual world. If Holmes is a transworld individual whose world-stages are all metaphysically well behaved at metaphysically well behaved worlds, how can he be a metaphysically impossible individual? To begin to answer this question, we ﬁrst need to remind ourselves of the distinction between two different ways in which a transworld individual may exhibit metaphysical impossibility. One way is for an individual to have at least one world-stage that exhibits some metaphysical impossibility, such as being both human and non-human at the same time, or being one million light years away from something that is both human and non-human at the same time. The other way is for an individual to have two or more world-stages that jointly exhibit some metaphysical impossibility. Holmes is a transworld individual who exhibits metaphysical impossibilities in the second way. Some pairs of Holmes’s world-stages are pairs of world-stages of actual individuals. Any two worlds at which such world-stages exist do not both belong to the local metaphysical space, the metaphysical space to which all and only metaphysically possible worlds belong. So, at least one of the pair of worlds belongs not to the local metaphysical space but to an alternative metaphysical space. I shall argue for this by reductio. We start with an arbitrary pair of Holmes’s world-stages that is a pair of world-stages of actual individuals. Let us say that the pair {Darwin’s world-stage, Carroll’s world-stage} is such a pair. Let us suppose that Darwin’s world-stage that is Holmes’s world-stage exists at w1 and Carroll’s world-stage that is Holmes’s world-stage exists at w2; so, Darwin is Holmes at w1 and Carroll is Holmes at w2. Assume for reductio that both w1 and w2 belong to the local metaphysical space, i.e., they are both metaphysically possible worlds. Holmes’s world-stage at w1 and Holmes’s world-stage at w2 are world-stages of one human being (viz., Holmes). Holmes’s world-stage at w1 is Darwin’s world-stage at w1. Holmes’s world-stage at w2 is Carroll’s world-stage at w2. So Darwin’s world-stage at w1 and Carroll’s world-stage at w2 are worldstages of one human being. So Darwin and Carroll are one human being. But they are two human beings, not one. (More cautiously put, the human being who is Darwin at w1 is one and the same human being who is Carroll at w2. But the former human being is Darwin, and the latter Carroll; they are two, not one.) A contradiction. Therefore, w1 and w2 do not both belong to the local metaphysical space, i.e. at least one of them is a metaphysically impossible world. How about the other world in the pair? So far we have seen no reason for doubting that it belongs to the local metaphysical space. If it belongs to the local metaphysical space and is a metaphysically possible world, then not all Holmes worlds are metaphysically impossible worlds and not all stages of Holmes are metaphysically impossible stages. If so, Holmes is a transworld individual some of whose world-stages are metaphysically possible and others metaphysically impossible. But then Holmes is just like us, actual individuals, except that he is

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non-actual. We are all transworld individuals some of whose world-stages are metaphysically possible and others metaphysically impossible; cf. Humphrey’s world-stage which is a poached egg. So, if the other world in the pair belongs to the local metaphysical space, then Holmes is just as metaphysically possible as we are. I shall now argue that the antecedent of this conditional is false. The argument is essentially the same as the one given in the previous paragraph. At least one of the worlds w1 and w2 does not belong to the local metaphysical space. Suppose that it is w1. The question is whether w2 belongs to the local metaphysical space. Assume that it does; this is the reductio assumption. Now take another pair of worlds, w3 and w4, at each of which Holmes has a worldstage that is also a world-stage of an actual individual; say, at w3 Jack the Ripper’s world-stage is Holmes’s world-stage, and at w4 Thomas Huxley’s world-stage is Holmes’s world-stage. An argument exactly parallel to the previous argument about w1 and w2 shows that at least one of the worlds w3 and w4 does not belong to the local metaphysical space. Suppose that it is w3. Then either w4 belongs to the local metaphysical space or it does not. If it does not, then {w1, w2} is a pair of worlds one of which is in the local metaphysical space and the other is not, whereas {w3, w4} is a pair of worlds both of which are outside the local metaphysical space. But the two pairs are arbitrarily picked, so this difference between them is unexplainable. So w4 must belong to the local metaphysical space. But then both w2 and w4 belong to the local metaphysical space. By running the same line of argument as before with w2 and w4, we will reach a contradiction as before. So, concerning any pair of worlds at each of which Holmes has a world-stage that is a world-stage of an actual individual, the assumption that one of the paired worlds belongs to the local metaphysical space should be rejected. Therefore, no such world belongs to the local metaphysical space, i.e. no such world is a metaphysically possible world.25 Cases where at one world Holmes has a world-stage that is a world-stage of an actual individual and at another world he has a world-stage that is a world-stage of a non-actual metaphysically possible individual are similar. Darwin is not a non-actual metaphysically possible individual, so Darwin and a non-actual metaphysically possible individual are two individuals, not one. Cases where Holmes’s world-stages at two worlds are both non-actual metaphysically possible individuals may also be handled in the same way, provided that the individuals are distinct. Thus, Holmes is a metaphysically impossible individual. Holmes does not have a world-stage at any metaphysically possible world. So any metaphysically possible world at which an individual uniquely satisﬁes the Holmes description is a world at which Holmes has no world-stage, i.e. the individual in question is not 25 By parity of reasoning, it is easy to show that no such world belongs to an alternative metaphysical space in which the same laws of metaphysics permeate as in the local metaphysical space and which is not indifferent to the distinction between any two actual individuals.

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Holmes. Thus, for example, even if at some metaphysically possible world you shake hands with an individual who uniquely satisﬁes the Holmes description, it is not the case that at that world you shake hands with Holmes, unless you are a metaphysically impossible individual yourself. We should remember that this conclusion agrees with Kripke’s position in Naming and Necessity, according to which Holmes is metaphysically impossible, and that we have reached it by applying Kripke’s idea of ﬁxing the reference of a proper name to sufﬁciently close non-actual worlds. I take this to mean that our reasoning above provides a partially Kripkean endorsement of Kripke’s position in Naming and Necessity, albeit rather backhanded. It seems correct to say that Holmes could have avoided the confrontation with Professor Moriarty at the Reichenbach Falls on 4 May 1891. But if Holmes is metaphysically impossible, how can it be correct to say that Holmes could have done anything? The answer to this question should be clear. The sense of ‘could’ in which Holmes could have avoided the confrontation at the Reichenbach Falls is not metaphysical possibility but a different kind of possibility which should be understood in terms of some appropriate accessibility relation between metaphysically impossible worlds. Within some alternative metaphysical space at which Holmes spreads out as a transworld individual, there is some world at which Holmes has a world-stage who avoids the confrontation. 10 .5 . IMAGINED-SEEN FICTIONAL WORLDS Many ﬁctional worlds are metaphysically impossible worlds26 at which a given ﬁctional story is true.27 Whether the ﬁctional story is true or not is independent 26 Gregory Currie argues that ﬁctional worlds are not metaphysically possible worlds on the grounds that (i) metaphysically possible worlds are determinate, (ii) metaphysically possible worlds are consistent, and (iii) for each ﬁctional world, there are many metaphysically possible worlds corresponding to it, with equal claim to being it (Currie 1990: 54–5). I agree that ﬁctional worlds are not determinate, but some metaphysically possible worlds are not determinate, either. If we take quantum physics at its face value, we must say that the actual world is not determinate, at least at the quantum level. And if we take the moral of Erwin Schro¨dinger’s famous thought experiment involving a cat at its face value, we must say that the lack of determinacy seeps into the macro-level as well. In addition, many actual matters of fact may well be vague rather than determinate. As for (ii), I agree that most ﬁctional worlds are inconsistent in many ways and that this makes them metaphysically impossible worlds. The point (iii) is reminiscent of Kripke’s charge that no unique metaphysically possible candidate animal species may be said to be the unicorn, and that no unique metaphysically possible candidate man may be said to be Holmes. This point is closely related to (i), and I see no solid basis in Currie’s reasoning for saying that we should not accept many ﬁctional worlds corresponding to a single given ﬁction. 27 David Kaplan (1973) says that the world of Sherlock Holmes stories is a world where the stories are truthfully told. David Lewis makes a similar suggestion: ‘The worlds we should consider, I suggest, are the worlds where the ﬁction is told, but as known fact rather than ﬁction’ (1978: 266). Gregory Currie (1990) generalizes this to characterize all ﬁctional worlds. William Lycan objects and says that not all ﬁctional stories posit a ﬁctional story teller as part of the story. As an example, he

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of whether any particular member of the audience of the story thinks or imagines it to be true (unless the story is written in such a way as to involve the requisite kind of audience participation). Once we ﬁx a ﬁctional story, we have ﬁxed the ﬁctional worlds. Fictional worlds in this sense are invariant over different members of the audience and over different audiences. There is, however, another sense of ‘ﬁctional world’ in which ﬁctional worlds are not so invariant. Foremost among the ﬁctional worlds in that sense are imagined-perceived ﬁctional worlds. They are worlds such that each audience member is expected to imagine perceiving the universe to be at them. The clearest examples of imaginedperceived ﬁctional worlds are imagined-seen ﬁctional worlds, typically to be found in cinema. In cinema viewing, the scenes are directly presented to the viewer visually (with sound), rather than being indirectly presented by description as in literature. When one watches a ﬁlm, one imagines seeing a scene depicted in the ﬁlm truly unfold in front of one’s eyes. To imagine seeing something is to imagine oneself as seeing something, just as to imagine hearing a story is to imagine oneself as hearing a story. This plain fact is shown by the obviousness of the answer to the query ‘Whom do you imagine seeing a cat on the mat?’ directed to someone who says, ‘I imagine seeing a cat on the mat’. The obvious answer is ‘Myself, of course’. When one imagines a cat being on the mat, what one imagines is a scene in which a cat is on the mat. The scene includes a cat and the mat, and in the scene the ﬁrst is on the second. When one imagines seeing a cat being on the mat, what one imagines is a different scene involving an additional item, namely, oneself. The scene includes a cat, the mat, and oneself, and in the scene the third sees the ﬁrst being on the second. When we see a narrative ﬁlm, we imagine seeing scenes depicted in the narrative story of the ﬁlm as unfolding before our eyes. When we see in the ﬁlm Singing in the Rain Gene Kelly sing the title tune and dance down the street set on the sound stage while sprinklers pour water over it, we imagine seeing Don Lockwood (the character Kelly plays) sing and dance down the street under heavy rain. We not only imagine Don Lockwood do this but also imagine seeing him do it. The difference between imagining and imagining seeing is the seeing. Seeing requires a seer. To imagine seeing is to imagine oneself seeing, just as to imagine jumping into the pool is to imagine oneself jumping into the pool. The scene one imagines when one imagines jumping into the pool includes oneself as part of the scene. In order to distinguish imagining jumping into the pool from imagining someone jumping into the pool, it is not enough to say that in the former but not in the latter the imagining is done from the viewpoint of oneself as opposed to a third-person viewpoint. It is also necessary to say that the oneself whose viewpoint is the viewpoint of the imagining is the jumper, who is in the tells the following short story: ‘A lizard basked in the sun. A breeze stirred the leaves of a ﬂower nearby. A bird ﬂew past. Too bad there was no one around to record the event’ (reported in Currie 1990: 155–6). Notice that Lycan could easily have continued, ‘… or to report the event truthfully’.

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scene. So, when one imagines jumping into the pool, the scene imagined includes oneself as part of the scene. It is important to note that by this I do not mean that the scene imagined must include oneself as visible in the scene. It may or may not; but either way, the scene imagined is imagined to be a scene in which one oneself exists and jumps into the pool. Likewise, when you imagine seeing Don Lockwood sing and dance in the rain, the scene you imagine seeing contains you as a part, albeit not as being visible in it. You are not part of the visual images in the ﬁlm, but you are not just imagining the scene presented by these images but imagining yourself seeing (the central part of ) the scene in which Lockwood is dancing, and this puts you right in (the peripheral part of ) the imagined scene, even though you do not imagine yourself seeing yourself in the scene. So you are part of the scene imagined seen. Either you are embodied in the scene so imagined or you are not. If you are embodied, your body is causally inert in the scene except for whatever causation is involved in the imagined visual perception of the scene. This is plain from, for example, the way the policeman fails to notice you as he gives a suspicious glance at Don Lockwood.28 Yet the scene is supposed to take place in a universe with the same kinds of physical events and states of affairs and no miracles. This makes whatever world at which the scene takes place a physically impossible world. But at the same time, the scene is not supposed to defy any actual laws of physics (in the rigid sense of ‘actual’), however good a dancer Kelly might be. This seems to make whatever world at which the scene takes place metaphysically impossible. If, on the other hand, you are not embodied in the scene imagined seen, then whatever world at which the scene takes place is a Cartesian dualist world. This does not automatically make it a metaphysically impossible world, but it is still a bizarre world at which a disembodied perceiver sees Don Lockwood do things as depicted in the ﬁlm without causal efﬁcaciousness except for whatever is involved in the imagined visual perception by the disembodied perceiver.29 Either way, the type of world the ﬁlm depicts the universe to be at and the type of world the audience imagines seeing the universe to be at when viewing the ﬁlm are rather different types of world.30 28 A more dramatic example is a frontal close-up shot of a seeing character. When you imagine seeing such a scene, the character takes no notice of you at all in the scene imagined seen. There are many more examples illustrating the causal inertness of the body of the subject of imagining in the scene imagined seen. 29 e.g. W. D. Hart (1988) defends the metaphysical possibility of worlds at which such causal interactions take place. 30 Even if we understand the imagined seeing to be an imagined situation in which someone else (other than the person doing the imagining) is doing the seeing, the same conclusion is obtainable, for the bizarreness (or, likely metaphysical impossibility) of whatever imagined-seen ﬁctional world results from the fact that the scene imagined seen contains the imagined seer, whether s/he is the imaginer or not. Some, like George Wilson (whose views we shall discuss in the next paragraph), might say that imagining someone else seeing a scene involves imagining a scene with that someone in it but that imagining (oneself) seeing a scene need not involve a scene with oneself in it. As I have just argued and shall continue to argue, I disagree.

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In an illuminating article on ﬁctional showing, George M. Wilson says, ‘But it does not follow that if a person imagines seeing a scene from a certain perspective, then he thereby also imagines being at a place which offers him that view.’31 Wilson may or may not be right in his claim, but what I have defended is the claim that if a person imagines seeing a scene from a certain perspective, then the imagined world, i.e. the world at which the scene takes place as (imagined to be) seen is a world at which the person exists and sees the scene while being located at a place which offers him that view. Whether he imagines himself being there or not, the (or, any) world at which the scene (imagined to be) seen takes place is a world at which he exists and sees the scene as imagined to be seen. There are worlds at which the scene takes place as imagined but without any perceiver seeing it the way it is imagined to be seen, but these worlds fail to capture what is imagined to be seen, as opposed to what is imagined. This can be shown by the following consideration. Suppose Bianca imagines seeing from the west Don Lockwood sing and dance in the rain, while Maria imagines seeing from the east Don Lockwood do the same thing in the same way. Bianca imagines seeing Lockwood dance away from her, whereas Maria imagines seeing him dance toward her. So what Bianca imagines seeing is different in an obvious way from what Maria imagines seeing. But any world at which Lockwood does as Bianca imagines him to do (as opposed to doing as she imagines seeing him do) is a world at which he does as Maria imagines him to do (as opposed to doing as she imagines seeing him do), and vice versa. Imagining seeing is not the same as imagining. When a person imagines seeing a scene, the visual perspective in which the scene is imagined to take place is essential to what is imagined seen in the way in which it is not when a person simply imagines a scene. Wilson says the following and intends it to be in opposition to the claim I defend: Just as I can imagine romping in the buff on Neptune without imagining anything about how I came to do so or about what makes it possible for me to be dancing on that distant planet, so also I can imagine having a (veridical) visual experience of a scene without imagining anything about how I came to have the experience or about what enables me to have it. In particular, I may imagine nothing about whether I am having that experience because I am situated face to face with what I see.32

Wilson can certainly imagine himself romping nude on Neptune without imagining how he got there or manages to romp there. But he cannot imagine himself romping on Neptune without imagining himself kinetically interacting with (some parts of) Neptune. I think the situation is analogous in the case of imagining seeing. To imagine seeing a scene is to imagine oneself seeing a scene. One cannot imagine oneself seeing a scene without imagining oneself visually

31

Wilson 1997: 303; his emphasis.

32

Ibid. 305–6; his emphasis.

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confronting the scene. This and Wilson’s Neptune example are equally straightforward instances of what is described by the general schema, ‘x cannot imagine y doing F without imagining y’. Let y be x, and we have the relevant special schema, ‘x cannot imagine x doing F without imagining x’, and I take it as evident that ‘x imagines himself doing F’ entails ‘x imagines x doing F’.33 It might be said that Wilson’s point is that he need not imagine the exact mechanism by which he romps on Neptune and analogously we need not imagine the exact mechanism by which we see the scene in question, and in particular, we need not imagine ourselves seeing the scene by visually confronting the scene. But this would not help Wilson. It is true that we need not imagine exactly how our rods and cones work when imagining seeing the scene, but we do need to imagine having a visual experience that is veridical, as Wilson himself puts it parenthetically. Veridicality makes it a genuine case of imagining seeing as opposed to a case of imagining having a visual experience. I may see a scene without being ‘situated face to face with what I see’, as Wilson puts it. For example, I may see a scene on a television set, where I and the television set are located in a room thousands of miles away from the scene I see. This, however, obviously does not help Wilson’s case, for the television camera still has to be ‘situated face to face with what I see’. Suppose that we avoid assuming anything as speciﬁc as television as the means by which I see the scene at the imagined world(s). Even then, to preserve the veridicality of my imagined visual experience, I need to imagine that there is some important relation holding between the scene and my visual experience. Perhaps it is a causal relation of some kind, perhaps not. But it has to be a broadly natural relation in some appropriate sense of ‘natural’. Whatever else may be true of the appropriate sense of ‘natural’, it is highly plausible to say that x and y can stand in a natural relation of the appropriate kind only if x and y are worldmates. If this is right, then even if Wilson is correct about the inessentiality of the ‘face to face’ confrontation with the scene imagined seen, the world(s) at which the scene takes place as imagined seen must also have the subject of the imagining exist at it (them). If I imagine seeing a scene S, thereby imagining a world w at which S takes place as seen by me, I must exist at w. The world w is the imagined-seen world (or one of the imagined-seen worlds) at which S occurs, I exist, and I see S.34 Gregory Currie would object. According to Currie, the claim I defend is contrary to ‘the experience of movie watching’ (his emphasis):

33 ‘X imagines x doing F’ does not entail ‘X imagines himself doing F’ (even if x is male). Such is the sense of ‘self ’ in ‘himself ’. 34 I hope it is clear that my contention has little to do with the view that every narrative ﬁlm is presented by a ‘grand image-maker’ (as separate from the director of the ﬁlm as such) or the view that every work of narrative literature is presented by a verbal narrator (separate from the author of the work as such). Cf. Metz 1974: 20–1, as cited in Wilson 1997: 295.

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Do I really identify my visual system, in imagination, with the camera, and imagine myself to be placed where the camera is? Do I imagine myself on the battleﬁeld, mysteriously immune to the violence around me, lying next to the lovers, somehow invisible to them, viewing Earth from deep space one minute, watching the dinner guests from the ceiling the next? None of this corresponds to my own experience of movie watching.35

If a perceptually and cognitively mature human being were to go to the cinema for the ﬁrst time in her life, she would imagine herself on the battleﬁeld, mysteriously immune to the violence around her, lying next to the lovers, somehow invisible to them, etc., and would thereby be bafﬂed. As she continued with her ﬁlm-viewing practice, however, she would quickly learn to ignore her place at whatever world of ﬁlm she were imagining seeing, largely owing to its mysterious and initially jarring total causal inertness at that world, and learn to enjoy imagining seeing the rest of what goes on at that world. The Curriesque complaint that the claim I defend is not true to our experience of ﬁlm watching is a result of forgetting how quickly and effectively human beings can ignore things which are inconvenient to the enjoyment of something at hand. We may easily remind ourselves of this fact by simply stepping into a virtual reality machine and imagining perceiving a ﬁctional scene surrounding us. Before becoming accustomed to such ‘surround’ virtual reality the way Currie is accustomed to watching ﬁlms, we will undoubtedly imagine ourselves on the battleﬁeld, mysteriously immune to the violence around us, lying next to the lovers, somehow invisible to them, etc., and be perturbed.36 Wilson himself provides an example of the relevant sort: In many ‘Old Dark House’ movies, it is ﬁctional that the ghosts are completely invisible to human eyes, but audience members imagine seeing them as glowing, diaphanous creatures gliding among the furniture. Still, it is not part of the viewers’ imaginings that they have special powers that permit them, unlike other human being, to see ghosts.37

Wilson calls the imagined scene ‘merely minimally coherent’.38 But that is an understatement. According to the imaginings of the viewers, the ghosts are completely invisible to human eyes, the viewers themselves are human, have no special powers, and can see the ghosts with their eyes, and no laws of nature are

35

Currie 1995: 171. It is worth noting that some kinds of ﬁctional scenes imagined seen are immune to my reasoning for metaphysical impossibility. They arise from ﬁctional stories which incorporate a viewer into the scenes to be imagined seen as the subject of the imagined seeing. Such stories may speak explicitly of such a viewer, or may not do so explicitly but implicitly imply the existence of such a viewer. As long as the stories do this in a metaphysically coherent way, the scenes imagined seen are metaphysically possible. I am not aware of any actual ﬁlm of narrative ﬁction that is a clear example of this kind. 37 Wilson 1997: 308. 38 Ibid. 308; his emphasis. 36

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breached. Such an imagined scene is metaphysically impossible. Wilson provides another example from literary ﬁction: Thus, it might be ﬁctional for the reader that she is reading the narrator’s diary even though it is clearly indicated, at the end of the work, that this diary must have been consumed in a story-culminating ﬁre.39

The reader imagines herself reading a diary which was destroyed in a ﬁre, say, a century ago. The universe at whatever world she imagines contains the diary, herself, the destruction of the diary in a ﬁre a century ago, and her reading of the diary now. Given that she imagines the world to be otherwise as familiar and mundane as her own actual world, this makes the imagined world impossible, certainly physically and probably metaphysically. She will be struck by the absurdity of the world she imagines but learn to ignore it so as to continue the enjoyment of reading the story. Surprisingly, Wilson says as much: When a reader steps back from the ﬁction and focuses upon the relevant facts, the situation will strike her as paradoxical. But in the course of reading the work, this same reader is likely to ignore or discount the conﬂict, and she surely will not stop imagining that what she is reading are the words of the diarist/narrator.40

This supports the claim I defend. Whatever world the reader imagines when she imagines herself reading the diary of the ﬁctional diarist/narrator is an impossible world but the reader will successfully ignore the impossibility of the world in her appreciation of the literary work. Wilson asserts that ‘the situation will strike her as paradoxical’ but the claim he defends, namely, the claim that the reader is not part of the situation she imagines when she imagines reading the diary, cannot offer a plausible explanation why. If the situation she imagines contains the diary and its destruction a century ago but does not contain her, a fortiori her reading the diary now, then why should this strike her as paradoxical? The claim I defend, on the other hand, readily offers a straightforward explanation. The world she imagines strikes her as paradoxical because it is paradoxical.41 39

Ibid. 309. Ibid. 309. What of Kendall Walton’s inﬂuential pretense theory of ﬁctional discourse? I have little to contribute to the discussion of this important topic in philosophy of art, except to say that Walton’s theory is compatible with my impossible-worlds view of ﬁctional discourse. For a similar claim, along with supporting arguments, of the compatibility between the pretense theory and a substantive metaphysical theory of possible worlds, see Zalta 2000. 40 41

11 Epistemology 1 1 . 1 . HOW DO WE KNOW? Brian Skyrms’s objection against David Lewis’s modal realism we examined in Chapter 5 concerned an epistemological issue involving mere (metaphysical) possibilia. As brieﬂy noted there, the objection did not concern the question ‘How could we know about talking donkeys?’ This question is easy to answer. We could know about talking donkeys if and only if at some possible world we do know about talking donkeys. At some possible world, we and talking donkeys exist and we know about them by empirical means. On the other hand, the question ‘How could we know about non-actual talking donkeys (in the non-rigid sense of ‘actual’)?’ is harder to answer and is the kind of question relevant to Skyrms’s objection. We could know about non-actual talking donkeys if and only if at some possible world we do know about non-actual talking donkeys, i.e. about talking donkeys that do not exist at that world. In Chapter 5, we defused Skyrms’s objection by introducing modal tense. It was an adequate response to Skyrms but did not address the question ‘How do we know about nonactualia?’ squarely. In this chapter, we shall try to address it. Actualists like Skyrms argue that we come to know the existence of things only by means of empirical evidence and that since we have no empirical evidence for the existence of non-actual objects, we do not know that they exist. In response, apart from the issue of different modal tenses implicitly involved here,1 the modal realist of the type I support will point out the relativity of existence, refuse to make the unqualiﬁed claim that non-actual objects exist, and maintain that merely possibly objects are real. The focus of discussion in this chapter is knowledge of the reality of things, not knowledge of the existence of things. I shall warn the reader that our discussion will not contain much that is entirely new or complete and those who seek to ﬁnd a novel or fully spelt-out answer to the section title question will be disappointed. I suspect that a truly satisfactory account of the kind of knowledge in question requires a satisfactory general account of knowledge of the reality of anything whatever. Such a general account requires a satisfactory account of knowledge of 1

See 5.6.

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the reality of, inter alia, mathematical objects (assuming that they are real), and I do not know exactly what to say about that. What the reader will ﬁnd in this chapter is a compilation of the relevant considerations long known to philosophers which are useful for answering the question in a way friendly to modal realism. Two issues are involved: the question of whether we can know the reality of some things without empirical evidence, and the question of whether we have any empirical evidence for the reality of non-actual beings (individuals, worlds, modal spaces, etc.). If the answer to the ﬁrst question is negative, the second question is crucial to the question of whether we can know the reality of nonactualia. If the answer to the ﬁrst question is afﬁrmative, however, the second question loses its urgency. Let us start with the ﬁrst question. Can we know the reality of something without empirical evidence? To answer this question, we need to be clear about what counts as empirical evidence for reality. Here we hit what appears to be an insurmountable wall. We are using the word ‘real’ in such a way that not only actual things but also non-actual things are real. Our knowledge of actual things is not in dispute. (Or so we assume.) Our concern is with our knowledge of non-actual things. Unfortunately, this knowledge is so radically in dispute that we lack sufﬁciently standard examples of it, let alone sufﬁciently standard examples of empirical evidence relevant to it. So it appears that we are in no position to be clear about what counts as empirical evidence for the reality of the non-actual. There are two strategies we could pursue at this point. One is to try to dispel the appearance and produce at least hypothetical examples of knowledge of the non-actual which are (or would be) sufﬁciently convincing to the opponents of such knowledge for the sake of discussion. The other is to consider relatively undisputed examples of knowledge and attempt to extract lessons from them that might apply to the case of the nonactual. We shall take the latter approach. We shall begin with our knowledge of actual individuals, like mute donkeys and gray elephants. We assume that we do indeed know of some such individuals that they are actual and that they are mute, are donkeys, are gray, are elephants, or whatever. We shall endeavor to learn from examining such knowledge. The best empirical evidence for the actuality of something seems to be unobstructed clear direct perception of that thing. In fact, perception even seems to entail actuality in the following sense: Metaphysically necessarily, for any object x, if one perceives x, then x is actual.2

2 ‘Actual’ in the non-rigid sense, of course. To be explicit, using modal tense, we say that metaphysically necessarily, for any object x, if one perceivesa x, then x isa actual. Our discussion in the subsequent passages should also be understood clearly with invisible modal-tensing subscripts. See 5.4 for details on modal tense.

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If no pink elephant is actual, then no matter how clearly and vividly it may appear to you perceptually that you are directly perceiving a pink elephant, no pink elephant is such that you are perceiving it. This, however, makes perceptual experience unusable as the sole source of evidence from which to infer actuality, for an occurrence of genuine perception of a particular object cannot be ascertained without prior ascertainment of the actuality of that object. On the other hand, no matter how strongly it may appear to you perceptually that you are not perceiving a pink elephant, if you stand in an appropriate perceptual relation to some particular pink elephant, you are perceiving that pink elephant.3 So one cannot rely on one’s own perceptual experience alone on a particular occasion to know the actuality or non-actuality of anything particular on that occasion. Yet it remains to be the case that coherently and systematically repeated episodes of apparent direct perception of an object and successful action of the right kind based on such apparent direct perception eventually yield considerable evidential weight for the genuineness of any further episode of the same type. Against such background, a particular perceptual episode in which it appears to you perceptually as if you are directly perceiving a gray elephant may give you at least prima facie evidence for the actuality of a gray elephant. Perception gives us evidence not only for the actuality of things we directly perceive but also for the actuality of things which are parts of things we directly perceive. If an elephant actually exists, every part of that elephant also actually exists. So any evidence for the actuality of an elephant is also evidence for the actuality of every part of it. Further, perception gives us evidence for the actuality of things only parts of which we directly perceive. If we directly perceive only the left side of a live elephant, our perception is evidence for the actuality of a whole elephant. Still further, perception gives us evidence for the actuality of things which are indispensable for an adequate explanation of what we perceive. What counts as indispensable and what counts as an adequate explanation are sensitive to the surrounding conceptual and theoretical framework. In one conceptual and theoretical framework, an observation of a remote star’s orbital anomaly might be evidence for a nearby black hole, and in another conceptual and theoretical framework, the same observation might be evidence for a subtle malfunction of the telescope. Can we know the actuality of anything independently of perceptual evidence in the above sense? The answer might appear to be ‘No’, for it might appear that perceptual evidence in the above sense is so comprehensive that it encompasses all evidence we could possibly have for the actuality of anything. When we have perceptual experiences, we seek a most powerful yet economical unifying explanation for them. As part of such an explanation, we naturally postulate many things as actual, having appropriate attributes, and standing in appropriate 3 The phenomenon known as blindsight might be considered to be an actual example of this kind.

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relations to one another as well as to us. If this picture is taken with sufﬁcient generality, how can it fail to cover any actuality claim we may wish to embrace? 1 1. 2. THE SELF There is an example individual whose actuality is knowable independently of perception, namely, the self. I believe that I am actual and my belief constitutes knowledge, but it is not justiﬁed by perception. That I know my own actuality is hardly contestable.4 But exactly how my belief in my own actuality amounts to knowledge is a very difﬁcult question to answer. The history of philosophy contains a number of famous answers, none of which offers a plausible justiﬁcation by perception. This, of course, does not mean that a successful perceptual justiﬁcation for one’s own actuality cannot be obtained. But the burden of proof is clearly on those who think that one’s own actuality must be justiﬁed perceptually. Suppose that it is established beyond reasonable doubt that one can—and probably does—know the actuality of oneself not by perception but in some other way. Then it is established beyond reasonable doubt that it is not impossible to know the actuality of something without perception. Does this help alleviate the epistemological pressure against non-actualia? Yes, it does to some extent. If the case of the self shows that in at least one case perception is not necessary for knowledge concerning an individual, then it becomes less surprising to be told that perception is not necessary in other cases of knowledge concerning individuals. At the same time, it might well be said that the self is a very special case and that whatever is true of the self need not generalize to other individuals. Such a response has some force. The self does seem special, especially epistemologically. So perhaps it should not surprise us to discover that the actuality of everything except the self should be known ultimately by perception. Thus, perhaps the epistemological situation concerning the actuality of the self should have no implication for the epistemological situation concerning the reality of non-actualia, or anything else other than the self. I think this may be a fair assessment of the situation. In any case, I believe that the attack against non-actualia on account of the indispensability of perception for justiﬁcation of actuality can be met independently of the epistemological status of the self.

4 Even if you, like Peter Unger (1979), believed that you yourself did not actually exist, your belief would have to be earned against a tremendously compelling force pulling you in the opposite direction. The fact that most philosophers do not seem to take Unger’s argument that he himself does not actually exist seriously at all is an indication of the strength of the force.

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1 1. 3 . INTENSIONALISM The argument I am about to give, I must concede, is an ad hominem argument of a sort. It is directed speciﬁcally at those theorists known as intensionalists. So nonintensionalist actualists, or extensionalist actualists, may not be moved at all. But such extensionalist actualists are most likely not to take important modal matters seriously to begin with. Since we assume that important modal matters should be taken seriously, the limited range of the argument is not particularly troublesome.5 Intensionalists are those who postulate intensional objects, such as propositions, properties, and relations, as irreducible sui generis objects. I claim that if such objects are not objectionable objects to embrace as actually existing, then either perception is not a necessary condition for the acceptability of an object as actual, or else the postulation of intensional objects as actual is justiﬁed by perception. If the former is the case, then the lesson for us is that perception is not a necessary condition for the acceptability of an object as real. If the latter, it is that there is no good reason to believe that the postulation of non-actualia cannot be justiﬁed by perception. Suppose that intensional objects are unobjectionable as actual objects and their postulation as irreducible sui generis objects is adequately justiﬁed. Then either the postulation of intensional objects is justiﬁed by perception or it is not. Suppose that it is not. Then perception is not a necessary condition for the acceptability of an object as actual. If this is to be a lesson for us concerning the epistemology of non-actualia, we should say that since knowledge of actuality need not have perceptual justiﬁcation, given that actuality is narrower than reality (i.e. all actual things are real but not vice versa), knowledge of reality need not have perceptual justiﬁcation. Suppose, on the other hand, that the postulation of intensional objects as irreducible sui generis objects is justiﬁed by perception. Then since intensional objects are not subject to direct perception themselves, the justiﬁcation of their postulation by perception must not be in terms of direct perception of them. So, the justiﬁcation of their postulation must be (at least partly) in terms of direct perception of other objects. What could such a justiﬁcation be like? We have but one sufﬁciently general and sufﬁciently plausible type of such justiﬁcation, namely, inference to the best explanation. We want to make some coherent and comprehensive sense of the perceptual experiences we undergo. We begin by postulating objects of direct perception and telling a story about what they are like and how they are related to one another and to us, in order to explain our perceptual experiences. Sooner or later, we reach a point at which we need to postulate further objects not directly perceivable to us in order to give a fully 5

Quine comes to mind as an arch-example of such an extensionalist actualist.

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satisfactory theory, explaining the behavior of the directly perceivable objects previously postulated. We may postulate whatever kind of not directly perceivable object is deemed appropriate for an adequate explanation of the behavior of the directly perceivable; what particular kinds of object are thus postulated is a highly theoretical question. If something like this is the way the postulation of intensional objects as irreducible sui generis objects is justiﬁed, then there is no good reason why the postulation of non-actual objects cannot be justiﬁed in the same roundabout and theory-laden way. I can think of two possible objections to this line of argument. First, it might be objected that intensional objects are directly perceivable. This is an objection based on confusion. Let us take properties as a representative kind of intensional object, and vision as a representative mode of direct perception. We cannot see properties. When we see a red sheet of paper, the object of our vision is the sheet, not the property redness, or paperhood, or sheethood, or any other property. We see the sheet as a result of photons bouncing off the surface of the sheet and reaching our eyes, triggering certain neuro-chemical occurrences in our brain. If photons did not bounce off the surface of the sheet or failed to reach our eyes, we would not directly see the sheet. It is not possible for photons to bounce off the surface of any property, however fancy, because no property, however fancy, has (or could have) a surface. Some might say that photon-bouncing is not necessary for vision. That may or may not be so, but vision is at least essentially a physical perceptual phenomenon, and as such, it requires its object to be physical. Perhaps, an object of vision might not even need to have a surface. But it needs to have some physical attributes. Otherwise, it would not be subject to physical processes, and a process of vision is a physical process. Properties are not physical objects and they lack physical attributes. It is a confusion to say that the fact that we may correctly say things like ‘She can see colors, for she is not color-blind’, ‘After regaining the sensitivity on her ﬁngertips, she can once again feel smoothness by touch’, and ‘Some of her taste buds are destroyed but she can still taste sweetness’ shows that properties like colors, smoothness, and sweetness are objects of direct perception. Such ordinary locutions are obviously intended to mean something like ‘She can see things as colored’, ‘She can feel things as smooth’, and ‘She can taste things as sweet’, respectively. It is extensional objects (things which are not intensional objects) like trafﬁc lights, table tops, and sugar cubes that are the objects of direct perception, not their properties. We also use perceptual locutions misleadingly when we mean to characterize our perceptual experiences rather than the objects of our perception. When we press on our eyeball we see red. Or so we say. But when we say this, we do not mean that when we press on our eyeball we see the property redness. Rather we mean that when we press on our eyeball we have a certain kind of visual experience, where the kind of experience has a certain chromatic quality which is termed ‘red’. In other words, we mean to be using the word ‘red’ to characterize

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the chromatic quality of the experience, not to refer to the object of perception. We should clearly distinguish between perceiving some thing and having a perceptual experience. Making the postulated objects of direct perception fancier would not help bridge the gap between them and properties. For example, sense-data theorists postulate sense data as the objects of direct perception. Sense data are not like trafﬁc lights, table tops, or sugar cubes. They are far more exotic. For instance, (visual) sense data have perceptual attributes but have hardly any physical attribute beyond two-dimensional extension. Exactly in what respect and exactly how much fancier they are than trafﬁc lights, etc., is a difﬁcult question.6 But whatever the correct answer to such a question might be, it remains that if sense data are supposed to be objects with perceptual attributes, their direct perceivability does not help establish the direct perceivability of properties, for properties do not have perceptual attributes; it is absurd to say that a property is red, loud, bitter, fragrant, hot, or rough.7 The second objection to my line of argument is that the postulation of nonactual objects cannot be justiﬁed in the same way as the postulation of intensional objects as irreducible sui generis objects because non-actual objects are signiﬁcantly different from intensional objects in some crucial respect. Here we do not have much to proceed with until a concrete proposal is made as to what the crucial respect in question is supposed to be and how signiﬁcant the alleged difference is. In the absence of such a proposal, we shall simply say that this objection is yet to be fully ﬂeshed out. Let me point out in this connection, however, that non-actual objects are much more similar to actual objects we readily embrace than intensional objects are. So if a certain degree of resemblance to the already postulated objects is a necessary condition for the admissibility of an object, non-actual objects stand a better chance of being admitted than do intensional objects. My chair and your liver are among the things we readily and routinely embrace in our ontology. 6 According to William Lycan, when we see a red after-image, we are seeing not any non-physical object but a fully physical red object which is non-actual. This proposal raises a number of interesting questions but this is not the place to explore them. Let us simply observe that a view like Lycan’s helps reduce the need for the claim that intensional objects are objects of direct perception. After all, if we actually see non-actual possible physical objects when we actually see after-images, it no longer seems preposterous to claim that we actually hear talking donkeys when we hallucinate or dream, and more generally, that we sometimes actually perceive some nonactualia. See Lycan 1987. 7 Some trope theorists identify ordinary physical objects with ‘bundles’ of tropes (particularized properties). Even if they are right, this will only make ‘bundles’ of tropes objects of direct perception, not tropes themselves. Some situation semanticists say that we can directly perceive not only physical objects but situations involving physical objects. If situations are objects of direct perception and are also intensional objects, then some intensional objects are objects of direct perception. It is unclear, however, that when we apparently directly perceive a situation, say, a bald eagle’s being shot down, we are directly perceiving an intensional object and hence not eo ipso directly perceiving, say, a US national bird’s being shot down.

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Non-actual chairs and non-actual livers are just like my chair and your liver in every important respect but one, namely, actuality. A non-actual chair may be made of wood, metal, or plastic, heavy or light, high or low, have a square seat or a round seat, have four legs or three, etc. A non-actual liver may be heavy or light, healthy or diseased, inside an organism or removed for transplant, etc. These attributes are attributes of ordinary chairs and ordinary livers around us that we readily accept as actual objects. In contrast, properties and other intensional objects are utterly unlike those ordinary objects around us that we readily accept, nor are they (supposed by the intensionalists to be) reducible to such ordinary objects. One further point: a non-actual chair is subject to perception. It is subject to be perceived by an equally non-actual person, just as Sherlock Holmes is subject to be perceived by Dr Watson. A non-actual chair or Holmes is not subject to be perceived by us at the actual world, because they are not actual. They are not perceivable to us at the actual world,8 but that is not because they are perceivable to no subject of perception at all. In contrast, properties fail to be perceivable to us at the actual world because they are perceivable to no subject of perception at all. 1 1 . 4 . WHAT PERCEPTION TELLS US I deny that perception gives us evidence for actuality in a sense which warrants skepticism about non-actualia. I do not deny that perception gives us evidence for actuality in some sense, but it is not a sense damaging to non-actualia. Perception provides evidence for the shape, color, texture, etc., of things and, somewhat more indirectly, evidence for the obtainment of certain spatiotemporal and other kindred relations between the things and the perceiver. When we perceive a four-legged red chair under normal circumstances, we realize that the chair is four-legged, is red, is a cause of our visual experience, stands in certain spatial relations to us (say, being in front of us), etc. We may also realize that the chair stands in certain relations to other things we have already related to ourselves, for example, that it is to the left of the window and on the table. Perception tells us that things are this way or that or related to other things in this way or that. What does this have to do with actuality? To say that perception gives us reason to believe in the actuality of what is perceived is not incorrect but grossly incomplete. When we perceive a chair in 8 There is a sense in which non-actual chairs may be said to be perceivable to us at the actual world. Assume that we are actually standing in a small empty room and it is possible for the room to contain a chair which is not identical with any actual chair. If the room did contain such a chair, we would see it. So, a non-actual chair may be said to be perceivable to us at the actual world. Obviously, however, this is not the sense of ‘perceivable’ we have in mind when we conﬁdently say that non-actual chairs are not perceivable to us at the actual world. What we have in mind is more like the sense in which Holmes is perceivable to Watson.

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front of us under normal circumstances, we come to believe that the chair is actual. This is a case of perception providing evidence for actuality, but perception gives evidence for actuality by giving evidence for actual existence. Perception warrants us to believe that the chair actually exists. Whatever actually exists is actual. Hence the chair is actual. If we want evidence for the actuality of actually existing objects, perception is a good method to employ. Remember that existence is relative to a domain. A domain is a collection of things. And to exist relative to a domain is to be included in the collection. The claim that the chair actually exists is a claim of existence which is true relative to the collection of some actual-world-stages of objects, say, the collection of actual-world-stages of objects which are actually in my ofﬁce. This is a case of direct perceptual evidence for the object of perception. We may also have indirect perceptual evidence for the object of inference to the best explanation. When we indirectly infer from assorted pieces of perceptual evidence that a black hole actually exists at the center of our galaxy, we come to believe that a black hole is among those objects which are at the center of our galaxy at the actual world. What perception gives us in such a case is indirect evidence for believing that the claim that a black hole exists is true relative to the collection of all actual-world-stages of objects which are actually at the center of our galaxy. In general, perception gives us (direct or indirect) evidence for the truth of an existence claim relative to a certain appropriate collection of actual-world-stages of objects. Shift to a different collection, and perception may lose its evidential force. My actual perception of a chair in my ofﬁce does not give me evidence for the truth of any existence claim relative to any collection of non-actual-worldstages of objects. So perception can provide no evidence for the existence of objects at any non-actual world.9 But this does not mean that non-actualia are not real. Instead it means that perception is limited in its power so that it can only indicate actuality; the range of its power is conﬁned to objects with actual-world-stages. Let us remind ourselves again that none of this implies that non-actualia are not subject to perception at all. Non-actual donkeys are just as ﬂesh and blood as actual donkeys around us and are equally subject to perception. They may not be subject to perception by us at the actual world, but we at the actual world (our @stages) are not the only perceptual subjects. Non-actual donkeys at a non-actual world are subject to perception by equally non-actual people around them at that world. 9 By this I do not mean to oppose the position that ultimately everything we believe must be justiﬁed by perception. My point is rather that actual perception can provide no evidence for the existence of objects at any non-actual world as directly as it can provide evidence for the existence of objects at the actual world. For actual perception to provide evidence for the existence of objects at a non-actual world (if that is what we want perception to do), a considerable amount of philosophical theoretical apparatus needs to be mobilized and the ultimate justiﬁcation by perception will be very indirect indeed (unless Lycan is right—see n. 6).

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11 .5 . ONTOLOGY It is customary to say that the domain of discourse is the totality of things under discussion, or things talked about. This is a mistake, as we noted in Chapter 3. The domain is the totality, the collection, of things over which variables range. The collection of things over which variables range may or may not be the totality of things under discussion. With a chicken bone in hand, you look around in the kitchen and say, ‘There is no trash container’. You are speaking of trash containers and saying that none of them is in the kitchen. Trash containers are under discussion. The collection of things in the kitchen is the domain. If your utterance is true in the context, trash containers are not among the members of the domain. When we talk about three-eyed green monsters and tell frightened Calvin correctly that they do not exist, the non-existence claim, like any nonexistence claim, is to be understood as implicitly relativized to a certain domain, say, the collection of things under Calvin’s bed, or things on Earth, or things in this galaxy, or some other restricted domain, at the actual world. It is not to be understood as relativized to the collection of things under discussion; three-eyed green monsters are under discussion. As an extensionalist, I say that irreducible sui generis intensional objects do not exist. I am speaking of intensional objects and saying that none of them exist. But relative to which domain am I saying this? The domain relative to which my statement is to be understood is left implicit. I certainly do not intend the domain to be the collection of all objects. For one thing, it may well be that such a collection is not coherently available.10 For another, I do not wish to deny that irreducible sui generis intensional objects are objects. I do deny that irreducible sui generis intensional objects are needed for philosophical theorizing, but I do not wish to afﬁrm that all abstract objects must be needed for philosophical theorizing. This means that I am prepared to assert that irreducible sui generis intensional objects are real, though not actual or perhaps not even metaphysically possible. I say that irreducible sui generis intensional objects exist (though they do not actually exist or perhaps even metaphysically possibly exist), where the intended domain includes abstract objects not needed for philosophical theorizing. Let us say that ontology is the study of the actual and the metaphysically possible. For the purpose of our discussion here, let us say that it does not include the metaphysically impossible, for ontology is part of metaphysics and the metaphysically impossible deﬁes metaphysics. When one’s ontology is ascertained, what one considers to be philosophically unneeded abstract objects should not be

10 Cf. Grim 1991. This suggests another example of divergence between what is under discussion and what is in the domain. It seems that we can talk about absolutely everything (cf. Cartwright 1994), while there is no collection of absolutely everything.

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counted into the realm one’s ontology embraces.11 Thus, when I discuss my ontology and mention such and such objects as being excluded from my ontology, I mean that such and such objects are not members of the intended domain, where the intended domain is to be ample enough to include metaphysical non-actualia yet meager enough to exclude irreducible sui generis intensional objects. 11 Should we not regard philosophically unneeded abstract objects as unﬁt for inclusion in any collection? If so, they are unﬁt not only for the ontological embrace but also for being included in any domain. But then should I not say that they do not exist at all, for the claim that they exist is then false relative to every domain? My short response is that, unlike Quine, I do not think that anything, including metaphysical non-actualia, and even philosophically unneeded objects and other probable metaphysical impossibilia, is unﬁt for inclusion in a collection.

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General Index A aboutness 262, 264–5, 272 abstractness 56 n. 15 actual world 2, 5, 13, 19, 41, 47, 62, 63, 65, 67, 80, 87–8, 184, 223–4, 226–8 actualism 1–3, 4, 5, 8, 10, 11, 12–13, 15–18, 42–3, 47, 62, 73, 80–1, 92, 97 n. 8, 183, 284, 288 and reduction of modality 147, 149, 150 see also ersatzism; possible worlds actuality 1–3, 8, 18, 41, 62–72, 87–91, 219, 268 non-rigid sense, see actuality tense and perception 285–8, 291–2 rigid sense 76–7, 78, 88, 197 n., 219 actuality tense 76–9, 80–1, 86, 88, 89, 91, 93, 181, 197 n., 219, 228, 230, 284 Adams, Robert 97 n. 8 Akiba, Ken 42 n., 132 n. 52 alethic modal realism, see modal realism alethic relativization 24, 29–30, 34–9, 70 vs context of utterance 38–9 analysis 8, 147–9, 150 analytic truth 243 n. 14 anti-haecceitism, see haecceitism anti-realism 8 Aristotle 3 art, conceptual 143 n. 64, 144 n. 68 assertion 157–8, 249 astrology 7 Austin, David 254–5 B Bach, Kent 169 n. 38 Ballarin, Roberta 149 n. 7 Bealer, George 162 n. belief 7 n. 12, 231–56 ascription 256 de se 194, 254 as a dyadic relation 169–70, 241, 255, 256 and ﬁction 258–9 belief sentences 6, 167 n., 168–71, 226, 255–6 and iteration 247–8 see also belief; propositions Benacerraf, Paul 162 Benacerraf ’s problem 11 n. 12, 162, 163, 231 Bergson, Henri 40 n. 25 Black, Max 116–18 Boe¨r, Steven 166–7

Boolos, George 51 n. 6 Braddon-Mitchell, David 218–20, 227 Braun, David 257–9 Bricker, Phillip 89 ‘Leibnizian realism’ 89–90 C Caplan, Ben 60–1 Carnap, Rudolf 4 n. 6, 163 n. 22, 172 n. 43, 198 n. Cartesian egos 145, 146 Cartwright, Richard 293 n. causal theories 112 causation 27, 40, 102, 110–12, 114–15 Chalmers, David 216–17, 228 Chisholm, Roderick 96, 121, 122 n., 134, 140 Church, Alonzo 172 n. 43, 198 n. cinema 278–83 closest-continuer theory 101–6, 108–9, 110, 127 n. 45, 128–30 and causation 102, 109–12 collections 4, 6, 38, 44, 52, 57, 91, 134, 155, 156, 187 n. 19, 196, 199, 202, 221, 231–3, 236, 237–40, 243 n. 15, 292, 293, 294 n. common sense 7, 107, 134, 137, 157–8 compossibility, metaphysical 200–2 conceivability 177, 204, 205 vs conceivedness 206 n. vs conceptual possibility 244 and logical possibility 216–17 and metaphysical possibility 205, 215–7 conceiving: and metaphysical possibility 205–15 concepts 73, 244 concreteness 10, 56 n. 15, 144 n. 69; see also Lewis, David, ‘conception of worlds’ Conee, Earl 189, 190 conjunction 184 consciousness 27, 124 unity of 113–16 consistency, see possibility, ‘and consistency’ constituent (modal) realism 9–12 individual 11–12, 13, 15, 18 non-individual 11, 15, 18–20 constitution, necessity of 144, 156, 176 n. 3 Constructivist Principle 6 content 239–40, 245, 249, 259

308

Index

context of utterance 38–9, 70–2, 75–6, 77, 165–8, 170, 239, 245–6, 255 contingency 79, 81 a priori 59 contradictions 182–6, 189, 190, 257–8 copula 79 cosmology 63 counterfactual conditionals 105–6, 120–1, 202, 217 Stalnaker–Lewis semantics for 186–7 and stipulation 118–21 see also counterpossible conditionals counterpart theory, see Lewis, David, ‘counterpart theory’ counterpossible conditionals 186–90, 202 extended Stalnaker–Lewis semantics for 187–90 Cresswell, M. J. 81 n. 19 Currie, Gregory 277 nn. 26 and 27, 281–2 D Davidson, Donald 7 n. 12, 36 n., 166, 167 paratactic theory of indirect discourse 165 deﬁnite descriptions 171–2, 175, 229, 241, 245, 246 demonstratives 254–5 sortal 167–8 de re/ de dicto distinction 16–18, 84 disquotational principle (DQ1, DQ2) 169, 251, 253, 256 distinctness (non-identity), necessity of 122 n., 188 Divers, John 10, 147, 203 n. 41, 214 n. domains of discourse 35, 36, 293 doxastic indecision 194–8, 199 Doyle, Arthur Conan 64, 66, 263, 266–7, 272 E Egan, Andy 232 n. 3 empirical evidence 284–6, 291–2 empty world 145 endurantism 14, 47 n. 36 entailment 43 epistemology 81, 221, 284–94 equivalence 149 material 174, 233 necessary 174–5 ersatzism 2, 9, 10, 119 n. 38, 150–2 temporal 150–2 see also actualism; possible worlds, ‘ersatz’ essence 3 Evans, Gareth 132 n. 51, 135, 229, 265 n. 15 events 20 existence 9, 49–61, 148 actual 49, 269–70; see also actuality

domain-relativity of 49–52, 91, 271, 284, 292 and ﬁctional names 265–71 at a metaphysical index 53, 65, 69 nature of 10, 49, 51, 54 and predication 55–7 vs reality 9, 23, 49, 54–5 existence predicate 258 unrestricted vs restricted use of the 55, 87 extensionalism 147–75, 288, 293 externalism 20–3, 103 about predicates 21, 22 about reference 20–1, 22 about truth conditions 22–3, 203 F facts 9, 200 modal 73, 150, 200 ﬁctional discourse 64–5, 66–7, 68, 257–83 and creationism 266–9 Fine, Kit 3, 189–90 Forbes, Graeme 95 n., 140 reduplication argument 128–9 four-dimensionalism 47 n. 36, 80–1, 94–6, 138 Frege, Gottlob 75 n. 5, 78 n. 11, 149 Fregean senses 256 G gaps (holes) 258–9 Gates, Bill 270 Geach, Peter 96 Gertler, Brie 177–8 Gibbard, Allan 142 n. 62 God 7 nn. 12 and 13, 111–12, 270 Goguen, J. A. 140 Goodman, Jeffrey 188–90 Grim, Patrick 5 n. 9 H haecceitism 97–9, 118, 119, 128 Hamlet 266, 270, 271 Hart, W. D. 279 n. 29 Hazen, Allen 64 n. 4 Heller, Mark 94–6, 133 n. ‘here’ 30–1, 65–9 Holmes, Sherlock 54, 64–5, 66–7, 68, 257–60, 262–5, 266, 268–9, 271, 272–3, 291 Horgan, Terence 146 n. Hyperblob 145–6 hyperworms (modal worms) 104, 130, 134, 140, 145 I identity 14, 40, 140, 218 ambiguity of 141–4

Index criterion of 99–100, 137 degrees of 140 determinacy of 138–9 and ﬁssion 100–2, 127 and fussion 100–2, 127 necessity of 122 n., 127, 141, 156, 218; see also Kripke, Saul, ‘and the necessity of identity’ personal 114 propositional 235 relative 142 trans-spatial 100–3, 104, 113 transtemporal 100–3, 104, 109, 111–12, 114, 121, 127 transworld 94–146, 179, 200, 214 n., 273 see also closest-continuer theory imagined-seen ﬁctional worlds 277–83 impossibility 3, 176–230 metaphysical 98 n. 12, 129, 221, 227, 275, 282 n. 36, 283, 293 see also impossible worlds impossible suppositions 191–3, 202, 219, 221 impossible worlds 6, 117, 118, 176–82, 203–5 logically 176, 180, 183–6 metaphysically 176, 180, 181, 186–91, 193–4, 197, 199, 200–1, 202, 203, 210, 211, 214, 215, 216, 219, 221, 224, 226–8, 230, 231–2, 233–40, 242, 243, 244, 249, 252, 255, 256, 275, 277, 279, 283 Russell–Quine–Lewis argument against 182–6 theoretical utility of 186 indexicality 89, 195, 222, 254 Indexist Principle 6 indices: alethic 6, 240 default 70–2 metaphysical 24–5, 31, 34–9, 42 n., 46, 49, 51, 52, 53, 56, 63, 65, 71, 91, 100, 109, 151, 152–3, 202, 239 modal 39, 41, 46, 48, 66, 70, 71–2, 91, 130, 150, 152, 176, 179, 181, 198, 220, 239, 240 spatial 27–31, 34, 39–40, 41, 70, 130, 150, 152, 239, 240 temporal 24–5, 27–8, 31, 34, 39–40, 41, 52, 70, 150, 152, 181, 220, 239 individuals 10–12, 20, 43, 69 actual 13, 16, 18, 99, 271, 275 concrete 10–12, 20, 38, 44, 147, 179 n. ﬁctional 257–60, 262–5, 266–77 impossible 180–1, 231–2, 260, 262–5, 274, 275–6, 294 n. overlapping 123–8

309

transworld 53, 94–146, 201, 273, 274, 275–6, 277 see also intensional objects; Kripke, Saul; objects; possibilia inference to the best explanation 288–9, 292 intensional objects 6, 21, 43, 157–75, 221, 288–91, 293–4 reduction of 157, 231–3 see also Fregean senses; meaning; twodimensionalism intensionalism 288–91 J Jack the Ripper 263, 273, 276 Jackson, Frank 218–20, 227 Johnson, David 147–8 Johnston, Mark 79 n. 12 Jubien, Michael 4 n. 6, 5 n. 9, 99 n. 15, 162 n. Judson, Whitcomb 229 justiﬁcation 81, 147 K Kamp, J. A. W. 26 n. 3 Kant, Immanuel 41 n. 27 Kaplan, David 12–13, 56, 148, 165, 214 n., 265 n. 13, 277 n. 27 automobile example 12–13, 20 cardinality paradox 237–8 haecceitism 97–8 transworld heir lines 140, 141 Kelly, Gene 278–9 King, Jeffrey C. 169 n. 38 Kratzer, Angelika 155 n. Kripke, Saul 59, 118, 174 n., 205–7, 226, 249, 272 argument against the identity theory 214, 217 argument by contrast 269–70 on ﬁctional individuals 259–65, 269–70, 272–4, 277 on the impossibility of Sherlock Holmes 262–5, 272–4, 277 on the impossibility of unicorns 260–2, 263, 277 n. 26 and misdescribing a world 207–9, 212–14 and modal intuition 208–9, 210, 212–13 and the necessity of identity 122 n., 127 n. 45, 141, 207 and the necessity of origin 144, 212; see also origin, necessity of and the puzzle about belief 250–3 and stipulation 118, 119–21, 209–14, 217–18 Kuratowski, Kazimierz 11 n. 12 L laws of nature 153, 154 Leibniz, Gottfried 3

310

Index

Leibniz’s Law of Identity 33, 132, 136, 242 n. 12 Leibniz’s principle of the identity of the indiscernible 117 Lewin, Kurt 100, 141 gen-identity 100, 108, 141 Lewis, David 7 n. 13, 42, 51, 62, 65, 147–8, 151, 157, 180, 181, 193, 195, 203, 230, 231, 277 n. 27 argument against impossible worlds 182–4, 185 conception of worlds 43–8, 69, 152–3, 179, 194, 198 counterpart theory 2, 14–16, 19, 47, 61 n. 27, 79, 83 n. 24, 88, 96, 105, 140–1, 147–9, 231 n. and haecceitism 97 n. 8, 98 indexical theory of actuality 68–9, 89 and Kaplan’s cardinality paradox 237–8 modal realism 1–3, 5, 6–7, 9, 10, 11, 12, 13, 18–19, 43–8, 73, 74, 81–93, 147, 205, 284 and reduction of modality 147, 149, 152, 231 n. and the similarity relation 104–6, 189–90 theory of counterfactual conditionals 105– 6, 120–1, 186–7, 189–90, 217 see also counterfactual conditionals; counterpossible conditionals Linsky, Bernard 56 n. 15, 145 n. literary criticism 266, 267, 268 Locke, John 114 Lockwood, Don 278–9, 280 logic 10, 50, 81 n. 19 classical 184, 189 formal 158, 191 n. 25 fuzzy 140 laws of 177, 179, 180, 184, 217 many-valued 140 modal 3, 9, 148 temporal 9 logical space 44, 97, 105, 181, 184, 193, 196, 198 Lycan, William G. 87, 92, 147–8, 166–7, 176 n. 1, 183, 185, 277 n. 27, 290 n. 6, 292 n. M McCarthy, Andrew 61 n. 25 McDaniel, Kris 14 n. 18, 18 n. 24, 47 n. 36 McGinn, Colin 79–80 Mackie, Penelope 18 n. 23, 128–30 McKinsey, Michael 169 n. 38 make-believe 63–4, 271 n.; see also pretense Mally–Zalta encoding 264 nn. 11 and 12, 271 Markosian, Ned 54–5 materialism 217 Mates, Benson 247

mathematics, laws of 177, 179 meaning 221–6 and expression 245–7 intensionalist theory of 221 see intensional objects; semantics; two-dimensionalism meaning-explanation 221–2 Meinong, Alexius: concept of subsistence 56 theory of objects 182, 271 n. memory 114, 124 causal theory of 112, 114 n. 33 and causation 114–16 and perception 114 n. 33 mental states 7 n. 12, 217, 239 mentalese 256 Menzel, Christopher 4 n. 6 mere-possibility tense 77–9, 80–1, 82, 86, 89, 91, 93, 181 metaphysical-impossibility tense 181–2 metaphysical space 57, 181, 184, 193, 195–8, 199, 201, 203, 218–21, 227, 230, 239, 275–6, 277 metaphysics 40, 49, 179, 182, 221, 293 laws of 120, 155, 156, 179, 201, 217, 227, 273 modal 9, 62, 80, 81, 137, 177, 221 modal axes 5, 41, 202–3 modal parts 38, 44, 53, 62, 113, 121, 140, 150, 181 modal primitivism 3–4 modal realism 1–2, 5, 6, 8–23, 24, 43–8, 49, 119, 205, 284, 285 constituent vs non-constituent 9–10; see also constituent (modal) realism extended 87 externalist motivation for 20, 23, 103 ﬁveþ-dimensionalist version of 96, 97, 105, 130, 202 and haecceitism 97–9 and the ‘incredulous stare’ 6–7 and modal tense 73–93 and reduction 147–53 modal reductionism 3, 65, 147 modal space 2, 5, 44, 48, 57, 60, 68, 69, 87, 91, 92, 94, 97, 104, 105, 123, 124, 155, 179, 205, 285 modal stages 104, 105, 107, 108, 109, 110, 111, 113, 114, 117, 118, 121–8, 130, 134, 140, 141, 143, 144, 145–6, 181; see also world-stages modal tense 10, 73–93, 181, 182, 197 n., 284; see also actuality tense; mere-possibility tense; metaphysical-impossibility tense; tense modalism 3 modality 3–4, 9, 80, 104, 127 alethic 8, 152

Index de dicto 45 de re 13–16, 18–20, 47, 105, 209–10, 212, 227–8, 230, 231 n. and possible worlds 3–4, 8; see also modal realism primitive 3–4 reduction of 1 n., 3, 4–5, 16, 65, 147–53, 157, 244 Moloch 269–70 N names 160–1, 208, 210, 229, 252 coreferential 248–9, 256, 259 empty 258–9 ﬁctional 263, 264, 265–71, 272 non-descriptiveness of 248–9 proper 160, 209–10, 212, 226, 248–9, 252, 259, 262, 264, 265, 271, 277 see also reference; rigid designators natural kind terms 211, 215, 221–7 natural kinds 202, 221–8, 261 necessity 3, 8, 42 n., 44, 59, 65, 79, 81, 174–5 a posteriori 205–18 absolute 153, 155 conceptual 153, 155, 175 logical 153, 155 metaphysical 153, 154, 155, 174, 223, 243 nomological 153, 154 primitive nature of 149 restricted 153–5 Nolan, Daniel 191 nominalism 8 ‘now’ 25–6, 30–1, 64, 67, 76, 77, 89 Nozick, Robert 101 n. 20, 102, 109, 110–12, 127 n. 45 numbers 10, 38, 162 O objectivity 41 objects 5, 9, 38 abstract 11, 12 n. 13, 56, 57, 63, 80, 145, 179 n., 266–8, 293, 294 n. extensional 43 indiscernible 116–18 ordinary physical 34, 38, 45, 52, 53, 63, 68, 97, 99, 107, 130, 131, 142, 143, 144, 145, 146, 149, 217; see also objects, ‘vague’ Platonic 8 trans-spatial 53 transtemporal 53 vague 130–9 see also individuals; intensional objects Old Testament 269 ontological commitment 50–1 ontology 293–4

311

origin, necessity of 128–9, 144, 156, 212, 273–4 over-identiﬁcation, problem of 121–3 overlap 14, 18, 45, 123–8; see also Lewis, David, ‘counterpart theory’ P Parsons, Josh 217 Parsons, Terence 84, 192–3 past, reality of the 22–3 Peacocke, Christopher: argument against modal realism 74, 85–6 perception 112, 113, 114 n. 33, 285–92; see also consciousness; imagined-seen ﬁctional worlds Perry, John 194 persistence through time 31–4, 68; see also closest-continuer theory; identity, ‘transtemporal’ Phillips, Ian 61 n. 25 physics 266, 268 ‘folk’ 7 places 6, 19, 35, 38, 40, 45 Plantinga, Alvin 157 notion of Æ–transform 59, 60 on propositions 157–8 Platonic forms 10, 38; see also objects, ‘Platonic’ possibile 12–13, 17–18, 20 possibilia 1 n., 5–6, 8, 11, 13, 14, 16, 44, 80, 92, 99, 153, 180, 276, 285 knowledge of 81–2, 92–3, 284–7 particular mere 12–13 realism about 11–12, 13, 18–20, 23, 49 possibility 1, 3, 4, 8, 42 n., 44, 65, 147, 149, 153–6, 176, 244 bare 178 conceptual 177–8, 243–4 and consistency 4–5, 16, 43, 149 degrees of 140–1 doxastic 178, 181, 193–8, 202, 204 epistemic 178, 226, 228 kinds of 176–7, 181–2, 196, 204 logical 177–8, 182, 204, 216 mere 41, 68, 78–9, 80 metaphysical 155–6, 177–8, 182, 200, 202, 204, 205–6, 212, 226, 277, 293 physical 182, 202 relativity of 176–7 restricted 77, 154 possible individuals, see possibilia possible worlds 1–2, 3–6, 8, 24–48, 91, 151 n. 9, 152, 153, 176–9 as abstract objects 1–2, 11, 62, 119 n. 38 chains of 107–12, 116, 117, 118, 121–8, 130, 134, 145, 218 closest 121, 273, 274

312

Index

possible worlds (cont.) existence at a 53, 69, 90–1 ersatz 42–3, 47, 62, 149, 150, 198 as metaphysical indices 39–42, 150, 153 ordering (arrangement) of 74, 75, 104–9, 121, 134 as points in modal space 2, 5, 69, 90 the possibility of 153–4 qualitatively indiscernible 98, 194, 195–8, 199–202, 228 stipulation (speciﬁcation) of 41–2, 99, 118– 21, 209–14, 217–18 and times 5–6; see also modal tense; indices, ‘temporal’; tense see also Lewis, ‘modal realism’; modal realism; modality, ‘and possible worlds’; worlds Potic, Matjaz 146 n. pragmatics 188 precisiﬁcation 135, 136 predicates 22, 140, 158, 161 predication 162, 258 predication without existence principle 56–7, 58 presentism 22 n., 54–5, 80–1, 92 presentness 65–9, 78, 89 pretense 228–30, 283 n. 41; see also makebelieve Priest, Graham 184 n. 14 Prior, A. N. 3 properties 4, 11, 43, 51, 97, 157–9, 161–2, 195, 202, 211, 246, 288 as collections of individuals 231–2 extrinsic 22 modal 79, 80, 211 and their mode of instantiation 79–80 monadic 18 and perception 289–91 structured 231 time-indexed 185 world-indexed 185; see also Plantinga, Alvin, ‘notion of Æ–transform’ see also intensional objects; propositions property dualism 216–17 propositional attitudes 217, 249 propositions 4, 6, 11, 15, 16, 18, 34–5, 38–9, 41–2, 43, 57, 61, 150, 174–5, 182 n. 8, 195, 231–56, 288 as abstract objects 57 as collections of worlds 57, 151, 232–42 de se 151 n. 9 Demonstrative theory of 164–8, 170–1, 172, 173, 241 gappy 258–9 logical structure of 159–75, 240–1, 247, 248, 250–1, 253–4 and modal Russellianism 240–2

Name theory of 159–64, 167, 170, 171, 173, 241 and revised modal Russellianism 243–7, 250, 254, 256 Russellian description theory of 171–4, 233, 240, 256 singular 13, 16–17, 57, 209, 265 truth-bearer conception of 173–4, 236, 237 Putnam, Hilary 192, 210 n. on meaning 221–6 Q quantiﬁcation 10, 50, 54, 74, 97 absolutely unrestricted vs restricted 55, 87, 90 n. 38, 238 domain of 51–2, 55, 62–3 existential 55 over worlds 233 universal 156, 203 quantum indeterminacy 41 n. 28, 277 n. 26 Quine, W. V. O. 27 n. 6, 50–1, 99, 165, 166 n. 27, 288 n., 294 n. objection against possibilia 83–5 see also impossible worlds, ‘Russell–Quine–Lewis argument against’ R realism 8–9, 10, 15, 18–20 ‘in an important sense’ 13, 15, 18, 19 reality 3, 41, 62, 80, 81, 92, 93, 131, 179 n., 203 vs actuality 40–1 knowledge of 284–5, 288 modal 2, 6 primitive nature of 9, 40, 49 ‘robust sense of ’ 1, 182, 268 see also existence; vagueness, ‘metaphysical view of ’ reductio ad absurdum 184 n. 14, 191, 193 reduction: and circularity 151, 152 conceptual 4, 5 semantic vs metaphysical 150 soft 150–3, 157 see also modality, ‘reduction of’ reference 20–1, 134–5, 138, 139, 149, 165, 168, 268 causal theory of 112, 262 deferred 27 n. 6, 165, 166, 167 direct 259, 271 ﬁxing 264–5, 272, 277 see also deﬁnite descriptions; names; rigid designators Reichenbach, Hans 31 n. 13 relations 43, 45, 51, 97, 157–9, 169 n. 38, 170, 232, 288, 291 accessibility 153–6, 177, 196, 277 closest-continuer 108–9, 121 constitution 162

Index counterpart 14, 140 earlier than 150 expression 161–3, 165–6, 170–1, 172, 245–7, 256 membership 51 part-of 51 proprietary 236, 244 see also intensional objects; similarity representation 15–16, 42, 158 narrowly vs broadly Lagadonian 47 see also Lewis, David, ‘counterpart theory’ Richard, Mark 162–3, 166, 253–4, 256 n. Rieber, Steven 31 n. 14 rigid designators 89, 208, 215, 226 Routley, Richard 84–5 Russell, Bertrand 74 n. 2, 171, 182, 256, 268; see also impossible worlds, ‘Russell– Quine–Lewis argument against’ Russell, Gillian 187 n. 19, 193 n. 29 S Salmon, Nathan 13, 119, 132 n. 51, 135, 138–9, 161 n., 169 ‘Four Worlds Paradox’ 128–30 on haecceitism 99 Noman example 13, 17–18, 20 Sanford, David 187 satisfaction, degrees of 140 Schiffer, Stephen 166 Schro¨dinger, Erwin 277 n. 26 self 89, 151 n. 9, 281 n. 33 actual 113, 228, 230, 287 Sellars, Wilfrid 166 n. 29 semantic contribution 241–5, 248–9, 250, 251, 256 semantics 38, 149, 188 modal 62, 140 S5 140 two-dimensional, see two-dimensionalism sense data 290 sentences 4, 8 n. 3, 11, 15, 34, 38–9, 42–3, 62, 70, 149, 159, 182 n. 8, 195, 239 attitude 244–5 and propositions 161–4, 165–7, 170, 171, 173, 237, 241, 245–7, 249, 258, 265 see also belief sentences sets 10, 11, 38, 157, 162 Shalkowski, Scott A. 5 n. 8, 149 n. 7 Sider, Theodore 149 n. 7 similarity 5, 14, 104–6, 107, 108, 109, 121, 123, 125, 127, 134, 140, 189–90, 218; see also Lewis, David, ‘counterpart theory’ singular terms 134, 211 situations 4, 11, 12, 290 n. 7 Skyrms, Brian: epistemic objection against modal realism 81–2, 92, 153, 284

313

regress argument against modal realism 203–5, 221 so-sein: actual 62–5, 66, 69 bare 66 here 67 merely possible 66 possible 66 there 67 Soames, Scott 161 n., 210 n., 243 n. 13, 249 solipsism 62, 89 sorites argument 132–3, 136, 140 sortal terms 97, 142, 143–5 souls 38 space 20, 24–48, 53, 94–7, 103 and time 31–4 space-time 34 spatial parts 32–3, 38, 44, 53, 103, 104, 113, 125, 130–1, 217, 232 n. 2 spatial points 19–20, 24, 27, 31, 34, 40, 41, 44, 53, 69, 103, 104, 239 spatial regions 19–20, 27–30, 31–4, 36, 38, 40, 41–2, 44, 46, 50, 71, 102, 103, 239, 240 spatio-temporal relatedness 43–6, 149 spatio-temporally isolated wholes 90–1 speech acts 157–8 Stalnaker, Robert 62, 80, 151, 157, 179 n. on belief 193–4, 230 theory of counterfactual conditionals 120–1, 186–7, 217 see also counterfactual conditionals; counterpossible conditionals states of affairs 4, 11, 12, 16, 20, 28, 43 statue/ lump of clay example 141–4 Stoljar, Daniel 209 n. 49 Sundback, Gideon 229 superblobs 145–6 supervaluation 135, 136 synonyms, principle on 241, 242, 248 T Tarski, Alfred: T-schema 58 temporal parts 32–3, 37, 44, 53, 100, 101–2, 104, 111, 112, 114, 115, 138, 139, 152, 181, 198, 232 n. 2 temporal points 20, 24, 27, 34, 40, 42 n., 53, 69, 91, 150, 239; see also time temporal regions 20, 34, 44; see also time temporal stages, see temporal parts temporality, see time tense 22, 50, 74–6, 78, 91 future 25, 75, 89 past 25, 37 n., 66, 75, 76, 77, 79, 83, 89 present 25–6, 29–30, 66, 75, 77, 80, 86, 89

314

Index

tense (cont.) semantics of 75–6 see also ‘here’; modal tense; ‘now’ ‘that’-clauses, see propositions theism 6–7 ‘thereness’ 67 things in general 17–18, 24–5, 45 Thomasson, Amie L. 268 Thomson, Judith Jarvis 96 time 9, 19–20, 24–48, 53, 65, 74, 94–7, 104, 110, 127, 150–2, 179 n., 240 A- and B-theories of 150 time travel 146 token-reﬂexive terms 31 translation, faithful 251–2, 256 transworld identity, see identity, ‘transworld’ transworld individuals, see individuals, ‘transworld’ tropes 290 n. 7 truth 3–4, 6, 9, 24–5, 29, 38, 42–3, 58–9, 61, 81, 149 truth conditions 15, 16, 17, 22, 23, 29, 30, 47, 60, 68 n. 8, 70–2, 76, 77, 106, 167, 173, 188, 231 n., 268 truth-relativizers 35–9, 62, 240; see also alethic relativization truth values 149, 232, 236; see also truthrelativizers Twain, Mark 40 n. 25 Twin Earth 192, 218–21 two-dimensionalism 178 n. 5, 215–17, 221–30, 272 n. 22 U Unger, Peter 287 n. universe 1–2, 36, 65, 90, 106, 131, 197–8, 200–1, 202, 223, 279 vs worlds 2, 44–8, 62, 63, 69 unrestricted mereological summation, principle of 180 V vagueness 42 n., 63, 99, 106–9, 125, 130–9, 179, 223, 237

epistemic view of 131–4, 137 metaphysical view of 131, 137–9 nihilistic view of 131, 134, 137 semantic view of 131, 134–7, 138, 139 validity, deductive 191, 193 van Fraassen, B. C. 135 n. van Inwagen, Peter 96, 102 n., 134 n., 153 on actuality 87–90 on ﬁctional individuals 260, 266, 267 ontic objection against modal realism 86–7, 92 W Walton, Kendall 271 n., 283 n. 41 Watson, Dr 64, 67, 68, 267, 272 n. 23, 274, 291 Wiggins, David 79, 97 Williams, Donald 34 n. 17 Williamson, Timothy 132 n. 51 Wilson, George 279 n. 30, 280–3 Wittgenstein, Ludwig 59 world-indexing, iterated 58–60 world-stages 38, 44, 46, 47, 48, 107, 114, 127 n. 45, 199–201, 232, 273, 275, 276, 277, 292; see also modal stages worlds 176 accessibility relation between 153–6, 177, 200 conceivable 217 ﬁctional 257–83 nature of 43–8, 176, 179; see also Lewis, David, ‘conception of worlds’; possible worlds normal vs abnormal 235, 236 semantically regular vs irregular 243–4, 249, 251 zombie 216 see also possible worlds Y Yoshida, Tadao 229 Z Zalta, Edward 56 n. 15, 145 n., 267n., 268, 283 n. 41; see also Mally–Zalta encoding Zeus 269–70