The Tensed Theory of Time WilliamLane Craig

THE TENSED THEORY OF TIME

SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE

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JAAKKO HINTIKKA, Boston University Editors: DIRK VAN DALEN, University of Utrecht, The Netherlands DONALD DAVIDSON, University of California, Berkeley THEa A.F. KUIPERS, University of Groningen, The Netherlands PATRICK SUPPES, Stanford University, California JAN waLEN-sKI, Jagiellonian University, Krakow, Poland

VOLUME 293

THE TENSED THEORY

OF TIME A Critical Examination by

WILLIAM LANE CRAIG Talbot School of Theology, Marietta, GA, U.S.A.

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data Craig, William Lane. The tensed theory of time : a critical examination / by William Lane Craig. p. cm. -- (Synthese library; v. 293) Includes bibliographical references and index. ISBN 978-90-481-5585-9 ISBN 978-94-015-9345-8 (eBook) DOI 10.1007/978-94-015-9345-8 1. Time--Philosophy. I. Title. II. Series. BD638 .C73 2000 115--dc21

00-064723

ISBN 978-90-481-5585-9

Printed on acid-free paper

All Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1st edition 2000 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

To ALVIN PLANTINGA who by his work and his life has pointed the way

TABLE OF CONTENTS

Preface

1X

PART I. ARGUMENTS FORAN A-THEORY OF TIME Section 1: The 1neliminability of Tense

Chapter 1

Introduction: Language, Tense, and Ontology

Chapter 2

The Old B-Theory of Language

23

Chapter 3

The New B-Theory of Language

66

Chapter 4

The B-Theory and Theories of Direct Reference

97

3

Section 2: The Experience of Tense

Chapter 5

Our Experience of Tense

131

PART II. ARGUMENTS AGAINST AN A-THEORY OF TIME Chapter 6

McTaggart's Paradox

169

Chapter 7

The Myth of Temporal Passage

218

Bibliography

259

Subject Index

279

Proper Name Index

283

vii

PREFACE

T

he present book and its companion volume The Tenseless Theory of Time: a Critical Examination are an attempt to adjudicate what one recent discussant has called "the most fundamental question in the philosophy of time," namely, "whether a static or a dynamic conception of the world is correct."! I had originally intended to treat this question in the space of a single volume; but the study swelled into two. I found that an adequate appraisal of these two competing theories of time requires a wide-ranging discussion of issues in metaphysics, philosophy of language, phenomenology, philosophy of science, philosophy of space and time, and even philosophy of religion, and that this simply could not be done in one volume. If these volumes succeed in making a contribution to the debate, it will be precisely because of the synoptic nature of the discussion therein. Too often the question of the nature of time has been prematurely answered by some philosopher or physicist simply because he is largely ignorant of relevant discussions outside his chosen field of expertise. In these two complementary but independent volumes I have attempted to appraise what I take to be the most important arguments drawn from a variety of fields for and against each theory of time. The two rival theories of time which are the subject of our examination have been known under a variety of names: the A- versus the B-Theory, the tensed versus the tenseless theory, the dynamic versus the static theory. None of these labels is wholly adequate. The terminology of A- and B-Theory has the advantage of being the traditional designations inspired by J. M. E. McTaggart; but these names are descriptively opaque. D. H. Mellor changed the vocabulary of the debate by speaking instead of tensed and tense less theories, but he has now reverted to speaking of the A- and B-Theories because his labels aroused confusion in the minds of many concerning tense as an ontological category and tense as a linguistic phenomenon. Michael Tooley prefers to speak of dynamic versus static theories, but this terminology, too, can be misleading, since the vast majority of A-theorists do not think of time as literally moving. In these volumes, I use such labels interchangeably but have for the most part stuck with the traditional A and B terminology. I have spoken of "the" tensed or tenseless theory of time, but this expression is purely stylistic. As we shall see, there is actually a family of A-Theories of time, and B-theorists, too, differ among themselves on certain key issues. I shall argue that many of these versions of the A- or B-Theory are, in fact, inconsistent and that a unique A- or B-theoretical paradigm exists; but I should not want to be thought to prejudice the issue in advance by my choice of words. I am intellectually indebted in this study to too many persons to recall by name; but I should like to acknowledge my special gratitude to Quentin Smith, from whom Michael Tooley, Time, Tense, and Causation (Oxford: Clarendon Press, 1997), p. 13. IX

x

I have learned a great deal about language and time, and to the late Simon J. Prokhovnik, the eminent Australian physicist, who helped me to see the wisdom of Lorentz. I should also like to thank The University of Chicago Press and Wesleyan University Press for permission to reproduce figures. I am indebted to my wife Jan for her faithful labor in production of the typescript and to my research assistants Ryan Takenaga, Mike Austin, and Narcis Brasov. I should also like to thank Edward White and the Day Foundation for their generous grant which helped to fund the production of the camera-ready copy and to Mark Jensen and Jennifer Jensen for meticulously bringing this book into its final form. Atlanta, Georgia

William Lane Craig

PART I ARGUMENTS FOR AN A-THEORY OF TIME

SECTION 1: THE INELIMINABILITY OF TENSE CHAPTER 1 INTRODUCTION:

"T

LANGUAGE, TENSE, AND ONTOLOGY

he main dispute in the philosophy of time," writes one recent combatant, "is about the status of the present."l Is the present an objective, independent feature of reality or is it merely a subjective feature of consciousness or, at best, a purely relational feature of events? Is time characterized by objective tense determinations like pastness, presentness, and futurity, or are the moments of time ordered only by tense less relations like earlier than, simultaneous with, and later than? Since J. M. E. McTaggart fIrst distinguished clearly between these two kinds of time, labeling them the A- and B-series respectively, philosophers of time have found it useful to adopt McTaggart's nomenclature, referring to theories of tensed time as A-Theories and theories of tenseless time as B-Theories. One of the most hotly contested issues in the struggle between A-theorists and B-theorists concerns the alleged ineliminability of tense from language or thought and the implications which this has for the nature of time. Accordingly in this section we shall consider what implications linguistic tense has for an adequate ontology of time. TENSED AND TENSELESS SENTENCES By "tense," one means in the fIrst instance that familiar aspect of language which serves to express something's pastness, presentness, futurity, or combination thereof (as in the future perfect tense), all of which fall under what McTaggart called Adeterminations, in contrast to tenseless B-relations like earlier than, simultaneous with, and later than. In English, tense is usually expressed by altering the form of the verb (for example, "I write," "I wrote," "I shall write"),2 but tense may also be expressed by a rich variety of adverbial phrases (for example, "now," "yesterday," "three days ago," "soon"), adjectives (for example, "past," "present," "future"), prepositional phrases (for example, "at present," "in yet two days' time," "by next 1. Butterfield, "Spatial and Temporal Parts," Philosophical Quarterly 35 (1985): 32. For an account of English grammatical tense, see Otto Jespersen, Essentials of English Grammar (London: Allen & Unwin, 1933). A very helpful discussion of the range of verbal tenses, some of which are not found in English, is provided by Hans Reichenbach, Elements of Symbolic Logic (London: Collier-Macmillan, 1947), pp. 288-297. The A-theorist would want to replace Reichenbach's "point of speech" with something like "the present moment" but would otherwise find his nine fundamental forms of verbal tense quite illuminating.

3

4

CHAPTER 1

Saturday"), and nouns (as in, for example, "Today is Saturday," "Now is when he leaves"). In certain languages, tense is not a feature of verbs at all, other devices being exclusively used to show the tense of a sentence. 3 But, as Gorman and Wessman point out, "all four thousand or so known languages enable their speakers to designate temporal relationships and to distinguish between past, present, and future events-though with varying degrees of difficulty.,,4 Thus, as Mellor points out, it makes no difference to the discussion how tenses are indicated; the point is that a tensed sentence indicates "how near or far from the present, past, or future, something is."s In equating grammatical tense with that feature of language which expresses Adeterminations, we imply either that sentences which do not express Adeterminations are tense less or that no such sentences exist. Although in ordinary language we typically assume that all our sentences are tensed, there are nonetheless classes of sentences which are plausibly regarded as tenseless, for example: (1) mathematical or logical sentences like "2+2=4"; (2) sentences referring to types as opposed to tokens, such as "The second movement of Dvorak's New World Symphony utilizes American folk melodies"; (3) sentences expressing certain universal generalizations like "All swans have necks"; (4) sentences expressing certain dispositions, which mayor may not ever be realized, like "This glass breaks easily"; (5) sentences about dated times or events related by B-determinations, such as "The 1996 presidential election is earlier than the 2008 presidential election.,,6 The verbs in such sentences, while sharing the same linguistic syntactical form as present-tense verbs, differ from them in their semantic content in that they convey no tense. 7 It is not incumbent upon the defender of tenseless sentences to maintain that such sentences (or the propositions they express) are timelessly true (or false); he may hold that true tenseless sentences are, in virtue of their tenselessness, omnitemporally true. Thus, a true tenseless sentence may be presently true, but that fact does not imply that the sentence is present-tensed. If a contingent, tenseless sentence is presently true, it is logically impossible for it to be false at another moment of time; but this is not the case for contingent, present-tensed sentences which are presently true. A tenseless sentence, then, can imply a tensed sentence (for example, "All swans have necks" implies that "Any swans which now exist have necks"). It might be rejoined that while purportedly tense less sentences fail to have a single tense, nonetheless they are in fact tensed because they each possess multiple See Richard M. Gale, The Language of Time, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1968), pp. 45-46. For example, in Eskimo, the noun puyok (smoke) has a past-tense form puyuthluk (what has been smoke) and a future-tense form puyoqkak (what will become smoke). 4 Bernard Gorman and Alden Wessman, "The Emergence of Human Awareness and Concepts of Time," in The Personal Experience of Time, Emotions, Personality, and Psychotherapy (New York: Plenum Press, 1977), pp. 44-45. 5 D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), p. 4. See discussion in Yehoshua Bar-Hillel, "Indexical Expressions," Mind 63 (1954): 359-379; Nelson Goodman, The Structure of Appearance, 2d ed. (New York: Bobbs-Merrill, 1966), pp. 366-368; Andros Loizou, The Reality of Time (Brookfield, Ver.: Gower, 1986), pp. 9-10, 99-101. 7 For a discussion of this distinction, see Quentin Smith, Language and Time (New York: Oxford University Press, 1993), p. 189.

INTRODUCTION: LANGUAGE, TENSE, AND ONTOLOGY

5

tenses, either disjunctively or conjunctively.s The semantic content of a purportedly tenseless verb will be either a disjunction of the past, present, and future tenses (for example, "was, is, or will be") or else a conjunction of these same tenses (for example, "was, is, and will be"). Thus, the meaning of a sentence like "The 1996 presidential election is earlier than the 2008 presidential election" is "The 1996 presidential election was, is, and will be earlier than the 2008 presidential election." The meaning of "All swans have necks" is "All swans had, have, or will have necks." Now the defender of tenseless sentences might well agree that such disjunctive or conjunctive sentences are entailed by the relevant tense less sentences; but do such multiply tensed sentences really express what the tenseless sentences mean? This seems dubious. Think of sentences employed in possible worlds semantics. When it is said that "The modal operator 'D' acts as a universal quantifier which takes as its range the possible worlds in a sphere of accessibility," do we mean by "takes" the conjunctive tense "took, takes, and will take"? That seems bizarre. If we assert "Socrates is not wise in W*" are we really asserting "Socrates was, is, or will be not wise in W*"? Are we not rather speaking tenselessly? Or if we say "In the actual world God foreknows p," do we really mean "In the actual world God foreknew, foreknows, or will foreknow p," or are we not rather deliberately abstracting from considerations of tense in order to reflect upon a certain question? Or consider sentences about event-types as opposed to their tokens: when I say "In Shakespeare's Julius Caesar Brutus's speech precedes Antony's funeral oration," I am talking about event-types which as such never occur. While the relevant eventtokens in a performance of the play can be rightly said to exist in temporal relations with one another, must I, indeed, can I, in speaking of the event-types, properly assert that the one either preceded, precedes, or will precede the other? Or what about universal generalizations involving fictitious entities, such as "Centaurs have the torso of a man on the body of a horse"? Is this really a conjunctively tensed statement? It might be said that the meaning of this sentence is something like "If Centaurs exist, existed, or will exist, then they have, had, or will have, etc." But is the meaning so arcane? Do we not mean simply to abstract from any tense in such a generalization? Or consider sentences about dispositions which are never realized, like "This chemical substance kills instantly." The substance may never actually kill anyone precisely because such a warning is believed. It might be said that this sentence has the same meaning as the present-tense counterfactual, "If anyone were to imbibe this chemical substance, it would kill him instantly." But while such a counterfactual is entailed by this sentence, so is the indicative conditional, "If anyone imbibes this chemical substance, it will kill him instantly." And these do not have the same meaning. So how can we with confidence claim that either of these sentences means the same as the purportedly tenseless sentence rather than is entailed by it? Or take sentences about B-determinations such as the one given above. When it is asserted in 1998 that "The 1996 election is earlier than the 2008 election," the disjuncts "was" or "will be" of the disjunctive tense are clearly inappropriate, since the relevant events are neither both past nor both future. But See Smith, Language and Time, pp. 188-192; Roderick M. Chisholm and Dean W. Zimmerman, "Theology and Tense," Nous 31 (1997): 262-265.

6

CHAPTER 1

how is the present-tense "is" any more appropriate in 1998, when the one event is past and the other future? A tense less "is" seems more appropriate. These sorts of examples supply prima facie evidence that there are tense less sentences. It certainly seems open to us merely to stipulate that such sentences are to be taken as tenseless, unless there is some overriding reason why a sentence must be tensed. 9 Smith attempts to provide such a reason. But the argument to which he repeatedly recurs in order to show that purportedly tenseless sentences not merely entail, but are synonymous with, multiply tensed ones is remarkably weak, indeed, counterproductive, viz., that the tenseless version and the multiply tensed version are mutually substitutable salva veritate in belief contexts. Smith claims that if it is true that "John believes that Socrates is wise," which reports his belief in a purportedly tenseless sentence, then it is also true that "John believes that Socrates was, is, or will be wise" (Smith, Language and Time, p. 191). Or again, with respect to sentences ascribing B-determinations to events, he claims that truth value is preserved if we substitute for "John believes that Plato's birth is earlier than Aristotle's" the multiply tensed sentence "John believes that Plato's birth is and always will be earlier than Aristotle's" (Ibid., p. 198). Or again, with respect to universal generalizations like "All humans are under nine feet tall," Smith asserts that this sentence is synonymous with "Being human and not under nine feet tall always was, is, and always will be unexemplified" because these are mutually substitutable in belief contexts (Ibid., pp. 200-20 I). But as recent literature concerning theories of Direct Reference (with which Smith is thoroughly familiar) has reminded us, belief contexts provide very slippery ground for inferences concerning entailments in such contexts. Poor, old John may never have even so much as entertained multiply tensed statements, much less believe them. Maybe he thinks Socrates is (like Athena, the goddess of wisdom) a mythological figure, who never did nor will exist. Maybe he is a die-hard defender oftenseless sentences who refuses to believe that Plato's birth is now and always will be earlier than Aristotle's. It seems very likely that Smith's unique and original analysis of material implication has never even occurred to John, so that he might well believe that universal generalizations are tenseless, rather than multiply tensed sentences. Since Smith holds that substitutability in belief contexts is a necessary condition of synonymy, the failure of purportedly tenseless and multiply tensed sentences to be mutually substitutable in such contexts shows that they do not mean the same thing. Thus, Smith's argument backfires. In any case, Smith notes that mutual substitutability in belief contexts is only a necessary, not a sufficient condition of synonymy. He attempts to close the gap by arguing that purportedly tenseless sentences are semantically correlated with multiply tensed ones in such a way that their parts have the same semantic content; for example, in "Socrates is wise" and "Socrates was, is, or will be wise," the semantic content of "Socrates" and "wise" in the two sentences is identical, as is the semantic content of "is" and "was, is, or will be" (Ibid., pp. 190-191). But that is precisely the question in dispute! Smith just assumes that if a semantic correlation is consistent with the undisputed semantic content of the two sentences, then this counts as a confirming reason in favor of synonymy. But there is no reason to think this assumption true, since non-synonymous sentences could be mutually entailing. Smith does present another consideration in favor of his position, viz., that no timeless states of affairs exist. This seems to be the principal argument for the meaning equivalence of typical mathematico-Iogical sentences and their conjunctively tensed counterparts, since the belief context argument would in this case be manifestly mistaken, as many philosophers do believe the tenseless sentences but do not believe the multiply tensed versions. Smith argues that abstract objects like numbers, properties, and so forth, are all temporal because they undergo relational change in being referred to successively by temporal agents. Since they are temporal, the purportedly tenseless sentences about such entities are really synonymous with conjunctively tensed sentences (Ibid., pp. 204-214). Similarly, purportedly tenseless sentences ascribing B-determinations to events are synonymous with conjunctively tensed sentences ascribing everlasting presentness to the events' state of being B-related. Since there are no timeless states (as seen above), this state must be temporal. If two events are Brelated, they are presently B-related, whether the events are past or present (Ibid., p. 197). With regard to the argument against timeless abstract objects and states, I think one might be justifiably skeptical whether the sort of "Cambridge change" envisioned by Smith is a sufficient condition of its subject's being temporal. The argument assumes without justification that being referred to by x is a real property that a thing acquires or loses. But the defender of timeless entities could regard sentences involving reference to such entities as true de dicto, not de reo Thus, "John believes that 2+2=4" means

INTRODUCTION: LANGUAGE, TENSE, AND ONTOLOGY

7

It would be helpful to have some criterion for distinguishing between what are undisputedly A-sentences and sentences which do not ostensibly ascribe Adeterminations. In his classic treatment The Language of Time, Richard Gale draws the following distinction between what he calls A-statements and B-statements: Any statement which is not necessarily true (false) is an A-statement if, and only if, it is made through the use of a sentence for which it is logically possible that two nonsimultaneous uses of this sentence make statements differing in truth value, even if both statements refer to the same things and the same places. Any statement is a B-statement if, and only if, it describes a temporal relation between events and is made through the use of a sentence for which it is the case that if it can now be used to make a true (false) statement then any past or future use of this sentence also makes a true (false) statement. 10

Gale's bifurcation would exclude from A-statement status a range of tensed sentences;ll but so long as it captured a class of tensed sentences as expressing Astatements, the discussion could proceed. Unfortunately, although Gale is, of course, free to defme his terms in whatever manner he wi.shes, his definitions involve controversial assumptions such that some A-theorists might be forced to say that there are no such things as A-statements according to these definitions. This would be the case, for example, for any A-theorist who holds to a non-propositional theory of belief, according to which there are no propositional objects of belief, their role being taken by the self-ascription of properties; or again, for any A-theorist who holds that the propositional content of a tensed sentence is tense less, the tense being contributed by non-propositional factors. Since these views merit discussion, it would be unwise to preclude them from the outset. More recently, Quentin Smith, whose Language and Time is destined to replace Gale's book as the standard work in this area, has tried to layout the defining conditions for A- and B-sentences in the following way: 12 A sentence is an A-sentence iff: i. It contains a future, present, or past-tensed copula and/or verb; it may also contain a temporal indexical, such as a temporal adverb or pronoun. that John believes the tenselessly true sentence "2+2=4", but does not mean that he believes of2 and of4 that 2 added to itself is 4. If his beliefs are not de re, then 2 and 4 do not acquire and lose the property being referred to by John. Hence, 2 and 4 could exist timelessly despite the fact that John makes reference to them at various times. But let that pass. The salient shortcoming of Smith's case is that he fails to justify the underlying presupposition that tenseless truths cannot refer to temporal entities. That this assumption is moot is evident from the fact that sentences ascribing B-determinations to temporal events are purportedly tenseless. How then does the demonstration that all entities and states are temporal go to show that there are no tenseless sentences about such things? Even if the tenseless sentences entail their multiply tensed counterparts, how does that prove that they are synonymous, that the former are not in fact tense less? Once again, Smith is forced to recur to his arguments about belief contexts and semantic correlations, which are in the case now under consideration manifestly inadequate. It seems to me, therefore, that Smith has failed to show that there are no tenseless sentences. lO Gale, Language of Time, pp. 42, 51. II E.g., mUltiply tensed sentences, sentences containing the adverb "always," tensed sentences which are broadly logically necessary, etc. The definitions also exclude a range of tenseless sentences from expressing B-statements, since only statements describing temporal relations between events are allowed. 12 Smith, Language and Time, pp. 6-7.

8

CHAPTER 1

ii. iii. iv. v.

It is explicitly or implicitly about an event, very broadly construed. It refers to the event's temporal position or ascribes to the event an n-adic temporal property. It refers to or ascribes a temporal position or property in such a way that they are determined by the sentence's tense. It is logically contingent, but is neither a universal generalization nor an omnitemporal disjunction.

A sentence is a B-sentence iff: i. It does not contain a tensed copula or verb or a temporal indexical. ii. It is explicitly or implicitly about an event. Ill. It refers directly or indirectly to the event's B-position or ascribes to the event a polyadic B-property, but does not ascribe to it an A-property. iv. It is logically contingent, but not a universal generalization.

Since Smith believes that B-sentences are, in fact, multiply tensed, he means in point (i) above that A-sentences have and B-sentences do not have singly tensed verbs. Precisely this last qualification provides the means of a considerable simplification of the distinction we want to draw. We can forget about most of Smith's conditions and simply say: 1.

An English sentence is an A-sentence iff it contains a singly tensed verb, a temporal indexical, or an A-predicate adjective.

2.

An English sentence is a B-sentence iff it contains a tenseless or multiply tensed verb and no temporal indexicals or A-predicate adjectives. MEANS OF EXPRESSING TENSE IN ENGLISH

Having thus distinguished between A- and B-sentences, we shall also find it helpful to inquire briefly about the nature of the English language's overarching ways of indicating tense: verbs, temporal indexicals, and A-predicate adjectives. Verbs

Verbal tense is a familiar and seemingly well-understood affair. The crucial insight of the pioneer of tense logic, A. N. Prior, was that verbal tense is in fact essentially adverbial in nature. 13 Prior noticed that instead of changing the form of the present-tense verb in order to indicate a different tense, one could just as easily leave the verb in the present-tense but add various adverbs to the sentence to do the job. This led Prior to propose that tense be analyzed in terms of a sentential operator on the present-tense sentence. Thus, the past-tense sentence "John caught the 8: 15 train to London" is to be analyzed in terms of the past-tense sentential operator "It was the case that" and the present-tense version of the sentence, so: "It was the case that John catches the 8: 15 train to London," which Prior symbolized Pp. I3 A. N. Prior, "Changes in Events and Changes in Things," in Papers on Time and Tense (Oxford: Clarendon Press, 1968), pp. 7-9.

INTRODUCTION: LANGUAGE, TENSE, AND ONTOLOGY

9

Analogously, the future-tense version of this same sentence is to be analyzed as "It will be the case that John catches the 8:15 train to London," symbolized Fp. Since the operand sentence remains in the present tense, the present-tense operator is vacuous and redundant. Like modal operators, to which they bear a close resemblance, tense operators can be iterated to form ever more complex tenses. For example, on Prior's analysis the future-perfect sentence "John will have caught the 8: 15 train to London" is to be analyzed as "It will be the case that it was the case that John catches the 8: 15 train to London" and symbolized FPp. One could string together tense operators to form endlessly complex tenses. In order to analyze sentences involving temporal quantification like "Three days ago John caught the 8: 15 train to London," one may introduce a variable after the tense-logical operators to indicate how many time units from the present it was or will be the case that p, thusly: Pnp. We need not at this point delve into the cottage industry that has grown up around tense logic in order to appreciate the beauty and perspicacity of Prior's analysis of verbal tense. Temporal Indexicals

By contrast, the nature of temporal indexicals and of indexicals in general is much less clear. Indexicals are usually defined as words whose respective referents are not given once for all in the way that the referent of a proper name or definite description is given, but whose respective referents vary in a systematic way from context to context. 14 There are four broad types of indexicals, examples of which serve to clarifY the above definition: 15 (1) personal indexicals such as "I," "you," "he," etc.; (2) temporal indexicals such as "now," "then," "yesterday," "today," "tomorrow," etc.; (3) spatial indexicals such as "here," "there," "nearby," "far away," etc., and (4) demonstratives such as "this," "that," "these," and "those." It is evident that the referent of such words will vary with the context. If John says, "I'm hungry!" and Jane says, ''I'm hungry!" they do not refer to the same person, despite their using the same words. To refer to the same person as John does, Jane must employ a different personal indexical, either "You're hungry!" or "He's hungry!" depending once again upon the context of who is being addressed by Jane. Similarly, the adage that "Tomorrow never comes" plays upon the indexical fact that when the day now referred to as "tomorrow" does arrive, it will be referred to by a new word, "today." In the case of spatial indexicals, two persons in a telephone conversation, for example, must use different indexical words to refer to the same place: "How's everything there?" asks the caller, to which the other replies, "Everything here is fine." Demonstratives are distinguished from other indexicals14 See, for example, Graeme Forbes, "Indexicals," in Handbook of Philosophical Logic, ed. D. Gabbay and F. Guenther, vol. IV: Topics in the Philosophy of Language, Synthese Library 167 (Dordrecht: D. Reidel, 1989), p. 463. 15 I omit from indexical status expressions indicating what is actually the case, though some thinkers, notably David Lewis, have defended actuality as an indexical notion. According to Lewis, what is actually the case varies from context to context, where the context is or includes the possible world in which the sentence is purported to be true (David Lewis, On the Plurality of Worlds [Oxford: Basil Blackwell, 1986], p. 93; cf. idem, "Anselm and Actuality," Noils 4 [1970]: 185). Lewis's comparison of "actual" with the temporal indexical "present" is suggestive and merits our discussion in the sequel.

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despite the fact that all indexicals have sometimes been misleadingly labeled "demonstratives" 16-by the fact that their user employs them to point to something, to direct attention to something. Other indexicals can be used demonstratively-for example, pointing to a spot on a map, one could say, "Right here!"-, but then the demonstrative force of the expression derives not from the indexical word, but from the accompanying physical demonstration. B1 contrast, demonstrative words do not require an accompanying demonstration; I for example, "That remark was unnecessary, Senator" or "This situation is perilous." Rather demonstratives have an inherent demonstrative force, though, of course, a physical demonstration may be necessary to communicate one's idea to another, as, for example, when one says, "I choose that one out of the lot." These examples make clear the context-dependent nature of the referents of indexical words. But very little reflection is required to see that it is not simply in virtue of their context-dependence that indexical words differ from proper names and definite descriptions, for the referents of proper names and definite descriptions are no more "given once for all" in a context-independent way than are the referents of indexicals. If one says, "Kennedy was assassinated by a deranged gunman," two persons could truly believe this sentence without referring to the same man. Who is referred to will depend upon the context of utterance to the same extent that "Now is when the meeting starts" so depends. Rather a salient difference between these types of referring expressions seems to have to do with the systematic way in which the referents of indexicals vary from context to context. The referent of a proper name or defmite description may differ from context to context, but, having determined the referent in a particular context, one may still use that same name to refer to the same individual in a different context. But in the case of indexicals, a systematically correlated class of words exists which must be used to pick out the same referent under appropriately different circumstances. For example, if we were talking about Kennedy's assassination and were clear that we meant the President, then at a later time and different place, talking to different persons, we still may use the name "Kennedy" to refer to the same person. But when we later refer to the moment which we once referred to as "now," we use the word "then"; to refer in another place to the location elsewhere referred to as "here," we say "there"; to refer to the person whom I called "you" in another encounter, I instead use the words "he" or "she." Of course, if the context changes in such a way that we are no longer 16 Most notably by David Kaplan, "On the Logic of Demonstratives," in Contemporary Perspectives in the Philosophy of Language, ed. Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein (Minneapolis: University of Minnesota Press, 1979), pp. 401-412; so also Palle Yourgrau, "Introduction," in Demonstratives, ed. Palle Yourgrau (New York: Oxford University Press, 1990), pp. 1-8. Kaplan later repented of this misleading terminology, favoring the term "indexical" (Idem, "Demonstratives: an Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals," in Themes from Kaplan, ed. Joseph Almog, John Perry, and Howard Wettstein [Oxford: Oxford University Press, 1989], p. 490). Unfortunately, he still misconstrues a demonstrative as an indexical requiring an associated demonstration (Ibid., pp. 490-492). However, in his "Afterthoughts," in Themes, pp. 587-588, he correctly states, "". the meaning of a demonstrative requires that each syntactic occurrence be associated with a directing intention.... The need for a directing intention to determine the referent of a demonstrative still allows us to distinguish the true demonstratives from the pure indexicals." 17 Very often, the precise contradictory is asserted; but this is erroneous, as is pointed out by Howard Wettstein, "Has Semantics Rested on a Mistake?" Journal of Philosophy 83 (1986): 196.

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talking about the President's assassination, but rather the Attorney General's, then "Kennedy" will have a different referent in those contexts. But there is no systematically correlated term to use in the new context to pick out the same referent picked out in the former context; one can only add additional information, for example, a first name or a fuller description, and these will be arbitrary. Thus, it seems to be the systematic way in which indexicals pick out different referents in different contexts that serves to distinguish them from proper names and definite descriptions. Kaplan expresses the point by asserting that the meaning of an indexical word, unlike proper names or definite descriptions, provides a rule of use which determines the referent in terms of certain aspects of the context. IS For example, the meaning of "I" determines a linguistic rule in English that the referent of the term in a given context will be the person tokening in speech or thought the sentence in which "I" appears; by contrast the meaning of "you" determines a rule that the referent is the individual being addressed. With respect to temporal indexicals, there are linguistic rules determined by the meanings of the words which stipulate that the time referred to is a moment or interval earlier than, simultaneous with, or later than the time of any tokening of the sentence. 19 By contrast, proper names and definite descriptions do not determine by the meaning of the words involved any such linguistic rules to fix their referents. The question now arises as to what relationship exists between verbs and temporal indexicals. Are verbs themselves temporal indexicals? It would seem so, for a sentence like "The meeting is starting" seems to mean, in virtue of its presenttense verb, the same as "The meeting is starting now." If that is the case, then it seems that just as the referent of "now" various systematically with the context, so the time implicitly referred to in the verb varies systematically with the context. Every time the present-tense sentence is tokened, a different time is referred to, and in order to refer to the same event at another time, we must use different forms of the verb, namely, past- or future-tense. Accordingly, verbs, too, seem to be temporal indexicals. What this position fails to take cognizance of is the necessity of what is called "double indexing" with respect to sentences which contain temporal indexicals and are governed by temporal operators. First noticed by Hans Kamp,20 the necessity of Kaplan, "Demonstratives," pp. 490-491. There are apparent, interesting exceptions to this practice; for example, "Churchill now faced the most critical moment of his career." For an entertaining discussion, see Quentin Smith, "The Multiple Uses oflndexicals," Synthese 78 (1989): 167-191. But I should say, and I think Smith would agree, that in such circumstances the temporal indexicals are in fact tenseless and therefore not truly temporal indexicals (Smith, Language and Time, p. 24, note 3.) 20 Hans Kamp, "Formal Properties of 'now'," Theoria 37 (1972): 227-273; see also A. N. Prior, "Now," Nails 2 (1968): 101-119; idem, '''Now' Corrected and Condensed," Nails 2 (1968): 411-412; Pavel Tichy, 'The Transiency of Truth," Theoria 46 (1980): 164-182. While recognizing the nonredundancy of "now," Tichy ostensibly opposes double indexing because it jettisons the principle that propositions take truth values relative to a world and a time in favor of the precept that propositions take truth values relative to a world, a time, and yet another time. On the conventional view, he asserts, whenever a proposition is asserted, a unique world is actual and a unique moment of time is current. Accordingly, he proposes to analyze a sentence like "It will be the case that Brown is not at home now" as expressing the proposition For some moment u, u is present and it will be the case that Brown is not at home at u. But I think that Tichy is clearly confusing semantics with ontology. Double indexing is a semantical feature of sentences that in no way denies that there is a unique moment of time which is 18

19

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double indexing arises from the fact that temporal indexicals in contexts governed by tense operators are not necessarily based on the time parameter specified by the tense operator in whose scope they lie, but may have a different temporal base. 21 For example, suppose during the Reagan presidency someone were to assert "The present U.S. president was once a Democrat." How does that differ from the assertion at the same time that "The U.S. president was once a Democrat"? The answer is that the indexical word "present" requires one to assess the referent of "U.S. president" relative to a different time than that indicated by the verbal tense, whereas in the absence of this indexical, there is only one temporal parameter. This ontologically present. Tichy's own analysis involves double indexing, since the time referred to by the future-tense operator is not the same time as u. Indeed, his analysis has the virtue of making the indexical time parameter's independence of the temporal operator perspicuous. Prior himself observed, " ... we can dispense with the non-redundant 'now' in favour of the redundant one. In other words, the non-redundant 'now' is non-redundant only in the sense that you cannot just erase it from a sentence and leave the sense of the whole the same; you can, however, erase it and get something with the same sense by altering the rest of the sentence somewhat" (Prior, "Now," p. 106). 21 For an outstanding account of double indexing and of temporal indexicals in general, see Nathan Salmon, "Tense and Singular Propositions," in Themes/rom Kaplan, pp. 354-367. Salmon's theory of indexicals is based on a semi-Fregean propositional analysis of tensed sentences. On Salmon's analysis, the semantic basis of a sentence is a propositional matrix, which consists of the referent of the subject of the sentence and the property ascribed to the referent by the sentence's predicate. The propositional matrix becomes a piece of information by attaching to it a particular time at which the property inheres in the referent. Sometimes it may be necessary to attach a particular location as well to obtain a genuine piece of information or proposition. The propositional matrix serves as the information value base for a tensed expression. "An indexical expression is precisely one that takes on different value bases with respect to different possible contexts" (Ibid., p. 346). As the context of utterance varies, the referent of such expressions varies, as I explain in the text. By contrast, a tensed sentence like "Frege is busy," while having different information value or propositional content at different times, has the same information value base or propositional matrix, viz. the complex consisting of Frege and the property of being busy. The time is implicitly built into the information value of the predicate, which is why such non-indexical sentences take on different truth values and different information values when uttered at different times, even though the expression is not indexical. For the same reason certain non-indexical definite descriptions like "the senior senator from California" take on different referents and different information values at different times. The distinctive feature of an indexical expression like "I" or "the present senior senator from California" is that it takes on different information value bases in different contexts. "The predicate 'be busy,' the definite description 'the senior senator from California,' and the sentence 'The senior senator from California is busy' all retain the same value base in all contexts. Their information value varies with the context, but not their information value base" (Ibid., p. 369). For example, the information value base of the aforementioned sentence is comprised of the senior senator and the property of being busy, and this base remains the same at all times though attached to different times. But the information value base of "The present senior senator from California is busy" will vary with the context of utterance because the time is included in the value base itself. The semantic difference between these similar expressions does not show up clearly in sentences in which the time attached to the value base is the same time as the time inherent in the value base of the indexical expression, but when double indexing is required because the times differ, the difference becomes clear, e.g., "In 1913 the senior senator from California was a child" versus "In 1913 the present senior senator from California was a child." According to Salmon, the function of indexicals like "present" or "now" is "primarily to affect the content base of its operand, eternalizing it and thereby sealing it off from the influence of external occurrences of temporal operators" (Ibid., p. 377). Salmon's characterization of indexicals depends on a Direct Reference Theory, propositions as objects of belief, and a tenseless view of information and is thus too controversial to serve as a general characterization of indexicals. But his focusing on the phenomenon of double indexing as distinctive of indexicals is an insight which transcends his theory. One can agree that indexicals are just those expressions which are such that they would be classed as indexical if Salmon's theory were correct.

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double indexing evinces the fact that temporal indexicals have a certain independence from the tense logical operators in whose scope they lie. Double indexing is a very common feature of ordinary language: "He assured me that he would arrive today," "We shall never forget what transpired three days ago," "What you said now troubles me." By contrast verbal tense and non-indexical temporal expressions do not require double indexing. For example, contrast the two sentences 3.

It will be the case tomorrow that I am sitting down.

4.

It will be the case tomorrow that I am now sitting down.

The first sentence requires only single indexing, since there is no indexical within the scope of the tense logical operator (the "tomorrow" serving to quantify the operator itself) and thus naturally means that tomorrow I shall be sitting down then. But the second sentence requires double indexing due to the indexical "now" within the scope of the operator and naturally means that my sitting down today will be the case tomorrow, that is, that tomorrow it will be true that "I was sitting down yesterday." The absence of double indexing for merely verbally tensed sentences reveals that the so-called "redundancy theory" of the "now,,22-that adding "now" to a present-tense sentence does not change the semantic character of that sentence-is incorrect. Even if the information value or propositional content of "It is 3 o'clock" and "It is now 3 o'clock" is the same, nevertheless these sentences differ in their semantic properties in that only the latter requires double indexing when in the scope of a tense-logical operator. Similarly, non-indexical time indicators do not require double indexing. Consider the sentence, "John said he would call me on the following day." The phrase "on the following day" does not express an A-determination, but a Bdetermination. Perhaps in the original context John said, "Mother will arrive on May 12, and I will call you the following day." The day referred to may now be past, present, or future. No double indexing is required because the phrase does not refer to any second time parameter. By contrast, if one reports, "John said he would call me tomorrow," the "tomorrow" refers not to the context of John's utterance, but to a second time parameter related to the reporter's present?3 Thus, non-indexical or B-theoretical temporal expressions do not require double indexing. Such considerations prompt Salmon to conclude: What is distinctive about indexical expressions (such as T, 'this tree,' or 'the present U.S. president') is not merely that the extension with respect to a context c (simpliciter) varies with the context c, or even that the intension or information value with respect to 22 See A. N. Prior, Time and Modality (Oxford: Clarendon Press, 1957), pp. 9-10; idem, "Changes in Events, pp. 8-10, 14-15; idem, "On Spurious Egocentricity," in Papers on Time and Tense, pp. 17-23. 23 Kaplan errs, therefore, in asserting that "yesterday" is an indexical and "one day ago" is an iterative temporal operator (Kaplan, "Logic of Demonstratives," p. 412). Compare "It will always be the case that John yawned yesterday" and "It will always be the case that John yawned one day ago." The expression "one day ago" refers to the time of the speaker's present and is not comparable to "on the preceding day." Thus, "One day ago it was the case that one day ago it was the case that John yawns" does not mean "John yawned the day before yesterday," for the second token of "one day ago" within the scope of the first requires an independent temporal reference point, unlike the iterative "on the preceding day."

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a context c (simpliciter) varies with the context c. That much may be true of even a non-indexical expression, such as 'the U.S. president' or 'Frege is busy.' What makes an expression indexical is that its extension with respect to a context c and a time t and a location I and a possible world w varies with the context c, even if the other parameters are held fixed 24

Consider the sentence, "In a in 1953 in the United States the present U.S. president was a Democrat." In this sentence w, t, and I are firmly fixed, but as the context of utterance c of this sentence varies, both the extension (or referent) of the expression "the present U.S. president" as well as the extension (or truth value) of the sentence as a whole vary. If c involves 1982, for example, the referent is Reagan and the sentence is true; but if c includes 1992 instead, then the referent is George Bush and the sentence is false. Hence, the expression "the present U.S. president" and the sentence as a whole are indexical in character. By contrast, if one considers the sentence "In a in 1953 in the United States the U.S. president was a Democrat," then the referent of the phrase "the U.S. president" never varies with the context of utterance c; any variation in its truth value would stem, not from this non-indexical phrase, but from the tensed verb, so that to make the extension of the sentence invariable we must stipulate that the verb be tenseless (which was, in fact, Salmon's assumption).25 Due to the necessity of double indexing, even a sentence having a tenseless verb but containing a temporal indexical will vary in its truth value with the context of utterance c. As a result of these brief reflections, I think it is clear what the ostensible function of temporal indexicals is: they ascribe A-determinations and/or Apositions. This prima facie function need not be a point of controversy: perhaps such A-ascriptions are eliminable or reducible in some way. But it seems to me almost undeniable that temporal indexicals are grammatically tensed expressions. After all, the paradigmatic A-determinations "past," "present," and "future," as well as "now," are all temporal indexicals?6 Sometimes temporal indexicals ascribe an A-determination without a specific position, for example, "past," "future," "long ago." But frequently, they ascribe A-positions, for example, "yesterday," "today," "tomorrow," "six days ago," "next Friday." The indexicals "now" and "present" ascribe A-positions, but are "accordion words" which can be stretched or compressed to fit the context. "Now" might signify the present instant, or the specious present of varying duration, or a moment of indeterminate length, or even the present era or epoch in geological or cosmic time. Indexicals which ascribe an A-series position thus have the dual function of picking out a position in the temporal series and ascribing to it pastness, presentness, or futurity.27 Salmon, "Tense and Singular Propositions," p. 360. The fact that the sentence must be tenseless might lead one to infer that verbs are, after all, temporal indexicals, since the extension of the sentence varies with c. But even so, verbal tenses do not require double indexing but can be iterated indefinitely with only single indexing; and this serves to distinguish verbal tense from temporal indexicals. 26 Care must be taken here, since as Goodman, Structure of Appearance, p. 368, points out, "past," "present," and "future" are often used as two-place B-predicates and are in such cases tenseless. See also George N. Schlesinger, Aspects of Time (Indianapolis: Hackett, 1980), p. 133. If Smith is correct, they can also function as A-non-indexicals. 27 Smith takes this to be not only their linguistic function, but also their semantic function (Smith, Language and Time, p. III; cf idem, "Temporal Indexicals," Erkenntnis 32 [1990]: 5-25). H

25

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A-Predicate Adjectives

With respect to A-predicate adjectives, Smith sets forth the interesting contention that A-determinations like "past," "present," and "future" are not indexical expressions just in case they are preceded by an A-copula, since in such a case they do not require double indexing when in the scope oftemporal operators. 28 Contrast, for example, the sentences "The storm is occurring now" and "The storm is present.,,29 When in the scope of a temporal operator, "now" requires double indexing, for example, "It will be the case tomorrow that the storm is occurring now." But "is present" remains singly indexed, for example, "It will be the case tomorrow that the storm is present." In this case "to be present" means "to have the property of presentness," and the sentence means that tomorrow there will be a storm. In this understanding, Smith agrees with Prior, who wrote, "In 'It will be the case tomorrow that my sitting down is present,' the presentness referred to is a presentness that will obtain tomorrow, i.e., at the time to which we are taken by the tensing prefix.,,30 The use of "present" following the tensed copula thus differs from the indexical use of the word in such sentences as "It will be the case tomorrow that the present storm is occurring" or "It will be the case tomorrow that the storm is presently occurring," which like the sentence containing "now" involve double indexing. It seems to me correct that expressions consisting of an A-determination preceded by a tensed copula are non-indexical, but it might be questioned whether they are in fact A-expressions. It might be contended that "past," "present," and "future" in such constructions are being used in the B-theoretical sense noted by Goodman. For example, when it is said, "It will be the case tomorrow that the storm is past," one means that the storm is earlier than the day specified by the operator, and when one says, "It was the case yesterday that the storm is future," one means later than the time specified. In the same way, to say, "It will be the case tomorrow that the storm is present" means that it will be simultaneous with the day in question. Hence, these expressions are not A-determinations. But I think that it is open to question whether such expressions are always used in this B-theoretical sense. When we comfort ourselves by saying, "Tomorrow this will all be past," we do not seem to be saying that it will be earlier than tomorrowindeed, that fact could be the source of our distress-but that it will have the Adetermination of being past. My point is not to rehearse here the experiential arguments for the A-Theory. Rather the point is, whatever the semantics of such sentences, ordinary language users seem to employ them to express Adeterminations, so it is simply incorrect to assert that expressions consisting of a copula + an A-determination do not in fact purport to ascribe A-determinations.

Smith, Language and Time, pp. 116-120; cf. pp. 74-77. Smith's point is even more obvious if we change the tense of the copula in accord with either single or double indexing, e.g. "It will be the case tomorrow that the storm was occurring now" and "It will be the case tomorrow that the storm will be present." In ordinary language we often shift the tense of the verb to conform to the time of reference. The artificiality of using tense operators on present-tense verbs obscures the meaning evident in ordinary language. 30 Prior, "Now," p. 104. 28

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Perhaps the best argument against regarding the expressions in question as a separate category of non-indexical A-expressions is to contend that they are really examples of verbal tense. Some A-theorists object to treating presentness as a property rather than as a tense logical operator and so would interpret Smith's sentence to mean "It will be the case tomorrow that the storm occurs" and the ascription of pastness to mean "It will be the case tomorrow that it was the case that the storm occurs" and the ascription of futurity to mean "It was the case yesterday that it will be the case that the storm occurs." Thus, the copula + A-determination is non-indexical because it really is verbal and, hence, a sentential tense operator. But while such an interpretation might serve as a sound semantical analysis of such sentences, the fact remains that on the linguistic-grammatical level the expressions in question just are not verbs, but a verb plus a predicate adjective. On the linguistic level Smith seems correct that we have here examples of non-indexical, non-verbal A-expressions. Quasi-Indexicals? Finally, we should ask whether there is a fourth type of linguistic expression used for expressing tense in English-what the late H.-N. Castafieda called "~uasi­ indicators," or-to keep more in line with our terminology-quasi-indexicals? He observed that in oratio obliqua (indirect discourse), that is to say, in a clause subordinated to a verb expressing a propositional attitude, the indexicals used by the original speaker in oratio recta (direct discourse) cannot be adequately captured by de dicto or de re expressions but require quasi-indexical words. Castafieda calls such words "quasi-" indexical because (i) they do not express an indexical reference made by the speaker of the oratio recta, and (ii) they are used to attribute implicit indexical references to that speaker. Consider, for example, the sentence "The Editor of Noils believes that he himself is a millionaire." This sentence entails a sentence such as "The Editor of Noils believes what he would express by saying, 'I am a millionaire'." But then the first sentence cannot be equivalent in meaning to a de dicto sentence like "The Editor of Noils believes that the Editor of Noils is a millionaire" because the latter sentence does not entail that the Editor of Noils believes himself to be a millionaire (perhaps he has not yet learned of his appointment to the editorship). But neither can the first sentence be interpreted as ascribing a de re belief to the Editor, such as "The Editor of Noils believes of the Editor of Noils that he is a millionaire," for this belief also fails to entail that the Editor of Noils believes he himself to be a millionaire (since it does not entail that he believes "I am the Editor of Noils"). Thus, in order to make an indexical reference repeatable by various persons, yet preserve its indexical character, we must use quasi-indexicals, which Castafieda proposed to mark with "*". Hector-Neri Castaileda, "'He': A Study in the Logic of Self-Consciousness," Ratio 8 (1966): 130157; idem, "Indicators and Quasi-Indicators," American Philosophical Quarterly 4 (1967): 85-100; idem, "Omniscience and Indexical Reference," Journal o/Philosophy 64 (1967): 203-210; idem, "On the Logic of Attributions of Self-Knowledge to Others," Journal 0/ Philosophy 65 (1968): 439-456. For a readable secondary account, see Esa Saarinen, "Castaileda's Philosophy of Language," in Hector-Neri Castaneda, ed. James E. Tomberlin, Profiles 6 (Dordrecht: D. Reidel, 1986), pp. 187-214. 31

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Although most of Castafieda's work concerned personal indexicals, the same point can be made about other indexicals, including temporal indexicals. Castafieda provides as an example the sentence "On May 15, 1911, the German Emperor believed that it was raining then·." What did the Kaiser believe in aratia recta?Not the de dicta belief that it was raining on the date in question, for he may have had no idea of the date; nor the de re belief concerning that day that it was a rainy day, for that does not entail that the day was present. What he believed was what he would have expressed by saying "It is now raining." Insightful as Castafieda's analysis is, it seems to me that he has not discovered a new logical term called "quasi-indexicals" but simply uncovered the fact of double indexing. The fact that such terms express, not the indexical references of the speaker of the oratio recta, but rather the indexical references of the speaker of the whole complex utterance, is due to double-indexing, not to a new logical term, quasi-indexicals. When one says, "On May 15, 1911, the German Emperor believed that it was raining then," the use of "then" is an ordinary indexical which necessitates double indexing of this sentence in virtue of its lying within the scope of the temporal operator. The fact that it is oratio obliqua is really a red herring, as is evident from the fact that if the time of the context of utterance is the same time as the time of the operator, then the word "then" becomes inappropriate in oratio obliqua: "The Emperor believes that it is raining now." In this case the two indices coincide. Similarly, when the context of utterance does not shift persons, then "he" is inappropriate: "I told you I was a millionaire." It is not the shift from oratio recta to oratio obliqua as such which requires a change in the indexical, but a shift in the context of utterance. As we noted earlier, indexicals come in systematically correlated pairs or triplets, and which of the group is appropriate for retaining the original reference varies as the context varies. Thus, in the case of temporal indexicals, "then" must be used instead of "now" to refer to times past or future with respect to the context of utterance (for some reason English fails to discriminate between past-then and future-then, so any time other than the present can be referred to as "then"). This change is required even while remaining within oratio recta. For example, one must in the context of 1995 say, "On May 15, 1911, it was raining then" or "On May 15, 1911, it was the case that it is then raining," rather than "On May 15, 1911, it was now raining." The indexical nature of "then" becomes apparent when we make the verb tenseless: "On May 15, 1911, it rains then," for the word "then" reveals that the context of utterance is not May 15, 1911. Castafieda thinks that quasi-indexicals necessarily have antecedents in the sentential context. Otherwise, a sentence like "The Emperor believed it was raining then" would be ambiguous. However, pace Castaneda, the necessity of an antecedent for temporal indexicals like "then," "past," or "future," is not due to their supposed quasi-indexical nature, but due to the fact that unlike their correlates "now" and "present," they ascribe only an A-determination but not an A-position, so that they need to be supplemented by another expression fixing the position. Indexicals ascribing both an A-determination and a temporal position require no antecedents; for example, "The Emperor believed it was raining yesterday." When evaluated in a context of utterance c including the date May 16, 1911, this sentence is unambiguous and true. In other contexts "yesterday" changes its referent, so that

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the sentence may be false. It behaves the same as "then" plus a date. What Castafieda took to be an essential property of so-called quasi-indexicals is in fact only a property ofindexicals which fail to ascribe an A-position. A similar point could be made about Castafieda's claim that from a quasiindexical in oratio obliqua one can infer an appropriate indexical originally in oratio recta, but that from an indexical in oratio obliqua one cannot infer that in the original oratio recta an indexical reference was made. For example, " ... when Gaskon says, 'Yesterday Privatus thought ... that it would be raining now (today),' Gaskon's statement both contains his own indexical uses of 'now' ('today') and fails to imply that Privatus referred indexically to the time at which Gaskon made his statement.,,32 Privatus, for all we know, could have actually said, "It will be raining on May 15," but Gaskon on May 15 reports this using an indexical. The reason behind this phenomenon is not, however, due to the fact that quasi-indexicals are a special term distinct from indexicals, but rather to the shift in the context of utterance such that the time parameter of the indexical does not coincide with the time of the oratio recta. But if they do coincide, then one can infer an indexical in the original oratio recta. Suppose Gaskon, talking on the telephone to Privatus about his expected visit, whispers to his wife, "Privatus says he's arriving today!" Then the "today" indicates both Gaskon's context of utterance as well as Privatus's and expresses what Privatus would say in oratio recta. 33 What Castaneda should have said, it seems, is that from a past- or future-tensed indexical in oratio obliqua which refers to the same time as the time of the oratio recta, one can infer a presenttensed indexical in oratio recta. But from a present-tensed indexical in oratio obliqua, one cannot infer an indexical expression in oratio recta, unless the oratio obliqua is reported in the present tense. I am not particularly concerned to assess the truth of this claim;34 rather my point is that there appears to be no justification for inventing a new singular term called "quasi-indexicals" in addition to ordinary indexicals.

Castai'ieda, "Omniscience," p. 206. Of course, one cannot infer that Privatus actually uttered the indexical word; perhaps he said, "I'm arriving this afternoon" or "I'm arriving at 3:00 p.m." But to the same degree, uncertainty as to the actual words in oratio recta also persists when we have a so-called quasi-indexical. Perhaps the Kaiser said "This is a rainy day" or, looking at his calendar, "May 15 is a rainy day." In both these cases, the point is that the persons believed something which could be expressed with present-tense indexicals like "now" or "today." Cf. Saarinen's complaint that, unlike "he himself," "then" and "there" do not inevitably attribute to someone the use of their indexical counterparts and are not therefore real quasi-indexicals (Saarinen, "Castai'ieda's Philosophy of Language," p. 201). I agree with Castai'ieda that this merely represents a deficit in natural language (Hector-Neri Castai'ieda, "Reply to Esa Saarinen," in Castaneda, pp. 349-350. 34 Castai'ieda himself confessed, "I cannot, however, muster a formal argument to show this" (Castai'ieda, "Indicators and Quasi-Indicators," p. 96). There is a very interesting exchange of views concerning the related issue of whether the proposition expressed by the quasi-indexical clause is the same as that expressed by the corresponding indexical clause in oratio recta in Robert Adams and Hector-Neri Castai'ieda, "Knowledge and Self: A Correspondence between Robert M. Adams and HectorNeri Castai'ieda," in Agent, Language, and the Structure of the World, ed. James E. Tomberlin (Indianapolis: Hackett Publishing, 1983), pp. 293-308, and Hector-Neri Castai'ieda, "Reply to John Perry: Meaning, Belief, and Reference," in Agent, Language, and Structure, p. 327. Although Castai'ieda gives up this claim, it seems to me that Adams's argument calls into question not so much this claim as the claim that someone who knows that another person knows that p also knows that p. 32 33

INTRODUCTION: LANGUAGE, TENSE, AND ONTOLOGY

19

LINGUISTIC AND ONTOLOGICAL TENSE

All of the above has been said concerning linguistic tense, such as we all know and use it. But the A-theorist claims that tense is real in a more fundamental sense, in an ontological or metaphysical sense, that the extra-linguistic world is itself characterized by A-determinations like past, present, and future, that there actually exists a "now" or a present moment of time. For the A-theorist tense in language is but a reflection of the way the world is, of ontological tense. This constitutes, of course, the great divide between A-theorists and B-theorists. The latter, while acknowledging the undeniable presence of tense in ordinary language, hold that reality itself is tenseless, that there are no tensed facts, no ontological past, present, or future. As Mellor explains, for the B-theorist there are no two possible worlds W and W* which are identical in their histories except for the fact that in W it is now 1995, while in W* it is now 1795: "".there is no tenseless difference between the two worlds. Indeed, there are not two worlds.... There is only one world, with things and events scattered throughout B-series time as they are throughout space, including both the eighteenth and twentieth centuries.,,35 For the B-theorist tense is a feature of language, not of the world. Many A-theorists maintain that tense cannot plausibly be regarded as a feature of language and thought alone, that language furnishes us, as it were, a sort of window on the world whereby we may apprehend the factual objectivity of tense. They argue that the ineliminability or irreducibility of tense in language and its indispensability for human life and action make it plausible that tense is a feature of reality as well as of language and that therefore the A-Theory is preferable to the BTheory. Against this claim, B-theorists have opposed two objections: (1) The tense that characterizes ordinary language is eliminable by translating sentences of ordinary language into a tense less canonical form which preserves the meaning of the ordinary language sentences. Linguistic A-determinations can be reduced to Bdeterminations by a variety of devices. Hence, the tense that characterizes ordinary language furnishes no insight into the actual nature of time itself. This point of view tends to be associated with the earlier generation of B-theorists, such as Russell, Reichenbach, Quine, and Smart, but tends to be rejected by contemporary Btheorists and so may conveniently be called "The Old B-Theory of Language.,,36 (2) While tense is an ineliminable feature of human language, indispensable for timely action in human affairs, nonetheless the fact that human language cannot be divested of tense has no ontological implications concerning the nature of time. For tenseless truth conditions can be given for all A-sentences, as well as B-sentences, so that it becomes gratuitous to posit tensed facts in order to make A-sentences true or false. Since nothing more than tense less facts is required in order for A-sentences to be true or false, the fact that tense is not eliminable from human language and thought Mellor, Real Time, p. 56; cf. p. 28, where he admits that unless the B-theorist shows that there is no difference between Wand W*, he cannot deny that the A-series describes a real aspect of the world. 36 An appellation I adapt from Smith, Language and Time, sees. I. 2-3; cf. idem, "Problems with the New Tenseless Theory of Time," Philosophical Studies 52 (1987): 371-392. I prefer my appellation because the theories in question are really theories of language, not time. Reichenbach, for example, held to an A-Theory of time, but a B-Theory of Language.

15

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CHAPTER 1

does not prove that there are tensed facts in addition to tenseless facts. This point of view characterizes many B-theorists of the contemporary generation such as D. H. Mellor and has certain affinities with recent theories of Direct Reference and so may conveniently be labeled "The New B-Theory of Language." In his most recent work, Mellor has crucially adjusted his view, abandoning truth conditions in favor of so-called truth makers of tensed sentences, and advocates what we might call "The Indexed B-Theory of Language." The purpose of the next three chapters will be to explore the extent to which tense in language and thought makes an A-Theory of time more plausible than a BTheory. But it is imp.ortant at the outset to be clear about the probative force of these arguments. Some thinkers mistakenly believe that the successful reduction or elimination of tense from language or the furnishing of tenseless truth conditions for A-sentences is a positive proof that tense is not ontologically real. For example, R. C. Coburn furnishes the following "coercive" argument against the A-Theory: 5.

Ifthe doctrine of passage is true, then there are A-facts.

6.

If there are A-facts, then they determine the truth values of tokens of A-sentences.

7.

It is false that A-facts determine the truth-values of tokens of Asentences.

8.

Therefore, the doctrine of passage is false. 3?

The problem with this line of argument is that the B-theoretical claim to provide successfully tenseless truth conditions or truth makers for A-sentences provides no warrant for accepting (7), since it could well be the case that tensed truth conditions and truth makers can be provided for A-sentences as wel1. 38 Thus, success in demonstrating the central claim of either the Old or New or Indexed B-Theory of 37 Robert C. Coburn, The Strangeness of the Ordinary: Problems and Issues in Contemporary Metaphysics (Savage, Md.: Rowman & Littlefield, 1990), p. 113. Coburn also provides the following

argument for a B-Theory: I. Either the truth-conditions of tokens of A-sentences are timeless or they are not. ii. If they are timeless, then the ostensible existence of A-facts is an illusion. iii. If they are not timeless, then, provided event e occurred five years ago, any token of the sentence "e happened five years ago" will be true regardless of the date of its occurrence. iv. It is false that any token of such a sentence is true regardless of the date of its occurrence. v. Therefore, the doctrine of passage is false. But Coburn presupposes unjustifiably that A-sentences cannot have both tenseless and tensed truthconditions; otherwise (ii) does not follow. Such a presupposition requires justification. In (iii) and (iv) he tries to justifY the denial that tensed truth conditions can be given; but these steps just are the nerve of McTaggart's Paradox as Mellor exposits it (D. H. Mellor, "Tense's Tenseless Truth Conditions," AnalYSis 46 [1986]: 171) and Coburn acknowledges his indebtedness to Mellor on this score (Coburn, Strangeness of the Ordinary, p. 114). Thus, the argument for the B-Theory relies on the positive demonstration that the A-Theory is fatally defective. 38 As emphasized by Graham Priest, "Tense and Truth Conditions," Analysis 46 (1986): 162-166; also Smith, Language and Time, chap. 4.

INTRODUCTION: LANGUAGE, TENSE, AND ONTOLOGY

21

Language respectively does not furnish positive evidence for the B-Theory; it only undercuts putative evidence for the A-Theory.39 Careful New B-theorists like Mellor recognize this fact and therefore realize that their case against tensed facts stands or falls with their demonstration of some positive defect in the A-Theory. That is why his defense of McTaggart's Paradox is Mellor's self-confessed linchpin in his case against tensed facts. Mellor is careful to claim no more on behalf of his tenseless account in Real Time than that it provides one explanation of the truth conditions for the truth of tensed sentence tokens, commenting, "That these simple types of tensed sentences have these token-reflexive truth conditions is really quite obvious, and is not seriously questioned. The serious question is whether this is all there is to the facts oftense.,,4o He acknowledges that the mere existence ofa totally tenseless account of tense differences is not itself enough to justify our accepting a tenseless account of tensed facts. "The account's mere existence does not prove its truth; and the existence of tenses is not disproved by showing how to save the phenomena of tense without them."41 In order to show that providing tenseless truth conditions "is all there is to the facts of tense," Mellor must prove that tensed facts are impossible: "Tense is so striking an aspect of reality that only the most compelling argument justifies denying it: namely, that the tensed view of time is self-contradictory and so cannot be true.,,42 We shall discuss Mellor's defense of Thus, one can have an A-theorist like Michael Tooley, who agrees that if tensed concepts are semantically basic, then an A-Theory of time is correct, but who also insists that if tenseless concepts are semantically basic, it does not follow that a B-Theory of time is correct (Michael Tooley, Time, Tense, and Causation [Oxford: Clarendon Press, 1997], pp. 18-19). Tooley goes so far as to reject premiss (5) of Coburn's argument. He holds that there are no tensed facts but that the body oftenseless facts which exist as of any given time varies from time to time. For discussion see the symposium on Tooley's book featuring comments by Storrs McCall, Nathan Oaklander, and Quentin Smith with Tooley's responses in Essays on Time and Related Topics, ed. L. Nathan Oaklander, Selected Papers of the Philosophy of Time Society Proceedings, 1995-1999, pp. 2-42. Tooley's rejection of (5) presupposes that his notion of "actual as of time t" is not a tensed concept. The difficulty, as Smith points out, is that Tooley takes this notion to be an undefined primitive, so that it is far from clear what is meant. Smith charges that as Tooley employs this notion, it appears to be synonymous to "exists earlier than or simultaneous with t," in which case Tooley's theory is not a dynamic theory of time at all. Tooley repudiates this charge, claiming that Smith himself must assume that these are not synonymous expressions. But, of course, Smith, unlike Tooley, accepts the reality of tensed facts, so that he is able to provide a tensed parsing of "actual as of time t." Tooley maintains that this crucial notion is not a tensed concept, since it would then not be neutral with respect to various A-theoretical ontologies, implying as it does an ontology according to which past and present entities alone are real and thereby excluding presentist and "full-future" ontologies. But this allegation seems incorrect. For example, A-theorists could leave "actual" as an undefined primitive and analyze "actual as of time t" as "actual by t's being present." A-theorists will just disagree among themselves as to which events are actual once t is present. If such disagreement is not permitted by Tooley's notion, then it is obviously not essential, as Tooley avers, to a dynamic theory of time. It is extraordinarily difficult to see how anyone with Tooley's ontology of a gradually accreting past can avoid tensed facts. For at any point in time there will be truths about which proper subset of the set of all tenseless facts is instantiated, and which subset that is is constantly changing. If Tooley tries to avoid this conclusion by saying that such subsets are only instantiated as of a time t, not Simpliciter, then we are back to the necessity ofa tensed parsing ofthat notion. Thus, it seems to me, Coburn's (5) is true. Still, the point remains that the provision of tenseless truth conditions for tensed sentences does not disprove the existence of tensed facts. 40 Mellor, Real Time, p. 42. 41 Ibid., p. 33. 42 Ibid., p. 5. In his Real Time II, Mellor does seem to subordinate McTaggart's Paradox to his argument against tensed facts as truth makers of tensed sentences, but even so his argument, if successful, 39

22

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McTaggart's Paradox in chapter 6; but for now we may simply note that in the absence of such a disproof of the A-Theory, the B-Theory of Language can at best claim to show that it is gratuitous or superfluous to posit ontological tenses on considerations of language and thought. Thus, the matter of this section concerns a positive argument for the A-Theory and B-theoretical defenses against it, not a positive argument for a B-Theory. The A-theorist's fundamental argument may be summarized as follows: 9.

Tensed sentences ostensibly ascribe ontological tenses.

10. Unless tensed sentences are shown to be reducible without loss of meaning to tenseless sentences or ontological tense is shown to be superfluous to human thought and action, the ostensible ascription of ontological tenses by tensed sentences ought to be accepted as veridical. 11. Tensed sentences have not been shown to be reducible without loss of meaning to tense less sentences. 12. Ontological tense has not been shown to be superfluous to human thought and action. 13. Therefore, the ostensible ascnptlOn of ontological tenses by tensed sentences ought to be accepted as veridical. Little needs to be said in defense of (9), for tensed sentences obviously purport to tell us something about the real world, not just language. When it is said that "The Second World War is past," this sentence purports to tell us an A-fact about reality, a fact about reality which was not the case 100 years ago. Premiss (10) expresses the conviction that unless there are some good reasons to call into question this ascription of ontological tense, then one ought to regard it as correct. Again this seems quite reasonable. A view of truth as correspondence requires that a true sentence or proposition correspond to the way the world is, and if some tensed sentences are true, then reality must be tensed, since such sentences purport to ascribe ontological tenses. If, on the other hand, proponents of the Old B-Theory of Language can succeed in showing that tensed sentences can be translated into tenseless sentences or proponents of the New B-Theory of Language can succeed in showing that tensed facts are not required for human thought and action, then one would not be obliged to concur in tensed sentences' ostensible ascription of ontological tense. Hence, the key premisses in the argument are (11) and (12), to which the next two chapters shall be devoted respectively.

at best demonstrates the superfluity of tensed facts (idem, Real Time 11 [London: Routledge, 1998], p. 75). We take up Mellor's revised view in chapter 3.

CHAPTER 2 THE OLD B-THEORY OF LANGUAGE

F

or the first three-quarters of the twentieth century, the standard answer of Btheorists to the challenge posed by tensed discourse was that linguistic tense is a superfluous and even annoying feature of ordinary language which philosophically and scientifically trained minds are only too glad to dispense with. Russell, who may be ranked among the progenitors of the Old B-Theory of Language, opined, "Both in thought and feeling, even though time be real, to realize the unimportance of time is the gate of wisdom.") By "time" Russell evidently meant A-series time, which he regarded as obscurant: " ... there is some sense--easier to feel than to state-in which time is an unimportant and superficial characteristic of reality. Past and future must be acknowledged to be as real as the present, and a certain emancipation from slavery to time is essential to philosophic thought.,,2 Russell did not deny that human language provides a clue into the nature of the world; on the contrary, he affirmed that "Although a grammatical distinction cannot be uncritically assumed to correspond to a genuine philosophical difference, yet the one is prima facie evidence of the other, and may often be most usefully employed as a source of discovery.,,3 Yet in the case of tense, Russell held ordinary language to be an impediment to philosophical and scientific understanding of the world and therefore in need of expurgation of its tensed elements. Other Old B-theorists shared this same disdain for ordinary tensed language. According to Goodman, " ... ordinary language deals with time by means of special devices that are used and understood with the greatest facility in everyday discourse but misused and misinterpreted with nearly as much facility in most philosophical discourse.,,4 Similarly Reichenbach, classing tense among the "Deficiencies of Traditional Grammar," declared, "Our present grammar as it is taught ... is based on obvious misunderstandings of the structure of language. We should like to hope that the results of symbolic logic will someday, in the form of a modernized grammar, find their way into elementary schools."s These thinkers, united in their conviction that language must be de-tensed, provided two fundamental ways of translating tensed sentences into tenseless, canonical statements: (i) replacing tensed expressions by appropriate dates and/or clock-times or (ii) analyzing tensed expressions in terms of token-reflexivity. Each of these two basic versions of the Old B-Theory of Language merits critical examination.

Bertrand Russell, "Mysticism and Logic," [1914] in Mysticism and Logic (London: George Allen & Unwin, 1963), p. 23. 2 Ibid., pp. 22-23. Cf. Bertrand Russell, The Principles of Mathematics (1903; London: George Allen & Unwin, 1985), p. 471. J Russell, Principles of Mathematics, p. 42. Nelson Goodman, The Structure of Appearance, 2d ed. (New York: Bobbs-Merrill, 1966), p. 355. Hans Reichenbach, Elements of Symbolic Logic (London: Collier-Macmillan, 1947), p. 255. His aspiration was to formulate a logistic grammar which could be used to develop a science oflanguage.

23

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CHAPTER

2

OLD B-THEORY OF DATE-SENTENCES

Bertrand Russell According to the date-sentence version of the Old B-Theory, tensed sentences can be translated without loss of meaning into sentences having tenseless verbs and outfitted with appropriate dates, all A-expressions having been eliminated. Thus, Russell in his review of MacColl's Symbolic Logic criticizes MacColl's classification of some statements as "variable," for example, the statement "Mrs. Brown is not at home," which, says MacColl, is sometimes true and sometimes false. 6 According to Russell, there is a distinction between words whose meanings vary with the context or the time they are employed-what Russell would later characterize as "egocentric particulars,,7-and the statements expressed by the words. "What is expressed by the form of words at any given instant is not itself variable; but at another instant, something else, equally invariable, is expressed by the same form of words."g The same sentence repeated in different contexts can thus express different statements. These statements will be free from "the defects of common speech" in that variable words will be replaced with invariable time indications. Accordingly, When we are told 'Mrs. Brown is not at home,' we know the time at which this is said, and therefore we know what is meant. But in order to express explicitly the whole of what is meant, it is necessary to add the date, and then the statement is no longer 'variable,' but always true or always false. It results that a variable statement is merely one whose meaning is ambiguous. Now logic ought not to be concerned with forms of words, but with what such forms mean; hence it is essential that logic should employ only forms of words which are unambiguous, and when this is done 'variable' statements disappear9

For the tensed sentence in question, then, Russell would substitute the tenseless "Mrs. Brown is not at home on May 8, 1906," for example. Noteworthy are Russell's phrases "what is meant" and "what such forms mean." His claim is that the tenseless sentence specifies the meaning of the tensed version, the only difference between them being that the tense less sentence makes explicit the date which we, the hearers of the tensed sentence, knew to be implied by it. Elsewhere he affirms that "'Present' and 'past' are primarily psychological terms, in the sense of involving different causal relations between the speaker and that of which he speaks; their other uses are all definable in terms of their primary use."lO We use the 8. Russell, critical notice of Symbolic Logic and Its Applications by Hugh MacColl, Mind 15 (1906):

256.

Bertrand Russell, An Inquiry into Meaning and Truth (London: George Allen & Unwin, (940), p. 108; idem, Human Knowledge: Its Scope and Limits (New York: Simon & Schuster, 1948), p. 84. 8 Russell, critical notice of SymboliC Logic, p. 256. Ibid., pp. 256-257. 10 Russell, Inquiry, p. 113. Cf. Bertrand Russell, "On the Experience of Time," Monist 25 (1915): 212233, where he bases knowledge of the present on the immediacy of sensation. Since there is no intrinsic difference between present and past objects, in order to distinguish between objects given as present and those given as past, the relation of the knowing subject to the object must be different in each case. Sensation is a special relation of subject and object which defines the present time in terms of it. "Sense 7

THE OLD B-THEORY OF LANGUAGE

25

present tense when causal influences upon us are direct and the past tense when indirect. Accordingly, "The two sentences, 'The Declaration of Independence was in 1776,' uttered by us, and 'The Declaration of Independence is in 1776,' which might have been uttered by Jefferson, have exactly the same meaning, but the former implies that the causation is indirect, and the latter that it is direct, or as direct as possible."ll According to Russell, "There is no question that the nonmental world can be fully described without the use of egocentric words," and his analysis of tense usage in terms of directness of causal influences "solves the problem of egocentric particulars, and shows that they are not needed in any part of the description of the world, whether physical or psychological."l2 Over his long career, Russell varied his views as to the nature of what it is that a sentence expresses.13 Early on he held that the propositions expressed by the words of a sentence contain the actual entities indicated by the words. For example, when a man occurs in a proposition, the proposition does not contain the concept a man, but rather some actual biped denoted by the concept. 14 On this view, propositions are abstract entities which have concrete entities as constituents, rather analogous to sets having concrete members. Later he claimed that a proposition is the content of a belief when it is expressed in words. "A proposition is a series of words (or sometimes a single word) expressing the kind of thing that can be asserted or denied."l5 He qualifies this by saying that there are image-propositions as well as word-propositions. On this view, then, propositions are linguistic or mental entities. Still later Russell defined propositions "as psychological occurrences of certain sorts"; "when two sentences have the same meaning, that is because they express the same proposition .... sentences signifY something other than themselves, which can be the same when the sentences differ. That this something must be psychological (or physiological) is made evident by the fact that propositions can be false.,,16 But Russell never varied in his commitment to the tenselessness of what sentences express or to the view that the meaning of tensed sentences is tenseless in its clearest expression. Russell's views on the connections between propositional content and meaning and the belief states and behavior of the sentient subject are very difficult to sort out data belonging to one (momentary) total experience are said to be present in that experience" (Ibid, p. 219). Knowledge of the past arises through immediate memory, which is a primitive relation between subject and object involving acquaintance with the object, though it is no longer given in sensation, in such a way that it is now felt as just past. Since we have no experience of the future, it is known only by inference descriptively as "what succeeds the present." II Russell, Inquiry, p. 113. 12 Ibid., pp. 109, 115. Russell later abandoned the claim that all indexical expressions are eliminable, but he continued to hold to the objective unreality of tense. See Janet Farrell Smith, "Russell on Indexicals and Scientific Knowledge," in Rereading Russell, ed. C. Wade Savage and C. Anthony Anderson, Minnesota Studies in the Philosophy of Science 12 (Minneapolis: University of Minnesota Press, 1989), pp. 119-137. 13 See Alan R. White, "Propositions and Sentences," in Bertrand Russell Memorial Volume, ed. George W. Roberts, Muirhead Library of Philosophy (London: George Allen & Unwin, 1979), pp. 22-23. 14 Russell, Principles of Mathematics, p. 47. 15 Bertrand Russell, The Analysis of Mind (London: George Allen & Unwin, 1921), p. 241. 16 Russell, Inquiry, p. 189.

26

CHAPTER

2

consistently. A belief has as its object a proposition which is identical with the significance of some sentence. 17 A belief need not be verbalized, but it is always possible (given a suitable vocabulary) to find a sentence signifying the fact that one has such-and-such a belief. "If this sentence begins 'I believe that' what follows the word 'that' is a sentence signifying a proposition, and the proposition is said to be what I am believing.,,18 Russell even affirms that animals have propositional beliefs; for example, a dog, when excited by the smell of a cat, believes the proposition that there is a cat. 19 Belief is on Russell's view just the psychophysiological state of the sentient organism?O Russell goes so far as to say that beliefs are the primary truth-bearers: "Truth is a property of beliefs, and derivatively of sentences which express beliefs. Truth consists in a certain relation between a belief and one or more facts other than the belief. When this relation is absent, the belief is false.,,21 Since there are no tensed facts for beliefs to be related to, the foregoing implies that there are no tensed beliefs; otherwise, all our tensed beliefs would be false, which is absurd. Thus, like propositions, beliefs must be tenseless. This would seem to imply that the psycho-physiological state of all sentient organisms is tenseless. Indeed, sometimes Russell seems to identify belief states and beliefs: he speaks of "the states of two persons" as "instances of the same belief," and treats sameness of belief states as a "definition of what constitutes the same belief."22 At the same time, however, Russell seems to affirm that a person's belief states are tensed, though the beliefs themselves and their propositional objects are tense less. This requires a distinction between belief states and beliefs: "My state is now made up of ideas (or images) or words, together with belief and a context which dates the occurrence .... ,,23 He distinguishes in this connection public time, in which physical and mental events take place, and private times, which are given in expectation and memory; the former is objective, the latter merely subjective: 'Now' has a similar twofold meaning, one subjective and one objective. When I review my life in memory, some of the things I remember seem a long time ago, others more recent, but all are in the past as compared with present percepts. This 'pastness,' however, is subjective: what I am remembering, I remember now, and my recollecting is a present fact. Ifmy memory is veridical, there was a fact to which my recollection has 17 For a critical discussion, see Alan R. White, "Belief as a Propositional AttitUde," in Russell Memorial Volume, pp. 242-252. 18 Russell, Inquiry, p. 180. 19 Ibid., p. 188; idem Human Knowledge, p. 95; in idem, Analysis of Mind, p. 243, he ascribes belief to a pigeon. 20 He states, "A belief as I understand the term, is a certain kind of state of body or mind or both. To avoid verbiage, I shall call it a state of an organism, and ignore the distinction of bodily and mental factors" (Russell, Human Knowledge, p. 145). 21 Ibid., p. 148. "Everything that there is in the world I call a 'fact' .... Facts are what make statements true or false.. I mean by a 'fact' something which is there, whether anybody thinks so or not" (Ibid., p. 143). 'The difference between a true and a false belief is like that between a wife and a spinster: in the case ofa true belief there is a fact to which it has a certain relation, but in the case ofa false belief there is no such fact" (Ibid., p. 149). See also idem, Analysis of Mind, pp. 231-232: beliefs "are the vehicles of truth and falsehood"; what makes a belief true or false is called a "fact." 22 Russell, InqUiry, p. 209. 23 Russell, Human Knowledge, p. 97. When I believe someone, " ... 1 believe what his words assert ... ," which would presumably be a tenseless proposition (Ibid., p. 100).

THE OLD B-THEORY OF LANGUAGE

27

a certain relation, partly causal, partly of similarity; this fact was objectively in the past. I maintain that in addition to the objective relation of before-and-after, by which events are ordered in a public time-series, there is a subjective relation of more-or-Iess remote, which holds between memories that all exist at the same objective time. The private time-series generated by this relation differs not only from person to person but from moment to moment in the life of anyone person. There is also a future in the private time-series, which is that of expectation. Both private and public time have, at each moment in the life of a percipient, one peculiar point, which is, at that moment, called 'now.,24

What I call "now" differs necessarily from what I call "now" on another occasion, underlining "the essential privacy of each individual's experience.,,25 As an egocentric particular, "now" would not represent anything in a purely material universe, for it depends upon the perspective of some perceiver. In particular, tense is fundamentally a private affair pertaining to one's psycho-physical state: "The tense of the verb--'will be,' 'is,' 'was'-expresses the difference of bodily state in the believer, according as he expects, perceives, or recollects. Tense applies primarily only to matters within my perceptive experience, and expresses the species of belief involved, not a character of what the belief indicates.,,26 Russell provides an engaging illustration of a tense less belief embodied in different belief states: Suppose I am a Dictator, and at 5 p.m. on October 22nd someone attempts to stab me with a dagger. As a result of reports by the secret police, I believe that this is going to happen; this is (or at least may be) a logically inferential belief; it may also be a belief produced by habit-inference. At 4:59 I see a known enemy taking a dagger from its sheath; at this moment I expect the assault. The inference to the immediate future now is not logical but habitual. A moment later, the assassin rushes forward, the blade pierces my coat, but is stopped by the shirt of chain armor that I wear next to the skin. At this instant, my belief is a matter of perception. Subsequently, the villain having Ibid., pp. 91-92. Cf. Bertrand Russell, The Problems of Philosophy (London: Oxford University Press, 1912), pp. 32, 102, where the B-determinations of events are said to be known by acquaintance, in contrast to the private time of temporal passage. Actually Russell here conflates the metric of time with the passage of time. See also idem, "Experience of Time," pp. 212-233, for the bifurcation of "mental time," which arises through relations of subject and object and gives rise to notions of past, present, and future, and "physical time," which arises through relations of object and object and involves the notions of simultaneity and succession. 25 Russell, Human Knowledge, p. 90. 26 Russell, InqUiry, p. 115. Commenting on the three kinds of belief-memory, expectation, and bare assent-, Russell wrote, "Each of these I regard as constituted by a certain feeling or complex of sensations, attached to the content believed. We may illustrate by an example. Suppose I am believing, by means of images, not words, that it will rain. We have here two interrelated elements, namely the content and the expectation. The content consists of images of (say) the visual appearance of rain.... Exactly the same content may enter into the memory 'it was raining' or the assent 'rain occurs.' The difference of these cases from each other and from expectation does not lie in the content. The difference lies in the nature of the belief-feeling" (Idem, AnalYSis of Mind, p. 250). He went on to confess that he could not analyze the sensations constituting respectively memory, expectation, and assent. It is interesting that in cases of beliefs about the past not involving memory, e.g. "Caesar conquered Gaul," Russell holds such a belief to be of the species of assent, viz., assent to a past-tensed proposition. Since he rejected tensed propositions, it is not clear how pastness gets attached to the tenseless contentwhy not assent to a B-sentence or proposition? H

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been beheaded, I have the experience of 'emotion recollected in tranquility', and my belief has become one of memory. It is obvious that my bodily and mental state is different on these four occasions, though what I am believing is the same throughout, in the sense that it can be indicated in the same words, viz. 'I believe that at 5 p.m. on October 22nd an attempt is made to stab me with a dagger'. (The 'is' here is timeless, not the present tense; it is like the 'is' in '4 is twice 2' f7

The example seems to contradict Russell's position that beliefs just are the psychophysical states of the sentient organism, which must correspond to objective facts in order to be true. Russell linked beliefs and belief states with behavior, but, again, it is difficult to sort out a consistent view. On the one hand, he seems to affirm that persons sharing belief in the same proposition will display the same behavior: "If you say to an Englishman 'there's a cat,' to a Frenchman 'voila un chat,' to a German 'da ist eine Katze,' and to an Italian 'ecco un gatto,' their implicit behaviors will be the same; this is what I mean by saying that they are all believing the same proposition, though they are believing quite different sentences.,,28 On this analysis, persons share the same belief if and only if they manifest the same behavior, though different sentences may be used to express that belief. This view seems to imply that someone who believes "Mrs. Brown is not at home today" will display the same behavior as he who believes "Mrs. Brown is not at home on May 8, 1906," since these express the same proposition. But then Russell goes on to say that, when verbal habits are sufficiently welldeveloped, two states are instances of the same belief if they can be expressed by the same sentence, or, in other words, when they cause the same behavior. 29 Here only a sufficient condition is stated, and it is a sentence which is made to express the belief. According to this analysis, if two belief states cause the same behavior or can be expressed by the same sentence, then the two belief states are instances of the same belief, and therefore express the same proposition. This view has the implication that two persons who on different days express their belief states by saying, "Mrs. Brown is not at home today" express the same proposition, which contradicts Russell's analysis of ego-centric particulars. Similarly, if two such persons behave similarly in not going to visit Mrs. Brown on the day each is in such a belief state, then they share the same belief-which again contradicts Russell's ego-centric analysis. Russell also states, " ... the states of two persons who speak the same language are instances of the same belief if there is a sentence S such that each, in reply to the question: 'do you believe S'?' replies 'I do,.,,30 But suppose we ask each of the persons above, "Do you believe that Mrs. Brown is not at home today?" Each will reply, "I do," which implies that they have the same belief-in contradiction to the ego-centric analysis. Russell also says, "Two sentences Sand S' Russell, Inquiry, p. 208. Ibid., p. 188. Cf. his remark, "Somebody says, 'Look out, there's a car coming,' and you act as you would if you saw the car. In this case you are believing what is signified by the phrase 'a car is coming'" (Idem, Human Knowledge, p. 145). It is difficult to avoid the inference that action springs, on the above analysis, from believing a tenseless proposition. See ibid., p. 101, where action is said to show "what it is that is being believed." 29 Russell, Inquiry, p. 193. 30 Ibid., p. 209. 27 28

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have the same significance if whoever believes the one believes the other.,,31 Russell surely meant to say "only if'---otherwise any two sentences at all might express the same proposition if it turns out that whoever believes one believes the other. But to say that a necessary condition of two sentences' expressing the same proposition is that whoever believes one also believes the other seems at odds with Russell's apparent claim that beliefs are expressed by tensed sentences and embodied in tensed belief states-suppose all those expecting the assassination attempt on the dictator, including the dictator and the assassin, were killed in the attempt: then the future-tense sentence expressing expectation of the event and the past-tense sentence expressing memory of the event do not express the same proposition, since it is not the case that whoever believes one believes the other; and this contradicts Russell's date-sentence analysis of tensed sentences. I do not raise these points as criticisms of Russell's theory, but merely as indications of how difficult it is to understand exactly what his theory was. According to Janet Smith, Russell "faces enormous problems in explaining how connections between private and public objects can be made in the order of knowledge.,,32 There seemed to be a real, unresolved tension in Russell's thought between tensed sentences, the tense less propositions they express, the belief state of someone believing a tense less proposition which he expresses via a tensed sentence, and the behavior or action which ensues as a result. Gottlob Frege The other great fountainhead of the date-sentence version of the Old B-Theory was Gottlob Frege, who addressed issues of tense in his epochal essay "Der Gedanke" (1918). By "a thought" Frege meant what we would call the propositional content or perhaps the information value of a sentence. 33 Although he distinguished the proposition expressed by a sentence from what he called the "sense" of a sentence, he maintained that every proposition is the sense of the sentence which expresses it, and that truth value attaches to the proposition or sense. 34 Sentences like commands or wishes, which do not assert anything and are therefore neither true nor false, have senses but do not express propositions. For Frege, then, the sense of an assertoric sentence comprised what we would call its Ibid. Smith, "Russell on Indexicals," p. 132. 33 "The thought," he writes, "in itself imperceptible by the senses, gets clothed in the perceptible garb of a sentence, and thereby we are able to grasp it. We say a sentence expresses a thought" (Gottlob Frege, "Thoughts," in Logical Investigations, trans. P. T. Geach and R. H. Stoothoff, ed. with a Preface by P. T. Geach, Library of Philosophy and Logic [Oxford: Basil Blackwell, 1977], p. 5). A thought is the content expressed in an assertoric or interrogative sentence and is itself the bearer of truth values in assertoric sentences (Ibid., pp. 4, 6-7). Thoughts are not ideas, but exist independently of consciousness; when a person grasps a thought, he does not create it, but simply comes to stand in a certain relation to something that already existed (Ibid., p. 17). Thoughts exist essentially changelessly, if not strictly timelessly (since they undergo relational changes in being grasped), and they are true or false in this same changeless way (Ibid., p. 28). 3~ Ibid., pp. 4-5. 31

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meaning and was identical with the propositional content of the sentence?5 Moreover, the sense of an expression served as the psychological intermediary by means of which we apprehend its referent and therefore determines the cognitive value ofthe expression. Between one's subjective, private idea of an object and the object itself, writes Frege, "lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself.,,36 He compares these three elements to one's observation of the moon through a telescope: the moon itself is the referent, one's retinal image is the idea, and the optical image of the moon on the lens inside the telescope is the sense, which is neither private nor sUbjective. When the same referent is apprehended via different senses, the cognitive states of the agents differ. Frege uses identity statements as an example: " . .. a = a and a = b are obviously statements of differing cognitive value; a = a holds apriori and ... is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established apriori.,,37 This difference in cognitive value can arise, says Frege, only if corresponding to the difference between the two linguistic expressions there is a difference in what he calls "the mode of presentation" of the referent. The difference in the way in which the referent is presented to the respective agents is determined by the difference in the senses of the expressions. For example, the expressions "the morning star" and "the evening star" both have the same referent, namely, Venus, but the senses of these expressions are different. Therefore, the sentence "The morning star is the evening star" is synthetic and a posteriori, in contrast to "The morning star is the morning

" In Frege's own vocabulary, the Bedeutung of a term or sentence was its referent; but our understanding will be clearer if we use contemporary vocabulary. Salmon explains that Frege conflates three linguistic attributes of a term or expression under the notion of "sense": (i) the purely conceptual representation of an object, (ii) the mechanism whereby the referent of a term is fixed, and (iii) the information value ofa term (Nathan V. Salmon, Reference and Essence [Princeton: Princeton University Press, 1981], pp. 12-13; cf. idem, "Reference and Information Content: Names and Descriptions," in Handbook of Philosophical Logic, ed. D. Gabbay and F. Guenther, vol. IV: Topics in the Philosophy of Language, Synthese Library 167 [Dordrecht: D. Reidel, 1989), p. 444). Since (i) and (iii) are conflated, and (iii) is independent of context, the conceptual representation of objects referred to by indexical expressions in a particular context must also be context-independent. Indexical expressions are thus purely descriptional in nature, and in the case oftemporal indexicals the definite descriptions will be datespecifications, as we shall see. Frege does not differentiate the meaning of such expressions from their descriptional content. Thus, on his theory, sentences which have different meanings (through their terms' having different descriptional content) may have the same referents but do not express the same propositions; and sentences expressing the same proposition must have the same meaning. Linguistic meaning in a particular context is thus indistinguishable from propositional content. Moreover, Frege did not seem to allow for any significant distinction of cognitive states of the knowing agent which is not determined by differences in meaning--except perhaps in the case of knowledge by direct acquaintance such as in the case of the first person indexical. Certainly with respect to time and temporal indexicals, it is meanings that individuate cognitive states. Since propositional content corresponds to meaning in a particular context and meaning in a particular context to the agent's cognitive state, it follows that agents grasping the same proposition are in similar cognitive states and that agents in similar cognitive states grasp the same proposition. ]6 Gottlob Frege, "On Sense and Meaning," in Translationsfrom the Philosophical Writings ofGottlob Frege, ed. Peter Geach and Max Black (Oxford: Basil Blackwell, 1952), p. 60. 37 Ibid., p. 56.

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star.,,38 Since the senses of these two sentences differ, so do the propositions, or thoughts, they express. Frege points out that if we replace a word in a sentence with another word having the same referent, this has no effect upon the truth value of the sentence. "Yet we can see that in such a case the thought changes; since, e.g., the thought in the sentence 'The morning star is a body illuminated by the Sun' differs from that in the sentence 'The evening star is a body illuminated by the Sun.' Anybody who did not know that the evening star is the morning star might hold the one thought to be true, the other false.,,39 Here the difference wrought by the distinct senses is manifest, not in one sentence's being synthetic and a priori in contrast to the other, but in the fact that a rational person might accept one while rejecting the other. The difference in the cognitive significance of these various sentences is due to the differences in their sense and, therefore, in their propositional content. For Frege the sense of proper names or singular terms is given by a definite description. 40 For example, the sense of "Aristotle" might be given as "the pupil of Plato and the teacher of Alexander the Great" or "the teacher of Alexander the Great who was born in Stagira." The relevance of this point for our concerns is that expressions indicating the time of an event are for Frege proper names. "Places, instants, stretches of time, logically considered are objects; hence the linguistic designation of a definite place, a definite instant, or a stretch of time is to be regarded as a proper name.,,41 This implies that expressions like "yesterday," "today," and "tomorrow" have senses. But Frege cautions that the same sense can be conveyed by different linguistic expressions, and although in an ideal language every expression would have a distinct sense, "".natural languages often do not satisfy this condition, and one must be content if the same word has the same sense in the same context.,,42 The context of utterance is thus crucial to an expression's sense, and we shall see that in Frege's view different temporal indexical expressions in appropriate contexts actually have the same sense, which will be a date description of the time of the event. In Frege's theory, then, the propositional content of a sentence, the meaning of that sentence, and the cognitive significance of that sentence are all in line with one another. A difference in cognitive significance between two sentences in the same context will correspond to a difference in meaning between the sentences and to the propositions expressed by the sentences. Turning to questions of tense, Frege emphasizes the disparity that often exists between sentential content and propositional content. He observes that sentential content often goes beyond the propositional content it expresses; for example, the word "but" instead of "and" intimates that what follows in the sentence contrasts 38 Frege remarks, "The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries" (Ibid., p. 56). The same verdict holds with respect to the discovery ofthe identity of the morning star and the evening star. 39 Ibid., p. 62 . •0 Ibid., p. 58 . •1 Ibid., p. 71. .2 Ibid., p. 58.

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with what precedes, but such "conversational suggestions" make no difference to the thought. 43 But analogously, the propositional content often exceeds the sentential content. The examples which he gives concern verbal tense and indexical expressions: The present tense is used in two ways: first, in order to indicate a time; second, in order to eliminate any temporal restriction, where timelessness or eternity is part of the thought-consider for instance the laws of mathematics. Which of the two cases occurs is not expressed but must be divined. If a time-indication is conveyed by the present tense one must know when the sentence was uttered in order to grasp the thought correctly. Therefore the time of utterance is part of the expression of the thought. If someone wants to say today what he expressed yesterday using the word 'today', he will replace this word with 'yesterday'. Although the thought is the same its verbal expression must be different in order that the change of sense which would otherwise be effected by the differing times of utterance may be canceled out. The case is the same with words like 'here' and 'there'. In all such cases the mere wording, as it can be preserved in writing, is not the complete expression of the thought; the knowledge of certain conditions accompanying the utterance, which are used as means of expressing the thought, is needed for us to grasp the thought correctly. Pointing the finger, hand gestures, glances may belong here too. The same utterance containing the word 'I' in the mouths of different men will express different thoughts of which some may be true, others false"

In this passage, Frege makes clear that knowledge of the grammatical content of a sentence is often insufficient for knowledge of the proposition expressed by that sentence in its historical context; knowledge of the context may be essential to knowing what proposition is expressed. The difficulty occasioned by verbal tense is that the present tense in a sentence can be either tenseless or tensed. Not only does the grammatical form of the sentence fail to reveal which is the case for any utterance of the sentence, but even worse, if the sentence is tensed, the grammatical content of the sentence fails to tell us what time is indicated in the proposition expressed by the sentence utterance. Frege implies that in a tensed sentence the propositional content exceeds the sentential content in that the time of utterance, which is known only from the context, is indicated in the proposition. Later in the same essay, Frege makes this assumption explicit: The thought we express by the Pythagorean theorem is surely timeless, eternal, unvarying. But are there not thoughts which are true today but false in six months' time? The thought, for example, that the tree there is covered with green leaves, will surely be false in six months' time. No, for it is not the same thought at all. The words 'This tree is covered with green leaves' are not sufficient by themselves to constitute the expression of a thought, for the time of utterance is involved as well. Without the timespecification thus given we have not a complete thought, i.e. we have no thought at all. Only a sentence with the time-specification filled out, a sentence complete in every respect, expresses a thought. But this thought, if it is true, is true not only today or tomorrow but timeiessly·5

In this passage Frege explains that the present-tense expression !This tree is covered with green leaveS! fails to give the propositional content of any sentence token "This tree is covered with green leaves" because it leaves out the time-specification 43 44 45

Frege, "Thoughts," p. 9. Ibid., pp. 10-11. Ibid., pp. 27-28.

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implicitly involved in the latter. Thus, these words fail to formulate a proposition. A proposition which is expressed by a tensed sentence token will involve a timespecification which will render the proposition as timeless, eternal, and unvarying as the Pythagorean Theorem. Such propositions, then, are analogous to Russell's tense less date-sentences. All propositions are as tenseless as "the laws of mathematics," and all propositions except those whose subject matter already concerns tenseless objects and relations must include time-specifications as implied by the time of the respective utterances of the sentences expressing the propositions. Frege's view also implies that successive utterances of the same sentence express different propositions, depending on how long an interval is indicated by the time specification, since utterances of the same sentence at successive intervals will implicitly express different time specifications. The propositional content of an utterance exceeds the sentential content of that utterance not only in the case of verbal tense, but also in cases of indexicals. In the afore-cited passage, Frege states that the same proposition can be expressed by two sentences if an indexical in one is replaced by an appropriate indexical in the other. As examples he mentions the temporal indexicals "today" and "yesterday," the spatial indexicals "here" and "there," the personal indexical "I," and hints at the demonstratives "this" and "that" in his comment on pointing and glances. Hence, with respect to temporal indexicals, the same proposition is expressed, for example, by "Today Tante Marie is visiting Frege" and "Yesterday Tante Marie was visiting Frege." But, as we have seen, the correct formulation of the proposition expressed by these two sentences in their appropriate contexts involves neither of the temporal indexicals. These are replaced by tense less time specifications; for example, "On May 13,1917, Tante Marie visits Frege." This formulates the propositional content expressed by both sentences in their respective contexts. Moreover, it is also the meaning of the two indexical sentences in their respective contexts. As Frege puts it, "Although the thought is the same its verbal expression must be different in order that the change of sense which would otherwise be effected by the differing times of utterance may be canceled OUt.,,46 The differently tensed sentences thus are synonymous in meaning. What holds for temporal indexicals holds for all other indexicals as well; all must be replaced by context-neutral expressions if the propositional content of sentences containing such expressions is to be made explicit. So with respect to Frege's sentence about the tree covered with green leaves, the propositional content of that sentence uttered in a specific context would be fully expressed by something like "On May 24, 1918, the maple tree in Gottlob Frege's back garden is covered with green leaves." Here the demonstrative "this" has been replaced by a definite description, the tense of the verb eliminated, and a tenseless date added to indicate when the described situation is the case. Finally, for Frege, it is our apprehension-or as he put it metaphorically, our grasping-of propositions that determines our actions, insofar as these are rationally chosen. The power of thinking is the special mental capacity which enables us to

""

Ibid., p. 10.

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grasp proposItIons, which exist independently of our minds. 47 In grasping new propositions and taking them to be true, our consciousness is changed, which in tum affects our actions and our intercourse with other people and the world about us. Frege asks, How does a thought act? By being grasped and taken to be true. This is a process in the inner world of a thinker which may have further consequences in this inner world, and which may also encroach on the sphere of the will and make itself noticeable in the outer world as well. If, for example, I grasp the thought we express by the theorem of Pythagoras, the consequence may be that I recognize it to be true, and further that I apply it in making a decision, which brings about the acceleration of masses. This is how our actions are usually led up to by acts of thinking and judging. And so thought may indirectly influence the motion of masses. The influence of man on man is brought about for the most part by thoughts. People communicate thoughts. How do they do this? They bring about changes in the common external world, and these are meant to be perceived by someone else, and so give him a chance to grasp a thought and take it to be true."

Thus, it is by our grasping the tenseless propositional content of a sentence as uttered in a context that we are spurred to rational thought and action.

wV

0. Quine

A more parsimonious Old B-theorist like W. V. O. Quine would not go so far as Frege in postulating the existence of propositions but would employ the same techniques to construct "eternal sentences" as paraphrases designed to replace the context-dependent tensed sentences. In order to specify the propositional content expressed by a tensed sentence, Quine observes, we must formulate an eternal sentence, that is to say, a sentence whose truth value stays fixed through time and from speaker to speaker49-Quine would also add "and from place to place."so Thus we need to eliminate verbal tenses and supplant words like "now" by a date and clock-reading or similar tenseless time indications. In order, then, to specify the proposition expressed by the utterance of some non-eternal sentence, we bracket some eternal sentence which means the proposition expressed. Thus, says Quine, "We have had to compose an appropriate eternal sentence anyway, and we would as well stop there."SI Since paraphrasing sentences of ordinary language into canonical

47

Ibid., pp. 24-25.

Ibid., pp. 28-29. Willard Van Orman Quine, Word and Object (Cambridge, Mass.: MIT Press, 1960), p. 193; cf. pp. 170,173. 50 See Willard Van Orman Quine, Elementary Logic, rev. ed. (New York: Harper Torchbooks, 1965), pp. 5-6: "The words 'I,' 'he,' 'Jones,' 'here,' remote,' and 'good' have the effect. .. of allowing the truth value of a sentence to vary with the speaker or scene or context. Words which have this effect must be supplanted by unambiguous words or phrases before we can accept a declarative sentence as a statement. It is only under such revision that a sentence may, as a single sentence in its own right, be said to have a truth value." 51 Quine, Word and Object, p. 208. As an example of an eternal sentence or statement, Quine provides "Henry Jones of Lee St., Tulsa, is ill on July 28, 1940," which corresponds to the tensed sentence "Henry Jones of Lee St., Tulsa, is ill" uttered on July 28, 1940 (idem, Elementary Logic, p. 6). 48

49

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notation eliminates ambiguities involved in the original sentences, an eternal sentence cannot be said to be strictly synonymous with its non-eternal counterpart. But the eternal sentence will be one that the original speaker could have uttered in place of his original utterance in the original circumstances without detriment, so far as he could foresee, to the project he was bent on. CRITIQUE OF THE DATE-SENTENCE THEORY Today, the date-sentence version of the Old B-Theory of Language is widely recognized to be a failure, since it is pretty obvious that, contrary to the theory, datesentences just do not mean the same thing as tensed, and particularly indexical, sentences. On the standard Russell-Frege Theory of Reference, there is no distinction between the propositional content and meaning of a tensed sentence in a particular context. Linguistic meanings are identical to propositional content, so that two sentences expressing the same propositional content do not differ in meaning. But it is evident that sentences conceived by the theory to have the same propositional content are often divergent in meaning. In particular, tensed sentences and their purported tenseless translations do not mean the same thing. Hence, one must either give up the view the sentences in question express the same propositional content-in which case they differ also in meaning, contrary to the translation thesis of the Old B-Theory-or else one must abandon the thesis that propositional content individuates linguistic meanings-which is equally fatal to the Old B-Theory's claim that date-sentences are synonymous with tensed sentences, since sentences expressing the same proposition could then differ in meaning. Two broad considerations serve to undermine the translation thesis of the datesentence version ofthe Old B-Theory. I. Tensed sentences are informative in a way that their purported, tenseless date-sentence translations are not, as is manifest from the unique role the former play in motivating thought and action. This was the point that Gale was driving at in his critique of the Old "B-Theory's attempt to analyze an A-statement into a Bstatement through the tenseless ascription of dates, e.g. 'S is ¢ at t/." He wrote, The latter statement describes a B-relation between S's being ¢ and the event seven time-units earlier than it which serves as the origin of the calendar, but does not entail that S's being ¢ or 17 is now present. Tensed or A-questions of the form 'Is Snow ¢?' and 'What is the date (time) now?' can be answered only by contingent A-statements. No amount of information about the B-relations between S's being ¢ and other events will answer this tensed question. 52

To borrow Russell's example, the tensed sentence "Mrs. Brown is not at home" provides potentially critical information in a given context which is manifestly not conveyed by its alleged tenseless translation "Mrs. Brown is not at home on May 8, 1906." In order for the tenseless sentence to convey that information, one must

52 Richard M. Gale, The Language of Time, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1968), p. 55.

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conjoin to it a sentence such as "It is (now) May 8, 1906" or "Today is May 8, 1906," which are obviously tensed statements. Although Schlesinger and Smith have objected that Gale's argument is questionbegging, their objections strike me as cavils about Gale's formulation of an insight which remains fundamentally correct. According to Schlesinger, Gale's complaint that tenseless translations of tensed statements fail to tell us whether the event referred to is past, present, or future is specious because on the B-Theory there simply are no such facts.53 Smith maintains that Gale begs the question by assuming as one of his premisses that a statement is an A-statement only if it ascribes Adeterminations. 54 One may, he says, allow Gale the premiss that A-sentences express A-statements, but only if A-statements are defined merely as the statements expressed by A-sentences. But whether A-statements ascribe A-determinations must be established by argument. Smith concedes that Gale does appeal to some examples of how A-sentences are used in daily life to support his point, but nevertheless, "In his discussion of these examples Gale retains his question-begging assumption that A-sentences express statements that refer to events with Adeterminations. ,,55 It seems to me, however, that Gale's loose style of argumentation is interpreted by these thinkers in a needlessly unsympathetic way. Gale himself formulates his reasoning in the following way: " ... because an A-statement cannot be rendered by a B-statement without loss of factual or informative content A-determinations cannot be reduced to B-relations.,,56 In order to show that B-statements cannot translate Astatements without meaning loss, Gale provides examples of situations in which appropriate action is facilitated by tensed sentences but would be rendered impossible by the substitution of their tenseless translations. He states, " ... it is a good idea to drive home the fact that A-expressions are ineliminable because they do convey some kind of factual information. This can best be done by giving examples of the informative role that A-sentences play in our daily lifes [sic] in which we carry on our commerce and traffic with the world and our fellow man.,,57 Gale gives the example of a soldier who must communicate to his commanding officer the moment at which the enemy advances to within 100 yards so that the officer can decide whether his forces should open fire. The soldier could obviously do this via an A-sentence like "The enemy is now within 100 yards." But it would be impossible for the soldier to communicate to the commander what he needs to know in order to issue the order via a tenseless date-sentence: For example, after spying the enemy within 100 yards and checking his calendar-watch, he could say, 'The enemy advances within 100 yards on December 12, 1966, at 4:01 p.m. E.S.T.' The statement made through the use of this sentence fails to convey George Schlesinger, Aspects of Time (Indianapolis: Hackett, 1980), p. 29. Quentin Smith, Language and Time (New York: Oxford University Press, 1993), p. 9. 55 Ibid., p. 25. 56 Gale, Language of Time, p. 69. Cf. idem, 'Tensed Statements," Philosophical Quarterly 12 (1962): 55-56 where he argues, against the Russellian theory, that since tensed statements have a different use than tenseless ones they must thereby differ in meaning from tenseless statements; if one says statements have meaning independently of use, Gale will argue that tensed statements differ in their pragmatic force from tenseless statements. 57 Gale, Language of Time, p. 56. 53

5'

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information about the A-determination of the event reported, since the company commander, upon hearing Joe's utterance, must check his own calendar-watch so as to find out that the date, and therefore the dated event, is now happening. 58

Smith is correct that Gale sloppily states that the problem with the tenseless sentence is its failure to convey information about the A-determination of the event. But, as we have seen, Gale does not define an A-statement in terms of its ascribing an Adetermination, but rather in terms of the want of repeatability of A-sentences,59 and the claim that the A-statement conveys information about A-determinations which its B-statement translation omits is an inference from its role in human life and intercourse. Such a procedure is in fact one that Smith himself utilizes. Moreover, Smith would agree that Schlesinger's response to Gale is all too facile. Of course, the B-theorist denies that there are extra-linguistic A-determinations and therefore affirms that tense less date-sentences report the same facts as do their corresponding A-sentences; but the thrust of Gale's argument, as the context of his remarks reveals, is that such a theory is wholly implausible because we can think and act on the basis of what we take to be true A-sentences in ways that are completely impossible on the basis of their tenseless counterparts alone. Actually, Gale himself does not fully appreciate the strength of his own illustration; for the soldier-not to speak of his commanding officer-cannot even check his watch to see at what time the enemy reaches the 100 yard point unless he can make the tensed judgements that "The enemy is now within 100 yards" and "My watch now reads 4:01.,,60 What Gale correctly emphasizes is that human thought and intercourse are facilitated by tensed beliefs in a way that would be impossible were those beliefs to be replaced by their tense less counterparts. The tensed sentences which express such beliefs cannot, 58 Ibid., pp. 57-58. Markosian astutely observes that Gale's illustration also involves a spatial "tense" of "within 100 yards," which Markosian uses to press a tu quoque argument against the A-theorist's call for objective tense (Ned Markosian, "On Language and the Passage of Time," Philosophical Studies 66 [1992]: 21-22). For a discussion of this argument, see chap. 4. Markosian misses the point of Gale's illustration by insisting that the tensed sentence and tenseless translation still express the same tenseless proposition. This moot question is irrelevant; what the illustration shows is that the two sentences do not have the same meaning, as is evident from the different behaviors that result from their utterance. Markosian's failing is that he equates a sentence token's meaning with the proposition it expresses; he is oblivious to the revolution wrought by Perry and others (see note 75 below) which has served to differentiate meaning and propositional content. 59 The deeper defect in Gale's argument lies in his definition of an A-statement. By a "statement," Gale apparently means a "proposition" (Gale, Language of Time, p. 40). But his definition of an A-statement does not seem to exclude that Fregean propositions are A-statements, since Frege held that nonsimultaneous sentence tokens of the same sentence type could express propositions differing in truth value. Take, for example, the sentence "It is raining." Let it be tokened in the same place, once while it is raining and later when it is not. On Frege's analysis, these two non-simultaneous uses of this sentence express statements differing in truth value, though they both refer to the same things and places, e.g., "It rains in Freiburg on June 6, 1916" and "It rains in Freiburg on June 7, 1916," and therefore each of these are A-statements! Gale just assumes that B-propositions are not expressed by tensed sentences lacking an explicit date. If we allow Fregean propositions to be classed among A-statements, then it is not true that all A-statements are informative in a way that B-statements are not. In this sense Gale illicitly assumes that all A-statements express A-determinations. 60 See illustration by Tobias Chapman, Time: a Philosophical AnalYSis, Synthese Library (Dordrecht: D. Reidel, 1982), p. 65; also David Lewis, "Attitudes De Dicto and De Se," Philosophical Review 88 (1979): 513-543.

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therefore, be plausibly said to have the same meaning as the corresponding tense less date-sentences. Therefore, the B-theorist has failed in his attempt to render ordinary language tenseless without loss of meaning. It might be thought that a view like Quine's, which does not claim synonymy for the canonical eternal sentences with their tensed counterparts, avoids the problem engendered by the Old B-Theory's translation thesis. But this would be to misunderstand Quine's notion of logical paraphrase. The reason synonymy is not claimed for the paraphrase is because we do not want to retain the ambiguities and infelicities in ordinary language sentences in the sentences of our logical notation. We want, says Quine, the paraphrase to be more informative, clearer, and simpler than the sentences of ordinary language. 61 For example, if an ordinary language speaker says, "Spinach is good" and means thereby "I like spinach" rather than "Spinach is vitaminous," then his sentence is true only for a few speakers. Words like this which allow the truth value of a sentence to vary with the speaker or context "must be supplanted by unambiguous words or phrases before we can accept a declarative sentence as a statement. It is only under such revision that a sentence may, as a single sentence in its own right, be said to have a truth value.,,62 Moreover, "A paraphrase into a canonical notation is good insofar as it tends to meet needs for which the original might be wanted.,,63 Paraphrasing is what we are up to when in a philosophical spirit we offer an 'analysis' or 'explication' of some hitherto inadequately formulated 'idea' or expression. We do not claim synonymy. We do not claim to make clear and explicit what the users of the unclear expression had unconsciously in mind all along. We do not expose hidden meanings ... ; we supply lacks. We fix on the particular functions of the unclear expression that make it worth troubling about, and then devise a substitute, clear and couched in terms to our liking, that fills those functions. Beyond those conditions of partial agreement, dictated by our interests and purposes, any traits of the explicans come under the head of' don't cares' .... 64

It seems pretty clear that the purpose of paraphrase is to eliminate the defects of

ordinary language, to capture what is essential ill it relative to one's purpose. Thus, the substitution of dates and tense less verbs for tensed verbs and indexicals is clearly conceived by Quine to be an improvement over ordinary language. The problem of temporal becoming is helped by this rephrasing of tense, he states, since temporal duration is put on a par with spatial extension. 65 Zeno's paradoxes become less puzzling "when time is looked upon as spacelike.,,66 And relativity theory "leaves no reasonable alternative to treating time as spacelike.,,67 It is evident, then, that the lack of strict synonymy of tense less date-sentences with the tensed sentences of ordinary language did not in Quine's mind imply that the latter reveal some Quine, Word and Object, pp. 159-161, 182. Quine, Elementary Logic, pp. 5-6. 63 Quine, Word and Object, p. 182. " ... there is no call to think of S' as synonymous with S. Its relation to S is just that the particular business that the speaker was on that occasion trying to get on with, with help of S among other things, can be managed well enough to suit him by using S' instead of S' (Ibid., p. 160). 64 Ibid., pp. 258-259. 65 Ibid., p. 170. 66 Ibid., p. 172. 67 Ibid. 61

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important facet of reality omitted by their tense less paraphrases. On the contrary, the date-sentences state clearly the truths which ordinary language sentences ambiguously and misleadingly express. Now, of course, if someone were to say that his project has no necessity of tensed sentences and that he therefore omits tense from his paraphrases as one of his "don't cares" without making a synonymy claim, then the A-theorist will simply say that such a one is entitled to his project, but that such a project is simply irrelevant to the A-theorist's claim that tense is ineliminable and irreducible for purposes of normal human thought and action. The last point deserves underlining. In response to Charles Sayward's charge that none of Quine's eternal sentences Sf will "serve at least as well as S in the context or situation in question and relative to our theoretical aims at that time" if our aim depends on knowledge of some tensed fact,68 William Lycan points out that the projects and aims Quine is concerned with are scientific in nature. 69 Quine is primarily suggesting how to regiment ordinary factual language into a canonical notation for unified science, explains Lycan, an ideal language in which to state our serious philosophical/scientific account of everything. Hence, we preserve in our canonical sentences what is scientifically important in ordinary language sentences but forget about its other functions. "His claim concerning eternal sentences is, by and large, just that non-eternal sentences can and ought to be replaced by eternal ones in the ideal language of science.,,7o Now if, indeed, Quine's projects are so limited as that, then I see no reason why the A-theorist should be at all concerned with the fact that tense has been omitted from the ideal language Quine proposes. He will simply point out that Quine has left out of account an essential aspect of time which is, apparently, irrelevant to Quine's project. Thus, it is not the fact that Quine proposes an ideal, scientific language which is tenseless which is the bone of contention between A-theorists and B-theorists: rather it is Quine's implicit assumption that science tells us the whole story concerning reality, and particularly the nature of time, that is the moot point. That Quine makes such an assumption with respect to time is evident from his above-cited remarks on the philosophical advantages to be gained from spatializing time. Quine's opinion of ontological tenses is only too evident in his brief response to 1. 1. C. Smart in the Quine Festschrift in the Library of Living Philosophers, when Quine comments, "1 was gratified by his scorn for the stubborn notion of the flow of time.,,7! Clearly Quine believes that tense is not only irrelevant to his project, but that the ideal language he proposes for science, which reduces all A-determinations to B-determinations, is adequate for the full description of the temporal features of Charles Sayward, "Propositions and Eternal Sentences," Mind 77 (1968): 537-542. William G. Lycan, "Eternal Sentences Again," Philosophical Studies 26 (1974): 411-418. 7() Ibid., p. 416. 71 W. V. O. Quine, "Reply to 1. 1. C. Smart," in The Philosophy of W. V Quine, Library of Living Philosophers 18, ed. Lewis Edwin Hahn and Paul Arthur Schilpp (LaSalle, Ill.: Open Court, 1986), p. 5 I 8. Smart had complained that tenses commit us to a particularity which is "contrary to the spirit of science" and that when tenses are understood metaphysically they lead to the objectionable notion of the flow of time (J. J. C. Smart, "Quine on Space-Time," in Philosophy of Quine, p. 5 I I). For discussion of Smart's views on the flow of time, see my Tenseless Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, forthcoming).

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the objective world. Quine simply assumes that a tense less language adequate for scientific theories is also adequate for metaphysics. It is this narrow scientism which the A-theorist finds so objectionable. What is remarkable is how deep the roots of this assumption go among Btheorists. Frege's view that the propositional content oftensed sentences is, in fact, tense less was motivated, at least in part, by his concern for having a firm foundation for science: 'Facts, facts, facts,' cries the scientist if he wants to bring home the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not acknowledge something to be the firm foundation of science if it depends on men's varying states of consciousness. The work of science does not consist in creation, but in the discovery of true thoughts. The astronomer can apply a mathematical truth in the investigation of long past events which took place when--on Earth at least-no-one had yet recognized that truth. He can do this because the truth of a thought is timeless.72

For Frege propositions could not be tensed, or this would destroy the firm foundation of science. Similarly, other patriarchs of the Old B-Theory, such as Russell, Reichenbach, Smart, and Griinbaum, tended to share the same scientistic attitude that if a purported temporal fact could not be expressed in the tense less language of science, then it was, for that very reason, not a fact at all. Lycan himself evinces this attitude, for after explaining the limited aims of Quine'S project and its canonical language, he turns around and tries to give an eliminative analysis of the tensed sentence "It is raining," such that the fact communicated by an utterance of this sentence is that it is raining in the vicinity of the man sitting next to Smith at the time at which he wakes up on the bus. 73 In the absence of some further justification for the assumption that science is capable of stating all the temporal facts there are, such B-theorists are at most warranted in claiming that they have no need of tense in the limited project of providing an ideal language for science. In The Tenseless Theory of Time: a Critical Examination, we shall examine the putative reasons for this assumption. But for now, it is worth noting that the Old B-theoretical attempt to eliminate tense from language is not one to which the A-theorist need object if its aims are limited in scope; it is only when one claims that one is giving a full-orbed analysis of tensed language which renders tense superfluous that the B-theorist's claims become both objectionable and evidently false. In more recent philosophical thought there has come a renewed appreciation of the importance of tense 74 and of what John Perry has called "the Essential Indexical.,,75 Indexical reference (along with verbal tense) has come to be seen as 72

Frege, "Thoughts," p. 25. Lycan, "Eternal Sentences," p. 417. It hardly needs to be said that his tenseless fact is not what one communicates to another person by the utterance "It is raining." See also the scientism evinced by Steven E. Boer and William G. Lycan, "Who, Me?" Philosophical Review 89 (1980): 445-446, where it is implied that tensed facts would be "surds in nature ... inaccessible to science" and therefore unreal. 74 See Steven T. Kuhn, "Tense and Time," in Topics in Philosophy of Language, pp. 513-514. 75 John Perry, "The Problem of the Essential Indexical," Noils 13 (1979): 3-29; idem, "Frege on Demonstratives," Philosophical Review 86 (1977): 474-497; idem, "Castai'leda on He and I," in Agent, Language, and Structure of the World, ed. James E. Tomberlin (Indianapolis: Hackett Publishing, 1983), pp. 15-42. For discussion, see Lewis, "Attitudes De Dicto and De Se," pp. 513-543; Palle Yourgrau, "Frege, Perry, and Demonstratives," Canadian Journal of Philosophy 12 (1982): 725-752; Patrick Grim, 73

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essential to explaining certain human thoughts and actions, which, in the absence of such indexical reference, could not take place. Perry provides a number of charming illustrations to prove the point, involving personal, temporal, and spatial indexicals, among them the case of a faculty member who must attend a departmental meeting at noon. The professor has believed all along, says Perry, that "The meeting starts at noon," but such a belief is insufficient to explain why at noon he gets up and leaves his office for the meeting. What explains his change in behavior is that he has come to believe "The meeting starts now." Perry might well have added that the professor could continue to believe the tenseless date-sentence "The faculty meeting on September 15, 1976, starts at noon," so that the change in his behavior is unrelated to any change in his tense less beliefs. What motivates a change in his action is his acquiring a new belief, for example, "It is now noon." It deserves to be underlined that even the simple act of looking at a clock and seeing that it is noon involves having a tensed belief-otherwise, all one has is a tenseless belief like "It is noon when the clock reads' 12:00' ," which will not motivate action at noon, unless one has the tensed belief "The clock now reads '12:00'." Perry asserts, "These indexicals are essential, in that replacement of them by other terms destroys the force of the explanation, or at least requires certain assumptions to be made to preserve it.,,76 Calling such indexical beliefs "self-locating beliefs," Perry contends that having a self-locating belief does not consist in believing a Fregean thought. Self-locating knowledge requires not just the grasping of certain Fregean thoughts but the grasping of them via the sense of certain sentences containing indexicals. 77 It is the sense entertained and not the thought apprehended, Perry concludes, that is tied to human action. It is therefore impossible that A-sentences should be synonymous with tenseless, non-indexical date-sentences. If they were, then there would be no explanation for the difference in behavior which results from grasping a Fregean proposition via an A-sentence rather than via its tenseless date-sentence translation. Reflecting on Perry's work, Patrick Grim concludes, '''Now,' it appears, is an essential indexical: essential to what is known in knowing ... that the meeting is starting now-just as 'I' is essential to what is known in knowing ... that I am making a mess.,,78 On the analogy of knowledge de se furnished by the first-person indexical "I," Grim proposes the nomenclature of knowledge de praesenti to refer to knowledge supplied by present-tense indexicals like "now.,,79 Tenseless datesentences do not supply knowledge de praesenti and so cannot be synonymous with (present-) tensed sentences.

"Against Omniscience: The Case from Essential Indexicals," Noils 19 (1985): 151-180; Howard Wettstein, "Has Semantics Rested on a Mistake?" Journal of Philosophy 83 (1986): 188; William Seager, "The Logic of Lost Lingens," Journal of Philosophical Logic 19 (1990): 407-428. We shall discuss the view of tense of Perry and other Direct Reference theorists when we come to the New 8- Theory of Language. 76 Perry, "Essential Indexical," p. 4. 77 Perry, "Frege on Demonstratives," p. 492. 78 Grim, "Omniscience," p. 156. 79 Actually knowledge de praesenti is a proper part of our knowledge de se.

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The ineptness of the Old B-Theory's translation thesis is underscored by the fact that tensed date-sentences of a relevant sort which are genuinely informative are supposed to be synonymous with tense less date-sentence translations which are either mere tautologies or, at best, insufficiently informative to replace their tensed counterparts as guides to rational human behavior. 80 Consider, for example, such tensed sentences as "Today is May 13" or "It is now 4:30." The tense less datesentence translations of these sentences are "May l3 is May 13" and "It is 4:30 at 4:30" respectively, which are tautologies. It cannot be reasonably maintained that the tensed date-sentences are, in fact, concealed tautologies, for such sentences are indispensable for human thought and action. Even if one wished to maintain that the proposition expressed by "Today is May l3" is "May l3 is May l3," it is still undeniable that the sentence "Today is May 13" does not mean "May l3 is May l3," since a tautologous sentence will not serve, say, to remind me to buy flowers for my wife for our anniversary. One can avoid reducing tensed date-sentences to tautologies by giving them a de re reading: it is true of t that it is May l3. On such an interpretation t could either be a moment of time or else a cluster of events, mental or physical, which serve as ersatz-times on some reductionistic analysis of time. 81 To say that "Today is May l3" is to pick out a moment of time or a cluster of events and to assign to it the date May l3. But while the tense less translation is then no longer tautologous, I think it is obvious that the tense less date-sentence is still utterly uninformative as to whether I should go out and buy flowers. For all it tells me of t is that "t is May l3," which cannot substitute for "Today is May l3" in guiding my action. Hence, I find William Lycan's defense of the informativeness and non-triviality of the eternal sentence "It is 4:30 at 4:30" to be unavailing. 82 According to Lycan, Smith deals with a similar argument under the head of the different confirmation conditions of tensed and tenseless date sentences (Smith, Language and Time, pp. 39-50). But it seems rather artificial to interpret these concerns in terms of confirmation conditions, and it is not clear to me that synonymous sentences must be confirmable or disconfirmable to the same degree by the same sort of observations. 81 Examples of reductionistic date-sentence theorists would be Russell and Griinbaum. Russell rejects Newton's substantival time and takes the "(" of physics to refer to instants which are defined as classes of events such that all the events in the class overlap and no event outside the class overlaps with every member of the class. An event is said to exist at an instant if it is a member of that instant. These instants are ordered into temporal series by the "earlier than" relation (Russell, Human Knowledge, pp. 266-277). It is interesting that Russell rejects substantival time because science does not require it. He seems to confuse "absolute" in the sense of "non-relativistic" with "substantival." Griinbaum treats the temporal indexical "now" as referring to some conceptualized awareness (Adolf Griinbaum, "The Status of Temporal Becoming," in Modern Science and Zeno 's Paradoxes [Middletown, Conn.: Wesleyan University Press, 1967], p. 8). He insists that "It is 3:00 now" is informative and means something like "3:00 is simultaneous with this conceptualized awareness," where this last expression is used referentially. Clearly, such a tenseless sentence does not translate the tensed sentence, and, interestingly, Griinbaum even seems to admit this, commenting that he is not trying to eliminate nowness in favor oftenseless temporal attributes-but then his inference that becoming is non-objective and minddependent seems a non sequitur. For further discussion ofGriinbaum's view, see my Tenseless Theory of Time. 82 Lycan, "Eternal Sentences," pp. 411-413. Cf. Boer and Lycan, "Who, MeT pp. 432-437, where "John believes that he himself is John" is analyzed as belief in an identity statement whose terms are rigid designators of the same person. How, they ask, could John be ignorant of a necessary identity of which he himself is a term? The answer is, by not knowing that he himself is a term of the proposition. Boer and Lycan beg the question by reducing the content of what John knows to a de re fact. Of course, he 80

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the second "4:30" can be understood as a de re expression. One who utters the sentence is predicating something of the moment 4:30, namely, the property of its having been 4:30 at that moment. The expression "It is 4:30 at" is a predicate expressing something like being located 4Y: hours after the moment when the sun reaches its highest point in the sky. Thus, it makes sense to say, for example, "It's lucky it was 4:30 at 4:30; if it had been 5:30 already, I'd have been in big trouble!" While Lycan is correct that the de re expression is not tautologous, it is not informative in the way that "It is now 4:30" is. Knowing of a certain moment that it tenselessly has the predicate of being located 4Y2 hours later than noon is useless to someone who wants to know if it's time to go horne. Indeed, Lycan's statement "It's lucky it was 4:30 at 4:30" is itself a tensed statement, informing the hearer of a token of this statement that the moment called 4:30 is past. But it is hard to imagine someone exclaiming, "It's lucky it is 4:30 at 4:30." What's lucky about that? Even on the most favorable reading for the B-theorist, then, it seems pretty obvious that tense less date-sentences are not synonymous with their tensed counterparts. Moreover, as Smith points out, a further difficulty with the de re interpretation arises. 83 Suppose one utters the sentence, "4:30 is now," and intends the reference to "4:30" to be de re, that is, to say of the moment that is called "4:30" that it is now. On the B-theorist's reckoning, this must be translated as "4:30 is at 4:30," or some other tautological locution in which both utterances of "4:30" refer de re to 4:30. Thus, one is back to the uninformative and trivial sentence which Lycan sought to avoid. Therefore, it seems clear that tensed date-sentences do not mean the same thing as their purported tense less date-sentence translations, for while the former are vital to human action, the latter are mere tautologies or so little informative as to make their replacement of their tensed counterparts an untenable suggestion. This conclusion serves to reinforce the central thrust of Gale's argument that A- and Bsentences are not synonymous, as is evident by the unique role played by the former in human affairs, an insight which subsequent work in the philosophy of language seems to have vindicated. Because Smith believes, as we have seen, that Gale's argument is questionbegging, he omits from his case against the Old B-Theory what historically has been the strongest argument against tenseless sentences as translations of tensed sentences, namely, the insufficiency of tense less sentences to explain timely action. Nevertheless, Smith does provide a sort of reformulation of Gale's argument which, if successful, would provide an independent reason for rejecting the date-sentence theory.84 Gale's complaint that B-sentences do not tell us whether the events they are about are past, present, or future is recast by Smith in terms of the tokenreflexive truth conditions of A-sentences. Smith argues that tenseless date-sentences do not possess the same token-reflexive truth conditions as tensed sentence tokens. knows that that very person is that very person; but he does not know that he himself is that very person. He needs knowledge de se as well. On the authors' distinction between pragmatics and semantics, see note 92. 83 Smith, Language and Time, p. 43. 84 Ibid .. sec. 2. 2.

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The truth value of an A-sentence token depends on the B-relation of the token to the event the token is about. For example, a token of a present-tense A-sentence is true iff the token occurs simultaneously with the event it is about. By contrast the truth value of a tenseless date-sentence (or its tokens) is independent of the time of its tokens. A tenseless date-sentence (or its tokens) is true iff the event it is about has the appropriate B-relation to the specified date. Thus, for example, the sentence token "The meeting starts now" is true iff the start of the meeting is simultaneous with the tokening of the sentence. But the sentence "The faculty meeting on September 15, 1976, starts at noon" is omnitemporally true, if true, regardless of the time of its tokening. Since it is a necessary condition of one sentence's being a translation of another that they have the same truth conditions, it follows that tenseless date-sentences cannot be translations of tensed sentences. 85 Smith's approach is engaging because it starts from what is common ground with many contemporary B-theorists, namely, the tenseless token-reflexive truth conditions of tensed sentences; nevertheless, I have reservations about the argument. It seems to me very dubious that tensed sentence tokens have tense less tokenreflexive truth conditions, and that for two reasons: (1) It is dubious that sentence tokens are truth bearers. When it is said that a sentence token is true or false, what is usually meant is that what the sentence token expresses, that is, the sentence type or the proposition, is true or false. A sentence token is more correctly said to be truly uttered, rather than to be true, and is so if and only if the proposition it expresses is true. But to hold that tokens themselves, that is, strings of sounds or printed shapes, are themselves truth bearers is very strange. It would make havoc of logical inference, for example. When premisses are said to imply a conclusion, a token truth bearer analysis would require that only that particular token is implied by those particular premisses; but those premisses would not imply a similar token printed elsewhere. And since tokens are contingent, how could entailments be possible, since it could be the case that, for the two tokens in question, the one token is true in some other world whereas the token it supposedly entails fails to be tokened in that world and so is not true? One might be tempted to remedy these problems by holding that propositions and sentence tokens are both truth bearers. But such a move only seems to make sense so long as the truth conditions for the token are identical to those of the proposition expressed. To introduce different, independent token-reflexive truth conditions would result in situations in which, for example, two tokens would not entail each other, even though the propositions they express would. But if sentence tokens are not truth bearers, then Smith's argument needs to be recast: a token of a present-tense A-sentence is truly uttered if and only if the token occurs simultaneously with the event it is about, whereas a datesentence token can be truly uttered regardless of the time. Then the argument can proceed. (2) It is dubious that tensed sentences have tenseless truth conditions. Certainly "The meeting starts now" can be truly uttered only if the meeting's start is simultaneous with the time of the token. But the simultaneity of the token with the It might be thought that Quine could evade this argument since he does not think sentence tokens are true or false and so have no truth conditions. But he must admit that tensed sentence tokens can be truly asserted, and Smith's argument can be recast in terms of the conditions under which tensed vs. tenseless sentences may be truly asserted.

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meeting's start does not at all appear to be a sufficient condition for the true assertion of "The meeting starts now." The meeting John Perry was talking about was simultaneous with his token about it back in 1976, but that is not sufficient for his assertion to be true. Indeed, on the presentist ontology of a pure A-Theory of time, that token does not even exist any more, so that it is hard to see how it can have any truth value at all, despite its simultaneity with the meeting's start. In order for the simultaneity of the token with the meeting's start to be a sufficient condition of the true utterance of the token, the "is" in "is simultaneous" must be tensed, that is to say, both must be present. But then one no longer has tenseless truth conditions, and one has begged the question in favor of the A-Theory. Smith would say that a tensed sentence has both tensed and tenseless truth conditions, given in different languages. What this amounts to is the claim that a present-tense token is uttered truly iff it occurs simultaneously with the event it is about. But this seems misleading, since on the A-Theory a tensed token is not literally truly uttered tenselessly; there is no tenseless tokening of the sentence. The A-theorist may adopt the tense less language as a sort ofJar;on de parler; but we need to be clear that such tense less conditions of truly uttering are not to be taken ontologically. Against his argument, Smith considers the objection that A-sentences, like Bsentences, do in fact have non-token-reflexive, date-specific truth conditions. As J. J. C. Smart points out, When a person P utters at a time t the sentence 'Event E is present' his assertion [utterance] is true if and only if E is at t. More trivially, when P says at t 'time t is now' his assertion is true if and only if t is at t so that if P says at t 't is now' his assertion is thereby true"6

So, for example, the sentence token uttered by Perry on September 15, 1976, "The meeting starts now" is true iff the meeting starts on September 15, 1976. These are precisely the same truth conditions as those for the B-sentence, "The meeting starts on September 15, 1976." Thus, it is false that A-sentences and their tenseless datesentence translations have different truth conditions. In response to this objection, Smith essays to prove that A-sentence tokens do not have such tense less, non-token reflexive, date-specific truth conditions. Unfortunately it seems to me that his argument in this regard is fallacious. 87 Mais J. J. C. Smart, "Time and Becoming," in Time and Cause, ed. Peter Van Inwagen (Dordrecht: D. Reidel, 1981), p. 5. 87 Smith's argument is that for some tensed utterance U, it is not the case that a necessary condition of U's truth is that the event described occur on the specified date. According to the non-to ken-reflexive, date-specific analysis, "Henry is ill" when uttered on July 28, 1940, is true only if Henry is ill on July 28, 1940. "In possible worlds terminology," says Smith, "this means that U is not true in any world in which Henry is not ill on July 28, 1940" (Language and Time, p. 35). But Smith shows that in other worlds Henry's illness may have been dated differently. This line of argument seems to involve an obvious faux pas. To say that a necessary condition of U is that Henry be ill on the specified date means only that "Henry is ill" uttered on July 28, 1940, materially implies "Henry is ill on July 28, 1940"; this is not an entailment, as Smith seems to assume, and therefore need not be true in all possible worlds. Smith tries to justify taking the biconditional, not as material equivalence, but as logical equivalence by pointing out that if the two sentences are only materially equivalent, then the date-sentence "no longer gives the meaning of the utterance 'Henry is ill'." "Only a stricter criterion of truth can make truth

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n'importe; his original argument remains untouched by the objection anyway. For his contention is that tense less date-sentences do not possess the same tokenreflexive truth conditions as tensed sentence tokens. Multiple formulations of the truth conditions for a class of sentences may be possible (witness the various proposals for stating the truth conditions of counterfactual conditionals 88). Therefore, the fact that non-token reflexive truth conditions can be given for Asentences does not imply that a token-reflexive formulation of their truth conditions cannot also be given. In fact, token-reflexive truth conditions can be given for tense less date-sentences as well: such a sentence is truly uttered iff a token of it can be truly uttered whether the token occurs before, simultaneously with, or after the event it describes. The point is that these are not the same token-reflexive truth conditions that obtain for tensed sentences. Therefore, if a necessary condition of synonymy of two sentences is sameness of truth conditions, it follows that Asentences do not have the same meaning as their supposed date-sentence translations. 89 Smith underscores his argument by noting that in virtue of their token-reflexive truth conditions, tensed sentence tokens have different entailment relations than their condition sentences meaning-giving, namely, the criterion that the clause mentioned after the biconditional is true in all and only the possible worlds in which the mentioned utterance is true" (Ibid., p. 38). But this response is both inadequate and misleading. Logical equivalence is not a sufficient condition of synonymy, as Smith himself recognizes .. To borrow one of Smith's own examples, "The sun has a shape" '" "The sun has a size". Yet these sentences are clearly not synonymous. Thus, the motivation to tum truth conditions into expressions of synonymy is not an adequate motivation for turning the material equivalence asserted in truth condition analyses into logical equivalence. In any case, Smith's response misleads because it sidetracks the issue. The question is whether non-tokenreflexive, date-specific truth conditions can be given for A-sentences, not whether those truth conditions give the meaning of A-sentences. Recall that the A-theorist is trying to show that A-sentences do not mean the same as B-sentences because they have different truth conditions respectively; the rejoinder of the Old B-theorist is that the argument fails because similar truth conditions can be given. It is not incumbent upon him to argue further that it is because of identical truth conditions that they mean the same thing. One final comment: in his arguments that the date of Henry's illness might be different in other possible words, Smith seems to have overlooked the fact that it is not truth conditions for U Simpliciter that are being offered, but for U-as-uttered-by-P-at-t. If, in some other world, t (the date of the event) is different, then so is U-as-uttered-by-P-at-t. Hence, one is not offering an exception to the truth conditions of the original utterance-in-context after all. This seems to have been the point which was made by Nathan Oaklander, "A Defense of the New Tenseless Theory of Time," Philosophical Quarterly 41 (1991): 37, and Smith's response fails to see that the time of the utterance parallels the time of the event, so that one never has a possible world in which there are different dates on each side of the biconditional operator. In the end, Smith admits that by world-indexing the sentences, one solves the problem of divergent dates; but he falls back on the argument that then synonymy has not been proved by the Btheorist-which succumbs to the same "burden of proof' criticism I raised above. The salutary feature of Smith's argument is that it raises the question, why think that an A-sentence and its purported tenseless translation have the same meaning? What positive proof does the Old Btheorist offer that they are synonymous? 88 See 1. L. Mackie, The Cement of the Universe (Oxford: Clarendon Press, 1974), pp. 53-54, 197-203. 89 To avoid misunderstanding, it should be said that one must employ the same formulation method of truth conditions for both of the sentences. Otherwise, an A-sentence could be shown not to be synonymous with itself by showing its token-reflexive truth conditions are not the same as its non-tokenreflexive truth conditions. The point I am making is that the token reflexive truth conditions of an Asentence are not the same as the token-reflexive truth conditions of a corresponding date-sentence.

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tenseless date-sentence counterparts. 90 For example, the truth of a token "Henry is ill" entails that Henry's illness is simultaneous with that token; but a true token of "Henry is ill on July 28, 1940" does not entail that Henry's illness occurs simultaneously with that token. The difference is due to the divergent tokenreflexive truth conditions for tensed and tenseless sentences: the latter can be true whether they are tokened before, at, or after the time of the event they describe, whereas the former can be true only if they are tokened at appropriate times relative to the event depending on the tense of the sentence. Since sentences having different entailments cannot have the same meaning, it follows that tensed and tenseless sentences do not translate each other. Here I should reiterate my objection that sentence tokens are not truth-bearers and therefore have no entailment relations, so that tensed and tenseless sentences do not differ in this respect. And it seems wrong to say in any case that the token itself has the entailment in question, rather than that the fact of the sentence's being tokened has this entailment. But Smith's argument can be re-cast to meet the objection: necessarily, if a present-tense sentence is truly tokened, that token occurs simultaneously with the event described by the sentence, but this is not the case for a tense less sentence. From the knowledge that a present-tense sentence is truly tokened, we may infer that the event described is simultaneous with the tokening; but from the knowledge that a tenseless sentence is truly tokened, we may make no inference about the time of the event in relation to the tokening. Tensed sentences are thus informative in a way tenseless date-sentences are not and therefore cannot mean the same thing. Goodman responded to this argument as follows: Against such translations, it is sometimes urged that they do not really convey the content of the originals. A spoken 'Randy is running now' tells us that the action takes place at the very moment of speaking, while a 'Randy runs [tenseless] on October 17, 1948, at 10 p.m., E.S.T.' does not tell us that the action takes place simultaneously with either utterance unless we know in addition that the time of the utterance is October 17, 1948, at 10 p.m., E.S.T. Since-the argument runs-we recognize the tenseless sentence as a translation of the tensed one only in the light of outside knowledge, we have no genuine translation at all. But this seems to me no more cogent than would the parallel argument that 'L'angleterre' is not a genuine translation of 'England' because we recognize it as a translation only if we know that L'angleterre is England 91

This answer is somewhat stupefying. "Angleterre" and "England" are just conventionally made to translate each other. Goodman's example would have had more relevance if he had used the celebrated "HesperuslPhosphorus" or "Cicero/Tully" examples where only in light of outside knowledge does one know that only one rather than two individuals is being referred to. But such examples would tend to support the A-theorist, since sentences involving the respective names, even if they express the same proposition, do not seem to have the same meaning. But in the "Angleterre/England" example, it is just a matter of knowing 90

91

Smith, Language and Time, sec. 2. 4. Goodman, Structure of Appearance, p. 370.

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both languages. In any case, with respect to the tensed and tense less sentences, the "outside knowledge" required in order to infer from the tense less sentence that the event is simultaneous with its tokening is quite clearly inadmissible, since no amount of knowledge of linguistic conventions or rules alone would permit the deduction of that fact from the tense less sentence alone. Besides, on the basis of such extraneous knowledge, what we recognize is not that the tense less sentence is a translation of the tensed one, but rather the opposite, that even if the tenseless sentence is tokened at the same time as the event described, such a circumstance is wholly accidental and that the sentence would be true even without such coincidence. This recognition serves to underline Smith's contention that tensed and tenseless sentences do not have the same tenseless (so-called) token-reflexive truth conditions and so are not identical in meaning. 92 Smith also launches into what I think is a misguided attack on those who hold that tensed and tenseless sentences have the same semantic content but differ by following different pragmatic rules (Steven E. Boer and William G. Lycan, "Who, Me?" Philosophical Review 89 [1980): 448-453; see also Milton Fisk, "A Pragmatic Account of Tenses," American Philosophical Quarterly 8 [1971): 94; Michelle Beer, "Temporal Indexicals and the Passage of Time," Philosophical Quarterly 38 [1988): 162). He does so, I think, because he identifies the meaning of a sentence with the propositional or semantic content it expresses; hence, he cannot allow that tensed and tenseless sentences differ in their meaning but express the same proposition. But the New B-theorists he attacks do not equate semantic content with meaning, so that their admission that semantically equivalent sentences follow different pragmatic rules is, in effect, an admission that the sentences do not have the same meaning. At any rate, Smith's argument, which crops up repeatedly in his book and work, seems to me unsound. He argues, first, that tensed sentence tokens are not semantically equivalent to their tenseless translations because counterfactuals like the tensed "John is asleep now, but he might not have been" are possibly true, whereas on the relational view of time their tenseless translations, in this case, "John is asleep at t, but there is some possible world in which t exists and John is not asleep at t" is necessarily false. The counterfactual is necessarily false if we take the relational view of times as sets of simultaneous events, for sets have their members essentially, and therefore if John is not sleeping at t then t does not exist. If, on the other hand, we adopt a substantivalist view of times as event-independent moments, then other possibly true A-sentence tokens are given necessarily false translations. For example, the true, July 23, 1986, A-sentence token "Necessarily, some time is present if time exists" is "Necessarily, some time is July 23, 1986, iftime exists," which is false, since in some possible world time ends before that date. Similarly, the true, April 14, 1989, A-sentence token "If April 14, 1989, were not present, it would be past or future, if actual at all," is translated by "If April 14, 1989, were not April 14, 1989, it would be earlier or later than April 14, 1989, if actual at all," which is necessarily false. Thus, such A-sentence tokens are not even materially equivalent to their supposed tenseless translations. Neither of these arguments is persuasive. The first depends on taking "set" as a technical mathematical notion, rather than as a looser notion of a collection. One that would seem particularly apt is that of a cluster concept, according to which clusters do not possess their members essentially and so may vary in membership without the identity of the cluster being destroyed. The relationalist could postulate time cluster concepts which take times to be constituted by clusters of events. Anyone of these events could be missing from the cluster without the identity of the time being abrogated. (For discussion, see Frederick Suppe, "The Search for Philosophic Understanding of Scientific Theories," in The Structure of Scientific Theories, 2d ed., ed. F. Suppe [Urbana, III.: University of Illinois Press, 1977), pp. 73-74). The second argument commits a fallacy which, ironically, Smith himself points out elsewhere. (For discussion, see Gilbert Plumer, "Expressions of Passage," Philosophical Quarterly 37 [1987): 341-354; Quentin Smith, "The Co-Reporting Theory of Ten sed and Tenseless Sentences," Philosophical Quarterly 40 [1990): 219-221.) When it is said that some time is present, this is not to assert that some time is the present moment, the "now." Otherwise in saying that tomorrow will be present, one would be asserting the absurdity that tomorrow will be the present moment, i.e., today. Rather what is meant is that the time in question has the property of presentness. When tomorrow comes, it, rather than the present moment, will have this property. Hence, the B-sentences translating Smith's A-sentences are not the absurdities he 92

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2. Tenseless date-sentences are iriformative in a way that their tensed counterparts are not, as is evident from ignorance of the relevant dates on the part of a cognizer of the tensed sentences. As we have seen, a person who knows only tenseless date-sentences will be wanting in information crucial to timely action which tensed sentences supply. But by the same token, a person who knows only tensed sentences with only indexical references to times will be ignorant of information supplied by date-sentence translations. Therefore, for any sentence, the tensed and tense less versions of it do not mean the same thing-and this even if, as New B-theorists contend, they express the same proposition. Russell, it will be recalled, asserted, "When we are told 'Mrs. Brown is not at home,' we know the time at which this is said, and therefore we know what is meant.,,93 Similarly, Frege held that "If a time-indication is conveyed by the present tense one must know when the sentence was uttered in order to grasp the thought correctly.,,94 But it seems obvious that one can understand the meaning of a tensed sentence and yet be completely ignorant of the date or clock time of the context of utterance. As Smith puts it, "I can perfectly well understand a token of 'Mrs. Brown is not at home' without knowing whether this token occurs at 2:55 p.m. or 3:20 p.m., on June 15th or June 16th. I could even-in case of amnesia-fail to know what century it is and still understand what is meant. ,,95 That one does correctly understand the tensed sentence is evident from appropriate changes in one's action which one's belief occasions. Or to borrow one of Perry's examples, one could receive a postcard with the name and address smudged out which says, "We're having a wonderful time-wish you were here!,,96 Even though one has no idea of the persons, place, or time referred to via these tensed and indexical expressions, the meaning of the sentence is completely obvious to anyone who has mastery of the linguistic rules governing the usage of such expressions. To fill in the date and so forth would supply additional information which is not known to the person who understands the dateless sentence. Similarly, if one found a note in a bottle from a castaway specifying his location and stating, "I have enough rations to survive only for a few weeks more," we clearly understand the meaning of the sentence, but knowledge of the date of the context of utterance would supply information crucial to the decision as to whether to mount a rescue operation. The distinction in meaning between tensed and tense less sentences is also evident in the fact that one can have a correct understanding of the respective meanings of a tensed sentence and its tense less translation and yet rationally reject alleges, but "Necessarily, some time has the property of presentness, if time exists" and "If April 14, 1989, did not have the property of presentness, then it would have the property of pastness or futurity, if actual at all." Of course, the B-theorist will regard such sentences as either false or vacuously true because there are on his view no such properties; but then it is question-begging for Smith to claim that the A-sentences are possibly true. He is hoist on the same petard as, on his view, Gale was. Fortunately, Smith's line of argument is not essential to his case, for he presents other, cogent arguments against New B-theorists. 93 Russell, critical notice of Symbolic Logic, p. 256. 94 Frege, "Thoughts," p. 10. 95 Smith, Language and Time, p. 56. 96 Perry, "Cognitive Significance and New Theories of Reference," Noils 22 (1988): 9.

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one while believing the other. As Perry points out, one might quite naturally accept that "The meeting starts at noon, September 15, 1976" and yet deny that "The meeting starts now" by losing track of the time. 97 According to Perry, we have no 97 Perry, "Frege on Demonstratives," p. 491. Perry's point holds whether one interprets date-sentences de dicta or de reo If one has lost track of the time, then one may deny not only that it is now noon, but also deny of the moment which is noon that it is now, all the while believing of that moment that it is when the meeting starts. Thus, Smith is correct that Grim, "Omniscience," pp. 157-158, is making a great to-do about nothing (Smith, Language and Time, pp. 60-61); indeed, I should say that Smith also overestimates the consequences of interpreting dates as referential expressions rather than attributive expressions. Grim tries to show that one may believe of some time that "The meeting is starting then" without believing that "The meeting is starting now," for one may be watching a live broadcast in which the time is mentioned, without one's realizing it is live. The problem with the example becomes evident when one recalls that the grammatical function of "now" is to indicate an A-series position, that is, to assign a temporal location and to ascribe presentness to it. But these same functions could also be carried out by referring de re to a time and using a verbal present-tense with respect to it. In Grim's example "The meeting is starting then," the verb is not tenseless, and "then" is misleading, since the function of "then" is to indicate times other than now. If we substitute t for "then," what one believes, in effect, is "The meeting is starting (and it is starting) at t." But in this case the sentence is synonymous with "The meeting is starting now," since the dual function of "now" has been taken over by the tensed verb and the de re date. Yet it is obvious that one can mistake a live broadcast for a taped broadcast, as Grim suggests, and so not realize of some time that it is now. So why does the illustration fail? The answer is that Grim fallaciously assumes that the tense in "The meeting is starting at t" pertains to the time of the events in the broadcast, when in fact what it pertains to is the time of the image of the meeting appearing presently on the television screen. One cannot properly say of the meeting itselfthat it is starting because one does not know that the broadcast is live. One must use a tenseless verb instead and say, "The meeting starts at t." Since the tense of the verb is lacking, this sentence, though it refers de re to the date, is not synonymous with "The meeting is starting now." Hence, a proper understanding of the broadcast illustration shows that a de re reference to a date cannot make a tenseless date-sentence synonymous with a tensed sentence. Smith's development of the point that tensed sentences and their tenseless date sentence translations are not intersubstitutable salva veritate in belief contexts leads him into a needless attack on Castaneda's theory of quasi-indexicals. Smith surmises that someone might contend that the reason intersubstitutability fails is because the expressions involved are quasi-indexicals, rather than because synonymy fails for the sentences in question. But as we have already seen, one may avoid quasiindexicals altogether simply by keeping the context of utterance in the present-tense: "John believes that the meeting starts at noon, September 15, 1976" may be true, but it may be false that "John believes that the meeting is starting now." And in any case, the use of so-called quasi-indexicals just amounts to the need for double indexing, as we have seen, and in no way eliminates tense. Smith attacks Castai'leda's further claim that what is expressed at one time using a temporal indexical can itself be expressed at another time using a quasi-indexical in oratio obliqua. He correctly points out that K's knowing at t\ that M knows at t2 that the Chrysler Building is then 1,086 feet tall does not imply that K knows the same fact that M knows, for K's knowledge is insufficient to tell him whether t2 is present or not. That M does have such knowledge is evident from his timely action in tuning into a broadcast using the new antenna atop the building. Unfortunately, this critique, while sound, is consistent with Castai'leda's claim if one rejects his principle P: If a sentence of the form 'X knows that a person Y knows that. .. ' formulates a true statement, then the person X knows the statement formulated by the clause filling the blank' ... ' (Castai'leda, "Omniscience," p. 307). Pointing out that in the case of personal indexicals someone who knows the complex proposition might fail to know the proposition expressed quasi-indexically because he does not know the identity of the person to whom the oratio obliqua is ascribed, Robert Adams rejected P (Adams and Castai'leda, "Correspondence," pp. 293-295; see also Grim, "Against Omniscience," pp. 166-167 for some good illustrations). A similar argument against P can be constructed using temporal indexicals. Suppose I know that Jones knew that he would arrive today. From P it follows that I know the same fact that Jones would express in oratio recta. But this is clearly wrong. Due to the phenomenon of double indexing, I have no idea of the device Jones used to refer to today. Jones might have known he would arrive at a

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choice but to make a break between what Frege called the sense of a sentence and the thought expressed by the sentence, that is to say, between the meaning and the propositional content of a sentence, which Frege, at least with respect to sentences involving tense and temporal indexicals, failed to distinguish. Even if a tensed sentence and a tenseless date-sentence express the same proposition, the two sentences do not mean the same thing. But that implies that the date-sentence version ofthe Old B-Theory of Language is untenable. As a result of considerations such as the foregoing, it is today acknowledged on almost all sides that the date-sentence translation thesis, and with it the datesentence version of the Old B-Theory of Language, was a failure. Indeed, it is remarkable that it persisted among intelligent thinkers as long as it did. According to New B-theorist D. H. Mellor, it is futile to try to give tenseless, non-tokenreflexive translations of tensed statements. "That is easily shown to be impossible. Nor could we dispense with the states of tensed belief which they express, because to get what we want we have to act at more or less specific times. To catch the six o'clock news, for example, I must turn on the radio then, which in practice means that I turn it on when I believe that it is six o'clock now.,,98 Because temporally token-reflexive thought and speech are both untranslatable and indispensable, Mellor agrees that there are inescapable objective truths about what is past, present, and future-even though, as we shall see, Mellor, as a New B-theorist, denies that anything really is past, present, or future in itself. OLD B-THEORY OF TOKEN-REFLEXIVE SENTENCES According to the token-reflexive version of the Old B-Theory, tensed sentences can be translated without loss of meaning into sentences having tense less verbs and certain calendar date of which I am unaware. Hence, P fails. By rejecting P, one could retain the claim that the same proposition is expressed in the indexical and quasi-indexical clauses. Interestingly Castaneda, conceding that he realized "embarrassingly slowly" that already in his article "He" he had established the difference between first-person propositions and their quasi-indexical counterparts, chooses to abandon, not P, but the propositional identity claim (Castaneda, "Reply to Perry," p. 327). He admits that this would destroy his argument against Kretzmann (Castaneda, "Correspondence," p. 301). Instead he holds that the quasi-indexical propositional guises are "intimately equivalent" to their corresponding indexical propositional guises (Ibid., p. 307). Upon reflection, he surmises that although his argument against Kretzmann has been weakened, it is not fatally so (Idem, "Reply to Perry," p. 327), perhaps because God can still be said to know all quasi-indexical facts (Idem, "Correspondence, p. 308). Although Castaileda thus had already conceded since 1979 Smith's point, still Smith needs to close off the alternative that someone might take of rejecting P while retaining the factual identity claim. The arguments we presented above already suggest this, for if the factual content of the expressions were identical, there is no reason this would not be transitive in the above cases. But the conclusion can be made more clearly by simply considering what one agent knows. What M knows in 1966 in truly saying, "The Chrysler Building is now 1,046 feet fall" is not known in his truly saying, "I know in 1966 that the Chrysler Building is 1,046 feet tall then," for this latter sentence does not tell him if he needs to get to work on the extension. Indeed, ifhe does not know the date he might believe the former sentence, but not the latter. Thus, the fact expressed "quasi-indexically" is not the same fact as that expressed indexically in oralio recla. It also follows that God's knowledge of merely "quasi-indexical" facts is not enough for omniscience. 9" D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), p. 6.

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outfitted, not with dates, but with expressions referring to the sentence-token itself, all A-expressions having been eliminated. While the date-sentence version of the Old B-Theory was propounded principally by philosophers of language, the tokenreflexive version tended to be the theory of choice among philosophers of space and time who were B-theorists.

Hans Reichenbach Hans Reichenbach, having read the manuscript for Russell's Inquiry into Meaning and Truth, in which Russell sought to define all ego-centric particulars in terms of "this" ("now," for example, meaning "the time of this"), proposes to analyze indexical expressions and tensed verbs in terms the expression "this token.,,99 According to Reichenbach, indexicals and demonstratives, as well as tensed verbs, refer in part to their respective tokens used in an act of speech or writing; referring thus to themselves, such words may be called "token-reflexive words." Such words postulate a relation between their respective tokens on any occasion and an appropriate non-indexical referent: "The word 'I,' for instance, means the same as 'the person who utters this token'; 'now' means the same as 'the time at which this token is uttered'; 'this table' means the same as 'the table pointed to by a gesture accompanying this token'."lOo This analysis implies that the meaning of, for example, the sentence, "I am now going shopping" is "The person who utters this token goes shopping at the time at which this token is uttered." What, then, is the meaning of the demonstrative expression "this token"? For Russell, "this" was a primitive, non-connotative, proper name which applies to only one object at a time and whose referent is continually changing. 101 But since Reichenbach proposes to analyze "this" itself token-reflexively, he appears to embark upon a vicious, infinite regress: "this token" means something like "the token to which attention is directed by this token." But Reichenbach averts this consequence by treating "this token" as a meta-linguistic expression: The symbol 'this token' is used to indicate an operation; the meaning of this operation cannot be formulated in the language itself but only in its metalanguage. All tokenreflexive words are pseudo-words; they can be replaced by proper words in combination with an operation, namely, the operation, 'this token'. 102

Reichenbach proposes to give the metalinguistic name "8' to a specific token, for example, an utterance of "This boy is tall." Analyzed token-reflexively, "this boy" means "the boy pointed to by a gesture accompanying e." By taking "this token" metalinguistically, Reichenbach avoids an infinite regress, for a sentence like "This token has five words" means "e has five words," e referring back to the indexical sentence, not the sentence in which "8' appears. This last example serves as well to bring out the fact that "8' is not itself a token-reflexive expression, so that we are enabled to re-write sentences originally in token-reflexive form in such a way that

99 100

101 102

Reichenbach, Symbolic Logic, sees. 50, 51. lbid., p. 284. Russell, Inquiry into Meaning and Truth, p. 110; idem, Human Knowledge, p. 85. Reichenbach, Symbolic Logic, p. 286.

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the symbol used is not token-reflexive. Thus, "I" is to be given the form "the x that spoke ()," "here" will be expressed by "the place z where ()was spoken," and "now" will be rendered as "the time t when ()was spoken." But what about verbal tense? Reichenbach proposes an analysis of verbal tense in terms of the point of speech, the point of the event, and the point of reference. 103 The point of speech is the time at which the token is uttered. The point of the event is the time at which the event described occurs. The point of reference is the point of departure for the temporal perspective on the event of the speaker. The difference of these various points can be made most clear by reflecting upon how Reichenbach uses them to analyze the structure of the six common English tenses: Past Perfect I had seen John

E

R S

Present I see John S,R,E I

Simple Past I saw John R,E I

Present Perfect I have seen John S

Simple Future I shall see John S,R I

E I

E

S,R I

Future Perfect I shall have seen John

S I

E I

R I

Unfortunately, Reichenbach gives no examples of how these tenses are to be rendered in tense less token-reflexive sentences. With respect to the present tense, the token ()of"I see John" presumably means "The person who utters ()sees John at the time of (J s utterance." But other tenses are more complicated. A token () of "I saw John" presumably means "The person who utters () sees John before the time of Us utterance and at the speaker's time of reference." A token ()of"! shall have seen John" presumably means "The person who utters () sees John after the time of (Js utterance and before the speaker's time of reference." And so it goes with the other tenses. The above translations are tenseless; we must resist the temptation to identify the time of utterance or point of speech S with the present moment. That S does not represent the present for Reichenbach is evident in his remark that in indirect discourse the point of speech sometimes shifts to the past. "Thus, 'I am cold' has a point of speech lying before that of 'I said that I was cold,.,,104 The idea is that "I am cold" was true before "I said ... " is true and therefore the point of speech of the former lies before that of the latter. Any point of time can serve as the point of speech, and thus Reichenbach's analysis is tense less.

103 104

Ibid., pp. 288-297. Ibid., p. 295.

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According to Reichenbach's theory, then, temporal indexicals and tensed verbs are token-reflexive expressions, and the goal of his analysis is to eliminate tokenreflexives from sentence tokens in order to arrive at tenseless translations of them. This is accomplished by naming the sentence token containing the token-reflexive words and then describing the B-relations obtaining between the time of the event described, the time of the named token's utterance, and the speaker's time of reference. J J C. Smart

Although he cites Reichenbach's work in support, J. J. C. Smart has propounded a less sophisticated and different token-reflexive analysis of tensed expressions. 105 He lays out his view as follows: Let us replace the words 'is past' by the words 'is earlier than this utterance.' (Note the transition to the tenseless 'is'.) Similarly, let us replace 'is present' and 'now' by 'is simultaneous with this utterance,' and 'is future' by 'is later than this utterance.' By 'utterance' here, I mean, in the case of spoken utterances the actual sounds that are uttered. In the case of written sentences (which extend through time) I mean the earliest time slices of such sentences (ink marks on paper). Notice that I am here talking of selfreferential utterances, not self-referential sentences. (The same sentence can be uttered on many occasions.) We can, following Reichenbach, call the utterance itself a 'token,' and this sort of reflexivity 'token-reflexivity.' Tenses can also be eliminated, since such a sentence as 'he will run' can be replaced by 'he runs at some future time' (with tenseless 'runs') and hence by 'he runs later than this utterance.' Similarly, 'he runs' means 'he runs (tenseless) simultaneous with this utterance,' and 'he ran' means 'he runs (tenseless) earlier than this utterance.' All the jobs which can be done by tenses can be done by means of the tenseless way of talking and the self-referential utterance 'this utterance.' 106

The principal differences between Smart and Reichenbach's views are: (i) Reichenbach posits a B-relation between the time of some sentence token and the event described by the token, whereas Smart posits a B-relation between the sentence token itself and the relevant event. Moreover, Smart takes no cognizance of the time of reference, as does Reichenbach, so that his analysis becomes considerably more cumbersome with respect to complex tenses. 107 (ii) Reichenbach eliminates the token-reflexivity of indexicals and tensed verbs by means of the proper name "0," whereas Smart retains token-reflexivity in his tenseless 105 1. 1. C. Smart, '''Tensed Statements': A Comment," Philosophical Quarterly 12 (1962): 264-265; idem, Philosophy and SCientific Realism, International Library of Philosophy and Scientific Method (London: Rout/edge & Kegan Paul, 1963), pp. 134-140; idem, "Introduction," in Problems ojSpace and Time, ed. 1. 1. C. Smart, Problems of Philosophy (New York: Macmillan Co., 1964), p. 18; Encyclopedia oj Philosophy (1967), s.v. "Time," by 1. 1. C. Smart. For a comparison of Reichenbach and Smart's views, see Jim Torgerson, "Reichenbach and Smart on Temporal Discourse," Philosophy Research Archives 14 (1988-89): 381-394. 106 Smart, Scientific Realism, pp. 133-134. 107 For example, he says, '''E was future, is present, and will become past' goes over into 'E is later than some utterance earlier than this utterance, is simultaneous with this utterance, and is earlier than some utterance later than this utterance.' This is about as near as we can get to it, and it will be seen that we have to refer to three different utterances" ("Time," p. 127). Later he appropriated Reichenbach's original insight, but by that time Smart had already been converted to the New B-Theory (Smart, "Quine on Space-time," pp. 508-509). See also Torgerson, "Reichenbach and Smart," pp. 387-388.

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translations, merely substituting the demonstrative expression "this token" for temporal indexical and tensed expressions. As a result, he runs into considerable difficulties as to whether he has succeeded in eliminating tense from his canonical translations or, at least, in giving a clear account of the meaning of this demonstrative expression. \08 The above citation makes it evident that in Smart's opinion the tenseless, demonstrative sentences have the same meaning as their tensed token counterparts, for "he runs" is said to mean "he runs simultaneous with this utterance." Elsewhere he later qualifies the translation thesis, remarking, For the present and future tenses we use 'simultaneous with this utterance' and 'later than this utterance.' Of course, this is not a strict translation. If I say, 'Caesar crosses the Rubicon earlier than this utterance,' I am referring to my utterance, whereas if you say, 'Caesar crossed the Rubicon,' you are implicitly referring to your utterance. Nevertheless, a tensed language is translatable into a tenseless language in the sense that the purposes subserved by the one, in which utterances covertly refer to themselves, can be subserved by the other in which utterances explicitly refer to themselves. 109 Cf. Russell's struggle to specity the meaning of "this" (Russell, Inquiry into Meaning and Truth, pp. 109-110). He observed that if we treat "this" as a concealed definite description such as "the object of attention," then it will always apply to everything that is ever "this," whereas in fact "this" applies to one thing at a time. But if we hold that "this" means "what I am now noticing," then we are involved in circularity, for we are trying to define "now" in terms of "this." Russell's point, I think, is that if we try to define "this" in terms of a definite description, then the indexical nature of the word will have been lost, which is contrary to English grammar; but if to retain its indexical character we define "this" in terms of other indexicals, then tense is not eliminated. So how does Smart understand the expression "this token"? Gale charged that such an expression is tensed, meaning something like "the present token" (Richard Gale, "Tensed Statements," Philosophical Quarterly 12 [1962]: 56). Smart retorts that Gale's objection is simply a dogmatic rejection of the analysis in terms of token-reflexiveness (Smart, Scientific Realism, p. 139). Elsewhere he states, "We have as good a right to say 'now' means 'simultaneous with this utterance' as our opponent has to say that 'this utterance' means 'the utterance which is now.' The notion of an utterance directly referring to itself does not seem to be a difficult one" ("Time," p. 127). But what is that notion? It is arguable that demonstratives are analyzable in terms of more basic indexicals but that the attempt to reduce indexicals to demonstratives is flawed. Thus Kaplan contends that it is "the sloppy thinker" who adopts a demonstrative theory of indexicals: that "I" is synonymous with "this person" along with an appropriate subjective demonstration, that "now" is synonymous with "this time" and "here" with "this place" along with appropriate demonstrations (David Kaplan, "Demonstratives: an Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals," in Themes from Kaplan, ed. Joseph Almog, John Perry, Howard Wettstein [Oxford: Oxford University Press, 1989], p. 534). These thinkers err, he says, (i) in thinking that the sense of the demonstration is the sense of the indexical, and (ii) in believing that such senses are necessarily associated with the uses of pure indexicals. Since "now" lacks an essential demonstrative sense, it cannot be legitimately analyzed in terms of "this _." By contrast "this" can, it seems, be analyzed as "the thing to which I am presently directing attention." Therefore, if we take "this token" as a de dicta expression, it means "the token to which I am presently directing attention," in which case tense has not been eliminated. Therefore, a reductive analysis of "now" in terms of "simultaneous with this token" cannot be given. On the other hand, if we take "this token" in Smart's canonical translation as referring de re, then it is like a rigidly referring proper name of the tenseless utterance containing it, not of the original tensed utterance as in Reichenbach's theory; e.g., "Caesar crosses the Rubicon earlier than U," where U is the token just made, not a token of "Caesar crossed the Rubicon." This avoids circularity, but only at the price exacted in note 110. 109 "Time," p. 127. Hence, Smart uses locutions like " ... a person who said that a certain event E is past could equally well have said, 'E is earlier than this utterance. '" 108

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Smart here begins to sense the difficulties occasioned by his failure to follow Reichenbach in eliminating all indexicals in his tenseless translations. For if both the tensed and tenseless utterances contain, implicitly or explicitly, a demonstrative self-reference, then they cannot mean the same thing, since they refer to different utterances. llO Reichenbach avoids this problem by giving the original tensed utterance the name "9' and making his translations refer back to it; but what Smart would have to say to achieve synonymy would be, "Caesar crosses the Rubicon earlier than that utterance," that is, earlier than "Caesar crossed the Rubicon." But then he would have abandoned his distinctive view that the canonical sentences are token-reflexive. Worse, such a move would undermine his construal of translatability in terms of replaceability, for if we were to replace "Caesar crossed the Rubicon" with "Caesar crosses the Rubicon earlier than that utterance," then "that utterance" would refer to nothing and so the sentence could not be true. III Moreover, since he substitutes for Reichenbach's time of the token just the token itself, Smart's view entails that even simultaneous utterances of "Caesar crossed the Rubicon" by two different people, not to speak of "Caesar crosses the Rubicon earlier than this utterance" tokened by a third, do not have the same meaning, since they all refer to different utterances! On Smart's view, then, even similar, simultaneous tensed tokens are not synonymous, much less their tenseless translations. Smart's adjusted notion of translation to indicate replaceability in the original context without detriment to the purposes for which the original token was uttered serves to underscore the fact that for Smart the tenseless canonical sentences are intended as substitutes for ordinary language expressions, not just as an ideal language for scientific theories. He concedes that the tensed view is a more adequate analysis of ordinary language but contends that ordinary language is then more at variance with science than on his view. "I advocate my way, because it fits our ordinary way of talking much more closely to our scientific way of looking at the world and it avoids unnecessary mystification.,,112 But he insists that his tense less language is just as good as tensed language for our ordinary purposes:

110 See the somewhat similar point made by Paul Fitzgerald, "Nowness and the Understanding of Time," in PSA 1972, Boston Studies for the Philosophy of Science 20, ed. Kenneth F. Schaffner and Robert S. Cohen (Dordrecht: D. Reidel, 1974), pp. 267-268, who notes that the tokens referred to by the tensed and tenseless tokens respectively are different, since they have a different number of words. Schlesinger's counter-argument that the tensed token is a sort of abbreviation for the tenseless one and so is referred to by "this token" (Schlesinger, Aspects of Time, p. 132) misses the point. For even if the tensed token abbreviates the tenseless one, there are still two tokens (after all, one is an abbreviation and the other is not!) and, hence, "this token" refers to each token in which it occurs. It must be kept in mind that Smart is not trying to give the propositional content of the tensed token, but analyzing it in terms of another token. (If we were to adjust Smart's theory such that the tenseless translation gives the propositional content of the tensed token, this would be incoherent because a proposition is not a token, yet the proposition would include a reference to "this token." To avoid this incoherence, we would have to take "this token" as a proper name referring de re to the original token. But then Smart's theory ceases to be distinct from Reichenbach's with respect to difference (ii) in the text, though the problems occasioned by difference (i) would remain.) III A point also made by Smith, Language and Time, p. 79. 112 Smart, Scientific Realism, p. 140. In his concern to fit ordinary language to the scientific way of looking at the world, we see Smart's scientism beginning to show itself; the unnecessary mystification he

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Nevertheless, the two analyses are in practice pretty well equivalent: in ordinary life a linguist will detect no difference between 'ordinary language,' as in accordance with my analysis, and 'ordinary language,' as in accordance with my opponent's analysis. Our ordinary language is just not quite so 'ordinary' as is our opponents', but it is just as good even for ordinary purposes. 111

Smart thus clearly affirms that tensed language is dispensable, not merely for science, but for ordinary life as well, and replaceable by tense less, token-reflexive sentences. CRITIQUE OF THE TOKEN-REFLEXIVE THEORY I think we shall see, however, that the token-reflexive version of the Old BTheory of Language shares the same major failing of the date-sentence version, besides having problems of its own: I. Tensed sentence tokens are informative in a way that their purported, tenseless translations are not, as is manifest from the unique role the former play in motivating thought and action. Again, the point is Gale's: the tensed sentence token "S is now ¢J' cannot be translated without loss of meaning as either "S's being rp is simultaneous with ¢" or "S's being rp is simultaneous with the occurrence of a token of'S is now rp'," for The B-statements in the analysans of these two analyses do not entail the A-statement in the analysandum: that S's being 1/1 is simultaneous with theta (the occurrence of a token of'S is now cjl') does not entail that S is now 1/1. These B-statements describe a Brelation between S's being 1/1 and a certain token event without entailing that either one of these events is now present (past, future). That they do not contain or entail information about the A-determination of an event can be seen by the fact that whenever someone uses the sentence, 'S's being 1/1 is simultaneous with theta (the occurrence of a token of "S is now 1/1"),' he has not forestalled the question whether S's being 1/1 (or the occurrence of theta) is now present (past, future). 114

Lest the above reasoning seem question-begging, we must recall that Gale proceeds to show how timely action depends upon the information furnished by tensed sentence tokens, information which would be lost if their tenseless counterparts were to replace them. Consider again the soldier who must communicate to his commanding officer the moment at which the enemy advances to within 100 yards: Suppose he spots the enemy within the 100-yard range and then whispers to himself the sentence, 'The enemy is now within 100 yards.' Let us give the metalinguistic proper name 'theta' to this token event. Immediately upon whispering this sentence to himself, Joe says out loud the B-sentence, 'The enemy's being within 100 yards is simultaneous with theta (the utterance by Joe of ' The enemy is now within 100 yards"),'.. This Bfears is the notion of time's passage, which we shall address in chap. 7. See also Smart, "Quine on Space-Time," p. 511, where his dual concerns are stated explicitly. 111 Smart, Scientific Realism, p. 140. Smart did finally come to abandon the translatability thesis of the Old B-Theory, acknowledging that tensed statements convey practical information which tenseless statements could not possibly have (1. J. C. Smart, Our Place in the Universe [Oxford: Basil Blackwell, 1989], p. 37). \14 Gale, Language of Time, p. 55. Gale misstates Reichenbach's view, which is that S's being 1/1 is simultaneous with the time of e, not with e itself.

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statement does not conveyor entail any information about the A-determination of the state of affairs of the enemy's being within 100 yards: it merely describes a B-relation of simultaneity between this state of affairs and the occurrence of a particular sentence token. lIS

The point is that the B-relation between either the time of the B-sentence token or the B-sentence token itself and the state of affairs described is a tense less relation, such that it is always true to assert that such a relation obtains tenselessly in the actual world; therefore, the communication of such information cannot facilitate timely action, such as is required in this case on the part of the company commander. Hence, the A-sentence token and the correlated B-sentence token do not mean the same thing. The above argument seems obviously applicable to Reichenbach's formulation of the token-reflexive version. Whether we take ''the time of (J' to be a de dicto or a de re expression, our knowing that some state of affairs obtains at that time clearly cannot facilitate the timely action made possible by our knowing that the state of affairs in question presently obtains. If the argument is less obviously applicable to Smart's formulation, it is only because "this token" seems to be a sort of surreptitious temporal indexical. But if we strip it of its temporal connotations-as we must if the translation is to be tenseless-, then all the B-sentence token tells us is that the token is tenselessly coincident with the event described-which is insufficient to explain timely action. 116 Although Perry did not discuss token-reflexive theories in his case for the essential indexical, a similar argument could have been made. Suppose, for clarity's sake, that only one token respectively ever occurs in history of the sentences "The faculty meeting starts at the time of (J' and "The faculty meeting starts simultaneous with this utterance." If "this utterance" is not surreptitiously tensed, then one could always believe that these tokens are true; they never change their truth values. But then one will never know when to get up and go to the meeting, since one will never liS Ibid., pp. 56-57. When Fitzgerald objects that A-sentence tokens do not of themselves supply information about A-determinations because the token could be a recording from an earlier time (Fitzgerald, "Nowness," p. 270), he is raising a problem about the communication of tensed facts which is extraneous to the problem of whether such facts exist. In order for tensed beliefs or facts to be communicated, the context of hearing or apprehension must be roughly the same as the context of utterance. When these do not roughly coincide, then the tensed facts are not communicated. Such divergence is a common experience with written A-sentence tokens. If anything, the inability to communicate tensed facts when the contexts of utterance and apprehension do not coincide serves to underline the difference between tensed and tenseless sentences, since the information conveyed by tenseless sentences can be communicated across diverse contexts. The point Fitzgerald makes about recordings is exactly what we should expect to be the case for tensed facts if they exist. 116 Smart fails to appreciate this point. In Smart, '''Tensed Statements'," p. 265, he notes that the reason Gale classes Smart's canonical sentences as tensed is because they are not freely repeatable, as a Bsentence should be. But the reason they are not freely repeatable, he explains, is because of the demonstrative "this," which picks out a new token upon each utterance, not because the sentence is tensed. Smart agrees that the tenseless "Kiss me simultaneous with this utterance" is not freely repeatable and so has a pragmatic function which cannot be served by a sentence lacking the demonstrative expression. The problem with Smart's analysis is that unless "this utterance" is tensed, one cannot even know whether the utterance is at a time which is past, present, or future, and so one cannot decide to obey the tenseless command. The token-reflexive version of the Old 8-Theory thus leads to frigidity, which ought to be enough to condemn any theory!

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come to believe that "The time of B is now" or "Now is simultaneous with the utterance 'The faculty meeting starts simultaneous with this utterance'." Indeed, on the translation thesis, all that these beliefs amount to is "The time of B is simultaneous with the time of B' or "The utterance 'The faculty meeting starts simultaneous with this utterance' is simultaneous with this utterance." What good does it do to know that two utterances are tenselessly simultaneous in trying to decide if it is time to go to the meeting? The token-reflexive version of the Old B-Theory thus does no better than the date-sentence version in explaining rational thought and behavior. This constitutes the major failing in the Old B-Theory of Language and has led to its demise. But the token-reflexive version has an additional flaw peculiar to it. 2. The token-reflexive theory can give no coherent account of the meaning of tensed sentences which are not tokened. It must be remembered that the tokenreflexive version of the Old B-Theory, unlike the Russell-Frege analysis, does not even try to give an account of propositional truth or even of the truth of sentence types. It is an exclusively sentence token analysis. But what account, then, is to be given of propositions or sentence types which are never tokened? Surely an objective account of the way the world is must include such propositions or sentences and does so independently of our tokening them even mentally. For we can cognize propositional functions like "At longitude m and latitude n on the surface of the Earth there stands a tree" and be confident that a bivalent sentence or proposition would result from our plugging in values for the variables, even though that sentence is never tokened. We shall never cognize the complete account of the world, but we feel that it must contain propositions or sentences which are true independently of our cognizing them. Smith thus maintains that while tensed and tense less sentence tokens are similar in important respects under the token-reflexive analysis, that analysis is inadequate to deal with what is expressed by such tokens respectively: This difference between A-sentences and token-reflexive sentences is perfectly compatible with several similarities between them. Each present tensed A-sentencetoken is true if and only if it is simultaneous with the event it is about. .. and entails that there is some sentence token simultaneous with the [event] it is about. Exactly the same holds true for the tokens of the token-reflexive sentence that corresponds to the Asentence. But whereas the similarities between these two sentences lie in the semantic rules about the tokens of these sentences, the differences between them lie in the rules about what is expressed by these tokens. What is expressed by a token of the tokenreflexive sentence is true if and only if it is expressed by a token which is simultaneous with the event the truth vehicle is about.... And the truth vehicle expressed entails that there is some token simultaneous with the event the truth vehicle is about. But none of these semantic characteristics apply to the truth vehicles expressed by tokens of normal A-sentences. What is expressed by a present tensed token of a normal A-sentence is true if it is expressed by a token that is simultaneous with the event it is about, but not only if it is expressed by such a token. It may be true even if it is not expressed by any token.... Moreover, ... what is expressed by the A-sentence-token does not entail that there is some token simultaneous with the event; even if the truth vehicle is in fact

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CHAPTER 2 expressed by such a token, there are some possible worlds in which the truth vehicle is true even though there are no tokens simultaneous with the event. 117

Smith's point seems common-sensical and intuitive. It seems obvious that what is expressed by "There is paper in the desk drawer" would be true even had one not uttered this true token and that what is expressed by "No language users exist" is possibly true. Notice that Smith assumes at this point that the token-reflexive theorist is willing to admit that there are truth bearers like propositions or sentence types which are expressed by sentence tokens. It is not evident, however, that the token-reflexive theorist does or can admit this. 118 Moreover, separating sentence tokens and the propositions or sentence types they express stirs up a hornet's nest of profound metaphysical issues, which merit a whole inquiry of their own. How do we know that such abstract entities exist independently of their expressing tokens? Even if a proposition would exist were we to plug in a value for a propositional variable (for then we would cognize its expressing token), that does not prove that propositions or sentence-types do exist, independently of our cognizing them. The token-reflexive theorist could agree, for example, that it is true that "There would be paper in the desk drawer, even had no one uttered 'There is paper in the desk drawer'" without Smith, Language and Time, pp. 84-85. If the token-reflexive theorist is willing to admit the existence of entities like sentence-types or propositions, what account does he propose to offer of them which is distinct from the date-sentence analysis? It is difficult to imagine what sort of coherent account could be given. The propositions expressed by the proposed tenseless translations are presumably of the form "S is pearlier than/simultaneous with/later than the time of (J and earlier than/simultaneous with/later than the speaker's point of reference." Obviously, untokened propositions cannot be of this form, since they have ex hypothesi no tokens and no speaker. Untokened propositions must have a different form than tokened propositions. For if the untokened propositions were to be tokened, they would have the above form, which they cannot have so long as they are untokened. It follows that untokened propositions are essentially incapable of being tokened. Since propositions are immutable, they cannot change their form in passing from being untokened to tokened. Rather the token previously unuttered or unthought expresses a different proposition than the untokened proposition. Hence, it is false that what is expressed by "The paper is in the desk drawer" would be true had no one uttered this token. Some other inexpressible proposition would be true instead. Nor does it seem to make any sense to say that what is expressed by "No language users exist" is possibly true or was once true. One cannot mean that the proposition expressed by these words is true in some other possible world or at some other time where there are no language users, for the proposition expressed by these words involves a reference to the tensed token (J and so cannot be true in {!s absence. Similarly, one cannot mean that some other proposition which would be expressed by (J at some other world or time without language users is true there because (J does not exist there. Nor can one mean that some other proposition which would be expressed by (J at some other world or time sans language users if it were tokened, though in fact it is not, is true there; for if (J were to be tokened in that other world or time, it would not express the same proposition as the untokened proposition, but would express the canonical proposition. So what is expressed by "No language users exist" is not possibly true; rather some other ineffable proposition is possibly true instead. If untokened propositions have neither the form of tenseless date-sentences nor of token-reflexivesentence tokens, what form do they have? Perhaps they have a proposition-reflexive form: "S is pearlier than/simultaneous with/later than the time of '1'," where 'I' is the proposition. Such a proposal makes no sense, however, for even if propositions have temporal duration, they do not presumably come to be and pass away, but are everlasting, so that there is no time earlier or later than '1'. In short, I do not know what to make of the claim that untokened propositions or sentence types exist on the token-reflexive view. 117

liS

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conceding that there would be some entity existing with a truth value in such a situation. Similarly, he could agree that the world could have existed devoid of language users without conceding that in such a situation there would also have existed an abstract object describing that situation and having the value "true." Moreover, those of us who are theists might ask how the existence of abstract entities like propositions would comport with God's aseity. The Platonistic view of infinite realms of metaphysically necessary, uncreated abstract objects posits a metaphysical pluralism which is radically opposed to the idea of God. How then can such objects exist? Perhaps one might appeal at this point to the divine ideas as a basis for the existence of propositional truth-bearers independent of human cognition but not metaphysically independent of God. Since God is omniscient, He must know only and all true propositions about the way the world is." 9 Hence, He at least must have a complete account of the world. But the B-theorist might rejoin that if God consciously cognizes all the propositions He believes, then these cognitions are, in effect, non-linguistic, mental tokens, and the token-reflexive analysis should apply to God's mental tokens as well as ours. The aforementioned propositional function can be assigned values, and the proposition obtained should be translated into, for example, "At longitude 10° and latitude 20° on the surface of the Earth stands a tree simultaneously with the time of 0' [Reichenbach] or "simultaneously with this mental token" [Smart]. Notice that both translations must assume that God is temporal, for in order for the tree's standing at m, n to be simultaneous with the time of His mental token () or with the tense less translation token, God's cognitions must be in time. Now at this stage of the argument, the assumption of divine temporality is unwarranted. How does the token-reflexive theorist know that God is not timeless, that His cognitions are not of the nature of tense less date-propositions rather than token-reflexive in nature? Theists who are (crypto-) B-theorists usually hold that the date-analysis provides a better model of divine omniscience than the tokenreflexive analysis. It would therefore be gratuitous to assume that God's mental tokens are token-reflexive simply in order to save the token-reflexive translation thesis. Still, it is noteworthy that the theistic B-theorist who embraces the tokenreflexive version of the Old B-Theory must hold that God exists in the B-theoretical time dimension. The determined advocate of the token-reflexive version of the Old B-Theory could maintain that his view is at least coherent, since any complete account of the world in terms of the divine ideas would not entail propositions which are untokened, and that therefore the token-reflexive analysis can be applied to God's cognitions as well as ours. But the applicability of the token-reflexive analysis to divine cognition further depends upon the deeper assumption that God consciously cognizes everything He knows. There are at least two reasons which make this 119 For more on this conception, see Quentin Smith, "The Conceptualist Argument for God's Existence," Faith and Philosophy 11 (1994): 38-49; for a related discussion see Thomas Morris and Christopher Menzel, "Absolute Creation," American Philosophical Quarterly 22 (1985): 353-362.

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assumption moot: (i) In order to know a fact, a person need not keep that fact present to consciousness. I know, for example, the equations of the multiplication table up to ten, but I do not have them always present to consciousness. In the same way, God's omniscience does not imply His cognizing consciously all that He knows. A model of divine omniscience according to which God knows all and only true propositions but does not hold them all present to consciousness as mental tokens may well appear to be more satisfactory than the model required by the token-reflexive analysis. (ii) Even more radically, there is a strong tradition in Christian thought that God is essentially simple and therefore does not literally possess a plurality of divine ideas or believe a multiplicity of propositions. 120 While the full-blown doctrine of divine simplicity does seem untenable,121 William Alston has argued effectively that full-blown simplicity is not required for a more modest doctrine of divine cognitive simplicity, according to which God's knowledge is essentially non-propositional in nature, and that such a doctrine has some positive advantages. 122 On such a model, there are no uncognized sentence-types or propositions; rather sentence-types or propositions exist as the result of finite, creaturely cognitive activity, which apprehends piecemeal what God knows as a seamless whole. If Alston's model is correct-and I must say that its advantages make it very attractive-,123 then linguistic or mental tokens, whether creaturely or divine, do not exhaust the reservoir of divine knowledge about the world. Because it depends solely upon linguistic or mental tokens, the token-reflexive analysis cannot give an adequate account of the way the world is. Perhaps the proponent of the token-reflexive analysis could counter the above argument by holding not only that all tensed tokens are susceptible to the tokenreflexive analysis, but also that anything God knows, if it were to be tokened mentally or linguistically, could also be so analyzed. But I think that it can be shown that such a move will still not rescue the token-reflexive version of the Old B-Theory from incoherence. 124 Consider, first of all, 1.

The era of linguistic or mental tokens exists.

This sentence-token means, on the token reflexive analysis, 2.

The era of linguistic or mental tokens exists simultaneously with the time of (1),

and is obviously true. But now consider

3.

The era of no linguistic or mental tokens exists.

120 See Thomas Aquinas Summa theologiae la.3. For a contemporary defense, see William E. Mann, "Divine Simplicity," ReligiOUS Studies 18 (1982): 451-471; idem, "Simplicity and Immutability in God," International Philosophical Quarterly 23 (1983): 267-276. 121 For a critique see Thomas V. Morris, "On God and Mann: A View of Divine Simplicity," in Anselmian Explorations (Notre Dame: University of Notre Dame Press, 1987), pp. 98-123. 122 William Alston, "Does God Have Beliefs?" Religious Studies 22 (\986): 287-306. 123 See comments in William Lane Craig, Divine Foreknowledge and Human Freedom, Studies in Intellectual History 19 (Leiden: E. J. Brill, 1991), pp. 10-11,288. 124 See the arguments of Smith, Language and Time, chap. 3. I have adapted Smith's examples to take cognizance of God's cognition, which Smith leaves out of account.

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During most of the history of the universe this seems to have been the case. The token-reflexive theorist must, however, translate (3) as 4.

The era of no linguistic or mental tokens exists simultaneous with the time of (3),

which is incoherent. The proponent of the token-reflexive theory must therefore regard (3) as impossible, since its translation describes an impossible state of affairs. He must maintain that 5.

The era of no linguistic or mental tokens existed.

is true, since it can be translated as 6.

The era of no linguistic or mental tokens exists earlier than the time of(5),

even though (5) cannot be, and therefore is never, true. 125 Thus, the token-reflexive theorist seems committed to the rather bizarre position that there can be facts about what existed at some time without there being at that time a corresponding fact about what exists. 126 Such a thesis is especially strange on a B-theoretical ontology, according to which all events are equally and tenselessly existent. In any case, prior to the existence of sentient creatures, God existed and knew what we express propositionally as (3). If God's knowledge is non-propositional, then the world was the way (3) describes it. The token-reflexive theorist cannot respond that if what God knew were to be tokened, then the token-reflexive analysis would apply to it, for if (3) were to be tokened, it would on that analysis be necessarily false. Thus, even if (3) cannot be truly affIrmed, it does express propositionally what God knew to be the case. If one rejects the non-propositional analysis of God's knowledge, then we must say that (5) is simply false, since there has never been a time devoid of God's mental tokens. But the token-reflexive theorist is committed to a stronger thesis than that: he must say that (3) is necessarily false, for so long as the non-propositional account is possible, (3) is possibly the way the world is, whereas (4) is not possibly the case. But herein lies a significant difference between (3) and (4). If (3) expresses a false proposition, even a necessarily false proposition, that is because it fails to correspond to reality; necessarily, there are always mental tokens. But (4) is internally self-contradictory, and that is why it is false. The one is broadly logically impossible (assuming that God's existence is broadly logically necessary and His knowledge necessarily propositional), while the other is narrowly or strictly logically impossible. Thus, even if the token-reflexive theorist holds that (3) is a 125 This example shows that the difficulty of translating (3) lies not in its ascription of some allegedly unintelligible property of presentness, as the B-theorist might be tempted to claim (cf. Smart, SCientific Realism, p. 134), but rather in the ineptness of the token-reflexive analysis of tensed expressions. 126 Note that we are not talking about so-called "soft facts" about the past, e.g., "Caesar died 2007 years before Saunders wrote his article" or "The world's greatest pianist was born at t." We are talking about the straightforward fact of there being no sentient creatures. See also Jeremy Butterfield, "Indexicals and Tense," in Exercises in AnalYSiS, ed. Ian Hacking (Cambridge: Cambridge University Press, 1985), pp. 72-73.

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necessarily false token, it is still not translated by (4), for the former, unlike the latter, is not strictly logically impossible. 127 The foregoing discussion makes it evident that one of the principal logical differences between an A-sentence token and its tenseless translation is that the latter entails that a token exists whereas the former does not. The token "Geraldine Ferraro is President of the United States" is false only if this token exists, but what it means does not entail that such a token exists. But the translation "Geraldine Ferraro is President of the United States simultaneously with the time of ()" entails as part of its meaning that the tensed token exists. This difference is obvious to anyone with a mastery of English, and its presence calls, not for a reform of the English language along token-reflexive lines, but for the jettisoning of the tokenreflexive analysis as an adequate account of what is meant by tensed and indexical sentences. 128 CONCLUSION In summary, the token-reflexive version of the Old B-Theory of Language fares no better than the date-sentence version in providing a means of translating tensed sentences into tenseless sentences without loss of meaning. Not only are the canonical translations incapable of facilitating rational thought and timely action, but no satisfactory account of untokened tensed sentences can be given on this theory. The Achilles' heel of the Old B-Theory of Language thus turned out to be its translation thesis that tensed sentences could be reformulated into a tense less canonical form without loss of meaning. This thesis has proved untenable. Hence, we can safely conclude premiss 7.

Tensed sentences have not been shown to be reducible without loss of meaning to tense less sentences

of the A-theorist's fundamental argument for the objective reality of tense; here, at least, a broad philosophical consensus has emerged. That takes us on to step 8.

Ontological tense has not been shown to be superfluous to human thought and action

127 A similar point can be made concerning the token-reflexive analysis of the first person indexical. The token "I am not tokening anything" is to be translated as "The person who tokens B tokens nothing simultaneously with the time of B." The former cannot be asserted, but the latter is self-contradictory. 128 When Hinckfuss differentiates between an analytic and an explicatory reduction of tensed sentences on the grounds that only an analytic reduction purports to provide synonymy of meaning and then claims that the token-reflexive analysis is intended to be merely explicatory, i.e., to provide a description which is as rich as the analysandum but more explicit, so that the objection fails that the tensed token, unlike the translation, does not entail that a token exists (Ian Hinckfuss, The Existence of Space and Time [Oxford: Clarendon Press, 1975], pp. 10,90), he is combining the outlook of the New B-Theory of Language with that of the Old. The New B-Theory admits that tensed sentences cannot be translated without meaning loss into tenseless sentences and that therefore the former are richer and more useful than the latter. Hinckfuss agrees that an effective objection to the explicatory translation thesis would be the demonstration that tensed statements are useful and/or interesting in a way that their tenseless counterparts are not (Ibid., p. 89).

THE OLD B-THEORY OF LANGUAGE

and to the New B-Theory of Language.

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CHAPTER 3 THE NEW B-THEORY OF LANGUAGE

H

aving shown that tensed sentences cannot be translated without meaning loss by either date-sentences or token-reflexive analyses, Richard Gale concluded that there must be tensed facts which are conveyed by tensed discourse: "That a statement containing an A-expression cannot be translated into a B-statement without loss of factual or informative content suggests that A-expressions are used to convey factual information, namely information about the A-determination of an event or state of affairs." \ New B-theorists, while conceding the untranslatability of tensed sentences by tenseless sentences, deny this implication. They argue that the ineliminability of tense from language has no implications for the objectivity of ontological tense. Thus, New B-theorist Nathan Oaklander explains, ... the old tenseless theory of time assumed that a logical analysis of ordinary language that eliminates tensed discourse, supported an ontological analysis of time that rejects transient temporal properties. The tenser shared that assumption, but argued that since no tenseless translations were successful, temporal becoming ... is necessary in any adequate account of time. Tensers, claim, in other words, that because tensed discourse is ineliminable, the detenser is mistaken and tensed properties and acts must exist. For a variety of reasons, ... recent defenders of the tenseless view have come to embrace the thesis that tensed sentences cannot be translated by tenseless ones without loss of meaning. Nevertheless, recent detensers have denied that the ineliminability of tensed language and thought entails the reality of temporal properties. According to the new tenseless theory of time, our need to think and talk in tensed terms is perfectly consistent with its being the case that time is timeless. Tensed discourse is indeed necessary for timely action, but tensed facts are not, since the truth conditions of tensed sentences can be expressed in a tenseless meta-language that describes unchanging temporal relations between and among events. 2

Oaklander's mention of the truth conditions of tensed sentences serves to highlight the respect in which the New Theory differs from the Old. The move made by New B-theorists has been to abandon the claim to provide tenseless translations of Asentences and to claim instead to provide tenseless truth conditions of A-sentences, So whereas Gale maintained that thus rendering ontological tense otiose. "Information about an event's A-determination seems to be part of the content of what is asserted or stated by someone who uses an A-sentence, since one of the truth-conditions of his statements is that the event reported by his A-statement has Richard Gale, The Language of Time, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1968), p. 55. 2 L. Nathan Oaklander, "A Defense of the New Tenseless Theory of Time," Philosophical Quarterly 41 (1991): 26-27. For other conscious rejections of the Old B-Theory by New B-theorists, see Jeremy Butterfield, "Indexicals and Tense," in Exercises in Analysis, ed. Ian Hacking (Cambridge: Cambridge University Press, 1985), pp. 69-87; Michelle Beer, "Temporal Indexicals and the Passage of Time," Philosophical Quarterly 38 (1988): 158-164. For an anthology on the New B-Theory, see L. Nathan Oaklander and Quentin Smith, eds., The New Theory of Time (New Haven: Yale University Press, 1994).

66

THE NEW B-THEORY OF LANGUAGE

67

the specific A-determination it is asserted to have,,,3 D. H. Mellor contends that "However complex the verbal tense of a sentence, ... nothing but tenseless facts are needed to settle the truth of its tokens. The objective truth-values of tensed sentences and judgments give no reason to suppose that there are tensed facts, i. e., that things and events really do have A-series positions.,,4 The key inference, as Oaklander phrases it above, in the New B-Theory's attempt to abort the A-theorist's argument for the objective reality of tense lies in the move from 1.

The truth conditions of tensed sentences can be expressed in a tense less metalanguage.

2.

Therefore, tensed facts are not necessary for timely action.

to

What warrants this inference? What hidden premisses serve to make this a valid argument? The B-theorist must be assuming 3.

There are no facts expressed by tensed sentences other than those expressed as their truth conditions.

Together with (l), (3) implies 4.

All the facts expressed by tensed sentences can be expressed in a tense less metalanguage.

Given the further assumption that 5.

Tensed discourse supplies all the facts necessary for timely action,

it follows from (4) that 6.

All the facts required for timely action can be expressed in a tenseless metalanguage,

or, in other words, (2). The key premisses in this argument, it seems to me, are assumptions (1) and (3), and so the New B-theorist's justification for these assumptions repays close attention. I propose to open the discussion with a look at the case for the New B-Theory of Language laid out by the leading New B-theorist of our day, D. H. Mellor. D. H. MELLOR'S NEW B-THEORY Mellor opens his book Real Time by announcing that he subscribes to a tokenreflexive account of "what makes tensed statements true or false," which allows him to keep tensed truths and falsehoods, while rejecting objectively tensed things,

Gale, Language afTime, pp. 55-56. D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), p. 45.

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events, and facts. 5 The fIrst step, he explains, in doing away with tensed facts is to trade them in for tensed truths. In 1984 Queen Elizabeth's birth had the tense 58 years past. "But all this means is that, made in 1984, this judgment about the Queen's age would be objectively true.,,6 Now what makes such a judgement objectively true? One could say that it is just the tensed fact corresponding to the judgement that makes it true on that date. But Mellor maintains ''that tensed facts are a myth, a fallacious reifIcation of the truth of tensed judgments.,,7 He proposes instead that it is tense less facts which make tensed judgements true or false. Key to his understanding is the distinction between sentence types and tokens, the most important feature of this distinction being that only tokens have defInite locations in time and space. With the exception of long-lived tokens (such as printed tokens), tokens of tensed sentence types are true or false without temporal qualifIcation; their truth value is an unchanging property of the token itself. Mellor includes among tokens mental judgements, which mayor may not be instances of sentence types; a non-linguistic mental token will be an instance of a non-linguistic judgement type. All tokens occur at specifIc dates, Mellor emphasizes, and this will enable him to say, without appeal to tensed facts, what makes them objectively true or false. Mellor observes that if the same tensed sentence type is tokened on two different occasions, it may well be the case that one token is true and the other false. "The truth or falsity of tensed sentences, therefore, are properties of their tokens rather than of their types."g Hence, in looking for the tenseless facts which give these sentences their truth or falsity, we must look for facts which vary appropriately from token to token even of the same sentence type. Given that sentence tokens have specifIc dates, Mellor proceeds, such facts are not hard to fmd. Suppose, for example, that one token of "The Queen is 58" occurs in 1984 and another in 1985. These dates, together with the date in April 1926 when the Queen was born, are enough to make the first of these tokens true and the other false. Given these dates, it is no coincidence that these tokens have these truth-values. Any token of the sentence 'The Queen is fifty-eight' has to be true if its date is fifty-eight years later than that of the Queen's birth, and any whose date is a year later than that has to be false. The truthvalues of these tokens follow directly from how their B series positions relate to that of the event they are about. 9

Mellor generalizes this result to take care of tokens of sentences having different tenses: ... any token of a past tense sentence, to the effect that some event happened N years (days, whatever) ago, will be true if its date is N years (days, etc.) later than the date of that event. Those are the tenseless conditions, and the only tenseless conditions, in which simple past tense sentence tokens will be true. They are what we may conveniently call the tenseless 'truth conditions' of these tokens. The truth conditions of future tense tokens are like those of past tense ones, only in order to be true these tokens have to be earlier, not later, than the events they are about...

Ibid., pp. 5-6. Ibid., p. 34. Ibid. Ibid., p. 40. Ibid., pp. 40-41.

THE NEW B-THEORY OF LANGUAGE

69

... For a present tense token to be true the event it refers to must occur within a specified B series interval containing the token itself. 10

It is interesting that Mellor here abstains from using the sentential connective "if and

only if' in characterizing the truth conditions of tensed sentences. By supplying only sufficient conditions, Mellor leaves it open that other, alternate accounts of their truth conditions might also be given-such as tensed truth conditions. Hence, he observes, "That these simple types of tensed sentences have these token-reflexive truth conditions is really quite obvious, and is not seriously questioned. The serious question is whether this is all there is to the facts of tense." 11 The complete answer to that question will depend on the cogency of Mellor's defense of McTaggart's Paradox, the examination of which we shall defer to chapter 6. In the meantime, Mellor provides a formula for constructing the tenseless truth conditions of more complex tenses than the simple ones above. Tense logicians advocate the following procedure for determining the truth value of a sentence with a complex tense: (i) put the tensed sentence into its standard tense logical form, namely, a present-tense core sentence prefixed by a number of tense operators indicating A-series positions; (ii) suppose the present moment to be shifted back to the A-series position indicated by the left-most operator; (iii) repeat that exercise with each successive operator to the right; (iv) ask if the core sentence would be true if the present moment actually did have the date arrived at for it by this process. If so, the original complex sentence is true; if not, false. Mellor proposes that we simply replace references to the present moment with references to dates, starting with the date of the sentence token being assessed: (i) put the tensed sentence into its standard tense logical form; (ii) determine how far the A-series position indicated by the left-most operator is from the present and take the date which is that far from the date when the token occurs; (iii) repeat that exercise for each of the operators to the right; (iv) ask if a token of the core sentence would have been true on the date arrived at by this process. If it would, the original complex sentence token is true; if not, false. It is perhaps noteworthy that Mellor in dealing with such complex tenses uses counterfactual truth conditions, since the core sentence is never actually tokened. The complex token is true if the core sentence would have been true, had it been tokened on the appropriate date. Mellor concludes, "However complex the verbal tense of a sentence, therefore, nothing but tenseless facts are needed to settle the truth of its tokens.,,12 Mellor emphasizes that his claim that tensed facts are not needed to make sentence tokens true or false does not imply that tensed discourse is translatable into a tense less idiom or that tensed discourse is dispensable for action and communication. On the contrary, Mellor argues at some length for the Concerning untranslatability, untranslatability and indispensability of tense. Mellor's argument is that tensed sentences and the tenseless sentences spelling out their truth conditions (and similarly, spatially indexical and spatially non-indexical sentences) have themselves different truth conditions and, since sameness of truth

10

II

12

Ibid., pp. 41-42. Ibid., p. 42. Ibid., p. 46.

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conditions is a necessary condition of synonymy, do not, therefore, have the same meaning. He explains: Let X = Cambridge and T = 1980, and let R be any token of 'Cambridge is here' and S be any token of 'It is now 1980.' ... Then R is true if and only if R occurs in Cambridge, and S is true if and only if it occurs in 1980. If a sentence giving another's truth conditions means what it does, R should mean the same as 'R occurs in Cambridge' and S should mean the same as 'S occurs in 1980.' But these sentences have different truth conditions. In particular, if true at all, they are true everywhere and at all times. If R does occur in Cambridge, that is a fact allover the world, and if S occurs in 1980, that is a fact at all times. You need not be in Cambridge in 1980 to meet true tokens of 'R occurs in Cambridge' and'S occurs in 1980.' But you do need to be in Cambridge in 1980 to meet the true tokens, R and S: for only there and then can R and S themselves be true. At all other places and at all other times, those tensed sentences would have been false, whereas their alleged translations are true everywhere and always. 13

But if "R occurs in Cambridge" does not translate R (= "Cambridge is here") and "8 occurs in 1980" does not translate 8 (="It is now 1980"), then no tenseless sentence will. And if simple, tensed sentences like these are untranslatable, certainly more complex tenses will be as well. Smith, however, argues that Mellor's view on the untranslatability of tensed sentences is self-contradictory.14 Consider any token 8 as above and any token T of the sentence "8 occurs in 1980." 8 and T are said not to translate each other because they have different truth conditions. But on Mellor's account of the truth conditions of tensed and tense less sentence tokens, they do, in fact, have the same truth conditions, namely, 8 is true iff 8 occurs in 1980 and T is true iff 8 occurs in 1980. Since Tis tense less it is not the case that T is true iff T occurs in 1980; it, unlike 8, is true at all times if true at all. But that difference does not indicate a difference in the truth conditions of 8 and T; on the contrary, these are identical. Nathan Oaklander, while admitting that Mellor "is not always as clear as he should be" and that there is therefore "some basis in the text for attributing an internal inconsistency to him," nevertheless maintains that the contradiction alleged by Smith results from Smith's inattentiveness to the type/token distinction. 15 Oaklander points out that on Mellor's view, sentence types do not, strictly speaking, have truth conditions, nor are they truth bearers. It is sentence tokens which are true or false and possess truth conditions. Nevertheless, says Oaklander, we can speak of the "truth conditions" of a sentence-type in "a Pickwickian sense.,,16 That sense is that tokens of a tensed sentence type may vary in truth value from time to time, while tokens of a tense less sentence type will not vary in truth value. Letting "S" be the sentence type "It is now 1980" and "8 (1980)" be a token of 8 uttered in 1980, Oaklander asserts that " ... the truth conditions of (the different tokens of) the sentence types'S' and'S (1980) occurs in 1980' are different, because a token of the tense less sentence may be true at a time when a token of the tensed sentence is Ibid., p. 74. Quentin Smith, Language and Time (New York: Oxford University Press, (993), p. 69; cf. his earlier essay "Problems with the New Tenseless Theory of Time," Philosophical Quarterly 52 (1987): 371-392. For a similar point concerning spatial indexicals, see David H. Sanford, critical notice of Real Time, by D. H. Mellor, Philosophical Review 93 (1984): 290-291. IS Oaklander, "Defense," pp. 28-31. 16 Ibid., p. 29. 13

14

THE NEW B-THEORY OF LANGUAGE

71

false.,,)7 This assertion of Oaklander's is, unfortunately, ambiguous as it stands, since it is not a matter of indifference whether one reads into the sentence the phrase enclosed in parentheses. If we are talking about the truth conditions of the tokens of the sentence types, then they may have identical truth conditions, as Smith argued. Indeed, Oaklander goes on to concede that " ... if we are considering'S' and'S occurs in 1980' as sentence tokens, then their truth conditions are the same: they are true if, and only if, S occurs in 1980.,,)8 (Even this statement is not quite accurate, as we shall see below.) But if, on the other hand, we are talking about the "truth conditions" of the sentence types, then we are talking about a Pickwickian sense only which is not clearly relevant to Smith's argument. Perhaps we can clarify the issue by considering again Mellor's sample sentences S and R as displayed in Figure 3.1 : TypeS It is now 1980

TypeR S occurs in 1980

~

~

Figure 3. J. Sentence types S and R have no spatio-temporallocation, whereas their respective tokens may occur successively and at different places.

Type S is as such neither true nor false. But for any token Sn of S, Sn is true iff Sn occurs in 1980. Notice that the Sj have different truth conditions: S) is true iff S) occurs in 1980, S2 is true iff S2 occurs in 1980, S3 is true iff S3 occurs in 1980, and so on. But type R is ambiguous: what is the S referred to by R? It cannot be the sentence type S, since that does not occur in 1980. 19 It must be a token of type S. But which, then, of the Sj does it refer to? Let us suppose that it refers to S), as illustrated in Figure 3.2. TypeR S) occurs in 1980

~ R2 R3

R)

Tokens

~

Figure. 3.2. Various tokens R j all referring to the token Sl of "It is now 1980."

Ibid. Ibid. 19 Herein lies Oaklander's error; he fails to specifY which token of S the tenseless sentence is referring to. If one insists that the type S does occur in time, then none of the Si have the same truth conditions as any of the R;, since the former refer to tokens and the latter to the type. This will be of no help to Mellor, however, for the problem resurfaces upon our asking for the truth conditions of, say, SI, which will be that SI occurs in 1980. We may then inquire as to the truth conditions of" SI occurs in 1980." 17

18

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Any token Rn of R is true iff S, occurs in 1980. Notice that all of the Ri have the same truth conditions. So when Mellor denies that S and R have the same truth conditions, he must mean types S and R. For at least S, does have the same truth conditions as the R i • But this puts Mellor into difficulty, since the sentence types as such have neither truth values nor truth conditions-at least the tensed ones do not. At best they can be said to possess Oaklander's Pickwickian "truth conditions": we can call type S true iff one of its tokens is true, whereas type R can be said to be true iff all of its tokens are true. That is something like a difference in truth conditions. But even here weaker conditions for the "truth" of R can be stated which are identical with those for S: type R is true iff one of its tokens is true. The fact that if one is true, all are true is interesting, but superfluous for stating its "truth" conditions. It seems to me, therefore, that Mellor misleads his reader when he denies synonymy of S and R on the basis of their differing truth conditions. The tokens S and R can have the same truth conditions on his analysis. The types S and R do not have any truth conditions. Rather what Mellor should say is that the types S and R are not synonymous because R is such that if one of its tokens is true, all of its tokens are true, whereas S is such that if one of its tokens is true, others of its tokens may be false. No two sentence types having such disparate logical properties can be synonymous. 20 But what of their respective tokens? Why would not S" say, mean the same as any Rn. since they have the same truth conditions? Here Mellor's argument fails, for it shows only why the types S and R are not synonymous, not why S, and some Rn are not synonymous. Mellor has, however, a second line of defense for his contention that tensed and tenseless sentence tokens differ in meaning: they differ in usage. 2 ' Only tensed sentence tokens can be used in order to tell people, for example, what time it is. This consideration was, as we saw in the last chapter, the Achilles Heel that rendered fatally vulnerable the Old B-Theory. But we also saw that it was precisely on the basis of such considerations that A-theorists claimed the reality of tense. Smith has put Mellor into something of a dilemma here: Either tensed and tenseless tokens differ in meaning or they do not. If they do not, then Mellor's theory collapses into the Old B-Theory and succumbs to its disabilities. If they do differ in meaning, as Mellor affirms, then what accounts for that difference? It cannot be the difference in their truth conditions, for these may be identical. Tensed facts would account for that difference in meaning, but such an account is not acceptable to Mellor. So what does he propose to replace it? 20 Oaklander himself comes to propose a similar modification of Mellor's theory: " ... tensed and tenseless sentence-types have tokens with different truth conditions, while ... tensed and tenseless sentence tokens themselves have the same truth conditions" (Oaklander, "Defense," p. 30). This statement of the theory is very ambiguous, however, and does not take cognizance of the fact that only the 1980 tokens of S have the same truth conditions as the tokens of R. In his response to Oaklander, Smith charges that the latter has misunderstood Mellor's theory, since that theory holds that tensed and tenseless sentence tokens have different truth conditions (Smith, Language and Time, p. 70-71). But this time it is Smith who misinterprets Mellor, for in the passage Smith cites, the varying versus unvarying truth conditions referred to are each of a single type respectively. As the Figures in our text illustrate, the truth conditions of the Si are varying, while the truth conditions of the Ri are unvarying. Thus, the "modification" is in line with Mellor'S theory. 21 Mellor, Real Time, pp. 75-77.

THE NEW B-THEORY OF LANGUAGE

73

Mellor recognizes that it may be tempting to explain the difference in meaning between tensed and tense less sentence tokens by appealing to tensed facts. He responds, fIrst, by agreeing that sometimes there must indeed be more to meaning than mere truth conditions. For example, given that mathematical truths are necessarily true, 2+2=4 iff there is no greatest prime number. But clearly 2+2=4 does not mean that there is no greatest prime number. But Mellor thinks that contingent tensed sentences are not like that. He asserts, "They may not have the same meaning as the tense less sentences which give their truth conditions, but those truth conditions surely give their meaning.,,22 By "give their meaning" Mellor means, I think, "give the rule of use for tensed sentences." Someone who knows the truth conditions of a tensed sentence understands how it is to be correctly used. Thus, Mellor says that anyone who knows, for all dates t, that "It is now f' is true during and only during t knows what "It is now ... " means. Given just this knowledge, he can use and understand tokens of any such present-tense sentence and distinguish it from all past and future tense sentences of which he also knows the tenseless truth conditions. "Here ... the different meanings of different sentences are differentiated, as they are not in mathematics, by their different truth conditions.,,23 According to Mellor, in order to give the meanings of tensed, contingent sentences, we need only say when in the real world they would actually be true?4 There is no aspect of tensed meaning which the tense less truth conditions fail to accommodate, but which tensed facts would supply. But if the tense less truth conditions give the meaning of tensed sentences, why do they not yield tense less translations of them? Because, answers Mellor, they do not have the same truth conditions: Now the truth conditions of tokens of... temporally tensed types vary with their temporal position. So therefore must the truth conditions of tokens of their translations. But what makes sentence types tenseless ... is that the truth conditions of their tokens do not vary in this way ... the truth conditions of tenseless sentences are not token-reflexive. No tenseless sentence, therefore, can have tokens whose truth conditions are ... always the same as those of a tensed sentence, because by definition the latter vary from ... time to time and the former do not. That is why no tenseless sentence can mean the same as a tensed one does: tenseless token-reflexive and non-token-reflexive truth conditions are bound to differ.25

Mellor thus tries to explain the difference in meaning between tensed and tense less sentences, made evident by their different uses, on the basis of their different truth conditions. But this response clearly fails in the cases where a tensed sentence token and a tense less sentence token have the same truth conditions. As in the case of mathematical equivalences, so in this case also there must be "more to meaning" than mere truth conditions. Mellor is quite correct that a difference in meaning does exist in this case, but it is very difficult to see how his account of why this is so is not explanatorily defIcient. One could not say, for example, that only sentence types, not tokens, are meaning bearers, for then all a type's tokens (if they are not meaningless) must express the same meaning, that of their type. But that is 22 23 24 25

Ibid., Ibid., Ibid., Ibid.,

p. 75. p. 76. p. 77. pp. 77-78.

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impossible, since the truth conditions of tensed tokens give the meanings of those tokens, and these conditions vary from time to time. Since S), S2, and S3 do not all have the same truth conditions, they do not express the same meaning. For the same reason, one could not say that tokens are meaning bearers and all tensed tokens of the same type bear the same meaning. In order to claim that all tokens of the same tensed type express or bear the same meaning, Mellor must give up the contention that tenseless truth conditions give the meaning of a token. But that would imply the unacceptable result that knowledge of a token's truth conditions does not provide knowledge of the rule of use for the token. Without such knowledge the Btheorist cannot explain timely actions?6 On Mellor's account it seems clearly possible that even if a tensed sentence type is not synonymous with a tenseless sentence type, a token of a tensed type is synonymous with a token of a tense less sentence type. Mellor denies that such synonymy is the case, but his theory seems to lack the resources for explaining why these tokens sharing identical truth conditions are not synonymous. The A-theorist has an explanation in the reality of tensed facts. Already it is difficult to suppress suspicions that if the truth conditions of all sentences are tenseless, then the New B-theorist's premiss 3.

There are no facts expressed by tensed sentences other than those expressed as their truth conditions.

is false. The burden of Mellor's analysis of the token-reflexive truth conditions of tensed sentence tokens is to demonstrate that such tenseless truth conditions inform the user of the rule of use of the tensed sentence token, so that he can use the tensed token correctly without knowledge of any tensed facts at all. But as we can recognize from our discussion of the Old B-Theory, knowledge of the tenseless, tokenreflexive truth conditions alone of a tensed sentence token will not allow us to use that token in a timely fashion. One may know of SI (="It is now 1980") that it is true iff it occurs in 1980, but without the tensed knowledge as to what time it is now, one will be completely in the dark as to whether it is appropriate to employ that token. One must be able to look at the calendar and judge, "It is now 1980." Mellor recognizes this, adding parenthetically to his account of how one understands the rule of use for a tensed token via its tenseless truth conditions: "(Granted, he also has to recognize what ... I called the 'presence of experience,' in order to tell that he is now hearing someone say, 'It is now T' ... ),,27 Indeed, he declares, "The presence of experience is the crux of the matter. Without a tenseless account of it, tenseless A more plausible route for Mellor to take would be to distinguish between the rule of use of a token, which is given by the tenseless truth conditions, and the linguistic meaning of the token, which is the same for all tokens and the type they exemplify. But then it would also seem necessary to distinguish propositional content from linguistic meaning, since "It is now raining" tokened on one date does not have the same information value as it does when tokened on another date. But then matters of fact become more closely aligned with propositional content rather than linguistic meaning, and thus different tokens having the same meaning may express different facts. What reason would there be, then, to think that tensed and tenseless tokens express the same facts? Because they are both given the same rule of use? How does having the same rule of use prove that two tokens express the same propositional content? 27 Mellor, Real Time, p. 76. 26

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truth conditions on their own will never dispose of tensed facts.,,28 If Mellor's view is not to share in the inadequacies of the Old B-Theory, then, he must provide anew, tenseless account of our experience of the present. It is important, therefore, that before looking at Mellor's arguments for the indispensability of tense, we provide some exposition of his tenseless account of the presence of experience. Mellor begins by observing that one can make mental judgements about one's present experiences, for example, that I am now free from pain. This judgement will be true iff I am having only pain-free experiences at the time I make the judgement. Suppose, then, I make judgements about temporal aspects of my experience, for example, that the experiences I am now having are present. Such a judgement is infallible and always true for any person. This presence of experience can be explained away in tenseless terms as follows: Now any token which says that an event is present will be true if and only if the event occurs at the same B series time as the token does. Those are the undisputed tokenreflexive truth conditions of all such judgments. But in this case the events to which presence is attributed are themselves picked out by the use of the present tense. Not all our experiences, past, present and to come, are alleged to have this A series property, only the experiences we are having now. But these, by the same token-reflexive definition of the present tense, are among the events which do have the property now ascribed to them: i.e. events occurring just when the judgment itself is made. So of course these judgments are always true. Their token-reflexive truth conditions are such that they cannot be anything else. In tenseless terms they are tautologies after all. That is the tenseless explanation of the presence of experience. 29

Reading and re-reading this citation, one is apt to ask oneself, "What explanation?" If I understand him correctly, Mellor is saying that in judging, "The experiences I am now having are present," I am ascribing presentness to present experiences. But to be a present experience, on Mellor's analysis, is to be an experience which occurs at the time of the judgement token about that experience. So to say that "A present experience is present" is to say that an experience simultaneous with that token is simultaneous with that token, which is tautologous. Granted that this analysis suffices to explain why this judgement is always true, how does it even approach explaining tensed beliefs or tensed belief states? How is the presence of experience "explained away" by the explanation that it is a necessary truth that "The experiences that I am now having are present"? How does this tautology provide the key to my successful employment of the tenseless rule of use for tensed sentences?30 28

29

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Ibid., p. 50. Ibid., p. 54. Elsewhere Mellor writes, "Now simultaneity with its subject matter is the defining truth condition of a present tense judgment, as opposed to a past or future tense one; so if I am thinking of my actions or experiences as happening while I am thinking of them, I am ipso facto thinking of them as being present. And that, I suggest, is all there is to the much vaunted presentness of our experience. Experiences in themselves, like events of every other kind, are neither past, present, nor future. It is only our simultaneous consciousness of them, as being simultaneous, which necessarily both has, and satisfies, the tenseless truth conditions of present tense judgments" (D. H. Mellor, "McTaggart, fixity, and coming true," in Reduction, Time and Reality, ed. Richard Healey [Cambridge: Cambridge University Press, 1981], p. 88).

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Profiting from the cntlque of Murray MacBeath, Mellor subsequently supplemented his account of the presence of experience. MacBeath, appealing to the Direct Reference semantics of John Perry, distinguished intentional facts from tenseless facts: our beliefs are irreducibly tensed but concern intentional facts only and so may be false; if they are true, it is only due to the tense less facts which make Mellor acknowledges that MacBeath's solution represents an them SO.31 improvement on Mellor's account ofthe feeling that experience occurs essentially in the present: I had located the feeling in a belief, accompanying an experience, that the experience is present-a belief that is, of course, a token-reflexive tautology. But since beliefs aim only at truth, and this truth is trivial, so (arguably) is the belief, which the felt presence of experience seems not to be. Beliefs, moreover, are not feelings.... For both these reasons my account was not really adequate. 32

But now Mellor believes he can account tenselessly for tensed feelings and emotions. First, he says he can allow the presence of experience to be felt, not just believed. Now the presence of experience can characterize one's belief state, even if the content of the belief itself is a tautology. Second, since feelings and emotions aim at more than truth, the feeling need not be as trivial as the belief content it is based on. For example, if my belief that I live in the present makes me glad to do so, my gladness may be significant even though the content of my belief is trivially true. Mellor obviously still has a lot of explaining to do. The fact that his theory provides no explanation for the existence of tensed belief states in a tenseless world underscores our previous suspicions that the New B-theorist's premiss (3) is false. But what is significant is that Mellor has here broken with the old Fregean model which did not discriminate between belief states and belief contents and has moved in the direction of post-Fregean Theories of Direct Reference. As the role of tense in such theories shall significantly occupy us in the next chapter, we pass by a discussion at this point, simply noting the shift. Mellor's modified theory appears to hold that one's cognitive state includes all sorts of tensed beliefs and feelings, one of these being that what one is experiencing now is present. But the object of that belief or feeling is an intentional fact, not an actual fact. On the basis of one's belief that the present is the time of those experiences, one can know how to use tensed sentence tokens on the basis of their tenseless, token-reflexive rules of use. Since only tenseless facts are needed to explain why those tokens are true or false and

Mellor seems to be saying that the presentness of experience amounts to no more than my thinking of my experiences as simultaneous with themselves. But this seems a patently inadequate explanation of why certain of my range of experiences are apprehended as present. If "The present experience is present" is said attributively, then the sentence is trivial for A- and Btheorist alike. If it is used referentially, then the B-theorist can only state that this statement is necessarily true in the sense that the designated experience is self-simultaneous. But he offers nothing to explain why we experience that moment, not merely as self-simultaneous (it is always that), but as present. By contrast, the A-theorist explains that we apprehend the designated experiences as present because they, and they alone, really are present, that is, they exist at the unique time which is ontologically present. 31 Murray MacBeath, "Mellor's Emeritus Headache," Ratio 25 (1983): 86-87. 32 D. H. Mellor, "MacBeath's Soluble Aspirin," Ratio 25 (1983): 92.

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since one's belief that one's experiences are present is necessarily true, no tensed facts are required by any of our tensed beliefs. As I indicated, Mellor argues not only for the untranslatability of tense, but also for its indispensability.33 "What makes tense indispensable," he says, "is that we cannot help having tensed beliefs. Partly we cannot help it because belief, including tensed belief, is what perceptions give us .... And whatever acts on its perceptions must have tensed beliefs. Action is what really makes tensed belief indispensable.,,34 But, Mellor insists, what action needs is the tensed belief, not the tensed fact. My beliefs are what make me act, not the facts which make them true or false. My actions will generally be successful, of course, only if the beliefs which generate them are true, but the truth of those beliefs requires only the tenseless facts stated in their token-reflexive truth conditions. Hence, tensed facts are dispensable for explaining timely action, but tensed beliefs are not. Mellor's account of tense's indispensability depends once more on the basis for the presence of experience. Why do perceptions give us tensed beliefs if reality is not itself tensed, if there are no tensed facts? Granted that action requires only tensed beliefs, not true beliefs, how is it that tensed belief exists at all in a tense less world? Tensed facts will be dispensable for timely action only if tensed beliefs can exist without real tense. But we have yet to see how it is that a tenseless world gives rise to tensed beliefs. CRITIQUE OF THE NEW B-THEORY Having exposited the core of Mellor's statement of the New B-Theory, let us now tum to an examination of its adequacy. One of the first things that strikes one about Mellor's theory is that, as a token-reflexive analysis, it seems to fall prey to the difficulties attending the token-reflexive analysis of the Old B-Theory, particularly Smart's version. 1. The New B-Theory violates logical implication relations in its truth conditions of tensed sentence tokens. One of the problems besetting Smart's tokenreflexive translations was that similar, simultaneous tokens of a tensed sentence tum out to have different meanings, since each refers to a different token, namely, each refers to itself. In the same way, on Mellor's token-reflexive analysis of truth conditions of tensed sentence tokens, two similar, simultaneous tokens have different truth conditions. For example, let R be one token of "It is now 1980" and S be another, simultaneous token of "It is now 1980." Accordingly, "It is now 1980" (=R) == R occurs in 1980. "It is now 1980" (=S) == S occurs in 1980.

The problem with this analysis, as Smith points out, is that while it is "an unimpeachable linguistic datum" that Rand S state logically equivalent facts, on Mellor's analysis they state different facts, for the fact that R occurs in 1980 is not JJ 34

Mellor, Real Time, pp. 78-88. Ibid., pp. 8 I -82.

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equivalent to the fact that S occurs in 1980. 35 Mellor's analysis neither explains nor is consistent with the logical equivalence of the facts stated by R and S. Given Mellor's identification of facts with truth conditions that obtain, Smith's objection does seem serious, indeed. If the only facts stated by R are the tenseless facts given in its token-reflexive truth conditions and similarly for S, then S and R cannot state the same fact, which is absurd. In his response to Smith, Oaklander admits that " ... tense less truth conditions cannot explain the logical equivalence" of S and R, but he denies that the New B-Theory must be able to do SO.36 Since tensed discourse and thought are ineliminable, "The logical connections among sentences in ordinary language do not represent ontological connections between facts in the world.',37 This reply seems to me unavailing. The New B-Theory holds that ontology admits no tense; there are no tensed facts. Accordingly, it provides an analysis of tensed sentences which purports to clarify in terms of their tenseless truth conditions what are the tense less facts which the tensed sentences state and which make them true. Tensed sentences state no other facts than these. But on the token-reflexive analysis, R and S state different facts. Either the Theory is therefore defective or else two simultaneous tokens of "It is now 1980" do not state the same fact, not even the same tenseless fact (never mind tensed facts). It is not hard to surmise that the former alternative is more likely than the latter to commend itself to most thinkers. But it seems to me that the New B-Theory's token-reflexive analysis is even more seriously flawed than Smith suggests. For surely it is also an unimpeachable datum that R entails S; but then we may validly argue

7. R -3 S. 8. S -3 S occurs in 1980. 9. :. R -3 S occurs in 1980. (H.S. 7, 8) But surely R does not entail that S occurs in 1980. Maybe only R was uttered in 1980. But then we are forced to say that (7) is false, that "It is now 1980" does not imply "It is now 1980." Mellor's theory engenders this untoward result because his truth-bearers are sentence tokens, not propositions or sentence types, and these Smith, Language and Time, p. 90; idem, "Problems with the New Tenseless Theory," pp. 374-384. Smith sometimes makes the tensed tokens synonymous, but dissimilar, e.g., "It is now 1980" and "1980 is present." Two synonymous sentence types are thus being tokened. But I do not see that this move contributes anything to the argument, since on the New B-Theory it is tokens which are the truth-bearers and recipients of truth conditions, so that even two similar tokens must have distinct token-reflexive truth conditions, as Smith comes to see in his revised version of the argument. 36 L. Nathan Oaklander, "The New Tenseless Theory of Time: a Reply to Smith," Philosophical Studies 58 (1990): 288. 37 Ibid., p. 290. Smith in his response to Oaklander (Smith, Language and Time, p. 13), errs in thinking that the New B-Theory draws ontological conclusions about the nature of time from the analysis it provides of tensed sentences' truth conditions. That analysis is primarily defensive (though some Btheorists may occasionally rashly claim more) in nature; the positive case for a B-theoretic ontology of time leans primarily on McTaggart's Paradox. Smith is correct that New B-theorists aim to construct a language that gives in truth condition sentences the meanings and entailments in a natural language, but Oaklander does not deny that-he denies that a logical entailment between two sentences corresponds to an ontological connection between things in the world. 3S

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tokens are given a token-reflexive analysis of their truth conditions. When we say R entails S, we mean that the propositional content of R entails that of S, not that the existence of R entails the existence of S; but Mellor's analysis has the consequence that either the truth of R does not entail the truth of S (since tokens are contingent entities and some worlds in which R exists do not include 8), which makes nonsense of logic, or else that the existence or occurrence of R does imply the existence of S, which would lead to the ontological proliferation of an infinite number of sentence tokens of "It is now 1980" (since all are entailed by R). In this regard, Oaklander's objection is doubly irrelevant. One is not claiming, pace Oaklander, that the logical equivalence of R and S requires an ontological connection between the facts that make R and S true. Rather one is claiming that the token-reflexive theory has an internal logical incoherence, in that sentences stating the conditions under which two logically equivalent sentences are true are not themselves logically equivalent. The logical/ontological bifurcation is a red herring. In a later piece, Oaklander confesses, "There does indeed appear to be a difficulty here for the token-reflexive analysis," which he proposes to elude by adopting Kaplan's views on indexicals. 38 But this represents the betrayal of Mellor's tokenreflexive analysis. For, as we shall see, while Direct Reference theorists generally take the propositional content of a tensed sentence to be tense less, so that tense less truth conditions can be stated relative to a context, time, and place, those truth conditions are not token-reflexive. I take Oaklander's abandonment of the tokenreflexive analysis of the truth conditions of tensed sentences to be the vindication of Smith's argument. What all this implies is that Mellor's theory does not in fact give the truth conditions for tensed sentences or their tokens. This may seem remarkable, for surely a token of "It is now 1980" is true if and only if it occurs in 1980! In a sense, that is so; that token can be truly uttered tenselessly if and only if the token occurs in 1980. That is to say, "R" is truly uttered == "R" occurs in 1980. "S" is truly uttered == "S" occurs in 1980. Such a formulation, so long as we recall that we are using a tense less far;on de parler, is unobjectionable logically, for neither the antecedents nor the consequents respectively are materially equivalent. But such a formulation is useless to the Btheorist, since what we have here are truth conditions, not for a pair of tensed sentences, but for two tense less sentences. The point remains that in order for what a tensed sentence expresses to be true or to be the case, there need not be a token at the appropriate time. Truth conditions are meant to specify under what conditions that which a sentence expresses is true. The perverse result of making tokens truthbearers and their truth conditions token-reflexive is that the truth-conditions no longer fulfill that function; rather they specify the conditions under which the token as such is true. Since a token cannot bear the truth value "true" unless it exists, the truth of tensed sentences requires the existence of sentence tokens. This leads in 38

Oaklander, "Defense," p. 32.

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turn to the incoherence explained above.

If to avoid this problem we make that which tokens express be the truth-bearers instead of the tokens themselves, then R and S express the same thing, say, a tensed proposition, and this proposition is not true if and only if R occurs in 1980. Even if one maintains that the proposition exists only if some token or other exists, it is not a necessary condition of the proposition's truth that any particular token R exists. Moreover, the tenseless occurrence of R in 1980 is not sufficient for the truth of the tensed proposition, since it is left undetermined whether the proposition is (present-tense) true. What seems to be needed is tensed facts. In order to obtain tensed truth conditions for tensed sentences, one needs to challenge the B-theorist's assumption that the "is true" in "R is true iff R occurs in 1980" is tenseless. If we take "is true" to be tensed, then the truth of the tenseless sentence to the right of the biconditional operator is not a sufficient condition for the truth of R. As Smith explains, "Suppose that the token T J of 'The storm is approaching' occurred two months ago, simultaneously with the storm's approach. Since the tenseless truth condition, T J' s being simultaneous with the approach of the storm, is met, TJ is true when it occurs. But it is false that TJ is (present tense) true. Rather TJ was true, namely, when the storm was approaching.,,39 In order for TJ to be presently true, a different condition is needed, namely, that T J is present. Graham Priest, in an interesting exchange with Mellor, has laid out such tensed truth conditions for both tensed and tenseless sentences. 40 The key move is to specifY the conditions under which some sentence is presently true. Thus, for example, "The Battle of Waterloo occurred in 1815" is (present tense) true iff the Battle of Waterloo occurred in 1815. The sample sentence is true at the time of my writing but was false in 1800, which is just as it should be. To give tensed truth conditions for tense less sentences, Priest takes the verb to be disjunctively tensed, which he abbreviates with the adverb "eternally." Thus, "The Battle of Waterloo occurs in 1815" is (present tense) true iff the Battle of Waterloo eternally occurs in 1815. If, as I have maintained, there are genuinely tenseless, not merely disjunctively or conjunctively tensed, sentences, I see no reason why Priest's account cannot give tensed truth conditions for these as well; for instance, "A square has four equal sides" is (present tense) true iff a square has four equal sides. As Priest notes, contradiction arises when one tries to give tense less truth conditions to a tensed sentence: "The Battle of Waterloo occurred in 1815" is (present tense) true iff the Battle of Waterloo occurs in 1815. For in such a case we should be forced to say that the sample sentence was true in 1800, which it was not. Mellor attacks Priest's tensed truth conditions by arguing on the basis of McTaggart's Paradox that such conditions lead to a vicious infinite regress; we shall examine that claim later. But Mellor also argues that it is inappropriate to posit tensed truth conditions for either sentence types or tokens. For any sentence type S, Smith, Language and Time, p. 99. I have altered some of Smith's stylistic conventions expressing tenseless and tensed verbs. 40 Graham Priest, ''Tense and Truth Conditions," AnalYSis 46 (1986): 162-166; D. H. Mellor, ''Tense's Tenseless Truth Conditions," Analysis 46 (1986): 167-172; Graham Priest, "Tense, Tense, and TENSE," Analysis 47 (1987): 184-187. See also Gilbert Plumer, "Expressions of Passage," Philosophical Quarterly 37 (1987): 345; E. 1. Lowe, The Possibility of Metaphysics (Oxford: Clarendon Press, 1998), pp.90-91. 39

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"S is true" is tensed only in virtue of the tense in S itself. Evidence for this claim lies in the fact that any token T of S asserted at a time can be replaced by a token "T is true" and retain the same truth conditions as T. So the predicate "is true" is not responsible for the tense of a tensed sentence "S is true." But Priest responds to Mellor that tensed states of affairs exist and obtain at different times, such that a past-tense sentence type can be presently true. For example, "The sun shone on the last day of 1986" is true iff the sun's having shown on that day is realized now. Priest's point is well-taken. On the A-Theory of time, it is not merely present-tense states of affairs which presently obtain, but also past- and future-tense states. 41 Moreover, I have contended that tenseless sentences can be presently true, for example, "God timelessly knows that E occurs at T " is tenseless but can be presently true. 42 In general, the fact that tenseless sentences can be presently true shows that "S is true" is not parasitic for its tense upon the tense of S and that therefore the giving of present-tense truth conditions is not inappropriate. Turning to sentence tokens, Mellor asserts that since sentence tokens never change their truth value, it must be in virtue of their unchanging B-relations to the events they are about that they are true or false. A tensed sentence type may have tokens which differ in truth value, but those respective truth values never change. Hence, "is true" is no more tensed when predicated of tensed sentence tokens than of tensed sentence types. But how does this conclusion follow? The A-theorist agrees that tokens do not change their truth values in the sense of exchanging truth and falsity. (Of course, we are talking here about transient tokens, what Mellor calls "event tokens," not enduring "thing tokens." Mellor agrees that thing tokens change their truth value over time.) But since on the A-Theory temporal becoming is real, tokens that once were true or false have ceased to exist and their truth values along with them; tokens which will someday be true or false do not yet exist and no more have a truth value than a merely possible object has existence. Tokens have only the truth values they presently have and these do not switch. Mellor, however, has the very strange interpretation that on the A-Theory all of the tokens of a sentence type, whether past, present, or future, periodically switch their truth values as the events described are future, then present, then past. This erroneous inference comes from combining Mellor's own B-theoretic ontology, according to which all tokens are equally existent, with A-theoretic becoming. Unfortunately, Priest falls into the trap: he thinks that the true token "It is the twentieth century" is presently true, but in ten This serves to answer Smith's question, "To what do the future tense propositions about future free decisions correspond?" (Quentin Smith, critical notice of Divine Foreknowledge and Human Freedom, by Wm. L. Craig, Philosophy and Phenomenological Research 53 [1993]: 494-495; cf. idem, "General Introduction: The Implications of the Tensed and Tenseless Theories of Time," in New Theory of Time, p. 9). What I meant by the reality referred to by the future-tense proposition was the things and events described by the proposition. Some A-theorists hold that because these concrete realities do not presently exist, a view of truth as correspondence requires that future-tense propositions about them fail to be true or false. My point was that correspondence requires only that they will exist. But I do not deny that there are tensed states of affairs corresponding to such propositions which presently obtain. However, we need not borrow a B-theoretic ontology in order for tensed states of affairs to obtain; see my remarks on Smith's view in chap. 6. 42 See Paul Helm, 'Timelessness and Foreknowledge," Mind 84 (1975): 524-527.

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years that numerically identical token will be false. 43 But the A-Theory requires no so wild a supposition: the token has a truth value only so long as it exists, and the moment it is no longer present it neither exists nor has a truth value. Thus, the Atheorist is in complete agreement that event tokens do not change their truth values. Hence, the unchanging truth values of tensed tokens does nothing to cast aspersion on present-tense truth conditions. Smith, who seems to flirt with the idea of combining a B-theoretic ontology with A-theoretic becoming, unfortunately fails to repudiate decisively either Mellor's objection or Priest's response. Instead, he proposes to escape the objection by positing token-reflexive truth conditions for A-sentence tokens. 44 He contends, for example, that 10. The token U of "John is dead" is true iff U and John's being dead are both present. Like Priest, Smith takes the "is true" to be present-tense, not tenseless, and (10) gives the "tensed truth conditions" of U. But if "is true" is present-tense, then it seems redundant to say that U and John's being dead must both be present. Why not simply 11. The token U of "John is dead" is (present tense) true iff John's being dead is present, as Priest suggested? Smith answers that (11) countenances U's now being true even if U exists at a past or future time rather than the present. That leads in turn to Mellor's objection about tokens' changing their truth values as time passes. Since Smith denies that U has truth values at times when it is not present, Mellor's objection is avoided. But Smith's concern with Mellor's objection is misplaced. On a pure A-theoretic ontology, U's being true entails Us being present. Hence, U is not now true if it existed in the past or will exist in the future. Worse still, it seems to me that Smith's own token-reflexive analysis falls prey to the same objection he urged against Mellor's analysis. Let U and V be simultaneous tokens of "John is dead." It follows from Smith's analysis that "U" == U and John's being dead are both present.

"V" == V and John's being dead are both present.

But while U and V state the same fact and are mutually entailing, it is not the case that their truth conditions state the same fact and are logically equivalent. Therefore, they cannot be the truth conditions of U and V. The only difference that I can see between the cases of Mellor and Smith is that Mellor is giving tenseless and Smith tensed truth conditions. But that makes no difference to the soundness of the 43

So does Mark Hinchliff, "McTaggart, Change, and Real Tense: A Critical Notice of Hugh Mellor's

Real Time 11," in Essays on Time and Related Topics, ed. L. Nathan Oaklander, Selected Papers of the Philosophy of Time Society Proceedings, 1995-1999, p. 44. It is astonishing that Hinchliff, as an avowed presentist, can think that a sentence token uttered in the past and which therefore does not exist has a truth value-not to mention a truth value different from that which it possessed when the token was present! 44 Smith, Language and Time, p. 103-104.

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objection. U and Veach presently imply the other and so their truth conditions should presently imply each other as well. Since they do not, Smith's analysis fails. The above considerations seem to me to underscore the ineptness of the whole token-reflexive approach to either truth conditions or meaning. What needs to be said is that tokens as such are not truth-bearers and can be called true or false only insofar as what they express is true or false and that the truth-conditions for what tokens express are not token-reflexive. Smith repeatedly is led into difficulty by his view that A-sentence tokens are truth-bearers with token-reflexive truth conditions. For example, he claims, " ... A-sentences are used to assert B-relations between the events denoted and the uses of the A-sentences.,,45 This is prima facie not the case, and I see no reason to think that despite appearances this claim is after all true. Rather what is the case is that the tokening of an A-sentence implies that a certain B-relation obtains between the token and the event it describes. On Smith's analysis, it follows that that which is expressed by the A-sentence token, or what Smith calls an A-proposition (that is, a tensed proposition), fails to contain all that the A-sentence asserts, since A-propositions do not even implicitly refer to their expressing tokens. 46 We can avoid this troublesome consequence by denying that tokens assert such relations; it is the fact of their tokening that implies such relations. It seems to me, therefore, that Graham Priest has correctly laid out the proper truth conditions for tensed sentences, in contrast to the defective, token-reflexive analysis of the New B-Theory championed by Mellor. 2. The New B-Theory can give no coherent account of the truth conditions of tensed sentences which are not tokened Like the Old B-Theory, the New B-Theory holds that sentence tokens are the truth-bearers. But what account shall we give of tensed sentences which remain untokened? In the context of another problem, Mellor does reflect on truth conditions for untokened sentences: When truth conditions are being given for token sentences, they need not include imaginary conditions in any problematic way. They must admittedly apply to imaginary as well as to real tokens. All the tokens of 'Cambridge is here' in Cambridge could by chance have occurred in King's College, making tokens of that sentence true as a matter of fact if and only if they occur in King's. But that again would only be a coincidence, and would not give the real meaning of 'Cambridge is here.' So we must consider all the actual places where tokens of this English sentence would be true, even if none are actually there. But although we have therefore to consider imaginary tokens, we have only to consider them in actual places. To give the (spatial or temporal) meanings of essentially tensed contingent sentences, we need only say when and where in the real world they would actually be true. In this case truth conditions seem to me both innocuous and effective: I find it

Ibid., p. 94. Smith holds that A-sentences express token-independent tensed propositions which change truth value over time and are therefore temporal. Although I have been speaking of the propositions expressed by A-sentences, I do not mean to prejudge the views of philosophers who shun propositions in favor of self-ascription of properties. My main intention has been to criticize the token-reflexive analysis, and our final position will have to take account of non-propositional analyses.

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CHAPTER 3 hard to see what aspect oftensed meaning they fail to accommodate. And certainly they fail to do nothing that tensed facts could do better.47

Here Mellor states that token-reflexive truth conditions apply to imaginary as well as real tokens, and he might be understood to hold that an untokened tensed sentence is true iff a token of that sentence would be true at a particular time and place. If this were Mellor's view, it would run into the same problems encountered by the Old B-Theory. What truth conditions, for example, are to be given for the following sentence? 12. There are no tokens. We cannot say that (12) is true iff a token of (12) would be true at a particular time t and place I, since a token of (12) is true iff that token is simultaneous with there being no tokens at t, I-which is incoherent. Such a view implies that no such untokened sentences are true. This may seem just as it should be for the B-theorist, except when one reflects that other untokened tensed sentences do satisfy the truth conditions for imaginary tokens. For example, 13. I am writing. is true iff a token of (13) would be true at t, I. There is no incoherence in such a token's being true: it is true iff my writing is simultaneous with the time of the token. Thus, the theory has a defmite defect in it, in that it cannot deal consistently with truth conditions for untokened tensed sentences. But the above incoherent theory is not, I think, a proper interpretation of Mellor's words. Mellor is not saying that imaginary tokens have truth conditions (as though non-existent tokens could possess a truth value!) or that untokened sentence types are bivalent (that would contradict his theory); rather he is saying that in stipulating the truth conditions for actual tokens, we need to consider not just where and when they are true, but also where and when similar tokens would be true. If all the tokens of "It is now 1980" happened to occur in January, anyone of those tokens S does not have the truth conditions "S occurs in January, 1980." Rather we recognize that similar tokens would be true if uttered anytime during 1980, so we do not delimit the time at which S must be true so narrOWly. Thus, Mellor does not espouse the incoherent theory. But then what account does he give of the truth of untokened sentences? So far as I can see, he gives none. And therein we see an aspect of tensed meaning which is not accommodated by his tenseless token-reflexive truth conditions. Such truth conditions fail to specify under which conditions what is stated by sentences like (12) is the case. Tensed facts do a better job in doing this because they are token independent. Graham Priest's present-tensed truth conditions apply not to tokens alone, but to sentence types, propositions, or what have you. If one holds that untokened propositions or sentence types do not exist and that God's knowledge is non-propositional in nature, one can still hold that God knows non-propositionally what reality is like and so knows, for example, what would be formulated 47 Mellor, Real Time, p. 77. Recall, too, that in the case of complex tensed sentences, Mellor's truth conditions concern a present-tense sentence which would be true if it were tokened.

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propositionally as "There are no tokens." During the Cretaceous Period, there may have been no proposition or abstract object expressed by (12) functioning as a truthbearer, but the Earth was then as (12) describes. Mellor's colleague and fellow B-theorist Jeremy Butterfield seems to have had a more acute realization of the problem these considerations pose to the tokenreflexive analysis of truth conditions than Mellor. 48 He notes the disagreeable consequence that an item not talked about during its existence is never present on such an analysis. He remarks on the disruption between tenses wrought by such a theory: the aforementioned item could be future and past, but never present; another item talked about only during its existence is then present, but never future or past. 49 Butterfield therefore shows himself to be open to tensed, non-tokened truth bearers, such as propositions. But he insists that temporal indexicals and verbal tenses are nonetheless context-dependent expressions. They simply require time-relative truth values for the sentences types or propositions in which they occur. Thus, in a world without minds items would still be past, present, and future, though in such a world they could not, of course, be judged to be so. In a world containing only colliding rocks, for example, the proposition that There is now a collision of rocks is true at some times and so collisions are present at those times. 50 Now at first blush, it might seem that Butterfield has simply given away the store for the B-theorist. If the tense of a sentence is part of its propositional content, then does not a view of truth as correspondence imply that reality is tensed? Indeed, Butterfield seems to affirm this himself, stating that the collisions mentioned in his illustration are present at the times when the propositions describing the collisions are true. His affirmation that items are past, present, and future in a world devoid of minds seems very difficult to square with a B-Theory of time. He denies that there are "perspectival facts;" but he never explains why such facts are not required by his propositions, nor does he give their truth conditions or say what makes them true. All he gives is a tu quoque argument concerning spatial indexicals: " ... no one wishes to infer that a description of reality is incomplete unless it specifies a 'here:' nor should we do so in the temporal case.,,51 On second reflection, however, perhaps a more charitable interpretation of Butterfield's view is possible. He seems to hold that propositions are temporal entities which change their truth values over time. The proposition that It is now J980 is true during 1980, but at no other time. (He must also hold, it seems, that propositions have different truth values in different places. The proposition that Cambridge is here is true in Cambridge, but false elsewhere.) Since truth-bearers are propositions, not sentence tokens, it is perfectly coherent to hold that the proposition that There are no tokens is true at a certain time and place. But, as we saw in our examination of the Old B-Theory, it is not clear how a coherent account of the truth conditions of such propositions can be given apart Butterfield, "Indexicals and Tense," pp. 70-74. So also Zdzislaw Augustynek, Time: Past, Present, Future, trans. Stanislaw Semczuk and Witold Strawinski, Nijhoff International Philosophy Series 30 (Dordrecht: Kluwer Academic Publishers, (991), p. 110. 49 Butterfield, "Indexicals and Tense," pp. 73-74. so Ibid., pp. 73-74. SI Ibid., p. 74.

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from tensed facts. Butterfield compares his view with David Lewis's modal realism: just as "actual" is a context-dependent expression referring relative to any world to just that world, so "now" is a context-dependent expression referring at any time to just that time. But Butterfield fails to take cognizance of the fact that on Lewis's theory "actual" is an indexical linguistic expression which is replaced in the propositional content expressed by a sentence by the specification of some world W, just as "now" is replaced by a time t. Butterfield, however, retains the indexical terms in specifying the propositional content, and therein lies the difficulty. Since a date-analysis of temporal indexicals is not open to him, Butterfield seems obliged to provide some sort of proposition-reflexive account of the truth conditions of a proposition whose content is tensed. But how is this to be done? One cannot maintain that the proposition p It is now 1980 is true iff p exists in 1980. For p exists in 1980 is always true. But p itself is usually false. If p is false, then it is also false that p exists in 1980 implies p. On the token-reflexive theory such an incoherence did not arise because if S is false then "S occurs in 1980" is also false. But on the proposition-reflexive view, the propositionp exists in 1980 is never false and so the biconditional sentence ''p iff p exists in 1980" is false. Smith, who like Butterfield accepts the reality of propositions with tensed content, also tries to provide tenseless, proposition-reflexive truth conditions for such propositions. 52 He asserts, in effect, that p is true when and only when p exists simultaneously with 1980. But this cannot be the truth conditions for p, since the sentential operator is not that of material equivalence, but a peculiar temporal operator "when and only when." This amounts to no more than saying that p is true just during 1980, which is, of course, correct, but does not state truth conditions for p. Smith attempts to justify the use of "when and only when" by stating that it brings out more clearly than "if and only if' the impermanence of p's possessing both truth and simultaneity with 1980. Such a justification is odd, since the biconditional operator as such does not imply that the properties ascribed to p by the sentences on each side of the operator are permanently possessed by p--for example, ''p is believed by John iff p is believed by Mary." Suppose, then, we substitute the biconditional operator for Smith's locution: p is true iff p exists simultaneously with 1980. Since p exists omnitemporally, p's existence is not simultaneous with 1980 in the sense of being coextensive, but it is simultaneous in the sense that p exists at every moment of 1980. So p is true iff p exists at every moment of 1980. This brings us right back to the incoherent proposition-reflexive view already discussed, for p is usually false, but the proposition that p exists at every moment of 1980 is never false. Thus it is with good reason that Smith shuns the biconditional operator in favor of "when and only when." I suspect that Smith realizes that this temporal locution does not state truth conditions, for he proceeds to re-phrase his truth conditions in terms of "if and only if' by adding dates: p at t iff p is simultaneous with 1980 at t. Now these are impeccable truth conditions; the only problem is that they are not the truth conditions for p or for any proposition variable in its truth value. They are the truth conditions for the tenseless proposition expressed by ''p-at-t'' or ''p is true at t." Such a proposition captures very nicely

52

Smith, Language and Time, sec. 4. 4.

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what Butterfield seemed to be saying: truth variable propositions are true at certain times and tense less truth conditions can be given for a proposition stating at what times such a proposition is true. But what has not been done is to provide tense less truth conditions for such propositions themselves. Hence, our first impression of Butterfield's position was correct: he has given away the store. In conceding that tense belongs to propositional content, he implies that reality is itself tensed. As for his tu quoque argument, we shall take that up in the sequel. It seems, therefore, that the New B-theorist has dealt no more successfully with the problem of untokened sentences than did his predecessor. We can coherently maintain neither that sentence types are true iff a token of that type would be true if it were uttered nor that propositions having tensed content exist but have truth conditions that do not involve real tense. Lest anyone think that we can make do in our account of the world with sentence tokens alone, we should remind ourselves that God knows how the world is wholly apart from sentence tokens, as we saw in our previous discussion. The New B-Theory is therefore untenable. 3. The New B-Theory conjlates the truth conditions of tensed sentences with the truth makers of tensed sentences. Throughout this entire debate there has gone unchallenged the implicit assumption on the part of the B-theorist that the provision of tenseless truth conditions is somehow relevant to the existence of tensed facts. If the truth conditions of a tensed sentence involve no reference to tensed facts, then tensed facts are presumably not needed to make the sentence true. The assumption is that what is stated as a tensed sentence's truth conditions is what makes the sentence true. That such an assumption is made by New B-theorists is easy to demonstrate. In introducing his token-reflexive account, Mellor says that tensed facts ... might still be what make tensed judgments true or false; ... But I will argue that actually quite a different fact makes this judgment true and that tensed facts are a myth.... I still have to supply my tenseless alternative, to say what makes tensed judgments true if tensed facts do not. ... The facts I am looking for must be undeniable facts, objective and tenseless, that will make tensed judgments true when they are true, and false when they are false. These facts ... will be my tenseless surrogates for the apparent facts of tense. 53

Similarly, Mellor's student Robin Le Poidevin asserts, "the statement that a given event is present (or past) is made true by that event's being located at a time simultaneous with (or earlier than) that of the statement, not by there being some non-relational property of 'presentness' exhibited (fleetingly) by either the event or the time at which it occurs"; "the facts which make a token tensed statement Mellor, Real Time, p. 34. " .. .I subscribe to the so-called 'token-retlexive' account of what makes tensed statements true or false, an account which lets me keep objective tensed truths and falsehoods while rejecting objectively tensed things, events, and facts" (Ibid., pp. 5-6). Cf. Mellor, "Fixity and coming true," p. 87; idem, ''Tense's Tenseless Truth Conditions," p. 171; idem, "I and Now," Proceedings of the Aristotelian Society 89 (1988-89): 81; idem, "An Interview with Professor Hugh Mellor," Cogito 7 (1993): 5. Even Priest, zealous to disprove tenseless facts, succumbs to this confusion: "We say what makes a sentence true, if it is, by giving its truth conditions. Thus, if we can spell out the truth conditions of all sentences (true or false) without mentioning a notion, that notion is certainly not part of reality" (Priest, "Tense and Truth Conditions," p. 162). That Priest can give tensed truth conditions even to tenseless sentences and thereby eliminate tenseless facts constitutes in my mind a reductio of the contlation of truth conditions and grounds of truth. 53

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concerning an event or state of affairs ... true concern the B-series relation between that event and the state of affairs referred to .... ,,54 Again, Oaklander claims that Mellor's token-reflexive account of tensed sentences' truth conditions "provides an objective basis for the truth value of any tensed sentence.,,55 Or again, MacBeath states, "if I were to say 'It is now 1989', what would make my utterance true ... is that my utterance is made in 1989.,,56 Hence, he straightforwardly affirms, "The facts in question ... are tenseless facts; but they make true tensed propositions," and "tensed propositions are made true by tenseless facts.,,57 Similarly, Keith Seddon affirms that tenseless truth conditions "make a tensed statement true.,,58 The assumption then is that what is stated as a tensed sentence's tense less, tokenreflexive truth conditions is what makes the tensed sentence true or provides a basis for its truth. But such an assumption is clearly confused: it conflates truth conditions with truth makers. The giving of truth conditions is a semantic exercise; specifying a truth maker for a statement's truth concerns ontology. One can layout semantic conditions which will permit one to determine for any sentence whether that sentence is true or false without saying anything at all about the ontological facts which make that sentence true. 59 Take, for example, sentences which express truths of mathematics or logic. Since necessary truths are mutually entailing, one can give adequate truth conditions for any necessary truth by means of another, for example, "A square is quadrilateral iff a triangle is trilateral." Yet no one would claim that what makes a square quadrilateral is the fact that a triangle is trilateral. Semantic truth conditions can be properly satisfied without specifying the basis for a sentence's truth. One could lay down adequate truth conditions for tensed sentences, for example, by stating that p is true iff God believes that p. But God's believing p is not the basis of p's truth; in fact, quite the opposite. Of course, as Mellor points out, there "must be more to meaning than truth conditions,,,6o but we are not now talking about meaning. Truth conditions need not give or have the same meaning as the sentence to be analyzed in order to fulfill their semantic function. Mellor might claim, however, that if a sentence gives both truth conditions and the meaning of the sentence under analysis that one thereby discloses what makes Robin Le Poidevin, Change, Cause, and Contradiction: A Defence of the Tenseless Theory of Time, Macmillan Studies in Contemporary Philosophy (London: Macmillan, 1991), pp. 13,4. 55 Oaklander, "Defense," p. 27; idem, "New Tenseless Theory," p. 290. 56 Murray MacBeath, "Omniscience and Eternity I," Aristotelian Society Supplementary Volume 63 (1989): 61. 57 Ibid., pp. 65, 66. 58 Keith Seddon, Time: a Philosophical Treatment (London: Croon Helm, 1987), p. 51. 59 On truth makers see the seminal piece by Kevin Mulligan, Peter Simons, and Barry Smith, "TruthMakers," Philosophy and Phenomenological Research 44 (1984): 287-321. They trace the roots of the notion of truth makers to the realist revival during the early part of the twentieth century. For thinkers like Russell, Wittgenstein, and Husserl there must be, in addition to truth bearers, whether these be sentences, propositions, or whatever, entities in virtue of which sentences and/or propositions are true. Such entities are variously identified as facts, states of affairs, etc. The discovery of a sentence's truth maker is quite a different exercise than the specification of its truth conditions, as is immediately evident from the fact that many types of true sentences have no truth makers. Cf. apropos remarks by John Perry on the varieties of truth conditions in A Companion to the Philosophy of Language, ed. Robert Hale and Crispin Wright, s.v. "Indexicals and Demonstratives" (Oxford: Blackwell Publishers, 1997), pp. 586-612. 60 Mellor, Real Time, p. 75. 54

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the sentence true and that such is what his token-reflexive truth conditions accomplish. But why think that merely giving the meaning of, rather than having the same meaning as, the analysandum is a sufficient condition, along with providing truth conditions, for discovering grounds of truth, especially when one recalls that "giving the meaning" means for Mellor something like "giving the rule of use"? According to the customary Tarski-schema for truth "It is now 1980" is true iff it is now 1980. Here the sentence stating the truth conditions also has the same meaning as the sentence under analysis. It is plausibly construed as also giving the grounds for the sentence's truth, namely, the tensed fact of 1980's being present. But why think that truth conditions which merely give the rule of use of the sentence tell us what makes the sentence true? In fact, an examination of the truth conditions for other sorts of sentences shows that supplying truth conditions and a rule of use is not sufficient to account for what makes a sentence true. Consider first the truth conditions supplied by possible worlds semantics for modal logic. According to that semantics a proposition is necessarily true iff it is true in all broadly logically possible worlds; a proposition is possibly true iff it is true in some broadly logically possible world. Accordingly, the proposition that D. H Mellor is an ardent B-theorist is possibly true iff in some possible world D. H. Mellor is an ardent B-theorist. Given these truth conditions, I understand the rule of use for the proposition under consideration. But the truth conditions do not inform me what are the grounds for the truth of the proposition. Possible world semantics furnish a sort of model for determining the possible or necessary truth value of propositions without pretending to tell us what makes these propositions true or false. As Plantinga remarks, we can't sensibly explain necessity as truth in all possible worlds; nor can we say that p's being true in all possible worlds is what makes p necessary. It may still be extremely useful to note the equivalence of p is necessary and p is true in all possible worlds: it is useful in the way diagrams and definitions are in mathematics; it enables us to see connections, entertain propositions and resolve questions that could otherwise be seen, entertained and resolved only with the greatest difficulty if at all. 61

Thus, possible worlds semantics for modal sentences constitute a counter-example to the claim that truth conditions supplying a rule of use disclose the grounds of a proposition's truth value. A second counter-example comes from similar semantics for counterfactual propositions. According to possible worlds semantics for counterfactuals, a "would" counterfactual is true in ex iff in all antecedent-permitting worlds which are most similar to ex, the consequent is also true. A "might" counterfactual is true in ex iff the consequent is true in some of the antecedent-permitting worlds most similar to ex. Thus, the proposition If Buchanan had won the Republican nomination in 1992, he would have lost the Presidential election is true iff in all worlds most similar to the actual world in which Buchanan wins the Republican nomination in 1992, he loses the Presidential election. These truth conditions also supply us with the correct rule of use of the counterfactual proposition. But once again, they do nothing to explain what makes the counterfactual proposition true. Again Plantinga Alvin Plantinga, "Reply to Robert Adams," in Alvin Plantinga, ed. James Tomberlin, Profiles 5 (Dordrecht: D. Reidel, 1985), p. 378.

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remarks, " ... we can't look to similarity, among possible worlds, as explaining counterfactuality, or as founding or grounding it. (Indeed, any founding or grounding in the neighborhood goes in the opposite direction.) We can't say that the truth of A ~ C is explained by the relevant statements about possible worlds, or that the relevant similarity relation is what makes it true.,,62 What makes these counterexamples particularly significant is that they both concern sentences governed by intensional operators, which puts them in the same class as tensed sentences, whose tense operators are also intensional in the sense that they are not truth-functional. 63 Since tense operators, like modal and counterfactual operators, are not truth functional, we should not expect that giving tense less tokenreflexive truth conditions of such sentences should reveal to us what make the sentences true, any more than do the truth conditions of modal and counterfactual sentences. The A-theorist could accept quite happily tenseless token-reflexive semantics for tensed sentences without esteeming the calculus for determining truth conditions under such a semantics as even relevant to the question of what makes tensed sentences true or false. Wholly apart from intensional contexts, the even deeper philosophical issue at stake here is the nature of conditionship. As Wertheimer and others have pointed out, there is an important difference between stating conditions and consequences and stating implication and entailment relations. 64 A biconditional operator does not state genuine conditions and consequences, otherwise a given fact is both a condition and a consequent of some other fact, as well as a condition and consequence of itself. Truth conditions are not really conditions in the proper sense of the word, for no relationship of consequence is involved. For example, "Socrates died" and "Xantippe became a widow" are logically equivalent and give an appropriate rule of use, but it would be fatuous to say that the former is true on the grounds or basis of the latter; quite the opposite. Stating mere truth conditions is not adequate for stating grounds of truth. In the case of the New B-theorist's tenseless

Ibid. See Nathan Salmon, "Reference and Infonnation Content: Names and Descriptions," in Handbook of Philosophical Logic, vol. 4: Topics in the Philosophy of Language, ed. D. Gabbay and F. Guenther, Synthese Library 167 (Dordrecht: D. Reidel, 1989), pp. 411-412, but especially idem, "Tense and Singular Propositions," in Themes from Kaplan, ed. Joseph Almog, John Perry, and Howard Wettstein (New York: Oxford University Press, 1989), pp. 362-366. Salmon points out that tense operators are not extensional operators by means of the following example: "2+2=5" and "It is cloudy" are equally false with respect to my actual context. But the tense operator "sometimes" has different consequences when these sentences are placed in its scope: "Sometimes 2+2=5" is false, but "Sometimes it is cloudy" is true. Since "sometimes" + present tense is not truth functional, it cannot be extensional. Salmon also points out that tense operators are not intensional either in the sense of being a function from a proposition to a truth value. For example, the sentences "The senior senator from California is a Republican" and "The present senior senator from California is a Republican" both have the same intension, or express the same proposition. But the sentences "Sometimes the senior senator from California is a Republican" and "Sometimes the present senior senator from California is a Republican" express different propositions due to the need for double indexing of the latter, the fonner sentence being true and the latter false. Salmon therefore regards tense operators as super-intensional operators operating on propositional matrices, e.g., the senior senator from California and the property of being a Republican. 64 Roger Wertheimer, "Conditions," Journal of Philosophy 65 (1968): 355-364; Jaegwon Kim, "Noncausal Connections," NOlls 8 (1974): 41-52.

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truth conditions for tensed sentences, I see no reason to think that these disclose the facts that make the tensed sentences true. On the contrary, if one accepts the need for truth makers, the A-theorist will insist that it is the facts stated as the tensed truth conditions of tensed sentences which explain any tenseless truth conditions that could be given. 65 The fact of 1980's being present makes "It is now 1980" (presently) true; therefore that token is (tenselessly) true iff it occurs in 1980. I am not persuaded that tenseless truth conditions for tensed sentences can be given; but my point is that even if they can, they are not what make the tensed sentences true, but are parasitic on the tensed facts, stated as the sentences' truth conditions, which do make such sentences true. MELLOR'S INDEXED B-THEORY Remarkably, in his revised Real Time II Mellor himself abandons the New BTheory of Language under the force of objections such as the above, particularly the New B-Theory's inability to provide truth conditions of tensed sentences which are not tokened. 66 But Mellor is not ready to embrace a tensed theory of time; instead he proposes what he calls the Indexical, or better, Indexed B-Theory of Language to replace the untenable New B-Theory.67 In proposing this new theory, Mellor clarifies that his interest is not so much in truth conditions of tensed sentences but in their truth makers. He claims that what both A- and B-theorists mean by "a beliefs truth condition is its so-called 'truthmaker', i. e. what in the world makes it true. What we disagree about is whether A-facts or B-facts ... make temporal beliefs true.,,68 Thus, one finds very little talk in Real Time II about truth conditions. Rather the concern is to deny that tensed facts are what make tensed sentences true. Indeed, Mellor is actually prepared to admit that there are tensed facts in the sense entailed by the disquotation principle; to give his example, "Jim races tomorrow" is true iff Jim races

E.g., Smith, Language and Time, sec. 4. 3. Since, however, I reject Smith's account of tensed truth conditions in favor of Priest's, I do not agree with Smith's reasons for the explanatory primacy of tensed facts. Nevertheless, the fact that tensed sentences require tensed truth conditions serves to answer the challenge of Clifford Williams, "The Date Analysis of Tensed Sentences," Australasian Journal of Philosophy 70 (1992): 199-200, that A-theorists must show that tensed and tenseless sentences differ not merely in their meanings, but in the states of affairs they describe. Williams appears to allow that tensed and tenseless sentences may have different truth conditions, but holds that the state of affairs described by a tensed sentence and its tenseless date-sentence counterpart may be the same, so that tensed facts have not been shown to exist. But a closer reading of Williams's remarks on p. 199 reveals that he both confuses truth conditions with the conditions requisite for our knowing certain sentence tokens to be true (i.e., alethic with cognitive conditions) and conflates truth conditions with sentences' meanings. In fact, Williams never states what the truth conditions for either tensed or tenseless sentences are. If he accepts Mellor's account, how does he remedy its defects? Ifhe rejects it, what does he propose in its stead? Our demonstration that tensed sentences require tensed truth conditions shows that the states of affairs described by tensed sentences do differ from those described by tenseless sentences (and this whether or not they make the sentences true). Against this argument, Williams poses a tu quoque riposte based on spatial indexicals, which we shall discuss in chap. 4. 66 D. H. Mellor, Real Time 11 (London: Routledge, 1998) pp. xi, 32. 67 Ibid., p. 34. 6' Ibid., p. xi. 65

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tomorrow. 69 This is a striking concession in light of the token-reflexive analysis defended in the original Real Time, for prima facie it coincides precisely with the Atheorist's argument from tensed language that a view of truth as correspondence implies the existence of tensed facts. 70 But Mellor insists that no such sense of "fact" "will settle the dispute between A- and B-theorists. For this does not tell us what makes it true, and hence a fact, that Jim races tomorrow.,,71 Notice that Mellor just assumes a truth maker ontology, which is a controversial assumption.72 The Atheorist might with some plausibility claim that he is far more certain of the reality of tensed facts on the basis of their ineliminability and indispensability than he is of the need for truth makers of tensed sentences. In any case, the A-theorist who does accept the need for truth makers will no doubt see the tensed facts corresponding to true tensed sentences as robust enough to serve as truth makers of those sentences. Presumably Mellor would point out that the disquotation principle would entail such facts as Cambridge is here, which no one, not even the A-theorist, regards as a truth maker. But, as we shall see in the next chapter, the A-theorist can plausibly offer a reductive analysis of such spatially "tensed" facts, an analysis not available for temporally tensed facts, and need not affirm the reality of any sort of indexical facts in order to affirm the objectivity of tense. Mellor goes on to claim that what is of importance in the present debate is not the facts which are "trivially true" in virtue of the disquotation principle, but facts "in a stronger truthmaker sense of 'fact' .,,73 Again, the question is whether the tensed facts which Mellor now seems to countenance might not be truth makers. In order to defeat the A-theorist's argument from the ineliminability of tense, Mellor must show that tensed facts are not truth makers. For even the demonstration that B-facts are truth makers does not entail that A-facts are not as well. It is a commonplace of discussions of truth makers that there is no one-to-one correspondence between truth makers and truths. Since Mellor now concedes the existence of tensed facts, Mellor must show them to be so effete that tensed sentences are not, so to speak, overdetermined by the facts, rendered true by both B-facts and A-facts. The Achilles Heel of the New B-Theory was its reliance on sentence tokens as truth bearers. So what will Mellor substitute in their place as the truth bearers in his Indexed Theory? He initially characterizes "A-truths" as "true A-beliefs" and speaks of such "a beliefs truth condition.,,74 But this is clearly problematic, since beliefs are not crucially different from sentence tokens as truth bearers-what about truths which no one believes? Mellor, however, soon expands the scope of his truth bearers to include not only beliefs, but also statements, sentences, and propositions. Ibid., p. 25. Recall premiss (10) of the argument outlined at the close of chapter 1. 71 Ibid., p. 25. 72 See, for example, the critique by Greg Restall, "Truthmakers, Entailment and Necessity," Australasian Journal of Philosophy 74 (1996): 331-340. In his "Truthmaker Realism," Australasian Journal of Philosophy 77 (1999): forthcoming, Barry Smith rejects the original theory crafted by Mulligan, Simons, and Smith, along with what he calls "truthmaker maximalism," the doctrine that every truth has a truth maker. In particular he makes the provocative suggestion that past- and future-tensed, contingent sentences may not have truth makers but had or will have truth makers. 73 Ibid. 7' Mellor, Real Time II, pp. 23, xi.

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Unfortunately, in contrast to the limpid exposition of Mellor's original book, Real Time II is a veritable terminological mare's nest. Mellor at first identifies propositions with "what sentences expressing beliefs mean.,,75 This is no mere slip, for he proceeds to state, "my belief that the earth is round is true if and only if the following are true: a statement of it; a sentence expressing it; and the proposition that is the meaning af this sentence and the cantent af this belief ... " 76 This usage is idiosyncratic, for the meaning of a sentence cannot be identified with what is normally called its propositional content; indeed, this was the chief insight of the New B-Theory in contrast to the Old. Detensers must break loose linguistic meaning from propositional content if they are to avoid objectively tensed facts. (Moreover, as we shall see, linguistic meaning cannot be identified with the contents of our beliefs either.) Now if by "proposition" Mellor means linguistic meaning, what does he mean by "statement"? He does not say. It is tempting to think that he means what we usually call a proposition. But that seems wrong, for he later rejects the existence of statements in this sense: What about statements, the entities postulated to distinguish what is said (a statement) from what we use to say it? We have good reasons to draw a distinction here, since we can use different sentences, e.g. in different languages, to say the same thing. But since we could draw the distinction just as well by saying that different sentences can express the same proposition, this is a weak reason for postulating statements as well as propositions 77

Here Mellor rejects the existence of "statements" (a.k.a. propositions) on the grounds that a common meaning (a "proposition") can be expressed by different sentences. In what sense, then, do statements exist? I think Mellor would say that statements are sentences reporting our doxastic attitudes: "I believe that. .. ," "I fear that. .. ," and so on. Mellor thinks the question of truth bearers is not in the end so important: For the issue here is not what the bearers of A-truth are-beliefs, statements, sentences or propositions-but what makes them true when they are true .... Whatever makes Abeliefs true at any A- or B-time will also make corresponding A-statements, A-sentences and A-propositions true at that time 78

On the contrary, the question of truth bearers is critical. For statements and sentences cannot solve the problems which brought down the New B-Theory of Language, since they do not exist at all times, nor can linguistic meanings do the job, since meanings are neither true nor false. Perhaps Mellor does intend to affirm the existence of what are customarily called propositions, his only mistake being to characterize a proposition as the meaning of a sentence. For example, he speaks of "my believing a proposition 'P' at a given A- or B-moment t" and treats propositions as truth bearers. 79 But if Mellor allows that the propositional content of tensed sentences includes the tense of the events described, then there is no denying that objective, tensed facts exist. Few, if any philosophers, would allow that there 75 76

77 78 79

Ibid., Ibid., Ibid., Ibid., Ibid.,

pp. 23-24 (my emphasis). p. 24 (my emphasis). p. 30. p. 24. p. 29.

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are propositions like Cambridge is here, an abstract object which has the property of being true only within the city limits of Cambridge but which lacks it everywhere else. But if Mellor is willing to allow tensed propositions as truth bearers, the debate is over. Whether they are ever believed or enunciated, such propositions exist and possess truth. It would then be very difficult to see how the facts corresponding with such propositions are not objective features of reality, even if Btheoretical truth makers also exist. So it is hard to see how Mellor could be talking about customary propositions as his truth bearers. That Mellor is not talking about ordinary propositions is further evident by his claim "B-facts can be tokens of A-propositions"-a conclusion he calls "crucial to the B_theory."so It is hard to know what to make of this. How can a fact be a token of a proposition? Neither sentence meanings nor customary propositions have tokens, nor do facts have types. In an attempt to bring some clarity to the discussion, Mellor fixes upon the following convention: "we may as well call statement types 'propositions,' ... keeping the word 'statement' for any spoken or inscribed ... token of a proposition."sl Mellor here speaks as if by "proposition" he means a sentence type. Again, he says, "If I say on I June that Jim races tomorrow, that statement is true; if I say it again on 2 June, that statement is false. Here are two tokens of the same A- proposition, one true and one false."s2 I take it, then, that Mellor is maintaining that his truth bearers include sentence types and that what he calls "propositions" are not propositions at all, but sentence types. It will be these truth bearers which he shall use to remedy the defects of the sentence token-reflexive account of the New B_Theory.s3 Mellor wants to show, then, that tensed sentence types are made true by tenseless facts. Letting P be a tensed sentence type and t a tenseless time, Mellor begins by observing, ... if 'P' is an A-proposition, my believing it at t is a B-fact, entailing nothing about how much earlier or later anything is than the present .... .. . even if! know on I June that Jim races tomorrow, which does entail that he races then, my token knowledge is still not an A-fact. For first, all it entails is that my belief that Jim races tomorrow is true, not that what makes it true is an A-fact, which is the point at issue. And second, my knowing on I June that Jim races tomorrow entails only the B-fact that he races on 2 June. It does not entail the A-fact that he races tomorrow, for it does not entail that I June is today."'

Mellor is mistaken here, and his mistake results from his failure to observe the rule of double indexing with respect to indexical terms. 85 For if I know (or knew) on 1 June that Jim races tomorrow, then double indexing requires that no matter where in the present or past 1 June is, the race will be tomorrow. If we know that Ibid. Ibid., p. 30. 82 Ibid., p. 31. 83 For another attempt to rescue the New B-Theory by appeal to sentence types, see L. A. Paul, "Truth Conditions of Tensed Sentence Types," Synthese III (1997): 53-71 and the critiques by Quentin Smith, "The 'Sentence-Type Version' of the Tenseless Theory of Time," Synthese (forthcoming); William Lane Craig, "On the Truth Conditions of Tensed Sentence Types," Synthese (forthcoming). 84 Mellor, Real Time II, pp. 29-30. 85 Recall our discussion in chap. I, pp. 6-9. 80

8!

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"tomorrow" refers to 2 June, then my knowing on 1 June that Jim races tomorrow entails that today is 1 June. Accordingly, what I know on 1 June is no mere B-fact, but an A-fact of some sort. Otherwise what I know on 1 June is not that Jim races tomorrow but at most that Jim races on the following day, or on the next day. So even if my believing Pat t is a B-fact, it does not follow that what I believe or know is some B-fact. Still it is obviously correct that my believing P at t can be construed tenselessly, even if P is tensed. Now with respect to tokens of P, Mellor is content to stick with the New B-Theory: what makes a token of Jim races tomorrow true is "the fact that the token is located a day earlier than the day on which Jim races."S6 So for any sentence type P about any event e, "any token of 'P' is true if and only if it is as much earlier or later than e as 'P' says the present is than e."S? But if there are no tokens of P, then this token-reflexive analysis cannot properly account for P's truth or falsity. So Mellor proposes to substitute times for tokens in this analysis. The new account reads: "any A- proposition 'P' about any event e is made true at any t by t's being as much earlier or later than e as 'P' says the present is than e."gg Mellor calls this account indexical because it indexes the truth values of tensed sentence types to times. P is not made true simpliciter, but at a time. Mellor thinks that such an account will be acceptable to A- and B-theorists alike, since A-theorists can plug in A-series locations for t and B-theorists B-series locations. His point is that either way will work. B-facts are enough, so that the ineliminability of tense from language does not require the existence of tensed facts in the robust sense of truth makers. The strength of the New B-Theory was that it claimed to state the truth conditions-and even, in Mellor's mind, the truth makers-of any tensed sentence simpliciter. But Mellor's Indexed Theory does not do either. s9 We are left wondering as to the truth conditions of P. The revised account cannot be construed in truth conditional terms, for then we should have: P is true at t == t is as much earlier or later than e as P says the present is than e

Here we have truth conditions, not for P, but for P's being true at t. If t is a B-time, then tense has been left altogether out of account. Considered as giving us a truth maker of P 's truth, the indexed account again fails to tell us what makes P true-it only tells us what ostensibly makes P true at t. But as we saw in our discussion of tensed truth conditions, we want to know what makes (present-tense) P true. We want to know, not what makes Jim races tomorrow true on June 1, but what makes it true that Jim races tomorrow or that Jim is racing. If tensed sentence types need truth makers, then we need tensed facts as the truth makers of such tensed sentence Mellor, Real Time II, p. 31. Ibid. 88 Ibid., p. 34. 89 The same problems attend Tooley's formulation of the Indexed B-Theory (Tooley, Time, Tense and Causation, pp. 200-201). According to Tooley, any utterance, at time t*, of the sentence "Event E is now occurring" is true at time t", It is true at time t that E lies in the present at time t*. This analysis provides neither truth conditions nor truth makers for "E is now occurring." 86

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types. For if there are no tensed truth makers, then it is inexplicable why P is truenot true at t, mind you, but simply true. CONCLUSION In summary, then, the New B-Theory of Language is as beset with serious difficulties as was the Old. New B-theorists agree that tense is ineliminable and indispensable but contend that that fact does not prove the reality of tense because tenseless token-reflexive truth conditions can be given for tensed sentences, so that ontological tense becomes gratuitous. But we have seen that the New B-Theory is logically defective in that it violates the implication relations in its truth conditions of tensed sentences, can give no coherent account of the truth conditions of untokened tensed sentences, and conflates the truth conditions with the truth makers of tensed sentences. New B-theorists have therefore failed to justify both premiss 1.

The truth conditions of tensed sentences can be expressed in a tense less metalanguage.

and premiss 3.

There are no facts expressed by tensed sentences other than those expressed as their truth conditions.

which underlay their inference that tensed facts are unnecessary. Quite the contrary, we have seen that it is plausible that both the truth conditions and grounds of truth of tensed sentences must involve tensed facts. The most recent rescension of the B-Theory, namely, the Indexed B-Theory of Language, abandons sentence tokens for sentence types and the provision of tokenreflexive truth conditions for the specification of tense less truth makers. By admitting the reality of tensed facts, as required by tensed truth bearers and a view of truth as correspondence, the Indexed Theory fatally compromises the tense less theory of time, unless it can be shown that tensed facts are too effete to serve as truth makers. But this the Indexed Theory does not even try to do. It simply offers to supply tenseless truth makers as well. Moreover, it fails even in that task, since it cannot tell us what makes a tensed truth true. It is thus impotent to stave off the inference to objectively tensed facts.

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e have seen in the foregoing chapters that tensed thought and language seem to necessitate the reality of tense. But all this still leaves us with the Btheorist's tu quoque argument, one of the most powerful in his arsenal: If the Atheorist's arguments for the reality of tense are correct, then there must be spatially "tensed" facts as well, which no one will admit. Accordingly, in this chapter we shall examine this final line of defense of the B-theorist. TEMPORAL AND SPATIAL "TENSES" So important is the tu quoque argument that Mellor devotes half a chapter to it. 1 He explains that the spatial analogues of dates are the spatial positions of things and events on maps, specified, for example, by latitude and longitude on the Earth's surface. The key feature of dates, as opposed to tenses, is that they are given by fixed spatial or temporal relations. Just as "World War II ends in 1945" is true whenever it is said, so "Cambridge is 52° North" is true wherever it is said. The spatial analogue of "now" is "here," and spatial tenses indicate how near or far something is from here. Any such indication which contains here is a spatial present tense, for example, less than a mile away. Analogues of the past- and future-tenses would be ten miles south of here and ten miles north of here. Spatial tenses, like temporal tenses, vary in a way that their corresponding dates do not. To someone in Cambridge, Cambridge is here and London is 60 miles to the South. But to someone in London, London is here and Cambridge 60 miles to the North. The spatial tenses of Cambridge and London vary systematically with spatial dates, just as temporal tenses vary with temporal dates. But spatial tenses, proceeds Mellor, can be explained away by means of tokenreflexive truth conditions. A token that London is 60 miles to the South is true at a spatial location which is 60 miles north of London, and false everywhere else. "Spatially tensed facts are redundant-they are not needed to account for the objective truth and falsity of simple spatially tensed sentences and judgments.,,2 "No one believes there are really spatially tensed facts such as London being sixty miles away from here.,,3 Nor is anyone impressed by the evident fact that all our experience happens to us here, wherever that may be. This is the spatial D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), pp. 58-66. Ibid., p. 63. Ibid., p. 64.

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analogue to the so-called presence of experience, and it constitutes the basis of our knowledge of other spatially tensed truths. Mellor observes, The spatial presence of experience should be as striking and central a phenomenon as its temporal presence is. But of course it isn't. We all know that the spatial presence of experience is a token-reflexive tautology: my experiences are wherever I am, so the token-reflexive definition of the spatial present tense makes me bound to be right if I judge them to be happening here 4

Mellor concludes, In short, despite there being spatial analogues of all the phenomena that have led many philosophers to believe in real temporal tenses, nobody believes in real spatial tenses. No one thinks that as well as being at latitude 52° North and longitude 0° East, sixty miles North of London, etc., Cambridge also has such spatially variable properties as being here. Whatever their views on time, all parties agree that, so far as space is concerned, things and events are--literally-neither here nor there. 5

Mellor might well have added that spatially tensed or indexical language is just as untranslatable and indispensable as temporally indexical language. Some of John Perry's memorable illustrations of "the essential indexical," such as Rudolf Lingens's being lost in the stacks of the Stanford Library, involve the need to have self-locating beliefs with respect to space. So unless one is willing to posit personal, temporal, and spatial subjective facts, "one cannot," in the words ofLe Poidevin and MacBeath, "argue from the ineliminability of tensed beliefs to the existence of tensed facts. For there would then be no reason to reject the argument from the ineliminability of spatially indexical beliefs to spatially subjective facts.,,6 The same arguments alleged to prove the reality of temporal tenses would also require us, it seems, to posit real spatial tenses, which is surely a sort of reductio ad absurdum of those arguments. DIRECT REFERENCE AND THE TU QUOQUE ARGUMENT It is at this juncture that the New B-Theory of Language overlaps with the new Theories of Direct Reference in philosophy of language, and an evaluation of the tu quoque argument requires that we examine more closely how such theories deal with the semantics of tense and indexicals. Given our interest in that particular facet of the theory, we may abstain from a discussion of the Direct Reference Theory's characteristic tenet that singular terms refer not by means of definite descriptions, but by including as constituents of propositions the concrete objects themselves and the properties ascribed to them, except insofar as that tenet becomes relevant to our concern with tense and indexical expressions. It will be recalled that one of the great difficulties facing both Russell and Frege was how to account for the cognitive significance of tensed and indexical expressions, given their view that the objects of our beliefs are tenseless, nonIbid. Ibid. Robin Le Poidevin and Murray MacBeath, "Introduction," in The Philosophy of Time, ed. R. Le Poidevin and M. MacBeath, Oxford Readings in Philosophy (Oxford: Oxford University Press, 1993), p. 3.

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indexical propositions; that is to say, if the propositional content of our beliefs is tenseless and non-indexical, then how is it that we find ourselves in belief states which are characterized by tense and indexicality? 7 It was their inability to account for the cognitive significance of tensed and indexical expressions which rendered them incapable of explaining timely action, and this failure led to the downfall of the Old B-Theory of Language. Similarly, on the New B-Theory, knowing the tenseless truth conditions of tensed and indexical expressions is useless for timely action without what Mellor calls "the presence of experience," which is, in effect, the cognitive significance of "I," "now," "here," and the present tense. The viability of the New B-Theory in explaining timely action apart from tensed facts depends on the adequacy of its account of the cognitive significance of tense and indexicals. Under the pressure of such concerns, Russell eventually abandoned the translation thesis of the Old B-Theory, holding that indexicality is ineliminable from language. 8 The seeds of destruction of the Old B-Theory were sown in Frege as well and eventually grew into the new Theory of Direct Reference. Immediately after Frege's discussion of temporal indexicals in "Der Gedanke" comes a fascinating excursus on the problems posed by the first-person indexical "I." Suppose Dr. Gustav Lauben says, "I was wounded," and that Leo Peter reports sometime later to Herbert Gamer, "Dr. Gustav Lauben was wounded." Suppose further that the Herren Peter and Gamer each associate definite descriptions with the proper name "Dr. Gustav Lauben" which, while uniquely picking out Lauben, are different and not known to be accurate by the other party. Gamer, therefore, does not associate the same propositional content with the sentence "Dr. Gustav Lauben was wounded" as Peter intended to express by that sentence. For each of the two, the same sentence has a different sense or meaning and therefore different propositions are grasped by them. Indeed, each could believe that the proposition grasped by the other is false, while accepting as true the proposition he grasps. Frege concludes, Accordingly, with a proper name, it is a matter of the way that the object so designated is presented. This may happen in different ways, and to every such way there corresponds a special sense of a sentence containing the proper name. The different thoughts thus obtained from the same sentences correspond in truth-value, of course; that is to say, if one is true then all are true, and if one is false then all are false. Nevertheless the difference must be recognized 9

Here Frege introduces the idea of a mode of presentation of a referent. For Frege the mode of presentation is the sense itself. The referent of a singular term is presented to us in different ways by the singular term's being given different

For facility of expression I shall call a proposition "indexical" just in case the correct linguistic expression of it involves indexical terms; if not I call it "non-indexical." Similarly, I call a proposition "tensed" just in case its correct linguistic expression involves tense; otherwise I call it "tenseless." • See Bertrand Russell, Human Knowledge: Its Scope and Limits (New York: Simon & Schuster, 1948), pp. 77, 84-93; for discussion, see Janet Farrell Smith, "Russell on Indexicals and Scientific Knowledge," in Rereading Russell, ed. C. Wade Savage and C. Anthony Andersen, Minnesota Studies in the Philosophy of Science 12 (Minneapolis: University of Minnesota Press, 1989), pp. 122-125. 9 Gottlob Frege, 'Thoughts," in Logical Investigations, trans. P. T. Geach and R. H. Stoothoff, ed. with a Preface by P. T. Geach. Library of Philosophy and Logic (Oxford: Basil Blackwell, 1977), p. 12.

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descriptional content, with the consequence that different propositions are expressed by the same sentence. Suppose now that Rudolf Lingens was present when Dr. Lauben spoke and later hears what Peter reports. Suppose that Lingens and Peter both understand by the name "Dr. Gustav Lauben" the doctor living at a certain address. They would then grasp the same proposition via Peter's utterance. So if Lauben's indexical sentence expresses the same proposition as does Peter's utterance, Lingens will know at once that the same incident is being spoken of. But suppose Lingens does not know Lauben personally and so does not know that the man whom he heard say, "I was wounded" was in fact Dr. Lauben. In such a case Lingens cannot know that the same incident is in question. So in this case, says Frege, the proposition expressed by Peter is not the same as that expressed by Dr. Lauben. The implication is that, in line with Frege's principles, Lauben's indexical utterance has a different sense than the non-indexical sentence. But what sense is that? Frege answers, Now everyone is presented to himself in a special and primitive way, in which he is presented to no-one else. So, when Dr. Lauben has the thought that he was wounded, he will probably be basing it on this primitive way in which he is presented to himself. And only Dr. Lauben himself can grasp thoughts specified in this way. But now he may want to communicate with others. He cannot communicate a thought he alone can grasp. Therefore, if he now says, 'I was wounded,' he must use 'I' in a sense of 'he who is speaking to you at this moment;' by doing this he makes the conditions accompanying his utterance serve towards the expression of a thought. 10

Perry has said of this passage that "nothing could be more out of the spirit of Frege's account of sense and thought."l1 In their Preface to Frege's essay, Geach and Stoothoff observe, " ... Frege affIrms (I) that any thought is by its nature communicable, (2) that thoughts about private sensations and sense qualities, and about the Cartesian I, are by their nature incommunicable. It is an immediate consequence that there can be no such thoughtS.,,12 If Dr. Lauben is not grasping a private, fIrst-person proposition, then the mode of presentation of himself to himself must not be by means of any sense of his proper name. There must be a mode of presentation which is outside the bounds of sense by means of which one grasps the same proposition that one's hearer does and yet in a way in which the cognitive signifIcance of that proposition is different for oneself and one's hearer. Unfortunately, Frege's theory cannot accommodate such a view, since, as we have seen, he explicitly affirms (3) that the mode of presentation of a referent is the sense of the singular term denoting it and that (4) the proposition expressed by a fIrstperson indexical sentence is not the same proposition as that expressed by any nonindexical sentence containing a singular term referring to the same person. Direct Reference theorists have taken inspiration from Frege's notion of a mode of presentation of a referent to attempt to formulate a consistent theory of reference which permits the cognitive signifIcance of a proposition being grasped to vary from person to person without admitting private or indexical propositions. In other words, Direct Reference theorists retain Frege's tenets (1) and (2), while abandoning 10 11

12

Ibid., pp. 12-13. John Perry, "Frege on Demonstratives," Philosophical Review 86 (1977): 474. P. T. Geach and R. H. Stoothoff, "Preface," to Logical Investigations, p. vii.

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(3) and (4). Direct Reference Theories are neo-Fregean in that on such theories the propositional content of a sentence is tenseless and non-indexical. A proposition on such theories is usually said to be a singular proposition: a sort of abstract entity which has as constituents the things or events described and the properties attributed to them. It is not denied that proper names have descriptive content associated with them, but it is denied that the referent is fixed by means of such descriptions. Singular terms refer directly to their denotata in the singular propositions expressed by sentences in which such terms occur, without any mediation by definite descriptions. So far as our inquiry is concerned, Direct Reference theorists' key difference with Frege is their breaking loose linguistic meaning from propositional content. The linguistic meaning of tensed and indexical sentences will be determined by the conventional rules of use for tense and indexicals in the language being used. For example, the rule of use for "I" is that it refers to the tokener of the sentence in which it occurs. Thus, the sentence "I was wounded" has the same linguistic meaning regardless of when and by whom it is token ed, but it expresses different propositions on different occasions of use. The term "I" will refer relative to one context to Dr. Lauben, but to someone else relative to another context. Similarly with tense: the property of being wounded must be ascribed to the person in question relative to a time. Thus, the propositional content of the sentence under consideration is, on one occasion of use, fully expressed by "Dr. Lauben is wounded on April 16, 1908." Spatial indexicals require a similar treatment: "It's raining hard here," while having the same linguistic meaning upon every occasion of use, expresses a propositional content like It rains hard on December 4, 1991, in Brussels, Belgium on one particular occasion. Kaplan calls the linguistic rules governing the use of indexical expressions the character of an expression, in contrast to its content. 13 Characters, he says, can be represented as functions from contexts to contents. A competent speaker knows more than the propositional content of "I" when he uses it; he also recognizes that the proper use of "I" is to refer to the speaker. Similarly, he knows that "now" refers to the time of the utterance and "here" to the place where it occurs. So as not to fall into the difficulties occasioned by untokened sentences on the token-reflexive analysis, Kaplan emphasizes the distinction between a context of use and circumstances of evaluation. Contexts of use have agents, but circumstances of evaluation include counterfactual situations, which generally do not. For example, the proposition expressed by the token "I do not exist" would be true in circumstances in which I do not exist, including those in which no agents exist. Thus, the meaning of indexical terms is relevant only to determining a referent in a context of use and not to determining a relevant individual in a circumstance of evaluation. If we took the meaning to be the propositional constituent, then in saying "I do not exist," the proposition would be true in a circumstance of 13 David Kaplan, 'The Logic of Demonstratives," in Contemporary Perspectives in the Philosophy of Language, ed. Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein (Minneapolis: University of Minnesota Press, 1979), pp. 403-407; idem, "Demonstratives: an Essay on the Semantics, Metaphysics and Epistemology of Demonstratives and Other Indexicals," in Themes from Kaplan, ed. Joseph Almog, John Perry, Howard Wettstein (Oxford: Oxford University Press, 1989), pp. 505-521.

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evaluation iff the speaker of the circumstances does not exist in the circumstances, which is absurd. Rather the actual context of use is employed to determine the relevant individual, time, or place, and then we query the various circumstances of evaluation with respect to that individual, that time, or that place. Kaplan's analysis brings to the fore the difficulty of dealing with negative existential propositions on the Direct Reference Theory, but we may leave that aside for now. The point is that the linguistic meaning of tensed and indexical expressions as given by English grammar determines the propositional content of a sentence containing such expressions relative to a context, time, and place but is not a part of that propositional content. Kaplan summarizes his view of indexical expressions: In the case of these words, the linguistic conventions which constitute meaning consist of rules specifying the referent of a given occurrence of the word ... in terms of various features of the context of the occurrence. Although these rules fix the referent and, in a very special sense, might be said to define the indexical, the way in which the rules are given does not provide a synonym for the indexical. The rules tell us for any possible occurrence of the indexical what the referent would be, but they do not constitute the content of such an occurrence. Indexicals are directly referential. The rules tell us what it is that is referred to. Thus, they determine the content (the propositional constituent) for a particular occurrence of an indexical. But they are not part of the content (they constitute no part of the propositional constituent).... Direct occurrences of an indexical (in different contexts) may not only have different referents, they may have distinct meanings in the sense of content.... But there is another sense of meaning in which, absent lexical or syntactical ambiguities, two occurrences of the same word or phrase must mean the same .... This sense of meaning-which I call character-is what determines the content of an occurrence of a word or phrase in a given context. For indexicals, the rules of language constitute the meaning in the sense of character. 14

Kaplan and Perry exploit the divorce between linguistic meaning and propositional content in order to explain cognitive significance. Although the sentences "The meeting starts now" and "The faculty meeting starts at noon, September 15, 1976, at Stanford University" express on a certain occasion of use the same proposition, they have a radically divergent cognitive significance in light of the different linguistic meanings they possess. The same propositional content is grasped under different modes of presentation by the cognizers and thus has a different cognitive significance for each of them. Frege's notion of the mode of presentation is no longer identified with the descriptional content of a singular term but is interpreted by Kaplan and Perry to be a way of grasping the propositional content of an expression via its linguistic meaning. Indeed, Kaplan identifies a character with a mode of presentation and in tum with an expression's cognitive significance: the cognitive significance of a phrase, he says, is to be identified with its character, the way the content is presented to us. IS What cognitive content presents Dr. Lauben to himself, asks Kaplan, but to nobody else? The answer is simply that Dr. Lauben is presented to himself under the character of "I." Similarly, "now" "is presented in a particular and primitive way, and this moment cannot be · ·m the same way. ,,16 presented at any 0 ther tune

14

IS 16

Kaplan, "Demonstratives and Other Indexicals," pp. 523-524. Ibid., p. 530. Ibid., pp. 533-534.

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Perry emphasizes that behavior is linked, not to propositional content, but to the mode of presentation of that content. For example, if someone believes "I am about to be attacked by a bear" and someone else believes in reference to him "He is about to be attacked by a bear," their beliefs both have the same propositional content, but their behavior will be different because this same content is grasped under different modes of presentation in virtue of the linguistic rules for "I" and "he." The one person climbs a tree to escape, while the other goes for help because the propositional content has for them a divergent cognitive significance. Similarly, if, as once actually happened to Ernst Mach,17 I see myself in a mirror without realizing that it is my own reflection and think "He is a shabby-looking, old teacher," I shall have a different belief state than I shall once I realize that it is my own likeness I see, even though identical propositional content is expressed by my coming to believe "I am a shabby-looking, old teacher." Only being in the latter belief state might induce me to improve my appearance. Paraphrasing Perry, Kaplan summarizes their view of cognitive significance and behavior: Why should we care under what character someone apprehends a thought, so long as he does? I can only sketch the barest suggestion of an answer here. We use the manner of presentation, the character, to individuate psychological states, in explaining and predicting action. It is the manner of presentation, the character and not the thought apprehended, that is tied to human action. When you and I have beliefs under the common character of 'A bear is about to attack me,' we behave similarly .... Different thoughts apprehended, same character, same behavior. When you and I both apprehend that I am about to be attacked by a bear, we behave differently... Same thought apprehended, different character, different behaviors. 18

The New B-theorist might well find Theories of Direct Reference to be quite congenial. By breaking linguistic meaning away from propositional content, one can associate tense with cognitive significance as determined by linguistic meaning and associate facts with tense less propositions expressed by tensed sentences. Because one has propositions as truth bearers, one can divest oneself of all the incoherencies and confusions of the token-reflexive analysis while maintaining the key contention of the New B-Theory that language is irreducibly tensed but that reality is tenseless. TENSE AND DIRECT REFERENCE THEORIES Tense and Propositions

But the A-theorist will rightly want to know on what basis the Direct Reference theorist knows that the propositional content expressed by tensed sentences is tenseless. This question has special point, since the A-theorist could accept the 17 E. Mach, Die Analyse der Empjindungen, 5th rev. ed. (lena: Gustav Fischer, 1906), p. 3. Mach relates, "I once boarded an omnibus after a very strenuous overnight train trip, just as another man entered from the other side. 'What a run-down old schoolmaster!' I thought. It was I myself, for across from me was a large mirror." 18 Kaplan, "Demonstratives and Other Indexicals," p. 532.

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Direct Reference Theory's account of indexical expressions without holding that tense and A-non-indexicals are thereby eliminated from propositional content. One could hold that propositions are tensed, but non-indexical; that indexical expressions are, indeed, peculiarly ego-centric, but that tense is not eliminated from propositional content because tense is not confined to indexical expressions. Indeed, Kaplan's own view can be interpreted along these lines. His theory is presented explicitly as an account of indexical expressions such as "I " "you" "here" "now" and so forth, not of verbal or non-indexical ten~e.19 He observes' that if ~e take' a present-tensed sentence like "I am writing" to involve implicitly an indexical, such that the sentence means "I am writing now," then we shall take the content to be the proposition "Kaplan is writing at 10 a.m. on 3/26/77." In this case, he says, what is said is eternal; it does not change its truth value over time, and the sentence will express different propositions at different times. 20 But Kaplan neither clearly endorses nor provides any argument for such a view, and his theory of indexicals does not require it. The A-theorist should hold on the basis of the linguistic data surveyed in chapter 1 that while "I am writing now" entails "I am writing," the latter neither entails nor has the same meaning as the former, since the present tense ascribes only an A-determination, not an A-position, whereas "now" does both. Moreover, the A-theorist could hold that the present tense is not ego-centric or token-reflexive, while, in accordance with Direct Reference Theories, "now," like The difference between the two becomes evident in other indexicals, is. propositions not involving agents. The A-theorist could agree that it was not true 120 million years ago that The largest trachodon is now laying her eggs here on the beach, but insist that the non-indexical, present-tense proposition that The largest trachodon is laying her eggs on the beach was true at that time. A tensed, indexicalfree sentence would express the same proposition on each occasion of use, but the proposition might sometimes be true and sometimes false. Kaplan's theory could thus be employed to eliminate temporal and spatial indexicals from propositional content without eliminating tense, thereby undercutting the New B-theorist's tu quoque argument. All that is required to determine such tensed propositional content is that the context of use relative to which the indexical sentence is analyzed be ontologically tensed, and Kaplan seems to endorse such an ontology, when he writes, There are certain categories of objects which clearly have no causal effects upon us. If such objects can be given names, the view that names are among the causal effects of their referents cannot be correct. I have in mind future individuals and merely possible individuals. Such putative entities are non-existent. * .Past individuals are also, on my view, non-existent, but they do affect us causally. 21

Here Kaplan clearly embraces an A-theoretic, presentist ontology, according to which past and future things are unreal. If the propositional content of indexical sentences is analyzed relative to contexts and times which are not merely tense less

19 20

21

Kaplan, "Logic of Demonstratives," p. 40I. Kaplan, "Demonstratives and Other Indexicals," p. 503. Kaplan, "Afterthoughts," in Themesfrom Kaplan, p. 607.

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dates, but onto logically tensed times, then the propositional content determined will be non-indexical, but tensed. It is important, therefore, that we ask why propositions must be tenseless. Nathan Salmon has addressed this issue and his arguments will repay examination. According to Salmon the propositional content of a sentence is the same as its information content, and " ... all information is eternal. The eternalness of information is central and fundamental to the very idea of a piece of information, and is part and parcel of a philosophically entrenched conception of information content.,,22 He cites Richard Cartwright to prove that the meaning of a present-tense sentence is not its information content: Consider, for this purpose, the words 'It's raining'. These are words, in the uttering of which, people often (though not always) assert something. But of course what is asserted varies from one occasion of their utterance to another. A person who utters them one day does not (normally) make the same statement as one who utters them the next; and one who utters them in Oberlin does not usually assert what is asserted by one who utters them in Detroit. But these variations in what is asserted are not accompanied by corresponding changes in meaning. The words 'It's raining' retain the same meaning throughout.... [One] who utters [these words] speaks correctly only if he [talks about] the weather at the time of his utterance and in his (more or less) immediate vicinity. It is this general fact about what the words mean which makes it possible for distinct utterances of them to vary as to statement made.... They are used, without any alteration in meaning, to assert now one thing, now another. 23

Cartwright's argument concerns the constancy of information over space as well as time. Salmon then cites G. E. Moore to show that a tensed sentence asserted on two different occasions expresses two different propositions: As a general rule, whenever we use a past tense to express a proposition, the fact that we use it is a sign that the proposition expressed is about the time at which we use it; so that if I say twice over 'Caesar was murdered', the proposition which I express on each occasion is a different one-the first being a proposition with regard to the earlier of the two times at which I use the words, to the effect that Caesar was murdered before that time, and the second a proposition with regard to the latter of the two, to the effect that he was murdered before that time. So much seems to me hardly open to question. 24

It must be said, however, that these are far from compelling arguments and seem to amount to little more than assertion. Cartwright's point that the linguistic meaning of a sentence may differ from its propositional content is a contention which the A-theorist may happily accept, especially with respect to indexical sentences. But why think that someone who says "It's raining" on one day and again the next does not make the same statement? Why can the same statement not be true one day and false the next? And if reality is tensed, why is it not enough, in order to speak correctly, to say that "It is raining in Detroit"? And if we do add a date to the propositional content, why must the proposition be tenseless? Why not a tensed verb, as in the proposition that It was raining in Detroit on December 2, I949? Indeed, does not this tensed proposition contain some important information Nathan Salmon, "Tense and Singular Propositions," in Themesfrom Kaplan, p. 342. Richard Cartwright, "Propositions," in Analytical Philosophy, ed. R. Butter (Oxford: Basil Blackwell, 1966), pp. 92-94. 24 G. E. Moore, "Facts and Propositions," in idem, Philosophical Papers (New York: Collier Books, 1962), p. 7I. 22 23

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which a tense less one omits? I do not see that Cartwright says anything to answer these questions. As for Moore's statement, appeal to common usage hardly supports his point. On the contrary, when one says "Caesar was murdered" the proposition expressed does not seem to be about the time of use at all, but about some past time or event. Two successive uses of this sentence seem to express exactly the same thing, that Caesar's murder is past. Ever since 44 BC precisely the same past-tense proposition seems to be truly expressed whenever this sentence is uttered. 25 It seems to me, therefore, that the question of the tenselessness of propositions is scarcely closed due to Cartwright or Moore's considerations. Salmon next provides some argumentation of his own to show that information is tenseless. Picking up on Frege's illustration, he maintains, Six months from now, when the tree in question is no longer covered with green leaves, the sentence (2) This tree is covered with green leaves uttered with reference to the tree in question, will express the information that the tree is then covered with green leaves. This will be misinformation; it will be false. But that information is false even now. What is true now is the information that the tree is covered with green leaves, i.e., the information that the tree is now covered with green leaves. This is the information that one would currently express by uttering sentence (2). It is eternally true, or at least true throughout the entire lifetime of the tree and never false. There is no piece of information concerning the tree's foliage that is true now but will be false in six months. 26

Notice that the first sentence of the above citation does not assert a B-determination, a tenseless date, but an A-determination: six months from now, (2) will express the information that the tree is then covered with green leaves. The "then" indicates that the information that will be expressed when the time comes is The tree is covered with green leaves, which is present-tensed, not tenseless. That information is not false now; it is (ex hypothesi) true now. Salmon gratuitously infers that a presenttense verb entails an indexical "now." But since tensed verbs ascribe Adeterminations without A-positions, whereas "now" ascribes both, that inference is incorrect. Thus, (2) does not express the information that the tree is now covered with green leaves. And even if it did, how could such information possibly be eternal, since "now" ascribes, not a B-position, but an A-position? Salmon provides no justification for a B-theoretical re-interpretation or translation of "now" in opposition to the linguistic data, not to speak of his de-tensing the verb. The information that is true now but false in six months is The tree is covered with green leaves (because in six months this tensed proposition will be false). Moreover, if propositions can contain temporal indexical elements, then the information expressed by "The tree is now covered with green leaves" will be false at any other time than the present, regardless of the tree's foliage, because the A-position referred to by "now" does not obtain at that time. Such an indexical proposition is identical with the proposition expressed by "The tree is covered with green leaves at t," where "is" is present-tensed and "f' is a date. At those other times either the 25 So also William and Martha Kneale, "Propositions and Time," in G. E. Moore: Essays in Retrospect, ed. Alice Ambrose and Morris Lazerowitz, Muirhead Library of Philosophy 9 (London: George Allen & Unwin, 1970), p. 232. 26 Salmon, "Tense and Singular Propositions," p. 344.

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proposition expressed by "The tree will be covered with green leaves at t" or by "The tree was covered with green leaves at t" is true. Salmon just assumes that when a time t is infused into the propositional matrix , the information is "eternalized" and so omnitemporally true or false. But that assumption is gratuitous, since the A-theorist will want to know why the inherence of the property in the tree at t is tenseless, rather than tensed. Salmon goes on to argue, appealing to an example from Mark Richard,27 that the tenselessness of cognitive information is reflected in our ordinary ascriptions of propositional attitudes. For if the objects of belief were not eternal, then from l.

In 1971 Mary believed that Nixon was president, and today she still believes that,

we could legitimately infer 2.

Today, Mary believes that Nixon is president,

which is insulting both to Mary and the logic of English. Rather we should infer 3.

Today, Mary believes that Nixon was president in 1971.

But this argument seems plainly inadequate. One cannot infer (3) from (1), for Mary might have forgotten the date of Nixon's tenure as President, so that while (1) is true, (3) is false. Indeed, Mary may never have been aware of the date of Nixon's Presidency, so that from (1) one cannot even infer 4.

In 1971 Mary believed that Nixon was President in 1971.

Perhaps I am being insulting to Mary,28 and (3) does follow (conversationally, at least) from (1). But then what is Mary's belief today according to (3)? It is a tensed belief. There is no doubt that Mary does not believe 5.

Nixon is President in 1971,

nor did she believe (5) in 1971. If all she believes were tenseless statements, she would not know who is currently in office or whom she would vote for-which conclusion is equally insulting to her. The Direct Reference theorist might say, of course, that this last point has to do, not with the content of Mary's belief, but with its cognitive significance. But the question we are asking is, on what basis do we know that the content of her belief is tenseless, despite appearances to the contrary? To all appearances, what she believed in 1971 was the tensed proposition Nixon is 27 Mark Richard, "Temporalism and Etemalism," Philosophical Studies 39 (1981): 3-4. Oddly enough, Richard thinks that the temporalist will agree that "Nixon is now President" expresses an eternal proposition. But the A-theorist would never make such a concession, since both "is" and "now" are tensed expressions. For a critique of Richard's argument, see Mark Aronszajn, "A Defense of Temporalism," Philosophical Studies 81 (1996): 71-95, who maintains that the inference from "Mary believed p" and "Mary still believes everything she has ever believed" to "Mary still believes p" is valid; it is eternalism which fails to warrant the correct inferences. 28 Though it would not be insulting if Mary is a child. My own daughter Charity believed in 1983 that "Reagan is President," but she never believed "Reagan is President in 1983." If! told someone that in 1983 Charity believed Reagan was President and that in 1990 she still believed that, the person would undoubtedly think that my daughter had not kept up on her current events.

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President and what she believes now is Nixon was President. Hence, it is far from clear that ordinary belief ascriptions bear out the tenselessness of information. In short, the arguments for the common assumption that the propositional content of a tensed sentence is tenseless are surprisingly weak. 29 The upshot is that one could accept the Direct Reference Theory's analysis of indexicals as not belonging to propositional content and yet plausibly maintain that propositions are tensed. This would significantly weaken the B-theorist's tu quoque argument because the elimination of temporal and spatial indexical facts would not imply the elimination of tensed facts. Still, the B-theorist might insist that his A-theoretical interlocutor cannot have it both ways. The same arguments based on timely action to show the reality of tense imply with equal force the reality of spatial and personal "tenses." If the A-theorist is willing to accept the explanation given by Direct Reference Theories for the cognitive significance of indexicals, what remaining ground is there for maintaining that propositions are tensed? If the Direct Reference Theory remedies the defects of the New B-Theory, what reason remains for preferring the A-Theory? Moreover, there is some intuitive warrant for taking propositions to be tenseless, I think we must admit. It seems very queer, for example, to say that someone who truly believed yesterday that "My birthday is tomorrow" has lost some information when he comes to believe on the following day "My birthday is today." In some sense, he seems to know the same information. Moreover, the communication of information across time requires that it be tense less as well as indexical-free. Rather than butt up against the "philosophically entrenched conception of information content" as tenseless, let us simply stipulate ex concessionis that the information or propositional content of a tensed sentence is its tenseless, non-indexical content. In this specialized sense of "information content" propositions are by definition tenseless. The question then becomes whether there is reason to think that there are tensed facts which lie outside what is captured by the information content of a sentence. Tense and Cognitive Significance

The answer to that question will depend on the adequacy of the Direct Reference Theory's account of cognitive significance. How is it that we have tensed beliefs if there is neither tensed propositional content of those beliefs nor extra-propositional tensed facts? According to the Theory, the cognitive significance of our beliefs depends upon their mode of presentation to us, and on the Kaplan-Perry version of that Theory the mode of presentation is a function of the linguistic meanings of the For further ineffectual arguments against tensed propositions, see Milton Fisk, "A Pragmatic Account of Tenses," American Philosophical Quarterly 8 (1971): 93-96. Fisk conflates non-indexical, tensed sentences with indexical ones. It is true that it is in virtue of the indexical that indexical, tensed sentences refer to a specific time. But Fisk errs in thinking that a non-indexical, tensed sentence only incompletely expresses a proposition; the A-theorist can hold that the tensed proposition is non-indexical, refers to no temporal position, and is variable in truth value due to its ascription of an A-determination. Fisk is therefore wrong when he argues that to determine the proposition expressed by a tensed sentence one must specifY the time of the token, which leads to an infinite regress. There is only an infinite regress of entailments, but not of propositional content or meaning. 29

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words used to express the proposition. For example, if I see someone's reflection in a mirror without realizing that it is my own and judge, "His pants are on fire" and then a moment later realize, "My pants are on fire," I grasp the same singular proposition under different modes of presentation, namely, a third person mode and a first person mode. The cognitive significance of the two modes is different and determinative for how I behave. The Kaplan-Perry account of cognitive significance, however, is pretty clearly inadequate. According to Howard Wettstein in his incisive critique, "The crucial problem for this account, given its thesis that cognitive states are to be individuated by linguistic meanings, is revealed by examples in which synonymous utterances differ in cognitive significance.,,3o Take the problem of informative identity statements, for example. In the mirror illustration above, I come to believe "I am the same person he is." The Kaplan-Perry analysis nicely accounts for the informativeness of the trivial propositional content of this sentence due to the different linguistic meanings of "I" and "he." But what about sentences of the form "He is the same person he is?" Wettstein imagines seeing a performer with halfface make-up from windows on opposite sides of an auditorium and telling someone looking through one window "He is the same person"-leading the addressee to the other window-"as he is." The cognitive significance of the first "he" differs from that of the second. But the Kaplan-Perry account is incapable of explaining this because the linguistic meaning is the same. A parallel illustration for temporal indexicals can be constructed: 3l imagine correcting someone at a New Year's Eve party in 1999 who thinks that the twenty-first century begins with the year 2000. We could say "The present century is the same as"-waiting past midnight-"the present century." The linguistic rules governing temporal indexicals can only treat this sentence as a triviality, thereby leaving its cognitive significance unexplained. Or consider the different cognitive significance of similar tokens. Two persons might both utter, "He is about to be attacked by a bear," where in fact a single individual is referred to, but where this fact is not obvious and hearers believe two different individuals are being referred to.32 In such a situation someone might believe one utterance and not the other. But since the purely linguistic meanings are identical, there is nothing to explain this difference in cognitive significance. Moreover, one might well behave differently depending on which of the two utterances one takes to be true or false. Because one's behavior varies, there must, on the Kaplan-Perry analysis, be differing belief states, or differences in cognitive significance. But there cannot be such differences, since the linguistic meaning of the utterances is the same. Howard Wettstein, "Has Semantics Rested on a Mistake?" Journal ofPhilosophy 8 (1986): 195. See also David Braun, "Demonstratives and their Linguistic Meanings," Noils 30 (1996): 147-148. 31 Pace Eros Corazza and J. t2 than about events at tn < t2. But, as Schlesinger observes, such a differential concern is a universal human experience. Take, for example, the difference in our attitudes toward one's birth and one's death. On the B-Theory the period of personal non-existence which lies tenselessly after one's death is of no more significance than the period of personal non-existence which lies tenselessly before one's birth. Yet whereas one looks back on his birth with joy, one looks forward to his death with anxiety, an anxiety which runs so deep that one's death, unlike one's birth, seems to place a question mark behind the value of life itself, as John Lucas eloquently explains: The future, just because it will one day be present, cannot but have some bearing on our present state of mind .... When the atomic bomb was discovered, many people believed, with reason, that the world would soon be destroyed, and found that that expectation took away the value of all that they did, and made everything seem futile and pointless. And the same applies to each individual as he contemplates his own future, and the implications of his own mortality. For we are afraid of death. Timor mortis conturbat me. It is therefore difficult to be dispassionate about the passage of time. ss

Of course, there have been philosophers who have looked on the future with no less equanimity than on the past. But as Schlesinger observes, such equanimity has typically been based, not on a B-Theory of time, but on subscription to values or

events. The feeling of relief is rational only if an event which was present no longer is; but whether that event existed before becoming present and exists after ceasing to be present is a further metaphysical question, which I discuss in my The Tenseless Theory o/Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, forthcoming). S4 Schlesinger, Aspects o/Time, p. 35. ss J. R. Lucas, A Treatise on Time and Space (London: Methuen, 1973), pp. 313-314.

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realities which were considered to transcend this fleeting and brief existence. 56 Indeed, in certain Eastern philosophical traditions, one should look with equanimity upon past, present, and future alike because time is ultimately unreal. Thus, Schlesinger rightly insists, Nobody, or hardly anybody, who has been concerned considerably with his present well-being and comforts, has advocated that our status of mind ought to be the same when contemplating our death as when contemplating our birth, etc. The sentiments required by the Russellian doctrine of time seem contrary to human nature. They seem contrary to human nature according to [Russellians'] own admission since they have refrained from advocating that in light of their analysis of temporal statements we ought to adopt these sentiments.... Russellians who claim to have convinced themselves that future events are no more moving towards us than past events do not fear the former any less than other people 57

Even persons who adopt stoic attitudes toward their own deaths never, on pain of insanity, truly free themselves from a differential concern with the future over against the past. We must agree with Lucas when he says, We are rational agents, making choices about what we shall do, and thus implicitly making up our minds about which of various possible future states of affairs is most worth bringing about. We cannot, so long as we have minds, avoid extending them towards the future, or take no thought whatever for the morrow, and cannot, while remaining rational agents, divorce time present from time future and time past, and concentrate on it to the exclusion of all else. We should not be in fetters to the future, but if we take a long view of ourselves, it must include some indication of what is going to happen, particularly what is going to happen at our hands, and what has happened, as well as what is happening now. 58

Again, these phenomenological data of temporal consciousness reinforce how deeply ingrained and strongly held are our beliefs about the tensedness of events. B-theorists have, as Schlesinger observed, been reluctant to dismiss as irrational our differing attitudes towards past and future events and have often instead tried to eke out of the B-Theory some basis for this difference. Oaklander, for example, disputes Schlesinger's allegation that on the B-Theory there is no "approach" of the future. 59 By such a charge, says Oaklander, Schlesinger means either (i) that there is no moving now or absolute becoming or (ii) that time does not have an objective direction or sense. Oaklander is being somewhat disingenuous here, for it is evident that Schlesinger meant that (i) characterizes the B-Theory, and he does not claim that Russell affirms (ii). But Oaklander hopes that by re-iterating the B-theorist's commitment to the asymmetry of time, he can salvage the rationality of our differing attitudes toward the past and future. On the B-Theory, the movement of events from future toward past and the intrinsic sense of time are based, he affirms, in the Schlesinger, Aspects o/Time, p. 37. See also discussion by Richard Sorabji, Time, Creation and the Continuum (Ithaca, N. Y: Cornell University Press, 1983), pp. 174-179. One must disagree, however, with Schlesinger's claim that the B-theorist is rational to feel certain emotions about present events, since for the B-theorist there is no present and so no grounds for rejoicing that something is occurring now. 57 Schlesinger, Aspects o/Time, pp. 38, 138. David Cockburn emphasizes, "really to live in accordance with the insight that 'all times and what happens at them, are equally real' ... would ... involve radical modifications in the ways in which most of us now live" (Other Times, Cambridge Studies in Philosophy [Cambridge: Cambridge University Press, 1997], p. 22; cf. pp. 135-140). 58 Lucas, Treatise, p. 313. 59 Oak1ander, Temporal Relations, pp. 140-159. 56

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genuine temporal relation of succession that obtains between events and in the synthetic a priori principle that time is asymmetrical. 60 Schlesinger errs in comparing B-theoretical time with space, he avers, for on the B-Theory our experiences are located in a temporal series with an inherent generating relation of earlier (later) than. "Consequently, even without a moving 'now' it makes all the difference in the world if at t2, an unpleasant experience is going to occur at a later time (t3) or if it occurred at an earlier time (tl).,,61 It seems to me quite evident that Oaklander's bid to substitute the asymmetry or anisotropy of time for temporal becoming is a failure. The only succession that exists in a B-theoretical model is the tenseless existence of events one after another, and the asymmetry of time means only that the tenseless ordering relations earlier/later than hold throughout the temporal structure. As Grtinbaum has emphasized, from temporal anisotropy, it does not follow that any sort of becoming exists. 62 Indeed, there are really two directions to time, one the "earlier than" direction and the other the "later than" direction, and it is wholly arbitrary in the absence of temporal becoming how these directions are laid on the series of events. The arrows of time could be rotated 180 0 without contradiction to the facts. Although appeal to thermodynamic and other physical considerations to ground "the" arrow of time continue to be popular, Lawrence Sklar has shown quite convincingly that all such processes presuppose a prior choice of temporal direction, so as to permit one to say, for example, that entropy increases in the "later than" direction. 63 In the absence of such a prior decision, it is completely arbitrary to denominate the direction of entropy increase among events "the future" or the "later than" direction rather than "the past" or the "earlier than" direction. Nor does anisotropy serve to invalidate Schlesinger's analogy with space, since space can also be anisotropic (for example, Aristotelian space, which involved a center of the universe). Thus, it is not at all evident why someone tenselessly existing at (2 and contemplating painful experiences at t, and t3 is rational in feeling relief about one and dread of the other. As Smith observes, such a person at all three times may hold the same tenselessly true beliefs, for example, " t, occurs earlier than one's relief at t2," " t3 occurs later than one's dread at t2," and so forth.64 Such beliefs provide no rational basis for a person tenselessly existing at t2 to feel relief about the tenseless Ibid., p. 146. Ibid., p. 157; similarly J. M. Shorter, "The Reality of Time," Philosophia 14 (1984): 338, who, after asserting that the "special nature" of the difference between before and after justifies our different attitudes, asks if it is necessary at such a fundamental level to say anything further on the matter. 62 Griinbaum, Philosophical Problems o/Space and Time, pp. 209-210, 314-315. 63 Lawrence Sklar, Space, Time, and Spacetime (Berkeley: University of California Press, 1976), section F of Chapter V. Cf. Lawrence Sklar, "Time in Experience and in Theoretical Description of the World," in Time's Arrows Today, ed. Steven F. Savitt (Cambridge: Cambridge University Press, 1995), pp. 217-229. 64 Smith, "Phenomenology of A-Time," p. 150. 'The problem is that any facts about the B-relations of the event that I could believe before the event I could just as well believe afterwards, and vice versa, so if B-facts are the only kind it is impossible to explain the difference in belief that causes the different emotions of eagerness and nostalgia. This difference is explicable only if it is assumed that before the event I believe the event is future and that after the event I believe it is past" (Ibid., p. 151). 60 61

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occurrence of the painful event earlier than tz or dread about the tenseless occurrence of the painful event later than t z, for the person can never know the fact, since there is none, that it is now tz. Oaklander attempts to ground our experience of becoming and our differential attitudes toward the past and future in the successive differences in the magnitude of the temporal intervals separating us from the event under consideration. He explains, My wish (anticipation) or utterance occurs tenselessly at tl and the event that I wish to occur is later than fl. At f2, my wish or utterance occurs (tenselessly), but the temporal span (duration) between t2 and fn is less than the temporal span between fl and tn. Finally, at fn, the experience of joy occurs (tenselessly) and so does the event e that I have been anticipating at tl and t2. On this account the passage of time is reflected in the fact that different wishes (thoughts) or utterances occur (tenselessly) at different times and at different temporal distances from the time at which event e occurs .... the experience of nostalgia occurs (tenselessly) at fn+! ... and fn is earlier than tn+l. As the temporal distance between fn and now (that is, the time referred to by the use of the word "now" in the utterance "I am now nostalgic" ... ) increases, we may be said to experience event e receding or passing more and more into the past. Thus, on the Russellian view, there is a justification of our different attitudes towards past and future events, and more importantly, there is a clear and intelligible sense in which time has the transiency required by our deeply felt impression. 65

It seems to me that this account is question-begging. Oaklander just assumes that on the B-Theory it is rational to experience anticipation or nostalgia at all before considering such feelings at successively shorter or longer intervals from the event. When we consider that for Oaklander "now" is merely an indexical expression referring to a moment of time, then it is not at all clear why believing "tz is closer to tn than is t J" should occasion anticipation or lead to a sense of temporal movement. Without a "moving now" which progresses toward tn, any feeling of becoming or anticipation is illusory and, hence, irrational to entertain. Similarly, it is wholly inappropriate to feel nostalgia rather than anticipation later than tn, since it is always tenselessly true that" tn+Z or t n+3 is later than tn." Since there is no truth about an objective present, feelings of dread or relief or feelings of dread rather than relief are just wholly out of place and should be discarded. Paul Horwich takes a somewhat different tack toward the question. He observes that there is a sort of value asymmetry associated with the past and future: if we could locate in our lives all our experiences, we would choose to have the painful ones all in the past and the pleasant ones in the future. This claim is no doubt exaggerated, for we should all like to have some pleasant memories, rather than be emotionally crippled by an utterly horrid past. Still Horwich makes a good point: we consider someone fortunate, for example, who ascends from rags to riches rather than descends from riches to rags, even if the sum total of years spent in weal or woe were exactly the same for both parties. Horwich goes on to notice that future events are not, however, in general more valued by us than past events; rather it is with respect to our own experiences alone that the future supersedes the past. Again, this claim is exaggerated, since most of us would wish for the world and for others as bright and happy a future as we wish for ourselves. Still our foremost 65

Oaklander, Temporal Relafions, pp. 141-142; cf. idem, "Experience ofTenseless Time."

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preoccupation is with our own experiences. Horwich asserts that what we now desire is that our future selfish desires will be satisfied, but that we do not to the same degree care that our past selfish desires were satisfied. I think Horwich probably underestimates the degree of remorse, guilt, and regret that most people carry; but still he makes a good point: we are oriented toward the future. Horwich then tries to explain this asymmetry in evolutionary terms, as due to a selectional advantage enjoyed by an organism which wanted its future selfish desires to be' satisfied over one which did not care. He makes three points: (i) Having the desire that future selfish desires be satisfied would increase the chances that those future desires would be satisfied; (ii) the satisfaction of those future desires would be conducive to survival and reproductive success; and (iii) having the desire that past desires were satisfied would not increase the chances that those past desires were satisfied. Thus, having a value asymmetry weighted in favor of future experiences has survival value and so has in the process of evolution become ingrained in homo sapiens, despite the fact that, on the B-Theory of time, no such temporal asymmetry exists. 66 Now I suspect that Horwich's speculative hypothesis is just another piece of socio-biological mythology.67 Apart from the fact that our orientation toward the future is broader than the desire for fulfillment of selfish desires, surely the fact that non-human animals, which lack our openness to the world and are restricted to the fulfillment of present desires, have fared well in the struggle for survival ought to make us suspicious that the selective advantage of having future desires is so great as to weed out all persons without it. And whether the satisfaction of such desires is conducive to survival depends entirely on what those desires are. True, desiring that past desires have been fulfilled could not, in the absence of backward causation, increase the chances of their fulfillment, but it could be selectively advantageous if regret or remorse over unfulfilled past desires were to prevent the organism from engaging in certain detrimental modes of behavior. So we might well be skeptical about such imaginative reconstructions. But all this would be to miss the point. The salient point is that Horwich's hypothesis is simply irrelevant to the argument under discussion, which concerns, not the psycho-biological origins of our differing attitudes toward past and future, but the rationality of them. As Schlesinger frames the argument, The existence of these differences is universally acknowledged and is shared by Russellians no less than by others. Nobody denounces these differences in attitudes as irrational; nobody advocates that our attitudes are to be reformed in the light of a clearheaded analysis of temporal relations. But there is a strong case for claiming that these differences are justified only if time also has a transient aspect.... On the Russellian view, which does not permit any changes and according to which all temporal relations are permanently fixed, it is very hard to justify such differences in attitude. 68

Horwich explicitly begs off discussing whether the value asymmetry which we experience is rational for us to hold and thereby fails to deflect the thrust of Horwich, Asymmetries, pp. 196-198. On the pseudo-scientific claims of socio-biology, see Philip Kitcher, Vaulting Ambition: Sociobiology and the Quest/or Human Nature (Cambridge, Mass.: MIT Press, 1985). 68 Schlesinger, Aspects a/Time, p. 34. 66

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Schlesinger's argument. 69 In line with Schlesinger's above-quoted generalization, Horwich simply affirms that he believes that it is rational and, moreover, that it does not require any rationale in order to be rational! This last claim is certainly wrong, for while it may be prudent for the B-theorist to allow himself to entertain beliefs which he knows to be false, nevertheless it is not rationaCo Only on the A-Theory, with its ontological distinctions between past, present, and future, can differential attitudes toward events of these sorts be rationally justified. The same misunderstanding vitiates Huw Price's response to the experiential argument. Price invites us to imagine a block universe inhabited by counterparts to ourselves in which time does not flow and asks, how would things seem if time didn't flow? Ifwe suppose for a moment that there is an objective flow of time, we seem to be able to imagine a world which would be just like ours, except that it would be a four-dimensional block universe rather than a threedimensional dynamic one. It is easy to see how to map events-at-times in the dynamic universe onto events-at-temporal-Iocations in the block universe. Among other things, our individual mental states get mapped over, moment by moment. But then surely our copies in the block universe would have the same experiences that we do---in which case they are not distinctive of a dynamic universe after all. Things would seem this way, even if we ourselves were elements of a block universe. '1

This is like arguing that because a brain in a vat being stimulated by electrodes would have the same experiences that we do, therefore our belief in the reality of the external world is neither properly basic nor warranted! But while such sceptical arguments may undermine attempts to argue from our experience to the realities experienced, they do nothing to defeat the rationality of basic beliefs formed in the context of such experiences. What is wanted from the B-theorist is some defeater of my tensed beliefs grounded in my differential experience of the past and future. Now a more temerarious B-theorist might argue precisely on socio-biological grounds that differential attitudes toward the past and future are in fact irrational and should be dispensed with. He might take his evolutionary account of these feelings as proof that the A-theorist is wrong about the ontology of time. At face value, so to argue would seem to commit the genetic fallacy. The A-theorist could maintain that having differential feelings about the past and future is selectively advantageous precisely because there really is a difference between past and future, so that an organism's evolving the capacity to apprehend and appreciate this difference makes Horwich, Asymmetries, p. 205; oddly enough, Oaklander, "Experience of Tenseless Time," pp. 164165, does seem to infer from the putative socio-biological origins of the asymmetry of past and future that while dread of the future may at times be natural, it is not therefore rational. 10 Garrett concedes, "We are biased towards the future--we care more about future experiences simply because they are future--and this bias would appear to be unjustified if the tenseless view of time is correct" (Garrett, "'Thank Goodness' Revisited," p. 204). All Garrett can offer by way of rejoinder is a tu quoque retort: what is it about the property of pastness which justifies caring less about past pains than present pains? Garrett's mistake is his assumption that on the A-Theory "Event e is past" entails e's having the property pastness (Ibid., p. 201). But on an A-theoretical presentist ontology, past events do not exist and the sentence is to be analyzed as affirming that it was the case that e is present. Thus, a past pain is a non-existent pain, and so no pain at all! Thus, we need not be concerned about it. By contrast a future pain is one that will become real and so ought to occasion concern. 11 Huw Price, Time's Arrow and Archimedes' Point (New York: Oxford University Press, 1996), pp. 14-15; cf. Steven F. Savitt, "The Replacement of Time," Australasian Journal of Philosophy 72 (1994): 467.

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it more suitably adapted to the real world, just as an organism's apprehension of the external world is selectively advantageous and makes it better adapted to the world because there really is an external world. Providing a physiological basis for our different feelings toward past and future does nothing to undermine the veridicality of such feelings. But perhaps the objection is more subtle than this. Perhaps the aim of the objection is to undermine our confidence in our belief-forming mechanisms by suggesting that these mechanisms cannot be relied upon to produce true beliefs, but rather beliefs which promote survival. If they happen to be true, that is purely accidental. Our belief that certain events are past, which occasions feelings of relief or nostalgia, and our belief that certain events are future, which engenders feelings of dread or anticipation, may seem to be properly basic, but in fact they are not because we can have no confidence in the mechanisms which produced such beliefs. A socio-biological, evolutionary account thus provides an undercutting defeater for our beliefs about the past and the future. But the problem with such reasoning, as Plantinga points out, is that it generates an undefeated defeater of itself.72 For the belief that our differential feelings and 72 Alvin Plantinga, "An Evolutionary Argument against Naturalism," Logos 12 (1991): 27-49. An excellent parallel illustration of the self-defeating nature of the envisaged line of reasoning is provided by philosopher of science Michael Ruse. According to Ruse, because our cognitive faculties were selected for on the basis of their conduciveness toward survival rather than success in arriving at truth, we cannot know that they are trustworthy. In discussing ethical principles, Ruse espouses the socio-biological line that morality is a biological adaptation which was selectively advantageous. "I do not mean that ethics is a total chimera, for it obviously exists in some sense. But I do claim that, considered as a rationally justifiable set of claims about an objective something, it is illusory .... Morality is just an aid to survival and reproduction, ... and any deeper meaning is illusory (although put on us for good biological reasons)" (Michael Ruse, "Evolutionary Theory and Christian Ethics," in The Darwinian Paradigm [London: Routledge, 1989], pp. 268-269). Unless Ruse is simply committing the genetic fallacy here, he must be interpreted as undermining the rationality of ethical beliefs on the basis of the untrustworthiness of our belief-forming mechanisms. The parallel between ethical beliefs and tensed beliefs is instructive, since many of both kinds of these beliefs are normally taken as properly basic. Just as Ruse is arguing that the origin of our moral beliefs is such as to render doubtful the veracity of those beliefs, so our hypothetical B-theorist dismisses tensed beliefs because the mechanisms which formed them were aiming only at survival, not truth. But just as the B-theorist finds it impossible to jettison his tensed beliefs, so Ruse also stubbornly hangs on to his moral beliefs. He declares, "The man who says that it is morally acceptable to rape little children is just as mistaken as the man who says 2+2=5" (idem, Darwinism Defended [London: Addison-Wesley, 1982], p. 275). What makes this statement ironic is that in his article on extraterrestrial rape, Ruse confesses that ultimately we do not know that 2+2=5; the belief that 2+2=4 could just be ingrained in us because it is biologically advantageous (idem, "Is Rape Wrong on Andromeda?" in Darwinian Paradigm)! Not only is Ruse's ethical principle thereby undermined, but his entire philosophical position is undercut, since it is itself the product of the same cognitive faculties which were formed by blind evolutionary pressures with no regard for the truth. Ruse himself confesses, "Everything I am saying could be totally mistaken. My claims could be simply things I believe because I am a more efficient reproducer if I believe them than otherwise." But then such claims are self-defeating. One reviewer comments, "Ruse manfully attempts to avoid the skepticism into which his position seems to trap him. He replies with an argument urging that scepticism cannot genuinely be adopted. Perhaps so; but Ruse has failed to see the chief issue, namely whether Ruse's epistemology leads to a skepticism which everyone wants to avoid. He has failed utterly to refute the clear argument which he himself has offered that it does" (David Gordon, critical notice of Taking Darwin Seriously, International Philosophical Quarterly 28 [1988]: 107-108).

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beliefs about past and future events are the product of unreliable belief-fonning mechanisms is itself a product of those same mechanisms, mechanisms which aim, not at truth, but survival. The B-theorist can therefore have no confidence at all that his reason for doubting the veracity of our tensed beliefs is true. Nor can he furnish any argument in its favor, since for any premiss he adduces he has an undefeated defeater, namely, the belief that our belief-fonning mechanisms are unreliable. Of course, the B-theorist might say that only some of our belief-fonning mechanisms are suspect, namely, those that produce tensed beliefs. But as Plantinga points out, if there are differences in the reliability of our cognitive faculties, surely perception and memory-which produce tensed beliefs-would be at an advantage over cognitive mechanisms which produce more theoretical beliefs. 73 I am much more certain that my headache is over, for example, than I am that the socio-biological reconstruction of the means by which I come by my tensed beliefs is true. The socio-biological argument against the proper basicality of our tensed beliefs is thus self-defeating. In summary, we have seen that our differing feelings about past and future events underline how deeply embedded and strongly held are our tensed beliefs. If the B-Theory were correct, those beliefs are false and our feelings of relief, nostalgia, dread, and anticipation therefore irrational. Since such feelings are indispensable, the B-Theory condemns us all to irrationality. Insofar as such feelings are appropriate, the A-Theory of time must be true. In the absence of any successful defeater for our beliefs about the past and future, those beliefs remain for us properly basic and therefore the feelings attending them wholly in order.

Our Experience o/Temporal Becoming A third and final aspect of our temporal experience which must be noted is our experience of temporal becoming. It is hard to think of anything that is more obvious to us than the fact of temporal becoming. It is as obvious to us as the existence of the external world. For we experience that world, not as a static tableau, but as a continual flux. The external world is presented to us as a tensed world. What could be more obvious than the fact that we see things coming to exist and ceasing to exist, that we experience events happening? We do not experience a world of things and events related merely by the tenseless relations earlier than, simultaneous with, and later than, but a world of events and things which are past, present, or future. Yet the reality of temporal becoming is even more obvious to us than the existence of the external world itself. For in the inner life of the mind we experience a continual change in the contents of consciousness, even in the absence of any apprehension of an external world, and this stream of consciousness alone constitutes for us a temporal series of tensed events. Some of our thoughts are now past, we are aware of our present mental experience, and we anticipate that we shall think new thoughts in the future. And there is no arresting of this flux of Thus, the position that our belief in the reality of tense and temporal becoming is not properly basic because of doubts engendered by evolutionary theory about the reliability of our belief-forming mechanisms cannot be rationally affirmed by us. 13 Plantinga, "Evolutionary Argument," p. 42.

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experience; there is constant and ineluctable becoming.74 If the experience of temporal becoming is an illusion, if in reality there is no such thing as temporal becoming, then it is hard to imagine what is left to us about which we should not be skeptical. 75 Our commitment to the reality of temporal becoming comes to expression in certain experiences and beliefs which are common to human beings. Schlesinger draws our attention to a wish like "I wish it were now 1968!" Perhaps I deeply regret some decisions I made at that time and wish that I had the chance to live through those years afresh, making the right decisions. Or perhaps those were particularly wonderful years in comparison with the bad times of the present, and I wish that I could be experiencing those good times rather than my present lot in life. As Schlesinger points out, even though there is no chance of my wish's fulfillment, there is no lack of clarity as to what exactly I am wishing for. "Anybody familiar with my plight would fully sympathize with me and unfailingly grasp what feature of the universe I should like to be different from what it is: instead of the NOW being at tt. I should like it to be at to.,,76 Schlesinger's illustration holds not only for See the interesting Auseinandersetzung between Delmas Kiernan-Lewis, "Not Over Yet: Prior's 'Thank Goodness' Argument," Philosophy 66 (1991): 241-243; L. Nathan Oaklander, "Thank Goodness It's Over," Philosophy 67 (1992): 256-258; 1. D. Kiernan-Lewis, "The Rediscovery of Tense: A Reply to Oaklander," Philosophy 69 (1994): 231-233. Lewis constructs an argument for the reality of tense analogous to the argument against physicalism based on the irreducibility of mental states like feeling pain to physical states. He asserts that I know what it is like to be aware that my headache has ceased. But I could not know this if the B-Theory were true. Therefore, the B-Theory is not true. Oaklander responds that Lewis begs the question, for on a B-Theory of time I do not know my headache has ceased in the A-theoretic sense of going out of existence. Oaklander fails to notice, however, that Lewis's argument was framed, not in terms of propositional knowledge (that my headache has ceased), but in terms of non-propositional knowledge (what it is like to be aware that my headache has ceased). Even if the B-theorist denies us the propositional knowledge that our headache has ceased, he cannot deny the phenomenological fact that we know what it is like to be aware that our headache has ceased. On the BTheory I have an undeniable awareness or experience of things' really ceasing to exist, even though they do not; in other words I am deceived by non-veridical experiences. In claiming that on the B-Theory of time I could not know what it is like to be aware that my headache has ceased, Lewis implies that such knowledge is inherently tensed. He argues, "Someone--say, a timeless God-who knew all but only the tenseless facts, and so knew my headache 'ceases' in the sense of there being times after which it tenselessly occurs, would still not know what it is like for a headache to cease. Since no analysis of my experience of the ceasing-to-exist of a headache in tenseless terms is possible, no tenseless reduction of my experience can succeed" (Kiernan-Lewis, "Rediscovery of Tense," p. 232). Thus, the very awareness of temporal becoming involves a becoming of awareness and so cannot be detensed. Lewis's challenge to the B-theorist is thus two-fold: (1) The B-theorist must explain how I can be deceived by the awareness that things cease to exist in cases where it is my inner experiences themselves of which I am aware that they cease to exist; and (2) The B-theorist must explain how an awareness of becoming can exist if reality is tenseless. 7S As Richard Taylor wrote, " ... it cannot be denied that things in time seem to pass into, through, and out of existence. That can be our datum or starting point, and if metaphysics declares this to be an illusion, then it is up to metaphysics to show that it is" (Richard Taylor, Metaphysics, 2d ed., Foundations of Philosophy [Englewood Cliffs, N. J.: Prentice-Hall, 1974], p. 82). 76 Schlesinger, Aspects of Time, p. 39. Unfortunately, he confuses the issue by equating the wish in question to be equivalent to what strikes me as the quite different wish that I were ten years younger. Cf. idem, "Time Flies," pp. 512-514. But Schlesinger takes the latter wish to mean, not that I should now be ten years younger than I am, but that, my birth date being held constant, the year ten years ago should be 74

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past, but also for future events. What child has not wished fervently that it were now Christmas morning? Sometimes, on the other hand, we wish that some unpleasant event which is now occurring were already past. Who has not been comforted in times of difficulty by the proverb, "This, too, shall pass"? In all such common experiences, we wish that the "now" were differently located than it is, or rather that some other moment in time were present than the moment which in fact is present. We thereby presuppose the reality of temporal becoming, since we evidently believe that the various moments in the temporal series become successively present. The B-theorist must regard every philosophically informed person who shares such experiences (including himself) as in that respect irrational. For such a one is wishing for something that is broadly logically impossible. As Mellor says, on the B-Theory there is no possible world which has a history exactly like our world except that the location of the present is in the eighteenth instead of the twentieth century. 77 But for the A-theorist, such a world is obviously possible, even if tenselessly formulated possible worlds semantics for modal sentences cannot take cognizance of such differences between worlds. For the B-theorist, what is at stake is not a mere deficiency of possible worlds semantics, but that there simply is no temporal property of presentness which events might possibly possess, nor any other metaphysical substitute for a property of presentness which could possibly render tense an objective feature of the world. The best that the B-theorist can do to make sense of such experiences is to misconstrue the wishes into B-theoretical substitutes, for example, "I wish that the events of the world were reconstituted in such a way that things appear to be exactly as they were in 1968," "I wish that I had not made the decisions which I did in 1968," "I wish that Christmas were celebrated on the seventeenth of December instead of the twenty-fifth," "I wish that this event had occurred earlier than it does," and so forth. These ersatz-wishes are clearly not what we are expressing in our original wishes! The B-theorist seems obligated to say that our real wishes, which are probably the universal experience of mankind, are just irrational. It might be said on behalf of the tense less time theorist that in the analogous case involving personal indexicals, we do sometimes wish for the logically impossible; for example, "I wish 1 were Sylvester Stallone!" Given the necessity of identity, present and, hence, I should be ten years younger (George N. Schlesinger to William L. Craig, 5 October 1993). 77 Mellor, Real Time, p. 28. It might be suggested that on Mellor's view such a wish is quite reasonable, being the wish that one should be (now) located elewhen in the one and only tenseless world. Such a wish, it might be said, is analogous to the wish to be elsewhere in the one and only spatial world, as in "I wish I were in Sydney!" (i.e., "I wish Sydney were here!"). But I do not think that this analysis succeeds. When I wish that it were now 1968, I am not simply wishing to be located in 1968 (when "It is now 1968" is true), for, since I myself was born in 1949, I am, on Mellor's tenseless view, in 1968, as really and as fully as I am in 1999. Nor can it be said that only a temporal stage of me is in 1968, since on Mellor's view things are continuants, only events having stages. So what more is there to wish for? Moreover, when I wish that I were in Sydney, I am not wishing that Sydney were here, for that would be to wish that Sydney were in the United States, which is not what I desire! I am wishing that I were there. But I am not analogously wishing that I were tenselessly re-Iocated to 1968 (since on Mellor's view I am already there in that mode), but, if! am wishing to be re-Iocated at all, to be in 1968 in a tensed mode of being. Hence, such a wish cannot be accommodated by Mellor's view.

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such a wish is logically impossible. Therefore, we must re-interpret such wishes if we want to retain belief in their rationality; for example, "I wish I had Sylvester Stallone's body and station in life." We are similarly justified in substituting tenseless stand-ins for ostensibly tensed wishes. But this objection is not decisive because the cases are not truly parallel. In the first place, a little reflection shows that what I really desire is Sylvester Stallone's body and station in life, not that I were Sylvester Stallone; otherwise I myself could not enjoy being Sylvester Stallone, since I would in that case not exist. 78 By contrast there is no such difficulty in wishing that some other time were present. Secondly, and more significantly, the violation of the necessity of identity would occur in the temporal case if I were to wish that the moment picked out by the indexical "now" were some other moment of time. But this is evidently not what I am wishing for. I do not wish that the twenty-fifth of December were the seventeenth of December, for example. Rather I am wishing that some other moment had the property (or mode) of presentness than the moment which does. On the tense less theory my wish comes out as logically impossible on either interpretation, in the one case due to the necessity of identity and in the other due to the non-existence of tense determinations. But on the tensed theory such a wish is possible without reinterpretation. Thus, the proponent of tense less time is forced to deny the rationality of my wish, since it presupposes a tensed theory of time. Not so, retorts Oaklander. He agrees that " ... such wishes are meaningful, and if the Russellian is committed to claiming that such wishes are devoid of meaning, then there is something wrong with the Russellian view.,,79 He also concedes that the B-theorist cannot account for the meaningfulness of a wish that the "now" be located elsewhere than it is. But he asserts that this is not the meaning of the wish expressed by saying, "I wish it were 1968." What then is the meaning of the wish? When I wish to be ten years younger, I have thoughts of myself ten years younger, I have thoughts of myself ten years ago and memories of persons and events that I have previously perceived. I would be wishing that I could be perceiving and not merely remembering these things I perceived ten years ago. Similarly, I would say that my wish that it was now 1968 would be the wish that certain events which already occurred, would now be occurring. That is, I wish that I was now perceiving events that are quite other than those I am in fact now perceiving. so

It seems to me quite obvious, however, that the above reconstruction is not at all what 1 wish for. My wish has nothing to do with my perceptions; 1 may be wholly unaware of what 1 am perceiving or what 1 should like to perceive. Besides, 1 am not wishing to have different perceptions-I could go to a hypnotist for that-I want it to be 1968, not just appear to me to be 1968. It is difficult to see that Schlesinger has misconstrued my wish in interpreting it as a desire that the "now" or the present See the brief, but interesting, comments of Price, Time's Arrow, p. 283. Oaklander, Temporal Relations, p. 159. Oaklander rather muddies the issue by drawing in the question of the meaning of such wishes, rather than their rationality. Schlesinger is partly to blame for this, in that he alleges that the B-theorist cannot make sense of such wishes. But the B-theorist does not maintain such wishes to be literally nonsensical or meaningless, but that what is meant is logically impossible. What Oaklander should say is that such wishes have tensed meanings, but tenseless truth conditions, and are therefore rational to entertain. 80 Oaklander, Temporal Relations, p. 160. 78

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be some moment in time other than the moment which is present. The A-theorist could accept Oak1ander's analysis that I wish the events of 1968 would now be occurring, for this is a tensed expression. In line with the New B-Theory of Language, however, Oaklander distinguishes the meaning of this wish from the conditions under which it would be fulfilled. What facts, then would have to exist in order for that wish to be fulfilled? Oaklander answers, " ... my wish that it was to would be satisfied if and only if the thought that is the wish corresponds to the fact that that thought is simultaneous with ... the time to."SI But the reader will recognize that this is just the old, tenseless, token-reflexive truth conditions analysis of tensed beliefs once more. It would be 1968 iff that token occurs in 1968. Not only do all our former objections to that account resurface, but worse still, Oaklander's analysis actually serves to reveal a further deficiency in that account. That account cannot tell us under what conditions my wish would be true, for if it were 1968, no such wish would be made, and so there would be no token on hand for which tokenreflexive truth conditions could be given. One cannot say that the token would be "It is 1968," for perhaps no one would utter such a token (cf. "I wish it were the Cretaceous Period"). Thus Oaklander is stuck with a meaningful wish, which can be rationally entertained, for which he can provide no conditions under which it would be fulfilled. By contrast, the A-theorist offers the straightforward and perspicuous account that the wish would be fulfilled iff it were 1968, that is, it were true that "1968 is present." Rather than try to defend the rationality of such wishes, B-theorist Robert Coburn chooses instead to bite the bullet: he admits that wishes such as the above do plausibly presuppose A-facts, but, he demurs, this just shows that some of the things we say make sense only against the background of a metaphysical theory which may tum out to be unacceptable. s2 That, however, is the moot question. We have already seen the failure of Coburn's allegedly compelling argument against the ATheory of time. s3 In the absence of any defeater for our belief in the reality of temporal becoming, such a belief remains properly basic and therefore rational. Another universal human experience which presupposes the reality of temporal becoming is the experience of waiting. 84 When we wait for something to happen, we are experiencing the lapse of moments of time in anticipation of the previsioned event. It is not that we simply experience the temporal interval between the date at which one begins to wait and the time at which the awaited event occurs to have a certain quantitative measure, even that it is long or short. Rather waiting involves the notion of the passage of time, which one lives through until the expected event occurs. Schlesinger's objection that waiting means merely to occupy the temporal positions to through tn,S5 which can be done in tenseless time, is inadequate as a phenomenological analysis of this experience. If waiting were merely a matter of tenselessly occupying a series of temporal positions, then it could be truly said, for

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Ibid., p. 161. Coburn, Strangeness of the Ordinary, p. Ill. Recall discussion in chapter I, pp. 20-22. A point originally obliquely made by Richard Gale, '''Here' and 'Now'," Monist 53 (J 969): 409. George Schlesinger, "The Similarities between Space and Time," Mind 84 (1975): 164.

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example, that my pen waited on my desk for me to pick it up, which is silly.86 A person who occupied a series of temporal positions but had no sense of temporal passage could not have any sense of waiting until some event occurred; the closest one can imagine to such a person would be a comatose individual, who, oblivious to the passage of time, cannot be said to await his recovering consciousness. About the best that the B-theorist can do with the experience of waiting is to admit its tensed character, but offer again his tenseless, token-reflexive truth conditions for beliefs presupposed by the experience, an approach which we have seen to be unavailing. In summary, then, we have seen via a phenomenological analysis of our temporal experience that we experience events as happening presently, that we have peculiar attitudes toward past and future events respectively, looking back on past events with feelings of relief or nostalgia, for example, and looking forward to future events with feelings of dread or anticipation, and that we experience the process of temporal becoming. Doubtless there are many other examples of the way in which our belief in the reality of tense is manifested in our experience, but these serve well to make it clear how basic, deeply ingrained, strongly held, and universal is our belief in the reality of tense and temporal becoming. Moreover, we saw that in each case B-theoretical attempts either to re-interpret our experiences in tenseless terms or to justify our feelings in the obtaining of tense less facts alone fails miserably. On a B-Theory of time, therefore, we are all, including B-theorists themselves, hopelessly mired in irrationality, prisoners to an illusion from which we are incapable of freeing ourselves. By contrast, if the A-Theory is true, our experiences and beliefs are entirely rational. Insofar, then, as we think that our temporal feelings are rationally entertained, we should embrace an A-Theory of time. CONCLUSION

I have argued that our belief in the reality of tense and temporal becoming is a basic belief grounded in our temporal experience. Whether that belief is properly basic will depend upon whether there are defeaters for any defeater of that belief which the detractor of tense and temporal becoming might propose. Thus far, I think it can be safely said that no successful defeater of our belief in the objectivity of tense has presented itself. Our belief has been neither rebutted nor undercut and therefore remains properly basic. But we have yet to consider the strongest objections to the A-Theory, objections which some B-theorists believe, perhaps even with reluctance, defeat our basic belief in the reality of tense and becoming. We shall examine those objections in the next Part. But an important point might well be made appropriately at this juncture as well. We have seen that there is such a thing as an intrinsic defeaterdefeater, a belief which enjoys such warrant for us that it simply overwhelms the 86 A point made by Gilbert Plumer, "Detecting Temporalities," Philosophy and Phenomenological Research 47 (1987): 459. In private correspondence (George N. Schlesinger to William L. Craig, 5 October 1993), Schlesinger complains that the example in the text "shows only that one needs consciousness or awareness of the magnitude of the interval." But clearly mere consciousness of the length of a temporal interval does not yield the experience of waiting.

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defeaters brought against it without specifically rebutting or undercutting them. It deserves to be asked whether our belief in the reality of tense and temporal becoming is not itself precisely such a superlatively warranted belief. Here our analysis of temporal consciousness becomes relevant. It is hard to imagine how any beliefs could be more powerfully warranted for us than, say, our belief in the presentness of my experience or in the fact of temporal becoming. What argument for the unreality of tense or temporal becoming could possibly be based on premisses more evident than our basic belief in that reality? McTaggart's Paradox?-hardly! Even in the absence of a resolution of that puzzle, McTaggart's Paradox, when compared to our basic belief in the reality of tense and temporal becoming, must take on the air of Zeno's Paradoxes of motion: an engaging and recalcitrant brain-teaser whose conclusion nobody really takes seriously.s7 I am far more certain of the reality of tense that I am of McTaggart's argument that tensed facts lead inevitably to self-contradiction. We have seen how tensed beliefs are so strongly held that no one can successfully divest himself of them and how their abandonment would generate repercussions throughout one's entire noetic structure. Indeed, I frankly must confess that B-theorists are a source of wonderment to me; I fmd it simply amazing that such persons can convince themselves that our most deeply seated and ineludible intuitions about the nature of reality are delusory. This leads to one final point: unlike many properly basic beliefs, such as perceptual or memory beliefs or beliefs grounded in testimony, the belief in the reality of tense and temporal becoming is universal. We all experience the presentness of our inner experiences and the process of temporal becoming. Therefore, belief in the reality of tense and temporal becoming is a belief which is basic to all persons. If I am correct that this belief is an intrinsic defeater which overwhelms the B-theoretical philosophical arguments brought against it, then it follows that belief in tense and temporal becoming is properly basic and thus rational not only for A-theorists, but for all persons, yes, that insofar as B-theorists reject this belief in favor of a tenseless view of time, they have a flawed noetic structure and are, therefore, in that respect irrational.

On behalf of the B-theorist, Schlesinger argues that Zeno's Paradoxes and McTaggart's Paradox are not analogous, since the B-theorist denies that it is in fact now tl and subsequently t2, so that he does not assert anything contrary to experience, whereas Zeno fails to offer any new interpretation of our observations which would entail that in fact no movement has taken place (Schlesinger, "Time Flies," p. 503). If I understand him correctly, Schlesinger's claim seems to be that Zeno admits that an object is at location II at tl and then at 12 at t2; while the B-theorist denies that it is now at tl and then now at t2. Zeno admits the facts, but says they lead to incoherence, whereas the B-theorist does not admit the tensed facts at all. But this seems to be a misinterpretation of Zeno. Zeno admits our experience of movement, but, as a Parmenidean who held that all is one, he denied the facts of movement and multiplicity. He entertains them only for the purpose of a reductio ad absurdum. Movement and multiplicity are shown to be illusory. Similarly, the B-theorist denies the facts of tense and temporal becoming, while admitting our experience of the same. He employs McTaggart's reasoning as a reductio argument against tensed facts. The situations thus seem quite parallel, and in both cases the veridicality of our experience overwhelms the effete philosophical arguments lodged against it. 87

PART II ARGUMENTS AGAINST AN A-THEORY OF TIME

CHAPTER 6 MCTAGGART'S PARADOX

U

ndoubtedly the most celebrated argument against an A-Theory of time is the attempt by the British idealist J. M. E. McTaggart to demonstrate that an Aseries of events is self-contradictory or leads to a vicious infinite regress of Atheoretic determinations. 1 Indeed, Richard Gale has remarked that "If one looks carefully enough into the multitudinous writings on time by analysts, one can detect a common underlying problem, that being that almost all of them were attempting to answer McTaggart's paradox.,,2 Although McTaggart himself regarded his demonstration as a proof that time does not exist, certain contemporary B-theorists employ versions of his argument to prove the unreality of tense and temporal becoming, which, they claim, are not essential to time. Let us begin with McTaggart's own statement of the argument. EXPOSITION OF MCTAGGART'S ARGUMENT McTaggart's argument consists of two parts. In the first part he argues that the A-theoretic determinations of events are essential to the temporality of those events, and in the second part he contends that these determinations of events are selfcontradictory. In short, " ... nothing that exists can be temporal, and ... therefore time is unreal.,,3 For " ... the A-series is essential to the nature of time, and ... any difficulty in the way of regarding the A-series as real is equally a difficulty in the way of regarding time as real.,,4 McTaggart's argument for time's unreality is apt to appear bewildering and even trivial, unless we first understand its metaphysical underpinnings. Key to comprehending the contradiction he sees in the reality of time is, I think, McTaggart's presupposition that the reality of time entails a B-theoretic event ontology to which objective temporal becoming is wedded. That McTaggart presupposes an event ontology is evident in his explanation of what an event is: The contents of any position in time form an event. The varied simultaneous contents of a single position are, of course, a plurality of events. But, like any other substance, they

Published first as J. Ellis McTaggart, 'The Unreality of Time," Mind 17 (1908): 457-474, the argument appears in chapter 33 of McTaggart's most important work, The Nature of Existence (1927), in which McTaggart responds to objections from Bertrand Russell and C. D. Broad, a B-theorist and an Atheorist respectively. For a good review ofthe literature see David 1. Farmer, Being in Time: The Nature of Time in Light of McTaggart's Paradox (Lanham, Md.: University Press of America, 1990). 2 Richard M. Gale, The Language of Time, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1968), p. 6. 3 10hn McTaggart Ellis McTaggart, The Nature of EXistence, 2 vols., ed. C. D. Broad (Cambridge: Cambridge University Press, 1927; rep. ed.: 1968),2: 9. 4 Ibid., 2: 11.

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CHAPTER 6 form a group, and this group is a compound substance. And a compound substance consisting of simultaneous events may properly be spoken of as itself an event. 5

McTaggart's view of events as substances is underlined by his analysis of change. In arguing that change is impossible without an A-series, he considers whether events, moments of time, or characteristics of events change. He never even raises the question as to whether things change. For if time is real, the fundamental substance in time is events, on McTaggart's view, and so these must change in some way if change is to be real. Moreover, it seems clear that McTaggart assumed that if time is real, then the substance-events are strung out in a B-series in which each member is equally real or existent. Temporal becoming consists in the fact that one after another of these events become successively present. McTaggart is quite willing to describe this as a sort of relative motion between the positions of the A-series and those of the Bseries: The movement of time consists in the fact that later and later terms pass into the present, or-which is the same fact expressed in another way-that presentness passes to later and later terms. Ifwe take it the first way, we are taking the B-series as sliding along a fixed A-series. If we take it the second way, we are taking the A-series as sliding along a fixed B-series 6

McTaggart thinks of time like a slide rule on which the A-positions and B-positions are moving relatively to each other in a certain line of motion. Because the motion is relative, the question of the direction of time's movement is ambiguous. "But if we ask what is the movement of either series, the question is not ambiguous. The movement of the A-series along the B-series is from earlier to later. The movement of the B-series along the A-series is from future to past.,,7 The language of movement is a spatial metaphor, but the philosophical content of the metaphor is that events first have the A-determination (whether this is a relation or property is a matter of indifference to McTaggart) of distant futurity, then near futurity, then presentness, then near pastness, then distant pastness, all of these except presentness admitting of degrees. Events which are future or past are just as real as events which are present: "We perceive events in time as being present, and those are the only events which we actually perceive. All other events which, by memory or by inference, we believe to be real, we regard as present, past, or future."s An event changes only in its steady Ibid., 2: 10. Ibid., 2: 10-11. Ibid., 2: II. Ibid. The equal ontological status of past, present, and future events is reinforced by McTaggart's view that the B-series is derivable from the combination of the A-series with a C-series, which is a timelessly ordered series based on an atemporal ordering relation like the relation greater than ordering the natural numbers. The conjunction of A-determinations with the C-series renders its members earlier/later than one another. He writes, "We can now see that the A series, together with the C series, is sufficient to give us time. For in order to get change, and change in a given direction, it is sufficient that one position in the C series should be Present, to the exclusion of all others, and that this characteristic of presentness should pass long the series in such a way that all positions on one side of the Present have been present, and all positions on the other side of it will be present. That which has been present is Past, that which will be present is Future.

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acquisition or loss of new A-determinations. For McTaggart, then, becoming present does not imply becoming existent. Rather events exist tenselessly in a Bseries and successively acquire the various A-determinations. With this understanding in mind, let us look at the first part of McTaggart's argument, that it is essential to time that its events form an A-series as well as a Bseries. He explicitly rejects the mind-dependence of becoming as incompatible with the real nature of time. For time involves change; there would be no time ifnothing changed. Therefore, if a B-series alone can constitute time, change must be possible without an A-series. McTaggart contends that this is not possible. First, events in a B-series can neither cease to be nor begin to be events. Any event N in a B-series "will always have a position in the time-series, and always has had one. That is, it always has been an event, and always will be one, and cannot begin or cease to be an event.,,9 McTaggart means that if it is true that N exists at to. it is always true that N exists at tn. The B-theoretical location of an event does not change. Secondly, neither can moments in absolute time cease or begin to be. By "absolute time" McTaggart seems to mean the series of temporal positions considered in abstraction from the events which exist at them. The moments of time in the B-series are just as permanent and unchanging as the events which are their contents. Finally, can events change in their characteristics? McTaggart responds that there is only one class of characteristics with respect to which events can change, and that is the determination of the events by the terms of the A-series. He writes, Take any event-the death of Queen Anne, for example-and consider what changes can take place in its characteristics. That it is a death, that it is the death of Anne Stuart, that it has such causes, that it has such effects---every characteristic of this sort never changes. 'Before the stars saw one another plain,' the event in question was the death of a Queen. At the last moment of time-if time has a last moment-it will still be the death of a Queen. And in every respect but one, it is equally devoid of change. But in one respect it does change. It was once an event in the far future. It became every moment an event in the nearer future. At last it was present. Then it became past, and will always remain past, though every moment it becomes further and further past. to

If there is any change, therefore, it can only be found in the A-series. Since time involves change, it follows that the A-series is essential to time. McTaggart then considers and rebuts three objections to his view. (i) Adeterminations are mind-dependent. McTaggart is reacting here to Russell's objection that to say that an event is "present" means that it is "simultaneous with this assertion." On Russell's account, change exists if two propositions which differ only with respect to the time involved differ in truth value, for example, it is true that "The poker is hot at t" and false that "The poker is hot at t'." McTaggart complains that Russell locates change in things rather than events and that his account leaves no room for change in the qualities of the thing. For example, it is always a quality of the poker that it is hot on Monday. Such a quality is true of it at any time. McTaggart thinks here of temporally-indexed properties (cf. worldThus, ... no other elements are required to constitute a time-series except an A series and a C series" (McTaggart, "Unreality ofTime," p. 463). McTaggart's final position is that only the C-series is real. 9 McTaggart, Nature of Existence, 2: 12. to Ibid., 2: 13.

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indexed properties). At any moment of time the poker has the property hot-at-tn • Since temporally-indexed properties do not change, the thing in which they inhere does not really change: "The fact that it is hot at one point in a series and cold at other points cannot give change, if neither of these facts change-and neither of them does.,,11 McTaggart compares the B-series to a spatial series, such as the Greenwich meridian. For two spatial points S and S', the proposition "At S the Greenwich meridian is within the U.K." is true, while the proposition "At S' the Greenwich meridian lies within the U.K." is false. But no one, asserts McTaggart, would say that this gives us change. "My contention is that if we remove the Aseries from the prima facie nature of time, we are left with a series which is not temporal, and which allows change no more than the series of latitudes does.,,12 (ii) Non-existent time series can be purely B-theoretical. McTaggart has in mind here the temporal series that appear in novels and plays. The events are temporally ordered according to an earlier than relation, but no event in the story has presentness. McTaggart answers that if anything is in time it exists. But what in these stories is existent?-nothing. It follows that the events of the story are not really in time and, hence, constitute no counter-example to the essentiality of the Aseries to time. (iii) There might be several real and independent time series. Because these series have no relation to each other, there is no real present. McTaggart answers that all that follows is that there is no unique present throughout the universe. If there are several B-series, then there would also be several A-series associated with them. Most people, concludes McTaggart, agree that the A-series is essential to time. Where the opposite is held, it is only to save the reality of time by showing the Aseries to be inessential. In the second part of his argument, McTaggart contends that an A-series cannot exist and, therefore, time cannot exist. He begins by noting that pastness, presentness, and futurity may be construed as either relations or qualities of events and also of moments of time, if these are taken as separate realities. McTaggart prefers the view that these are relations, but he correctly observes that his chief argument does not depend on which alternative one adopts. 13 Ibid., 2: 15. Ibid. 13 In secs. 327-328 McTaggart has a curious excursus on A-determinations as relations, his preferred view. He maintains that if anything is, for example, present, then it must be present in relation to something else outside the time series. For A-determinations change, but relations between members of the time series do not change. Hence, there must be some entity X outside the time series in relation to which one term of the A-series is uniquely present, the rest being past or future. McTaggart cannot imagine what X might be, and yet its existence, he insists, is foundational to the A-series. The difficulty encountered in the supposition of such an entity as X is that this entity-say, a timeless God-would itself be "temporalized" if some event in time were uniquely present in relation to it. The relation present to seems to be a symmetrical relation, especially when understood to single out a unique temporal term. Moreover, as different terms become present in relation to God; God would undergo extrinsic change and so be temporal. Perhaps X could be construed to be a moment of hyper-time, relative to which one moment of time is uniquely present. But then we could ask all over again what it is for a moment of hyper-time to be hyper-present, and we embark on an infinite regress. So if A-determinations are relational, they must be relations to other terms in the time series. Buller and Foster point out that A-determinations could be construed as relations to items in either the A-series or the B-series (David J. Buller and Thomas R. Foster, "The New Paradox of Temporal Transience," II

12

MCTAGGART'S PARADOX

173

McTaggart observes that past, present, and future are incompatible determinations. Every event must be one or another, but no event can be more than one. But, he continues, every event has all three determinations. "If M is past, it has been present and future. If it is future, it will be present and past. If it is present, it has been future and will be past. Thus all three characteristics belong to each event.,,14 The A-series therefore seems inconsistent. It is impossible to state this difficulty, McTaggart admits, without almost giving the solution. "It is never true, the answer will run, that M is present, past, and future. It is present, will be past, and has been future. ... The characteristics are only incompatible when they are simultaneous, and there is no contradiction to this in the fact that each term has all of them successively.,,15 But what, he asks, do we mean by the tensed verbs "is," "has been," "will be?" When we say that X is Y, we are asserting X to be Y at a moment of present time. With the past tense we assert X to be Y at a moment of past time, and with the future tense we assert X to be Y at a moment of future time. "Thus our first statement about M-that it is present, will be past, and has been future-means that M is present at a moment of present time, past at some moment of future time, and future at some moment of past time.,,16 Here McTaggart substitutes the event M for X and makes Y to be an Adetermination. Thus, if we say that M will be past, then we are asserting M to be past at a future moment of time. If we say M has been future, we are asserting M to be future at a past moment of time. If we say that M is present, we are asserting M to be present at the present moment of time. Therefore, M does not have futurity, presentness, and pastness all at the same time, but successively at different times. But McTaggart thinks this solves nothing. He writes, If M is present, there is no moment of past time at which it is past. But the moments of future time, in which it is past are equally moments of past time, in which it cannot be past. Again, that M is future and will be present and past means that M is future at a moment of present time, and present and past at different moments of future time. In that case it cannot be present or past at any moments of past time. But all the moments of future time, in which M will be present or past, are equally moments of past time. And thus again we get a contradiction, since the moments at which M has anyone of the three determinations of the A-series are also moments at which it cannot have that determination. 11

Philosophical Quarterly 42 [1992]: 358-359). With respect to the A-series, an event E is future relative to some moment ten years ago. With respect to the B-series, E is past relative to 1 October 1994. McTaggart here addresses only the second option, which effectively reduces A-determinations to Bdeterminations. On the first option, A-determinations are changing relations, for the moment picked out by the A-position ten years ago changes every year, so that E is not changelessly future relative to a moment ten years ago. The difficulty with this option is that it iterates tenses relative to the present, which must then be present relative to the present relative to the present, and so on, which seems, as McTaggart complains, to be either a vicious circle or infinite regress. Perhaps for these reasons, with the possible exception of Schlesinger, no A-theorist has followed McTaggart in construing A-determinations as relations; most take them to be intrinsic properties. 14 McTaggart, Nature of Existence, 2: 20. IS Ibid., 2: 21. 16 Ibid. 11 McTaggart, Nature of Existence, 2: 21.

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This argument needs some explanation. The first sentence means that if we take M to be a present event, then in the past there is no time at which M could truly be asserted to be past. On the contrary, when those times were present, M had the determination of futurity. The next sentence is very difficult: what does McTaggart mean when he says that the moments of future time are equally moments of past time? He seems to mean that the series of moments which are future relative to the present moment are in the past relative to some future moment. Of course, not all future moments relative to the present are in the past of any given future event, but an arbitrarily large number are, and for McTaggart's purposes all he needs is one such moment. So the idea seems to be that M is in the past of some hypothetical future event. Thus, M both has and has not the A-determination of pastness. In the next sentence McTaggart considers the case in which M is a future event. He points out that in such a case M cannot have the determinations of pastness or presentness at any moment of past time. For in the past, as in the present, M was a future event. But, McTaggart repeats, all the moments of future time are also moments of past time. So M both can and cannot be past. His conclusion is that any moment of time t at which Mhas, say, pastness is also a moment at which Mhas presentness. This might still seem to be a pseudo-contradiction. For M has pastness at t only when t is past and presentness at t only when t is present, so that there is no contradiction. But McTaggart considers this response only a postponement of the inevitable. For the same contradiction about M's A-determinations also dogs t's Adeterminations. In his 1908 article, McTaggart claimed that attributing A-determinations to events successively leads either to a vicious circle or to a vicious infinite regress. With respect to the former, he indicts the solution because it assumes the existence of time in order to account for the way in which moments are past, present and future. Time then must be presupposed to account for the A series. But we have already seen that the A series has to be assumed in order to account for time. Accordingly the A series has to be pre-supposed in order to account for the A series. And this is clearly a vicious circle. What we have done is this-to meet the difficulty that my writing of this article has the characteristics of past, present and future, we say that it is present, has been future, and will be past. But 'has been' is only distinguished from 'is' by being existence in the past and not in the present, and 'will be' is only distinguished from both by being existence in the future. Thus our statement comes to this-that the event in question is present in the present, future in the past, past in the future. And it is clear that there is a vicious circle if we endeavour to assign the characteristics of present, future and past by the criterion of present, past and future. 18

The same difficulty, he says, can be put in another way, in which case the fallacy exhibits itself as an infinite regress: If we avoid the incompatibility of the three characteristics by asserting that M is present, has been future, and will be past, we are constructing a second A series, within which the first falls, in the same way in which events fall within the first. It may be doubted whether any intelligible meaning can be given to the assertion that time is in time. But, in any case, the second A series will suffer from the same difficulty as the first, which can only be removed by placing it inside a third A series. The same principle will place the third inside a fourth, and so on without end. You can never get 18

McTaggart, "Unreality ofTime," pp. 468-469.

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McTAGGART'S PARADOX rid of the contradiction, for, by the act of removing it from what is to be explained, you produce it over again in the explanation. And so the explanation is invalid. 19

Sanford claims not only that the vicious circularity argument is fallacious, but that McTaggart himself came to see it as such and so abandoned it, along with the argument about endless hyper-times, in The Nature of Existence, where he speaks of an infmite regress only in terms of the single time series. The charge of vicious circularity will not stick, avers Sanford, because one is not trying to analyze or defme the A-series. "McTaggart's argument is a reductio ad absurdum: a contradiction follows from the assumption that there is an A-series. The same assumption from which a contradiction is said to follow surely cannot be disallowed in the attempt to show that it does not really follow.,,20 But if there is no vicious circularity, opines Sanford, neither is there any infinite regress of hyper-times formed by trying to avoid the circularity. It seems, however, that Sanford has taken insufficient cognizance of McTaggart's argument's being lodged against A-determinations construed as relations. If we relativize A-determinations to terms in the A-series, as the proffered explanation suggests, then we do seem to encounter vicious circularity. For Mis present only in relation to the present; but the present is present only in relation to itself, which is arguably circular. By relativizing A-determinations to times in the A-series itself, one never arrives at a privileged present. It still remains to be asked when the present is present, since the present moment is also past and future at other times. The fact that McTaggart says that "the same difficulty" can be recast as an infinite regress of hyper-times shows, I think, that the circularity McTaggart envisions is such as I suggest. In order to specify when the present moment is present, one could have recourse to a hyper-time in which presentness traverses the time series (Figure 6.1). present

t3 present

t2

present

t\ ~L-

__________________________________

To Figure 6. J. At successive moments of hyper-time T, successive moments of time t become present. Thus, for example, t2 becomes present at T2.

The problem is only temporarily solved, however, for now we shall have to ask when the hyper-present becomes hyper-present. To answer that question, one will have to posit a third dimension of time, and so on, ad infinitum. "Thus," McTaggart Ibid., p. 469. The fact that he speaks of time's being in time shows that he is contemplating an infinite regress of time dimensions, not an infinite regress of increasingly complex tenses. 20 David H. Sanford, "McTaggart on Time," Philosophy 43 (1968): 373. 19

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concludes, "a contradiction arises if the A series is asserted of reality when the A series is taken as a series ofrelations.,,21 In The Nature of Existence McTaggart formulates the difficulty as follows: If we try to avoid this by saying of these moments what had been previously said of M itself-that some moment, for example, is future, and will be present and past-then 'is' and 'will be' have the same meaning as before. Our statement, then, means that the moment in question is future at a present moment, and will be present and past at different moments of future time. This, of course, is the same difficulty over again. And so on, infinitely. Such an infinity is vicious. The attribution of the characteristics past, present, and future to the terms of any series leads to a contradiction, unless it is specified that they have them successively. This means, as we have seen, that they have them in relation to terms specified as past, present, and future. These again, to avoid a like contradiction, must in tum be specified as past, present, and future. And since this continues infinitely, the first set ofterms never escapes from contradiction at a1l. l l

Although McTaggart mentions explicitly neither the vicious circle nor hyper-times, it is very dubious that the above reasoning rerresents a change of mind on McTaggart's part. As David Farmer observes,2 not only the structure of the argument as a whole, but even the wording reproduces the 1908 article, and McTaggart himself, in a footnote concerning Broad's refutation of McTaggart's view, explains, "I have published my views on time, pretty nearly in their present shape, in Mind for 1908.,,24 The argument in The Nature of Existence is broadly worded so as to comprise both the alternatives of the 1908 article; if understood to refer to a single time series then the regress resembles the vicious circle rather than the series of hyper-times. But if A-determinations cannot be understood as intra-temporal relations, then what about our construing them as qualities, or monadic properties? "Are there," McTaggart queries, "three qualities-futurity, presentness, and pastness, and are events continually changing the first for the second, and the second for the third?,,25 No, insists McTaggart, for the contradiction ... would arise in the same way supposing that pastness, presentness, and futurity were original qualities, and not, as we have decided that they are, relations. For it would still be the case that they were characteristics which were incompatible with one another, and whichever had one of them would also have the other. And it is from this that the contradiction arises. 26

Even if we take presentness to be a monadic property of an event or time, it remains the case that that event or time is not changelessly present but is only temporarily present. (Another way of putting this is to say that that same moment or event also has futurity and pastness.) So when does it acquire the property of presentness? The answer can only be "at the present," and we are off on an infinite regress. The

McTaggart, "Unreality of Time," p. 469. McTaggart, Nature of Existence, 2: 21-22. 23 Farmer, Being in Time, p. 87; so also Paul Marhenke, "McTaggart's Analysis of Time," in The Problem of Time, University of California Publications in Philosophy 18 (Berkeley: University of California Press, 1935), p. lSI. 24 McTaggart, Nature of Existence, 2: 23. 25 McTaggart, "Unreality of Time," p. 469. 26 McTaggart, Nature of EXistence, 2: 22. 21

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contradiction of the same time or event's having pastness, presentness, and futurity remains unrelieved. ASSESSMENT OF MCTAGGART'S ARGUMENT C. D. Broad's great commentary An Examination of McTaggart's Philosophy may serve us well as a framework for the assessment of McTaggart's argument. In Broad's opinion, "The fallacy in McTaggart's argument consists in treating absolute becoming as if it were a species of qualitative change, and trying to replace temporal copulas by non-temporal copulas and temporal adjectives.'.27 Let us look at each of these criticisms in turn.

Temporal Becoming as Qualitative Change With regard to the first, by "qualitative change" Broad refers to a type of change in which an enduring subject acquires qualities which it previously did not possess?8 McTaggart holds that, as a temporal series, a B-series is a process of perpetual qualitative change, and that unless the terms of the series have A-characteristics with respect to which they change, then the series cannot be a process of qualitative change. 29 But Broad dismisses McTaggart's arguments contra Russell that a Bseries without A-characteristics would not constitute a process of qualitative change as "thoroughly confused and inconclusive.,,30 For it is things, not events, which are the subject of qualitative change. True, no event or tense less fact changes; but this is irrelevant. For on Russell's view, change is the history ofa thing having different properties at different times. Change consists in a conjunction of facts which neither change nor are about change. And although McTaggart asserts that an earlier than relation would not obtain in the absence of A-characteristics, he has not shown this. Hence, there has been no good reason given to deny that qualitative change obtains in a simple B-series. Moreover, temporal becoming is not to be construed as qualitative change. "To become hot" is not like "to become present" because the latter does not imply an enduring subject and in reference to events simply means ''to happen." A distinction must thus be made between qualitative change and absolute becoming: "Sentences like 'This water became hot' or 'This noise became louder' record facts of qualitative change. Sentences like 'This event became present' record facts of absolute becoming.',31 Unfortunately, McTaggart construes becoming present as a qualitative change in the terms of the B-series and so speaks of becoming as a sort of motion of the present. "The characteristic of presentness is then supposed to move along this series of event-particles, in the direction from earlier to later, as the light from a policeman's bull's-eye might move along a row of

C. D. Broad, An Examination of McTaggart's Philosophy, 2 vots. (Cambridge: Cambridge University Press, 1938; rep. ed.: New York: Octagon Books, 1976),2: 317. 28 Ibid., 2: 280. 2. Ibid., 2: 292. 30 Ibid., 2: 300. 31 Ibid., 2: 280. 27

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pilings.,,32 Such a conception is insuperably problematic33 and leads eventually to McTaggart's alleged contradiction in the reality of time: Thus change has to be postulated in a sense not contemplated by the theory, viz., the steady movement of the quality of presentedness along the series in the direction from earlier to later. If we try to deal with this kind of change in the way in which the theory deals with the qualitative changes that take place in the course of my experience, we shall be committed to making each term in the original series a term in a second series in a second time-dimension. We shall have events of the second order, viz., the becoming presented of events of the first order 34

But absolute becoming is not a qualitative change nor a second order event. There are no events which first have the quality of futurity, which they then exchange successively for new qualities of presentness and pastness: When I utter the sentence 'It has rained' I do not mean that, in some mysterious nontemporal sense of 'is,' there is a rainy event, which momentarily possessed the quality of presentness and has now lost it and acquired instead some determinate form of the quality of pastness. What I mean is that raininess has been, and no longer is being, manifested in my neighbourhood. When I utter the sentence, 'It will rain,' I do not mean that in some mysterious, non-temporal sense of 'is,' there is a rainy event, which now possesses some determinate form of the quality of futurity and will in course of time lose futurity and acquire instead the quality of presentness. What I mean is that raininess will be, but is not now being manifested in my neighbourhood 35

Broad makes a very interesting comparison between McTaggart's argument and one version of Anselm's ontological argument. Anselm argued that God is greater if He exists than if He does not and, since He is the greatest conceivable being, He must therefore exist. The fallacy in this reasoning lies in the assumption that merely possible objects exist and so can possess properties and be compared to actual being in respect to greatness. 36 But if x exists in some possible world Wand does not exist 32 Ibid., 2: 227. Broad urged that both the policeman's bull's eye metaphor and the growing past metaphor of temporal becoming err in presupposing that phases of the world which have not yet supervened or have been already superseded in some sense co-exist with each other and the present. Smart's retort, "If 'coexist' means 'coexist now' then we can reply that past and present stages do not coexist now but they coexist (using this verb tenselessly) and of course they coexist at different times" (1. J. C. Smart, "Time and Becoming," in Time and Cause, ed. Peter Van Inwagen, Philosophical Studies Series in Philosophy [Dordrecht: D. Reidel, 1980], p. 9), is unworthy of Broad, who as a former Btheorist most certainly was aware of and did not confuse these two senses (Hastings' Encyclopaedia of Religion and EthiCS, s.v. 'Time," by C. D. Broad). His point is that by asserting the tenseless coexistence of all things/events (i.e., presupposing a B-theoretic ontology), one turns temporal becoming into a kind of qualitative change, which it is not, thereby landing one in McTaggart's Paradox. For a contemporary analogue of the policeman's bull's-eye, see Errol E. Harris, The Reality of Time, SUNY Series in Philosophy (Albany, N. Y.: State University of New York Press, 1988), pp. 24, 31, who lands himself squarely in McTaggart's Paradox by construing temporal becoming like a film (the B-series) passing over the lens of a projector (the present moment). 33 We may reserve discussion of these difficulties for chap. 7 on the myth of passage. 34 Broad, Examination, 2: 308. By "presentedness," Broad has reference to the specious present. 35 Ibid., 2: 316. 36 See Alvin Plantinga, The Nature of Necessity, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1974), pp. 209-210. Broad himself said that Anselm's argument presupposes that there "is sense in talking of a comparison between a non-existent term and an existent one; and it produces the impression that this is like comparing two existing terms, e.g., a corpse and a living organism, one of which lacks life and the other of which has it" (C. D. Broad, Religion, Philosophy and Psychical Research [London: Routledge, Kegan & Paul, 1953], p. 182).

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in W', x is not greater in W than it is in W', nor does it lack some great-making property in W' in comparison to W. Rather there simply is no x in W'. Similarly, past and future things or events do not lack some quality of presentness or possess in its place the qualities of pastness or futurity instead. Rather they simply do not exist at all. Temporal becoming consists in things' coming to be absolutely. Thus, McTaggart's fallacy lay in his pursuing the "hopeless tack" of treating temporal becoming as a type of qualitative change. 3? It seems to me that Broad's critique is quite correct. Although McTaggart himself preferred the view that A-determinations are relations rather than qualities, his analysis of temporal becoming does treat it as a sort of qualitative change insofar as he attempts to combine a B-theoretic ontology with A-theoretic becoming. On a pure A-theoretic ontology, the only temporal items which exist exist presently. In other words, the pure A-Theory entails a metaphysic of presentism. On a presentist ontology, past and future events/things/times are not real or existent and, hence, do not exemplify properties like pastness or futurity. Hence, there can be no question of an entity's trading in futurity for presentness or cashing in presentness for pastness. Rather entities come to be and pass away absolutely, so that the only temporal entities there are are the present ones. Thus, the source of McTaggart's Paradox lies not in the A-series, but in McTaggart's peculiar marriage of the A- and B-series. By adopting a B-theoretic ontology according to which all moments are equally real and ascribing changing A-determinations to them, McTaggart winds up with a multitude of "presents," none of which is privileged, so that contradiction seems inevitable. 38 That a pure A-Theory of time is immune to McTaggart's argument is evident from the way in which he responds to C. D. Broad's critique in Scientific Thought. In this work Broad had defended a sort of hybrid A-B-Theory according to which past and present events are real, but future events do not exist. 39 He conjoined with this process ontology the view that future-tense propositions are not bivalent and lack a truth value. After criticizing Broad's denial of the Principle of Bivalence for future-tense statements, McTaggart turns his attention to Broad's ontology. What is interesting is that he admits that Broad's rejection of the reality of the future does enable one to escape McTaggart's argument to a degree, since no event has the ABroad, Examination, 2: 302. For a good statement of this point, see Gale, Language of Time, pp. 30-31,240. See also the very interesting piece by Franklin C. Mason, "The Presence of Experience and Two Theories About Time," Southern Journal of Philosophy 35 (1997): 75-89, who argues from the presentness of experience to presentism. If all times are equally real and at two different times I make the judgement "The experiences I have now occur at present," then one judgement must be false; but each is self-evidently true. So all times cannot be equally real; if there are A-facts, presentism is true. 39 Broad wrote, "Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. The past is thus as real as the present. On the other hand, the essence of a present event is, not that it precedes future events, but that there is quite literally nothing to which it has the relation of precedence. The sum total of existence is always increasing and it is this which gives the time series a sense as well as an order" (c. D. Broad, Scientific Thought, pp. 66-67). For a contemporary defense of this theory, see Michael Tooley, Time, Tense, and Causation (Oxford: Clarendon Press, 1997). 37

38

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determination of futurity. But since on Broad's peculiar view the past is as real as the present, McTaggart's argument will still go through: ... time would still, on Dr. Broad's theory, involve the contradiction described above (p. 20). For although, if Dr. Broad were right, no moment would have the three incompatible characteristics of past, present, and future, yet each ofthem ... would have the two incompatible characteristics of past and present. And this would be sufficient to produce the contradiction. 4O

This response is telling, because it shows that it is the B-theoretical reality of events that lies at the source of the difficulty. If the reality of future events is denied, then there are no events having the determination of futurity. But on the early Broad's hybrid view, past events do have a B-theoretical reality, and so the argument can be recast in terms of the determinations of pastness and presentness alone. McTaggart explains, But even then it would be true that, when we say M is past, we mean that it has been present at some time of past time, and is past at a moment of present time, and that, when we say M is present, we mean that it is present at a moment of present time. As much as this Dr. Broad can say, and as much as this he must say, ifhe admits that each event ... is both present and past. Thus we distinguish the presentness and pastness of events by reference to past and present moments. But every moment which is past is also present. And if we attempt to remove this difficulty by saying that it is past and has been present, then we get an infinite vicious series .... 41

When we compare this reiteration of the argument with McTaggart's first statement of it, we find that he has preserved the illustration of M's being present and substituted the case of M's being past for M's being future. But notice how much less can be said about M's being present. Previously it was said that M is present at a moment of present time, past at some moment of future time, and future at some moment of past time. On Broad's view, all that can be said is that it is present at a moment of present time. But when M is past, it can still be truly asserted on Broad's view that M has been present at a moment of past time and is past at a moment of present time. One thus refers to moments of time to distinguish when events have the determinations of pastness and presentness. Then, for the claim that moments of future time are equally moments of past time, McTaggart substitutes the claim that every moment which is past is also present. The point once again seems to be that even on Broad's ontology one has all these various, existent past events each of which is also a "present" in its own right. So which moment really is present? The one which is present now?-but that is to embark down the path of infinite regress. Thus, McTaggart's handling of Broad's objection confirms that it is the attempted combination of a B-theoretical ontology with A-theoretical becoming that generates the contradiction. Deny the reality of future events and no threat to the reality of becoming issues from that quarter. If we adopt a thoroughgoing Atheoretical ontology and deny the reality of past events as well, then McTaggart's

40 41

McTaggart, Nature of Existence, 2: 26. Ibid., 2: 27.

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Paradox disappears completely.42 For then only present events/things/times exist, and all that remains of McTaggart's A-determinations is that M has presentness at the present time. Since there is only one present, there is no sense in asking when the present moment is present. Hence, it seems to me that in his response to Broad, McTaggart not only reveals the source of his difficulty to lie in the misguided combination of B-theoretical ontology with A-theoretical becoming but also shows us the way out of his conundrum in the adherence to a consistent A-theoretical ontology consonant with A-theoretical becoming. McTaggart's mistake has more recently been committed all over again by Storrs McCall. McCall's aim was to draft a coherent model of the universe which involves objective temporal becoming.43 He begins by contrasting four theories, which may be represented diagrammatically:

A. Traditional Minkowskian View

B. Distinguished Branch Theory

C. Multiple Reality Theory

D. Dynamic Theory

Figure 6.2. Four models of temporality.

Theory A is identified as the traditional Minkowskian model, according to which the universe is a four-dimensional, spatio-temporal manifold in which all past, present, and future events are located. The diagram represents the history of the whole universe and is a straight line because every event is completely "attribute-specific." Theory B, the distinguished branch theory, represents the universe as a branched structure, each branch being a four-dimensional Minkowski manifold. The stem represents the actual history of the universe (and is thus distinguished), while the other branches represent "histories" which the universe could, but does not, follow. Theory C, the multiple reality model, differs from B in that no branch is distinguished as the universe's actual history. Rather, as in the Many Worlds Levison concurs: " ... if we do not assume that there is (tenselessly) any event which successively occupies past, present, and future temporal positions, then McTaggart's incompatibility argument cannot get off the ground" (Arnold B. Levison, "Events and Time's Flow," Mind 96 [1987]: 350). 43 Storrs McCall, "Objective Time Flow," Philosophy a/SCience 43 (1976): 337-362; cf. idem, A Model a/the Universe, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, I 994). 42

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Interpretation of quantum physics, the universe follows equally all the branches and so consists of all of them. Theory D, the dynamic theory, differs from the first three in that there cannot be a single diagram of the universe's history, but must be a multiplicity of dendriform diagrams indexed to times:

1800

(

1900

( (

1976

1996

Figure 6.3. Model of temporal flow.

The universe at each time is the whole tree, trunk (the past and present) and branches (the future) together. All the branches are equally real, and nothing indicates which branch will eventually form part of the trunk. But as time "flows," branches of the universe tree drop away, and the trunk of the tree grows. In this way, objective becoming is incorporated into our model of the universe. McCall implicitly commits McTaggart's mistake of trying to marry A-theoretic becoming to a B-theoretic ontology. For he conceives of the future branches of the universe as actually existing four-dimensional, spatio-temporal manifolds, just as real as the trunk. He states, "The representation of temporal becoming is accomplished by the introduction of indeterministic universe-models; each model representing the universe at a time. The models depict the past as a single fourdimensional manifold, and the future as a branched structure of such manifolds.,,44 The problem is that each universe tree already includes in it a time dimension, so that to have branches successively falling away from the tree requires a hyper-time in which this progressive pruning takes place. Since time is already built into the branching structure, any change of that structure must occur in hyper-time; any changes in first-level time are already accommodated in the very branching of the structure itself. Thus, 1. 1. C. Smart aptly compares McCall's model to a deck of cards, each card with a universe tree on it and cards higher in the deck portraying trees with progressively longer trunkS. 45 To get objective time flow, one adds a dealer who lifts a comer of the deck with his thumb and lets the cards fall seriatim. This clearly presupposes a time above time. McCall senses that his dendritical model involves such a hyper-time, and his response is instructive . ... the analogy with a three-dimensional tree, which grows and changes in time, should not be carried too far. A second time dimension would be an extravagance in a theory that is already extravagant enough. The extravagance can be avoided in one of two ways. We can, if we wish, deny that every entity which is different at different times is an entity which changes. * Alternatively, we can say that the progressive falling away of future branches on the universe-tree does not 'take' time but instead 'generates' time.t 44

4S

McCall, "Objective Time Flow," p. 337. Smart, "Time and Becoming," p. 7.

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• The inference x is a three-dimensional object x is different at different times Therefore x changes can be correct, without remaining correct if we replace '3-dimensional' by '4dimensional.' lowe this observation to Jonathan Bennett. t This alternative was suggested by one of the referees 46

Here McCall offers two reasons why the succession of different sets of futurebranches does not imply a hyper-temporal dimension. The first, Bennett's escape route, is futile, for when we say that a four-dimensional entity is "different at different times," we normally have reference to the time co-ordinates within the manifold, so that no change afthe manifold, but only in the manifold occurs. But when McCall asserts that the manifold itself is "different at different times," he can only have reference to hyper-times, not to time co-ordinates within the manifold. It is not something within the manifold that changes or even the manifold itself in the sense that it is different at one co-ordinate time compared to a later co-ordinate time (that is the case on a single card depicting the dendriform history), rather the whole dendritical past, present, and futures are different at different times. 47 But then these can only be the extravagant hyper-times which McCall rightly rejects. 48 As for the second, the referee's alternative, McCall has, I fear, little to thank him for, since the time generated by the falling away of branches is precisely the hypertime! McCall, however, came to settle on this second alternative as his solution, writing: the universe tree, though it changes, does not change in time. Rather, its change constitutes the flow of time. Branch attrition, in the model, is what time flow is. Therefore, branch attrition cannot take place in time, any more than time flow can take place in time.49

Now certainly the branched structure cannot change in first-level time, since that time is already depicted in the structure. But it could change in hyper-time, and it is McCall, "Objective Time Flow," p. 348. McCall writes, "If it be objected that the universe-tree which we have spoken of as constituting 'the universe' is a different universe-tree from one instant to the next, so that the extensions of 'past event,' 'present event,' and 'possible future event' change with time, then it can only be replied that this is correct, and reflects the dynamic character of theory D" (McCall, "Objective Time Flow," p. 347). The different instants at which the whole tree is different are the hyper-instants, since on a single tree the universe is different from one co-ordinate time to another and yet this does not yield a dynamic theory. To get dynamism, the extensions of past, present, and possible future must change with hyper-time, not just on a single tree. 48 In private correspondence with Smart, McCall states that the universe at t is the universe and that the universe at t', whether earlier or later, does not exist. But the difficulty with this A-theoretic assertion becomes evident when we ask: which t-the co-ordinate t or the hyper-time t? Since on McCall's model the whole tree-past, present, and future branches-exists at t, it is clear that t is a moment of hyper-time, so that his assertion only amounts to an affirmation of the A-theoretical nature of hyper-time. In the same correspondence McCall emphasizes that there can be no card of some future time, since nothing now indicates what the trunk shall then be. Again, however, the future time spoken of has to have reference to the hyper-time. McCall is denying that before the dealer flips a card in the hyper-present it (or any other future card) exists. That only reaffirms that the hyper-future (like the hyper-past) does not exist; but in the hyper-present the past-present trunk and future branches of ordinary time all exist. 49 McCall, Model of the Universe, pp. 30-3 I. 46 47

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difficult to see why progressive branch attrition would not necessitate the existence of just such a second-level time. Such change would constitute the flow of hypertime, not offrrst-Ievel time. Perhaps the point can be reinforced by considering other things McCall has to say. For example, he says that the universe can be considered as either an enduring 3-D object or as a 4-D space-time object. In the latter case, it would be "an enormous branched four-dimensional object: the branched model in fact."so But why is this the case? McCall accepts the truth of future-tense as well as past- and present-tense propositions. There is at any point and always was only one branch that represents the veritable future. So if considered from the 4-D perspective, why would the universe not be an enormous, long, four-dimensional trunk? That is the way the universe really is, once tense is abstracted. All those branches are nothing but alternate futures which are never incorporated into time's line. What McCall envisions as the 4-D picture of the universe is in fact the universe at the first instant of its existence, before any branches attrit. As he writes, "At the moment the individual comes into being its four-dimensional representation is a branched structure with no trunk; throughout its life it progressively sheds branches until...it eventually becomes a single unbranched four-dimensional volume located in the past."SI McCall might claim that the 4-D picture I envision is in fact the universe at the last instant of its existence. But surely this standoff results only because on McCall's metaphysic, there is no single 4-D picture of the universe: the 4-D structure itself is changing, which requires or constitutes a hyper-time. Or consider the question from the angle of actualism versus modal realism about possible worlds. McCall makes it quite clear that on his model future branches are every bit as real and concrete as the worlds of the modal realist. s2 Although he characterizes the future as potential in contrast to the past and present as actual, for McCall these are merely indexical terms. For the people existing in space and time on some future branch, their time is actual, as well as events lying in the interval between us and them which are only potential for us. On McCall's model, the flow of time corresponds to the transition from potentiality to actuality. Such persons become actual or present when all the alternative branches drop away. But when does that occur? Well, it occurs just at the time at which they exist. But for them that time has arrived; they are actual, they are present, alternative branches have disappeared. Why should we think our time to be privileged over theirs? The fact is that no perspective on which branches have attrited and which have yet to do so is preferred. But McCall's model requires that time's flow, even if reference frame dependent, involves a non-relational attrition of branches for each inertial frame. His model is incoherent in trying to have a non-relational theory of presentness coupled with a relational theory of actuality. If actuality is relative to time, then so is temporal flow, since to become actual corresponds to becoming present, which corresponds to branch attrition. This avoids hyper-time but also abandons a dynamic, evolving branch structure, since from an absolute perspective there is no attrition at all. On the other hand, if one affirms that temporal becoming is nonso St S2

Ibid., p. 217. Ibid., p. 223; cf. p. 227. Ibid., p. 198.

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relational, then so is the actuality of temporal events, which entails that either a branched structure does not exist or else it is evolving in hyper-time. Perhaps worse still, McCall's model entails that persons existing on some branch which will not in fact be the future are as actual and real relative to themselves and to us as are persons on the branch representing the veritable future. But then what reason exists for regarding one branch as the future and the other as a mere alternative? Inhabitants of each one must regard themselves as our true future and the other as the mere ersatz-future. Moreover, each group would be correct in so doing, since we are the true past of each branch. Since actuality is relative, for inhabitants of each branch it is the other branch which has attrited and no longer exists. Thus, no branches attrit absolutely, and reality is relative to branches as well as times. This conclusion is not only outlandish but contradicts the heart of McCall's model, which posits absolute branch attrition. If one clings to absolute branch attrition, then one must posit a hyper-time, a sort of God's-eye point of view, in which 4-D branches are successively pared away. A branched model in hyper-time is, however, also outlandish. Persons on various branches are all future relative to us at a certain moment of hyper-time, but later in hyper-time inhabitants of only one branch are future with respect to us at that earlier moment. Thus, contradictory future-tense propositions about events in first level time may both be true (relative to different branches) until the advance of hyper-time lops off all but one of the branches. At one moment of hyper-time we may have a real past in first-level time, only to lose it when our branch and we are annihilated by the advance of hyper-time. We unfortunates may perish twice-over: once when our world-line ends and again when our world-line is annihilated by branch attrition in hyper-time. Even if we are among the lucky ones who exist on a branch which becomes part of the tree trunk, nevertheless, as 4-D objects composed of branching temporal parts, we are constantly losing parts of ourselves as hypertime rolls relentlessly on, chopping off alternative branches. These other parts, should they learn of our good fortune, may well look on us parts begrudgingly, and, if time travel in first-level time is ever perfected on one of their branches, strive to return to the node where their branch leaves the trunk and to enter our time (perhaps to stick it to us!) before the march of hyper-time seals off this escape route forever. It is better, then, to deny the branched model of the universe altogether in favor of presentism, according to which the future is a realm of mere potentialities--or rather to interpret the branching model, not realistically as a representation of spacetime, but as an abstract structure depicting possible ways the future course of events might proceed. But to interpret it realistically is to succumb to McTaggart's flawed conception of time and becoming. As Broad came to see in his Examination, the consistent A-theoretic model is one in which only the present exists, so that the dendritical diagram looks like Fig. 6.4.

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Figure 6.4. Model of temporal becoming according to which only the present is real.

On this model the past, though actualized, no longer obtains, whereas the future consists of unactualized possibilities. To use the analogy of the deck of cards, the tree now runs through the deck and on each card appears only as a threedimensional slice of the tree trunk. If the universe as depicted on a particular card exists (present tense), then slices depicted on previously laid cards, having once been present or actual, no longer exist, while slices depicted on cards yet to be laid do not exist. To incorporate indeterminism, one can stipulate that whereas the pastpresent consists of a single series of cards, the future can be dealt from a number of possible decks and so can be represented as a dendriform realm of physical possibilities. The thickness of the slice representing the present depends on the thickness of the cards being played: is one talking about present seconds, present hours, present days, or what? The duration stipulated to be present will be an arbitrary, finite duration centered on a present instant. 53 Such a model has an Atheoretic ontology combined with A-theoretic becoming and so constitutes a consistent model of time which escapes McTaggart's Paradox. An examination of the arguments of contemporary proponents of McTaggart's Paradox reveals that, despite their often quite different formulations of the paradox, they, too, are presupposing a B-theoretic ontology coupled with A-theoretic becoming, so that adoption of a pure A-Theory oftime undermines their case. For example, Mellor seems to understand temporal becoming as a qualitative change of tenses. Thus, he says that "change ... is something having incompatible properties at different dates, such as being at different temperatures or in different places;" Andros Loizou explains, " ... no event or state of affairs is ever present simpliciter-it is present by implicit or explicit reference to a kind of events or states of affairs, as when we speak of the present eclipse, or by reference to a time scale, as when we speak of the present hour or day, and so on" (Andros Loizou, The Reality of Time [Brookfield, Ver.: Gower, 1986], p. 156; see also D. H. Mellor, Real Time [Cambridge: Cambridge University Press, 1981], pp. 17-18; Alan Padgett, God, Eternity, and the Nature of Time [New York: St. Martin's Press, 1992], p. 115). Broad never discerned this solution and so was forced into adopting the Augustinian view that the present is a durationless instant or "event particle" and finally into espousing-ironically-the existence of a second time dimension in which the present event particle endures (C. W. K. Mundie, "Broad's Views about Time," in The Philosophy ofe. D. Broad, ed. Paul Arthur Schilpp, Library of Living Philosophers [New York: Tudor, 1959], p. 367; C. D. Broad, "A Reply to My Critics," in Philosophy ofe. D. Broad, pp. 767-772)1 S3

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according to the A-Theory, "Change is the changing tense of things and events moving from future to past.,,54 On the A-Theory, "Futurity, temporal presence, and pastness are all supposed to be real non-relational properties which everything in time successively possesses, changing objectively as it exchanges each of these properties for the next.,,55 Elsewhere he speaks of "the inexorable movement of the present along the B-series.,,56 Expressions such as these make it clear that Mellor has failed to appreciate Broad's point that there is an irreducibly characteristic feature of time ... called 'Absolute Becoming.' It should be sharply distinguished from qualitative change .... This seems to me to be the rock-bottom peculiarity of time, distinguishing temporal sequence from all other instances of one-dimensional order, such as that of points on a line, numbers in order of magnitude, and so on 57

Similarly, Mellor's former student and collaborator Robin Le Poidevin, while repudiating the charge that McTaggart's Paradox depends on an event ontology of tenselessly existing events,58 in fact only repudiates event ontology but affirms that the metaphysic underlying McTaggart's argument involves a B-series of temporal terms which are all on an ontological par. He explains that we take reality to be temporally extended, so that the totality of facts must include not only present but past facts. That leads to his re-statement of McTaggart's argument: We can now see the nature of McTaggart's contradiction. Reality consists both of present and past fact. It is a present fact that the First World War is past; symbolically: Pp and a past fact that the First World War is present; symbolically: Np But these facts cannot both obtain. Yet if there are tensed facts, they do. So there are no tensed facts. 59

Le Poidevin assumes that the First World War tenselessly exists and has the property of being present; but it also tenselessly has the property of pastness, which is contradictory.6o Any attempt to relativize these properties or their possession to ,. 55 56

Mellor, Real Time, pp. 89-90. Ibid., p. 4. Ibid., p. 24. Cf. L. Nathan Oaklander, "Zeilicovici on Temporal Becoming," Philosophia 21 (1991):

329: "On the traditional tensed, or A-theory of time, the NOW is a particular or a property that moves along an ordered, but as yet non-temporal, C-series. The terms of the Cseries exist (tenselessly) in unchanging relations to each other, and these unchanging relations become temporal relations as the NOW moves across them, so that one term, e is NOW when another term, e' is future and then. when the NOW 'hits' e', that is, when e' is present, e is past." 57 Broad, "Reply to My Critics," p. 766. 58 Robin Le Poidevin, Change. Cause. and Contradiction: A Defense of the Tenseless Theory of Time (London: Macmillan, 1991), p. 30. 59 Ibid., p. 33. 60 This assumption comes to the fore even more clearly in his later comment on this passage. In response to the objection that one should say, not that it is a past fact that WWI is present, but that it is a past fact that WWI was present, which is not contradictory, Le Poidevin answers, "To this I would reply: 'what, then, do people mean when they say that the past is real, but the future not? After all there will be future states of affairs, so the future will be real, just as the past was real. Wherein lies the asymmetry? The answer must be that, although the dinosaurs (for example) are extinct, they are still real to the extent that it is

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times will either reduce them to B-relations (for example, present at t) or lead to an infmite regress (for example, present at present at .... ).61 Hence, concludes Le Poidevin, the tenser has to say that only present facts comprise reality, a view he characterizes as "temporal solipsism." Such a metaphysic, he admits, is immune to McTaggart's argument. What this discussion reveals, then, is that McTaggart's Paradox is not really an argument against an A-Theory of time at all. It is in fact an argument against a hybrid A-B-Theory which combines tenseless ontology with temporary intrinsic properties oftense. 62 The consistent A-theorist, who regards temporal becoming as real, rejects, like the B-theorist, this hybrid theory and so may dismiss McTaggart's argument as an irrelevancy.

they and their properties which make statements about dinosaurs true, not present evidence in the form of fossils, etc.... To make sense of the past's being real and the future not, we have to talk of being real simpliciter, not once being real, or being about to be real''' (Robin Le Poidevin, "Lowe on McTaggart," Mind 102 [1993]: 168). Although Le Poidevin's characterization of the reality ofthe dinosaurs could be given an acceptable sense by the presentist (viz., by taking "make" tenselessly rather than as present-tense), still it is clear that he intends to assert the equivalence of their ontological status with that of present day existents-otherwise there would be no asymmetry of past and future existents; future things and their properties would make future-tense statements about them true, which renders the future as real as the past. As Broad came to see, the consistent A-theorist does regard the past and the future as equally real: past and future events/things/times alike do not exist. The asymmetry between past and future lies not in their ontological status, but in the fact that in the present there are traces only of the past, and this fact is rooted in the impossibility of backward causation, which is founded, in tum, upon the objective reality of temporal becoming (William Lane Craig, Divine Foreknowledge and Human Freedom: The Coherence of Theism: Omniscience, Studies in Intellectual History 19 [Leiden: E. 1. Brill, 1991], pp. 150-153). To say that the past and future are unreal is not to assert that the Principle of Bivalence fails for future-tense propositions or statements anymore than for past-tense propositions (Ibid., pp. 43-63). 61 A point nicely made by Buller and Foster, "New Paradox," pp. 358-359; also Zdzislaw Augustynek, Time: Past, Present, and Future, trans. Stanislaw Semczuk and Witold Strawinski, Nijhofflnternational Philosophy Series 30 (Dordrecht: Kluwer Academic Publishers, 1991), p. liS; J. M. Shorter "The Reality of Time," Philosophia 14 (1984): 324. Shorter overlooks, however, the possibility of relativizing Adeterminations to the A-series rather than the B-series. 62 I have come to see that McTaggart's argument is in fact a special case of the more general problem of intrinsic change or the problem of temporary intrinsics. A-determinations are taken to be intrinsic properties which are exemplified by temporal items. But some event e cannot have both the properties of presentness and pastness, for example. Attempts to construe A-determinations as extrinsic properties will lead either to their reduction to B-relations (if one relativizes to terms in the B-series) or else to a vicious regress (if one relativizes to terms in the A-series). Therefore, e is either permanently present or there are no such properties as A-determinations. Since the former is absurd, the latter follows. The solution to McTaggart's Paradox is the same as the solution to the general problem of temporary intrinsics, viz. presentism. See discussion in The Tenseless Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, forthcoming), chapter 9. What makes McTaggart's case special is that the perdurantist solution does not even apply to it because e need not persist over time at all but may exist only at an instant t. Hence, we are not concerned, as usual, with an entity which persists from t to t*, has different intrinsic properties at each temporal location, and yet remains self-identical. Rather e exists only at t and yet is self-identical at that moment despite its being the case that e-at-t has both presentness and pastness. Because e does not persist through time, there is no place for a solution postulating temporal parts of e each having different intrinsic properties (e.g., presentness and pastness). It is a strange case of e's synchronic identity being diachronically preserved. To prevent e's self-identity's being destroyed over time, one must either deny that there are any such properties as A-determinations or else adopt a presentist metaphysic.

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Tenseless Predication ofA-Determinations

The second part of Broad's critique, it will be recalled, is that in the predication of A-determinations McTaggart misguidedly tries to replace the tensed copula "is" with a tenseless copula plus some temporal adjective. According to Broad, when I say, "Eating my breakfast is past," the "is" is not the tenseless copula used in "37 is a prime number," but is in the present tense. 63 Similarly, if we take the copula in "The event e is present" to be tense less, then every utterance of this sentence on my part would record the same fact-but in fact earlier or later utterances of this sentence would be false. In his argument, McTaggart, however, takes such a copula as tenseless. In his analysis, "8 is now P" means "There is a moment t, such that 8 has P at t and t is present." (So "M is now present" means "There is a moment t, such that M has presentness at I and t is present.") Broad comments that the predicate "having P at I" belongs to 8 timelessly or sempitemally if it belongs to 8 at all. We are tempted to think that the clause "t is present" is timeless, too. But this would lead to contradiction, since t is also past and future in the same timeless sense. What Broad means here is that if such sentences as "t is present," "t was future," and "t will be past" are to be analyzed in terms of a tenseless copula plus complex temporal predicates, then t possesses tenselessly all three predicates in the same way, which is contradictory. But if we therefore say the "is" is tensed, then one embarks on an infmite regress. For "I is present" must be analyzed to mean "There is a moment I' such that t has presentness at I' and t' is present," and so on ad infinitum. "At every stage of the analysis you will have a copula which, if taken to be non-temporal, leads to a contradiction, and, if taken to be temporal, needs to be analyzed further in terms of temporal predicates and non-temporal copulas.,,64 What the infmite regress argument really shows is that temporal copulas cannot be replaced by non-temporal copulas plus temporal predicates. Temporal facts are ineliminable and form the very essence of time. Broad's second critique raises the issue of how we ought to understand the ascription of A-determinations to temporal entities, whether these be events, things, or times. On the basis of our previous discussion of temporal indexicals,65 it seems to me that the A-theorist should at the outset draw a distinction between indexical and non-indexical ascriptions of A-determinations. As we saw, temporal indexicals like "now" plausibly have a certain ego-centric character which is not part of the propositional content of sentences containing such words. On the other hand ascriptions of A-determinations by non-indexical expressions like tensed verbs and predicate adjectives following a tensed copula do not imply the existence of a sentient subject. Hence, we should not speak of a mind-independent property of "nowness" of temporal entities, as many authors are wont to do, but rather, like McTaggart, of presentness. An event's occurring now will depend on its relation to some sentient subject, but its being present will be mind-independent and objective. Furthermore, on the A-Theory of time, we should not understand grammatical ascriptions of pastness and futurity as in "Past injustices must be forgotten" or "The

64

Broad, Examination, 2: 272. Ibid., 2: 315.

61

See chaps. 1 and 4.

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future space station will further space research" to postulate the literal inherence of properties of pastness and futurity in the events/things/times so described. 66 On a presentist ontology, such entities do not exist and so possess no properties. Rather they did or will possess properties, and it is this tense distinction that is expressed by referring to such entities as past or future. The A-theorist thus agrees with the Btheorist that pastness and futurity are relational predicates, but he will differ in anchoring these relations in what is non-relationally present. The construal of pastness and futurity as relational predicates should not be taken to mean that these are relational properties inhering in events. Rather such ascriptions should be parsed as asserting that the entity in question did or will exist; for example, "One must forget the injustices which occurred" and "The space station will exist and further space research." Furthermore, odd locutions like "E is present in the past" or "E is present in the future" should be construed to mean that the statement "E is present" either was true or will be true. 67 Hence, only ascriptions of presentness may be taken literally as the possession of an A-determination by some temporal entity; in the case of non-present A-determinations, we are to understand ascriptions of them in terms of what was or will be the case.

Contra the presupposition of Eddy M. Zemach, "Time and Self," Analysis 39 (1979): 143-147; David Zeilicovici, "A (Dis)solution of McTaggart's Paradox," Ratio 28 (1986): 187. This sort of hybrid A-B-Theory, such as is defended by Smith (Quentin Smith, "The Infinite Regress of Temporal Attributions," Southern Journal of Philosophy 24 [1986]: 383-396; idem, "The Logical Structure of the Debate about McTaggart's Paradox," Philosophy Research Archives 14 [1988-89]: 371-379, the latter being a reply to L. Nathan Oaklander, "McTaggart's Paradox and the Infinite Regress of Temporal Attributions: a Reply to Smith," Southern Journal of Philosophy 25 [1987]: 425-431) has been aptly characterized by Fitzgerald as a "property acquisition model" of temporal becoming (Paul Fitzgerald, "Nowness and the Understanding of Time," in PSA 1972, BSPS 20, ed. Kenneth F. Schaffner and Robert S. Cohen [Dordrecht: D. Reidel, 1974], p. 261). But while we can perhaps make sense of, say, "The presidency of Bill Clinton presently has presentness," it does not seem intelligible to assert, 'The Battle of Waterloo presently has pastness," since the Battle of Waterloo does not exist or occur at the present time. Yet Smith's view that the pastness or futurity of an event presently inheres in that event seems to imply such a conclusion. So long as event e is present, we can make sense of Smith's contention that the futurity of e's pastness presently inheres in e and likewise that the pastness of e's futurity presently inheres in e. But if e is a past or future event, it seems unintelligible to claim that presentness inheres in the inherence of pastness/futurity in e, since e does not presently exist so as to sustain the inherence of any properties in it. Perhaps Smith would prefer to say of a past event that pastness presently inheres in the inherence of presentness in e. But then events never lose or acquire their property of presentness; what changes is the tense of presentness's inherence in e. But that interpretation seems as unintelligible as the first interpretation; for how can pastness presently inhere in e's presentness, if e is a past event, since e's presentness does not exist at the present time? 67 See E. 1. Lowe, "The Indexical Fallacy in McTaggart's Proof of the Unreality of Time," Mind 96 (1987): 64-66, who seems, however, unduly diffident about tensed ascriptions of presentness to events, e.g., "E will be present," which is unobjectionable so long as "present" is not an indexical synonymous with "now," as Lowe mistakenly believes. Cf. E. J. Lowe, "Comment on Le Poi devin," Mind 102 (1993): 171-173, where he objects to embedding one temporal indexical in the scope of another. But as the phenomenon of double indexing attests, such embedding is common and unproblematic, so long as we use the proper indexical, e.g., "Yesterday he promised to call today." Lowe's objection is really directed at failures to change the indexical words appropriately. But in ascriptions of presentness to an event, e.g., "Ninety years ago WWI was present," Lowe fails to see that "present" is not an indexical word. In general the point of such paraphrases as offered in the text is to make it perspicuous that the original locutions do not in fact involve the ontological commitments some might take them to have (cf. William P. Alston, "Ontological Commitments," Philosophical Studies 9 [1958]: 8-17). 66

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Thus, when McTaggart says that "M will be past" means "M is past in the future," we should not understand the latter locution, as he does, to ascribe the property of pastness to an event which presently exists in the future. Rather we should take the latter locution to express the proposition that it will be the case that it was the case that M occurs. The tense logical operators operate on sentences which are irreducibly presenttensed. That is why a present-tense operator "It is now the case" is redundant. Thus, McTaggart is wrong-headed to try to analyze the meaning of "M is present" as "M is present at a moment of present time," for unless the "is" is tenseless, an infmite regress is generated. In an early analysis of McTaggart's article, John Wisdom contended that "M is present" entails, but does not mean, that "M is present at a moment which is present." He argues, It looks true to say that 'This is red' means 'This is red at the present moment.' But I think that to say this is to make a mistake like that made by one who says 'This is red' means 'This is characterized by red.' This is red entails immediately this is characterized by red, and the second fact differs only slightly from the first. Similarly 'This is red' entails 'This is red at the present moment,' and the second fact differs only very slightly from the first. But to suppose that 'this is red' means 'this is characterized by red' involves a vicious circle, for then 'this is characterized by red' means 'this is characterized by "is characterized by red",' and thus 'characterized by' is a constituent of itself. Similarly to suppose 'This is red' means 'This is red at the moment which is present' involves that the temporal 'is' is a constituent of itself, unless both the 'is's' in the second sense are timeless. 68

Since the infinite regress is one of entailings, rather than meanings, it is benign, rather than vicious. Nor does it lead to extra time dimensions, since the entailed moments are moments in the selfsame temporal series: the t' at which the present moment t is present just is the identical moment. Thus, this endless series of entailments is not at all worrisome. 69 What, then, does it mean to say, "t is present?" It seems to me that Broad is correct that temporal determinations of this sort are irreducible. 70 Of course, one John Wisdom, "Time, Fact and Substance," Proceedings o/the Aristotelian Society 29 (1928-29): 83. Following Wisdom are L. Susan Stebbing, "Some Ambiguities in Discussions conceming Time," in Philosophy and History, ed. Raymond Klibansky and H. 1. Paton (New York: Harper & Row; Harper Torchbooks, 1963), pp. 114-116; Richard Swinburne, "Tensed Facts," American Philosophical Quarterly 27 (1990): 118. Mink indicts the Wisdom-Stebbing response because, while it does not make sense to ask "When is x present?", it does make sense to ask "When was x present?" The statement "x is past" must mean, not merely entail, "x is past at a moment of time which is present" because it is equivalent to "x was present at a moment oftime which was past" (Louis O. Mink, "Time, McTaggart and Pickwickian Language," Philosophical Quarterly 10 [1960]: 257). I must confess that the force of this argument escapes me. Mink seems to take "x was present at a moment oftime which was past" to be the answer to "When was x present?" But if this is the answer, then it is absurd to ask "When was x present?" for the answer is the tautologous "in the past!" A proper answer would be to give a date, and a similar answer could be given to the query, "When is x present?" 69 It is not clear whether Smith, "Infinite Regress," pp. 383-396 and Smith, "Logical Structure," pp. 371-379 means to assert a regress of meanings or entailments, for he speaks both of providing an analysis of "£ is present" and of drawing a series of entailments from it. If he really means to provide an analysis of the meaning of"£ is present," then his regress is not benign. 70 Mink charges that the refusal to analyze A- characteristics in terms of B-characteristics has serious negative consequences, e.g., complex tenses cannot be analyzed as complications of simple ones without 68

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could, if one wished, adopt a tense logical operator N for "It is now the case" which would operate on tense less sentences with the stipulation that the resultant sentence has the meaning of a present-tense sentence. Contradiction would not then result from tenseless copulas' being employed with temporal predicates, since it would, for example, be true that N eM is present), but false that N eM is past). Contradiction arises only from tenseless ascription of A-determinations in the absence of adverbial operators. On the above stipulation we could say that "M is present" means N eM is present). So long as the sentence means the same thing whether the tense is expressed verbally, adverbially, predicatively, or whatever, it is of no consequence how the tense is expressed. 71 The point remains that temporal entities' exemplification of their properties is irreducibly tensed. Now if, as I have maintained, pastness and futurity are not to be construed as properties, what about the premier A-determination of presentness itself? Is it a property? On this question there exists an intra-mural, if somewhat muffled, debate among A-theorists. All agree that tense is an objective feature of reality; the dispute concerns the place of tense in one's ontology-what exactly is presentness? A good many A-theorists have followed A. N. Prior in denying that presentness should be considered a property possessed by things/events/ times. Responding to C. D. Broad's point that an event does not possess properties except at the time at which it is present, Prior goes further to deny both that one's ontology ought to include events and that tense determinations are properties of either events or things. He asserts, 'Is present,' 'is past,' etc., are only quasi-predicates, and events only quasi-subjects. 'X's starting to be Y is past' just means 'It has been that X is starting to be Y,' and the subject here is not 'X's starting to be Y' but X. And in 'It will always be that it has been that X is starting to be Y,' the subject is still only X; there is just no need at all to think of another subject, X's starting to be Y, as momentarily doing something called 'being present' and then doing something else called 'being past' for much longer; and no need to argue as to whether X's starting to be Y 'is' only at the moment when it does the thing called being present, or also throughout the longer period when it does the other thing. It is X which comes to have started to be Y, and it is of X that it comes to be always the case that it once started to be Y; the other entities are superfluous, and we see how to do without them, how to stop treating them as subjects, when we see how to stop treating their temporal qualifications ('past,' etc.) as predicates, by rephrasings which replace them with propositional prefixes ('It has been that,' etc.) analogous to negation 72

the same explanation's applying to simple tenses as well, such as analyzing the past tense as past with respect to the present (Mink, "Time," p. 258). But the A-theorist could maintain that requirements of real tense necessitate a minimum of three determinations and no more. 7\ Mellor, Real Time, pp. 3-4. Failing to assimilate this point is Ferrel Christensen, "McTaggart's Paradox and the Nature of Time" Philosophical Quarterly 24 (1974): 289-299. He insists that tenses are adverbial operators, not predicates, because the latter generates an infinite regress. But the regress in question is, as Wisdom saw, entirely benign. For this reason one cannot agree with Shorter that "If we read the sentences 'E is future' and 'E is past' ... as containing a purely predicative copula, they are entirely compatible" (Shorter, "Reality of Time," p. 325). For these sentences mean the same thing as "E will be" and "E has been" respectively, which are incompatible. 72 A. N. Prior, "Precursors of Tense Logic," in Past, Present and Future (Oxford: Clarendon Press, 1967),p.18.

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Prior wants to excise events from one's ontology, and the way to do this, he believes, is to deny that tense determinations are properties; rather they are propositional operators. We should no more reify tense operators than we do the operator of negation. We may leave to the side Prior's rejection of an event ontology, since an Atheorist could agree with Prior on this score and still consider presentness to be a Rather Prior's relevant claim is that tense property of things or times. determinations are propositional operators rather than properties. On Prior's view, as Christensen explains, tenses are adverbial in nature and thus radically different from predicates: tenses do not tell what the properties of an individual are, but rather when an individual has its properties. 73 Thus, presentness is not a property of any event/thing/time. Smith, however, has bitingly criticized what he calls the "no-property" view as obscure and unintelligible. Smith's fundamental complaint is that the construal of tenses as propositional operators is a semantical thesis only, which leaves unaddressed the metaphysical question "in what ontological category should we place what is told' by tenses?74 Since A-theorists agree that tenses are not just egocentric features of human thought and language, there must be some feature of reality corresponding to the tenses we use. What in the propositional content of a present-tensed sentence corresponds to the tense in that sentence? Since any intelligible theory of tense attempts to classify the semantic relata of tenses in terms of some ontological category, Prior's theory, in failing to do so, is unintelligible. Smith does not respond to Prior's comparison of tense operators to the operator of negation. It certainly seems a defensible theory to hold that there is no ontological correlate to the sentential operator of negation. One's ontology seems to become unnecessarily bloated if we countenance negative properties corresponding to every description which is not true of a thing. When we assert that something is not orange, we are not normally ascribing to it the property of being not-orange, but are just denying that it has the property of being orange. Similarly, perhaps presentness is not a property which things/events/times possess; rather our use of the present tense just indicates the reality of the things/events/time described. Indeed, in a later piece Prior claims that the present and the real are one and the same concept: "the present simply is the real considered in relation to two particular species of unreality, namely the past and the future.,,75 Rejecting modal realism, Prior states that other worlds are made by prefixing "X is the case" with a phrase like "It could be that." What is real involves no such prefix. Similarly, "the present is real and the past and future are not. And I want to suggest that the reality of the present consists in what the reality of anything else consists in, namely the absence of a qualifying prefix.,,76 This last remark illustrates the conflation of semantics and ontology that so exasperates Smith, for the reality of the lamp before me on my desk Christensen, "McTaggart's Paradox," p. 297. Quentin Smith, Language and Time (New York: Oxford University Press, 1994), p. 166. 75 A. N. Prior, "The Notion of the Present," Studium Generale 23 (1970): 245. Similarly, Christensen has recently asserted, "To be present is simply to be, to exist, and to be present at a given time is just to exist at that time-no less and no more" (F. M. Christensen, Space-like Time [Toronto: University of Toronto Press, 1993], p. 168; cf. p. 226). 76 Prior, "Notion of the Present," pp. 246-247. 73

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does not consist in the absence of a qualifying prefix, since prefixes do not operate on lamps. And while the sentence "The lamp is on my desk" lacks a tense logical operator, it is hard to see how the reality of my lamp or its location consists in this sentence's (or the proposition expressed by it) lacking an operator. Moreover, the analogy between tense operators and modal operators is much closer than that of the former with the negation operator, and it undeniable that modal sentences or propositions raise a host of questions for ontology. The demonstrated inadequacy of Prior's views of modal assertions 77 makes one more than suspicious that the ontological questions concerning tense ascriptions cannot be so neatly circumvented as Prior hoped. Still, the connection between presentness and reality which Prior affIrmed is inescapable on a presentist ontology and suggests that we could perhaps make progress on the problem raised by Smith by exploring the question of existence. If to be present is simply to exist, as Prior suggests, then our ontological classification of existence will tell us whether presentness is a property, as Smith claims. So what is it for a thing to exist; more specifically, is existence a property? Readers who are philosophers of religion will immediately realize that this question has been extensively aired in the centuries-old debate over the ontological argument, which in some versions treats existence as a great-making property which God, as the greatest conceivable being, must possess. 78 It was characteristic of Immanuel Kant's refutation to deny that existence is a real predicate, or, more perspicuously, a property. He wrote, 'Being' is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing. It is merely the positing of the thing, or of certain determinations, as existing in themselves. Logically, it is merely the copula of a judgment. The proposition, 'God is omnipotent,' contains two concepts, each of which has its object-God and omnipotence. The small word 'is' adds no new predicate, but only serves to posit the predicate in its relation to the subject. If, now, we take the subject (God) with all its predicates (among which is omnipotence), and say 'God is,' or 'There is a God,' we attach no new predicate to the concept of God, but only posit the subject in itself with all its predicates, and indeed posit it as being an object that stands in relation to my concept. The content of both must be one and the same; nothing can have been added to the concept, which expresses merely what is possible, by my thinking its object (through the expression 'it is') as given absolutely. Otherwise stated, the real contains no more than the really possible. A hundred real thalers do not contain the least coin more than a hundred possible thalers .... By whatever and by however many predicates we may think a thing--even if we completely determine it- we do not make the least addition to the thing when we further declare that this thing is. Otherwise, it would not be exactly the same thing that exists, but something more than we had thought in the concept; and we could not, therefore, say that the exact object of my concept exists. 79

See the incisive critique by Alvin Plantinga, "On Existentialism," Philosophical Studies 44 (1983): 1-20. 78 For helpful anthologies and bibliographies, see Alvin Plantinga, ed., The Ontological Argument, with an Introduction by Richard Taylor (Garden City, N. Y.: Doubleday, 1965), and John H. Hick and Arthur C. McGill, eds., The Many-jaced Argument (New York: Macmillan Co., 1967). 79 Immanuel Kant, Immanuel Kant's "Critique of Pure Reason," trans. Norman Kemp Smith (London: Macmillan, 1929), pp. 504-505 (A5981B626-A599/B627); cf. p. 502 (A5951B623). 77

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This passage contains both a positive characterization of existence in terms other than its being a property, as well as a negative critique of the position that existence is a property. In a detailed and careful analysis of the negative critique, Plantinga has argued persuasively that Kant fails to specifY a sense of "predicate" such that, in that sense, it is clear both that existence is not a predicate and that Anselm's argument requires it to be one. 80 In point of fact, Plantinga is able to specifY a sense in which existence is not a real predicate or property, though that sense turns out to be irrelevant to the cogency of the ontological argument (which is a matter of indifference for our present discussion). Plantinga interprets Kant's dictum that the content of an object and the content of the concept of that object must be the same along the following lines: call the concept whose content includes all (and only) the properties an object has the whole concept of that object. Call the concept whose content contains just those properties which are members of the content of the whole concept of an object o and neither entail nor are entailed by a property P the whole concept of 0 diminished with respect to p.8t (Roughly, a whole concept diminished with respect to P is that concept minus P.) Now let C t be the whole concept of some object 0, and let C2 be the whole concept of 0 diminished with respect to some property P, say, pinkness, and let C3 be the whole concept of 0 diminished with respect to existence (on the assumption that existence is a property). Kant's point is that existence is then unlike other properties like pinkness in that there are no possible worlds in which C3 , but not Ct. is exemplified, whereas there are worlds in which C2 , but not Ct. is exemplified. Since C t and C3 are mutually entailing, they are equivalent concepts; in adding existence to C3 one does not come up with a new concept. So if a predicate P represents a property only if it is not the case that a whole concept diminished with respect to P is equivalent to the corresponding whole concept, then existence, concludes Plantinga, is not a property. Readers familiar with Plantinga's later Nature of Necessity may be surprised at this conclusion, since in that work he routinely speaks of existence as a property, indeed, a property which every object possesses essentially, since in every world in which an object exists it obviously has existence. But a closer reading reveals that Plantinga is arguing ex concessionis, his main concern being to analyze not the nature of existence, but of necessity. Thus, he explains that some properties are "trivially essential. Among them will be the property of existence-if, once more, we momentarily concede that existence is a property."S2 In God and Other Minds, which Plantinga in his later work references concerning whether existence is a property,S3 his main burden is not to refute Kant's claim that existence is not a property but to rebut Kant's contention that existential propositions cannot be Alvin Plantinga, God and Other Minds (Ithaca, N. Y.: Cornell University Press, 1967), pp. 29-38. Ibid., p. 35. Plantinga adds a further qualification which I omit for simplicity's sake. 82 Alvin Plantinga, The Nature of Necessity, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1974), p. 61. 83 Ibid., p. 137. Here Plantinga declines to take the easy way out of the classical argument for merely possible objects by denying that existence and non-existence are properties. So he says most of the arguments against their being properties are inconclusive and at best show existence, if a property, to be atypical. He does not repudiate his analysis in God and Other Minds and himself comes to the conclusion that non-existence is, at least, not a property. 80 81

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necessarily true, and this concern carries through to his defense of the ontological argument in The Nature of Necessity. Agreement with Kant that existence is not a property in no way implies agreement that existential propositions are all contingent or that no being exists necessarily. Thus, Plantinga concludes, Giving a clear explanation of the claim that existence is not a real predicate, this interpretation also shows an interesting respect in which existence differs from other predicates or properties. Unfortunately, it seems to have no particular bearing on Anselm's argument.... Anselm argues that the proposition God exists is necessarily true; but neither this claim nor his argument for it entails or presupposes that existence is a predicate in the sense just explained. 84

What Kant's argument does show, Plantinga thinks, is that one cannot define things into existence: "it shows that one cannot, by adding existence to a concept that has application contingently if at all, get a concept that is necessarily exemplified."s5 For any concept C, if it is a contingent truth that C is exemplified, it is also a contingent truth that the concept of C plus existence is exemplified. Thus, the Kantian critique, in Plantinga's assessment, makes a valuable, positive contribution to our understanding of existence and certain fallacious versions of the ontological argument. Refusing to allow property status to existence also affords us the benefit of an explanation of why existence, when construed as a property, is so anomalous in comparison with other properties. These anomalies were noted in particular by C. D. Broad and G. E. Moore. Broad observed that negative existential propositions like Dragons do not exist cannot be what he called "characterizing propositions," that is, propositions which ascribe some property to an object. s6 For, in the example, there are no such things as dragons to possess the property of non-existence. Moreover, if one tries to analyze negative existential propositions in familiar ways proposed for analyzing negative characterizing propositions, self-contradiction results. For example, on the conditional interpretation, the proposition at issue might be expressed by the sentence "Ifthere were any dragons, none of them would exist" and on the instantial interpretation by the sentence "There are dragons and none of them exist," both of which are self-contradictory. Broad proceeded to argue that affirmative existential propositions like Cats exist are also not characterizing propositions. For on the conditional interpretation this proposition would be expressed by the sentence "If there were any cats, none of them would fail to exist" and on the instantial interpretation by the sentence "There are cats and none of them fail to exist," both of which are "mere platitudes,,,s7 which Cats exist is not. Plantinga, God and Other Minds, p. 36. Ibid., p. 37. 86 C. D. Broad, "Arguments for the Existence of God," [1925], in Religion. Philosophy and Psychical Research, International Library of Psychology, Philosophy, and Scientific Method (New York: Humanities Press, 1969), pp. 182-183. 87 Plantinga objects to Broad's characterization of ''There are cats and none of them fails to exist" as a platitude, since this sentence entails that cats do exist and so is not a mere tautology (Plantinga, God and Other Minds, p. 41). But perhaps we need not construe "mere platitudes" as tautologies; we could take Broad to be saying that the complex sentences analyzing existential propositions become redundant (of course, if there are cats, they exist!), while the sentences analyzing genuinely characterizing propositions do not. 84 85

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In his God and Other Minds, Plantinga protested Broad's assertion that there are no subject-predicate propositions about dragons as "plainly outrageous," furnishing the counterexample Dragons are beasts of fable. 88 But this seems to confuse sentences with propositions; Broad does not deny that there are sentences whose subject is dragons, but he denies that there are propositions ascribing properties to dragons. In his Nature of Necessity, Plantinga in effect endorses Broad's position when he maintains that any world in which a predicative singular proposition is true is one in which the subject of that proposition has existence. 89 Negative existential propositions are not to be construed as ascribing the property of non-existence to some (merely possible) object; rather they are to be interpreted as asserting that it is false that some object has the property of existing. Plantinga rejects "descriptivism" with regard to creatures of fiction; the descriptivist (falsely) assumes that in fiction we are talking about an object, say, Hamlet, and predicating a property of it. But Plantinga maintains that creatures of fiction are not subjects having properties in the actual world, nor do fictional names denote anything, being merely stylistic variants of variables. Fictional stories "are about nothing at all and the names they contain denote neither actual nor possible subjects.,,9o Thus, Plantinga comes to aftirm Broad's position, which he had earlier rejected, and his arguments that there are no merely possible objects go to confirm Broad's view. Still, this only shows that Broad was correct that negative existential propositions do not ascribe a property of non-existence. One could agree with this and yet construe affirmative existential propositions (about real objects) as ascribing the property of existence. In response to Broad's argument that affirmative existential propositions do not ascribe the property of existence, Plantinga points out that not all characterizing propositions, whether general or singular, are susceptible to either the conditional or instantial interpretation. For example, neither the general proposition Buffalo once abounded on the Great Plains nor the singular proposition Cerberus is my favorite beast offable can be analyzed along these lines. 91 Broad, however, could respond to Plantinga that none of Plantinga's examples concerns propositions which ascribe properties to individual objects. 92 General propositions which fail to ascribe properties to every individual in a class or singular statements about creatures of fiction do not ascribe properties to objects and so provide no basis for thinking that affirmative existential propositions, in being insusceptible to the conditional and instantial analyses, nevertheless do ascribe the property of existence to objects. Moore pointed out further peculiarities of affirmative existential propositions if they are construed as ascribing a property.93 Unlike the statement "Tame tigers growl," the statement "Tame tigers exist" cannot be meaningfully interpreted as "All tame tigers exist" or "Most tame tigers exist;" it can only mean "Some tame tigers exist." Moreover, if we negate this statement, we have "Some tame tigers do not Plantinga, God and Other Minds, p. 40. Plantinga, Nature a/Necessity, p. 150. 9n Ibid.,p. 163;cf. 158-160. 91 Plantinga, God and Other Minds, p. 41. 92 See Jerome Schaffer, "Existence, Predication, and the Ontological Argument," in Many-faced Argument, p. 234. Schaffer's difficulties with Kant's argument that existence is not a property are implicitly met by Plantinga's analysis exposited above. 93 G. E. Moore, "Is Existence a Predicate?" [1936], in Ontological Argument, pp. 73-80. 88 89

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exist"-which appears to mean that there are some tame tigers which do not exist. With other property ascriptions, as in "Some tame tigers growl," we may insert "do not" before the predicate and have a meaningful statement, but this cannot be done with the predicate "exist." Moreover, when one says, "Some tame tigers growl," this asserts that the propositional function x is a tame tiger and growls has a value which is true. By contrast, when one says "Some tame tigers exist," this asserts, not that the propositional function x is a tame tiger and exists has a value which is true, but simply that x is a tame tiger has a value which is true. These anomalies go to suggest that existence should not be taken to be a property. Alston complains that Moore's anomalies do not show that existence is not a property, but only that it is a special property.94 But this response strikes me as somewhat too facile. If existence is a property, then why is it so special? The only reason I can think of is that it would be an essential property of everything that exists. But that seems to provide no explanation for the quantification anomalies noted by Moore. Moreover, other trivially essential properties, like being colored if orange, when ascribed to tame tigers, do not yield the same anomalies. Most importantly, the anomalies noted by Broad and Moore become perspicuous on the Kantian analysis that existence is not a property, whereas they remain simply mysterious on the "special property" view, which fact constitutes confirmatory evidence for the Kantian position. A third consideration in favor of the view that existence is not a property is that things are explanatorily or logically prior to the properties that inhere in them or that are possessed by them, in which case a thing would have to exist logically prior to its having the property of existence, which is incoherent. Alston explains, Before we can attach any predicate to anything ('round,' 'heavy,' 'in my pocket,' 'belongs to Jones,' 'difficult to understand'), we must presuppose that it exists. If we were not making that assumption we could not even raise the question whether a given predicate attaches to it. ... On this basis it is easy to show that 'exists' cannot be a predicate. If the existence of the subject must be presupposed before we can set about attaching (withholding, wondering whether to attach) any predicate to (from) it, we will also be too late either to apply or to withhold a predicate of existence.... And the denial of such a predicate would contradict the essential conditions of any predication: 5

This seems to me to be a very powerful argument rooted in the very nature of what it is to be a property of something. Alston considers the argument as it stands to be indecisive because things may have different modes of existence, such as in fiction or in the imagination, which do not presuppose the real existence of the subject logically prior to the inherence of properties in it. He adjusts the argument by contending that real existence cannot be attributed to something existing in another mode. This analysis would still preclude real existence's being a property, since real existence could not inhere in anything but a real existent, in which case the original problem resurfaces. But I think it is clear that we need not even concede so much as Alston does. Plantinga's analysis of merely possible objects and of creatures of fiction in particular shows convincingly that to speak, as Alston does, of "nonreal

94

95

William P. Alston, "The Ontological Argument Revisited," in Ontological Argument, p. 88. Ibid., p. 89.

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modes of existence,,96 is simply self-contradictory.97 The only things that have existence are, obviously, things that exist in the actual world. But the very nature of what it is to be a property precludes existence's being a property of such things. We have good reasons, then, for thinking that existence is not a property. But then what is it? Here we may recur to Kant's positive characterization of existence. According to Kant, existence is the positing of the subject with all its predicates as an object. Similarly, non-existence is the rejection of or absence of a subject's being posited with all its predicates. 98 Both Broad and Moore also defended similar conceptions of existence. 99 On this view, for a thing to exist is for its individual essence (or, alternatively, its whole concept) to be instantiated. In either case, to exist is to exemplify properties. Among philosophers of religion Thomas Aquinas stands out as the foremost advocate of such a conception of being, not as a property, but as an act whereby a thing's essence is instantiated. lOo

Ibid., p. 103. Plantinga, Nature of Necessity, chaps. 7, 8. 98 Kant, Critique, p. 502 (A594-595/B622-623). 99 According to Broad, existential propositions are not about things, but about properties, or characteristi cs: "What they assert is that these characteristics do apply to something or that they do not apply to anything, as the case may be. 'Cats exist' is equivalent to 'The defining characteristics of the word "cat" apply to something.' Again 'Dragons do not exist' is equivalent to 'The defining characteristics of the word "dragon" do not apply to anything.' Suppose, e.g., that a 'dragon' is defined as a reptile which flies and breathes fire. Then the statement that dragons do not exist is equivalent to the statement that nothing combines the three properties of being a reptile, of flying, and of breathing fire" (Broad, "Existence of God," p. 183). Moore also thought of existence in terms of the exemplification of properties: " ... what 'Lions are real' means is that some particular property or other-I will say, for the sake of brevity, the property of being a lion ... does in fact belong to something-that there are things which have it, or, to put it another way, that the conception of being a lion is a conception which does apply to some things-that there are things which fall under it. And similarly what 'Unicorns are unreal' means is that the property of being a unicorn belongs to nothing. Now, if this is so, then it seems to me, in a very important sense, 'real' and 'unreal' do not in this usage stand for any conceptions at all.. .. ... To say that it did would be to imply that it stood for some property of which we are asserting that everything which has the property of 'being a lion' also has this other property. But we are not, in fact, asserting any such thing. We are not asserting of any property called 'reality' that it belongs to lions, as in the assertion 'lions are mammalian' we are asserting of the property of 'being a mammal' that it belongs to lions. The two propositions 'Lions are real' 'Lions are mammalian,' though grammatically similar, are in reality of wholly different forms; and one difference between them may be expressed by saying that whereas 'mammalian' does stand for a property or conception, the very point of this usage of 'real' is that it does not" (G. E. Moore, "The Conception of Reality," Proceedings of the Aristotelian Society 18 [191718]: 114-116). 100 Thomas Aquinas De ente et essentia 3; idem, Summa theologiae la. 3. 5. ad 2; idem Summa contra gentiles I. 22. 7. In this Aquinas was anticipated by the Arabic philosopher ibn Sina, as pointed out by F. Rahman, "Essence and Existence in Avicenna," Mediaeval and Renaissance Studies 4 (1958): 1-17. Of course, Thomas uses "essence" in the Aristotelian sense, not in the sense of an individual essence; but the salient point is that existence is an instantial act. 96 97

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Such an understanding of existence is utterly unlike Russell's bizarre view that existence is a property of propositional functions rather than individuals, 101 an interpretation entertained by Smith in his effort to understand the "no property" view of presentness. 102 Smith argues that if presentness is a so-called second order property of properties or propositional truth values, then it is also a first order property of things and events. But not only is his argument loaded with gratuitous metaphysical freight, 103 it erroneously assumes that presentness is any sort of property at all. If we assimilate presentness to existence and construe a thing's existence as the act of exemplification of its properties then presentness is neither a first nor second order property. If, like Smith, we wish to admit events into our ontology, then we should hold that what is existence for things is occurrence for events. Just as a thing exists by either its individual essence or whole concept's being instantiated, so an event occurs by the state of affairs describing it's being instantiated. Thus, existence and occurrence are not properly construed as properties; they are acts. As already suggested, there is on a presentist ontology an extremely tight link between existence and presentness. If a thing's being present is the same as that thing's existing, then presentness is no more a property than existence. Indeed, some of the very arguments against existence's being a property recur in a parallel form with respect to presentness. For example, in order to possess the property of presentness, a thing or event must already be present, which is self-contradictory. On a presentist ontology past or future events cannot possess the property of 101 Russell's very confused statement of this view may be found in Bertrand Russell, "The Philosophy of Logical Atomism," [1918], in Logic and Knowledge, ed. Robert Charles Marsh (London: George Allen & Unwin, 1956), pp. 232-241. Russell says that if you take any propositional function like x is a man and assert that it is sometimes true, that gives you the fundamental meaning of "existence." When one says, "Men exist," what one means is that there is at least one value for x such that x is a man is true. So existence is a predicate or property of a propositional function. "It is of propositional functions that you can assert or deny existence" (Ibid., p. 232). On Russell's view, then, individual objects do not exist. This seems crazy until we appreciate the fact that Russell has completely redefined "existence." When he says that it is a property of propositional functions, he is not using the word in the sense expressed when we say that there are propositional functions. Rather he redefines the word to indicate the property being sometimes true. We might be inclined to say that he is at liberty to define words as he pleases, but insist that there is some correlative concept to existence that would apply to individual objects in the world. But, incredibly, Russell denies this: "It is a sheer mistake to say that there is anything analogous to existence that you can say about them" (Ibid., p. 241). Thus, Russell's view really is crazy. In any case, Russell's view is problematic because propositional functions are neither true nor false; propositions are. So existence must be the property being of the form x is a _ _ (where " _ _" is filled by a common noun denoting a thing) and having a value for x such that the resulting proposition is sometimes true. Unfortunately, Russell identifies the notion of sometimes with the notion of the possible, so that even if the proposition is only possibly true, the sentence expressing it, e.g., "Unicorns exist" is true. 102 Smith, Language and Time, pp. 168-169. This is unfortunate, since Russell's view is not representative of philosophers who hold that existence is not a property. See, e.g., Moore's rejection of Russell's characterization of existence as a property of propositional functions (Moore, "Is Existence a Predicate?" p. 81). 103 For example, Smith takes it for granted that "There is an explosion" ascribes the property being exemplified to the property of exploding. But there is no reason to think that the act of exemplification is a property (not to mention that no reason has been given to think that exploding is ascribed by this sentence either). Smith also assumes that the state of affairs described by the proposition John is running has the concrete individual John as a constituent. But since states of affairs are typically construed as abstract entities existing necessarily, John, as a concrete contingent, cannot be part of one.

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presentness; the property of presentness can only inhere in things/events/times that are present. One might attempt to elude this problem along Smith's line by maintaining that presentness also inheres in the inherence of presentness in events, and also in the inherence of presentness's inherence in presentness's inherence in events ad infinitum. 104 But it is clear that in the case at hand, this is not a benign, but a vicious, infinite regress, since at every level, like the first, the contradiction exists that logically prior to the inherence of presentness in an event, the event must already be present in order to possess any properties. Sosa raises a related problem when he asks about the nature of having the property of presentness. lOS Suppose we interpret the sentence "The flash is present" to ascribe to the flash the property of presentness. This property cannot be possessed tenselessly; otherwise either the present would be fixed at the time of the flash or the flash at one time would be present at all times. But if we say that the having of presentness is itself tensed, then the property of presentness seems superfluous. There would be no content in saying, "The flash now-has the property of being present" over and above saying "The flash now-is." Thus, the attempt to construe the propositional content of a present-tense sentence as a property of presentness is self-defeating. A further difficulty is that a property like presentness would be a timeless universal, since it is possessed by many entities. But then it seems unintelligible how this timeless abstract object can be related to concrete particulars so as to locate them temporally. The same problem arises for the construal of presentness as any other kind of abstract object, say, a relation between a thing and its properties. 106 How can a timeless abstract object like a relation temporally connect other abstract objects like properties to a concrete object? Perhaps one could avoid the difficulty by holding abstract objects to be temporal, not timeless, or by distinguishing between abstract properties and temporal property instances, but it is not evident that these complications afford a more plausible alternative to presentness's not being a property. So, as I say, the grounds for regarding existence as not being a property echo on a presentist ontology for presentness as well. To be present seems to be identical with to exist. It is interesting that in his early work, Smith himself appeared to accept this identification. He held that "nothing more than to be present is needed to provide ... a meaning of existing" both in the existentialist sense and the sense of reference; "existing itself is the temporal present.,,107 He denies that tenseless existence is real existence; rather "The temporal sense of 'being' is (identically) the existential sense of 'being' .,,108 Rejecting a B-theoretical ontology, he declares, ... 'time exists' does mean time is present, if the latter assertion is understood appropriately to mean time is present in a sequential manner. The assertion that 'time is 104 105

28.

Smith, Language and Time, p. 172. Ernest Sosa, "The Status of Becoming: What Is Happening Now?" Journal of Philosophy 76 (1979):

\06 Cf. Reinhardt Grossmann, The Existence of the World, The Problems of Philosophy: Their Past and Present (London: Routledge, 1992), p. 20; cf. p. 102. 107 Quentin Smith, The Felt Meanings of the World (West Lafayette, Ind.: Purdue University Press, 1986), pp. 161-162. 108 Ibid., p. 166.

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present' is false only if it is misinterpreted to mean the intervals which make up time are simultaneously rather than successively present. 'Time exists,' properly explicated, means that the intervals of time are present one after the other and that one of these intervals currently is present. Since it is intervals of time whose existence is being characterized, 'to exist' does not mean here to occupy an interval which is present, but simply to be present. 109

These words are consonant with a presentist ontology according to which to be present simply is to exist. 110 Nevertheless, I think we would be hasty to embrace the strict identity of presentness and existence. For in the absence of some argument, we have no reason to regard timeless existence as impossible. In particular, no good reason has been given to think that God cannot be timeless sans creation, and, of course, many philosophers think that a host of abstract objects exist timelessly. We cannot therefore rule timeless existence out of court by a definition. Rather it seems to me that presentness is properly construed as a mode of existence.l11 There are two modes of existing, timeless existence and temporal existence, and presentness is identical with this second mode. There are two ways of exemplifying properties: timelessly or presently. On a presentist ontology, to exist temporally is to be present. Since presentness is identical with temporal existence (or occurrence) and existence is not a property, neither is presentness a property. Presentness is the act of temporal being. If, then, neither pastness nor futurity are properties possessed by any event/thing/time, and presentness itself is a mode of being, what impact do these conclusions have on McTaggart's Paradox? To see, consider Mellor's reformulation of McTaggart's argument. Past, present, and future tenses, Mellor asserts, are mutually incompatible properties of things and events. That is to say, letting P, N, and F be respectively the properties of being past, present, and future, and e any event, it is the case that 1. Pe I- -Ne; Nel- -Fe; Fel- -Pe, etc.

But because tenses are always changing, everything must have them all. That is to say, it is the case that

2. Pe&Ne&Fe

Ibid., p. 167-168. Since Smith goes on to deny that being is a "real predicate" (Ibid., p. 173), it follows that neither is presentness. III Interestingly, Christensen interprets Prior's view as holding that the notions of having occurred, occurring presently, and being going to occur are "modes of being, not relations (or properties)" and endorses this view himself (Christensen, Space-like Time, p. 122; cf. pp. 61, 123, 174). This interpretation is not quite right, however, since Prior held the past and the future to be unreal, so that these tense determinations cannot, like presentness, be construed as modes of being. Notice, too, that if we take necessity and contingency to be also modes of existence (Ibid., p. 61), then things have complex, or mixed, modes of being: a thing may exist (i) atemporally and necessarily, (ii) atemporally and contingently, (iii) temporally and necessarily, or (iv) temporally and contingently. Whether all these mixed modes are broadly logically possible is a matter of debate (see my God, Time, and Eternity [Dordrecht: Kluwer Academic Publishers, forthcoming]). 109 110

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Since nothing can have incompatible properties, it follows that nothing in reality has tenses. The riposte to this argument is that nothing has incompatible tenses at the same time. Things and events only have these properties successively, and there is no reason why things cannot have incompatible properties at different times. Thus, if e is present, it will be past and has been future, or 3. FPe & Ne & PFe,

which is compatible with (1). At this point Mellor's reconstruction of McTaggart's argument takes a peculiar twist. Mellor interprets him to assert that there are more complicated tenses than those in (3) and that every event must possess these complex tenses as well. For example, whatever has a simple tense has it now; that is 4. PeI-NPe;Nel- Ne;FeI-NFe.

Moreover, whatever is past was present and was future; and whatever is future will be present and will be past, so that 5. Pel- PNe; Pel- PFe; Fe I- FNe; Fe I- FPe.

Moreover, events in the remote past were still past in the recent past, and events in the remote future will still be future in the near future, so that we also have the tenses PP and FF. But now McTaggart's Paradox resurfaces: In place then of the original three simple tenses, we have the nine compound tenses PP, PN, PF; NP, NN, NF; FP, FN, FF. But McTaggart's argument applies just as well to them. Because of the way tense incessantly changes, any event that has any of these nine tenses has to have them all; but they are not all mutually compatible. For example, FF and PP are incompatible, since what will be future cannot also have been past. And NP, NN and NF are even more clearly incompatible, because they are equivalent to the simple P, Nand F. The riposte will again be made, that events do not have these incompatible tenses all at once. But again, saying in tensed terms just when they do have them only generates another set of properties, including mutually incompatible ones like PPP, NNN and FFF, all of which every event has to have. There is, in other words, an endless regress of ripostes and rebuttals, a regress that is vicious because at no stage in it can all the supposed tensed facts be consistently stated. ll2

It might be thought that Mellor's argument is easily dismissed because it simply repeats the mistakes of linking temporal predicates with tense less copulas and taking pastness and futurity to be properties of events. Indeed, Godfrey-Smith argues that Mellor's iterated temporal predicates are simply incoherent: 'PFe' is ill-formed. IfP is syntactically a predicate, i.e. forms a sentence when attached to a singular term e, then it cannot be used to qualify a sentential expression. 'PFe' reads '(e is future) is past' which is nonsense. Perhaps e can be modified by a temporal predicate (though that is misleading), but one cannot modify sentences with verbs. Complex tenses require predicate or sentential modifiers, i.e. adverbs. Mellor's compound tenses appear to be intelligible because of our familiarity with A. N. Prior's

112

Mellor, Real Time, p. 94.

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CHAPTER 6 very different use of 'P' and 'F' as sentential operators, which modify not events but propositions, and do so in a perfectly coherent, elegant and orderly fashion. \13

But Mellor's argument can be understood merely in terms of the truth of past- and future-tense propositions. 114 His symbols can be construed as tense logical operators on the statement "e occurs," and even if only the property of presentness is possessed by any event, propositions like Pe and Fe are nonetheless true. Since Pe and Ne and Fe are all true in the actual world, it may be alleged that the A-Theory involves a self-contradiction. If the A-theorist responds by asserting (3), then he has embarked on a vicious, infinite regress. Given an ontology of presentism, however, Mellor's reasoning falls flatly on its face. The regress is a regress of entailments, not meanings, and is therefore inconsequential insofar as its endlessness is concerned. It matters not a bit that Pe, for example, entails NPe, for these entailments do not imply the existence of any sort of hyper-time above ordinary A-series time. Nor is such a regress vicious because, given an A-theoretic ontology, there simply is no contradiction even on the first level. 1l5 For (3) represents the ground-level statement at which the A-theorist enters the debate, and it is not self-contradictory. Nor need there be any fear of a contradiction's resulting from Mellor's ascription of the other six binary tenses to e, for they cannot all be ascribed to e at the same level. The A-theorist begins at the lowest level with Ne and at this same level Mellor's binary tense predicates FP and PF are also properly ascribed to e: 3. FPe & Ne & PFe.

But what if e is past? Then we begin with 3'. FPe & Pe & (PFe v PPe v PNe)

1IJ William Godfrey-Smith, critical notice of Real Time, by D. H. Mellor, Australasian Journal of Philosophy 61 (1983): 110. Godfrey-Smith's criticism is correct as far as it goes, but Mellor insists that his argument succeeds whether 'P' and 'F' are construed as predicates or operators, and so one cannot cut off debate here. 114 Cf. Robin Le Poidevin and D. H. Mellor, "Time, Change, and the 'Indexical Fallacy'," Mind 96 (1987): 536, who point out that eliminating complex tenses by stating when a proposition is true merely results in the incompatible properties being truth values rather than tenses. Mellor insists, "The plain fact is that nothing can have mutually incompatible properties, whether they be tenses or truth values: neither events, things, facts, propositions, sentences, nor anything else" (Mellor, Real Time, p. 96). The fact that the predicates 'P', 'F', etc., can be construed as tense logical operators undercuts the analysis of David H. Sanford, "Infinite Regress Arguments," in PrinCiples of Philosophical Reasoning, ed. James H. Fetzer, APQ Library of Philosophy (Totowa, N. J.: Rowman & Allanheld, 1984), pp. 98-101, who charges that any expression containing both F and P is a vacuous tense expression, since such a determination can neither be gained nor lost. Thus, he says, in (3) two of the conj uncts are vacuous, and all that is being asserted is Ne. But the fact that expressions containing both F and P are not vacuous becomes evident when we, in Prioresque fashion, insert units of time into the formulae, e.g., PmF(m+n)e (A. N. Prior, "The Formalities of Omniscience," in Papers on Time and Tense [Oxford: Clarendon, 1968], pp. 29-32). And Sanford's analysis fails to address the alleged contradiction that ifNe is true, then Pe and Fe cannot also be true, thus precluding a complete description ofreality. Le Poidevin and Mellor are absolutely correct that the contradiction involved in a complete description of reality is eliminable only by giving tenseless B-series truth conditions of A-tensed sentences-but one thereby loses real tense. 115 So D. W. Gottschalk, "McTaggart on Time," Mind 39 (1930): 38; see also Smith, "Logical Structure," pp. 372-373.

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as our ground-level entry point. On the other hand, if e is future, then we start with 3". (FNe v FFe v FPe)& Fe & PFe.

Notice that e thus possesses all nine binary temporal predicates and does so without contradiction, since they are not all possessed at the same level. 116 One can continue via entailments to generate higher levels, but at no level will a contradiction obtain. Any regress is thus benign. Of course, it is true that there are three points of groundlevel entry, and these represent alternative starting points, so that three separate hierarchies of levels are formed. But how is that paradoxical? One's starting point is either Pe or Ne or Fe. Which of these first-level temporal predicates is appropriate depends on the banal biographical fact of whether one's concern with e coincides with e's obtaining. To assume that for every person it is possible to choose any of these entry points is to presuppose that it is the case that (2), which the A-Theory denies. Michael Dummett muses that McTaggart seems to presuppose that reality must be something of which there exists a complete description. 1I7 But, Dummett reflects, if time is real, then there is no complete description of reality. There would be one maximal description of reality in which the statement "Event M is happening" plays a part, another maximal description in which "Event M has happened" plays a part instead, and still another in which "Event M will happen" plays a part instead. Therefore, we must, concludes Dummett, abandon the 116 Since the temporal predicate N in front of any other temporal predicate is superfluous, Pe, Ne, and Fe are the same as NPe, NNe, and NFe respectively. The disjunctions are inclusive, not exclusive, and which binary disjunctive one ascribes to e will depend on how remotely one regresses or advances into the past or future. The disjunctives are thus all compatible temporal predicates of e. See further E. 1. Lowe, "Reply to Le Poidevin and Mellor," Mind 96 (1987): 541, who points out that for any tensed sentence such as 'Ne', if 'Ne' was true or is (now) true or will be true, then also 'Ne' was false or is (now) false or will be false, from which no contradiction follows. In his "McTaggart's Paradox Revisited," Mind 101 (1992): 323-326, Lowe synthesizes the A-theorist's position by saying that every event is such that it is or was or will be truly describable as past, and is or was or will be truly describable as present, and is or was or will be truly describable as future, which he symbolizes as 6**' (NT 'Np' v PT 'Np' v FT 'Np') & (NT 'Pp' v PT 'Pp' v FT 'Pp') & (NT 'Fp' v PT 'Fp' v FT 'Fp'). Le Poidevin complains that (6**) does not represent the passage of time and so presumably fails as a substitute for one of the original premisses in McTaggart's argument (Le Poidevin, "Lowe on McTaggart," p. 167). This complaint is strange because neither does Mellor's (I) or (2) represent the passage of time, so that (6**) is substitutable for (2). In any case, surely (6**) does represent the passage of time, since the same tense operator in each conjunct cannot operate on the true disjunct, on pain of contradiction, so that differently tensed statements will be true in each conjunct. This difference in tense does represent the flow of time. The fact that a spatial analogue to (6**) can be constructed is irrelevant, since the A-theorist does not read temporally tensed locutions tenselessly or token-reflexively as he would spatially indexed locutions. (6**) presupposes, but is not meant to prove, the reality of tensed facts. 117 Michael Dummett, "A Defense of McTaggart's Proof of the Unreality of Time," Philosophical Review 69 (1960): 503. See also Mink, "Time," pp. 260-261, who points out that there is a series of Aseries, as different events are present. The reason McTaggart's Paradox arises again and again, he suggests, is that we find it necessary to think about the world both A-theoretically and B-theoretically, "which we can neither simultaneously express nor separately perfect." See also J. N. Findlay, "Time: A Treatment of Some Puzzles," in The Philosophy of Time, ed. Richard Gale (London: Macmillan, 1968), pp. 161-162; P. T. Geach, Truth, Love, and Immortality: An Introduction to McTaggart's Philosophy (Berkeley, Calif.: University of California Press, 1979), p. 100.

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prejudice that there must be a complete description of reality. In another place, Dummett contrasts the positions of the "realist" (B-theorist) and the "anti-realist" (A-theorist) with regard to the possibility ofa complete description of reality: What the realist would like to do is to stand in thought outside the whole temporal process and describe the whole from a point which has no temporal position at all, but surveys all temporal positions in a single glance: from this standpoint-the standpoint of the description which the realist wants to give-the different points of time have a relation of temporal precedence between themselves, but no temporal relation to the standpoint of the description-i. e., they are not being considered as past, as present or as future. The anti-realist takes more seriously the fact that we are immersed in time: being so immersed, we cannot frame any description of the world as it would appear to one who was not in time, but we can only describe it as it is, i.e., as it is now. liS

These reflections certainly seem apropos for Mellor. Once we abandon the prejudice Dummett speaks of-that is to say, once we admit that tense is a real, irreducible feature of reality-, then there is no objection to having three alternative ground-level temporal predicates with their respective entailments ranged hierarchically above them. Dummett's point also has important implications for possible worlds semantics. For the reality of tense implies that there can be no complete and consistent characterization of a possible world in terms of true propositions or states of affairs.1\9 If propositions are held to be tensed, then any characterization of a possible world in terms of a maximal conjunction of consistent propositions is bound to be radically incomplete, indeed, to characterize a possible world only at t. On the other hand, if one holds that propositions are tenseless, then consistent, maximal conjunctions of such propositions are at hand, but they will fail to capture the non-propositional, tensed features of each world in which time exists. Commenting on Dummett's view, Horwich admits that McTaggart's Paradox is thereby resolved: " ... if there is no time-neutral body of absolute facts, there is no contradiction. Thus, by denying the assumption of this totality, McTaggart's objection can be sidestepped.,,120 But, Horwich complains, there is a substantial cost to this solution. Denying the assumption that there is a totality of facts "seems quite bizarre, unless independently motivated."l2l And independent motivation for denying this assumption is supplied, he concedes, in the tree model of reality: "For the tree model purports to show, independently of anything to do with now, that there is no complete, time-neutral body offacts .... In the context of that model, [Atheorists'] best reply to McTaggart is not ad hoc: genuine change can be achieved without contradiction.,,122 But the problem is that, according to Horwich, the main motivation for adopting the tree model of reality is the avoidance of fatalism, fear of which is unfounded, since fatalism can be resolved without recourse to the tree model. 118 Michael Dummett, "The Reality of the Past," Proceedings of the Aristotelian Society 69 (1968-69): 252-253. If the A-Theory is correct, then there is no standpoint, even for God, such as is envisioned by the realist. Contrast the possibility of a spaceless being, as in Dummett, "Defense of McTaggart's Proof," pp. 500-501. 119 Le Poidevin and Mellor, "Time," p. 536. 120 Paul Horwich, Asymmetries in Time (Cambridge, Mass.: MIT Press, 1987), p. 27. 121 Ibid. 122 Ibid., p. 28.

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We may certainly agree with Horwich that fatalism follows neither from the antecedent truth of future contingent propositions nor from a B-Theory of time; nor, we may add, does an A-Theory imply that future contingent propositions are all truth valueless, non-bivalent, or false. 123 As we have seen, a proper construction of the tree model of temporal becoming does not deny that there is an actual branch which represents the future. What properly motivates adoption of a tree model of temporal becoming is the complex notion of temporal modality, such as Freddoso has sought to explicate. 124 Philosophers of space and time can profit from the extensive debate conducted by philosophers of religion over the notion of temporal necessity.125 What the tree model attempts to portray graphically is the idea that the past is somehow temporally necessary whereas the future is temporally contingent. The debate concerns the extent to which the past is necessary. The employment of a dendritical model of temporal modality does not, however, as Horwich points out, 126 entail temporal becoming, since an indexical use of "the past," "the present," and so forth would suffice to capture the idea that certain propositions belonging to submoments earlier than t are temporally necessary at t. In any case, it is not the tree model per se which enables the A-theorist to elude McTaggart's Paradox: it is rather the doctrine of objective becoming, which could be graphically displayed as the successive actualization of the history of the actual world. It is this model of a successively instantiated, rather than tenselessly existing, actual world that precludes the existence of a "totality of facts." In the context of such a model, not only is Dummett's point not bizarre, but it is intuitively obvious, even if perhaps startling and exhilarating-the sort of insight of which one asks how it ever could have escaped one's attention. As for whether there exists some independent motivation for adopting such a model, the A-theorist may repeat Mellor's words, "Tense is so striking an aspect of reality that only the most compelling argument justifies denying it .... ,,127 This may not be an independent motivation, but it may certainly be an adequate one. With regard to McTaggart's Paradox, all the A-theorist is obliged to show is that a plausible model exists in which tense and temporal becoming are objective features of reality, and McTaggart's objection is thereby defused. By Horwich's own admission, the A-theorist appears to have been equal to that challenge. PRESENTISM AND TEMPORAL SOLIPSISM Given the presentist ontology of the A-Theory of time, I have argued, McTaggart's argument is simply misdirected as a refutation of tensed theories of time. Indeed, Le Poidevin asserts that presentism "represents the only means to See discussion in Craig, Divine Foreknowledge and Human Freedom, chaps. IV, VII, Appendix. Alfred 1. Freddoso, "Accidental Necessity and Logical Determinism," Journal of Philosophy 80 (1983): 257-278. 125 See Craig, Divine Foreknowledge and Human Freedom, chap. IX; also my "Temporal Necessity; Hard Facts/Soft Facts," International Journalfor Philosophy of Religion 20 (1986): 65-91, for a review and discussion of the debate. 126 Horwich, Asymmetries in Time, p. 27; see also Peter Kroes, Time: Its Structure and Role in Physical Theories, Synthese Library 179 (Dordrecht: D. Reidel, 1985), p. 202. l27 Mellor, Real Time, p. 5. 123

124

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block McTaggart's proof of the unreality of time consistently with the assumption of a non-relational past, present, and future.,,128 Nevertheless, Le Poidevin rejects the solution of presentism because, he claims, it entails certain objectionable doctrines characteristic of temporal solipsism, to wit: 1.

The extension of the existential quantifier is restricted to presently existing objects.

2.

Relations obtain only between contemporaries, that is, objects existing at the same time.

3.

Past and future tenses are to be interpreted as sentential operators on core present-tense sentences, the present tense not requiring representation by an operator.

4.

Instants are logical constructions out of propositions.

5.

Past- and future-tense statements have only present facts as their truth conditions, that is, what makes a certain statement about the past or future true is the evidence that at present exists. 129

I shall argue that presentism does not entail temporal solipsism so defined and that the debate over presentism so closely parallels the debate over modal realism that a consistent position requires either modal realism cum B-Theory of time or some sort of actual ism cum A-Theory of time. Presentism is the doctrine that the only temporal items which exist are those which are present. Any number of writers have remarked on the parallel between presentism and actualism with respect to possible worlds. 130 Following Plantinga, we may conceive of a possible world as a maximal possible state of affairs, where a state of affairs S is maximal if for every state of affairs S', S includes S' or S precludes S'. So conceived, possible worlds and the states of affairs which comprise them are normally understood to be tense less states of affairs; otherwise we could never speak of events' occurring at different times in a possible world, since, as McTaggart's Paradox discloses, there is no maximal or complete description of a temporal world over time due to tensed facts. Hence, the worlds described in possible worlds semantics are tenseless possible worlds. In order to handle tensed Le Poidevin, Change, Cause, and Contradiction, p. 36. These are all theses defended by A. N. Prior. Cf. the similar exposition of the views of Prior in contrast to those of Quine by Jeremy Butterfield, "Prior's Conception of Time," Proceedings of the Aristotelian SOCiety 84 (1983-84): 193-209. 130 The account given here is based on Nicholas Wolterstorff, "Can Ontology Do without Events?" Grazer Philosophische Studien 7/8 (1979): 188-189; Alvin Plantinga, The Nature of Necessity, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1974), pp. 44-49. For further discussion see John Bigelow, "Worlds Enough for Time," Noils 25 (1991): 1-19; Philip Percival, "Indices of Truth and Temporal Propositions," Philosophical Quarterly 39 (1989): 190-199; Richard M. Gale, "Lewis' Indexical Argument for World-Relative Actuality," Dialogue 28 (1989): 289-304; Palle Yourgrau, "On Time and Actuality: The Dilemma of Privileged Position," British Journal for the Philosophy of Science 37 (1986): 405-417; Graeme Forbes, "Actuality and Context Dependence I," Analysis 43 (1983): 123128. 128 129

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facts, we need to allow tensed states of affairs as well, like the Battle o/Waterloo's having occurred and Bush's being President, to be constituents of possible worlds. A tensed possible world is a maximal possible state of affairs at some time t of arbitrarily stipulated duration, whether an instant, an arbitrarily brief moment, an hour, a day, and so forth. Tensed possible worlds which did, do, or will obtain are tensed actual worlds. The tensed actual world at t will be the tensed actual world which obtains when t's being present obtains, or more simply, when t is present. The world which presently obtains is simply the tensed actual world. Tensed actual worlds constitute the tensed history of the actual world a, for they are respectively comprised of all states of affairs entailed by a and each successive t's being present. This may be generalized to any possible world W: the tensed history of W will be all the tensed possible worlds constituted by the states of affairs entailed by Wand each successive t's being present in W. To say that a temporal entity x exists in a tenseless possible world W is to say that if W were actual, x would exist (tenselessly) at some time t; or again, x exists in W if it is impossible that Wobtain and x fail to exist (tenselessly) at some time t. Analogously, to say that x exists in a tensed possible world Wt is to say that if Wt were actual, then x would exist (present-tense). To say that x exists in a tensed actual world at is to say that when at becomes actual, then x exists (present-tense); it is impossible when at obtains that x does not exist (present-tense). With respect to tenseless possible worlds, to say that Socrates has in W the property of being snub-nosed is to say that Socrates would have (tenselessly) the property of being snub-nosed, were W to be actual; the state of affairs W's being actual and Socrates's not being (tenselessly) snub-nosed is impossible. Analogously, to say that Socrates has in a tensed possible world Wt the property of being snub-nosed is to say that Socrates would have (present-tense) the property of being snub-nosed, were Wt to be actual; the state of affairs Wt's being actual and Socrates's not being (present-tense) snub-nosed is impossible. To say that Socrates has in a tensed actual world at the property of being snub-nosed is to say that when at becomes actual, then Socrates has (present-tense) the property of being snubnosed; it is impossible when at obtains that Socrates is (present-tense) not snubnosed. Each tense less possible world exists in each world. The actual world a is the maximal state of affairs that obtains (tenselessly). Were some other world actual, a would not obtain but would still exist as a possible state of affairs. Since only a is in fact actual, none of the other tenseless possible worlds is actual, but each one is actual in or at itself. Each world W has the property of actuality in W and in W alone. That also goes for a. But a is not merely actual in a, but also actual simpliciter. Thus, a is uniquely distinguished as the actual world, the one tense less possible world that obtains. Analogously, each tensed possible world exists in each such world. The tensed actual world v is the maximal state of affairs that obtains (present-tense). Were some other tensed possible world actual, then v would not obtain, but it would still exist as a tensed possible state of affairs. By the same token, when some other tensed actual world obtains (present-tense), then v either does not yet or no longer obtains, but v nonetheless exists as a tensed actual state of

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affairs. Since valone is (present-tense) actual, none of the other tensed actual worlds (not to speak of tensed merely possible worlds) is (present-tense) actual, though they either were or will be actual. Still each tensed world, including v, is actual in itself. But v is not merely actual in v, but also actual simpliCiter. Thus, v is uniquely distinguished as the tensed actual world, the one tensed possible world which obtains (present-tense). Does such a model of presentism entail or imply temporal solipsism, as Le Poidevin alleges? I think not. 1. The range of the existential quantifier. If past and future times do not exist, then purely past and future individuals (like Napoleon and Queen Elizabeth II's great grandchildren) do not exist. So if the existential quantifier is to be tied to existence, the objection goes, its range must reflect this restriction. It is certainly correct on the presentist view that non-present individuals do not exist (present-tense). But the A-theorist or presentist need not be committed to a reductive or eliminative analysis of tenseless discourse. I see no reason at all why the presentist should object either to certain artificial tenseless languages or to tenseless statements or propositions in a language which includes tense. The language of quantified classical logic is obviously an example of an artificial tenseless language, and the presentist is under no obligation to reform it by introducing tense. He simply takes Quine's tenseless dictum that "To be is to be a value of a bound variable" not to tell the whole truth about being. Since Quine is, as we have seen, a B-theorist and a partisan of the Old B-Theory of Language, such an equation was unproblematic from his point of view; but given an A-theoretic understanding of time, tense, and temporal becoming, being cannot be simply equated with what is postulated to exist by the tense less existential quantifier in classical logic. Le Poidevin says that he just assumes, "with Quine, that a theory which involves ineliminable quantification over F's is committed to a realist position over F's."l3l The presentist agrees that in the tenseless universe of discourse of classical logic, individuals within the scope of the existential quantifier in true propositions do have (tenselessly) reality. The presentist will understand the tenseless existential quantifier to take as its range all individuals in a, the tense less actual world. True statements of the form (3y) (y=x) tell us only that x exists in a, and even if x is a purely past individual, the presentist has no reason to deny that tenseless truth about x. On the basis of the A-Theory of time, he just does not invest tense less existential quantification with the sort of metaphysical significance that Quine does. On the other hand, if the presentist does wish to propose a reform of classical logic so that he can endorse unqualifiedly Quine's dictum, he could adopt the suggestion of some A-theorists that the existential quantifier (3x) be read as disjunctively tensed: "there is, was, or will be some x such that.,,132 By making the quantifier disjunctively tensed, the presentist brings within its scope· all individuals in all the tensed actual worlds. This move will undoubtedly complicate 10gic,133 but Le Poidevin, Change. Cause, and Contradiction, p. 38. So Smith, Language and Time, p. 192. m See Robert Merrihew Adams, "Time and Thisness," Midwest Studies in Philosophy 11 (1986): 321322, who admits that by regarding the existential quantifier as disjunctively tensed the presentist has the 131

132

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the presentist will justifiably insist that if one wishes to adequately capture being in logical notation, then simplicity may have to be sacrificed for metaphysical accuracy; if one wants a complete account, one cannot just suppress important metaphysical distinctions out of a desire for economy of logical expression. Alternatively, the presentist can avail himself of the resources of tense logic and stipulate that the existential quantifier fall within the scope of the relevant tense operator: for example, P(3x). (See further the comment on argument [3] below.) In this way he neatly combines Quine's dictum with the insights afforded by tense logic. 2. Relations between non-contemporaries. Relations cannot, on the presentist's view, hold between non-contemporaneous objects because at least one of the relata is unreal. So the objection goes. This objection, if applied equably, ought to drive one to modal realism as well as the B-Theory of time, for if it is correct, there can exist no relations between individuals in a and some other possible world W-no transworld identity, no greater or more perfect than relation, no relation of any kind-for these other individuals are unreal. For any paraphrase aimed at eliminating such relations-for example, God's being greater in a than in W because of His knowledge only in a of future contingents might be understood as the claim that God would be less great were He ignorant of future contingents-, a suitable, analogous paraphrase ought to be available to the presentist-for example, my being shorter than my grandfather could be construed as the claim that were my grandfather to exist today, I should be shorter than him. If transworld relations are taken to exist, not between actual and non-actual individuals, but between world-indexed individuals, for example, Socrates-in-a and Socrates-in-W, both of whom do exist, then why cannot transtemporal relations be similarly construed as relations between tensed worldindexed individuals, for example, Le Poidevin-in-v and Socrates-in-at ? Transtemporal relations seem to present no greater challenge to the metaphysician than transworld relations. Moreover, it is rather misleading, as the above comparison makes clear, to speak of non-contemporaries as simply unreal. For unlike merely possible objects, both of them do exist in the actual world. They are just not real at the same time. The question, then, is why there cannot be transtemporal relations between individuals who are real at different times. This serves to raise the more fundamental question of the ontological status of relations, an adjudication of which lies beyond the scope of this study. Are relations mind-independent entities or merely conceptual in nature? If the latter, then it is not evident that there is any problem at all in transtemporal relations. Relations between me and my grandfather would depend on the mind of the person making the resources to reproduce classical logic consistent with his commitment to the non-existence of non-present entities but complains that the increased complexity is acceptable only if supported by strong enough metaphysical intuitions. On the basis of our investigations in secs. I. I, 2, I think we can safely say that the intuitions backing presentism are enormously strong. That Adams himself feels these intuitions is evident from the fact that he cannot bring himself to let the existential quantifier range over future individuals, consistent with a B-Theory of time, so that he is left with the incoherent half-way theory enunciated by Broad in his middle period. See further Michael Woods, "Existence and Tense," in Truth and Meaning, ed. Gareth Evans and John McDowell (Oxford: Clarendon Press, 1976), pp. 248-262.

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comparison, whether a human person or God, and would not depend on the items being related being contemporaries. If the former, then relations are abstract objects which plausibly do not exist in time at all. Non-contemporaries stand in a relation at their respective times and the timelessly existing relation reaches across time to relate the two individuals. 134 As for the individuals themselves, we could ascribe to them relational properties: Socrates, at the time he existed, had the property of going to be referred to by William Craig or the property of being referred to by William Craig at tn. He no longer has that property, but I now have the property of referring to Socrates. 135 The relation between us can be analyzed in terms of such relational properties or said to exist timelessly in virtue of such properties. 3. Tense logical operators on present-tense sentences. The characteristic claim of tense logic that past and future tenses are to be interpreted as sentential operators on core present-tense sentences is said to be required by (4) that instants are logical constructions out ofpropositions. Though typical in tense logic, regarding the operand sentence as present-tense is not inevitable, as we have observed, so long as the tenseless operand when conjoined with the present-tense operator is understood to be synonymous with a present-tense sentence rather than to assert the present truth of a tense less sentence. Moreover, many A-theorists interested in ontology eschew tense logic as a reliable guide to ontology, regarding it as a semantics without much metaphysical import. 136 In other words, they reject the metaphysical claim that instants are logical 134 See Adams's discussion of names for future individuals in "Time and Thisness," p. 322-328, where he cautions against inferring the present existence of singular propositions about future individuals from the fact that we can entertain, assert, or believe them: "For perhaps the relations of entertaining, asserting, and believing can obtain between thoughts and utterances occurring at one time and propositions existing only at a later time" (p. 323). Transtemporal relations, he suggests, could exist timelessly or as a whole in an extended period of time without existing at any instant during the period (Ibid., p. 320). This would undercut the central thesis of L. Nathan Oaklander's book Temporal Relations and Temporal Becoming (Lanham, Md.: University Press of America, 1984), pp. 5-22, in which Oaklander argues that on an ATheory of time temporal relations like earlier than cannot exist. (Cf. F. M. Christensen, Space-like Time [Toronto: University of Toronto Press, 1993], p. 128, who infers from the reducibility ofB-relations to Adeterminations that the former are dispensable and even non-existent). m This seems to me to solve the difficulty seen by James Cargile, "Tense and Existence," in Cause, Mind, and Reality, ed. John Heil, Philosophical Studies Series 47 (Dordrecht: Kluwer Academic Publishers, 1989), p. 166, whose question, "If I refer to x, does not x have the property of being referred to?" reveals the tacit assumption that the properties referring to x and being referred to by y must be possessed by x and y at the same time, which begs the question. No reason has been given why these properties cannot be possessed by x and y respectively in succession. Wolterstorff, "Ontology without Events," pp. 190-192 denies that past- (and future-) tense propositions have individuals as constituents. They are made up wholly of properties, which, being sempitemal, can be referred to at any time. Thus, being able to refer to past and future individuals, though impossible, is not necessary for stating the truth conditions of sentences about them. Contrast Adams, "Time and Thisness," pp. 319-320. On the other hand, Roderick Chisholm, The First Person (Minneapolis: University of Minnesota Press, 1981), pp. 125126; idem, "Referring to Things that No Longer Exist," in Action Theory and Philosophy of Mind, ed. James Tomberlin, Philosophical Perspectives 4 (Atascadero, Calif.: Ridgeway Publishing Co., 1990), p. 554, proposes to solve the problem by positing some sempitemal entity contemporaneous with both referent and referee which did have (or will have) the property of being such that there exists an x such that x is F. For the A-theorist God will nicely fill the role of the sempitemal entity. Cf. the etemalist solution proposed by Jonathan L. Kvanvig, "Adams on Actualism and Presentism," Philosophy and Phenomenological Research 5 (1989): 297. 136 See, for example, Smith, Language and Time, pp. 166-169.

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constructions out of propositions; and since (3) is said to be problematic only in conjunction with that claim, it follows that if one rejects (4), the presentist who holds to the purely semantic thesis that past and future tenses are to be interpreted as sentential operators on core present-tense sentences does so unproblematically. 4. Instants as logical constructions out of propositions. Since past and future times do not exist, the presentist must allegedly analyze them reductively in terms of past and future tense propositions: an instant of time is a conjunction of propositions which would ordinarily be said to be true at that time. The presentist should want no part of, nor is he obliged to embrace, such reductionism. Instants or moments of time are obviously not conjunctions of propositions.137 Moments of time elapse, and I exist at the present moment; but a conjunction of abstract objects is itself an abstract object, which does not elapse, neither at which do I exist. Moreover, to claim that an instant is identical "with all the propositions which would ordinarily be described as being (contingently) true at that instant,,138 is manifestly explanatorily circular, since instants are defined in terms of instants. Although one could conceive of tensed possible worlds as constructed out of propositions rather than states of affairs, the semantics given here does not equate tensed actual worlds with the instants or moments of time at which they obtain. The difference between a tensed world and a moment of time is not trivial, for worlds possess their inhabitants essentially, but times do not. 139 It is impossible that v obtain and I not exist, but the present moment could have existed without me. Le Poidevin also errs in thinking that in the presentist's states of affairs which do not presently obtain do not exist, thus requiring recourse to propositions as stand-ins for times. According to the semantics given here, temporal worlds which do not obtain nonetheless exist. Given the existence of these worlds, there is no difficulty in explaining the truth of past- and future-tense propositions in terms of truth in some world. 5. Present facts alone as the truth conditions of past- and future-tense statements. Since past and future facts do not exist, all that is left to make statements about the past or future true is the present evidence about facts causally connected with past and future states of affairs. Given indeterminism, the Principle of Bivalence fails for a good many such statements. This objection obviously confuses truth conditions with truth makers of past- and future-tense statements. On the presentist semantics given here, a future-tense statement is true iff there exists some tensed actual world at t in which the presenttense version of the statement is true, where t has not elapsed by the present moment. A past-tense statement is true iff there exists some tensed actual world at t in which the present-tense version of the statement is true, where t has elapsed by the present moment. Those are the truth-conditions of past- and future-tense statements; but they are not what make the statements true. Ultimately what makes the statements true is that reality was or will be as the statements describe; when the IJ7

Cf. the remarks of Peter Van Inwagen, "Indexicality and Actuality," Philosophical Review 89 (1980):

406. Le Poidevin, Change, Cause, and Contradiction, p. 37. As noted by Van Inwagen, "Indexicality and Actuality," p. 404; cf. Quentin Smith, "The New Theory of Reference Entails Absolute Time and Space," Philosophy o/Science 58 (1991): 411-416. 138 139

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time comes, for example, a sea battle is going on, and therefore the statement made the day before, "There will be a sea battle tomorrow," was true. There are tensed facts corresponding to what tensed statements assert, but past- and future-tense facts exist because of the present-tense facts which did or will exist. 140 Certainly the grounds of the truth of tensed statements is not present evidence causally connected to the events in question, and there is no reason the presentist should adopt such a verificationist viewpoint. In sum, there are no compelling reasons to believe that presentism entails temporal solipsism. The latter is an idiosyncratic doctrine associated with the views of A. N. Prior and not logically connected with the A-Theory of time. But we can go further. It is already obvious that the B-Theory of time is quite parallel to modal realism, so that we may appropriately refer to it as chronal realism. Indeed, these doctrines are so analogous that a modal McTaggart's Paradox arises for those who reject modal realism, and if actualism is deemed a legitimate alternative to modal realism, then so must presentism to chronal realism. The modal McTaggart's Paradox runs as follows: 141 Various positions in logical space are mutually incompatible. An object or event which is actual cannot also be merely possible; nor can an event or object which is merely possible be actual. But every contingent object or event has to be both actual and merely possible. It is almost impossible to state this difficulty without also giving the solution. It will be said that nothing is simply actual or merely possible, but actual in Wand merely possible in W*. But this leads to an infinite regress, for we must now inquire whether W or W* is actual. Since W is actual in Wand W* is actual in W*, we must posit some hyper-actuality in which W or W* is actual; but then the same question arises again for the actuality of that hyper-actual world. The contradiction thus remains unrelieved. The modal McTaggart's Paradox can be formulated along Mellor's lines by letting Pe = "e is merely possible" and Ae = "e is actual." The argument is that See Freddoso, "Accidental Necessity and Logical Determinism," p. 264. He writes, "I take the claim that the pure present is metaphysically primary to be tantamount to the assertion that for any moment t and any logically possible world w there is a set k of purely present-tense propositions such that (a) each member of k is true at t in w, and (b) k determines what is true at t in w in a temporally independent way, i.e., in a way which does not temporally depend on what has been or will be true at moments of w other than t" (Ibid., p. 266). That this implies a sort of power over the past (as well as the future) is explained by idem, "Accidental Necessity and Power over the Past," Pacific Philosophical Quarterly 63 (1982): 54-68. For a discussion see my Divine Foreknowledge and Human Freedom, pp. 83-90, 179-190. If one does not accept that propositions are tensed, then one could reformulate the metaphysical primacy of the pure present in terms of non-propositional, present-tensed features of reality (e.g., God's de se knowledge of what He is creating). Adams fails to appreciate the above point when he complains that on presentism "the facts about the past and future must have their whole ontological basis in the present" so that the ontological basis of the fact that a battle was fought at Waterloo "is not something that is or was a battle" (Adams, "Time and Thisness," p. 322). I can only understand Adams to mean that on the presentist view the grounds for the truth of "A battle was fought at Waterloo" is the present fact that a battle was fought at Waterloo, which is not itself a battle. But while there surely is such a tensed fact or state of affairs corresponding to the above statement, such a fact is not ultimate, but obtains because a purely present-tense fact-a battle is being/ought at Waterloo--did obtain, and the ontological basis ofthat fact was a battle. 141 See M. 1. Cresswell, "Modality and Mellor's McTaggart," Studia Logica 49 (1990): 163-170. 1"0

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6. Pe I- -Ae and Ael- -Pe

7. Pe&Ae Since (6) and (7) are incompatible, modal properties are unreal. The riposte is that e is actual, but possibly is merely possible: 8. PPe&Ae But this riposte does not work because these complex modal properties are also incompatible with each other, for example, PAAe and AAAe, so that a vicious infmite regress is generated. In response to the modal McTaggart's Paradox, Le Poidevin adopts unhesitatingly the actualist solution: "The doctrine that only the actual world is real avoids the modal paradox just as the doctrine that only the present is real avoids McTaggart's paradox.,,142 He observes that the modal paradox only defeats someone who both accepts modal realism and thinks that there is a non-relational distinction between actual and merely possible. Parity of reasoning requires that McTaggart's Paradox only defeats someone who both accepts chronal realism and thinks that there is a non-relational distinction between present and past or future. This fact is instructive because it shows that hybrid A-B-theorists, like Smith,143 are in real trouble in the face of McTaggart's Paradox. While not gainsaying the presentist's refutation, Smith argues that McTaggart's Paradox can be beaten without abandoning a B-theoretic ontology or A-theoretic becoming. He maintains that McTaggart assumed unnecessarily that the infinite regress of moments must involve a hierarchy of levels, "that in order for a moment to be present it must occupy a higher level present moment, so that the answer to the question 'when does presentness inhere in the first level moment?' is 'at a second level moment which (is) present'."I44 But in Smith's opinion, a more economical answer would be "that 'presentness inheres in the first level moment at present,' this answer meaning that the inherence of presentness in the first level moment is itself present, i.e. presentness not only inheres in the moment but also in its own inherence in the moment.,,145 Although a benign infmite regress of present inherences is generated, this is unproblematic because one never transcends the single time dimension. On Smith's view, though all moments equally exist, only one is uniquely present at present; all the rest are past or future at present (or, perhaps, present in the past or future). The best sense I can make of Smith's view is to say that while every time has the property of being present at itself, only one time has the absolute property of being Le Poidevin, Change, Cause, and Contradiction, p. 35. See note 66. Tooley is a hybrid A-B-theorist in that he holds to the reality of the past and present, but not the future; he would avert McTaggart's Paradox by denying that there are intrinsic properties of tense (Michael Tooley, Time. Tense. and Causation [Oxford: Clarendon Press, 1997], pp. 226-229). But I have already charged that Tooley's "reality accretion" model must involve tensed facts; moreover, events seem to change on his view even in their relational tensed properties, since, e.g., a past event acquires the relational property past with respect to some event only once the latter becomes present (p. 323). Such change is all one needs to generate a McTaggart's Paradox. 144 Smith, "Infinite Regress of Temporal Attributions," p. 386. 14S Ibid. See also Smith, "Logical Structure," pp. 373-374. 142 143

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present. Times which are not present are presently past or presently future, and only one time is presently present. To prevent an infinite regress, we must take being presently present to be equivalent to just being present. The absolute property of presentness moves along the B-series, thereby constituting the flow of time. Because of the changing tense determinations, there can be no one, complete description of reality, just as the presentist maintains. The problem with this view is that the absolute property of presentness becomes unintelligible or vacuous. Since every time exists and every time is present when it exists, it is wholly mysterious what more is added to it when it becomes absolutely present. If to become present is not, as the presentist maintains, to become real or existent, then what is it? I must confess that the notion of presentness on such a theory seems utterly opaque to me. It is as if one were to say that all possible worlds are equally real (not merely as states of affairs, but as concrete realities), but that only one is actual. The notion of what it is to be actual would then become vacuous. Similarly, unless one means that moments of time become successively present in a hyper-time (which Smith denies), then there just is no content left in asserting that each time, all of which are equally real and each of which is present at itself, becomes successively present. The modal and chronal paradoxes thus threaten us, not so much with contradiction as with the evacuation of content from our concepts of actuality and presentness. The hybrid actualist-realist has to say that although all worlds are equally real, only one is actual, and the hybrid A-B-theorist has to say that although all times are equally real, only one is present, both of which are unintelligible. To make these notions intelligible, a hyper-world or hyper-time has to be posited in which one world is actual and one time present; but then we are off on an infinite regress. The question facing the defender of McTaggart's Paradox, then, is, given the close analogy between modal and chronal realism, with what justification can one advocate actual ism with respect to possible worlds but reject presentism with respect to time? The same sorts of argument lodged against temporal solipsism can be lodged against modal solipsism; for example, that we must scotch quantified modal logic, deny relations like trans-world identity, reduce worlds to conjunctions of propositions, and make non-modal facts alone the basis of the truth of modal statements. The moves made by the serious actualist to avoid these difficulties are paralleled by moves available to the presentist to avoid temporal solipsism. The Btheorist thus faces a very serious tu quoque dilemma of his own: if McTaggart's reasoning justifies chronal realism, then a parallel argument justifies modal realism; if one escapes modal realism by embracing actual ism, then a parallel escape route is available through presentism; and if one raises objections to presentism based on temporal solipsism, parallel objections arise with respect to actualism, objections to which solutions available to the actualist are paralleled by solutions open to the presentist. In short, it is gratuitous to accept a B-Theory of time on the grounds of McTaggart's Paradox without also embracing modal realism. It needs only to be added that those rare individuals who, like David Lewis, consistently advocate both

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modal and chronal realism [md themselves saddled with a metaphysic which is, to say the least, strikingly unappealing. 146 CONCLUSION With regard to McTaggart's Paradox, then, we have seen that in McTaggart's own version of the argument, he misconstrued the nature of time by supposing that the reality of time entails a B-theoretic event ontology wedded with A-theoretic temporal becoming. All events in the actual world are equally instantiated and existent, and temporal becoming consists in the spotlight of the present's moving across the series of events. Events in the B-series successively assume the determinations of pastness, presentness, and futurity. Such a view immediately provokes the question: since every event or moment in the series becomes present, which moment deserves to be called the present? If one answers, the present moment which is present, one illicitly assumes a time above time in which each moment having presentness becomes present. A proper construal of A-theoretic ontology and temporal becoming undercuts this conundrum. For if only present events exist, then there simply are no events which have the determinations of pastness or futurity. To say that an event e is past or future is to assert that either the statement "e occurred" or "e will occur" is true. Temporal becoming is thus not a species of change, but is more like creation/annihilation in that there is no enduring subject which sheds one temporal determination for another. Thus, Broad's appellation "absolute becoming" is particularly apt. McTaggart's Paradox cannot arise, since the only events there are are present events. Moreover, we saw that it is a mistake to analyze "e is present" to mean "e has presentness at t and t is present." This entailment is true and leads to a benign, infinite regress of entailments, but as an analysis of meaning, it is simply misconceived. Presentness is a primitive temporal determination which is wellunderstood. According to the A-theorist, it is an objective and ineliminable feature of temporal things and events. The reality of tense entails that a complete and consistent description of the world is impossible. Certain contemporary B-theorists illicitly presuppose that such a complete and consistent description can or ought to be given, an assumption which begs the question by supposing that there is no objective tense. But if, as the A-theorist maintains, tense is an objective feature of reality, then this assumption is simply false and McTaggart's Paradox cannot get off the ground. Finally, given the close analogy between chronal and modal realism, it is gratuitous to embrace chronal realism on the basis of McTaggart's reasoning while refusing to adopt modal realism as well. If the temporal theorist wishes to adopt a B-Theory of time, then, he will be well-advised to [md other grounds than McTaggart's misconceived argument.

146 See David Lewis, On the Plurality afWarlcis (Oxford: Basil Blackwell, 1986), pp. 93, 98, 137. For a critique see Van Inwagen, "Indexicality and Actuality," pp. 415-417.

CHAPTER 7 THE MYTH OF TEMPORAL PASSAGE

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he notion that time is dynamic, that it flows or passes, is a common and ancient motif in the history of Western philosophy, at least as old as Heraclitus.! The hymnist Isaac Watts poetically expressed this notion in the lines: Time, like an ever rolling stream, Bears all its sons away; They fly, forgotten, as a dream Dies at the op'ning day2

McTaggart, as we have seen, thought of the flow of time as a literal motion of Adeterminations along the tenselessly existing B-series of events. He asserts, "The movement of time consists in the fact that later and later terms pass into the present, or-which is the same fact expressed in another way-that presentness passes to later and later terms.,,3 The A-series of tensed determinations and the B-series of tenselessly related terms are in relative motion with respect to one another: "The movement of the A series along the B series is from earlier to later. The movement of the B series along the A series is from future to past.,,4 OBJECTIONS TO TEMPORAL PASSAGE

The Flow a/Time It was McTaggart's construal of temporal becoming as a sort of motion that drew the fire of C. D. Broad. In discussing what he called the "Transitory Aspect of Temporal Facts" (temporal becoming) as distinguished from the "Extensive Aspect of Temporal Facts" (temporal extension and temporal relations), Broad denied that absolute becoming can be explained as motion. 5 For, (i) if something moves, it must do so with a determinate velocity. To ask how fast something moves is to ask how great a distance it will have traversed in unit time-lapse. But in the case of temporal becoming, the distance traversed just is the time-lapse. So it is meaningless to ask, "How great a time-lapse will presentness have traversed in unit time-lapse?" (ii) For a brief survey, see Encyclopedia of Philosophy (1967), s.v. "Change," by Milic Capek. Isaac Watts, "0 God, Our Help in Ages Past," in The Hymnal (Waco, Tex.: Word Music, 1986), no. 52. The hymn is based on Psalm 90, but Watts's hypostatization oftime as a rolling stream derives from extra-biblical tradition. 3 John McTaggart Ellis McTaggart, The Nature of EXistence, 2 vols., ed. C. D. Broad (Cambridge: Cambridge University Press, 1927; rep. ed.: 1968),2: 10. 4 Ibid.,2: II. C. D. Broad, Examination of McTaggart's Philosophy, 2 vols. (Cambridge: Cambridge University Press, 1938; rep. ed.: New York: Octagon Books, 1976),2: 277-280.

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The acquisition and loss of presentness by an instantaneous event would itself be an instantaneous event of the second order. In this second order, the first order event has a sort of temporal history: first it is future, then it is present, then it is past. But by definition an instantaneous event has no history. Therefore, there must exist a second order time dimension in which second order events (for example, the loss of futurity, the acquisition of presentness) occur. But in that case presentness has to move along the second order time dimension as well, which leads to an infinite regress. In other words, if one grants that temporal becoming is a motion, McTaggart's Paradox is cogent. Broad therefore denied that temporal becoming is a species of motion. Since past and future events/things/times do not exist, temporal becoming cannot be construed as the motion of presentness from one term to another. On Broad's view temporal becoming seems to be just the tensed, as opposed to tense less, existing of each term. The attack upon a literal interpretation of time's flow was thus initiated by an Atheorist. But a little more than a decade after the publication of Broad's Examination B-theorists began to use the same arguments to attack the A-Theory itself. D. C. Williams charged that the A-Theory is infected with "the disastrous myth of passage.,,6 Quoting Santayana to the effect that "The essence of nowness runs like fire along the fuse of time,"? Williams apparently thought that according to the A-Theory, all events, whether past, present, or future, are equally real and that these are carried past the observer by the flow of time. 8 Against such a conception objections reminiscent of Broad's are lodged. What Williams took to be the ATheory is, however, evidently McTaggart's hybrid A-B-Theory, which marries Atheoretical becoming to a B-theoretical event ontology. For his part, Williams plumps for a B-theoretical interpretation of the relativistic space-time manifold of events. He seems to think that temporal becoming is incompatible with relativity theory, for he denounces the "prophets of passage" because they "melt back into the Donald C. Williams, ''The Myth of Passage," Journal oj Philosophy 48 (1951): 471. George Santayana, The Realms oj Being (New York: Charles Scribners Sons, 1942), p. 491. Cf. the oft-cited mischaracterization of the B-Theory by Hermann Weyl: "The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time" (Hermann Weyl, Philosophy oj Mathematics and Natural SCience, trans. Olaf Helmer, rev. ed. [Princeton: Princeton University Press, 1949], p. 116). Gronbaum bends over backwards in an attempt to place an acceptable interpretation on Weyl's words (Adolf GrOnbaum, Philosophical Problems ojSpace and Time, 2d ed., Boston Studies in the Philosophy of Science [Dordrecht: D. Reidel, 1973], pp. 328-329), for which he is chided by Smart as being "too kind" to Weyl, whose metaphor is "highly misleading" (1. J. C. Smart, "Introduction," in Problems oj Space and Time, ed. J. J. C. Smart, Problems of Philosophy [New York: Macmillan Co., 1964], p. 18). Such misleading characterizations of temporal becoming are all too frequent. S Williams, "Myth of Passage," p. 461, says that on an A-Theory of time we speak as if "the perceiving mind were stationary while time flows by like a river, with the flotsam of events upon it." Cf. his claim that it is the myth of passage which inclines one to the idea of time travel (Ibid., pp. 462-463). On the contrary, it is the B-theoretical ontology that so inclines one, for past events actually exist "back there" and future events "up ahead," on the analogy of spatial locations to which one may travel. Wells himself, like Williams, presented a confused conflation of the A- and B-Theories (H. G. Wells, The Time Machine [New York: Berkeley Publishing, 1957], pp. 5-18). Contemporary proponents oftime travel are inevitably B-theorists; for discussion see my Divine Foreknowledge and Human Freedom: The Coherence ojTheism: OmniSCience, Brill's Studies in Intellectual History 19 (Leiden: E. J. Brill, 1991), pp.150-153.

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primitive magma of confusion and plurality the best and sharpest instruments which the mind has forged.,,9 Williams's article exerted considerable influence, and his coinage "the myth of passage" was adopted by J. 1. C. Smart and became a centerpiece of Smart's case against the A-Theory of time. \0 Actually Smart had already reiterated Broad's arguments against a literal flow of time two years prior to the publication of Williams's critique in an article bearing the Heraclitan title "The River of Time." 11 According to Smart the flow of time is a metaphor which comes from spatializing time and reitying events. Properly construed, events are just happenings to things and so neither become present nor come into existence. To think of events as flowing by in time implies a second time dimension with respect to which the flow of events along the first time dimension is measured, and then there must be a third time dimension to measure the flow of the second, ad infinitum. Moreover, a literal flow of time forces on us "the pseudo question 'How fast am I advancing through time?' or 'How fast did time flow yesterday?"': We do not know how we ought to set about answering it. What sort of measurements ought we to make? We do not even know the sort of units in which our answer should be expressed. 'I am advancing through time at how many seconds per -1' we might begin, and then we should have to stop. What could possibly fill the blank? Not 'seconds' surely. In that case the most we could hope for would be the not very illuminating remark that there is just one second in every second. 12

The flow of time is thus metaphorical; but it is so in a "philosophically important" way, for this way of talking is in some sense "natural to us" and, at first sight, nearly unavoidable. 13 So long as we separate such metaphorical talk from philosophical discussion, counsels Smart, there is no reason why we should not sing "Time like an ever-rolling stream" with a clear logical conscience. 14 But after the publication of Williams's piece, Smart's benign attitude seemed to change. Now the flow of time had become "a dangerous metaphor.,,15 Not only is it absurd to say that events come into existence, but "In the four-dimensional way of talking, of course, we must not say even that things come into existence-we replace talk of a building coming into existence at t by talk of the earliest time slice of the building being at t.,,16 Objections to the literal flow of time have become arguments against the A-Theory itself, so that Smart marvels concerning Broad that

Williams, "Myth of Passage," p. 471. See 1. J. C. Smart, 'The Temporal Asymmetry of the World," Analysis 14 (1953-54): 79-83; idem, Philosophy and Scientific Realism, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1963), pp. 134-148; idem, "Introduction," pp. 17-22, in which Williams's article is anthologized; Encyclopedia of Philosophy (1967), s.v. "Time," by idem, where "The Myth of Passage" serves as a heading for major sections of the article and bibliography and in which Smart refers to Williams's article as a "brilliant criticism"; idem, "Time and Becoming," in Time and Cause, ed. Peter Van Inwagen, Philosophical Studies Series in Philosophy (Dordrecht: D. Reidel, 1980), pp. 3-4. II J. J. C. Smart, 'The River of Time," Mind 58 (1949): 483-494. 12 Ibid., p. 485. 13 Ibid" p. 483. 14 Ibid., p. 494. 15 Smart, "Temporal Asymmetry," p. 81. 16 Smart, Scientific Realism, p. 135. 10

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he is "so clear headed that it is hard to understand why he rejected his earlier theory."l7 What may be said of Williams and Smart's employment of Broad's objections to rebut the A-Theory? In the first place, it seems clear that insofar as attacks on the flow of time are directed at the sort of motion of A-determinations along a B-series of events such as was envisioned by McTaggart, they do nothing to undermine a pure A-Theory of time or temporal becoming, for as presentists A-theorists typically deny a literal flow of time. A. N. Prior speaks for most contemporary A-theorists when he states that time's flow or passage "is just a metaphor.,,18 According to Prior, the argument about the flow of time is either pedantic or perverse: pedantic if it means to show only that talk of time's flow is figurative, for everyone knows that; perverse if it means to deny the truth which the figure conveys, which everyone also knoWS. l9 Prior concurs with Broad's point (reiterated by Smart and Williams) that it is things, not events, which change, and he suggests the use of adverbial tense operators like "It was the case that" to reformulate sentences whose surface grammar describes changes in events into statements contrasting what was or will be the case with what is now the case. He concludes, "The flow of time, we would then say, is merely metaphorical, not only because what is meant by it isn't a genuine movement, but further because what is meant by it isn't a genuine change; but the force of the metaphor can still be explained-we use the metaphor because what we call the flow of time does fit the above formula.,,20 What the metaphor serves to express is the truth that there are tensed facts. As Christensen says, "Talk of the successive passage of events into the present, and all the rest, is just a highly derivative way of saying that events exist successively: El was occurring and now E2 is occurring, and El is not occurring any longer. The only thing our 'passage of time' locutions really say, ultimately, is what is said by the temporal adverbs from which they are all derived.,,2l With respect to the myth of passage, then, B-theorists appear to have been attacking a straw man. More recently, Smart acknowledges that A-theorists take talk of time's flow to be metaphorical. He interprets the metaphor of motion as indicative of objective temporal becoming. But now he demands, "The question is whether one can make Smart, "Introduction," p. 22. Arthur N. Prior, "Changes in Events and Changes in Things," in Papers on Time and Tense (Oxford: Clarendon Press, 1968), p. 1. The chief exception to this rule has been George Schlesinger, who has repeatedly (and, I think, vainly) tried to defend the literal movement of what he calls the NOW along the B-series. See George Schlesinger, Aspects of Time (indianapolis: Hackett, 1980); idem, "How Time Flies," Mind 91 (1982): 501-523; idem, "How to Navigate the River of Time," Philosophical Quarterly 35 (1985): 91-92; idem, "E Pur Si Muove," Philosophical Quarterly 41 (1991): 427-441; idem, "A Short Defense of Transience," Philosophical Quarterly 43 (1993): 359-361. Cf. Ned Markosian, "How Fast Does Time Pass?" Philosophy and Phenomenological Research 53 (1993): 829-844. For effective critiques of Schlesinger's proposals, see L. Nathan Oaklander, Temporal Relations and Temporal Becoming (Lanham, Md.: University Press of America, 1984), pp. 74-75; idem, "McTaggart, Schlesinger, and the Two-Dimensional Time Hypothesis," Philosophical Quarterly 33 (1985): 391-397; idem, "A Reply to Schlesinger," Philosophical Quarterly 35 (1985): 93-94; Keith Seddon, Time: a Philosophical Treatment (London: Croon Helm, 1987), p. 19; David 1. Buller and Thomas R. Foster, "The New Paradox of Temporal Transience," Philosophical Quarterly 42 (\992): 357-366. 19 A. N. Prior, "Time after Time," Mind 67 (1958): 244. 20 Prior, "Changes," pp. 11-12. 21 Ferrel Christensen, "The Source of the River of Time," Ratio 18 (1976): 140. 17

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any clearer sense of this than one can of passage or flow as simple motion.,,22 He thinks not. For normally we speak of something's becoming something or otherfor example, someone's becoming fat; but absolute becoming is conceived to be a monadic predicate. "In the pure becoming of an event, what does the event become?,,23 But Smart's question is strangely misconceived, for he himself repeatedly underlined Broad's point that it is things, not events, that become and that an event is the becoming of some thing( s). 24 In the pure becoming of some thing, as we have seen, the thing becomes actual. Nor is becoming any kind of a predicate. At most presentness could be said to be a monadic predicate or property. Smart goes on to acknowledge that it is coherent to say that an event becomes present, but he charges that such an explanation is unhelpful "since every event becomes present at some time or other.,,25 But this objection embodies a confusion between "present-at-t" and "present." The description of any event may include the predicate "present-att," where "f' is assigned some appropriate value, but only present events can be truly described as present simpliciter. Hence, I see no sound objection issuing from Smart's comer to taking time's flow as a metaphor for absolute becoming, that is to say, the successive actualization of states of affairs or events' and/or things' acquisition of the property of presentness. The Rate a/the Lapse a/Events

Still an objection may linger at this point. Perhaps one could ask, "How quickly do states of affairs become actual? At what rate do things or events acquire presentness?" But the meaningfulness of such a query appears to depend on whether one adopts a relational or substantival view of time. P. 1. Zwart, a relational A-theorist, argues that the flow of time is nothing else than the flow of events. 26 Hence, the rate of flow is the number of events occurring per unit of time (that is, per standard clock event). Zwart thinks that while it is meaningful to speak of the rate of the flow of events, it is without significance. For the rate of time's flow is the ratio of the total number of events in the whole universe in a certain period of time to the number of the earth's revolutions in that same period, and, since events are infinite in number, the ratio is indefinite. But surely Zwart's analysis of the rate of the flow of events is mistaken. For we could on his account increase the number of events per unit time, thus speeding up the "flow" of events, simply by enlarging the spatial extent of the universe so as to encompass more events, which ought to be Smart, "Time and Becoming," p. 4. Ibid., p. 5. The argument makes little advance over Smart, "Introduction," p. 21. 24 "Now this use of 'become' is no more applicable to events than is the ordinary transitive use. Events do not come into existence; they occur or happen" (Smart, "River of Time," p. 486); talk of events' coming into existence is "a breach of logical grammar" (idem, "Temporal Asymmetry," p. 81); things come into existence, change, or stay the same, but to say that an event came into existence or changed would be "absurd" (idem, Scientific Realism, p. 135); " ... we can talk of continuants as coming into existence or ceasing to exist, but we cannot similarly talk of a 'coming-into-existence' itself as coming into existence or ceasing to exist" (Encyclopedia of Philosophy, s.v. "Time"). 25 "Time and Becoming," p. 5. 26 P. 1. Zwart, 'The Flow ofTime," Synthese 24 (1972): 135-141. 22 23

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irrelevant to the rate of events' occurrence. 27 Nor is it adequate to consider an arbitrary, fmite segment of the universe to calculate the rate, for some parts may be more quiescent and, hence, have fewer events occurring per unit time, than others. And even if we took from a large-scale homogeneous and isotropic universe a typical segment, still the universe could vary in eventfulness over time, which would force us to say that the rate of the flow of events is increasing or decreasing. Rather in order to calculate the rate of the flow of events what we must do is count the number of events in a periodic process that occur during the unit time. But such a comparison is evidently uninfonnative and bound to yield a tautological result, for any truly periodic process is itself a standard clock, so that what one winds up doing is comparing the standard clock with itself. Hence, on a relational view of time, it is idle to ask for the rate at which events occur. If, therefore, we interpret temporal flow along the lines of Smart's suggestion as the becoming of things or events, then no non-trivial query about the rate of time's flow can arise. On the other hand, on a substantival view of time, the meaningfulness of the query will seem to depend on whether one takes the metric of time to be conventional or not. This fact emerges from the brief exchange between GIiinbaum and Smart on this issue. GIiinbaum had claimed, " ... the concept of the transiency of the now or of the flow of time is a qualitative concept without any metrical ingredients. Hence the entirely non-metrical concept represented by the metaphor 'forward flow' is not at all vulnerable to the metrical reductio ad absurdum offered by 1. J. C. Smart .... ,,28 But Smart's objection was not aimed at Griinbaum's analysis of temporal becoming according to which " ... the 'flux of time' or transiency of the 'now' has a meaning only in the context of the egocentric perspectives of sentient organisms and does not also have relevance to the relations between purely inanimate individual recording instruments and the environmental physical events they register .... ,,29 As Smart says, " .. .if this is all that is meant by a 'flux of time' then there is indeed such a flux.,,30 But Smart's criticism was directed at those analyses according to which temporal becoming is an objective feature of the world; the facts to which GIiinbaum draws attention serve to "explain the illusion that there is a flux, in the sense of motion through time.,,31 Nonetheless, GIiinbaum's remarks do serve to highlight a salient feature of the argument: its metrical character. The objection concerning the rate of the flow of events is an objection that is based on the ratio consisting of the number of events per unit time interval. In order to speak non-trivially of the rate of the flow of events, it will be necessary to compare the number of events occurring during equal, non-identical intervals. Otherwise, one could choose as his interval the entire duration of the universe and come up with the uninfonnative sum of the events that 27 I am assuming that the universe is spatially finite. If Zwart's characterization of the rate of flow of events bars this assumption, then it is inadequate, for there are many cosmological models which posit the spatial finitude of the universe. If he means that in a spatially finite universe, an infinite number of events occurs during a finite temporal interval, then this characterization only reinforces the necessity of focusing on the events of a single periodic process in order to obtain a rate of events' flow. 28 GrOnbaum, Philosophical Problems o/Space and Time, p. 329. 29 Ibid., p. 325. 30 Smart, "Introduction," p. 17. 31 Ibid., p. 18.

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have occurred during its history as the rate of the flow of events; or one could pick only one proper subinterval and count the number of events occurring during it alone, which would tell us nothing about whether the rate of flow is steady, decreasing, or increasing; or we could select proper sub-intervals without regard to their lengths, in which case comparisons between them would be useless until ratios for equal intervals were determined. But the determination of equal temporal intervals is a matter of the metric of time. If one holds that the metric of time is non-conventional, except in the trivial semantic sense, then it will be quite meaningful to speak of the rate of the flow of events. This will be the number of beats of a standard clock, say, a cesium atomic clock, per unit interval of substantival time. It is perfectly meaningful in such a case to speak of the rate of the flow of events increasing or decreasing. It might be said that such a determination of the rate of flow is meaningless because if there were, say, overnight a universal and uniform increase in the rate at which events occur, no one could notice the difference. Since the standard clock would itself be speeded up, its measure of the rate of flow would be unchanged. This objection, however, overlooks the fact that such a uniform increase in the rate of events' flow, even if undetectable by the standard clock, would produce other dislocations in certain physical laws in which time plays a role that would manifest themselves empirically.32 Imagine, for example, what would happen if accelerations or decelerations would overnight undergo a tenfold increase in their rate. In order for the alteration in the rate of events' flow to be undetectable, there would have to occur concomitantly a universal adjustment of the appropriate laws of physics. In such a case, we might infer that overnight only the laws of physics had been changed rather than that the rate of events' flow had changed; but such an inference is by no means inevitable. More importantly, however, wholly apart from whatever conclusion we might draw, God would know if the rate at which physical events occurred were to suffer an overnight alteration. Indeed, it is quite conceivable that God could cause the rate of the atomic clock and all other periodic processes to increase or decrease overnight and that He could so alter the laws of physics to conceal this fact from us. Even if God exists in a sort of metaphysical time such as Newton envisioned,33 He could effect changes in physical time which would leave Him quite unaffected. In fact, if substantival time has a non-conventional metric, then it is meaningful to speak of an increase of the rate of the flow of events in metaphysical time as well. In such a case, God's own mental events and actions would occur more quickly in metaphysical time than before the increase. This need not be mysterious, as it seems to be with regard to the stream of physical events; if, for example, God were counting at the rate of one number per arbitrarily designated time unit, He could decide to start counting twice See analogous reasoning with regard to a nocturnal doubling of the universe in size in George Schlesinger, "What Does the Denial of Absolute Space Mean?" Australasian Journal of Philosophy 45 (1967): 46. The objection to the meaningfulness of the universe's doubling in size or the flow of events' doubling in rate is just one more example of the defunct positivism which has so influenced philosophy of space and time during the twentieth century. For obviously, that these doublings should take place and be accompanied by radical and sweeping changes in physical laws that serve to conceal what has happened is meaningful (and, if God exists, possible), whether anyone can verify it or not! 33 For discussion see my God, Time, and Eternity (Dordrecht: Kluwer Academic Publishers, forthcoming), chap. 5.

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as fast, two numbers per given time unit. Given a substantival view of time endowed with a non-conventional metric, it is quite intelligible to ask how quickly events acquire the property of presentness or become actual. If, on the other hand, we adopt the view that the metric of substantival time is non-trivially conventional, then Smart's metrical objection seems to find no purchase. For in such a case there do not exist factually objective equal temporal intervals to serve as the basis of comparison of how many events are occurring per unit interval. We can theoretically determine how many beats of the standard clock occur in the interval (a, b) and how many in the interval (b, c), but with no objective fact of the matter that the distance (a, b) equals the distance (b, c), it is impossible for there to be a non-trivial, factually objective rate at which events happen. Even God could not know the rate of events' flow, for there just is no objective fact of the matter to be known concerning the equality of temporal intervals. Hence, I am skeptical of Smart's unexplicated claim that "Ascription of a metric to time is not necessary for the argument, but supposing that time can be measured in seconds, the difficulty comes out very clearly.,,34 Without a non-conventional metric, God could at best know only how many events of the conventionally selected standard clock occur between any t and t', which is uninformative as to any rate at which events occur. This conclusion is significant, for it implies that conventionalists like Smart cannot coherently press the "myth of passage" objection, nor is the objection meaningful for a theist like Alan Padgett, who holds that God exists in non-metrical time 35 ; for on these views the locution "the rate of the flow of events" is simply malformed. For conventionalist A-theorists, events do become present or actual successively, but they do not do so at any sort of objective rate. So if we take the metaphor of the flow of time to refer to the successive actualization of things and/or events, then the question concerning the rate at which this takes place is, depending on one's view of time, either malformed or not unanswerable. The Rate a/the Lapse a/Time

Still, perhaps the question needs to be pushed a notch further. For the original metaphor concerned the flow of time, not the flow of events, and on a nonconventionalist, substantival view of time, it seems meaningful to ask for the rate at which successive temporal intervals are actualized. Another way of seeing the point is to reflect on the fact that unlike B-theorists, A-theorists hold that intervals or moments of time do not simply exist tenselessly at their appointed stations (the extensive aspect of time), but that they elapse (transitory aspect of time), and the notion of an interval's elapsing can seem somewhat analogous to motion. Accordingly, one might demand to know the rate at which temporal intervals elapse (or are actualized), believing this to entail the aforementioned absurdities. But now the substantivalist seems to find himself in a position analogous to that of his relationalist colleague. To ask how fast a unit of time elapses is to ask how 34

3~

Encyclopedia of Philosophy, s.y. "Time." Alan Padgett, God, Eternity, and the Nature of Time, Library of Philosophy and Religion (New

York: St. Martin's, 1992), pp. 125-130.

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many units of time transpire in a unit of time, and the answer can only be, one. This is the point that A. N. Prior was getting at when he wrote, Surely the answer to this question is obvious. I am now exactly a year older than I was a year ago; it has taken me exactly a year to become a year older; and quite generally, the rate of this change is one time-unit per time-unit. Nor does any mysterious 'supertime' enter into this calculation. It has taken exactly one year of ordinary time for my age to increase by one year of ordinary time, and that is all there is to it. 36

Smart rejoins that the incorrectness of this answer can be seen by reminding ourselves of what motion through space is. 37 To say that two particles are moving at a uniform velocity relative to each other is to say that their world lines are at an angle to each other in space-time. If they are at rest, their world lines are parallel to each other. So, Smart exclaims, how on earth could one represent a movement of one second? This rejoinder seems to assume that if temporal becoming is real, then the flow of time must be represented on a Minkowski space-time diagram. But such an assumption seems silly, since the whole point of the diagram was to represent the dimensions of space and time as axes in a geometrical 4-space. So, of course, the lapse of time will not or cannot be represented on the diagram. 38 I suspect that the reason Smart thinks that this want in the diagranunatical representation reflects some ontological absence is because he has reified the representations of the diagram into an ontological space-time, and "To talk of anything's moving through space-time is to bring time into the story twice over and in an illegitimate manner.,,39 But such a hypostatization of the diagram's contents is a gratuitous and questionbegging assumption of a B-theoretical ontology. The A-theorist rejects this ontology of a tenselessly existing space-time and so sees no grounds for thinking that the failure of temporal becoming to be represented in a mathematical diagram implies any metaphysical dearth. Moreover, since A-theorists take the flow of time as a metaphor for temporal becoming or for the reality of tensed facts rather than as a description of a literal motion of time, Smart's expectation that temporal becoming or the lapse of time should appear on the Minkowski diagram if it is real is doubly unwarranted. 40 It seems to me, therefore, that if one asks how quickly temporal intervals elapse or are actualized, Prior's answer, though uninformative, is quite correct. As Padgett says, "It is not the answer which is absurd so much as the question itself.,,41 The prophets of the myth of passage seem to have erred, therefore, in thinking that Broad's arguments against McTaggart's literal construal of the flow of time could be turned against the A-Theory itself. A-theorists typically construe the flow of time to be a metaphor for the reality of tensed facts or temporal becoming, and Prior, "Time after Time," p. 244; cf. idem, "Changes in Event and Changes in Things," p. 2. Smart, "Time and Becoming," p. 4. 38 The insignificance for the reality of temporal process of failing to be representable on a Minkowski diagram is underlined by N. Lawrence, "Temporal Passage and Spatial Metaphor," in The Study o/Time II, ed. 1. T. Fraser and N. Lawrence (Berlin: Springer Verlag, 1975), pp. 196-205. 39 Encyclopedia 0/ Philosophy, s. v. "Time." 40 Similarly, Christensen's objection to Prior's characterization of the rate of time's flow fails, since Prior did not conceive of it as a literal motion (Christensen, "Source of the River of Time," p. 132). 41 Padgett, God. Eternity. and the Nature o/Time, p. Ill. 36 37

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whether one adopts a relationalist or substantivalist metaphysic of time, no absurdity has been shown in speaking of the objective becoming of things and/or events or of the successive lapse or actualization oftemporal intervals. OBJECTIONS TO TEMPORAL BECOMING

The "Empty Future"

But perhaps there are other insuperable problems with the philosophical doctrine of objective temporal becoming. For example, a pure A-theoretic ontology entails what Paul Fitzgerald has called "the empty future theory"; that is to say, the view that the future is unreal, literally nothing. 42 The passage of time in the world involves the progressive actualization of what was formerly only potential or not fully real-what Fitzgerald labels a "reality acquisition model" of absolute becoming. 43 Since a consistent theory of objective becoming entails an "empty past theory" as well, as we saw in our discussion of McTaggart's Paradox, a preferable (and, moreover, less misleading) terminological characterization of an A-theoretic ontology is "presentism." Presentism holds that while the present and/or the contents of the present (whether things, events, or whatever) exist, neither the past nor the future and/or their contents exist. A strong form of this doctrine asserts that only the present and/or its contents exist, thereby ruling out the existence of timeless entities. A moderate presentist holds that in addition to presently existing entities, there are also timeless entities, perhaps numbers, propositions, even God. Since both forms of this doctrine are consistent with objective temporal becoming, an Atheorist could consistently adhere to either form, and therefore we may be spared the task of inquiring whether any timeless entities exist. What problems, then, are there with the philosophical doctrine of presentism? We may dismiss at the outset Fitzgerald's objections to an "empty future" theory. He maintains that the theory entails a denial of bivalence for future-tense statements and that such a denial is incompatible with the fact that we do have some knowledge of the future. 44 We may agree that we do know some future-tense statements, but Fitzgerald incorrectly assumed that an "empty future" theory entails a denial of the Principle of Bivalence for such statements. 45 Fitzgerald was no doubt misled by the historical fact that some A-theorists have denied bivalence of futuretense statements into thinking that the "empty future" theory itself entails or implies such a denial. In general Fitzgerald's error is his conflation of semantics and ontology. The presentist's ontological claim that future entities do not exist does not imply the semantical thesis of the denial of the Principle of Bivalence for futurePaul Fitzgerald, "Is the Future Partly Unreal?" Review of Metaphysics 21 (1967-68): 421-423; cf. idem, "The Truth about Tomorrow's Sea Fight," Journal of Philosophy 66 (1969): 308. 43 Paul Fitzgerald, "Nowness and the Understanding of Time," in PSA 1972, Boston Studies in the Philosophy of Science 20, ed. Kenneth F. Schaffner and Robert S. Cohen (Dordrecht: D. Reidel, 1974), p. 260. 44 Fitzgerald, "Future Partly Unreal," p. 422, 427; idem, "Tomorrow's Sea Fight," p. 309. 45 Contra see Craig, Divine Foreknowledge and Human Freedom, pp. 43-63. 42

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tense statements, any more than his ontological claim that past entities do not exist implies the semantical thesis that past-tense statements are neither true nor false. 46 If the "fullness" or existence of the past or future amounts to no more than the semantical thesis that past- and future-tense statements are governed by the Principle of Bivalence, then, of course, the past and the future exist in this sense. But this sense of "existence" is irrelevant to the issue of the ontological status of past and ' future events/things/times.47 Fitzgerald also asserts that the "empty future" theory is "flatly incompatible" with the Special and General Theories of Relativity.48 This objection is based on regarding Einsteinian relativity as making "plausible claims about the actual structure of physical space-time," rather than as "a set of fictions" or "a mere computational device.,,49 It also rests on the assumption that time itself is isomorphic to the temporal dimension of the structure of physical space-time. Both of these assumptions are, however, controversial and hardly incumbent upon us. so The Extent ofthe Present

In his article on the myth of passage, Williams also pressed a different argument against presentism: he asserted that he found it incredible as a point of logic that only the things that exist "now" exist, "because a concrete object can no more exist with zero duration than with zero breadth and length."sl The key move in this objection-which is a puzzle about the ontology of time at least as old as Aristotles2-is the equation of the present with an instant oftime. This was in fact 46 For a similar conflation of ontology and semantics on the part of an A-theorist, see Genevieve Lloyd, "Time and Existence," Philosophy 53 (1978): 215-228. She wants to deny bivalence for future-tense propositions on the basis of the unreality of future things, but she cannot bring herself to endorse Prior's view that by parallel reasoning there are no past-tense facts either. Thus, she is forced to hold that something's being past does not "take it beyond reality" or "remove it altogether from the order of things." She seems to be approximating the model of time in Broad's Scientific Thought, which we saw to be incoherent. 47 These considerations also serve to answer the objections of Melvin M. Schuster, "On the Denial of Past and Future Existence," Review of Metaphysics 21 (1967-68): 447-467, who claims that the presentist's view that some event E existed at t, but no longer exists at t2 is contradictory because at t2 he wants to deny E's existence at all times, yet he must admit it exists at t,. In saying things have ceased to exist, Schuster asserts, the presentist must admit that they existed at prior times. But when he claims that nothing outside the present exists, he must deny their existence. Schuster is obviously confused. He thinks that "E existed in the past" means "E has (present tense) existence at that past time." But the former statement is not to be understood as the latter admittedly incoherent statement but as "It was the case that E exists." The reality of the past and future consists in the present truth or falsity of past- and present-tense statements. At t2 the presentist does not wish to deny that "E existed at t," is true; nor is this inconsistent with his believing truly at t2 "E does not exist." 48 Fitzgerald, "Future Partly Unreal," p. 428. 49 Fitzgerald, "Tomorrow's Sea Fight," p. 307. 50 See discussion in my The Tenseless Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, forthcoming), Pt. I, sec. I. 5' Williams, "Myth of Passage," p. 459. 52 Aristotle Physics 4.10.21 7b33-2I 8a9. For an excellent discussion of the early history of this conundrum, see Richard Sorabji, Time. Creation and the Continuum (Ithaca, N. Y.: Cornell University Press, 1983), pp. 7-63. Augustine in particular agonized eloquently over this problem (Augustine, Confessions 9.15-28).

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Broad's view in his Examination; he conceived of temporal becoming as the successive actualization of instantaneous "event-particles," so that all that actually exists (leaving aside the question of timeless entities) is the present event-particle. Bertrand Russell parodied such a view as "solipsism of the moment,,,53 and Broad himself felt so uncomfortable with this position that late in life he entertained the existence of a second time dimension in which first order event-particles endure. 54 The Instantaneous Present Now what exactly is the problem with construing the present as a present instant? The objection under consideration states that such a construal is problematic because no concrete object can exist for zero duration; if it exists at all, it will have some temporal duration. If, therefore, the present has no duration, no concrete object can exist, which is absurd. Now the degree to which we find this objection cogent will depend in the first place on our view of the reality of instants (and, analogously, points). Although my own sympathies are with a sort of Peircean view of the continuum according to which a line exists primarily as a whole rather than as a collection of ordered points and so is only potentially infinitely divisible, instants being merely ideal points,55 so that I tend to agree with Williams's objection, nevertheless it must be said that a great many philosophers have no difficulty at all with the notion of real points and instants. Space is composed of an actually, non-denumerably infinite number of extensionless points and time of an actually, non-denumerably infinite number of durationless instants. Or again, the four-dimensional space-time manifold is composed of an actually, non-denumerably infinite number of space-time points. In fact in contemporary cosmology, the initial cosmological singularity which spawned our four-dimensional space-time manifold is sometimes represented in the standard model precisely as a durationless, extensionless point which exists on the boundary of space-time. Some contemporary thinkers take this singularity to be, not a mathematical idealization, but a real entity. Thus, Frank Tipler, appealing to Penrose's construction of a cboundary to space-time on which singular points lie, claims that" ... if the initial cboundary of the Universe is an initial singularity, we can receive information from this singularity, just as we can receive information from any other regular spacetime point in our past light cone. Thus it seems reasonable to say it really exists, if such is the initial c-boundary.,,56 If, then, we do concede that real instants exist, Bertrand Russell, Human Knowledge (New York: Simon and Schuster, 1948), p. 181. C. D. Broad, "A Reply to My Critics," in The Philosophy ofe. D. Broad, ed. Paul Arthur Schilpp, Library of Living Philosophers (New York: Tudor, 1959), pp. 769-772, in response to Robert Leet Patterson, "A Critical Account of Broad's Estimate of McTaggart," in Philosophy ofC. D. Broad, p. 155, who had demanded what the notion of an event-particle is: "That nothing is real except the event particle which is present? But this will leave us with a reality which has no duration at all." 55 C. S. Peirce, "On Continuous Series and the Infinitesimal," in The New Elements of Mathematics, 5 vols., ed. Carolyn Eisele, vol. IIIII: Mathematical Miscellanea (The Hague: Mouton, 1976), pp. 125-127. See also A. W. Moore, The Infinite (London: Routledge, 1990), pp. 104, 122, 156-158. 56 Frank 1. Tipler, "Achieved Spacetime Infinity," Nature 325 (15 January 1987), p. 20. When one reads Penrose, on the other hand, it seems pretty clear that he takes singular points and the c-boundary on which they lie as idealizations only (Roger Penrose, "Singularities of Spacetime," in Theoretical 53

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some further reason has to be given why the present cannot consist of a single instant of time. Perhaps the above mention of a space-time boundary provides a clue. For instants are not typically conceived to be temporal intervals, but boundary points of temporal intervals. They are like the end-points of a line segment; if the end-points are removed, then one has a finite interval open at both ends. If, then, the present is an instant, it must be the end-point of the past and the beginning-point of the future, the boundary between past and future. In the case of a finite temporal interval [0, 1] centered on the present instant, the past would be the half-open interval [0, Y:z), and the future would be the half-open interval (Y:z, 1]. But only the point designated "Y:z" would exist. Therein, however, lies the difficulty: for boundary points cannot exist independently of the intervals which they bound. Even in the case of an initial cosmological singularity, although that point does not bound a past interval, it bounds a future interval; similarly in the case of an eschatological cosmological singularity, the past is bounded by it even though it bounds no future interval. But if both past and future intervals were removed, the boundary between them would simply disappear. Sorabji attempts to avert the force of this argument by contending that there is a sense, acceptable to the presentist, in which the past and future do exist. 57 This sense is the opposite of the sense in which we say, "There is no past" at a first moment of time or "There is no future" at a last moment of time. Suppose someone were to make such statements at embedded moments of time. We would then contradict him, saying, "There is a past" or "There is a future." In this sense the past and/or future exist to serve as intervals bounded by the present instant. But it seems clear that this argument will not save the day for the presentist. For Sorabji's sense in which the past and/or future exists is a semantic sense only: pasttense statements and/or future-tense statements are true at the relevant moments of time. But the present instant is, on the view we are considering, not a semantical construction, but a moment of ontological time which must bound intervals of ontological time. Onto logically speaking, all that exists on this view is the single boundary instant, which seems impossible. One way of saving the notion of an instantaneous present from this criticism would be to contend that an instant can be an interval after all, an interval of zero duration. The presentist could assert that boundary points could not exist as boundaries in the absence of the intervals they bound, but that all that that consideration shows is that when the open intervals they bound are removed, they cease to be boundary points and exist merely as points. Thus, the present exists not as a boundary to the past or the future, but simply as a durationless part or degenerate interval of time. But regarding instants and particularly the present instant as a degenerate interval of time seems to create insuperable problems for temporal becoming. Because reality is conceived to be the progressive actualization of new instants,

PrinCiples in Astrophysics and Relativity, ed. Norman R. Lebovitz, William H. Reid, and Peter O. Vandervoort [Chicago: University of Chicago Press, 1978], pp. 217-243). See also note 89 below. 57 Sorabji, Time, Creation and the Continuum, pp. 12-13.

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Zeno's paradoxes of motion and quantity seem to become inescapable. 58 How can time progress instant by instant, since instants have no immediate successors? Like Achilles in the Dichotomy Paradox, the present instant would be frozen into immobility; it could not elapse to be succeeded by another, for before any new instant could be actualized an infmite number of prior instants would have to be actualized first. And even if the present instant could elapse, how could any nonzero interval of time elapse, since the addition of durationless instants will never add up to the lapse of a single nanosecond of time? But if no non-zero interval of time ever elapses, temporal passage is impossible. The intelligibility of instantaneous temporal becoming became the subject of an interesting debate between Adolf GrUnbaum and A-theorists such as William James and Alfred North Whitehead, who had, on the basis of their application of Zeno's reasoning to temporal becoming, defended the atomicity of temporal passage. James, for example, in discussing Russell's mathematical solution to Zeno's paradoxes of motion, discerned that the paradoxes were relevant to the nature of temporal becoming itself: ... the real difficulty ... concerns the 'growing' variety of infinity exclusively, and not the 'standing' variety, which is all that [8. Russell] envisages when he assumes the race already to have been run and thinks that the only problem that remains is that of numerically equating the paths. The real difficulty may be almost called physical, for it attends the process offormation of the paths. Moreover, two paths are not needed-that of either runner alone, or even the lapse of empty time involves the difficulty, which is that of touching a goal when an interval needing to be traversed first keeps permanently reproducing itself and getting in your way. Of course the same quantum can be produced in various manners.... God, as the orthodox believe, created the spacecontinuum, with its infinite parts already standing in it, by an instantaneous fiat. Past time now stands in infinite perspective, and may conceivably have been created so ... for our retrospection only, and all at once. 'Omega' was created by a single decree, a single act of definition in Prof Cantor's mind. But whoso actually traverses a continuum, can do so by no process continuous in the mathematical sense. Be it short or long, each point must be occupied in its due order of succession; and if the points are necessarily infinite, their end cannot be reached .... 'Enumeration' is, in short, the whole possible method of occupation of the series of positions ... ; and when Mr. Russell solves the puzzle by saying as he does, that 'the definition of whole and part without enumeration is the key to the whole mystery, * he seems to me deliberately to throwaway his case.

*The Philosophy of Mathematics, i, 361.59

It is noteworthy that (i) James applies the paradox to the lapse of time alone, not

simply to physical motion; (ii) he sees the problem to be inextricably bound up with becoming, for he is willing to adopt a B-theoretic continuum as a description of the For a brief statement of this point, see Encyclopedia of Philosophy, s.v. "Time." See also the interesting proposal of Hugh R. King, "Aristotle and the Paradoxes of Zeno," Journal of Philosophy 46 (1949): 657-670, who seeks to elude the problem by maintaining that there is no advance of the present through time; rather the present is stationary, so to speak, and the past issues out of it. On this model, the future is unreal, the past is real, and the present is the boundary of the past. "The act of becoming lies, so to speak, outside the extensive continuum of space and time" (Ibid., p. 69); it is the bound of physical time. But it is not clear that such a model would not involve a sort of mirror-image ofZeno's Paradoxes, e.g., how can an event-particle recede one instant into the past, since the present instant has no immediate predecessor? Or how could the past grow instant by instant? 59 William James, Some Problems ofPhilosophy (1911; rep. ed.: New York: Longmans, Green and Co., 1931), pp. 181-183. 58

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past (this being only a "standing" infinity), allowing that God could create it en bloc, so to speak, though He could not actualize such a continuum progressively (since this would be to complete a "growing" infmity); and (iii) he maintains that the progressive actualization of a continuous temporal interval involves not only succession (temporal anisotropy, or ordering relations of earlier/later than among temporal particulars), but "enumeration" or consecutiveness (instantiation of temporal particulars one by one and therefore one after another), which is omitted in Russell's Cantorian, static solution to the puzzle. Whitehead, Russell's erstwhile collaborator, citing "the authority of William James" and commenting, "In substance I agree with his argument from Zeno ... ,,,60 held that Zeno's Dichotomy Paradox in particular revealed that temporal becoming cannot be continuous. Like James, he applied the paradox to time itself: ... Zeno understated his argument. He should have urged it against the current notion of time itself, and not against motion, which involves relations between time and space. For, what becomes has duration. But no duration can become until a smaller duration (part of the former) has antecedently come into being .... The same argument applies to this smaller duration, and so on. 61

If becoming is continuous, then before a new second can become present, the first half of that second must first become; but before the first half-second becomes, the first quarter-second must become, and so on indefinitely. "Thus if we consider the process of becoming up to the beginnin~ of the second in question and ask what then becomes, no answer can be given." 2 Whitehead observes that it would be incoherent to claim that an initial instant of the second first becomes: "The difficulty is not evaded by assuming that something becomes at each non-extensive instant of time. For at the beginning of the second of time there is no next instant at which something can become.,,63 But" ... every act of becoming must have an immediate successor, if we admit that something becomes. For otherwise we cannot point out what creature becomes as we enter upon the second in question.,,64 Like James, Whitehead was content to let the past be a continuous time, but he denied continuity of temporal becoming: "There is a becoming of continuity, but no continuity of becoming. The actual occasions are creatures which become, and they constitute a continuously extensive world. In other words, extensiveness becomes, but 'becoming' is not itself extensive.,,65 Whitehead therefore propounded a so-called epochal theory of time, according to which temporal becoming proceeds in finite quanta. 66 Alfred North Whitehead, Process and Reality, corr. ed., ed. David Ray Griffin and Donald W. Sherburne (New York: Free Press, 1978), p. 68. 61 Alfred North Whitehead, Science and the Modern World (New York: Macmillan Co., 1925), p. 127. 62 Whitehead, Process and Reality, p. 68. 63 Ibid. 64 Ibid., p. 69. 65 Ibid., p. 35. 66 He explains, "A duration .. .is an epoch, i.e., an arrest.... Time is sheer succession of epochal durations.... Thus the divisibility and extensiveness is within the given duration. The epochal duration is not realised via its successive divisible parts, but is given with its parts .... 60

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In an early article excerpted from his doctoral dissertation, Adolf Grilnbaum disputed the arguments of James, Whitehead, and others against the continuity of temporal becoming. 67 Grilnbaum's key move was to argue that " ... an event can occur successively though not consecutively at each of a continuum of... points.,,68 Continuous temporal becoming is possible because temporal becoming entails only succession, not consecutiveness. Unfortunately Grilnbaum's argument for this conclusion is question-begging in favor of the B-Theory of time and misconstrues his opponents' position. His argument is question-begging because the account of temporal becoming which he adopts is not that of his A-theoretical opponents, but the static, B-theoretic account which lay at the foundation of Russell's solution to the Zenonian paradoxes. Thus, he holds motion to be "a set of events, ordered by the relation 'later than'" and proceeds to analyze that relation causally (causal theory oftime).69 He winds up with a B-theoretical ontology: Events simply are or occur. .. but they do not advance into a pre-existing frame called 'time.' Reichenbach puts the matter clearly by saying: 'Die Zeit ist der Ordnungstypus der Kausalreihen. '* Thus time is a system of relations between events, and as the events are, so are their relations. An event does not move and neither do any of its relations. *Reichenbach, Ax. Rei., p. 12.70

Given this analysis of the ontology of time, ... it now becomes entirely intelligible that influence relations can exist between events in a network of dependence such that the events constitute a linear Cantorian continuum with respect to the relation 'later than'! In this way the concept of 'later-than' becomes the key to the temporal order without involving the nextness property.7I

But, as I say, all ofthis is, of course, massively question-begging in favor ofthe B-Theory, since Grilnbaum's opponents agree that given a tense less, B-theoretical ontology, time can be regarded as continuous; but their claim is that if temporal becoming involves the progressive coming into being of time or the parts of time, then it cannot be continuous. In order for Grilnbaum's refutation to succeed, he has Thus time is the succession of elements in themselves divisible and contiguous .... Temporalisation is realisation. Temporalisation is not another continuous process. It is an atomic succession. Thus time is atomic (i.e., epochal), though what is temporalised is divisible" (Whitehead, Science and the Modern World, pp. 125-126). In a critique of Whitehead's view, Chappell claims that for Whitehead the becoming of time atoms has to be instantaneous (V. C. Chappell, "Whitehead's Theory of Becoming," in Alfred North Whitehead, ed. with an Introduction by George L. Kline [Englewood Cliffs, N. J.: Prentice-Hall, 1963], pp. 73-74). But such a characterization is misleading. Since time is epochal, there are no instants of becoming. What Chappell should say is that each atom, or actual occasion, comes to be as a whole, not part by part. On the basis of his mischaracterization Chappell goes on to argue that Whitehead's view is self-contradictory because an actual occasion which is extended from to to tl begins at the time of its happening (viz., to), which is itself instantaneous (Ibid., p. 75). The error is that the time of the atom's happening just is the whole atom; the actual occasion does not happen at 10, but at the interval to- tl. 67 Adolf Gronbaum, "Relativity and the Atomicity of Becoming," Review of Metaphysics 4 (1950-51): 143-186. A revised version of this piece later appeared in idem, Modern Science and Zeno's Paradoxes (London: Allen & Unwin, 1968). 68 GrOnbaum, "Atomicity of Becoming," p. 143. 69 Ibid., p. 154. 70 GrOnbaum, "Atomicity of Becoming," p. 172. 71 Ibid., pp. 168-169.

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to show that objective, A-theoretical temporal becoming can proceed nonconsecutively. That he has not even attempted to do. On the contrary, his contention that it is the tenseless later than relation which supplies the key to succession without consecutiveness suggests that he would concede his opponents' point. For it seems that in Griinbaum's opinion, succession can exist without consecutiveness if and only if succession is analyzed in terms of the tenseless Brelation later than alone. If succession involves A-determinations like present, then moments which become successively present become consecutively present. From the A-theoretical point of view, Griinbaum has said nothing to prove that temporal becoming can be successive but not consecutive, for his analysis of temporal becoming not only excludes consecutiveness, but genuine succession as well. In his becomingless ontology of time, neither exists. Thus, he seems implicitly to concede that one could not have A-theoretical succession of the parts of time without their becoming consecutively present. Griinbaum also seriously misconstrues his opponents' position in that he interprets their insistence that temporal becoming involve consecutiveness to be the result of their misunderstanding temporal becoming in terms of experientially sensed becoming, which, Griinbaum admits, does involve "nextness" due to the fmite velocity of neural processes.72 But none of his opponents bases his case on the nature of psychological experience of events; their analysis pertains to the objective and progressive actualization of being in time. Nothing in Griinbaum's mature writings on Zeno's paradoxes of motion would seem to alter these conclusions. Although these writings tend to focus on the issue of whether an infinite number of tasks can be completed in a fmite time,73 we still fmd Griinbaum insisting that it is our minimum threshold of duration awareness which makes us erroneously think that there is a positive lower bound on the duration of each task, so that we intuitively infer that Achilles can never reach his destination because we cannot in a finite time contemplate one by one all of the subintervals in the progression. 74 And Griinbaum's solution still consists in evacuating succession of any notion of A-theoretic becoming: Ibid., p. 165. See, for example, Gr1lnbaum, Modern Science and Zeno's Paradoxes. For a discussion of the "modern Eleatics" and their infinity machines, see the appendix "The Kalam Cosmological Argument and Zeno's Paradoxes," in Wm. L. Craig, The Kalam Cosmological Argument, Library of Philosophy and Religion (London: Macmillan, 1979), pp. 175-188. See in this connection the Auseinandersetzung between 1. Q. Adams, "Gr1lnbaum's Solution to Zeno's Paradoxes," Philosophia 3 (1973): 43-50, and Adolf Gr1lnbaum, "Reply to 1. Q. Adams' 'GrOnbaum's Solution to Zeno's Paradoxes'," Philosophia 3 (1973): 51-57. Adams gives an illustration involving a relay race in which runners traverse progressively shorter distances and, observing that there is no last runner to carry the baton to the end of the course, demands how anybody could be there at the finish, holding the baton. Gr1lnbaum's response is to assimilate the A-theoretical temporal race to a tenselessly existing continuum, as is evident in his remark, "If [Adams] has not succumbed to the temptations of the threshold-fallacy in drawing this inference, why does he regard his question 'how does the baton get thereT as more legitimate than the following hypothetical silly question, which he would presumably dismiss as mathematically untutored: 'How can a sequence of order type ro+ I have a last element while being devoid of a next-to-the-Iast element, so that the last element is preceded by an infinite progression of order type roT" (Ibid., p. 55). Adams's question is legitimate because it concerns a causal, temporal order, not a logical, tenseless order. 74 Gr1lnbaum, Philosophical Problems o/Space and Time, pp. 633, 636, 850.

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What is the basis for the view that the very meaning of temporal succession involves that events follow upon one another seriatim, like the consecutive beats of the heart, and not densely? The answer can be none other than that this feeling derives from a tacit appeal to the properties of the time-order experienced intuitively in human consciousness.... No wonder therefore if on such an intuitively grounded meaning of temporal succession, there is an ever present feeling that if physical events are to succeed one another in time, their order of occurrence must also be discrete, if it is to be a temporal order at all. It follows that a refutation of Zeno will be at hand, if the psychological criterion of temporal sequence can be supplanted by a strictly physical criterion of 'event B is later than event A' that does not entail a discrete temporal order, but allows a dense order instead. Fortunately a criterion of time-order based on the statistics of the thermodynamic behavior of classes of physical systems each of whose members is quasi-isolated for a limited time provides a criterion with precisely these required properties. 7s

Here we have the same B-theoretical analysis of temporal succession in terms of the later than relation, which is further analyzed in terms of the causal theory of time. No wonder, then, that after surveying the various proffered solutions to Zeno's paradoxes of motion, Whitrow concludes that we are left with two ways of resolving the paradoxes: either (i) abandon the concept of becoming or temporal transition (GrUnbaum), or (ii) abandon the assumption of the infinite divisibility of time (Whitehead)! 76 It does seem to me that if we regard the present as an instant of time and construe instants to be durationless (degenerate) intervals of time, then instantaneous temporal becoming is absurd. This may be seen from two angles. On the one hand, an analysis of A-theoretical becoming reveals that temporal becoming entails (i) that only one part of time is actual or present, (ii) that the several parts of time are actual one after another, and (iii) that every part of time was, is, or will be actual. Conditions (i) and (ii) guarantee that temporal succession is not exhaustively analyzed by a B-theoretical analysis of the parts of time as tenselessly ordered by the later than relation. Rather temporal succession involves the progressive actualization of the parts of time and their lapse into non-actuality. Conditions (i) and (ii) also entail that several parts of time cannot be present together. The parts of time elapse one by one. Condition (iii) precludes any parts of time's being skipped over in the process of temporal becoming. One by one, one after another, every part of time becomes actual and transpires. These conditions for A-theoretical becoming seem to leave no room for the non-consecutive passage of parts of time. But since instants are non-consecutive, they cannot, therefore, be the basic units of temporal becoming. From another angle, let us suppose on the other hand that the basic parts of time are instants. In order for the present instant to elapse, it must be succeeded by another. But there is no immediate successor to the present instant. Before the succeeding instant can become present, an infmite number of intermediate instants will have to have become present first. The point is not the fallacious inference that it would therefore take an infmite amount of time for the succeeding instant to

Adolf Grllnbaum, "Modern Science and the Refutation of the Paradoxes of Zeno," in Zeno's Paradoxes, ed. Wesley C. Salmon (Indianapolis: Bobbs-Merrill, 1970), p. 173. 76 G. J. Whitrow, The Natural Philosophy a/Time, 2d ed. (Oxford: Clarendon Press, 1980), p. 200.

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become actual. 77 Rather the point is that no instant at all can succeed the present instant, if temporal becoming proceeds instant by instant. For no instant can immediately succeed the present, nor can any instant non-immediately succeed the present. The present would therefore exist as the nunc stans of the classical doctrine of eternity, not the nunc movens of A-theoretic time. Not only does the identification of the present with a degenerate interval of time thus fall prey to Zeno's paradoxes of motion, but, moreover, it also falls into the snare of Zeno's paradoxes of plurality. Again, William James makes the point: The antinomy of mathematically continuous growth is thus but one more of those many ways in which our conceptual transformation of perceptual experience makes it less comprehensible than ever. That being should immediately and by finite quantities add itself to being, may indeed be something which an onlooking intellect fails to understand; but that being should be identified with the consummation of an endless chain of units (such as 'points'), no one of which contains any amount whatever of the being (such as 'space') expected to result, this is something which our intellect not only fails to understand, but which it finds absurd. The substitution of 'arithmetization' for intuition thus seems, iftaken as a description of reality, to be only a partial success 78

If we conceive temporal becoming to proceed instant by instant, the length of time between some past event or moment and the present could never increase, since the lapse of durationless instants adds nothing to the interval between that past instant and the present instant. But then there is no "flow" of time at all, and we are left again with the nunc stans of the present instant, never able to recede into the past. The doctrine of the instantaneous present is thus incompatible with objective temporal becoming. Griinbaum also took up this issue in another early article on the nature of the linear continuum. 79 A brief examination of Griinbaum's argument will serve to highlight the fact that however consistent the analysis of a spatial continuum as composed of extentionless, degenerate intervals may be, such an analysis fails for A-theoretic time. According to Griinbaum, the metrical question raised by Zeno's paradoxes of quantity is how zero length can be assigned to unity point sets or degenerate intervals, but positive finite lengths to non-degenerate intervals, which are unions of those points. "Zeno is challenging us to obtain a result differing from zero when determining the length of a finite interval on the basis of the known zero lengths of 77 As supposed by R. M. Blake, "The Paradox of Temporal Process," Journal oj Philosophy 23 (1926): 650-653. It is interesting that in response to Whitehead's challenge, "How does the succeeding interval get started?" Blake has to appeal to non-zero intervals of time as the units of becoming: "by the occurrence of a part of it which is earliest of some set offractional parts, but which itself contains various sets of fractional parts within each of which sets some members of the set are earlier than others" (Ibid., p. 654). Except for the language of temporal parts, this solution comes very close to that which I defend below and is inconsistent with an instantaneous present, since what becomes present is never an instant, but a (conceptually divisible) finite temporal interval. 78 James, Some Problems oj Philosophy, pp. 185-186. 79 Adolf Grtlnbaum, "A Consistent Conception of the Extended Linear Continuum as an Aggregate of Unextended Elements," Philosophy oj Science 19 (1952): 288-306. This early piece, also excerpted from GrOnbaum's doctoral dissertation, was subsequently revised and corrected in the first edition of Philosophical Problems oj Space and Time, pp. 158-176, and again in Modern Science and Zeno's Paradoxes, pp. 114-140. His final remarks and corrections are to be found in Appendix 10 to the second edition of Philosophical Problems ojSpace and Time, pp. 808-820.

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its degenerate subintervals, each of which has a single point as its only member."so For Griinbaum the issue devolves down to the additivity of length in various manifolds. In a discrete manifold, length is countably additive: if an interval is the union of subintervals, no two of which share a common point, then its length is the arithmetic sum of the individual lengths of the subintervals. Even in a denumerably dense manifold length is countably additive: if an interval is the union of a finite or a denumerably infinite number of subintervals, no two of which share a common point, then its length is equal to the arithmetic sum of the individual lengths of the subintervals. If space and time were construed to be merely dense manifolds, then the sort of metrical contradiction envisioned by Zeno would, indeed, result. For example, if we consider the length (or measure) of the denumerably infinite set of rational points between and including 0 and 1, then if we take as our subintervals the open intervals (0, V,) and (V" 1), the length of the interval is V, + v, = I; but if we take as our subintervals the rational points themselves, then the length of the interval is 0 + 0 + 0 +... = O. Now length in a continuous manifold is countably additive in the same sense as it is for a merely dense manifold. But the reason the theory of the continuum is not inconsistent in its affirmation of the countable additivity of length and duration and its affirmation that extended intervals are unions of degenerate intervals (either extensionless points or durationless instants) is because the points or instants of an extended interval are not merely denumerably infinite. sl Since there are non-denumerably infinitely many points or instants in any extended interval, interval length in a continuous manifold cannot be defined in terms of an arithmetic sum of degenerate intervals. Griinbaum concludes, "Though the finite interval (a, b) is the union of a continuum of degenerate subintervals, we cannot meaningfully determine its length in our theory by 'adding' the individual zero lengths of the degenerate subintervals. We are here confronted with an instance in which settheoretic addition is possible while arithmetic addition is not."S2 But Griinbaum's analysis proves fatal to the notion of continuous temporal becoming in terms of the accretion of degenerate temporal intervals. For temporal becoming is arithmetically additive in nature. One instant (on the hypothesis of the instantaneous present) is added after another; a past interval is formed by the successive addition of instants as they elapse. Therefore, temporal becoming cannot be continuous because a non-denumerable infinity cannot be formed by addition. Since temporal becoming proceeds by addition, temporal length or duration is countablyadditive. If the present were a mere durationless instant, then Zeno would be correct that the addition of further such degenerate intervals could not add up to a finite positive interval of time. In his mature work on this subject, Grtinbaum came to see that length is not countably additive even for a merely denumerably dense manifold. "For metrical consistency," observed G. Massey in his critique of Grtinbaum's geochronometry, "precludes the countable additivity of measures on denumerable dense manifolds

80 81

82

Griinbaum, Philosophical Problems o/Space and Time, p. 164. Ibid., p. 809. Ibid., p. 171.

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and the finite additivity of measures on discrete manifolds.,,83 Therefore, Massey seems to be saying, in order to maintain a consistent metrical theory we simply must deny the countable additivity of length for both dense and continuous manifolds. Length with respect to space and time must not be countably additive. But as Griinbaum correctly points out,84 those who reject the analysis of space and time as continua demand that length and duration possess a certain specified sort of additivity on broadly physical grounds, so that to simply point out that consistency requires that measures on neither dense nor continuous manifolds be countably additive only entrenches them in their denial that space and time are dense or continuous. What one must do to refute them is to challenge the grounds upon which they infer that space and time must be countably additive in the standard sense. Normally, the countable additivity of length means that the length of an interval which is the union of a finite or denumerable sequence of subintervals, no two of which share a common point, is equal to the arithmetic sum of the lengths of the members of that sequence. On this standard account, dense manifolds are not countably additive. Massey, however, proposes a non-standard sort of countable additivity that does characterize dense manifolds and does not lead to the Zenonian paradoxes. 8s According to Massey's non-standard account, we are to consider any interval which is the union of a finite or denumerable sequence of subintervals such that each member of the sequence has exactly one point in common with its predecessor, if any, and also with its successor, if any, and furthermore is disjoint from all the other members of the sequence. In other words, the subintervals are non-degenerate intervals lying end-to-end and having common respective endpoints. Then the length of the interval is the arithmetic sum of the lengths of the subintervals. The question, states Griinbaum, is whether there are broadly physical grounds which show that any denumerably dense manifold requires at least the standard countable additivity for length or whether Massey's non-standard countable additivity will suffice. Although Griinbaum at first thought that broadly physical grounds could be adduced for requiring standard countable additivity for merely dense manifolds, so that it is the non-denumerability of continua which provides physical grounds for releasing them from this requirement, he later recanted this opinion. 86 The denseness property of both denumerably and non-denumerably dense manifolds precludes our demanding anything beyond Massey's non-standard countable additivity. On Massey's account length measures on both denumerably and non-denumerably dense manifolds are additive and yet they are so in such a way that Zeno's paradoxes of plurality cannot arise. But (leaving aside the case of space) we have seen that there are broadly physical grounds not considered by Griinbaum for demanding that standard countable additivity hold for time, namely, the objectivity of A-theoretical becoming. Because the past is constituted by the lapse of one instant after another, temporal becoming is countably additive in the standard sense. It cannot be additive in Massey's nonK) Gerald Massey, "Toward a Clarification of GrOnbaum's Concept ofIntrinsic Metric," Philosophy of Science 36 (1969): 337. K4 GrOnbaum, Philosophical Problems ojSpace and Time, pp. 811-812. K5 Ibid., p. 477. 116 Ibid., pp. 815-819.

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standard sense simply because in order to be so the two instants constituting the endpoints of the subintervals would have to be simultaneously present, which contradicts the hypothesis. In fact, Massey's countable additivity, when applied to temporal becoming, describes precisely the sort of becoming in terms of temporal quanta that atomists like James and Whitehead advocate. Of course, it hardly needs to be said that the reason that Griinbaum does not consider temporal becoming as grounds for affirming the standard countable additivity of length or, rather, duration is because he does not believe in objective temporal becoming. His characteristic tense less, B-theoretical ontology of time provides no grounds for analyzing the structure of time differently than the structure of a static spatial continuum. Once we recognize the physical objectivity of temporal becoming, however, space and time can no longer be simply assumed to be structurally isomorphous. If temporal becoming is objective and only the present exists, then the arithmetical additivity of becoming precludes the identification of the present with an instant of time. Thus, instantaneous presentism, insofar as it construes the present instant to be a degenerate temporal interval, seems to succumb both to Zeno's paradoxes of motion and to his paradoxes ofplurality.87 The Atomic Present But if"the present" does not refer to the present instant, what does it refer to? A number of thinkers have suggested that time does in fact exist in physically minimal units, or time atoms called "chronons." According to this perspective, the continuity of time is purely conceptual, not real. As G. J. Whitrow states, " ... although the hypothesis that time is truly continuous has definite mathematical advantages, it is 87 Broad himself was disquieted by another difficulty in the notion of the instantaneous present which again goes all the way back to Aristotle: the problem of the ceasing instant (Broad, "Reply to My Critics," p. 768. See also Aristotle Physics 4.IO.218a9-11, 16-21. For a historical survey, see Sorabji, Time, Creation and the Continuum, pp. 7-63). Broad noticed that if we say that each present temporal phase is literally instantaneous, then we must say that at one and the same instant a temporal phase supervenes and is superseded, which sounds palpably absurd. In other words, the present and/or its contents come to be and cease to be simultaneously, which is self-contradictory. This difficulty, which closely resembles the ancient sorites paradoxes concerning starting and stopping, does not, however, seem to present any new, insuperable problem for Broad's view. Sorabji explains, " ... we must distinguish between the present and the perfect tense: we can never say, using the present tense, that the present instant is ceasing to exist. But we can say of what we once called the present instant that it has ceased to exist. When? The ... answer would be: at any subsequent instant you like, however c1ose-a millionth of a second later, or a two millionth. There will be no first subsequent instant" (Sorabji, Time, Creation and the Continuum, p. 10). In contemporary cosmology, the relation of the initial cosmological singularity to moments of time is conceived along these lines; the singularity is not a moment of time, but bounds time, and there is no first instant of time and, hence, no instant at which the singularity ceases to exist. No matter how close one approaches it in the open interval (0, I], it will at every instant have ceased to exist. This example serves to bring out the fact that the problem of the ceasing instant is not endemical to the A-Theory; even B-theories of tenseiessly existing instants face the question of when an event which exists at some instant ceases to exist, and the answer will be the same. If there is a problem for Broad's view arising from the ceasing instant, it will be the same difficulty as raised above concerning the impossibility of instantaneous becoming, namely, that on his view instants must have immediate precursors and successors, which is impossible. Unless the difficulties appertaining to the becoming of a durationless interval can be resolved, the A-theorist ought, therefore, to reject the underlying equation between the present and the present instant.

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an idealization, and not an actual characteristic of physical time.,,88 According to temporal atomists, there is a limit to the division of any temporal duration into constituent intervals. Usually this limit is associated with certain minimal physical quantities. For example, the effective diameter of elementary particles such as the proton or electron is 10- 13 cm; when this length is divided by the limit velocity of light in vacuo, the temporal interval for light to cross such a distance is 10-23 to 10-24 sec. This interval would constitute a chronon. Alternatively, employing the gravitational constant, Planck's constant, and the velocity of light, one may obtain the so-called Planck length -VGli/c3= 10-33 cm. When this length is divided by the speed of light, the interval obtained, called the Planck time, is 10-43 sec. This, too, could represent a chronon of time. The fact that time is on this view granular rather than continuous does not imply that one may not mathematically divide chronons into smaller intervals; but such intervals are mere idealizations having no ontological counterpart. 89 Capek protests that this notion of time atoms of Whitrow, Natural Philosophy a/Time, p. 200. Whitrow explains, "Acceptance of the ideas of spatial and temporal atomicity in physics does not, of course, preclude us from applying mathematical concepts of space and time involving numerical continuity in our calculations, but the infinite divisibility associated with these concepts will then be purely mathematical and will not correspond to anything physical" (Ibid., p. 201). Penrose analogously distinguishes between a physical interpretation and a mathematical treatment of entities involving lengths of 10- 13 cm or less (Penrose, "Singularities," pp. 217-218). He explains that as a singularity is approached, ordinary physical objects, even elementary particles, cannot exist due to the mounting gravitational tidal forces. Without particles to probe the geometry, he says, it is hard to see how the description of a continuous background space-time could then be meaningfully sustained. Although this breakdown occurs already at radii of space-time curvature of 10- 13 cm, most physicists continue to employ classical notions of space-time geometry all the way until the Planck length. At this scale a new physics is required to proceed further. "Thus, the physical interpretation of the term 'spacetime singularity' is a region in which curvatures have become so enormously large that our normal physical theories break down.... But from the point of view of a precise mathematical treatment, such a treatment is rather negative and unmanageable. In the absence of a good physical theory of such high curvature regions, we must concentrate, instead, on those regions where the normal pseudo-Riemannian picture of spacetime still holds good. We need assume not that the accuracy of our mathematical model is perfect, but that it holds good to a high degree down to the kind of dimension (say 10- 13 cm or 10.33 ) that we are concerned with. For radii of a curvature smaller than that dimension our model would be meaningless as a picture of reality. If desired those portions of high curvature can be deleted from the model, leaving a pseudo-Riemannian manifold which is mathematically extendible to a somewhat larger one (namely, to the one obtained by reinstating the deleted portions). However, normally it is mathematically more convenient to include the highly curved portions and to work instead with a maximally extended manifold. In any case, the singularities themselves are not to be part of the pseudo-Riemannian manifold (which is viewed as consisting of mathematically 'nonsingular' points only). Instead these singularities constitute a kind of boundary (or portion of a boundary) for the spacetime manifold .... The boundary can be constructed according to any of several precise (though unfortunately inequivalent) mathematical prescriptions" (Ibid., p. 218). After furnishing a procedure for defining a point p in a space-time manifold M, Penrose comments, "The advantage of representing p in this way is that a slight generalization of these sets enables us to represent not just ordinary points p of M but certain extra 'ideal points' which may be thought of as constituting a kind of boundary to M" (Ibid., p. 220). That these boundary points are mathematical idealizations is evident not only from the fact that some are singular and therefore "do not make consistent physical sense" (Ibid., p. 230), but also by the fact that some are non-singular points existing at infinity "supplying 88 89

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determinate length is incoherent, for "What does the alleged existence of chronons mean if not the assertion that two successive instants are separated by an interval of the order of 10-24 second?,,90 "The concept of chronon seems to imply its own boundaries; and as these boundaries are instantaneous in nature, the concept of instant is surreptitiously introduced by the very theory which purports to eliminate it.,,91 It is not clear to me, however, that the atomist's admission of instants as boundaries to chronon-Iength intervals is itself incoherent, so long as he does not consider instants to be constituents of time or intervals which can be present. As mere boundaries of the basic constituents of time, they do not represent the admission that there are parts of time which are instantaneously present. But the possession of even ideal boundaries seems to occasion a more difficult problem for atomists, as we may see from an illustration by Sorabji. 92 We can conceptually compare a chronon interval bounded by the instants (a, b) with a similar interval (c, d), such that a is located between c and d. Such an overlap of chronons cannot actually obtain, since chronon intervals represent physically minimal temporal distances and since separate temporal intervals cannot be directly compared to each other. But we can imagine two clocks which each register the lapse of chronons, but are "out of synch," such that" ... the rests of one, far from being atomic, are punctuated by the transitions of another,,,93 so that instant a is physically located between c and d. Thus, there would be an interval (a, d) measured by the two clocks which is less than a chronon. Sorabji's intuitively appealing picture may not, however, be physically possible. For how could two chronon clocks ever get "out of synch"? Since chronons are minimal temporal distances, it would be physically impossible to construct two accurate clocks such that one starts recording chronons mid-way through the unit interval recorded on the other clock, for there is no such point. And if the clocks were originally synchronized, it is impossible for one to skip or lose half a beat and then proceed to record accurate chronon intervals, for there is no such time interval as required by a half-beat. If they become no longer synchronized, it can only be because one clock is no longer accurately registering chronons. But to have two accurately running chronon clocks which fail to keep time in tandem seems a physical impossibility. In any case, chronons may not, when properly conceived, involve boundary instants at all. Capek points out that Heisenberg'S Uncertainty Principle also holds for the simultaneous determination of energy and time: I'!. E I'!. t ~ Ii. Thus, if we ideal future endpoints to future-endless timelike (or nUll) curves," which, interpreted realistically, is selfcontradictory (Ibid., p. 221). 90 Milic Capek, The Philosophical Impact 0/ Contemporary Physics (Princeton: D. Van Nostrand, 1961, p. 234; cf. idem, "The Fiction ofInstants," in The Study o/Time, ed. J. T. Fraser, F. C. Haber, and G. H. MOiler (Berlin: Springer Verlag, 1972), pp. 332-344. 91 Capek, Philosophical Impact o/Contemporary Physics, p. 231. Whitrow seems to miss the point of Capek's objection when he rejoins that if in nature time is a succession of minimal processes, then these cannot have beginnings and ends (Whitrow, Natural Philosophy o/Time, p. 204). For while it is correct that no processes can proceed from an initial to a final state during a chronon, still if the interval itselfhas a definite, positive length it would have beginning and end points. 92 Sorabji, Time, Creation and the Continuum, pp. 367, 382-383. Sorabji himself is arguing that one cannot infer atomicity of time from atomicity of space and uses the two clock illustration to show that space might be atomic without time's being atomic. 93 Ibid., p. 383.

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were to make an instantaneous cut in the temporal flow, the energy at that instant would be completely undetermined. Capek takes this to prove that it takes a certain finite amount of time for the universe to take on a precise form, that is, there are plausibly minimal time intervals in which the universe comes to be. But a further implication of this indeterminacy would seem to be that the boundaries of a chronon cannot be firmly fixed; there will be a degree of indeterminacy in its length. Thus, chronons should not be thought of like marbles sitting in a line, touching at common boundary points; rather their limits are indeterminate and successive chronons blur or shade into each other. On such a model temporal becoming does not occur in fixed, instantaneously bounded units. Grlinbaum, however, disputes that such an appeal to quantum theory can justify the chronon doctrine. 94 For every point of continuous physical space is a potential, sharply defined position and every instant potentially the time of a physical event. The Uncertainty Principle does not abrogate this sense of continuity. But the atomist will not be troubled by this riposte, I think, since he can deny that there is a continuum of even potential points and instants. And even if he admits such a mathematical structure of space and time, he could still maintain that time itself can only be present in intervals of chronons and that no pairs of ideal instants accurately mark the boundaries of a chronon, its having a duration which is not determinate below a certain bound. An A-theorist who is an atomist would maintain that only the present chronon exists and that temporal becoming consists in the successive actualization of chronons and/or their contents. Thus, the present is not a durationless instant (that being a mere idealization), and any present chronon has ceased to exist at the immediately succeeding chronon. One disturbing feature of such a model of temporal becoming, however, is that temporal becoming seems to be "jerky" rather than smooth. 95 Reality unfolds like the successive frames of a movie film projected on a screen: too quickly for the discontinuities to be noticed, but in "leaps" nevertheless. This analogy can be misleading, however. It gives the impression that one misses out on something happening in between the frames. But with atomic time, this is not the case. The juxtaposed chronons cannot be separated by the length of a chronon or there would be a chronon between them; but they cannot be separated by a length less than a chronon since there literally is no such length. The chronons either blur together where they touch or else share a common ideal instant as a boundary. So nothing can happen in between chronons. Moreover, the chronons are so tiny that no physical processes can occur during them. To imagine a light beam in transit halfGrunbaum, Modern Science and Zeno 's Paradoxes, p. 246. Blake fails to appreciate this fact when, in response to James and Whitehead's atomic views of time, he complained that a whole, every part of which is simultaneous, cannot be properly characterized as a duration or involve a definite lapse of time (Blake, "Temporal Process," p. 649). If we take "duration" and "lapse" purely extensively, however, then it is easy to see how a chronon which occurs as a whole can have a finite temporal extension. But if we take these terms transitively, then it is no part of the atomist's doctrine that chronons themselves each endure through time; rather they are the units of duration, which is, on that account, discontinuous. The real problem for Whitehead, it seems to me, is that the temporal parts of a chronon must, as parts, be earlier/later than one another, which contradicts the idea that they all exist simultaneously when a chronon is present or actual. The temporal atomist should deny that chronons have parts, even if chronons are conceptually divisible. Everything that happens at a chronon happens simultaneously, which implies that change occurs in leaps.

94

95

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way across the Planck length is an idealization which has literally no counterpart in reality. It is not as though we miss out on some aspect of reality by construing time as composed of chronons, therefore, since it is impossible for anything to happen in less time than a chronon. Still it remains the case that change is discontinuous, and this does seem unsettling. Defenders of discrete views of time thus have to accept the bizarre implications of the modem versions of Zeno's Stadium paradox. We are invited to envisage two rows of atoms moving in opposite directions relative to a row of atoms at rest at a rate of one atom per chronon of time (Fig. 7.1).

+-A

S

B

2 2 2

3 3 3

A

•

2

S

3 2

B

3 2

3

Figure 7.1. Zeno's Stadium paradox.

At consecutive chronons, we find AI and BI aligned and then A3 and BI aligned, which seems absurd since A2 and BI were never aligned, and yet to pass from its alignment with AI to its alignment with A3, BI must have at some time been aligned with A2. If we say that such an alignment did occur, then it took place during the interval of less than a chronon, which is ex hypothesi impossible. Therefore, we must say that in reality a discontinuous jump occurred from the alignment of AI and B\ to the alignment of A3 and B\. Such an implication may be difficult enough to swallow, but Griinbaum argues that the paradox is even deeper.96 He invites us to imagine that rows A and S are in motion with respect to B (Fig. 7.2).

+-A

2 2

3 3--.

A

S

B

2

3

B

2

3

S 2

2 3

3

Figure 7.2. Griinbaum's Stadium paradox.

In this case, it is the alignment of A2 and S\ which is skipped. Griinbaum now invites us to compare the "event-status" of the alignment of A2 and BI and of the alignment of A2 and S\ in Figures 7.1 and 7.2. Whether these alignments have the status of actual events depends on whether a chronon exists at which the respective points are aligned. The alignment of A2 and B\ is not a real event in the situation pictured in Fig. 7.1, but it is a real event in the situation of Fig. 7.2. Conversely, in Fig. 7.2 the alignment of A2 and S I is not an event, but it is in Fig. 7.1. Thus, whether an alignment qualifies as an event or not depends on the relative velocity of the two columns; but present day kinematic knowledge gives no hint of the possibility of the dependence of event status on relative motion. Presumably Griinbaum's deeper paradox rests on the absence of absolute motion, so that whether 96

Griinbaum, Modern Science and Zeno 's Paradoxes, pp. 247-249.

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A and B are both moving or one of them is at rest depends on one's frame of reference, with the result that what are taken to be events in one frame of reference (where one column is at rest) are not events in another frame of reference (where both columns are moving). If the atomist adopts a Neo-Lorentzian physical interpretation of the Special Theory of Relativity, however, then there is absolute motion in the sense that there is a preferential frame with respect to which things move. 97 In that case, whether something is an event will depend on whether it is an event with respect to this fundamental frame. We can, for example, replace Zeno's stadium with the fundamental frame of space and let A and B move with respect to it. If A and B are both in motion relative to the preferred frame, then the alignment of A2 and B 1 never occurs as a real event; on the other hand, if either A or B is at rest in the fundamental frame, then each consecutive alignment has the ontological status of an event. Event status thus depends on absolute, not relative motion. Of course, on the local level the observers associated with A and B may be ignorant of their velocity relative to the preferred frame and so think that some alignment which is an event is not an event or vice versa (recall that chronons are so brief that the alignments are not observable). So Grilnbaum's deeper paradox would not arise. Still, we are left with the original paradox, which is the peculiar result of an atomistic analysis of temporal becoming. But given the weirdness of the quantum realm,98 such disquietude as this may occasion may not seem to be a very powerful incentive to reject the ontology of chronons. Perhaps the more serious objection to this analysis is that it is based on a defunct positivistic analysis of time. Why should it be thought relevant to the ontological structure of time that a light beam crosses the Planck length in 10-43 sec? Even on a purely physical level, tachyons (particles which travel at superluminal velocities) are nomologically possible, and a tachyonic beam could cross the Planck length in less than 10-43 sec. So why are such intervals not real intervals of time? At the very most, the appeal to minimal physical distances and minimal processes only provides limits to our measurements of time, not to time itself. Even if physical time is structured in chronons, there is no reason to think that time itself is as well, for it is not evident that God could not, say, count at a rate of one number per unit time of 10- 100 sec. Since our inquiry into the "myth of passage" concerns time itself, not our physical measures thereof, the structure of physical time is irrelevant (however interesting). We should need some metaphysical argument in order justifiably to conclude that time itself is atomic in nature. Now it could be that the problem of the durationless present does provide adequate metaphysical grounds for thinking that time is in fact ontologically discrete rather than continuous. But if some less counter-intuitive solution to the problem is available, then, in view of the peculiarity of discontinuous temporal becoming, that solution ought to be preferred. 97 For a defense of such an interpretation see Simon 1. Prokhovnik, Light in Einstein's Universe (Dordrecht: D. Reidel, 1985); see further Tim Maudlin, Quantum Non-Locality and Relativity, Aristotelian Society Series 13 (Oxford: Blackwell, 1994), chaps. 7, 8. 98 As one commentator has recently remarked, "every known ontology that is compatible with the phenomena, as codified by quantum theory, is 'grotesque' in some way" (Henry P. Stapp, "Transcending Newton's Legacy," in Some Truer Method, ed. Frank Durham and Robert D. Parrington [New York: Columbia University Press, 1990], p. 233).

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The Non-Metrical Present And, in fact, such a solution is forthcoming and has already been adumbrated in chapter 6. We can maintain that the extent of the present depends upon the extent of the entity described as present. To quote again Andros Loizou: " ... no event or state of affairs is ever present simpliciter-it is present by implicit or explicit reference to a kind of events or states of affairs, as when we speak of the present eclipse, or by reference to a time scale, as when we speak of the present hour or day, and so on.,,99 According to this view, to ask, "What is the duration of the present?" is a malformed question, analogous to the query, "What is the extent of here?" In order to answer this latter question, it must be specified what it is that is here: are we talking about the point of an atomic collision, the office in which I sit, or our solar system's place in the galaxy? The spatial extension designated by "here" depends upon the context in which the term is used. Similarly, the temporal extension designated by "present" covers a similar range: we speak of the present vibration of an atomic clock or the present war or the present stage in the evolution of the sun. There is no such thing as "the present" simpliciter: it is always "the present ___," where the blank is usually filled by a reference to some thing or event. The duration of the present will be as long or as short as the event or thing under discussion. But what if we wish to speak of time itself, rather than of events and things? How long is the present time? This question, however, remains ambiguous and becomes trivial when it is made precise. Consider the spatial analogy: how big is the space which is here? The question is too ambiguous to allow an answer; but if we specify, "How big is the cubic meter which is here?" the answer is the correct but trivial reply, "A cubic meter." Similarly, if we make our question about the present more precise by asking, "How long is the present second?", the reply can only be "A second." It is thus wrong-headed to ask how long the present is, for, as Christensen points out, there is no such metrical particular as simply "the present." I 00 The view proposed here is essentially Bergson's doctrine of duree reel/e. In Bergson's view real duration is not composed of instants or time atoms but is onto logically prior to our mathematization of it. All metrical concepts of time are secondary constructions. He wrote, "As soon as we make a line correspond to a duration, to portions of this line there must correspond 'portions of duration' and to an extremity of the line, an 'extremity of duration'; such is the instant-something that does not exist actually, but virtually." 101 Prior seems to have held a similar view. In Prior's thinking the notion of being present is equivalent to simply existing. He wrote, "the present simply is the real Andros Loizou, The Reality of Time (Brookfield, Ver.: Gower, 1986), p. 156; see also D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), pp. 17-18; Padgett, God, Eternity, and the Nature of Time, p. 115). 100 F. M. Christensen, Space-like Time (Toronto: University of Toronto Press, 1993), p. 123. 101 Henri Bergson, Duration and Simultaneity, trans. Leon Jacobsen, with an Introduction by Herbert Dingle, Library of Liberal Arts (Indianapolis: Bobbs-Merrill, 1965), p. 53. Bergson's misguided attack upon relativity theory has led to an unfortunate neglect of his otherwise interesting thoughts on the nature of time. For a good discussion see Philip Turetzky, Time, Problems of Philosophy (London: Routledge, 1998), chap. 13. 99

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considered in relation to two particular species of unreality, namely the past and the future.,,102 As such, the concept of the present is a primitive, pre-metrical notion. According to Prior, instants are "artificial entities," and "all talk which appears to be about them and the 'time series' which they are supposed to constitute, is just disguised talk about what is and has been and will be the case.,,103 Prior saw in his tense logic the superiority of his philosophy of time over Bergson's; but like Bergson, Prior also held to the primitiveness of real duration. He simply believed himself able to construct a tenseless system of dates out of more primitive talk about what is and has been and will be the case. He declared, ... the basic reality is things acting. But even in this flux there is a pattern, and this pattern I try to trace with my tense logic, and it is because this pattern exists that men have been able to construct their seemingly timeless frame of dates. Dates, like classes, are a wonderfully and tremendously useful invention, but they are an invention; the reality is things acting.... I think it is important that people who care for rigorism and formalism should not leave the basic flux and flow of things in the hands of existentialists and Bergsonians and others who love darkness rather than light, but we should enter this realm of life and time, not to destroy it, but to master it with our techniques. 10.

I have argued previously that Prior's equation of presentness and existence should be qualified so as not to rule out a priori the possibility of timeless existence. Rather presentness should be construed as a mode of existence, a temporal as opposed to a timeless mode of being. But Prior's essential insight is one which the presentist does well to appropriate: as a mode of being, presentness does not involve metrical ideas. The question of the extent of the present arises only when we apply metrical concepts to existence. Such a view does not entail metric conventionalism with respect to time but only that there is no privileged unit in which temporal becoming occurs. Once one has determined to refer to units of, say, seconds, then there need be nothing conventional about the length of one event as measured in seconds compared to the length of another event similarly measured. We can still say truly that the duration of the Kentucky Derby was objectively shorter than the Boston Marathon. But suppose some temporal atomist were to press the question, "What is the minimum spatial length or temporal duration?" It seems to me that one could coherently reply that once one has decided to apply quantitative concepts to time there need be no such minimum length or temporal duration because both space and time are potentially infinitely divisible. 105 The duration stipulated to be present will 102 A. N. Prior, "The Notion of the Present," Studium Generale 23 (1970): 245. Cf. Christensen, Spacelike Time, pp. 168; 226. 103 A. N. Prior, Papers on Time and Tense (Oxford: Oxford University Press, 1968), p. 123. 104 A. N. Prior, unpublished manuscript, courtesy of Peter 0hrstrom and Per Hasle. 105 As Griinbaum points out, infinite divisibility does not by itself give rise to Zeno's paradoxes, for these result only if we postulate an actual infinity of points ab initio. " ... any attribution of (infinite) 'divisibility' to a Cantorian line must be based on the fact that ab initio that line and the intervals are already 'divided' into an actual dense infinity of point-elements of which the line (interval) is the aggregate. Accordingly, the Cantorian line can be said to be already actually infinitely divided" (Griinbaum, Philosophical Problems o/Space and Time, p. 169). By contrast if we think of the line as a whole as logically prior to any points designated on it, then it is not an ordered aggregate of points nor actually infinitely divided. On the view I am suggesting, a line is not even an infinity of potential points, but the points designated on it are potentially infinite in number. Pari passu an interval of time as a

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be an arbitrary, finite duration centered on a conceptually specified instant. Any temporal interval which is contextually taken to be the present interval is susceptible of being conceptually divided into shorter temporal phases which will be past, present, and future respectively. For example, in certain contexts it is appropriate to refer to the present minute; but if we wish to narrow our consideration of what is going on now, we are at liberty to divide the minute into seconds and to focus on the present second. The present minute can thus be analyzed into a past phase composed of seconds earlier than the present second, a present phase which is the present second, and a future phase composed of the later seconds remaining in the minute. This process of narrowing can be continued indefinitely, with the present instant as a conceptual limit, so that there is no minimal temporal interval which is now. \06 This feature of the present deeply troubled Augustine, who in his Confessions argues that if the present interval is potentially infinitely divisible, then no interval, no matter how small, can be truly said to be present, since it has past and future parts; but if the present is actually infinitely divisible into instantaneous parts, then time vanishes, since the past and future are unreal and the present a durationless moment. \07 The nerve of Augustine'S argument against some interval of positive duration's being present is the assumption that in order to be present, the interval in question must be incapable of analysis into past, present, and future phases. But if what we have said so far is correct, this assumption is not incumbent upon the Atheorist. He may instead hold that an interval is present if any phase of it is present. Loizou states, Now Augustine's mistake consists in thinking that a certain principle of containment, of relation between part and whole, which has application in the cases of the past and the future, also has application in the case of the present: just as, if X is past or future, all its parts are respectively past or future, so if X is present, all its parts are present.... What is wrong with Augustine'S argument is the principle 'if X is present, then all the parts of X must be present.' ... it is legitimate to speak of extended present events as events which are present despite (or even by virtue of) the fact that they have past and future phases or parts .... the fact that X is happening does not entail that P, Q and R (the phases of X) are happening-rather it entails that P has happened, Q is happening, and R is yet to happen. And the same procedure applies, recursively. to the present phase Q of X. ... The procedure can be carried on indefinitely; but at no point in the procedure do we arrive at an instant. "'s whole duration is logically prior to the (potentially infinite) divisions we may make of it. Cf. Peirce's proposal that we replace points by series. Then every part of a line is still a series and divisible into further series. "Let any mode of measure be carried to its limit of precision. Still each number will designate not an indivisible part; but a series of series, ad infinitum" (Peirce, "Continuous Series," p. 126). 106 The non-instantaneous character of present intervals has led to some very interesting developments in durational logic, stemming from the work of the medieval thinker Jean Buridan. See Peter 0hrstmm and Per F. V. Hasle, Temporal Logic, Studies in Linguistics and Philosophy 57 (Dordrecht: Kluwer Academic Publishers, 1995), pp. 43-51; C. L. Hamblin, "Instants and Intervals," in The Study of Time, ed. 1. T. Fraser, F. C. Haber, and G. H. Moller (Berlin: Springer Verlag, 1972), pp. 324-331. 107 Augustine Corifessions 11.15.19-20. lOS Andros Loizou, Reality of Time, pp. 44-45. Loizou's view is that an interval may be present even though it is not wholly present (i.e., not all its parts are present). I prefer to say that an interval may be present simpliciter even though we can divide it into sub-intervals which are not every one present. Thus, the present minute is qua minute present Simpliciter, but if we divide it into seconds, then only one

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On Loizou's account, only temporal intervals can be present; an instant is merely an ideal limit toward which the process of division converges. Instants may also be conceived as the boundaries of intervals, but they are not properly parts of time in that only intervals are ever present; there is no such entity as "the present instant." A non-metrical understanding of the present enables us to avert the problem of the extent of the present. We avoid Zeno' s Paradoxes of both motion and quantity: of quantity because neither time nor the present is constituted by durationless instants, though instants can be conceptually specified within any interval of time, and of motion because temporal becoming does not proceed instant by instant, nor by indivisible quanta, though instants and quanta can be specified within any interval that does come to be. TEMPORAL BECOMING AND THE DIRECTION OF TIME Not only does the doctrine of temporal becoming survive its pretended defeaters, but it also brings positive advantages. One advantage to be gained from the adoption of a presentist metaphysic of A-theoretic becoming is that such a viewpoint, in contrast to the B-Theory, provides a perspicuous basis for the asymmetry of time. In contrast to actual space, time certainly appears to be asymmetrical-indeed, the A-theorist would probably hold that time, in contrast to space, is essentially asymmetrical. 109 The asymmetry of time consists at least in two distinct, but still frequently confused, features of time: (i) the direction of time and (ii) the anisotropy of time. The direction of time has to do with its orientation, that is to say, with its ordinal structure. By way of illustration, rank in the armed services is an ordinally structured series of statuses from, say, private to general. The series has an orientation from lower to higher rank; one is not first a five-star general, then a major, then a captain, then a private. The sequence of ranks is thus oriented or has a direction. In the same way, the series of temporal events or moments has a direction, namely, from past to future. One may arbitrarily select some moment and designate it as first, and then there will be a second moment later than it, then a third later still, and so forth. Time is thus oriented toward the future, a feature which is often called "the arrow of time." A second asymmetry of time is its anisotropy, that is to say, its being ordered by the earlier thanllater than relations. Series which are anisotropic do not necessarily possess an orientation; for example, the temperature gradient is ordered by the relations colder than/hotter than but has no orientation. Temperature readings may move in either direction along the gradient. In the same way, some philosophers hold that while time is anisotropic, it has no unique direction or arrow. If a series has a direction, then it follows necessarily that it is anisotropic as well, though anisotropy is not a guarantee of directionality.

second is qua second present simpliciter. If any sub-interval of an interval is present, then the whole interval is as such present. 109 Aristotelian space was not symmetrical, so that the symmetry of space is a contingent matter. But the A-theorist, especially if he distinguishes between metaphysical and physical time, will not be apt to admit that time could be symmetrical.

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The A-theorist fmds in the objectivity of temporal becoming a philosophical justification for the doctrine of the direction of time and thereby for the anisotropy of time. The B-Theory, by contrast, seems so deficient in resources for the justification of these notions that many B-theorists are forced either to regard the directionality and anisotropy of time as surd givens or to deny their existence altogether. For the A-theorist, the direction of time is rooted in the impossibility of a backward "flow" of time. This can be seen by consideration of the impossibility of backward continuing. 110 Temporal continuing is not simply the tenseless temporal extension of some continuant. The successive moments of the continuant's duration do not all tenselessly exist; they come into being and pass away serially. Thus, if some thing exists at the present moment, then in order for it to continue to exist through a multiplicity of moments, there must come to exist another moment in addition to the present moment. But such an additional moment can only be after the present moment. It seems completely unintelligible to say that the additional moment is before the present moment. In that case we should say that the thing continued to exist from the prior moment to the present moment. But on an Atheoretic ontology of presentism, it makes no sense at all to say that it continued to exist from the present moment to the past moment. Continuing is only intelligible if it proceeds forward in time, from a given moment to a subsequent moment. To be sure, we can easily imagine the series of events' occurring in reverse order, like a film's being run backwards; but the reversed-order events still occur one after the other. What is impossible to conceive is that the moments of time themselves should elapse in reverse order. To elapse is necessarily to occur one after the other. Thus, the ontology of the A-Theory requires that time have a direction. Grlinbaum complains that" ... it is a mere tautology to say that the Now shifts from earlier to later.... By the same token, the assertion that the 'flow' of time is unidirectional is a tautology, as is the claim that time 'flows' from the past to the future.,,11I But while the statement that "The 'flow' of time is from the past to the future" does seem to be metaphysically necessary, I cannot see any reason to think that on the A-Theory it is tautologous. Perhaps it is tautologous on Griinbaum's construal of "nowness" and time's "flow" as mind-dependent. On his view the anisotropy of time is due to the development and increasing entropy of thermodynamic branch systems in the universe. Since our bodies, and particularly our brains, are entropic, the direction of psychological time always coincides with the direction of physical time. Since "nowness" is purely psychological in nature, having to do with the contents of awareness, the "movement" of the "now" must coincide with the direction of entropy increase. As entropy increases, so does the store of memories, and time is experienced as "flowing" forward. Moreover, as 1.1. C. Smart has pointed out, even in the case of a thermodynamically reversed universe of declining entropy, " ... the 'backwards' world will tum out to be indistinguishable from our ordinary 'forwards' universe" because precognition would replace memory and the illusion of the advance of time would be from the later tz to t I." liZ Since the 110 111 112

See Sarah Waterlow, "Backwards Causation and Continuing," Mind 83 (1974): 372-387. Grunbaum, Philosophical Problems of Space and Time, pp. 315-316. Smart, "Temporal Asymmetry," pp. 82-83.

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"flow" of time is not an objective feature of the physical world, but is a psychological phenomenon defmed in terms of the mind-dependence of "nowness," and since the direction of psychological time is that of entropy increase, it follows that even if entropy were declining the "flow" of time would still be forwards, from the psychological past to the psychological future. Indeed, it seems that the hypothesis of a universe of declining entropy over time is a self-contradiction on GIiinbaum's view, since the future is by definition the direction of greater entropy. Thus, on GIiinbaum's view, it does seem analytically true that time "flows" from earlier to later. But it does not follow that that proposition is merely analytically true on an A-theoretic understanding of the terms. Given an A-theoretic ontology of time, objective temporal becoming does provide an explanatory basis for the direction and anisotropy of time. By contrast, B-theoretical attempts to spell out the direction and/or anisotropy of time in terms of physical processes, whether nomologically necessary or merely de facto, have proved unconvincing. B-theorist Steven Savitt, complaining that no advance has been made on this question over the last two decades, expresses the difficulty: "The idea here is that if, modulo as usual the decay of the neutral K meson, basic physical laws are time reversal invariant and if there is no flow of time, then from the atemporal view there is no objective distinction between past and future directions of time".113 At issue here are the much-discussed questions of whether the laws of nature are all time-reversal invariant (that is to say, whether it is nomologically possible for a system to evolve from state S to S' in time Dt and another system from S' to SinDt) and what de facto time-asymmetrical processes in the universe exist. The challenge is to fmd some physical basis for distinguishing past from future. The implicit physical reductionism of this whole endeavor is noteworthy. Since tense is a matter of metaphysics, not physics, A-theorists tend to reject reductionist views of time. From the standpoint of a classical A-theorist like Isaac Newton, the failure of reductionistic attempts to explain time's asymmetry is patent, since the physical processes are at best mere sensible measures of time, not constitutive of time itself. As Newton observed, Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time .... 114

In Newton's thinking time itself is grounded in the being of God, who endures sempiternally wholly independently of the physical universe, and thus physical processes can at best constitute mere sensible measures of time itself. In the General Scholium to the Principia, which he added in 17l3, he maintained that absolute time and space are constituted by the divine attributes of eternity and omnipresence: 113 Steven Savitt, "The Direction of Time," British Journal/or the Philosophy o/Science 47 (1996): 364 (first emphasis mine). 114 Isaac Newton, Sir Isaac Newton's 'Mathematical Principles 0/ Natural Philosophy' and his 'System 0/ the World,' trans. Andrew Motte, rev. with an Appendix by Florian Cajori, 2 vols. (Los Angeles: University of California Press, 1966), vol. 1, p. 6.

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He is eternal and infinite ... ; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity.... He is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present; and, by existing always and everywhere, he constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere. 115

Newton could easily have imagined a possible world in which God creates a universe lacking any of the typically proposed thermodynamic, cosmological, and other "arrows" of time and yet, due to a succession of contents of consciousness on His part, experiences the sequential development of the universe according to the lapse of His metaphysical time. Given the coherence of Newton's temporal theism, it is possible for time to be asymmetrical even in the absence of any asymmetric physical processes. Thus, B-theorist Craig Callender is simply mistaken when he states that the "the problem of the direction of time ... is essentially that the classical equations of motion are time-reversal invariant" .116 That is a quite separate issue, and there is no guarantee that an explanation of the existence of asymmetric physical processes in the world will also be a solution to the question of time's asymmetry. But wholly apart from Newton's theism, physically reductionistic accounts of temporal directionality and/or anisotropy have little to commend themselves.117 For the suggested physical arrows of the universe are neither necessary nor sufficient for time's having a direction and/or anisotropy. In the first place, such physical asymmetries do not seem necessary for temporal asymmetry. Assume, for example, that all natural laws are time-reversal invariant. Does that imply that the distinction between earlier and later is vacuous, that, say, Lincoln's birth did not occur before his death? Are we not more certain of this latter fact than we are of the doctrine that temporal asymmetry is to be defined in terms of lawlike time-reversal invariance? Sklar invites us to suppose, analogously, that all interactions were invariant under the spatial reflection transformation. Would this mean that we could not tell if a glove were right- or left-handed? That seems absurd. "And it would be equally absurd to believe that just because the laws of nature are time-reversal invariant ... we could not have pairs of events related by one being later in time than the other. ... ,,118 Black points out that if we deny the anisotropy of time, then (i) we cannot say that the Battle of Hastings happened Ibid., p. 545. Craig Callender, "What is 'The Problem of the Direction of Time'?" Philosophy of Science 64 (1997): S 223-234. 117 See Arthur Eddington, The Nature of the PhYSical World, introd. by Sir Edmund Whittaker, Everyman's Library (London: J. M. Dent & Sons, 1928, rep. ed. 1964), pp. 75-IIO; Max Black, "The Direction of Time," AnalysiS 19 (1958-59): 54-63; Bernard Mayo, "The Open Future," Mind 71 (1962): 1-14; John Earman, "An Attempt to Add a Little Direction to 'The Problem of the Direction of Time'," Philosophy of Science 41(1974): 15-47; Lawrence Sklar, Space, Time, and Spacetime (Berkeley: University of California Press, 1976), pp. 352-4II; Kenneth Denbigh, Three Concepts of Time (Berlin: Springer Verlag, 1981), pp. 15-47; Paul Horwich, Asymmetries in Time (Cambridge, Mass.: MIT Press, 1987), pp. 37-71; Steven Savitt, Time's Arrow Today (Cambridge: Cambridge University Press, 1996); Huw Price, Time's Arrow and Archimedes' Point (New York: Oxford University Press, 1997). 118 Sklar, Space, Time, and Spacetime, p. 399. Cf. idem, "Up and Down, Left and Right, Past and Future," in The Philosophy of Time, ed. R. Le Poidevin and M. MacBeath, Oxford Readings in Philosophy (Oxford: Oxford University Press, 1993), p. 101. liS

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before the Battle of Waterloo; (ii) we must say that if A, B, C are causally-linked events, then for some observer A is the final member of the series, not the first; and (iii) we have to admit that there could be regions of the universe in which time is "running in reverse.,,119 But such hypotheses seem absurd. Black rightly concluded, "It therefore seems to me just as certain as anything can be that time does have a 'direction,' if that expression is taken to mean that time is not 'isotropic' .... ,,120 Even if we convinced ourselves that the temporal becoming of events is illusory, how could we doubt that events, especially mental events in our own consciousness, occur earlier or later than one another? We do not have a comparable certainty of the reductionist thesis that time asymmetry depends on physical asymmetries. As Sklar says, there is surely something implausible about a philosophical analysis which makes the existence of such an obvious feature of the world as temporal asymmetry hinge upon the existence of physical features that may well not exist. 121 De facto reductionists like Grtinbaum would agree that lawlike physical asymmetry is not a necessary condition for temporal anisotropy; but de facto asymmetries are. But even this claim is dubious. If it were physiologically possible for us to exist in a state of total equilibrium, we should admittedly not have the sort of temporal awareness we now have. As Grtinbaum says, "If we were unfortunate enough to be surviving while immersed in one vast cosmic equilibrium, it would then be unutterably dull to the point of loss of our psychological time sense.,,122 More than that, however; in such a case, on Grtinbaum's analysis, we should have to say that time itself is isotropic, that fluctuations from that state are not even ordered by relations of earlier thanllater than. But that seems counter-intuitive: surely there are fluctuations in the state of equilibrium which are temporally prior to other fluctuations. If we existed in such an equilibrium state, we should not be able to detect the anisotropy of time, so long as our consciousness remained linked to our brains; but there is no reason to accept the verificationist inference that temporal asymmetry would not therefore exist. 123 On the other hand, neither do such physical asymmetries seem sufficient for temporal asymmetry. Sklar invites us to envision a universe with time-reversal noninvariant laws. 124 The obtaining of such laws need not imply any asymmetry in time, for the universe could be static (one thinks, for example, of the empty de Sitter universe). In such a case, time is anisotropic, since the noninvariant laws obtain, even though nothing ever happens! It is difficult to see how the presence of such laws serves to generate time asymmetry even though no asymmetrical physical processes ever occur. Suppose, then, that they do occur. How is the situation Black, "Direction of Time," p. 62. Ibid., p. 63. 121 Sklar, Space, Time, and Spacetime, p. 399. In his "Time in Experience and in Theoretical Description of the World," in Time's Arrow Today, p. 218, Sklar observes that basing the asymmetry of time on thermodynamics, though self-evident to many philosophers of science, seems "manifestly absurd" and "so ludicrous as to be dismissed without argument" by many perceptive philosophers. 122 Grilnbaum, Philosophical Problems ojSpace and Time, p. 290. 123 Also relevant at this point are the anti-relationalist arguments of Sydney Shoemaker, "Time without Change," Journal of Philosophy 66 (1969): 363-381; cf. W.-H. Newton-Smith, The Structure oj Time, International Library of Philosophy (London: Routledge, Kegan & Paul, 1980), chaps. 4, 10. 124 Sklar, Space, Time, and Spacetime, p. 401. 119

120

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253

fundamentally different from a universe in which time-reversal invariant laws do obtain, but in fact the time-reversed processes never occur? It is difficult to see why time should be anisotropic in the one case but not in the other. It might be said that when asymmetrical physical processes occur, temporal anisotropy is generated. But here we may see the arbitrariness of the whole reductionist approach to these questions. For why should we regard one direction of the process as earlier and the other direction as later rather than vice versa? If this is not to be pure convention, there must be some non-physical feature which serves to demarcate earlier from later directions. Sklar writes, If we define 'e2 is later than e,' in terms of 'e2 is R to e,' where R is the 'other' asymmetric defining relation, couldn't we equally well have defined the later-than relation by the converse asymmetric relation to R? But is this 'arbitrariness' of which events are taken to be later than other events really what we take the situation to be? We could, of course, trivially decide to interchange the words 'is earlier than' and 'is later than' in all contexts, but is it the case that what we mean when we say that one event is, for example, later than another, arbitrarily specifiable in terms of any other asymmetric relation the events have to one another as a matter of law? Isn't the situation rather that if we find out that there is some asymmetric relation law-like associated with a particular temporal relation, that on the basis of this empirical discovery we can from then on 'test' for the temporal relationship by looking for the other relation? But if this is correct, the lawlike association of the two relations is an empirical discovery, requiring an independent ascertainability of an independentlyexisting temporal relationship and not a definition of the temporal relationship at all. '25

Sklar's analysis may be extended to de facto physical asymmetries. 126 The statements that higher entropy states occur later or that entropy tends to increase presuppose a human judgement concerning which states occur earlier or later which is logically independent of the physical processes themselves. The fact that entropy states of a process range in value between higher and lower numbers tells us nothing about which values exist later. 127 Think again of Smart's thermodynamically reversed universe. It seems intuitively obvious that such a world is not a logical contradiction, that despite the illusion of the denizens of that world that entropy is increasing, in fact it is a world in which earlier states have higher entropy than later states. It would be philosophical tyranny to rule out such a world on definitional grounds. The possibility of such a world undermines the reductionist notion that necessarily higher entropy states are later states than low entropy states. Sklar concludes, " ... there is in the world an asymmetric relation holding among events, the temporal priority relation, and ... we can know when this relation holds or fails to hold, at least sometimes, without relying upon any features of the lawlike

Ibid., pp. 403-404. See discussion in Earman, "Direction of Time," pp. 29-45, who notes that nobody maintains that space is asymmetrical because ofthe defacto asymmetries between left- and right-handed objects. Why then is time supposed to be different from space in this respect? See also the somewhat confused discussion by Denbigh, Three Concepts, pp. 15-39; idem, An Inventive Universe (London: Hutchinson, 1975), pp. 40-52; also Mayo, "Open Future," pp. 3-4. '27 As Denbigh says, "What natural processes actually display is a mutual consistency or parallelism (e.g., of entropy change, statistically if not absolutely) but they do not in themselves display the qualities of being earlier than or later than. These qualities have to be read into the physical situation by the observer" (K. G. Denbigh, "In Defense of the Direction of Time," Studium Generale 23 [1970]: 238). 125

'26

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nature of the world in time.,,\28 How can we know whether a world obtains in which the lawlike evolution of a system during Dt proceeds from S to S' or from S' to S? "The naive answer, and I believe the correct one, is that we know which set of generalizations truly describes the world because we know independently of our knowledge of the lawlike behavior of physical processes in time, what the actual time order of events really is. Only this 'independent' knowledge of temporal order would allow us to decide which of the lawlike descriptions is, in fact, the true lawlike description of the world.,,\29 In the inner life of my mind I directly experience the succession of experiences one after the other, and this same later than relation seems to characterize events in the world. If external events are discovered to be also related by some entropically characterizable relation, such a discovery would at best show that there exists an empirically established correlation, but not identity, of that entropic relation with the temporal relation. For inner events "are really later and earlier than one another and our 'pretty simple, immediate experience' of this relation cannot with impunity be detached as merely a causally induced secondary quality not properly thought of as a direct experience of the real afterness relation which exists in the world only as an entropically characterizable relation.,,130 In this sense, says Sklar, there is no need for a "theory of the direction oftime"-"we may suppose that at least some relations of temporal priority are also among the directly inspectable features of events." 13 \ The attempt to ground the anisotropy and orientation of time in either lawlike or de facto physical asymmetries thus seems to be futile, the physical processes at issue being at best mere sensible measures of time, not constitutive of time, and neither necessary nor sufficient conditions for the anisotropy of time or time's arrow. We have seen that physical reductionists conflate the question of the direction of time with the question of why there are asymmetric physical processes in nature. The Atheorist answers the first question in terms of the objectivity of temporal becoming. That answer presupposed, the A-theorist is also in a position to say something informative about the second question as well. Consider, for example, the conundrum of why the entropy of thermodynamically closed systems tends to increase. On the statistical understanding of the Second Law, higher entropy states are more probable than lower entropy states, and thus any given state is more likely to evolve into a higher entropy state. But in the absence of any a priori direction of time, a state when considered from an atemporal perspective is just as likely to be preceded as succeeded by higher entropy states, since natural laws are time-reversal invariant (Fig. 7. 3).

Sklar, Space, Time, and Spacetime, p. 399. Ibid., p. 402. 130 Idem, "Up and Down," p. 116. cr. idem, Physics and Chance (Cambridge: Cambridge University Press, 1993), p. 410. 131 Idem, Space, Time, and Spacetime, pp. 410-411. 128

129

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THE MYTH OF TEMPORAL PASSAGE

entropy

time Figure 7.3. Given the temporal symmetry of natural laws and no direction of time, entropy is just as likely to be higher at t] than t2 as higher at t3 than t2 on a statistical understanding of the Second Law-which contradicts observation.

Since an entropy increase in one direction is an entropy decrease in the opposite direction, it follows that in the absence of an a priori direction of time entropy should remain roughly at a maximum. This was, in fact, the conclusion to which Boltzmann was driven: that the universe exists in an overall condition of equilibrium, and our present state is but a random fluctuation from the equilibrium state. Boltzmann's hypothesis, however, faces enormous difficulties, as Price has shown.132 He concludes that "a purely statistical explanation of the low-entropy condition of the present and past universe is unsatisfactory ... " and that a viable alternative must involve "an extra ingredient.,,]33 The A-theorist of time proposes that that extra ingredient is objective temporal becoming. Given the reality of temporal becoming, there is no possibility of backward continuing and therefore, even given time-reversal invariant laws, the "increase" in entropy illustrated in Fig. 7.3 from t2 to t\ is ruled out because it is really a decrease from t] to t2 and such decreases are statistically improbable. Laws may be time-reversal invariant, but if time itself never reverses, one need not worry about why entropy states at any moment tn were not preceded by higher entropy states. Given that 10 infallibly succeeds 10-], a statistical understanding of the Second Law predicts an increase at 10 in comparison with tn_1 and thus lower entropy at tn_1 than at tn. Granted, the objective reality of temporal becoming does not explain why the universe at any point in the past had the specific quantity of entropy that it did, but it does explain why entropy is lower in the earlier than direction. It is remarkable that so simple and perspicuous an explanation of physical arrows of time continues to be ignored by philosophers, who under the influence of physical reductionism agonize

Price, Time's Arrow, pp. 34-36. Ibid., p. 37; cf. Craig Callender, "The View from No-when," British journal/or the Philosophy Science 49 (1988): 135-\59. IJ2

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fruitlessly over the apparently inexplicable asymmetry of physical processes governed by time-reversal invariant laws. 134 The A-theorist can also point out that on the A-Theory of time not only is the direction of time grounded in the objectivity of temporal becoming, but anisotropic temporal relations can be explained in terms of the objectivity of A-determinations such as past, present, and future and the A-series of temporal moments characterized by such determinations. The point goes all the way back to McTaggart. 135 Although he considered both the A-series of moments characterized by past, present, and future and the B-series of moments ordered by the earlier than/later than relations to be essential to time, he regarded the latter as dependent upon the former, maintaining that the relation earlier than was definable in terms of the A-series: "The term P is earlier than the term Q, if it is ever past while Q is present, or present while Q is future.,,136 A number of A-theorists have argued this same point, and D. H. Mellor seems to concur: The A series could easily distinguish earlier and later. To be earlier is to be more past or less future, to be later is to be more future or less past. Specifically, e is earlier than e* if e is sometime present when e* is future and sometime past when e* is present, whereas e* is never present when e is future or past when e is present. Earlier and later are clearly definable by the order in which things, events and dates cease to be future and become first present and then past; and the difference between them is that everything moves from future to past, not vice versa. 137

Mellor's concern in this context is not with providing some justification for the Btheorist's belief that tenseless temporal particulars are ordered by the relations earlier than/later than-he just assumes that they are-, but rather with providing some justification for the anisotropy of time and in particular for time's having an orientation on the B-Theory. The point he wishes to make is that on the A-Theory, the two directions of time are distinguishable and one direction is preferred; but in fact he makes here a much more fundamental point, namely, that the very temporal relations which lie at the heart of the B-Theory of time are derivable from the Aseries. Mellor actually appears to present three different ways of defining "earlier than/later than" in terms of the A-Theory: Dl: D2:

to be earlier than to be later than e is earlier than e*

def.

e is later than e*

def

def. def.

to be more past or less future than to be more future or less past than when e is present e* is future, and when e* is present e is past; and when e is present e* is not past and when e is future e* is not present when e* is present e is future, and when e is present e*is past; and when e* is present e is not

134 But see the excellent comments on "The Second Law and the Difference between Past and Future," by Carl Friedrich von Weizsllcker, The Unity of Nature, trans. Francis 1. Zucker (New York: Farrar, Strauss, & Giroux, 1980), esp. pp. 138, 141, 145. m McTaggart, Nature of Existence, 2: 30. 136 Ibid., 2: 271. 137 Mellor, Real Time, p. 140.

THE MYTH OF TEMPORAL PASSAGE

D3:

e is earlier than e*

def.

e is later than e*

def.

257

past and when e* is future e is not present e ceases to be future and becomes present first, and e*ceases to be future and becomes present second; and e ceases to be present and becomes past first, and e* ceases to be present and becomes past second e* ceases to be future and becomes present first, and e ceases to be future and becomes present second; and e* ceases to be present and becomes past first, and e ceases to be present and becomes past second

I have elsewhere defended each of the above reductive analyses against objections. 138 It seems that Mellor is quite right that if the A-Theory of time is true, the A-theorist can account for the existence of asymmetrical B-relations by founding them on the reality of tensed facts. By contrast, the B-theorist who wants to affirm the anisotropy of time seems obliged to regard temporal asymmetry as an inexplicable given. But his assumption of temporal asymmetry seems gratuitous, given a B-theoretical ontology of time. On the B-Theory of time, there just does not seem to be any asymmetry between "past" and "future"-both directions of time are exactly alike and there seems no reason to call one "earlier" and the other "later." Hence, some B-theorists like Horwich and Price boldly and consistently assert that time is completely isotropic. Such a claim, however, seems fantastic in light of our temporal experience of before and after. For the B-theorist to therefore claim in light of that experience that the Bseries of temporal moments has the primitive properties of direction and/or anisotropy seems ad hoc. That experience should rather motivate us to adopt a theory of time in which some metaphysical foundation for these properties is supplied. Thus, ironically, the myth, or better, metaphor of temporal passage, when properly analyzed, far from undermining the A-Theory, actually serves to highlight its superiority to the B-Theory. CONCLUSION The notion that the myth of temporal passage somehow defeats the A-Theory of time is therefore mistaken. Pure A-theorists do not affirm a literal motion of the present along a series of temporal positions or events. That was the error of McTaggart, for which the A-theorist Broad indicted him. B-theorists like Smart and Williams who employed Broad's arguments in defense of the B-Theory were attacking a straw man. Rather most A-theorists have consistently affirmed that talk of time's flow is metaphorical for objective temporal becoming. Questions concerning the rate at

138 See my The Tenseless Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, forthcoming), chap. 7.

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which temporal becoming occurs eventually wind up, whether one adopts a relationalist or a substantivalist view of time, demanding trivialities. Absolute becoming implies a temporal ontology of presentism. Persuasive objections may be brought against our regarding the present as either instantaneous or atomic. The most plausible construction of presentism holds that the expression "the present" must be completed by reference to some non-degenerate interval of time, which is itself potentially infinitely divisible and may be analyzed into subintervals which are respectively past, present, and future. This construction yields one of the major philosophical assets of the A-Theory: the evident asymmetry of time becomes explicable, whereas on the B-Theory it is simply postulated or denied. This positive advantage of the A-Theory is supererogatory, since we are examining B-theoretical arguments against the ATheory, so that a mere defense of the latter is sufficient to render the B-theorist's criticism nugatory. We have thus seen that both the principal objections lodged against the ATheory of time by B-theorists, namely, McTaggart's Paradox and the Myth of Passage, are unsound, being directed at the straw man of the hybrid A-B-Theory, which incoherently weds A-theoretic becoming to a B-theoretic ontology. Given a metaphysic of presentism, the A-Theory not only averts these objections but also makes positive contributions to our understanding of modality and time. In conclusion, we have examined and determined to be sound two arguments for the reality of tensed facts and temporal becoming, the argument from the Ineliminability of Tense and the argument from our Experience of Tense, and we have rejected as fallacious the principal objections typically lodged against the ATheory. This provides prima facie warrant for an A-Theory of time. But before a final verdict can be pronounced, the similar task of examining and assessing the chief arguments for and against the B-Theory of time must also be carried out. It is to that task that we shall turn in The Tenseless Theory of Time.

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