As Time Goes By: Eternal facts in an Ageing Universe 9783897857483

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CorreiaJRosenkranz . As Tune Goes By

Fabrice Correia and Sven Rosenkranz

As Time Goes By Etemal Facts in an Ageing Universe

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menus PADERBORN

Gedruckt mit Unterstützung des Ministerio de Ciencia e Innovaci6n, Madrid (FFI200806153), und der Faculre des Lettres, Universire de Geneve (Fabrice Correias overheads funds). Cover illustration: Artur Serra Costa, Untided, 2011, digital photo graph © Courtesy of the artist

Bibliografische Infonnation Der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar.

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Alle Rechte vorbehalten. Dieses Werk sowie einzelne Teile desselben sind urheberrechdich geschützt. Jede Verwertung in anderen als den gesetzlich zulässigen Fällen ist ohne vorherige Zustimmung des Verlages nicht zulässig. Printed in Germany Einbandgestaltung: Anne Nitsche, Dülmen (www.junit-netzwerk.de) Satz: Rhema - Tun Doherty, Münster [ChH] (www.rhema-verlag.de) Druck: AZ Druck und Datentechnik GmbH, Kempten ISBN 978-3-89785-748-3

And no matter what the progress Or what may yet be proved The simple /acts 0/ life are such They cannot be removed. Hennan Hupfeld, 'As Time Goes By' (1931)

Table of Contents Preface ..................................... .

9

1. The Metaphysical V-Turn ...................... .

15

2. Real Work for an A-Theory

27

3. Launching the Tense Machine

................... .

39

Appendix ................................. .

51

4. Criteria for Realist Views of Tense

................ .

55

5. Presentism ................................ .

71

6. Recurrentism

87

.............................. .

7. Anti-Recurrentism: Escaping Fine's Trilemma

........ .

95

8. Eternal Facts in an Ageing Vniverse

103

9. Epilogue: Averting Hostile Takeover

115

References

................................... 127

Index ....................................... 129

Preface In the beginning there was the idea, which quickly took shape, that

there is an intuitively plausible and otherwise attractive view of reality as tensed which, for reasons still inexplicable to us, has been almost entirely ignored in extant metaphysics of time (see Chisholm 1990 for one notable exception). Yet, after careful study of Kit Fine's massive paper "Tense and Reality", to which we owe both insight and inspiration, we soon found ourselves embroiled in endless discussions about what the other views were with which our view was meant to contrast (Fine 2005: 261-320). It thus soon became clear that in order to show its merits, much more had to be done than merely to articulate this nonstandard A-theory and extract its consequences. We thus set ourselves the task of first getting all possible competitors into focus. This turned out to be a huge undertaking, which ultimately explains why what was originally conceived as a paper tumed into a book. St Augustine famously complained that time proves elusive once the task is undertaken to give a philosophical account of what it is. A cursory look at the current literature on the philosophy of time suggests that not much has changed in this respect. Despite its conceptual sophistication and logical advances, contemporary philosophy would still seem to be at sea when it comes to the metaphysics of time. This is not to say that contemporary philosophers of time suffer from any indecision as to which sentences to affinn or reject. Quite the contrary, different patterns of assent and dissent can clearly be made out. Yet, these differences would often seem to betray a startling unclarity about what is at issue rather than express a disagreement about what is understood by all parties to be a single metaphysical doctrine. Many a discussion is obfuscated by inchoate pictures and tacit assumptions on either side about how to understand the debated claims and consequently about how to assess arguments for or against them. The best evidence for this intolerable state is provided by McTaggart's argument for the unreality of time. That some of the best philosophers of time have so widely disagreed on its proper formulation and assessment is itself a small-scale scandal. 1 1 See MeTaggart 1908 and 1927. Whereas most follow Broad 1938 and Prior 1967 in regarding McTaggart's argument as fallacious, Mellor 1998 and, to some extent,

10

Preface

Even if tenns like 'tensed property', 'tensed fact' or 'passage of time' are good candidates for theory-laden tenns, and so may acquire quite a different significance depending on the theory which embeds them, this can be no excuse. For, these tenns can acquire such a different significance only if not all the tenns do so. There should therefore be enunciable principles marking the contrasting ways in which these tenns are being understood. However, such principles are hardly ever stated. And even when they are stated, debates about their relative merits are mostly perceived as being intemal to the camp of those who take themselves to defend arealist view of tense. By contrast, proponents of anti-realism about tense, the B-theorists, would appear to have no stake in such debates, if only because they shirk the puzzling tenns right from the start. But this appearance is deceptive. Arguments meant to count in favour of anti-realism cannot properly be gauged until it is settled whether they count against all available versions of realism. In this book, we aim to achieve more clarity and systematicity in this area than, to the best of our knowledge, has been achieved before. To this end, we give an exhaustive classification of mutually exclusive A-theories in tenns of a set of precise criteria. Yet, as advertised in the beginning, we do not merely aim at a taxonomy of different realisms about tense, but also intend to explore a so far neglected A-theory that combines many of the virtues that the B-theory claims for itself, while avoiding many of the vices that afflict more standard A-theories. The plan for this book is as follows. In chapter 1, we offer an answer to the question of what the general distinction between A- and B-theories amounts to, contrasting this issue with the issue of what is involved in taking tense seriously. Thus we give a general fonnulation of what makes a theory an A-theory and what makes a theory a B-theory of time. In chapter 2, we then go on to specify desiderata that A -theories ought to fulfil, including minimal constraints on the conception of Dummett 1978 think that it is effective. But they do so for quite different reasons. This is no sutprise as they give completely different reconstructions of the argument whose connections with the original remain obscure. Although Oaklander 2004 would seem to agree with Mellor, his reconstruction of Mc'Thggart' s argument, as weil as his reasons for endorsing it, differ considerably from those suggested by Mellor. Lowe 1987 rejects both Mc'Thggart's original argument and Dummett's reconstruction, but for reasons contrary to those given by Broad and Prior. Fine 2005 gives yet another version of the argument and suggests different ways of responding to it.

Preface

11

time' s passage, or temporal change, as a real phenomenon, which will be fleshed out dilierently by dilierent theories. Chapter 3 introduces the three key notions of constitution, truthmaking and fact-content, as weIl as definitions, axioms and derived principles involving them. Even if some of our definitions or axioms may, for all we know, be contested by some, their explicit formulation will at least ensure that qualms about the arguments we subsequently devise on their basis can be traced back to qualms about these definitions and axioms themselves. We thus aim to guarantee a high degree of argumentative perspicuousness and rigour. In chapter 4, we give precise criteria for distinguishing dilierent versions of the A-theory which, modulo certain. assumptions about the structure of time and the existence of facts, allow us to arrive at an exhaustive classification of mutually exclusive views. These criteria are both metaphysical and semantic in character. By their means, we identify a hitherto neglected family of views. Chapters 5 to 7 discuss three families of views, including Presentism and the non-standard view we aim to explore in more detail in the remainder of the book. In each case, we first show that to each of these views there corresponds a pre-theoretical picture of temporal reality which either influences philosophizing about time or at least has the potential to do so. Dur characterisation of the respective views in terms of the proposed criteria can be seen as an attempt to give cognitive, non-pictorial content to these pictures, which is precisely what, according to a leading worker in the field, metaphysicians should do (Dummett 1991: 10). Subsequently, we discuss how these views fare in the light of the desiderata identified in chapter 2. In chapter 7, where we discuss our favourite A-theory, we show how this theory can escape the McTaggartian trilemma recently put forth by Fine (Fine 2005: 270-76). As it turns out, the mere availability of this view exposes Fine's argument as unsound. In chapter 8, we then devise a systematic metaphysics and semantics for a particular version of this non-standard A-theory which would seem to fare best in the light of the previously identified desiderata. In so doing, we give an account of the nature of tensed facts, offer a reduction of times, and of the temporal order, in terms of such facts and their properties and relations, and provide a full semantics, statable exclusively in tensed terms, for both the A- and the B-language. As it turns out, our preferred A-theory shares many nice features with the

12

Preface

B-theory, and so arguments promoting these features can just as weil be taken as arguments in its favour. Nevertheless our preferred view is a genuine A-theory and not just a B-theory in disguise. This will be shown in chapter 9 which brings our discussion to a dose. Everyone has to start somewhere. There is no such thing as a philosophical account free of any presuppositions. Thus, we make certain assumptions about time and its structure that we will not subject to further discussion. First, we will ignore the impact that relativistic physics is commonly thought to have on the metaphysics of time. Arguably, certain prominent A-theories such as Presentism are at odds with relativistic physics, and hence would otherwise drop out of the picture. Moreover, there is some reason to believe that, at least as far as Special Relativity is concemed, our preferred A-theory can be extended so as to heed its results. Lastly, to the extent that it is as yet an open issue how relativistic physics might be reconciled with quantum mechanics, it would be premature to discard, from the onset, any metaphysical views that are in tension with the former. Secondly, we assume that the time-order is transitive, asymmetric and linear. We thereby exdude both cydic time and branching time. Thirdly, we assume that time is measurable so that, given any two times, there is a certain number which measures their distance, given a previously chosen time-unit (e.g. that of a day). Besides these assumptions about time and its structure, we also assume that talk about facts in general and quantification over such facts in particular make good sense. We thereby exdude certain varieties of deflationism about fact-talk (Field 1994 and Horwich 1998). When discussing semantics, we furthermore assume the truth-conditional paradigm. We thereby exdude certain views that take some notion of assertibility distinct from truth to be the core concept of semantic theorizing (Dummett 1978, 1993 and 2004). Work on this book involved a lot of traveJling back and forth between Geneva, where Fabrice presently holds a Swiss National Science Foundation Professorship (University of Geneva, project PP001-114758), and Barcelona, where Sven holds a Research Professorship at the Catalan Institute for Research and Advanced Studies (ICREA). It soon tumed out that most of the work had to be done face to face, with telecommunication being a last resort, not only because we often feit the need to go through arguments with paper and pen, but also because

Preface

13

our sometimes rather different ways of thinking about philosophical issues required the opportunity of instant clarification. For a long time, we tried to publish some of the ideas put forth in this book in the form of articles. With one exception (Correia and Rosenkranz forthcoming), the experience has been rather frustrating. The majority of referee reports we received complained that our ways of conceiving the debate deviate from the standard and, oddly, declared this a chief reason for rejecting the submitted work. One would have thought that at least in academic philosophy a fresh look at weIl-worn problems would always be welcome. Not so. Fortunately, we both had ample opportunity to present, joincly or separately, earlier versions of the material contained in this book to expert audiences in Barcelona, Berlin, Geneva, Krakow and other places. Thanks to all who participated in discussion on those occasions and especially to those who took the pains to read through earlier, rather convoluted manuscripts. Special thanks go to Ofra Magidor, Elia Zardini, Kit Fine, Dean Zimmerman, Ghislain Guigon, Manuel Garcia-Carpintero and Carl Hoefer who provided us with immensely valuable feedback that helped to significancly improve our arguments and to clarify our own ideas. We would also like to acknowledge that the research leading to these results has received funding from the European Community's Seventh Framework Programme under grant agreement PITN-GA-2009-238128, and was also partially funded by the Consolider-Ingenio project CSD2009-0056, the project FFI 2008-06153 and the project HUM2007-61108, all financed by the Spanish Ministry of Science and Innovation (MICINN), as weIl as by the project CRSI11-127488, financed by the Swiss National Science Foundation. Our final thanks go to Artur Serra Costa for the cover illustration and to Michael Kienecker from mentis for his support throughout the publication process.

1 The Metaphysical V-Turn Following MeTaggart, we distinguish between the A-series and the B-series of time. The A-series is meant to order events, facts and times according to whether they are past, present or future. The B-series is meant to order events, facts and times according to whether they are earlier than, simultaneous with or later than one another (MeTaggart 1908 and 1927). Following common usage, we also distinguish between the A- and the B-theory of time. Very roughly put, and as a first approximation, the B-theory is the view that all that can truly be said about the A-series is grounded in the totality of facts about the B-series, while it is not the case that all that can truly be said about the B-series is grounded in the totality of facts about the A-series. The A-theory, by contrast, denies that all that can truly be said about the A-series is grounded in the totality of facts about the B-series. Although we consider this rough characterisation as ultimately correct, it is quite obscure how these opposed metaphysical claims are best understood. There was a time, not all too long ago, when such metaphysical contentions were greeted with the utmost suspicion. Unless explicable as verifiable claims about language, or so the then prevalent doctrine ruled, their obscurity had to be perceived as symptomatic of a muddled mind rather than a hidden truth of depth. For some time now, this linguistic approach to metaphysics has lost much of its appeal, even if it has recently been resuscitated in the context of what goes by the name of 'metametaphysics' (see e. g. Hirsch 2005). Whether or not it is wise to conceive of all metaphysical problems as infelicitously stated problems about language, it is always a recommendable exercise to check whether they can be so recast. For, unless it can be convicted of skirting the issue, such an exercise holds out the promise of sett1ing metaphysical disputes in a quick and elegant way. In this chapter we explore where this leads us when applied to the dispute between A- and B-theorists. On the face of it, the distinction between A- and B-theories of time concems items of a distinctive ontological category: facts. According to Frege, facts just are true propositions (Frege 1918/19); and once this has been granted it is only a minor step, for the linguistic philosopher anyway, to recast talk about facts as talk about true statements. What

16

1. The Metaphysical V-Turn

it is for truths to be grounded in the totality of other truths will then naturally be conceived in terms of the reducibility of the former to the latter (cl. Dummett 1993: 230-76). Accordingly, B-theorists are pictured as claiming that truths about the A-series are reducible to the totality of truths about the B-series but not conversely, while A -theorists are pictured as denying that truths about the A -series can be so reduced. Grounding thus becomes a relation between vocabularies rather than a relation between language and non-linguistic reality. This raises the question of what statements about the A- and statements about the B-series respectively are. It would certainly not be in the spirit of the linguistic approach to answer this question by invoking the A- and the B-series as comprising features of temporal reality that these statements respectively purport to depict. For this would amount to reinflating fact-talk. On the linguistic approach, statements about the A-series (the A-statements) and statements about the B-series (the B-statements) are more naturally deflned in terms of certain of their linguistic features and the cognitive function these features serve. As we shall see, this way of proceeding is instructive quite independently from whether the linguistic approach is endorsed. Given their respective tasks to express different kinds of temporal orderings, A-statements essentially involve tense-inflections and may in addition contain tense-expressions like 'present', 'one day ago' or 'twO days hence', whereas B-statements involve neither tense-inflections nor tense-expressions but instead date-terms and tenseless expressions like 'onJuly 28 th 2061', 'is one day earlier than' or 'is two days later than'. Surface grammar may demand that all statements alike involve tenseinflections. But from the viewpoint of logical analysis B-statements could serve their cognitive function equally weIl if this requirement was lifted. Thus, aB-statement like 'Halley's comet passes through its perihelion on July 28th 2061' is meant to inform us about the position of Halley's comet onJuly 28th 2061, and in order for it to do so we do not need to lmow whether the 28 th of July 2061 is in the future. If it is lmown to be in the future, surface grammar may demand that the statement be rendered as 'Halley' s comet will pass through its perihelion on July 28 th 2061' , but this further piece of information is nothing we need to possess in order to lmow how things stand with Halley' s comet on July 28th 2061. Similarly, even if 'passes' is grammatically in the present tense, the present truth of the B-statement 'Halley's comet passes through its perihelion on July 28 th 2061' does not require that Halley's comet

1. The Metaphysical U-Turn

17

passes through its perihelion at the present time. H this B-statement is true at all, it is true at any time, and this despite the fact that Halley's comet passes through its perihelion at some times but not at others. By contrast, an A-statement like 'Halley's comet passes through its perihelion' could not serve its cognitive function unless its present truth required that Halley's comet passes through its perihelion at the present time: if it did not require this, you would not, on hearing it, go to the telescope to confirm, however indirectly, whether this was so, after the appropriate delay. Part of the cogninve function of the simplest statements of the A-Ianguage is the communication of propositions belief in which rationalises timely action. An A-statement can serve this function only to the extent to which it is not always true. It is only if the inflected verbal phrase of an A-statement is modified by appropriate modifiers like 'always' or 'sometimes', or is conjoined with a matching tensed noun phrase like 'the present time' (as in 'The present time is present'), or is embedded in 10gica1ly more complex constructions, that this A-statement can be guaranteed to have a stable truth-value. Below, we will first define the A-statements and then the B-statements. For reasons of simplicity and ease of discussion, we will assume throughout that both languages, the A-Ianguage and the B-language, or suitable idealisations of them, are super-expressive in the sense that they contain a name for every object and suitable predications to capture all the ways these objects respectively are. Let us now define the A-statements in two stages as folIows. First, we define the basic A-statements which come in two varieties, structural and material:

Basic structural A -statements Time t is present Time t is n days in the past Tune t is n days in the future

Basic material A -statements Presendy, R(ab ...) n days ago, R(ab ... ) n days hence, R(ab .. .).

We here stipulate that the A-Ianguage be regimented as folIows: tenses are only ever represented by means of tense-Iogical operators or the tensed predicates 'is present', 'is n days in the past' and 'is n days in the future'. Consequendy, any expression replacing 'R' will itself be regarded as tense-free. 2 We also stipulate that 'R' will only ever be re2 1bis treatment of basic material A-statements bas the consequence that the tense-Iogical operators occurring in such statements do not function logico-grarrunatically in the

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1. The Metaphysical V-Turn

placed by a monadic or polyadic predicate q> which is such that q> is logically simple and such that, possibly, q> is only temporarily satisfied. We thus exelude replacements by predicates such as 'is bent or not', 'is a number' etc. Here and in what folIows, we understand the predicates 'is present' and cognates, as weIl as the operators 'presently' and cognates, as sensitive to tense-Iogical embedding. Thus, for instance, if 't is present' is true, then 'One day hence, t is present' will be false; and similady, if 'Presently, Sam is philosophizing' is true, then 'One day hence, presently, Sam is philosophizing', which is equivalent to 'One day hence, Sam is philosophizing', may be false. Note also that we will treat a11 basic A -statements apt to locate events in the A -series as basic material A-statements about their occurrence, e.g. 'Event e presently occurs', 'Event e occurred n days ago' etc. Thus, basic structural A-statements are here understood to be exelusively about the A-series locations of

times. We now define the A-statements as those statements that are either basic A-statements or can be built from these or corresponding open sentences by means of the truth-functional connectives, the quantifiers and the metric tense-Iogical operators, by means of which the elassical operators 'sometimes in the past', 'always' etc. can a11 be defined (see chapter 2 for details). Of course, tensed language can in principle be much richer, as it may furthermore contain connectives like 'until' and same way as when they modify tensed statements, as does 'presendy' in 'Presendy, n days ago, p': in basic material A-statements, they rather modify tense-free predications (d. Wiggins' treatment of modal expressions as predicate modifiers instead of sentential operators in his 1976). Instead, we could have followed Prior' s suggestion of taking 'R' as intrinsically tensed in order to have a uniform view about the grammatical function of the tense-logical operators (prior 1967: 14-15). But for the sake of systematically comparing the A- and the B-language, we will stick to the present treatment. This treatment has the consequence that 'R(ab ... )' is an incomplete expression. To mark its incompleteness, we might think of it as containing the proform 'then', whose antecedent in a basic material A-statement is the prefixed tense-logical operator (see Grover, Camp and Belnap 1975 on proforms). We leave open which semantics 'then' is supposed to have in this context. On one natural view, 'Presendy, Dorothy is happy then' is equivalent to 'Dorothy is happy at the present time', '3 days hence, Dorothy is happy then' is equivalent to 'Dorothy is happy at the time which is 3 days later than the present time', and similarly for all other basic material A-statements. Note that this requires there to be an ontology of times that not all A-theorists are willing to countenance.

1. The Metaphysical U-Turn

19

'after' or a rigid presentness operator etc. But for present purposes, the proposed definition of the A-statements will do, since, on the linguistic approach, B-theorists at least claim that the A-statements as defined can be reduced to B-statements. 3 To the definition of B-statements we now turn. Again, they are defined in a two-stage process. First we define the basic B-statements, which again are either structural or material:

Basic structural B-statements

Basic material B-statements

Tune t is simultaneous with time t' Tune t is n days earlier than time t' Time t is n days later than time t'

At time t, R(ab .. .).

For the purpose of comparing both languages, we here again assurne that 'R' is used as a placeholder for tense-free expressions which are logically simple and possibly only temporarily satisfied. 4 As in the case of the A-Ianguage, we here take it that the only basic structural B-statements are ab out the B-series locations of times, while B-statements apt to locate events in the B-series will be understood to be basic material B-statements such as 'Event e occurs at time t', etc., or complex B-statements such as 'For some times t and t', e occurs at t and e' occurs at t' and t is simultaneous with t", etc. We now define the B-statements as those statements that are either basic B-statements or can be built from these or corresponding open sentences by means of the truth-functional connectives and the quan-

3 Note that so-caIled cross-temporal tensed statements such as 'Aristotle was more

intelligent than Herben presently is' can be understood as A-statements, in the sense in which A-statements were defined. To see this, let the A-language contain the three-place predicate ' ... is then more intelligent than ... is ... days later than then', where both occurrences of 'then' are proforms with the sarne antecedent (see previous foomote). Then our statement is equivalent to the A-statement 'For some n, n days ago, Aristotle is then more intelligent than Herben is n days later than then'. 4 Hin our account of the A-language we had adopted Prior's conception of taking 'R' as

intrinsically tensed, we would have had to think of what 'R' here stands for as being of a different logico-grammatical category. See last but one foomote. H we again think of 'R( ab ... )' as containing the proform 'then', the antecedent of this proform in a basic material B-statement will accordingly be the prefixed temporal modifier. On the view adumbrated in the last but one foomote, 'On 4th of July 2009 at lOarn, Dorothy is happy then' is equivalent to 'Dorothy is happy on 4th of July 2009 at lOarn', and similarly for all other basic material B-statements.

20

1. The Metaphysical V-Turn

tifiers. Of course, tenseless language can be much richer, as it may also contain connectives such as 'because' or 'although' etc. But on the linguistic approach, B-theorists at least claim that the B-statements, as defined, cannot be reduced to the A-statements, as defined, while the latter can be reduced to the former. 5 What is the relevant notion of reducibility being invoked here? For well-known reasons, the reducibility of the A- to the B-Ianguage cannot coherently be thought to require the translatability of A-statements into B-statements, where translation preserves the proposition expressed and propositions are the objects of propositional attitudes. The case here is similar to the one of statements involving the first-person pronoun and those involving names or definite descriptions instead (d. Perry 1979). Just as we cannot translate statements involving 'I' - like 'I am causing a mess', as uttered by John - into statements such as 'John is causing a mess' or 'Sally's best friend is causing a mess', we cannot translate statements such as 'The meeting is presently held' into statements such as 'The meeting is held at noon on 4th of July 2008' or 'lbe meeting is held simultaneously with the town hall' s inauguration'. As hinted at above in our discussion of the cognitive function of either type of statement, propositional attitudes whose contents are expressed by A-statements (A-propositions) playa distinctive role in our cognitive economy unmatched by attitudes whose contents are expressed by B-statements (B-propositions) (see Prior 1959 and 2003; Mellor 1998). To this extent, anyone should take tense seriously, even B-theorists. Accordingly, lest we deliberately caricature their view, we cannot assume that translatability is what B-theorists have in mind when making their reductionist claim. Instead, they should be taken to understand reducibility to require no more than preservation of tmth-conditions. The finding that the A-Ianguage cannot be translated into the B-lan-

5 The expression 'At t' can also be thought of as a tense-logical operator that operates

on, e.g., basic material A-statements. Note that if it is used in this way, 'At t' needs a tensed complement if it is not to be otiose, and the expressions 'R(ab ... )' composing the A- and the B-language are not of this kind. Consequendy, the use made of 'At t' within the B-language is rather different. Although the tense-logical operator 'At t' is not part of the A-language as we defined it, it can be introduced into this language by means of the following definition: At t, ip =df always, (t is present:J ip), where 'ip' ranges over A-statements.

1. The Metaphysical V-Turn

21

guage does not entail that such a preservation of truth-conditions cannot be achieved. Given that basic A-statements may vary in truth-value over time, to specify their truth-conditions is to specify conditions for their truthat-a-time. The basic A-statements can thus be reduced to B-statements in the following way:

't is present' is true at t' == t is simultaneous with t' 't is n days in the past' is true at t' == t is n days earlier than t' 't is n days in the future' is true at t' == t is n days later than t' 'Presently, R(ab ... )' is true at t == at t, R(ab ... )

'n days ago, R(ab ... )' is true at t == at some time n days earlier than t, R(ab ... ) 'n days hence, R(ab ... )' is true at t == at some time n days later than t, R(ab ... ).6

In order to account for complex tenses involving iterations of tense-Iogical operators like 'presently', 'n days ago' and 'n days hence' , B-theorists will have to add the following general clauses: 'Presently, 'P' is true at t == 'P is true at t

'n days ago, cp' is true at t == 'P is true at some time n days earlier

thant 'n days hence, 'P' is true at t == 'P is true at some time n days later than t. Given all this, it is obvious how to complete the truth-functional reduction. The A-theory would thus seem to fail. 6

Here and in what folIows, we will help ourselves to substitutional quantification so as to allow formulations of three types of claims, exemplified below, without thereby committing any use-mention fallacy: For all x, 'x is F is true iff x is F For all p, 'p' is true iff p For some G, if 'Gab' is true, then 'Gba' is true. Any qualms about substitutional quantification concerning the richness of the language that provides the substitution-classes can be allayed by recasting what we say in terms of schemata or by employing the Tarskian machinery involving infinite sequences or assignments to variables. But for convenience's sake, we will stick to substitutional quantification.

22

1. The Metaphysical U-Turn

Yet, trus establishes only the first half of the B-theorists' one-way reducibility claim. If the second half of this claim cannot be established, neither can the B-theory, at least on the construal of it suggested by the linguistic turn. Alas, as Mc'Thggart clearly saw, basic B-statements can be reduced to complex A-statements, thanks to the following equivalences: Always, [t is simultaneous with t' == sometimes, both t and t' are present] Always, [t is n days earlier than t' == sometimes, t is n days in the past and t' is present] Always, [t is n days later than t' == sometimes, t is present and t' is n days in the future] Always, [at t, R(ab ... ) == sometimes, t is present and presently,

R(ab ... )], where 'Presently, R(ab ... )' is a basic material A-statement and 'Sometimes cp' is equivalent to 'Presently cp, or k days ago cp, for some k, or m days hence cp, for some m' (McTaggart 1927: §610; see also Prior 1967: 4). Given trus recipe for basic B-statements, it is obvious how to reduce all B-statements to A-statements. This establishes:

(#) The A-language is reducible to the B-language, and the B-language is reducible to the A-language. Given the linguistic approach, (#) implies that both the B-theory and the A-theory are wrong. 7 Taking the linguistic turn, we seem to have

7 B-theorists typically give truth-conditions for cross-temporal tensed statements such

as 'Aristotle was more intelligent than Herbert presently is' in terms of four-place predicates which cannot be merely temporarily satisfied, e. g. ' ... is at ... more intelligent than ... is at ... '. Such predicates do not belong to the B-language as we have defined it. Nevertheless, like the A-language, the B-language contains three-place predicates such as ' ... is then more intelligent than ... is ... days later than then'. These predicates can, in conjunction with temporal modifiers of type 'at time t', be used to provide truth-conditions for these cross-temporal tensed statements in B-terms. Accordingly, cross-temporal tensed statements do not present counterexamples to (#).In addition, tenseless statements that can be formulated in terms of the aforementioned fourplace predicates are equivalent to B-statements formulated in terms of such three-place predicates and temporal modifiers, so that to this extent, the B-Ianguage, as here defined, is not ladung in expressive power.

1. The Metaphysical U-Turn

23

arrived at a dead end. For anyone who believes, as we do, that this is far too quick a way with a respectable, even if still somewhat obscure, metaphysical distinction, it is time to redirect our course. The result of the foregoing shows that any further debate would be pointless if grounding could solely be understood in terms of reducibility. However, those engaged in the debate typically have more metaphysical notions of fact and grounding in mind, which concern the relation between our descriptions of reality and reality itself, rather than relations between different descriptions of that reality. Moreover, the notion of grounding is typically meant to apply to bits of reality, i. e. facts or col1ections of facts, and bits of language. We therefore suggest to invoke a robust, metaphysical notion of fact and to understand grounding in terms of trnth-determination. Thus, irrespectively of reducibility in both directions, there would still seem to be room for disagreement about what determines the truth-values of the respective right- and left-hand sides of the aforementioned equivalences. If we conceive of facts as what determines truth-values, there can accordingly still be disagreement about what facts there are. We accordingly agree with Fine that a linguistic construal of the divide between the A- and the B-theory will not do, and that this divide should instead be characterised in metaphysical terms (Fine 2005: 264-70). 8lnstead of asking what statements involve (tense-expressions, tense-inflections etc.), we should rather ask what kinds of properties and relations facts involve. We distinguish between A-properties and -relations and B-properties and -relations:

8

Fine also invokes facts, but claims tbat taIk about facts is ultimately to be recast in terms of statements involving tbe operator 'It is true in reality tbat' (Fine 2005: 268). In what follows, we will quantify over facts and tbus leave Fine's reductive enterprise aside. H tbe reductive task can be carried out at it is to be expected tbat whatever we say can also be recast in terms of statements involving Fine's operator. In a similar vein, Wright seeks to account for tbe direction of explanation, or trutb-determination, across equivalences witbout quantifying over facts (Wright 1992: 24-29, 108-24, 191-99). It is unclear whetber generalisations we wish to make about such equivalences can be made witbout quantification over facts. Again, if tbis should prove feasible, it is to be expected tbat whatever we say can likewise be said in terms of statements involving 'because' witbout ontological commitment to facts.

an,

an

24

1. The Metaphysical V-Turn

A -properties and -relations heing present heing n days in the past heing n days in the future heing presently F heing presently R-related to heing F n days in the past heing n days in the past R-related to heing F n days in the future heing n days in the future R-related to

B-properties and -relations heing simultaneous with heing n days earlier than heing n days later than heingF at t being at t R-related to, where the first three entries in either list mention properties, or relations, of times. Atomic tensed facts are composed of a suhject, or several suhjects in a certain order, and A-properties or -relations as predicahles. Call such facts 'A-facts'. Tenseless facts do not have any A-properties or -relations as predicahles. Call those tenseless facts which are composed of a suhject, or several suhjects in a certain order, and B-properties or -relations as predicahles 'B-facts'. Then, (atomic) temporal facts will he either A-facts or B-facts. In the light of these considerations, the B-theorists' key claim should he reformulated as follows: there are B-facts, and all A-statements have their truth-value determined hy such B-facts. Two questions immediately arise. First, on this view, can some B-statements fail to have their truth-value determined hy B-facts? Secondly, can B-theorists nonetheless countenance A-facts? The answer to the first question is a clear 'no': this much is already guaranteed hy (4i'). Given that facts are essentially the kinds of things that contrihute to the determination of truth-values, any positive answer to the second question would he entirely unmotivated: the B-facts would already he all the facts needed to account for the truth-values of all the A- and B-statements. We therefore suggest the following general characterisation of the B-theory:

1. The Metaphysical V-Turn

(B-theory)

25

There are atomic temporal facts, but all these facts are B-facts; and all A- and B-statements have their truthvalue determined by B-facts.

Thus, as Fine suggests, the B-theory can appropriately be described as anti-realism about tense (Fine 2005: 262). What about the A-theory? As a first approximation, consider: (A-theory'~) There are A-facts; and some A-statements have their

truth-value determined by A-facts. 50 characterised, the A-theory can correspondingly be conceived as realism about tense. Yet, this characterisation in principle allows for two types of A-theory. The first type of A-theory claims that among the temporal facts, there are only A-facts, and that all A- and B-statements have their truth-value determined by these A-facts. The second, weaker type of A-theory contends that there are A-facts, and that some A-statements have their truth-value determined by A-facts, while some B-statements have their truth-value determined by B-facts. On reflection, however, the second type of A-theory is no live option. For which are the A-statements which have their truth-value determined by A-facts, and which are the B-statements which have their truth-value determined by B-facts? 5uppose it was suggested that all A-statements have their truth-value determined by A-facts and alt B-statements have their truth-value determined by B-facts. This would be entirely unmotivated: if all the A-statements have their truth-value determined by A-facts, then by (#) so do all the B-statements. Accordingly, there would then be no reason to countenance B-facts in addition to A-facts, because all the facts needed to determine the truth-values of B-statements would already be in the bag. Altematively, it might be suggested that all basic A-statements have their truth-value determined by A-facts and all basic B-statements have their truth-value determined by B-facts. But accepting either conjunct again leads to a pointless, and to this extent illicit, multiplication of truth-determining facts. Thus, if the first conjunct is true, then by compositionality, all the A-statements, basic or non-basic, have their truth-value determined by A-facts. By (#), all the B-statements also have their truth-value determined by A-facts. Countenancing B-facts would thus lead to overdetermination, and such an overdetermination lacks any rationale. The same applies, mutatis mutandis, to the second conjunct.

26

1. The Metaphysical U-Turn

Given all that, and given that no other prineipled option appears to be available, we eondude that the A-theory is best eonstrued thus: (A-theory) There are atomie temporal facts, but all these facts are A-facts; and all A- and B-statements have their truth-value determined by A-facts. Both the A- and the B-theory can thus be seen to eombine a metaphysical thesis with a semantie thesis. As we shall see, there are many different A-theories, or versions thereof, and how these metaphysical and semantie theses are to be understood will vary from version to version. The above eharacterisation of the A-theory should therefore be seen as a minimal eharacterisation on whieh all these versions eonverge.

2

Real Work for an A-Theory In this chapter, we lay down a number of desiderata that A-theories should fulfil. All but the first concern the semantic and metaphysical role of A-facts and thus are specmc to realism about tense. The first desideratum by contrast derives from a general constraint on metaphysical theories and can be formulated thus: (Real-1) If arealist view of tense is true, then it is always true. Although metaphysical theories, like any other theories, are fallible, they should nonetheless come without any sell-by-date: if true, they should always be true. This constraint on realist theories of tense is not at all trivial because these theories will include theoretical claims which are significantly tensed. It is familiar from the debate about physicalism that some metaphysical views involve modal claims which are nonetheless taken to be themselves metaphysically contingent (cl. Jackson 1998: 11-13). Exploiting the analogy between modality and tense (prior 1970), it might therefore be suggested that Real-1 illegitimately rules out cogent views about temporal reality involving tensed theoretical claims which, on these views, are only temporarily true. We reject this extension of the analogy, for the following reason. While it is not in general a constraint on theories that they issue in metaphysically necessary claims whenever they are true, it is in general a constraint on theories that they retain their validity, if any, after the date of their conception and do not acquire it on that date, having been invalid before. 9 The dispute between the A- and the B-theory of time turns on the issue of whether there are any tensed facts. Given the equivalences mentioned in the previous chapter, proponents of either theory are bound to agree that A- and B-statements alike can be used to say something true about temporal reality, and also bound to recognise that proponents of the respective other theory must and can agree to this. In

9

We will, however, demand that the metaphysical theories we are concemed with here are individuated by claims that are at least nomologically necessary if true at a11 (see chapter 4).

28

2. Real Work for an A-Theory

particu1ar, A-theorists must acknowledge that B-theorists admit true A-propositions as contents of propositional attitudes (cl. Mellor 1998; Zimmerman 2005). Given the specifics of A-to-B reduction, A-theorists must also recognise that B-theorists can readily admit that basic A-statements have their truth-values determined by temporal facts. However, B-theorists will be ready to countenance A-facts at most in the deflated sense of 'fact' according to which facts are nothing but true propositions. By contrast, A-theorists will insist that there are A-facts in a more demanding sense of 'fact', viz. one in which they are apt to determine the truth-value of A-statements. Thus, the minimal characterisation of A -theories given in chapter 1, together with Real-1, implies that A-theories ought to validate: (Real-2) Always, if an A-statement is true, it is determined to be true by the A-facts. Before we proceed to make more precise what this involves, let us first adopt the following convention governing the use of 'n days from the present', which we will follow throughout the remainder of the book: 'n days from the present' is used for 'presently' in case n = 0, for '-n days aga' in case n< 0, and for 'n days hence' in case n > o.

Oftentimes we will abbreviate 'n days from the present' by 'D/. For the case of basic material A-statements, we take it that on any A-theory the following principle holds: Always, [a basic material A-statement 5 is determined to be true == there is a set of basic material A-statements S and a function d assigning a number to each of the members of S such that (i) for every 5' ES, d(s') days from the present, 5' is made true by some A-fact, and (ü) necessarily, for all n, if for every 5" ES, n+d(s") days from the present, 5" is true, then n days from the present, 5 is true].

It follows from this principle that whenever an A-fact makes 'n days from the present, p' true, m days from the present, the statement' n-m days from the present, p' is determined to be true. Whenever a basic material A-statement is made true, there then is some A -fact that makes it true. By contrast, a basic material A -statement 5 may presently be determined to be true although presently no A-fact

2. Real Work for an A-Theory

29

does the determining. It will do if, for some n, n days from the present, some suitable A-fact makes another basic material A-statement true whose truth necessitates that -n days from the present, 5 is true. Still, provided that the aforementioned principie holds, there would be no truth-determination for basic material A-statements if there was never any truth-making by A-facts. So we may say that, given the principIe, whenever a basic material A-statement is determined to be true, it is determined to be true by the A-facts, in the sense in which Real-2 demands this of all true A-statements. Let the material A-statements be those statements that are either basic material A-statements or can be boot from these or corresponding open sentences by means of the truth-functional connectives, the quantifiers and the metric tense-Iogica1 operators. Real-2 implies that, always, if a basic material A-statement is true, it is determined to be true by the A-facts. H this implication holds, there is then a natural way to conceive of truth-determination by A-facts for material A-statements: if true, their truth can be explained in terms of which basic material A-statements are determined to be true in conjunction with the truth-clauses for the classical connectives, the quantifiers and the metric tense-Iogica1 operators. Depending on one's preferred conception of the nature of times, whether one treats them as sui generis or not, the manoeuvre can be extended to appIy to all A-statements, either by invoking a further, analogous principie about the truth-determination of basic structural A-statements in terms of the truth-making of others, or by devising a reduction that accounts for the truth of basic structural A-statements in terms of the truth of material A -statements. In either case, the preceding remarks are sufficient to ensure that it will then be equally appropriate to think of the truth of any A-statement as being determined by the A-facts. Although we believe that talk about reality being constituted by tensed facts, which are in turn composed of tensed properties and relations, is in principie apt to take us beyond the deflationary conception of facts as true propositions, we also believe that the right to this inflated fact-talk must be earned and so be immunised against easy deflation. This right can be earned by assigning A-facts an explanatory role which true A-propositions cannot dis charge, in particular the role of making some A-statements true and determining the truth-value of others. Real-2 is precisely meant to do this. But it should also be clear

30

2. Real Work for an A-Theory

that the explanatory role of A-facts, which makes them differ from true A-propositions, cannot be exhausted by their being whatever temporal facts serve as truth-makers, and so truth-determiners, for A-statements: B-facts, if any, can serve this role equally wen. There are further desiderata that A-theories of time should fulfil. Although there may be many more, we here specify only three such further desiderata that concern the nature of temporal change and the relationships between tensed language and temporal reality. Appeal to A-facts is typically based on the idea that only those temporal facts which are A- but not B-facts can account for the reality of time's passage. B-facts, if any, do not change, neither numerically nor qualitatively. If, in reality, time passes, there will accordingly be something that has a basis in temporal facts, yet cannot be accounted for in terms of B-facts. Hence, if time really passes, A-facts turn out to be indispensable. They thus discharge an explanatory role over and above their role as truth-makers. So what is the passage of time and how can it be explained by, or grounded in, temporal facts so as to reveal its objective nature? Answers to this question will not be wholly independent from the respective A-theories that typically differ in their conceptions of A-facts or at least in their conceptions of how reality is constituted by them. But even at this stage we can at least specify some general constraints on the notion of time' s passage as a real and objective phenomenon that will then need to be fleshed out, in their respective ways, by the different A-theories in question. A-facts, however they may in detail be conceived, must then be shown to playa crucial role in an account of how these general constraints can be met. At the very least, and whatever conception of temporal reality is assumed, regarding time' s passage as areal phenomenon implies taking reality itself to continually change in some way or other. Thus, it should always be the case that temporal reality as it then is differs in some way from reality as it was or will be. ln the light of our convention goveming the use of 'n days from the present', we can express what it takes to treat time' s passage as a real phenomenon in the following way. Let 'the facts which constitute reality are different from what they are n days from the present' be short for

2. Real Work for an A-Themy

31

'the facts X which constitute reality are such that, n days from the present, either the facts Y which constitute reality are distinct from X, or there is a fact f which constitutes reality and is relevantly qualitatively different from what it is like -n days from the present' . Then realist views of tense should validate the claim that (Real-3) Always, for every n distinct from 0, the facts which constitute reality are different from what they are n days from the present. It is a common thought, amongst philosophers anyway, that our conception of objectivity entails that what is conceived to be objectively the case should be taken to allow for adescription that is independent from our particular perspective, in the sense of being in principle available from each such perspective (see Williams 1978: 64-65, 211-12, 241-46; Nagel 1986: 74-77; andDummett 1978: 356). Objectivity, the slogan goes, entails intersubjectivity; and intersubjectivity would seem to require that different subjects, speaking from different perspectives, can agree on a single description of how things are. The assumption that there should in principle be a perspective-independem description in this sense is, however, conditional on the further assumption that what is objectively the case does not differ whenever the relevant perspectives do. This further assumption is most natural in cases in which different perspectives can be adopted, by different subjects, at the same time, for then there is no sense attached to the idea that what is objectively the case might itself change from perspective to perspective. At any time, what is objectively the case is what is objectively the case, and that' s that. So whenever a difference in perspective implies a difference in what is objectively the case, some time must have lapsed for that difference in what is objectively the case to have materialised; and then a difference in perspective must itself imply a difference in the times at which they are adopted. Most cases in which talk about differing perspectives makes sense do not validate this implication. However, if the relevant perspectives are temporal and there is real temporal change, then the further assumption, that what is objectively the case does not differ whenever the relevant perspectives do, cannot be made. Consequently, reality as it objectively is cannot be presumed to be exhaustively describable in the same way irrespectively of which

32

2. Real Work for an A-Theory

perspective the describer, however ineluctably, adopts. Reality changes in tandem with changes in temporal perspective; and so, at any one time, adescription of how things objectively are as judged at that time need not be one that is likewise available at any other time. Indeed, only basic A-statements would seem apt to record temporal change: B-statements, if true, are true at all times and convey the same information at all times. So even if they should also be said to be made true by A-facts, they will either be made true by different A-facts at different times or by the same A-fact that has, though, different features at different times. Accordingly, whatever the changes in reality are that account for the passage of time - be they changes in what A-facts there are, or changes in what features these facts have - B-statements are incapable of recording these changes, and that quite independently from whether they have A-facts as truth-makers. To this end, basic A-statements are needed; and as noted in chapter 1, basic A-statements change in truth-value over time. Yet, for all that, this need not imply that the slogan that objectivity implies intersubjectivity is ill-conceived. Rather, this slogan needs to be adapted to the case at hand, taking proper account of the existence of perspectives that are temporal and thus change with time. Thus, what should still be demanded of a conception of temporal change as objective is that this very change can in principle be described from any temporal perspective, albeit in different ways. Even if the truth of any such description depends on the perspective we adopt when giving it, the temporal change we thus describe is not itself dependent on this perspective but can be appreciated for what it is from any other perspective by means of another description whose truth in turn depends on that other perspective. If we identify the temporal perspective associated with a given time with all the A-statements that can truly be made at that time, and think of real temporal change, if any, in terms of a difference between reality as it is at any given time and reality as it is at any other time, then we obtain the following realism-relevant constraint: realist views of tense should validate the claim that (Real-4) Always, for every m and every n, if m days from the present, the facts which constitute reality are different from what they are n days from the present, then the true A-statements have truth-conditions which entail that this is so.

2. Real Work for an A-Theory

33

H Real-4 cannot be validated, no proof can be given that the temporal change we conceive from each particular temporal perspective is something we conceive of as independent from that perspective. And yet, Real-4 is still compatible with the idea, at odds with realism about temporal change, that it is the change in our own temporal perspective that brings about, or metaphysica1ly grounds, a change in how things are. Yet, this offends against our conception of how things are from each temporal perspective as being independent from the fact that we adopt that perspective, however ineluctably so, given our own existence in time. So, even if a difference in temporal perspective implies a difference in how things are and vice versa, we must still be said to conceive of this co-implication as being due to a dependence of how things are as described from our own perspective on how things objectively are. Accordingly, that reality changes in tandem with changes in our temporal perspective should neither be understood to suggest that a change in perspective brings about, or metaphysica1ly grounds, a change in how things are, nor be understood to suggest that both changes occur independently from each other but at the same pace. Rather, the thought must be that our temporal perspective shifts in virtue of a change in how things objectively are: a shift in temporal perspective is not just a shift in epistemic angle but itself the unavoidable result of a change in what this epistemic angle is an angle on. We thus lay down that realist views of tense should validate that (Real-S) Always, for every n, if the facts which constitute reality are different from what they are n days from the present, then the true A-statements are different from what they are n days from the present partly because of the particular way in which those facts do so differ, where 'the true A-statements are different from what they are n days from the present' abbreviates 'the true A-statements S are such that n days from the present, the true A-statements T are distinct from S'. Note that the insertion of 'partly' in Rea1-S is necessary, for the following reason. The true A-statements may be different from what they are n days from the present partly because, m days from the present, with m n, there is a fact f that (i) neither constitutes reality -m days from the present (ii) nor constitutes reality n-m days from the present, but (iii) which nonetheless determines some statement 'm days from the present, p' to be true -m days from the present while

*

2. Real Work for an A-Theory

34

(iv) determining the distinct statement 'm-n days from the present, p' to be true n-m days from the present. We have thus arrived at a list of desiderata in the light of which we can later assess the relative merits and shortcomings of different versions of the A-theory. In formulating these desiderata, we made essential use of the tense-Iogical operator 'always'. Yet, there are at least two different interpretations of 'always' that we have to take into account, the standard interpretation and the deviant interpretation. To distinguish these interpretations, let us first exploit the aforementioned convention governing 'n days from the present' in order to define the more familiar tense-Iogical operators in terms of metric tense-Iogical operators of that form:

In the past, Cf> ==df for some n< 0, n days from the present, Cf>

==df for some n > 0, n days from the present, Cf> Sometimes, Cf> ==df for some n, n days from the present, Cf>

In the future,

Cf>

and Always,

Cf>

==df for every n, n days from the present, Cf>,

where in each case 'Cf>' ranges over A-statements. On the standard interpretation, the metric tense-Iogical operator 'n days from the present' underwrites at least one of the following two equivalences: Always, [n days from the present, Cf> == for some time t n days from the present time, at t, Cf>] Always, [n days from the present, the present time, at t, Cf>],

Cf>

== for all times t n days from

where 't is n days from t" is short for 't is simultaneous with t" if n = 0, for 't is n days later than t" if n > 0, and for 't is -n days earlier than t" if n < 0. Hthe time-order is linear and the time-line extends indefinitely in both directions, then these equivalences are themselves equivalent. Given these assumptions, the standard interpretation implies that the following equivalences hold in addition:

== at the present time, Cf>] [for some n > 0, n days from the present, Cf> == for some t

Always, [0 days from the present, Always, later than the present time, at t,

Cf>]

Cf>

2. Real Work for an A-Theory

35

Always, [for some n< 0, n days from the present, cp == for some time t earlier than the present time, at t, cp] Always, [for some n, n days from the present, cp == for some time t, at t, cp] and Always, [for every n, n days from the present, cp == for every time t,

att, cp]. The standard interpretation is silent on whether the right-hand sides of any of these equivalences are analyses of their respective left-hand sides or vice versa. Thus, while those who take times to be entities sui generis may view the clauses involving quantification over times as more basic, ersatzists may view the clauses involving no more than quantification over numbers as more basic. Note, however, that even if one takes times to be entities sui generis, one may still take the clauses involving no more than quantification over numbers as more basic. For the clauses involving quantification over times still make use of a tense-logical operator of the form 'At t'; and the significance of this operator is not yet explained by taking times to be entities sui generis. On the most straightforward analysis, the following explains the significance of 'At t': at t, cp == for all n, n days from the present, (t is present::) ~), where '~' ranges over A-statements. 10 Since the right-hand side makes essential use of the metric tense-logical operator 'n days from the present', even a robust realist about times may refuse to take the above clauses involving quantification over times as more basic. In any case, we will often refer to the standard interpretation as 'the standard interpretation of tense-logical operators in terms of quantification over times' , taking talk about interpretations here to be neutral on the direction of analysis. The standard interpretation contrasts with the deviant interpretation. On the deviant interpretation, the familiar tense-logical operators, though definable in terms of metric tense-logical operators in the way suggested, resist further interpretation in terms of quantification over times. In particular, friends of the deviant interpretation will rejeet both of the aforementioned two principles:

10 See footnote 5.

36

2. Real Work for an A-Theory

Always, [n days from the present, 'I' == for some time t n days from the present time, at t, '1'] Always, [n days from the present, 'I' == for all times t n days from the present time, at t, 'I']. The distinction between these two interpretations has its analogue in the distinction between modalism and its opponents. Just as the modalist denies that quantification over possible worlds is apt to capture, or elucidate, the significance of our use of modal operators and thus rejects her opponent's quantification over possible worlds, the friend of the deviant interpretation denies that quantification over times is apt to capture, or elucidate, the significance of our use of tense-Iogica1 operators and thus rejects the standard interpretation. The deviant interpretation is of particular interest to those Presentists who only countenance one time, i. e. the present time, and yet hesitate to attribute massive error to ordinary speakers or to make a vast range of their claims about the past and future trivially true. They would have to do one of the latter, if they accepted one of the two standard principles for 'n days from the present' stated above. In the remainder, we will treat the standard interpretation as the default interpretation deviation from which must be justified. Such a justification will be forthcoming once it can be shown that speakers would otherwise have to be credited with massive error in their use of the familiar tense-Iogica1 operators or be said to make mostly trivial pronouncements about the past or future. One attempt to show this is precisely to argue for Presentism of the kind just adumbrated (see chapter 5). We will henceforth assume that, irrespectively of whether one opts for the standard or the deviant interpretation, one is committed to hold that always, there is a time which is the present time. Thus, we may take even friends of the deviant interpretation to accept: Always, [0 days from the present, 'I' == at the present time, '1'], just as modal anti-realists are happy to accept that necessarily, there is a unique actual world and necessarily, [actually, 'I' iff in the actua1 world,

'1']. Whether the standard or the deviant interpretation is assumed, on either view the following equivalence will always hold: at t, 'I' == always, (t is present::> '1'), where 'at t' functions as a tense-Iogical operator and

2. Real Work for an A-Theory

37

'cp' ranges over A-statements. Consequendy, proponents of either view can move freely from A-statements of the form 'At t, 0 days from the present, R(ab ... )', where 'At t' functions as a tense-logical operator, to B-statements of the form 'At t, R(ab ... )', where 'At t' does not function that way, and vice Vffia. For recall that B-statements of the latter form underwrite the following equivalence which always holds: at t, R(ab ... ) == sometimes, (t is present and 0 days from the present, R(ab .. .)). Given that, always, there is one and only one time that is present, it follows that (always, (t is present::J 0 days from the present, R(ab .. .))) == sometimes, (t is present and 0 days from the present, R(ab ...)). Consequendy, B-statements of the form 'At t, R(ab ... )' are always equivalent to A-statements of the form 'At t, 0 days from the present, R(ab ... )' . Whether understood in terms of the standard Or in terms of the deviant interpretation, the five desiderata previously identified - the Reals - will suffice for the comparative assessment of different versions of the A-theory which we introduce in chapter 4. This comparative assessment, in the light of the desiderata, will then be undertaken in chapters 5 to 7. We readily admit that some of the desiderata are negotiable, and so forego any pretensions that the criticisms we will launch on their basis are, without exception, free of any bias. The Reals, as formulated, draw on the notions of truth-making and constitution. Before we can proceed, we must say mOre about what these notions involve and how they interconnect. This is the purpose of the next chapter, where we will also introduce the notion of the content of a fact.

3 Launehing the Tense Machine In this chapter, we introduce the three key notions of constitution, truthmaking and Jact-content, lay down definitions and axioms involving them and derive further principles from these axioms and definitions. The definitions, axioms and derived principles will set the stage for the classmcation of A-theories that we devise in chapter 4. There, we will use criteria that also involve the three key notions and thus bear inferential connections to the definitions, axioms and derived principles presented here. These inferential connections allow us to prove certain theorems which in turn enable us to give an exhaustive classmcation of mutually exclusive realist views of tense. The proofs of these theorems, as weil as most of the definitions, axioms and principles on which they draw, not only presuppose commitment to the ontologica1 category of facts and the truth-conditional paradigrn in semantics but also certain unargued-for assumptions about time and its structure which were mentioned in the preface, viz. that space-time is non-relativistic, that the time-order is transitive, asymmetrie and linear, and that time is measurable so that, given any two times, there is a certain number which measures their distance, given a previously chosen time-unit (e.g. that of a day). When introducing definitions, axioms and derived principles, we shalliabel them according to the foilowing conventions: 'DI', 'D2', 'D3' etc. denote definitions; 'Al', 'A2', 'A3' etc. denote axioms; and 'PI', 'P2', 'P3' etc. denote principles derived from axioms and definitions. Although we will not always say so, we assume, in compliance with Real-I, that all the axioms, and a Jortiori all the derived principIes, always hold. In most cases, we state the definitions, axioms and derived principles in the vernacular first and then give their appropriate formalisations immediately thereafter. Whenever we state them again in subsequent chapters, we will only give their formalisations. In formulating the definitions, axioms and derived principles, as weil as the criteria to be introduced in chapter 4, we make use of quantification over times, usingthe variable 't' and primed and indexed versions thereof. Quantification over times may either be taken to be sensitive to tense-Iogica1 embedding or be taken to be insensitive to

40

3. Launehing the Tense Machine

such embedding. Throughout, we will presume that quantification over times is neither itself relativised to times, nor reducible to quantification over times which iso We will use the following symbol as a quantifier over times: '3:'. Irrespectively of whether or not one takes '3:t', '3:t" etc. to be sensitive to tense-logical embedding, in either case it will be treated as expressing the most basic notion of quantification over times. We will use 'V' as the corresponding universal quantifier over times, defined in terms of the existential quantifier in the usual way. The reason for our use of these non-standard symbols is precisely that it will as yet be left undetermined whether quantification over times is or is not sensitive to tense-logical embedding. We will use 'm', 'n' etc. as variables ranging over numbers. Quantification over numbers will throughout be understood as being neither sensitive to tense-logical embedding nor relativised to times, and hence as being absolute. In line with how we will use '3' in the context of fact-talk later, we here presuppose that throughout, '3m', '3n' etc. express such quantification over numbers, the corresponding universal quantification being expressed by ''''Im', ''''In' etc. Quantification over expressions of the A-language willlikewise be taken to be absolute, and the same quantifier symbols will be used for the purpose. We do not want to presuppose any specific view about what times are, but we do impose the following constraints on talk about times: (Al) There is a time which is the present time.

3:t(t = to). (A2) All times are of the same nature as the present time, whatever that nature may be (e.g. maximal spatiotemporally related wholes, or maximal consistent totalities of facts, ... ).

Vt(t is of the same nature as to), where 'to' abbreviates the tensed description 'the present time'. So Presentists who take the present time to be the only time which is concrete (or consists in a totality of concrete entities) while all other times are merely abstract (or consist in totalities of merely abstract entities), will here be characterised as holding that there is but one time, i. e. the present time. 11 11

Markosian argues that there are in fact two present cimes, a concrete one and an abstract one. On that view, non-present cimes are of the same nature as the latter, while there

3. Launehing the Tense Machine

41

Given the availability of the deviant interpretation of the tense-Iogical operators introduced in the previous chapter, recasting such Presentist views in this way prejudges no issues: on the one hand, as far as our critical discussion goes, we will exclusively be concemed with that part of the object-language that is devoid of basic structural A-statements; and any ersatzist account of times as purely abstract entities will have to draw on no more than this part of the A-language anyway. On the other hand, the desiderata which were set out in the previous chapter, and which serve as criteria of evaluation, were all formulated in tense-Iogical terms. Consequently, given the availability of the deviant interpretation, denying that there are any times besides the present time does not ab initio put one in any worse position vis-a-vis the desiderata. Reality is the totality of facts. We shall talk about facts constituting reality and about facts constituting reality at a time. Before explicating these locutions, we first distinguish between temporally relative and temporally absolute notions of quantification. We shall use '3' for absolute existential quantification, and the universal quantifier ''r;j' as its dual. We distinguish between two relative notions of existential quantification, one that is relativised to times and one that is tensed. We shall use '3/ for existential quantification relativised to time t, and 'E' for the tensed quantifier. The form '3,xFx' should not be confused with the fonn 'At time t, ExFx', where 'At time t' functions as a tense-Iogical operator. '3,xFx' is true at time to iff among the objects which exist at t, some are F at to, whereas 'At time t, ExFx' is true at time to iff among the objects which exist at t, some are F at t. Thus, neither form entails the other. For instance, let t be a certain time in the year 1600. Then '3,x(x is a dodo alive at t & x has become extinct)' is true at the present time, since there were dodos at t and the whole species has become extinct by the late 17th century. Yet 'At time t, Ex(x is a dodo alive at t & x has is no non-present time of the same nature as the fmmer (Markosian 2004: 75-79). Depending on which of these present times, the concrete or the abstract, is taken as the value of 'to' in Al and A2, Markosian's view will be classified differendy. Note that this does not undermine our aspiration to arrive at an exhaustive classification of mutually exclusive views. For, once it is decided which of Markosian's present times is chosen as the value of 'to', the concrete or the abstract present time, then in the light of A2 quantification over times must be understood in a correspondingly unifonn way. On either choice, Markosian cannot but locate bis view in one place within our classification to the exclusion of any other.

42

3. Launehing the Tense Machine

become extinct)' is false at the present time, because whatever is alive at t cannot have become extinct at t. Obversely, let t be a time at which Neil Armstrong was walking on the moon. Then 'At time t, Ex(x is walking on the moon)' is true at the present time, but '3 t x(x is walking on the moon)' is not, since nothing that existed at t is presendy walking on themoon. We henceforth use 'f' and primed versions thereof as variables ranging over A-facts. There may be disagreement about whether the more basic notion of existential quantification over A-facts is absolute or relative. We assume that any of the views to be considered has a definite answer to this question. H the more basic notion is taken to be absolute, then following the policy just introduced, we let '31' stand for it. In this case, '3 tl' is taken to be defined as follows: 3t/Ff =df 3fFf, and 'EI' as follows: EfFf =df 3tJF f. On that view, thus, '3fF I' is always equivalent to '3 tfFI', '3 tJFI' and 'EfFI'. Let us define ''EI' as follows: 'EfF f =df 3nDn 3tJD- nFf.12 On that view, irrespectively of whether one opts for the standard or the deviant interpretation of the tense-Iogical operators, '3fF f' will always be equivalent to ''EfFf' (see appendix to this chapter). H the more basic notion is taken to be relative, it is either taken to be relativised to times, in which case, following our policy, we let '3t/' stand for it, or taken to be tensed, in which case we let 'EI' stand for it, again following our policy. In the former case, we define '31' as follows: 3fF f =df at3 tfFf, and 'EI' as follows: EfF f =df 3tofFf. We take it that even in this case, '3 tl' is not sensitive to tense-Iogical embedding. (Of course, '3 to l' is so sensitive, given only that, unlike the variable 't', 'ta' is a tensed description.) Consequendy, since 'At t, 3tofFI' is always equivalent to 'At t, at'(t' is present and 3t rfFf)', which in turn is always equivalent to 'At t, 3tfF 1', 'At t, 3tJF I' is always equivalent to '3t/(at t, Ff)'. Consequendy, on the standard interpretation of the tense-Iogical operators '3fFI' will always be equivalentto ''EfF 1'. By contrast, on the deviant interpretation, '3fF f' will always be equivalent

12 Variable 'n' should be so chosen that it does not appear free in 'Ff', on pain of making

the definition defective. Simi!ar conditions on the choice of variables will tacidy be assumed in other definitions below.

3. Launching the Tense Machine

43

"EfFf' just in case '3:t' is not sensitive to tense-logical embedding (see appendix). Next consider the case in which the more basic notion is taken to be tensed. Then we deflne '3rf' as follows: 3t fFf =df 3nD n(t is present& Ef(D-nFf)', and '31' again as follows: 3fFf =df3:t3rfFf· In this case again, '3 t f' is not sensitive to tense-logical embedding. On this account, as on any of the others, 'EfFI' is always equivalent to '3 to fFf'. As before, on the standard interpretation, '3fFI' will always be equivalent to ''L,fFf', and on the deviant interpretation, '3fFf' will always be equivalent to ''L,fFf' just in case '3:t' is not sensitive to tense-logical embedding (see appendix). Proofs of these claims will be given in the appendix to this chapter. We will call a11 views on which '3fFf' is not always equivalent to ''L,fFf' funky. The distinction between funky and non-funky views will become important in chapter 5, where we will discuss how Presentists can comply with the Reals. With these considerations conceming existential quantification in place, we now stipulatively deflne absolute and relative constitution in terms of existential quantification over A-facts: to

(D1) C(f) =df 31' (f = 1') (D2) c(f,t) =df 3 t f' (f = f'),

where 'C(f)' abbreviates 'f constitutes reality' and 'c(f,t)' abbreviates 'f constitutes reality at t'. Given that '3fFI' and '3:t3rfFI' are always equivalent, we accordingly get: (P1) C(f) =3:tc(f,t).

For those who take the basic notion of quantification to be absolute, D2 boils down to: c(f,t) =df 31' (f = 1'),

and so, for them, absolute constitution is more basic than relative constitution. By contrast, those who take the basic notion of quantification to be relative deny that '31' (f = 1')' is sufficient for 'c(f,t)'. We shall call those who take the basic notion of quantification to be absolute, and hence absolute constitution to be more basic than relative constitution, eternalists. Etemalists hold that for something to be a fact is for it to constitute reality at some time and that a11 it takes

44

3. Launching the Tense Machine

for something to constitute reality at any given time is for it to be a fact. On this view, facts are etemal. By contrast, for those who take the basic notion of quancification to be relative, D1 bOlls down to:

C(f) =df 3.t3t!' (f = ['), and so, for them, relative constitution is more basic than absolute constitution. Those who take the basic notion of quancification to be relative, and hence relative constitution to be more basic than absolute constitution, concur with the etemalists that for something to be a fact is for it to constitute reality at some time, but they deny that all it takes for something to constitute reality at any given time is for it to do so at some time. Still, they may or may not be sempiternalists. Sempitemalists hold that although for something to constitute reality at some time is not ipso facta for it to constitute reality at t, for any time t, it is nonetheless a further fact about temporal reality that all facts constitute reality at all times. Sempitemalists thus deny that there is factudl variation over time in the following sense of 'factual variation': (D3) There is factual variation =df 3.t3.t'3f(C(f,t) & ~c(f,t')). On this, sempitemalists and etemalists agree. But this should not obscure the fact that they hold opposed views about the nature of quancification and hence constitution. Their opposition lies in their disagreement about which notion of quancification is basic, and so which notion of constitution is more basic than the other. Never mind whether one regards basic quancification as absolute or relative, on either view, the following axiom is taken to hold: (A3) Every fact constitutes reality at some time.

3.tc(f,t). A3 and all the following axioms and derived principles must be understood as having their free variables bound by outer universal quancifiers of the appropriate sorts. We henceforth use 's' and primed versions thereof as ranging over basic material A-statements, and 'p', 'q' etc. as ranging over the tensefree predications from which basic material A-statements are built (see chapter 1). Unless indicated otherwise, we mean A-facts whenever we

45

3. Launehing the Tense Machine

speak of facts, and basic material A-statements whenever we speak of statements . Next consider: (A4) Some fact constitutes reality at the present time.

3fc(f,ta), where 'ta' is again short for the tensed description 'the present time'. All views to be considered will be taken to accept A4. Some of the views to be considered even entail it. Next we lay down the following definition of the truth-set of a fact at a time: (D4) The truth-set of a fact at a given time is the set of a11 the statements that this fact makes true at that time.

TS(f,t)

=df

{s If makes 5 true at t}.

It is of the essence of facts that they sometime serve as truth-makers. Even if our A-language as it presently is does not contain for each fact a statement sometimes made true by that fact, an idealised version of that language will. Furthermore, in order to serve as a truth-maker at a given time, a fact must exist at that time. We thus take the following two principles as axioms: (A5) Every fact at some time makes some statement true.

3.tTS(f,t) * 0.

(A6) If a fact makes some statement true at a given time, then it constitutes reality at that time.

TS(f,t) * 0

::J

c(f,t).

Facts have a content in the sense that they satisfy fact-descriptions of the form 'is a fact that 5'. Accordingly, to specify conditions under which a fact satisfies such adescription is to specify conditions under which that fact has a specmc content. We define satisfaction, and hence (fact-)content, as follows: (D5) A fact satisfies a given fact-description at a given time just in case if this fact were to make any statement true at that time, it would make the statement corresponding to that fact-description true at that time.

f satisfies 'is a fact that 5' at t =df (TS(f,t)

*0

D--+ 5 E

TS(f,t)).

3. Launching the Tense Machine

46

We here assume an interpretation of subjunctive conditionals according to which such a conditional is not already true if its antecedent is impossible (d. Nolan 1997). Next we lay down the following definition of the statement-set of a fact at a time: (D6) The statement-set of a fact at a given time is the set of all the statements whose corresponding fact-descriptions this fact satisfies at thattime.

SS(f,t) =df {s 1I satisfies 'is a fact that s' at t}.

From DS and D6 we can derive: (P2)

H a fact makes a given statement true at a given time then it satisfies the corresponding fact-description at that time.

TS(f,t) s; SS(f,t). Thus, suppose that statement s belongs to TS(f,t). Then trivially, TS(f,t) '* 0. Exploiting the general principle that if A and Bare true, then so is A D---+ B, it follows that TS(f,t) * 0 D---+ 5 E TS(j,t), and so, by DS and D6, that s belongs to SS(f,t). DS and D6 also allow us to derive: (P3)

Ha fact makes some statement true at a given time, then it makes all and only the members of its statement-set at that time true at thattime.

TS(f,t) '* 0 ::> TS(f,t) = SS(f,t).

'*

Thus, suppose that TS(f,t) 0 and that s belongs to SS(f,t). Then by D6 and DS, TS(f,t) 0 D-+ s E TS(f,t). So by modus ponens for the subjunctive conditional, s belongs to TS(f,t). This establishes that TS(f,t) 0::> TS(f,t);2 SS(f,t). By P2, we immediately have TS(f,t) 0 ::> TS(f,t) s; SS(f,t). Facts are not ineffable. Even if our A-Ianguage as it presently is does not contain a fact-description for every fact, an idealised version of that language will. We thus lay down:

'*

'*

'*

(A7) For every time and every fact, there is some fact-description which this fact satisfies at that time.

SS(f,t),* 0.

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3. Launching the Tense Machine

We also assume as unproblematic that, at any one time, facts only ever satisfy fact-descriptions with the same tense in their embedded

that-clause: (A8) At no time does a fact satisfy both 'is a fact that n days from the present, p' and 'is a fact that m days from the present, cf with m distinct from n.

n * m ::J -, { 'DnP', 'Dmq'} ~ SS(f,t),

where, to recall, 'DnP' abbreviates 'n days from the present, p'. We cannot assume the stronger principle: At no time does a fact satisfy both 'is a fact that n days from the present, p' and 'is a fact that m days from the present, q' with m distinct from n or p non-equivalent to q.

(n* m v -,DV'iD; V' k(DkP == Dkq)) ::J -,{ 'Dnp','Dmq'} SS(f,t).

~

For it is plausible to say e. g. that if a fact satisfies 'is a fact that n days from the present, a is red' at a given time, it also satisfies 'is a fact that n days from the present, a is coloured' at that time. 13 In addition to AS and A7, we presuppose that an idealised version of our A-language satisfies the following constraint: 13 On one view, dererrninables are equivalent to the disjunction of their deterrninates, and

so are logically complex. Insofar as we impose the same restriction on the predicates featuring in fact-descriptions that we imposed on those which feature in basic A-statements, that view would make the stronger principle immune to such counterexamples. Yet this view about determinables is controversial, and we therefore do not want to assume it. Not to assume such a view, and so rather to allow that facts satisfying determinate descriptions also satisfy determinable descriptions, is not to open the floodgates and claim that if 'O\fiD; \f k(DkP::J Dkq))' holds, then anything that satisfies 'is a fact that n days from the present, p' also satisfies 'is a fact that n days from the present, q'. Thus, consider the fact that presently a is red and the distinct fact that presently a is oval-shaped whose truth-sets are now non-ernpty. H both these facts were presently to satisfy the description 'is a fact that presently, a is extended', then by D5, both these facts would make 'Presently, a is extended' true. However, we might reasonably wish to maintain that a fact makes a statement true only if it explains the truth of that statement in some more demanding sense of 'explain': while a red thing is coloured at a given time in virtue of its being red at that time - its being red explains why it is true to call it 'coloured' -, it is not the case that a red thing is extended at a given time in virtue of its being red at that time - its being red does not explain why it is true to call it 'extended'.

48

(A9)

3. Launehing the Tense Machine

For any time, if two facts have the same statement-set at that time, then, at that time, they have the same subjects in the same order and the same predicables.

SS(f,t) = SS(f',t) ::> at t,! and f' have the same subjects in the same order and the same predicables.

For example, if at t, both! and f' satisfy Cis a fact that n days from the present, a is coloured', yet ! has the property of being red as its predicable, while f' has the property of being blue as its predicable, then the idealised A-Ianguage will contain fact-descriptions apt to capture this difference between! and f' so that the statement-set of! at twill differ from the statement-set of f' at t (e.g. the first but not the second will contain n days from the present, ais red'). As we shall see, A-theories differ according to whether or not they allow facts to change their fact-descriptions over time. The following two principles, though neutral on this matter, formulate some constraints on either type of theory: C

(A10) Either for every fact and every fact-description, this fact satisfies this fact-description at all times if it does so at any time, or for every fact and every fact-description, this fact does not satisfy this fact-description at distinct times.

VtVt'V!(SS(f,t) = SS(f,t')) v VtVt'V!(t* t'::> SS(f,t) n SS(f,t') = 0). For any view on which there is only one time, AlO will be vacuously true. For all other views, AlO is just the expression of a claim of systematicity with respect to content-ascriptions: whether a given fact ! differs in content from time to time or does not do so, in neither case will it behave any differently from any other fact. (All) For any two times t and t' such that t' is m days from t, if some fact satisfies Cis a fact that n days from the present, p' at t but not at t', then it satisfies Cis a fact that (n-m) days from the present, p' at t'.

(t' is m days from t & cDnP' E SS(f,t)) ::> ('DnP' I$: SS(f,t') ::> cDn_mp' E SS(f,t')). Again, for any view on which there is but one time, All will be vacuously true. On any other view, All specifies the only sensible way

49

3. Launehing the Tense Machine

in which one and the same fact may be said to differ in content from time to time. The following principle can be derived from AIO and All: (P4)

For any two facts, if these facts have the same statement-set at one time, they also have the same statement-set at any other time.

55(f,t) = 55(f',t) => 55(f,t') = 55(f',t'). Thus, suppose 55(f,t) = 55(/"t). Then there are three cases we have to consider. Case 1: the first disjunct of AIO holds. Then trivially, 55(f,t') = 55(/"t'). Case 2: the second disjunct of AIO holds and t = t'. Then trivially, 55(f,t') = 55(f',t'). Case 3: the second disjunct of AIO holds and t* t'. Then t is m days from t' with m*O. Let 'DnP' be a member of 55(f,t'). By the second disjunct of AIO, 'DnP' $ 55(f,t), and so by All, 'Dn-mp' E 55(f,t). Therefore, 'Dn-ml E 55(/"t). By the second disjunct of AIO, it follows that 'Dn-mP' $ 55(f',t'). By All, we have: 'DnP' E 55(/"t'). We have thus established that 55(f,t') !; 55(f',t'). The proof that 55(f,t') ;2 55(f',t') proceeds along the same lines. Next consider:

(A12) If two facts have the same statement-set at some time and at some time both constitute reality, then they are identica1.

55(f,t) = 55(f',t) => «c(f,t') & C(/"t')) => f

= /').

The rationale for this axiom is this. 5uppose 55(/"t) = 55(f,t). By P4, then, for all t", 55(/"t") = 55(f,t"). By A9, f and /' always share the same subjects in the same order and the same predicables. 50 supposing that fand /' both constitute reality at t', it is hard to see how fand /' could nonetheless be distinct. From A12, P3, A6 and A7, we can derive: (PS)

If all and only the members of the statement-set of fact f at a given time are made true at that time by some fact /', then if f constitutes reality at that time, fand /' are identica1.

T5(f',t) = 55(f,t) => (c(f,t) => f = /'). Thus, suppose T5(f',t) = 55(f,t). Then by P3 and A7, 55(f',t) = 55(f,t). By A6 and A7, /' constitutes reality at t. 50 supposing that f also constitutes reality at t, then by A12, f = /'.

50

3. Launehing the Tense Machine

We lay down the following principle of parsimony as a further axIom: (Al3) For any two times t and t' such that t' is m days from t, if a fact makes 'n days from the present, p' true at t, then there is no distinct fact that makes the statement 'n-m days from the present, p' true at t'.

(t' is m days from t & j =*' j') ::::> ('DnP' TS(j',t')).

E

TS(f,t)

::::>

'Dn-mp' $

The rationale for accepting this principle as a further axiom is this. Suppose that t' is m days from t and that 'DnP' E TS(f,t). Consequently, given the necessity of the truth-value links, that 'Dn-mp' is true at t' is necessitated, and fully accounted for, by its being the case that 'DnP' E TS(f,t), and so it need not be made true at t' by any further fact distinct from j. Postulating such a further fact would be to sin against Ockham's principle of ontological parsimony.14 Let us define incompatibility of fact-contents as folIows: (D7)

The content of j at t is incompatible with the content of j' at t' =df j satisfies a fact-description at t and j' satisfies another fact-description at t' such that the statements corresponding to these fact-descriptions cannot be true together.

INc(j,t,j',t') =df 3s3s'(s E SS(f,t) & s' E SS(f',t') & --.O(3nD n (s & s')), where 'INc(j,t,j',t'), is short for 'The content of j at t is incompatible with the content of j' at t". We will occasionally speak of two facts j and j' having incompatible contents at some times and thereby mean that .3:t.3:t' INc(j,t,j',t'). To the extent that there is more than one time at which some fact constitutes reality, i. e. that there are at least two distinct 'non-empty' times, it is natural to think of temporal reality as being variegated over 14

A 13 remains plausible even if it is demanded that a fact makes a statement true only if it explains the truth of that statement, in the demanding sense in which, say, the fact that presently, ais red does not explain the present truth of 'Presently, a is extended'. Thus, if f makes 'Presently, a is red' true at t, and so explains why 'Presently, aisred' is true at t, then for any time t' m days from t, the truth at t' of '-m days from the present, a is red' requires no further explanation not already provided for by f's making 'Presently, ais red' true at t.

51

3. Launehing the Tense Machine

time in the sense that, at different times, different tensed statements are made true that cannot joincly be true at any one time. Bearing in mind P3, i.e. TS(f,t):::j:: 0 ~ TS(f,t) = SS(f,t), we thus lay down: (A14) If there are facts constituting reality at distinct times, then there are also facts with incompatible contents at distinct times such that each makes the corresponding statement true at those times.

3f3f'3.d.t'(t:::j:: t' & C(f,t) & C(f',t'))

~

3f3f'3.t3.t'(t:::j:: t' &

TS(f,t):::j:: 0 & TS(f',t'):::j:: 0 & INC(f,t,f',t')). This completes our list of definitions, axioms and derived principles. In the next chapter, we will introduce a set of criteria that will enable us to give an exhaustive classification of mutually exclusive A-theories.

Appendix I. If the more basic notion of quantification over A-facts is taken to be absolute, '31' stands for that notion, and the following definitions are adopted: (Def.1) 3t fFf

3fFf (Def. 2) EfF f =df 3to f Ff· (Def. 3) ~fFf =df 3nD n3t JD- nFf. =df

Lemma 1. '3fFI' is always equivalent to '3 t fF 1', '3 t JF 1', 'EfF I' and '~fFI'.

Proof The only stated equivalence which is not trivial is the fourth one. It can be shown to hold as follows. By (Def. 3), '~fFI' is always equivalent to '3nD n3t JD -nF f'. Since '3fFI' is always equivalent to '3 t JFI', it follows that '~fFI' is always equivalent to '3nD n3fD_ nF1'. But since '3' is absolute, it is not sensitive to tenselogical embedding, and consequencly '3nD n3fD -nF f' is always equivalent to '3f3nD nD_ nFI', which, by tense-logical reasoning, is always equivalent to '3fFI'. Hence, '3fFI' is always equivalent to '~fFI'.

QED 11. If the more basic notion of quantification over A-facts is taken to be relativised to times, '3 tl' stands for that notion, and (Def. 3) as well as the following definitions are adopted:

52

3. Launehing the Tense Machine

(Def.4) 3fFf=-df'3.t3 tfFf (Def. 5) EfF f

=-df

3to f Ff.

Lemma 2. (i) H quantification over times is sensitive to tense-logical embedding, then '3fFf' is always equivalent to 'EfFf'. (ii) On the standard interpretation of the tense-logical operators, '3fF f' is always equivalent to 'LIFf'. (iii) On the deviant interpretation, '3fFf' is always equivalent to '~fFI' iff ''3.t' is not sensitive to tense-logical embedding.

Proof of (i). By (Def. 4), '3fFf' is always equivalent to ''3.t3tfFf'. H quantification over times is sensitive to tense-logical embedding, then the latter is always equivalent to '3tofFf', which by (Def. 5) is always equivalent to 'EfF

1'.

Proof of (ii). By (Def. 3), '~fFf' is always equivalent to '3nD n3tof D -nF Assuming the standard interpretation of the tense-logical operators, the latter is always equivalent to:

1'.

(a) 3n'3.t(t is n days from to & at t: 3t of'3.t'(t' is -n days from t & at t': Ff)).

Hquantification over times is sensitive to tense-logical embedding, then (a) is always equivalent to '3 tofFf' and so by (Def. 5) to 'EfFf'. By (i) above, we can conclude that '3fFI' is always equivalent to '~fF f'. Suppose now that quantification over times is not sensitive to tense-logical embedding. Then (a) is always equivalent to:

(b) 3n'3.t(t is n days from to & at t: 3tf at to: Ff), which is always equivalent to ''3.t3 tfFf', and hence by (Def. 4) to '3fFf'. Thus, if quantification over times is not sensitive to tenselogical embedding, then again '3fFf' is always equivalent to '~fFf'.

Proof of (iii). Assurne now the deviant interpretation of the tense-logical operators. Suppose first that quantification over times is sensitive ''3.t3 t fF f' is always equivalent to '3 tofF which is obviously not always equivalent to '3nD n3tofD_ n Ff'. Hence in this case, '~fFf' is not always equivalent to '3fFf'. Suppose now that quantification over times is not sensitive to tense-logical embedding. Given that '3nD n3tofD -nFI' is always equivalent to '3nD n'3.t(t is present & 3tfD_ nFf)', it follows that '~fFI' is always to tense-logical embedding. Then

1',

3. Launehing the Tense Machine

53

equivalent to 'at3nD n{t is present & 3tfD_ nFf)'. Given that every time is sometimes present, and that '3,' is never sensitive to tense-logical embedding, the latter is always equivalent to 'at3 tf3nD nD- nFf', which in turn is always equivalent to 'at3 tfFf'. Hence by (Def. 4), '3fFf' is always equivalent to ''L,fFf'. QED

III. If the more basic notion of quantification over A-facts is taken to be tensed, 'EI' will stand for that notion, and (Def. 3) and (Def. 4) as weIl as the foIlowing definition will be adopted: (Def. 6) 3,fFf =df 3nD n{t is present & EfD_nFf). Lemma 3. (i) If 'at' is sensitive to tense-logical embedding, then '3fFI' is always equivalent to 'EfF f'. (ü) On the standard interpretation of the tense-logical operators, '3fFf' is always equivalent to ''L,fFf'. (üi) By contrast, on the deviant interpretation, '3fFI' is always equivalent to ''L,fFf' iff 'at' is not sensitive to tense-logical embedding. (iv) 'EfFI' is always equivalent to '3 t JF1'.

Proof of (i). By (Def. 4), '3fFf' is always equivalent to 'at3 tfFf', which by (Def. 6) is always equivalent to:

(c) at3nD n(t is present & EfD_nFf).

If quantification over times is sensitive to tense-logical embedding, then clearly (c) is always equivalent to 'EfFf'. Proof of (ü) and (üi). By (Def. 3), ''L,fFf' is always equivalent to '3nDn3tJD-nFf', and by (Def. 6), the latter is always equivalent to:

(d) 3nD n3mDm{to is present & EfD-mD-nFf). Since always, to is present, (d) is always equivalent to:

(e) 3kDk EfD_ k Ff. By (Def.4), '3fFI' is always equivalentto 'at3tfF1', which by (Def. 6) is always equivalent to:

(f) at3nD n(t is present & EfD_nF f). Suppose first that 'at' is not sensitive to tense-logical embedding. Then (f) is equivalent to '3nD nat(t is present & EfD_nF f)" and since there is always a present time, this is equivalent to (e). So in this case, '3fFI' is always equivalent to ''L,fFf'. Suppose now that 'at' is sensitive to

54

3. Launching the Tense Machine

tense-Iogical embedding. Then as we saw above, (f) is equivalent to 'EfFf'. Clearly, granted the deviant interpretation of the tense-Iogical operators, (e) is not always equivalent to 'EfFf', and so in this case, '3fFf' is not always equivalent to T.fFf'. Suppose now that the standard interpretation is correct. Then (e) is always equivalent to: (g) 3k3:t(t is k days from to & at t: Ef3:t'(t' is -k days from t & at t':

Ff)). Given that '3:t' is sensitive to tense-Iogical embedding, (g) must be always equivalent to 'EfFf'. Hence in this case, '3fFf' is always equivalent to ''L.fFf'.

Proof of (iv). By (Def. 6), on its intended reading, '3 t JF f' is always equivalent to:

(h) 3:t(t= to & 3nDn(t is present & EfD_nF f)). Since always, to is present, and always, any time identical with to is such that it is only present 0 days from the present, (h) is always equivalent to 'EfF f'. QED

4

Criteria for Realist Views of Tense In this chapter, we devise an exhaustive classification of mutually exclusive realist views of tense. To this end, we introduce a set of criteria for distinguishing between them. These criteria are given as principles and are labeled using descriptive names in small caps which will allow us to name the views classified by their means in systematic ways. For every criterion, each view either accepts it or denies it. Acceptance is understood to imply taking the relevant principle as being lawlike and hence as nomologica1ly necessary. Sometimes denial implies taking the negation as being nomologica1ly necessary. Sometimes it merely implies taking the negation as being nomologically possible. (Assuming that at least in the present context, 'ON. entails 'DON., none of the views to be considered takes the claims they accept to be true or false merely as a matter of course.) Accordingly, we take the space of dialectical possibilities to be determined not by the criteria themselves, but rather by their nomological necessitations. In later chapters, we shall treat other controversial principles, that allow us to draw further distinctions, in just the same way and also label them using descriptive names in small caps. All the criteria are formulated in terms of quantification over times. That is, there are no additional criteria in play that would only be equivalent to some of the first kind if the standard interpretation was adopted. This does not imply any illicit presumption in favour of the standard interpretation. We are after an exhaustive classification of mutually exclusive views; and for this purpose one such classification will do. Even those who opt for the deviant interpretation will have to pronounce on the alethic status of the criteria we lay down. Adding further criteria would merely yield a second classification; and there is no clear use such a second classification would have. In chapters 5 to 7, we will then criticise the views identified in the light of the desiderata set out in chapter 2. At that stage, it will indeed be crucial to bear in mind that the deviant interpretation is available and also that there are those views we ca1led funky at the beginning of the last chapter. But neither the availability of the deviant interpretation nor that of funky views undermines the classification of the views to be criticised.

56

4. Criteria for Realist Views of Tense

We shall see that the definitions, axioms and derived principles given in the previous chapter allow us to prove certain theorems conceming the relations between the criteria suggested. These theorems are boldfaced and will be labeled using 'Tl', 'T2', 'T3' etc. Their proofs will be given immediately after their introduction. 'Proof' marks the beginning of a proof, 'QED' marks its end. The first two criteria to be introduced in this chapter are refinements of criteria originally conceived by Fine (Fine 2005: 271). The remaining criteria, by contrast, are entirely new. We will discuss the relation between these criteria and those proposed by Fine more fully in chapters 7 and 9. The first criterion can be formulated thus: (ABSOLUTISM)

The basic notion of constitution is absolute (etemalism), or it is relative but there is no factual variation

(sempitemalism) . c(f,t). Here, and in what follows, whenever we speak of the basic notion of constitution being absolute (relative), this will be shorthand for saying that the absolute (relative) notion of constitution is more basic than the relative (absolute) notion. Recall that to deny that there is factual variation is to deny that there are twO times and a fact such that this fact constitutes reality at one of these times but not at the other:

(D3) There is factual variation =df at3.t'3f(C(f,t) & -,C(f,t'». ABSOLUTISM contrasts with RELATIVISM according to which the basic notion of constitution is relative and there is factual variation in this sense. Although either claim is meant to be put forward as being nomologically necessary, we take ABSOLUTISM and RELATIVISM to exhaust the options: acceptance of RELATIVISM equals acceptance of NON-ABSOLUTISM and so denial of ABSOLUTISM. Which notion of constitution is more basic is no nomologically contingent affair, and, we submit, it is not a nomologically contingent affair either whether or not there is factual variation. For this reason, there is no need to list RELATIVISM as a further criterion. A-theories may also differ depending on whether or not they endorse the following claim, which serves as our second criterion:

4. eriteria for Realist Views of Tense

57

(NEUTRALITY) Some fact constitutes reality at some time distinct from the present time.

3f'Flt(t* to & c(f,t)). Given A4, NEUTRALITY entails that there are at least two distinct times t and t' such that some fact constitutes reality at t and some fact constitutes reality at t': (A4)

3fC(f,to).

Denial of NEUTRALITY entails A4. For, given realism about A-facts and A3, some fact constitutes reality at some time, so if NEUTRALITY fails, this time must be the present time: (A3)

'Fltc(f,t).

We shall take denial of NEUTRALITY, and so acceptance of NONNEUTRALITY, to equal acceptance of PRESENTISM according to which ''VfVt(t* to => -,C(f,t))' holds as a matter of nomological necessity. Whether there is a non-empty time besides the present time cannot reasonably be taken to be a nomologically contingent affair. There is thus no reason to list PRESENTISM as a further criterion. The third criterion formulates a sufficient condition for the identity of facts:

(UNIQUENESS) H two facts have the same statement-set at some time, they are identical.

SS(f,t) = SS(f',t) => f

=

1'.

Notice that UNIQUENESS is stronger than A12: (A12) SS(f,t)

= SS(f',t) => «c(f,t') & C(f',t')) => f = 1').

Just like ABSOLUTISM and NEUTRALITY, UNIQUENESS is meant to be put forward as a claim that holds as a matter of nomological necessity. To deny that UNIQUENESS holds as a matter of nomological necessity is not yet to accept '3f3f''Flt(SS(f,t) = SS(f',t) & f *1')' as true, let alone to accept it as nomologically necessary. Given A5, A6, P3, P4 and P5, the truth of '3f3f''Flt(SS(f,t) = SS(f',t) & f 1')' would imply the claim that some statement is true at different times:

*

(A5) (A6)

'FltTS(f,t) * (2) TS(f,t) * (2) => c(f,t)

58

4. eriteria for Realist Views ofTense

(P3)

TS(f,t) * 0

(P4)

SS(f,t) = SS(f/,t) :::> SS(f,t ' ) = SS(f',t ' )

(P5)

TS(f/,t) = SS(f,t) :::> (C(f,t)

:::> TS(f,t)

= SS(f,t) :::> f

= 1').

Such claims about the nomologically contingent course of history cannot reasonably be viewed as an integral part of any metaphysical theory. Thus, in order to deny UNIQUENESS it will do to accept '3f3f' 3:t(SS(f,t) = SS(f',t) & f 1')' as nomologically possible. Given that 'ON. entails 'DON., this claim will itself be put forward as holding with nomological necessity. Our fourth criterion concems the content of facts across time:

*

(FIXED-CONTENT)

A fact has the same statement-set at all times.

SS(f,t) = SS(f,t ' ). According to FIXED-CONTENT, if a fact satisfies 'is a fact that n days from the present, p' at some time, it does so at all times. FIXEDCONTENT contrasts with (SHIFTy-CONTENT)

A fact has disjoint statement-sets at dilierent times.

t* t ' :::> SS(f,t) n SS(f,t ' ) = 0. Given All, SHIFTY-CONTENT implies that if at t, a given fact satisfies 'is a fact that n days from the present, p', then at t ' m days from t, that fact satisfies 'is a fact that n-m days from the present, p': (All) (t' is m days from t & 'DnP'

E

SS(f,t))

:::>

('DnP'

~ SS(f,t' ) :::>

'Dn-mp' E SS(f,t ' )). Given AIO, FIXED-CONTENT and SHIFTy-CONTENT exhaust the options, and hence there is no middle ground between denial of one and acceptance of the respective other: (Al 0) VtVt'Vf(SS(f,t) = SS(f,t ' )) v VtVt'Vf(t* t ' :::> SS(f,t) n

SS(f,t ' ) = 0).

However, as the following theorem shows, some views can accept both these principles, which makes it worthwhile including SHIFTYCONTENT as a further criterion alongside FIXED-CONTENT:

4. eriteria für Realist Views üf Tense

(Tl)

59

If ABSOLUTISM and NON-NEUTRAllTY both hold, then both FIXED-CONTENT and SHIFlY-CONTENT hold.

Proof Assume NON-NEUTRALITY and ABSOLUTISM. Suppose then that there is a time t distinct from the present time. Given A4 and ABSOLUTISM, there is a fact which constitutes reality at t: (A4)

3fC(f,to).

This contradicts NON-NEUTRALITY. Therefore, there is only one time, i. e. the present time. Consequently, FIXED-CONTENT is trivially true and SHIFTy-CONTENT is vacuously true. QED Accordingly Absolutist Presentists will accept both FIXED-CONTENT and SHIFTY-CONTENT. By contrast, Relativist Presentists must choose between them:

(T2)

IfNoN-ABSOLUTIsM and NON-NEUTRALITY both hold, then not both FIXED-CONTENT and SHIFlY-CONTENT hold.

Proof Assume NON-NEUTRALITY. Then by A3, there is a present time and all facts constitute reality at it and at no other time: (A3)

~tc(f,t).

Suppose NON-ABSOLUTISM. Then by A7, there is a time t m days from the present time with m 0 and a fact f such that f satisfies a fact-description 'is a fact that n days from the present, p' at t, but does not constitute reality at t:

*

(A7)

SS(f,t) * 0.

Suppose both FIXED-CONTENT and SHIFTY-CONTENT hold. Then given FIXED-CONTENT, at the present time, f satisfies 'is a fact that n days from the present, p'. By SHIFTY-CONTENT and Alt, at the present time, f satisfies 'is a fact that n +m days from the present, p' : (Alt) (t' is m days from t & 'Dnp'

E

SS(f,t» => ('DnP'

'Dn-mp' E SS(f,t'».

*SS(f,t') =>

However, this contradicts A8: (A8)

n * m => -.{ 'DnP' ,'Dmq'} ~ SS(f,t).

So not both FIXED-CONTENT and SHIFTy-CONTENT hold. QED Similarly, the following theorem holds:

60

(T3)

4. eriteria for Realist Views of Tense

H NEUTRAUfY holds, then not both FIXED-CONTENT and SHIFTY-CONTENT hold.

Proof Assume NEUTRALITY. Let f be a fact constituting reaIity at

*'

a time t m days from the present time with m o. By A7, at t, f satisfies some fact-description Cis a fact that n days from the present, p'. Suppose both FIXED-CONTENT and SHIFTY-CONTENT hold. Given FlXED-CONTENT, at the present time, f satisfies Cis a fact that n days from the present, p'. By SHIFTY-CONTENT and All, at the present time, f satisfies cis a fact that n +m days from the present, p'. This contradicts A8. QED We next prove theorems that yield sufficient conditions for UNIQUENESS:

(T4)

H ABSOLUTISM holds, then so does UNIQUENESS.

Proof Let fand I' be facts and t be a time such that SS(f,t) = SS(f',t). By Al2, then, for every time t', if both C(f,t') and C(f',t'), then f =

1':

(Al2) SS(f,t) = SS(f',t) => «C(f,t') & C(f',t'» => f =

1').

By A3, if we assurne ABSOLUTISM, we can conclude that f (A3)

= 1':

'a.tC(f,t).

Therefore, if ABSOLUTISM holds, UNIQUENESS holds. QED

(T5)

H NON-NEUTRAUfY holds, then so does UNIQUENESS.

I'

Proof Let fand be facts and t be a time such that SS(f,t) = SS(f',t). Assurne NON-NEUTRALITY. Then by A3, C(f,to) and C(f',to). By Al2, then,f = Therefore, UNIQUENESS holds. QED

1'.

(T6)

H SHIFTY-CONTENT holds, then so does UNIQUENESS.

Proof Assume that UNIQUENESS fails. By A7, there then are a time t and two distinct facts fand I' such that, at t, f and I' satisfy some fact-description cis a fact that n days from the present, p' : (A7)

SS(f,t) *' 0.

By AS, there is a t' k days from t and a t" 0 days from t' such that, at t', f makes some statement true and, at t", makes some statement true:

I'

4. Criteria for Realist Views of Tense

(A5)

61

3:tTS(f,t) * 0.

f

By SHIFTY-CONTENT and All, at t', satisfies 'is a fact that n-k days from the present, p' and, at t", satisfies 'is a fact that n-(k+o) days from the present, p':

I'

(All) (t' is m days from t & 'DnP' E SS(f,t)) :::> ('Dnp' 'Dn-mp' E SS(f,t')).

$

SS(f,t') :::>

f

By P3, at t', makes 'n-k days from the present, p' true and, at t", makes 'n-(k+ 0) days from the present, p' true:

(P3)

TS(f,t)

*0

I'

:::> TS(f,t) = SS(f,t).

By A13, it follows that

f = 1':

(A13) (t' is m days from t & f TS(f',t')).

* 1') :::> ('DnP' E TS(f,t) :::> 'Dn-mp' $

Contradiction! So UNIQUENESS holds. QED Theorems Tl to T6 show that the following are the only consistent positions:

+ NON-NEUTRALITY SHIFTY-CONTENT + UNIQUENESS

(I) ABSOLUTISM

+ FIXED-CONTENT +

(TI) RELATIVISM + NON-NEUTRALITY + FIXED-CONTENT + UNIQUENESS

(llI) RELATIVISM

+ NON-NEUTRALITY + SHIFTY-CONTENT +

UNIQUENESS

+ NEUTRALITY + FIXED-CONTENT +

(IV) ABSOLUTISM UNIQUENESS

(V) RELATIVISM + NEUTRALITY + FlXED-CONTENT + UNIQUENESS

(VI) ABSOLUTISM + NEUTRALITY + SHIFTy-CONTENT + UNIQUENESS

(Vll) RELATIVISM

+ NEUTRALITY + SHIFTY-CONTENT +

UNIQUENESS

(VIII) RELATIVISM + NEUTRALITY + FIXED-CONTENT + NON-UNIQUENESS

4. eriteria for Realist Views of Tense

62

All these positions are mutually exclusive. Position (I) is what we called 'Absolutist Presentism', while (II) and (III) are two versions of what we called 'Relativist Presentism'. As we shall see in due course, there is a natural way of grouping the remainder: positions (IV) and (V) are versions of what we shall call 'Recurrentism', while (VI), (VII) and (VIll) are versions of what we shall call 'Non-Recurrentism'. As we shall see, (VIll) allows for two versions, one of which has an important feature in common with (VII). Consider: (RECURRENCE)

H a fact f makes all the statements in its statement-set at a given time true at that time, then if some fact /' makes all and only those statements true at another time, f and /' are identical. (t' * t & SS(f,t) ~ TS(f,t) & TS(f',t') = SS(f,t)) ::) f = /'.

RECURRENCE in effect claims that, for all statements made true by a given fact at one time, if exactly the same statements were to be made true at another time, their truth-maker would again be that same fact which would accordingly 'recur' in the sense of giving a reprise in its role as a truth-maker of the same statements. The opposite claim is: (ANTI-REcURRENCE)

Ha fact f makes all the statements in its statement-set at a given time true at that time, then if some fact /' makes all and only those statements true at another time, f and /' are distinct.

(t' * t & SS(f,t) ~ TS(f,t) & TS(f',t') = SS(f,t)) ::) f * /'.

It is evident that Presentists, be they Absolutists or Relativists, must accept both RECURRENCE and ANTI-REcURRENCE: while for the Absolutist Presentist the first conjunct of the common antecedent is false as a matter of principle, for the Relativist Presentist there are no two distinct times underwriting the remaining conjuncts, given only A6 and A7:

* 0 ::) c(f,t) SS(f,t) * 0.

(A6) TS(f,t) (A7)

To effect the advertised grouping of positions (IV) and (V) and positions (VI), (VII) and (VIll), respectively, we prove the following theorems:

4. Criteria for Realist Views of Tense (T7)

63

IfFIXED-CONfENT and UNIQUENESS both hold, then so does RECURRENCE.

Proof Suppose that the antecedent of RECURRENCE is satisfied, i. e. that there are two facts f and I' and two distinct times t and t' such that f makes all the members of its statement-set at t true at t and I' makes all and only the members of the statement-set of f at t true at t'. By A7 above and P3, the statement-set of I' at t' = the statement-set of f at t: (P3)

TS(f,t) '*' 0 ~ TS(f,t) = SS(f,t).

By FIXED-CONTENT, it follows that the statement-set of I' at t' = the statement-set of f at t'. By UNIQUENESS, it follows that f = 1'. So RECURRENCE holds. QED (T8)

If NEUTRAUfY and RECURRENCE both hold, then both FIXED-CONfENT and UNIQUENESS hold.

Proof (a) Consider a world in which a given object a occupies exactly the same region of space bat two distinct times t and t'. Consequently, both at t and at t', the statement 'Presently, a occupies b' is true. Assume further that in that world, that statement is respectively made true at these times by some facts f and I' which are composed, at the respective times, of the subjects a and b and the occupation relation as their predicable. Arguably, since 'b' specifies the exact location, the A-statements made true by f at t = the A-statements made true by I' at t', and so by P3, the statement-set of I' at t' = the statement-set of f att:

(P3)

TS(f,t) '*' 0 ~ TS(f,t) = SS(f,t)

This world will accordingly be a world in which the antecedent of RECURRENCE is satisfied. H NON-NEUTRALITY held, it would hold as a matter of nomological necessity, and a fortiori such a world would not be nomologically possible. By contrast, if NEUTRALITY holds, then there is no ground for denying that such a world is nomologically possible. Therefore, it can be assumed that there is a nomologically possible world in which the antecedent of RECURRENCE holds. (b) We next prove that if there is such a nomologically possible world and RECURRENCE is accepted as nomologically necessary, then so should be FIXED-CONTENT. Suppose RECURRENCE holds as a matter of nomological necessity and consider a nomologically possible world where

64

4. Criteria for Realist Views of Tense

the antecedent of RECURRENCE is satisfied. Then by RECURRENCE, there is a fact! and two distinct times t and t' such that ! makes all the members of its statement-set at t true at t, and all and only these members true at t'. It follows by P3 above that the statement-set of! at t' = the statement-set of! at t. By AIO, FIXED-CONTENT follows:

(Al 0) VtVt'V!(SS(f,t) = SS(f,t'» v VtVt'V!(t* t':::) SS(f,t) n SS(f,t') = O).

This estabüshes that FIXED-CONTENT is nomologically possible. Given what we said at the beginning of this chapter, acceptance of FIXEDCONTENT as nomologically necessary is the only remaining theoretical option. (c) We lastly prove that if RECURRENCE and FIXED-CONTENT hold, so does UNIQUENESS. Assume that UNIQUENESS fails, i. e. that there are two facts! and /' and a time t such that the statement-set of ! at t = the statement-set of /' at t, but! Given P3 above, FIXED-CONTENT and AS, there is a time t' such that ! makes all the members of its statement-set at t' true at t', and a time t" such that /' makes all and only the members of the statement-set of! at t' true at t":

* /'.

(AS)

3:tTS(f,t) * 0.

So by RECURRENCE, ! = /'. Contradiction! UNIQUENESS folIows.

QED (T9)

If SHIFIY-CONTENT holds, then so does ANn-RECURRENCE.

Proof Assume SHIFTY-CONTENT. Suppose that the antecedent of ANTI-REcURRENCE holds. Then, by P3 and A7, there are two distinct times t and t' and two facts! and /' such that SS(f,t) = SS(/"t') O:

° : :) TS(f,t)

(P3)

TS(f,t) *

(A7)

SS(f,t) * O.

*

= SS(f,t)

Assume for reductio that! = /' and hence that SS(f,t) = SS(f,t') *0. By SHIFTY-CONTENT, SS(f,t) n SS(f,t') = 0. Contradiction! Hence, and the consequent of ANTI-REcURRENCE holds. QED !

* /'

(TIO) If FIXED-CONTENT holds and UNIQUENESS does not hold, then RECURRENCE does not hold.

4. Criteria for Realist Views of Tense

65

Proof. By T5, if UNIQUENESS does not hold, NON-NEUTRALITY does not hold and so NEUTRALITY holds. So, by T8, if FIXED-CONTENT holds while UNIQUENESS does not hold, RECURRENCE does not hold either. QED Now if we could avail ourselves of the following lemma: Either RECURRENCE holds or ANn-REcURRENCE holds, then by T10 we could arrive at the conclusion that the combination of accepting FIXED-CONTENT and rejecting UNIQUENESS commits the A-theorist to acceptance of ANTI-RECURRENCE. This lemma has a certain plausibility. For suppose that it fails. Then there is some A-fact that may perform the same truth-making role on two distinct occasions, and two distinct A-facts! and /' and two distinct times t and t' such that! may perform the truth-making role at t that /' perforrns at t'. Arguably, if there is an A-fact that can perform the same truth-making role on distinct occasions, then this should be a possibility for any A-fact, in particular for f. What then could prevent ! from repeating its truth-making role at t'? Hnothing could, then by A6, P3 and A12, ! = /', contrary to what was assumed: (A6)

TS(f,t) '*' 0 ::> C(!,t)

(P3)

TS(f,t) '*' 0

::::> TS(f,t)

= SS(f,t)

(A12) SS(f,t) = SS(/"t) ::> ((C(!,t') & C(/"t')) ::>! = /'). Hit is accordingly said to be the existence of /' at t' that prevents! from repeating its truth-making role at t', then this evidently presupposes that ! and /' are distinct existences. It has some plausibility to think that this presupposition is ultimately based on the conception of A-facts as being the kind of entities that are located at a unique time, which latter would evidently be incompatible with the idea that they might perform their truth-making role on distinct occasions, as failure of ANTI-REcURRENCE demands. However, it is far from clear whether this line of reasoning is compelling. Thus, on those RELATIVIST views according to which A-facts may linger on, making the same statements true throughout that period, but eventua11y go out of existence, there is no principled reason to deny the possibility that after that period history repeats itself so that those same statements become true again. Pending further argument against such views, we are thus bound to rest content with the weaker conclu-

66

4. Criteria for Realist Views of Tense

sion that TI0 establishes: acceptance of FIXED-CONTENT and rejection of UNIQUENESS at most commit the A-theorist to NON-REcURRENCE. Using RECURRENCE and ANTI-REcURRENCE as further criteria, we thus arrive at the following classification of A-theories:

Absolutist Presentism is the view we previously listed as (1). It combines acceptance of ABSOLUTISM, NON-NEUTRALITY and UNIQUENESS.1t entails that the present time is the only time that there is and that FIXED-CONTENT, SHIFTY-CONTENT, RECURRENCE and ANTI-REcURRENCE are aß triviaßy true for that reason: denial of NEUTRALITY implies that the present time is the only time at which some fact constitutes reality, while ABsoLUTISM implies that any fact that constitutes reality at some time does so at aß times.

Relativist Presentism combines acceptance of RELATIVISM, NON-NEUTRALITY and UNIQUENESS. It entails that there are times distinct from the present time aß of which are empty in the sense that no fact constitutes reality at them and that RECURRENCE and ANTI-RECURRENCE are vacuously true because of this: RELATIVISM implies that 'C(j,t)' is false for some values of 'f' and 't', while NON-NEUTRALITY implies that for any value of 't' distinct from the present time, 'C(j,t)' is false for aß values of 'f'. Since facts satisfy fact-descriptions even at times at which they do not constitute reality, Relativist Presentists can either opt for FIXEDCONTENT (the view previously listed as (TI)) or SHIFTY-CONTENT (the view previously listed as (III)).

Absolutist Recurrentism is the view we previously listed as (IV). It combines acceptance of ABSOLUTISM, NEUTRALITY and FIXED-CONTENT. By T4 and T7, this implies commitment to both UNIQUENESS and RECURRENCE. The view entails that some facts constitute reality at distinct times: given A4, i. e. '3jc(j,to)', NEUTRALITY implies that there are distinct times at which some fact constitutes reality, while ABSOLUTISM implies that any such fact also constitutes reality at the respective other time. According to this view, a fact satisfies the same fact-descriptions at aß times and so, if a fact

4. Criteria for Realist Views of Tense

67

makes some statements true at dilierent times, it makes the very same statements true at those times. H two facts make some statements true at dilierent times, and they make the very same statements true at those dilierent times, then they are identical. All this follows from this view's commitment to UNIQUENESS, FIXED-CONTENT and RECURRENCE.

Relativist Recurrentism is the view we previously listed as (V). It combines acceptance of RELATIVISM, NEUTRALITY, UNIQUENESS and FlXED-CONTENT. By T7, this implies commitment to RECURRENCE. This view entails that there are distinct times at which some fact constitutes reality, where not a1l of these facts constitute reality at a1l times: given A4, NEUTRALITY implies that there are distinct times at which some fact constitutes reality, while RELATIVISM implies that there is a time at which some such fact fails to constitute reality. This view's commitment to FIXED-CONTENT implies that, on this view, a fact satisfies the same fact-descriptions at a1l times and so, if at dilierent times a fact makes some statement true, it makes the very same statements true at those times. By P3, its commitment to RECURRENCE implies that, on this view, if two facts make some statements true at dilierent times, and they make the very same statements true at those dilierent times, they are identical.

Absolutist Anti-Recurrentism is the view we previously listed as (VI) (and which elsewhere we ca1led 'dynamic absolutism', see Correia and Rosenkranz forthcoming). It combines acceptance of ABSOLUTISM, NEUTRALITY and SHIFTY-CONTENT. By T6 and T9, this implies commitment to both UNIQUENESS and ANTI-RECURRENCE. Just like Absolutist Recurrentism, it entails that some facts constitute reality at distinct times: A4 and NEUTRALITY jointly imply that there are two distinct non-empty times, while ABSOLUTISM implies that any fact that constitutes reality at any one these times constitutes reality at a1l times. According to this view, a fact satisfies distinct fact-descriptions at dilierent times and so, if at dilierent times a fact makes some statement true, it makes distinct statements true at those times. The latter follows from the view's commitment to SHIFTy-CONTENT. Commitment to UNIQUENESS and ANTI-RECURRENCE implies commitment to the following claims: distinct facts cannot satisfy the very same fact-descriptions at any one time and if two

68

4. eriteria for Realist Views of Tense

facts make some statements true at different times, and make the very same statements true at those times, then they are rustinet.

Relativist Non-Recurrentism combines acceptance of RELATIVISM, NEUTRALITY and NON-REcURRENCE. Just like Relativist Recurrentism, it entails that there are rustinet non-empty times such that for some time t, some faet constituting reality at one of these non-empty times fails to constitute reality at t: A4 and NEUTRALITY joincly imply that there are rustinet times at which some faet constitutes reality, while RELATIVISM implies that there is factual variation and so a time at which some such faet fails to constitute reality. Relativist Non-Recurrentists can either accept SHIFTy-CONTENT, in which case, by T6, they must accept UNIQUENESS (this is the position we previously listed as (VII)), or accept FIXED-CONTENT, in which case, by T7, they must rejeet UNIQUENESS (this is the position we previously listed as (VIll)). By T9, position (VII) is committed to ANTI-RECURRENCE, which is why it may be referred to as 'Relativist Anti-Recurrentism'. By contrast, proponents of position (VIII) have a choice: either they opt for ANTI-REcURRENCE, and so for another version of Relativist Anti-Recurrentism, or they rejeet both RECURRENCE and ANTI-RECURRENCE, and so opt for a view which may be called 'Hybrid Relativism'. There are accordingly two versions of Relativist Presentism and three versions of Relativist Non-Recurrentism. Whereas both versions of Relativist Presentism imply UNIQUENESS, only the SHIFTY-CONTENT version of Relativist Non-Recurrentism implies UNIQUENESS. The two FIXED-CONTENT versions of Relativist Non-Recurrentism are the only realist views of tense that deny UNIQUENESS. Our dassification can be represented by means of the following flowchart (p. 69). The flowchart makes vivid that any A-theory in line with our assumptions about time and its structure must be located within our dassification and cannot be located in more than one place. On any view according to which the dass of all basic material A-statements is partitioned in such a way that there is a one-to-one correspondence r between these partitions and A-facts such that for every time t, all the members of a partition 1t are true at t iff r(1t) makes them all, and only them, true at t, RECURRENCE will hold. To realise that realists about tense may rejeet RECURRENCE, and so need

-!'(")

~. ~.

Ö' ...

~

~

~

a. ~

~

."

a-

...0

70

4. Criteria for Realist Views of Tense

not subscribe to this assumption, is important, as it allows hitherto neglected versions of the A-theory to come into clear view. It would seem that many philosophers of time presuppose that realists about tense cannot but accept RECURRENCE, and FIXED-CONTENT, lest they be left with no conception of tensed facts at all (for an exarnple of this type of reasoning, see Mellor 1998: 78-81). At least, this would explain why positions accepting SHIFTY-CONTENT and so ANTI-REcURRENCE have never been explored. As we shall argue in chapter 7, and further substantiate in chapters 8 and 9, any such presupposition is mistaken. In fact, the comparative assessment in chapters 5 to 7 will show that there is aversion of Non-Recurrentism that fares much better than any of the Presentist or Recurrentist views here identified, at least as far as compliance with the desiderata is concemed.

5 Presentism In this chapter and the next, we illustrate each of the Presentist and the Recurrentist realist views of tense by (i) elaborating on the metaphysical picture associated with that view and (ii) devising a toy story and showing how the view accounts for the truth of that story in line with Real-2. The credentials of each view are then examined by (iii) checking how it fares in the light of the remaining desiderata identified in chapter 2, i. e. Real-l and Real-3 to Real-5. The present chapter is devoted to the diseussion of Presentism, and chapter 6 to the diseussion of Reeurrentism. In chapter 7, we will do the same for Absolutist Anti-Recurrentism. We will ignore the other (relativist) versions of Non-Reeurrentism. Instead, we will develop a particular version of Absolutist Anti-Reeurrentism in some detail, which, given the non-standard nature of Non-Reeurrentism, we consider to be more important than diseussion of all its varieties. To illustrate the different views to be diseussed, it will do to foeus on basic material A-statements. For convenience's sake, we will assume that the basic material A-statements composing our toy story are each determined to be true by a single A-fact. Even assuming realism about A-facts, that a statement is a true basic material A-statement will typically not be sufficient for it to be determined to be true by a single such fact. Appropriating an example given by Davidson, the true statement 'Two days ago, John was sunburnt' is best understood to be determined to be true by at least two facts, e. g. one deterrnining that more than two days ago, John was exposed to the sun, and one deterrnining that two days ago, John's skin was in a characteristic state of irritation. Even if no basic material A-statement of our actual A-language is ever determined to be true by a single A-fact, and so none is ever made true by a single such fact, an idealised version of our language will contain basic material A-statements of the relevant kind. This type of idealisation was presupposed ever since we introduced, in chapter 3, axioms Iike A5, A7 and A9, and we continue making this presupposition. What we here assume in addition is that basic material A-statements concerning the protagonist of our toy story and his states and actions are of the desired kind.

72

5. Presentism

Thus, consider the following simple story:

Sam is presently philosophizing. One day ago, Sam was asleep. One day hence, Sam will be asleep. Now let us ask:

What must temporal reality be like in order for our story to be trne? In asking this question, we presuppose that our story is true and hence that certain past-tensed and certain future-tensed statements are true. We furthermore presuppose that none of the following two statements is true:

One day ago, Sam was not asleep One day hence, Sam will not be asleep, and so, as we may put it, that our toy story is not vacuously true. Neither of these assumptions is uncontroversiaI. Thus, Absolutist Presentism and Relativist Presentism imply that there are no non-empty future or past times, so if proponents of these views endorsed the standard interpretation of tense-Iogical operators, they would have to reject at least one of these assumptions. However, proponents of Presentism typically claim to hold 'the "common sense" view, i. e. the one that the average person on the street would accept' and then go to great lengths in order to save appearances (Markosian 2004: 48).15 Given the availability of the deviant interpretation, there is no need for Presentists to attribute massive error or massive vacuity to ordinary talk which our toy story is meant to provide an example of. Now, there are several different answers that philosophers would give, depending on which among the previously identified views they endorse. Suppose, first, that 'a' names the present time, secondly that provided that there are any times earlier than the present time, 'a - 1' 15 Admittedly, Markosian thinks that ordinary speakers are systematically deceived about the truth-conditions of A-statements meant to express singular propositions about things that do not presently exist (Markosian 2004: 72). However, assuming as we do that Sam presently exists, this flirtation with revisionism does nothing to undermine the general point that, as far as this is possible at all, Presentists aim to validate ordinary ulk. For, if Presentism had revisionist consequences even with respect to future- or past-tensed statements about things that presently exist, Iittle would be left of the idea that Presentism is the view that comes naturally to the average person.

73

5. Presentism

names the time one day ago, and thirdly that provided that there are any times later than the present time, 'a + l' names the time one day hence. In what follows, we will represent those of the views that accept the existence of times earlier than, and of times later than, the present time by means of tables of the following kind: Present ~

a-l

I[u]

a

I[u]

k]

a+l

Views that deny the existence of past or future times will be represented by correspondingly truncated tables that lack the respective columns. The cells contain descriptions of the facts that constitute reality at the respective times, according to the view in question. These facts constitute reality in the absolute sense of 'constitution' (at least as far as is required for our story to be true). Note also that the fact-descriptions in the respective cells will be understood as being given at the present time a. If according to a given view, the entries of two adjacent cells are the same, we will merge these cells in the table for that view. The entries will consist of definite descriptions of facts. The reference-conditions for the expression 'the fact that s' can be specified thus: for every fand every time t, 'the fact that s' refers to f at t iff (a) f satisfies 'is a fact that s' at t and (b) for every J', if J' also satisfies the predicate at t, then f = J', where satisfaction of fact-descriptions is understood in terms of D5: (D5)

f

satisfies 'is a fact that s' at t =df (TS(f,t) * 0 D--+ s E TS(f,t)).

We will assume that, on the views to be discussed in this chapter and chapters 6 and 7, the fact-descriptions and the facts in our example are such that condition (b) is satisfied. For simplicity's sake, we will exclusively be concemed with the most parsimonious versions of the views, i. e. those versions that posit the least number of facts in order to account for the truth of our toy story. Some of the views will invoke truth-determination as this notion

74

5. Presentism

was characterised in chapter 2. Some of the views will moreover appeal to the following principle: (MINIMALISM)

Only statements of the form '0 days from the present,

p' are ever made true. se TS(f,t) :::> 3p(s = 'Dop'). Which views these are will become clear in what follows. With these preliminaries being in place, let us accordingly now turn to the first of the views identified in chapter 4, i. e. Ahsolutist Presentism. The metaphysical picture associated with Absolutist Presentism can be described as follows: reality does not extend beyond the present, it is like a point event without duration. Something akin to the Russellian idea that the universe might have popped into existence, replete with traces of an apparent past and future tendencies, is here endorsed as a true depiction of reality. The present truth of our past- and futuretensed statements thus is strangely dissociated from any past or future portions of reality they are so naturally taken to describe. Recall that Absolutist Presentists deny that there are any cimes besides the present time. This has two consequences: the table for this view will be truncated and only contain one column; and as we shall see in due course, the view will have to opt for the deviant interpretation of tense-logical operators, given that our toy story is supposed to be non-vacuously true. According to one natural suggestion, the table for Absolutist Presentism looks like this: Present !

a

The fact that presendy Sam is philosophizing The fact that one day ago Sam was asleep The fact that one day hence Sam will be asleep

In accordance with this table, Absolutist Presentism accounts for the truth of our toy story by invoking truth-making only: the fact that presently Sam is philosophizing makes 'Sam is presendy philosophizing' true at a, the fact that one day ago Sam was asleep makes 'One

5. Presentism

75

day ago, Sam was asleep' true at a, the fact that one day hence Sam will be asleep makes 'One day hence, Sam will be asleep' true at a. As far as our toy story goes, Absolutist Presentism thus complies with Real-2 according to which an A-statement is determined to be true by the A-facts, whenever it is true. Note, though, that if Absolutist Presentists accepted the standard interpretation of the tense-Iogical operators in terms of quantification over times, this account of the truth of our toy story would be flawed: if 'n days from the present, p' is taken to be equivalent to 'For all times t n days from the present time, at t, p', both 'One day ago, Sam was asleep' and 'One day hence, Sam will be asleep' will prove vaeuously true, while if 'n days from the present, p' is taken to be equivalent to 'For some time t n days from the present time, at t, p', then both these statements will be false (see chapter 2). Thus, on condition that our toy story is non-vaeuously true, and Real-2 is in place, Absolutist Presentists cannot accept the standard interpretation but must opt for the deviant interpretation instead. Let us therefore foeus on that version of Absolutist Presentism that accepts the deviant interpretation, and critically examine whether, and if so how, it can comply with the desiderata Real-l and Real-3 to Real-5. Let us start with Real-l and ask whether the view can comply with it on the deviant interpretation of 'always': (Real-l) If arealist view of tense is true, then it is always true. Among the theoretical principles accepted by Absolutist Presentists which are clearly sensitive to tense-Iogical embedding are NON-NEuTRALITY and A4. Thus by Real-l, they should endorse (1): (1) Always, there is no time distinct from the present time such that some fact constitutes reality at it.

'V nD n-.3f3:t(t * to & C(f,t)).

Given ABSOLUTISM, (1) is equivalent to:

'VnD nVt(t* to). Since 'Vt'VnDn(t* to)' contradicts Al, i.e. '3:t(t = to)', proponents of the view under consideration must take '3:t' to be sensitive to tenselogical embedding. They can do so without going funky only if they take the more basic notion of existential quantification over A-facts to

76

5. Presentism

be absolute, where to go funky is to deny that '3[' is always equivalent to '3nD n3 tofD_n' (see chapter 3). Given thattheymusttake '3:t' to be sensitive to tense-logical embedding, the other principles they accept, viz. UNIQUENESS, FIXED-CONTENT and SHIFTY-CONTENT, will also be tensed. But it is unproblematical for them to hold that the latter principles are always true. By Real-i, proponents of this view should also endorse: (2) Always, some fact constitutes reality at the present time. V nD n3fc(f,to). Given ABSOLUTISM, (2) is equivalent to: VnD n3fC(f)· Let us assume that the more basic notion of existential quantification is

absolute. Then 'VnD n3fC(f)' will be equivalent to: 3fVnDnC(f).

The latter already follows from a straightforward implication of that assumption in conjunction with A4 (i.e. '3fC(f,to)'), viz.: VfVnDnC(f).

Consequendy, again under that assumption, Absolutist Presentists can comply with Real-3 only by holding that these facts qualitatively change overtime: (Real-3) Always, for every n distinct from 0, the facts which constitute reality are different from what they are n days from the present. It is open to Absolutist Presentists to accept the following manifestation assumption: (MANIFESTATION)

Those diachronie qualitative differences in facts which are relevant for the passage of time manifest themselves in diachronie differences in the tense of the that-clauses of the fact-descriptions these facts satisfy, and conversely, diachronie differences in the tense of those that-clauses are manifestations of such diachronie qualitative differences in facts.

MANIFESTATION involves

some rather hefty idealisations regarding the expressive power of the A-Ianguage, but those were already at work

5. Presencism

77

when we laid down our axioms in chapter 3. Even apart from these idealisations, MANIFESTATION is a substantial metaphysical thesis, and as such requires argument. But there is no a primi reason for thinking that no such argument can be provided. With MANIFESTATION being in place, Absolutist Presentists can invoke the tensed version of SHIFTY-CONTENT: Always, for all J, if s belongs to f' s statement-set, then for all n distinct from 0, n days from the present, s does not belong to f's statement-set, and a tensed version of All: Always, for all J, if 'DnP' belongs to f's statement-set, then for all m, m days from the present, if 'DnP' does not belong to f's statement-set, then 'Dn-mp' does. Given these, it is then pretty straightforward how Absolutist Presentists can comply with Real-3, and similarly with Real-4. However, under the same assumptions, it becomes entirely unclear why Absolutist Presentists would want to reject NEUTRALITY. For plausibly, every A-fact sometimes satisfies a fact-description of the form 'is a fact that presently, p' where 'Presently, p' is a basic material A-statement, and, equally plausibly, always, there is some fact constituting reality that satisfies such adescription. So, given: (A8) n * m => -.{'Dnp','Dmq'} ~ SS(j,t), it is possible to reduce times to classes of A-facts, as follows. Say that two A-facts J and f' are contemporaneous just in case for some n, p and q, 'DnP' belongs to f's statement-set and 'Dnq' belongs to f"s statementset. Contemporaneousness will then be an equivalence relation, and the times can be identified with the corresponding equivalence classes. 16 Given the availability of such a reduction, Absolutist Presentists are hard pressed to explain what it is about the present time that precludes that there are other times distinct from it, and so on what grounds they oppose Absolutist Anti-Recurrentism. One suggestion might be that there would be such other times only on condition that for any n distinct from 0, how the facts are n days from the present explains the 16

A complete reduction would in addition have to reduce the temporal order. We show how this can be done in chapter 8.

78

5. Presentism

truth of A-statements which is not yet explained by how they presently are. Absolutist Presentists rnight deny that this condition is satisfied. But then, this would underrnine their attempt to comply with Real-S: (Real-S) Always, for every n, if the facts which constitute reality are different from what they are n days from the present, then the true A-statements are different from what they are n days from the present partly because of the particular way in which those facts do so differ. Let us now turn to those versions of Absolutist Presentism which take the more basic notion of existential quantification to be relative. As we saw, Absolutist Presentism of whichever variety can comply with Real-l only on condition of taking quantification over times to be sensitive to tense-Iogica1 embedding. We also saw that any such view must opt for the deviant interpretation of the tense-Iogica1 operators if it is to be compatible with the non-vacuous truth of our little toy story. Taken together, these comrnitments imply that those versions of Absolutist Presentism which take the more basic notion of existential quantification to be relative must go funky, in the sense defined in chapter 3: they must deny that '3/, is always equivalent to '3nD n 3t JD- n ' (see chapter 3). It is open to Absolutist Presentists of this kind to give the very same table as before, in which case, under sirnilar assumptions, they are equally subject to the challenge posed by the availability of a reduction of times. However, given the funkiness of their view, for them a more parsimonious way of accounting for the truth of the toy story is to adopt MrNIMALISM and to offer the following table instead:

Present ~

a

The fact that presently Sam is philosophizing

In accordance with this table, Absolutist Presentism may attempt to account for the truth of our toy story along the following lines: the fact that presently Sam is philosophizing makes 'Sam is presently philosophizing' true at a; one day ago, there was the fact that Sam is asleep, which then made 'Sam is asleep' true, and necessarily, if a day before a,

5. Presentism

79

'Sam is asleep' was true, then 'One day ago, Sam was asleep' is true at a; and mutatis mutandis for the truth at a of 'One day hence, Sam will be asleep'. Given funkiness, saying that one day ago there was the fact that Sam is asleep need not imply that there is the fact that Sam was asleep one day ago. In this way, these Absolutist Presentists indeed satisfy the letter of Real-2, but arguably not its spirit. For talk about truth-determination was meant to capture a relation of grounding between true A-statements and A-facts. In the explanation of the truth of the past- and futuretensed statements of the toy story, no A-facts are being mentioned. At most we can say that in each case, an A-proposition is being stated. If explanations of such types already suffice for meeting Real-2, then it becomes unc1ear why the B-theorist cannot equally comply with it. Recall that the right to assume the existence of A-facts over and above true A-propositions had to be earned, and the rationale of Real-2 was precisely to identify an explanatory task that only A-facts, and not true A-propositions, could fulfil. In conc1usion, either Absolutist Presentists face the charge of not meeting the requirement that A -truths be grounded in A -facts, or else, in their attempt to meet a minimal requirement on temporal change, they are under considerable pressure to resist hostile takeover by Absolutist Anti-Recurrentists. Let us now turn to Absolutist Presentism' s relativist cousin, i. e. Relatz'vist Presentism, to see whether it is bener suited to comply with all the desiderata. As we saw in chapter 4, there are two versions of Relativist Presentism, one that accepts FIXED-CoNTENT and another that accepts SHIFTY-CONTENT instead. However, our discussion will proceed at a level of generality that ensures that our considerations affect both these versions alike. There is thus no reason to consider them separately. Recall that unlike Absolutist Presentists, Relativist Presentists countenance times other than the present time, but concur with Absolutist Presentists that there are no non-empty times other than the present time. The metaphysical picture associated with Relativist Presentism would accordingly seem to be just like the Absolutist Presentists' picture, only with an odd twist: the time line extends into the past and future, yet there is nothing that really happens or occurs beyond what presently happens or occurs. Trrnes other than the present are like empty containers.

80

5. Presentism

A straightforward suggestion of what the table for Relativist Presentism looks like is accordingly this: Present ~

a-l

a

a+l

The fact that presently Sam is philosophizing The fact that one day ago Sam was asleep The fact that one day hence Sam will be asleep

H this table is adequate, then Relativist Presentists are naturally taken to account for the truth of our toy story in just the same way Absolutist Presentists did in the case of their first table: the fact that presendy Sam is philosophizing makes 'Sam is presendy philosophizing' true at a, the fact that one day ago Sam was asleep makes 'One day ago, Sam was asleep' true at a, the fact that one day hence Sam will be asleep makes 'One day hence, Sam will be asleep' true at a. As far as our toy story goes, Relativist Presentists can thus comply with Real-2. ean Relativist Presentists comply with the remaining desiderata identified in chapter 2? And if so, how do they do so? Before answering these questions, let us ask whether Relativist Presentists can take quantification over times to be sensitive to tense-logical embedding. For a Presentist, to claim that quantification over times is sensitive to tense-logical embedding makes sense only insofar as the view is that always, the range of '.'3:t' is restricted to the time that is then present. However, Relativist Presentists are committed to there being factual variation, and so to there being at least two times, which is incompatible with the latter thought. Therefore, Relativist Presentists should deny that quantification over times is sensitive to tense-logical embedding. A corollary of this is that for them, '3/, is not sensitive to tense-logical embedding either. As Relativists, Relativist Presentists must take the more basic notion of quantification over A-facts to be relative, and so to be either relativised to times or tensed. Suppose that the more basic notion of quantification is relativised to times, which as we have hitheno assumed, is not in turn tensed. Then '3/ -' is defined as '~t3rf -', and since neither '~t' nor '3 t/ , is sensitive to tense-Iogical embedding, '3/, cannot be so sensitive. Suppose alternatively that the more basic notion of quantification is tensed. Then '3/- ' is defined again as '~t3t/ -',

5. Presentism

81

which in this case boils down to '3:t3nD n (t is present & EfD_ n -)'. Given that '3:t' is not sensitive to tense-Iogical embedding and given the shape of what here follows '3:t', again, '31' cannot be so sensitive. Relativist Presentists accept an ontology of times distinct from the present time and so prima facie have no reason to object to the standard interpretation of tense-Iogical operators in terms of quantification over times. Suppose then that they do accept the standard interpretation. H so, they will face the following problems when trying to comply with the desiderata. First consider Real-1. In the light of Real-1, Relativist Presentists should say that their claim 'There is no time distinct from the present such that some fact constitutes reality at it' is always true. Thus in particular, given the standard interpretation, they should endorse: (3) For every time t, at t: -,3:t'3f(t is earlier than t' & f constitutes reality at t'). Now let a e be a time earlier than the present time, e. g. a -1. From (3) we then obtain: (4) At a e : -,3:t3f(a e is earlier than t & f constitutes reality at t). Given that on the Relativist Presentists' view, neither '3:t' nor '31' is sensitive to tense-Iogical embedding, (4) implies : (5) At a: -,3:t3f(a e is earlier than t & f constitutes reality at t). Given A 4, according to which some fact constitutes reality at the present time, and the assumptions that a is the present time and that a e is before a, (5) cannot be true. Rejecting A4 is no option for Relativist Presentists, given only that they believe that there are any tensed facts at all. Let us now move on to Real-3. In its standard interpretation, Real-3 is tantamount to: For all distinct times t and t', at t, the facts X which constitute reality are such that, at t', either the facts Y which constitute reality are distinct from X or there is a fact f which constitutes reality which is relevantly qualitatively different from what it is like at t. Take any two times t and t' distinct from the present time. 17 Then the facts that constitute reality at t are the facts that constitute reality at t', 17 Strictly speaking, Relativist Presentists who claim that there is variation are only com-

mitted

to

there being two times, the present time and another, empty time. But,

82

5. Presentism

namely none. For the same reason, there is no fact which constitutes reality at both t and t' which could at t' be qualitatively different from what it is like at t. So given the standard interpretation of the tenselogical operators, Real-3 fails. All this strongly suggests that Relativist Presentists are better off opting for the deviant interpretation. Once this interpretation is adopted, it is in principle possible to give an alternative, MINIMALIST explanation of the truth of our toy story based on the same table as above, where the truth of the past- and the future-tensed statements is explained in terms of truth-determination as folIows: the fact that one day ago, Sam was asleep is such that one day ago, it made 'Sam is asleep' true, and necessarily, if a day before a, 'Sam is asleep' was true, then 'One day ago, Sam was asleep' is true at a; and mutatis mutandis for the truth at a of 'One day hence, Sam will be alseep'. (Note that this MINIMALIST explanation is available only to those Relativist Presentists who endorse SHIFTY-CONTENT .) Given their commitment to the deviant interpretation, the Relativist Presentists' view will be funky iff it treats quantification over times to be sensitive to tense-Iogical embedding (see appendix to chapter 3). As we have seen, they cannot treat quantification over times to be sensitive to tense-Iogical embedding. Accordingly, they must opt for a view which is not funky. This in turn means that on their view, '31' is always equivalent to '3nD n3tofD_n'. It can then be shown that they should accept the folIowing general principle:

'itnD n'itfD_nC(f,to).

Proof Suppose for reductio that 3nDn3fD- n-,C(f,to). By the assumption that the tensed version of AS always holds, it folIows that 3nDn3f(3mDmf makes some statement true & D-n-,C(f,to)):

U makes some statement true).

(AS') 'itnD n'itf3mD m

U

By tense-Iogical reasoning, it folIows that 3m3nD n3fDm makes some statement true & D-(m+n)-'c(f,to)). H the tensed version of A6 always holds, so should the folIowing strengthening:

plausibly, if they countenance one empty time distinct from the present, they also countenance many empty times.

5. Presentism

83

(A6') "d nD n"d f"d mDm(f makes some statement true ::> f constitutes reality). By A6', we can infer that 3m3nDnD m3,of(f makes some statement true & D-(m+nr-,c(f,to». By tense-Iogical reasoning again, it follows that 3m3nDm+n3,of(f makes some statement true & D_(m+n)....,C(f, to». By simplification and tense-Iogical reasoning, we can infer that 3nDn3,ofD- n....,C(f,to). Given that '3nD n3,ofD_n' is always equivalent to '31', we can condude that 3f....,C(f,to). But this goes against Presentism. So given Relativist Presentism, '''d nD n"d fD_nC(f,to)' follows. QED Given Real-l, Relativist Presentists are further committed to daiming that the principle just proved always holds, and so that always, facts always constitute reality, which is, as it were, a tensed version of

an

sempitemalism. With these considerations in place, let us now ask how Relativist Presentists can comply with Real-3. The result just proved implies that they cannot account for temporal change in terms of numerical distinctness. Instead, they must, just as Absolutist Presentists, go for a combination of MANIFESTATION and the tensed version of SHIFTYCONTENT. Under the previously identified additional assumptions, they accordingly have the means necessary to reduce times to classes of contemporaneous A-facts. However, any such reduction would be in tension with their Presentism: once times are identified with such dasses, for a fact to belang to such a dass should plausibly be taken to be sufficient in order for that fact to constitute reality at the corresponding time, in which case more than one time would be non-empty. So Relativist Presentists either owe us an account of what times are if not such classes, or must appeal to anation of constitution at a time which stands in need of explanation. But the result just proved has an even more puzzling consequence. Let 'g-' be a name for the fact that Sam is presently philosophizing. Then given that Ca' names the present time, it follows that C(g-,a). By the result just proved, and the finding that its proof rests on assumptions that always hold, we have:

an

"d mD m"d nDn"d fD_nC(f,to), one instance of which being 'DtD_ t "dfDtC(f,to)'. The latter is equivalent to '''dfDtC(f,to)', which in turn implies 'DtC(g-,to)'.1t follows

84

5. Presentism

that tomorrow, .7 still exists. By Relativist Presentism, the same goes for a. By Relativist Presentism again, we have:

Vt(t is one day before to :::> -,3fC(f,t)). By Real-l, this should always hold, and in particular this should hold tomorrow. Thus: One day hence, Vt(t is one day before to:::> -,3fC(f,t)). But given that the order of time is permanent, the following likewise holds: One day hence, ais one day before to. By tense-Iogica1 reasoning, we can conclude that: One day hence,.7 exists & a exists & -,C(.7,a). Relative constitution was defined as follows: C(f,t) =df 3,1'(1' = f). So far we have been assuming that '3,1' is not sensitive to tenselogica1 embedding (see chapter 3). It now turns out that Relativist Presentists must deny this assumption, and thereby conceive of relative constitution as being further relativised to whichever time is present. This would also allow them to block the previous argument that derived their commitment to (5) from the assumption that they opt for the standard interpretation of the tense-logical operators. For that argument also relied on the premise that '3,1' is not sensitive to tense-logical embedding. However, the thought that relative constitution is further relativised to whichever time is present makes the Relativist Presentists' view radically relativist, because from no temporal perspective can the whole of temporal reality as changing be described by saying what the facts are at various temporal distances from that perspective (d. MacFarlane 2003; Dummett 2004: 75-77, 83-84). So even if on that reading of relative constitution, from each perspective Real-4 will hold, that reading defies the purpose for which Real-4 was laid down in the first place, viz. to ensure that temporal change is objective insofar as the very same variation in what facts there are, or as to how they are, can in principle be described, albeit in different ways, from all perspectives. This concludes our discussion ofPresentism. Its upshot is that either Presentism's commitment to NON-NEUTRALITY proves unmotivated, because a reduction of times is readily available to them that would

5. Presentism

85

ensure that there are non-empty past and future times, or its compliance with all the Reals can only be secured by seriously comprornising the latter's rationale.

6 Recurrentism This chapter is devoted to the discussion of the third and the fourth of the views identified in chapter 4, Absolutist Recurrentism and Relativist Recurrentism. We start by considering Absolutist Recurrentism. According to the metaphysical picture associated with Absolutist Recurrentism, the world is replete with permanently existing and immutable facts, including ones with incompatible contents at the same times, that make themselves felt, potentially repeatedly, at different times by making statements true at those times. H they ever recur as truth-makers, then owing to their immutability, they make exactly the same statements true. Reality itself thus is multi-faceted, and it is our true descriptions of it that bring certain of its facets into prominence and sometimes the same such facets at different times. The passage of time would seem to consist in nothing but the temporally variegated truth-making by permanently existing and immutable facts. The table for this view looks as follows: Present ~

a-l

I

a

I

a+l

The fact that presently Sam is philosophizing The fact presently Sam is asleep

Absolutist Recurrentists account for the truth of our toy story by invoking truth-making and truth-determination. The fact that presently Sam is philosophizing makes 'Presently, Sam is philosophizing' true at a. The fact that presently Sam is asleep makes 'Presently, Sam is asleep' true at a -1 and, given the characterisation of truth-determination in chapter 2, thereby determines 'One day ago, Sam was asleep' to be true at a. The same fact also makes 'Presently, Sam is asleep' true at a + 1 and, given the characterisation of truth-determination, thereby determines 'One day hence Sam will be asleep' to be true at a. So,

88

6. Recurrentism

as far as our toy story goes, Absolutist Recurrentism can be seen to comply with Real-2. Note that given its commitment to ABSOLUTISM and FIXED-CONTENT, Absolutist Recurrentism implies that, in so far as our toy story is true, reality is constituted both by the fact that Sam is presently asleep and the fact that Sam is presently philosophizing (and so not asleep). Recall our definition of incompatibility of fact-contents: (D7) The content of j at t is incompatible with the content of f' at t' =df j satisfies a fact-description at t and f' satisfies another fact-description at t' such that the statements corresponding to these fact-descriptions cannot be true together.

INc(j,t,f',t') =df 3535'(5 E SS(f,t) & 5' E SS(f',t') & -.03nD n (s & 5')). We now define strong-incompatibility of fact-contents as fol1ows: (D8) Facts j and f' have strongly-incompatible contents at t =df the content of j at t is incompatible with the content of f' at t.

STINc(j,!"t) =df INc(j,t,!"t). Hence, on the Absolutist Recurrentists' view, COHERENCE fails: (COHERENCE)

Reality is at no time constituted by two facts j and f' such that j and f' have strongly-incompatible contents at that time.

-.'H.t3f3f'(C(j,t) & C(f',t) & STINC(j,f',t)). We take COHERENCE to be the principle which Fine calls by that very name (Fine 2005: 271). Thus, Absolutist Recurrentism would seem to be identical with the position Fine calls 'fragmentalism' (Fine 2005: 280-82). Rejecting COHERENCE, proponents of Absolutist Recurrentism must consequently deny ÜMNIPOTENCE on pain of contradiction: (ÜMNIPOTENCE) If a fact constitutes reality at a time, it makes some statement true at that time.

C(j,t) ::J TS(f,t) =*= 0. Since on Fine's characterisation of the view, fragmentalism does not entail that there are any true contradictions (Fine 2005: 282), fragmentalists willlikewise reject ÜMNIPOTENCE.

6. Recurrentism

89

It follows from the failure of OMNIPOTENCE that some fact may constitute reality at a time without making any statement true at that time. Given ABSOLUTISM, it also follows that although all facts constitute reality at all times and at all times satisfy fact-descriptions, not all of them may at all times be stated, and so picked out, by means of corresponding A-statements: for a fact to be stated by a given basic A-statement is for that fact to make that statement true. Now, there is a certain implausibility to the claim that while it is of the essence of a fact to sometime make an A-statement true, as AS demands, a fact may nonetheless constitute reality at a time without, at that very time, making any A-statement true. And it would seem equally implausible to maintain that while facts always constitute reality and always satisfy fact-descriptions, they cannot always be stated by means of A-statements that correspond to those very fact-descriptions. Rejection of OMNIPOTENCE would seem problematical for yet another reason, having to do with the nature of truth-making. Assume that OMNIPOTENCE fails. This amounts to assuming that a fact's constituting reality at t is not sufficient for that fact to make some basic A-statement true at t. If a fact constitutes reality at t, then it exists at t, and vice versa. Yet, if the fact that s exists at t, how can the basic A-statement es, nonetheless fail to be made true by this fact at t? What more is required to make the basic A-statement es, true at t than that there exists, at t, the fact that s? If in making this statement, one eo ipso laid claim to more than that this fact exists at the time of making it, viz. that one' s statement be furthermore made true by such a fact at the time of making it, then the timely existence of such a fact alone may after all be thought to be insufficient for making true one's claim. Arguably, that the statement 'S' is made true at t by the fact that s is never made true by the fact that s, even if this fact contributes to its being deterrnined to be true. Yet, whatever one invariably demands of a world whenever one makes a given statement about it, should be something that this statement can itself be understood to state whenever made. But then, appearances to the contrary notwithstanding, the statement es, is never made true by the fact that s, since ex hypothesi this fact never makes it true that the statement is made true by that fact. So the fact that s never makes any A-statement true, which violates AS. According to Fine' s fragmentalist view, temporal reality, though incoherent as a whole, fragments into mutually incoherent pockets

90

6. Recurrentism

of mutually coherent facts. According to Fine, fragmenta1ists identify times with such maximally coherent fragments (Fine 2005: 281). Being true at a time can accordingly be identified with being true of such a fragment. It may now be deemed perfectly intelligible why a fact' s constituting temporal reality at a given time will not suffice for the corresponding A-statement's being true at that time: for, although any fact is part of temporal reality as a whole, and so constitutes it absolutely at any time, it will not thereby belong to all the fragments. However, it is now a legitimate question to ask why if being true at a time is identified with being true of a fragment, we cannot likewise identify constituting reality at a time with belonging to a fragment and consequently accept that there is factual variation in the sense of: (D3) There is factual variation =df ~t~t'3f(c(f,t) & -,C(f,t'». But if there is factual variation in this sense, then ABSOLUTISM is false! After all, what does it mean to belong to a time if not to constitute reality at that time? Hthe only way to stabilise denial of OMNIPOTENCE is by denying ABSOLUTISM, then Fine's fragmentalist can get no mileage out of her claim that reality fragments into pockets of mutually coherent facts. H there is any other way, its roots must lie in a rather different conception of what it is for a fact to belong to a time. But then what conception might this be? Let us now consider how Absolutist Recurrentism fares in the light of the desiderata Real-1 and Real-3 to Real-5. Given their acceptance of both non-empty past and non-empty future times, Absolutist Recurrentists can without further ado accept the standard interpretation of the tense-logical operators in terms of quantification over times. For them, opting for the deviant interpretation - and so rejecting the equivalence between statements involving quantification over times and those that merely involve quantification over numbers measuring temporal distances from the present time would have no point. Among the time-sensitive theoretical principles accepted by Absolutist Recurrentists are NEUTRALITY and A4 (i. e. '3fC(f,to)'). Given their acceptance of both non-empty past and non-empty future times, and given the present truth of NEUTRALITY and A4, whichever time is present, it will, on the Absolutist Recurrentists' view, hold at that time that some fact constitutes reality at that time and some fact constitutes reality at some other time. Absolutist Recurrentists accordingly have

6. Recurrentism

91

no problem in complying with Real-1 which, to recall, deman ('DnP' E TS(f,t) ::> 'Dn-mp' 4:

In the light of A13, Relativist Recurrentists who invoke the aforesaid principle can thus be seen to accept: (MINIMALISM)

5E

TS(f,t) ::> 3p(s = 'Dop').

What then about Real-S? To begin with, note that Relativist Recurrentism forces us to distinguish between present temporal reality and a temporal 'über-reality' comprising all the realities-at-a-time.1t is unclear whether this makes sense. Consider the fol1owing analogy with space: for semantic reasons, we may get used to saying that the statement 'm mettes to the north from here, p', if true here, is not made true here by any fact but is only determined to be true here by whatever fact f makes the statement 'Here, p' true m mettes to the north from here. But the suggestion that f constitutes reality m mettes to the north from here, hut does not constitute reality here, is hard to swallow. Although spatial analogies must he handled with care, it does seem equally implausible to say that the statement 'One day hence, Sam will he asleep' is determined to be presendy true by a fact that does not constitute present reality but only reality-one-day-hence. This sttongly suggests that our ordinary conception of reality is the conception of what Relativist Recurrentists infelicitously call 'über-reality'. Similarly, we naturally regard this reality as being composed of, or constituted by, what Relativist Recurrentists infelicitously subsurne under 'a fact's constituting a reality-at-a-time'. In other words, we naturally regard a fact as consisting in reality' s having a certain feature, whereas Relativist Recurrentists regard a fact as a feature a reality may or may not have. On the MINIMALIST version of Relativist Recurrentism considered here, there is indeed a one-to-one correspondence between facts and sets of present-tensed A-statements, such that a fact constitutes reality at a time iff all the members of the corresponding set of statements are true at that time. It is therefore natural to accuse Relativist Recurrentists of reading features of language, or propositional

94

6. Recurrentism

thought, into temporal reality. Indeed, the Relativist Recurrentists' use of the notion of relative constitution as applied to A-facts, according to their preferred conception of them, can hanDy be told apart from the notion of relative truth as applied to A-propositions. It is therefore highly doubtful whether Relativist Recurrentists can make a successful case that their view is a genuine A-theory according to the conception laid out in chapter 1, and equally doubtful whether they can comply with Real-5, given that explanatory links should be asymmetrical. To conclude, either Recurrentists accept ABSOLUTISM, in which case they fail to comply with Real-3, or else they accept RELATIVISM, in which case on the most straightforward vindication of Real-4, they are vulnerable to the charge of reading features of language into reality, and thereby of failing to comply with Real-5.

7 Anti-Recurrentism: Escaping Fine' s Trilemma In this chapter, we shall discuss Ahsolutist Anti-Recurrentism (or what we elsewhere called 'dynamic absolutism', see Correia and Rosenkranz fonhcoming), aversion of which we will characterise in more detail in chapter 8. As advertised, we will not discuss the other (Relativist) versions of Non-Recurrentism. To the best of our knowledge, NonRecurrentist views are nowhere discussed in the extant literature on time and tense. Already for this reason, we consider it to be more important to devise an in-depth account of one such non-standard view than to give a brief sketch of aIl of them. Moreover, we regard Absolutist Anti-Recurrentism to be the most interesting and powerful version of Non-Recurrentism. Following the same pattern as before, we start by having a doser look at Absolutist Anti-Recurrentism first and examine how this view fares in the light of the desiderata set out in chapter 2. Absolutist Anti-Recurrentists have their own picture of temporal reality. On that picture, the world is composed of facts that exist at aIl times, yet at no time have strongly-incompatible contents. They continually change in content as time goes by, and these changes in content reflect qualitative changes in the facts themselves. The whole universe continually ages, as it were, and with it aIl the facts that compose it. This is what, according to Absolutist Anti-Recurrentism, the passage of time consists in. The view's table for our toy story looks as follows: Present a-l

I

l a

The fact that presently Sam is philosophizing The fact that one day ago Sam was asleep The fact that one day hence Sam will be asleep

I

a+l

96

7. Anti-Recurrentism: Escaping Fine's Trilemma

Absolutist Anti-Recurrentists give the same account of the truth of our toy story as non-funky Absolutist Presentists: the fact that presently Sam is philosophizing makes 'Sam is presently philosophizing' true at a, the fact that one day ago Sam was asleep makes 'One day ago, Sam was asleep' true at a, the fact that one day hence Sam will be asleep makes 'One day hence, Sam will be asleep' true at a. Absolutist Anti-Recurrentism thus complies with Real-2, according to which an A-statement is determined to be true by the A-facts, whenever it is true. However, instead of assuming, with non-funky Absolutist Presentists, that all statements of our story are made true at the present time, Absolutist Anti-Recurrentists may in principle also opt for MINIMAL15M and claim that only present-tensed statements are ever made true, in which case their semantic account of the truth of our toy story would have to appeal to truth-determination over and above truth-making. Acceptance of MINIMALISM would require rejection of OMNIPOTENCE, though, which is undesirable in the light of the comments made in chapter 6. Absolutist Anti-Recurrentists should therefore accept OMNIPOTENCE and reject MINIMAL15M. By accepting OMNIPOTENCE, they are thereby committed to COHERENCE. However, any view that entails SHIFTy-CONTENT, and a fortiori any version of Absolutist Anti-Recurrentism, implies COHERENCE:

(Tlt) If SHIFTY-CONTENT holds, then so does COHERENCE.

Proof Suppose COHERENCE fails. Then there are a time t and two facts

and f' constituting reality at that time such that at t, f satisfies 'is a fact that n days from the present, p' and f' satisfies 'is a fact that m days from the present, q' and 'n days from the present, p & m days from the present, q' is always impossible. By AS, there is a time t' k days from t and a time t" 0 days from t such that f makes some statement true at t' and f' makes some statement true at t":

f

(AS)

3:tTS(f,t) * 0.

By SHIFTY-CONTENT and All, at t', f satisfies 'is a fact that n-k days from the present, p', and at t" f' satisfies 'is a fact that m-o days from the present, q': (All)

(t' is m days from t & 'DnP'

'Dn-mP' E sS(f,t'».

E

SS(f,t»

::::>

('DnP'

~

SS(f,t') ::::>

7. Anti-Recurrentism: Escaping Fine's Trilemma

97

By P3, f makes 'n-k days from the present, p' true at t', and f' makes 'm-o days from the present, q' true at t": (P3)

TS(f,t) =1= 0

::J

TS(f,t) = SS(f,t).

It follows that both 'n days from the present, p' and 'm days from the present, q' are true at t, which is impossible. QED Just Iike Recurrentists, and for the same reasons, Absolutist AntiRecurrentists can accept the standard interpretation of the tense-Iogical operators in terms of quantification over times, while accepting the deviant interpretation would have no point. They also have no problem in complying with Real-l, according to which their view must be always true if true at all. They can comply with this desideratum for the same reasons as Absolutist Recurrentists: on their view, there are Iikewise no empty times. According to Absolutist Anti-Recurrentism, facts continually change their statement-sets. Given certain idealisations about language, already made in chapter 3, it is open to proponents of this view to follow the Presentists' example and accept: (MANIFESTATION)

Those diachronie qualitative differences in facts which are relevant for the passage of time manifest themselves in diachronie differences in the tense of the that-clauses of the fact-descriptions these facts satisfy, and conversely, diachronie differences in the tense of those that-clauses are manifestations of such diachronie qualitative differences in facts.

Given MANIFESTATION, we see how Absolutist Anti-Recurrentists, who, to recall, accept SHIFTy-CONTENT, can comply with Real-3: (Real-3) Always, for every n distinct from 0, the facts which constitute reality are different from what they are n days from the present. Accordingly, with MANIFESTATION being in place, Absolutist AntiRecurrentists can also comply with Real-4 by invoking the principle that a statement of the form' n days from the present, p' is true at a time t iff it is made true at t by some fact, and the following equivalences: 'n days from the present, p' is made true at t by fact f iff at t, f satisfies the description 'is a fact that n days from the present, p', iff at the time n days from t, f satisfies the description 'is a fact that presently, p':

98

7. Anti-Recurrentism: Escaping Fine's Trilemma

(Real-4) Always, for every m and every n, if m days from the present, the facts which constitute reality are different from what they are n days from the present, then the true A-statements have truth-conditions which entail that this is so. Given MANIFESTATION, Absolutist Anti-Recurrentists can also comply with Real-5, because their account of the truth-conditions for A-statements guarantees that whenever there is a diachronie difference in the qualitative nature of A-facts, there is a corresponding difference in true A-statements owing to that diachronie difference in the qualitative nature of those facts: (Real-5) Always, for every n, if the facts which constitute reality are different from what they are n days from the present, then the true A-statements are different from what they are n days from the present partly because of the particular way in which those facts do so differ. MANIFESTATION is a substantial metaphysical thesis that needs to be defended. For unless it can be substantiated, Absolutist Anti-Recurrentism is open to the charge that it reads features of language, i. e. differences in satisfied fact-descriptions, into reality. We will address this challenge in chapter 8, where we will devise a metaphysics and semantics for this view which takes us some way towards meeting this requirement. Before we do so, we shall here bring out some further notable features of the view and subsequently show how it can escape a trilemma recently devised by Fine (2005). Absolutist Anti-Recurrentists accept ABsOLUTISM and SHIFTYCONTENT and so endorse:

(*)

If f constitutes reality at time t and is, at t, the fact that n days from the present, p, then if t' is m days from t, f constitutes reality at t' and is, at t', the fact that n-m days from the present, p.

To see that (*) follows from ABSOLUTISM and SHIFTY-CONTENT, suppose that there is, at t, a unique fact f that, at t, satisfies 'is a fact that n days from the present, p'. Let t' be m days from t. By SHIFTy-CONTENT, All and ABSOLUTISM, f both constitutes reality at t' and, at t', satisfies 'is a fact that n-m days from the present, p':

7. Anti-Recurrentism: Escaping Fine's Trilemma

(All) (t' is m days from t & 'DnP' 'Dn-mp' E 5S(f,t'».

E

99

SS(f,t» ::> ('DnP' $ SS(f,t') ::>

5uppose for reductio that, at t', there is a distinct fact f' that, at t', satisfies that same description. By SHIFTY-CONTENT and All, at t, f' satisfies 'is a fact that n days from the present, p'. 1his contradicts the assumption that f uniquely satisfies that fact-description at t. ( *) is an intuitively plausible principle, whose non-vacuous truth no other realist view of tense implies. Its intuitiveness is somewhat obscured by the fact that it is couched in terms of constitution. But given ABSOLUTISM, the principle is equivalent to:

( * *) Hf is, at time t, the fact that n days from the present, p, then if t' is m days from t, fis, at t', the fact that n-m days from the present,p. Thus formulated, the principle is much more intuitive; and as the discussion towards the end of chapter 6 revealed, ABSOLUTISM itself is more faithful to ordinary talk about facts. Although B-theorists may also endorse (*) (see chapter 9), once ABSOLUTISM and MANIFESTATION are in place, (*) can itself be seen as an expression of the passage of time. The same considerations determine what, on trus view, the table for our toy story will look like in a day's time: Present .j.

a

I

a+l

I

a+2

The fact that one day ago Sam was philosophizing The fact that two days ago Sam was asleep The fact that presently Sam is asleep

Our fact-descriptions can thus be seen to track the changes in the tensed facts which are said to explain in what sense reality changes as time goes by. Fine argues that any view that combines realism about tense, ABsoLUTISM and NEUTRALITY must violate COHERENCE (Fine 2005: 272, 274). Given TII, however, any version of Absolutist Anti-Recurrentism provides a counterexample to Fine's conclusion. Using our own crite-

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7. Anti-Recurrentism: Escaping Fine's Trilemma

ria, we can reconstruct Fine's McTaggartian argument (see Fine 2005: 271-72) and pinpoint where exactly it breaks down. 18 Our reconstruction runs as follows. From realism about tense, it follows that there are tensed facts, e. g.: (1) There is the fact that presently Kit is sitting. From (1) and A3, we can derive: (2) There is a time at which this fact constitutes reality. Given the realist's commitment to A4, we can safely assume that this fact constitutes reality at the present time. Thus, we obtain: (3) The fact that presently Kit is sitting constitutes reality at the present time. Given NEUTRALITY, there are tensed facts constituting reality at a time distinct from the present time. In the light of A14, which implies that if NEUTRALITY holds reality is variegated over time, there are accordingly at least two tensed facts each of which at some time makes some statement true, such that these facts have incompatible contents with respect to those times. Given A6, which says that making a statement true at a time entails constituting reality at that time, it follows that there are at least two tensed facts and two times such that one fact constitutes reality at One of these times, while the other fact constitutes reality at the other time, and such that these facts have incompatible contents with respect to those times. Given the definition of incompatibility of factcontents, D7, and the evident impossibility of 'Presently, Kit is sitting & presently, Kit is standing' , a witness for this existential generalisation would be the conjunction of (3) and: ~k~~~~~~~~~~~~~~ Kit is standing constitutes reality.

Given ABSOLUTIsM, (3) yields:

18

In fonnulating his argument, Fine at some points makes use of the tenn 'ohtains'. However, several passages in his 2005 suggest that he understands it as heing synonymous with 'constitutes reality'. Accordingly, our reconstruction will he in tenns of constitution.

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(5) The fact that presencly Kit is sitting constitutes reality at the time one day from the present time.

In order to derive a violation of COHERENCE from (4) and (5), one must assume that (5) implies: (6) At the time one day from the present time, the fact that presencly Kit is sitting constitutes reality. This implication will hold if FIXED-CONTENT holds. But this implication will fail if SHIFTY-CONTENT holds. Given A10, SHIFTy-CONTENT and FIXED-CONTENT exhaust the options. So without FIXED-CONTENT Fine's conclusion cannot be established. Fine set out to demonstrate that given realism about tense, the combination of NEUTRALITY and ABSOLUTISM is inconsistent with COHERENCE. The availability of Absolutist Anti-Recurrentism shows that Fine' s argument rests on an unargued-for assumption, viz. FIXEDCONTENT, and is to this extent defective. This is not to say, though, that Fine's argument is unsound, for it will succeed if Absolutist AntiRecurrentism ultimately proves unstable or unable to deliver. The next chapter aims to defuse any such charge and to show that Absolutist Anti-Recurrentism affords asound metaphysics and a workable semantics. In particular, it will be shown how MANIFESTATION can be substantiated in these terms and so how Absolutist Anti-Recurrentism can ultimately live up to its aspiration to yield the most convincing response to the demands imposed by the desiderata.

8 Etemal Facts in an Ageing Universe In this chapter, we defend aversion of Absolutist Anti-Recurrentism which accepts OMNIPOTENCE. On that view, there is no extensional difference between constituting reality and truth-making, and every fact constitutes reality at all times. To this end, we first posit an ontology of A-facts and their components and lay down several principles these facts and fact-components obey. Then we devise the first part of our semantics for the A- and B-languages by laying down semantic principles governing basic material A- and B-statements. After that, we give a reduction of times in terms of classes of A-facts and finally complete our semantics by devising principles governing basic structural A- and B-statements. We shall use 'M1', 'M2', 'M3' etc. in order to label metaphysical principles concerning A-facts and their components, '51', '52', '53' etc. in order to label semantic principles, and 'R1', 'R2', 'R3' etc. in order to label reductive theses concerning times. The first two metaphysical principles concem the composition of A-facts and the nature of their components:

(M1) There are monadic A-facts and relational A-facts. Each monadic A-fact is (tenselessly) composed of one subject and one predicable. The subject of a monadic A-fact can be any object whatsoever. 19 The predicable of a monadic A-fact is a monadic tensed property. Each relational A-fact is (tenselessly) composed of several subjects in a certain order and one predicable. The subjects of a relational A-fact can be any objects whatsoever. The predicable of a relational A-fact is a polyadic tensed property.20

19

20

More carefuIly, the subject of a monadic A-fact can be any object whatsoever provided that it is capable of satisfying open sentences of the type 'n days from the present, R(x)', where 'R' is as stated in chapter 1. So, abstract objects like numbers or Euclidean triangles are exduded. The same restriction applies to the subjects of relational A-facts. The notion of an order which enters the composition of A-facts may be thought to be problematic. See Fine 2000 for an alternative account that shows how reference to order can be avoided.

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(M2) The tensed property which is the predicable of an A-fact is associated with a unique item we call a proto-property. Where is the predicable of an A-fact and q, the corresponding protoproperty, given any time t, there is a unique n such that at t, is the property of being-q,-n-days-from-the-present. To illustrate, the fact that three days hence, Sam will be sitting is composed of Sam, the subject of the fact, and of the tensed property of sitting three days hence, the predicable of that fact. The proto-property associated with that tensed property is the proto-property of sitting. We assume that if a fact constitutes reality at a time and so exists at that time, then its components likewise exist at that time. It follows that predicables, proto-properties, but also the subjects of facts, always exist (cf. Chisholm 1990 and Zimmerman 2005). Consequently, in order to account for true statements such as 'The Colossus of Rhodes no longer exists', we are forced to invoke a distinct tensed property of existence such that to say of an object x that it has that property is never the same as to say of x that it satisfies '3y(y = x)'. The next two principles respectively concem the identity of, and change in, the predicables of A-facts: (M3) Two predicables are identical iff there is a proto-property q, and a time t such that at t, both predicables are identical to the property of being-q,-O-days-from-the-present. (M4) Predicables qualitatively change through time. Qualitative change of predicables is govemed by the following two laws, holding of any predicable and corresponding proto-property q,: (i) there is a time at which is the property ofheing-q,-O-daysfrom-the-present; and (ü) if at time t, is the property of beingq,-O-days-from-the-present, then at the time which is n days from t, is the property of heing-q,-(-n)-days-from-the-present. The next two principles correspond to M3 and M4, hut respectively concem the identity of, and change in, A-facts: (M5) Two A-facts are identical iff they have the same subjects in the same order and the same predicable. (M6) Although A-facts always have numerically the same components, they nevertheless qualitatively change through time by having their predicables qualitatively change through time.

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Thus, for instance, the fact that three days hence, Sam will be sitting is identica1 with the fact which one day ago was the fact that four days hence, Sam would be sitting. This also validates principle ( *) mentioned in the previous chapter. Whenever an A-fact f has the property of being--n-days-fromthe-present as its predicable, for given n and , we may say that both f' s predicable and f itself then have the tense-asped of n-days-from-thepresent-ness, and derivatively that they then have a past-tense-aspect if n is negative, a present-tense-aspect if n equals zero and a future-tenseaspect if n is positive. This completes the account of our basic ontology. One will get a better grip on this ontology once certain semantic considerations are put forward, which will be done next. One of the principal aims of this chapter is to give a full semantics for all A- and B-statements, as these were defined in chapter 1, which is formulated in terms of the entities of our ontology. We begin with the basic material A-statements which, given our convention governing the use of 'n days from the present', are those of the following form: 'n days from the present, R(ab ...)'.

To each such statement, there correspond three subsentential expresSlOns:

'R-ing' 'the property of R-ing-n-days-from-the-present' 'the fact that n days from the present, R(ab .. .)'.

Not all expressions of either type will be used in the metalanguage in order to refer. In particular, which expressions of type 'R-ing' will be used to refer is determined by the proto-properties that there are. For example, assume that, where 'F' is a specific colour term (e.g. 'red'), whatever makes 'n days from the present, a is F' true at a time also makes 'n days from the present, ais coloured' true at that time. Then, given AB, it is plausible to conclude that 'being F' and 'being coloured' cannot both refer to a proto-property: (AB) (t' is m days from t & f TS(f',t')).

* /') :J ('Dnp' E TS(f,t) :J 'Dn-mp' Et:

For suppose that 'being coloured' is the proto-property of some A-fact f. By A5, f will at some time t make some basic material A-statement

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true, e. g. 'k days from the present, a is coloured'. Since a can be coloured only by being of a specific colour, some statement of the form 'k days from the present, a is F', where 'F' is some colour term, must also be true at t. Since a' s being F k days from the present is never necessitated by a' s being coloured k days from the present, the latter statement is not determined to be true at t by J. H 'being F' also refers to a proto-property, then it is plausible to assume that there is an A-fact f' with this proto-property, and so distinct from J, that determines' k days from the present, a is F' to be true at t. There must accordingly be a time t' m days from t such that f' makes 'k +m days from the present, ais F' true at t'. Given our assumption, f' accordingly makes 'k+m days from the present, ais coloured' true at t'. Ex hypothesi, however, J also makes 'k days from the present, ais coloured' true at t. This contradicts A13. So not both 'being coloured' and 'being F' refer to proto-properties. We shall use 'm' and variants thereof in place of 'R' whenever 'R-ing' is intended to range over proto-properties, and will call basic material A-statements of the form 'n days from the present, m(ab ... )' core A -statements. Similarly, we will call basic material B-statements of the form 'At time t, m(ab ... )' core B-statements. As we shall see, the core A-statements are those basic material A-statements that if true are made true by the A-facts as characterised in the previous section. According to the general characterisation of the A-theory given in chapter 1, all basic material A-statements are, if true, determined to be true by A-facts. The following are natural assumptions to make for an A-theorist: For every basic material A-statement s which is not a core statement, for all times t, if s is true at t, then there is a family X of core A-statements such that (i) all the members of X are true at t, and (ii) necessarily, if all the members of X are true at a time, then so is s. For every basic material B-statement s which is not a core statement, if s is true, then there is a family X of core B-statements such that (iii) all the members of X are true, and (iv) necessarily, if all the members of X are true, then so is s. For every non-core A-statement s and time tat which it is true, we call (s,t) the dass of families which satisfy conditions (i) and (ii), and for every true non-core B-statement s, we call (s) the dass of families which satisfy conditions (iii) and (iv).

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Before giving the truth-conditions for the core A-statements, we lay down reference-conditions for each type of subsentential expression which we are going to use in the meta-language: (51)

Each expression of type 'ffi-ing' always refers to one and the same proto--property.

(52)

Each expression of type 'The property of ffi-ing-n-days-fromthe-present' always refers to a tensed property, capable of being the predicable of an A-fact, whose corresponding proto--property is ffi-ing.

(53) Hat time t, 'the property of ffi-ing-n-days-from-the-present' refers to property