TO DO

Need to rearrange the presentation of this material.

• Part 4 and part 2 of the lecture need to be combined;
• the Prior discussion needs to be treated as a response to the B-theory argument that ‘dinosaurs exist in the past’ is like ‘black swans exist in Australia’.
• The indexical discussion needs to be integrated into the discussion of the temporalist/eternalist dispute.

Metaphysical Theories of Time

Time and Time Travel

• Last time we discussed time travel and Lewis’s proposed resolution of the puzzling temporal discrepancies in time travel.
• His proposal had two ingredients:
  1. There is a single dimension of external time, in a four-dimensional spacetime manifold, in which every event has a spatiotemporal location, and every object that persists through time occupies a trajectory, a region extended in both space and time;
  2. Along the trajectory of each object is defined that object’s personal time.
  • Time travel is what happens when the personal time of an object doesn’t line up with external time.
• In this part of the course, we’ll look at whether the structure of external time that Lewis presupposes is adequate.
• Is time a dimension like space? Or does that picture leave something out?
• Today, an overview of the issues: terminology, definitions, and the structure of the field.

A-series and B-series

• In a famous but deeply confusing paper, McTaggart (1908) notices that we have two ways of talking about time.
  1. We can talk in terms of events or moments being past, present and future. (The A-series.)
  2. Or we can talk in terms of events, or moments, being earlier than and later than one another. (The B-series.)
• While they are clearly related, the second way of talking simply structures the series of moments; the first way also locates the present moment within that structure.
• Note this allows us to translate between the approaches.
  • From A-series to B-series:
    • \(t\) is earlier than \(t'\) iff when \(t\) is present, \(t'\) is future;
    • \(t\) is later than \(t'\) iff when \(t\) is present, \(t'\) is past.
  • From B-series to A-series: (note we need to use the notion of now):
    • \(t\) is past iff \(t'\) is now and \(t\) is earlier than \(t'\);
    • \(t\) is future iff \(t'\) is now and \(t\) is later than \(t'\).

A-theory and B-theory

• So the A-series and B-series are two ways of talking about the same series of moments.
• A key difference is that the A-series adds a distinguished moment – the present – around which the series of moments is oriented.
• Is this difference substantive, or merely terminological?
• The A-theory says it is genuine: the A-series way of talking better represents what is really going on with the structure of time.
• The B-theory says it is merely apparent. Past, present, and future tense are not additional features of reality, but merely arise due to our perspective on the B-series.

The B-theoretic picture

One can easily get the idea that the notions of past, present, and future apply objectively to the universe. In contrast, I shall argue that the concepts of past, present, and future have significance only relative to human thought and utterance and do not apply to the universe as such. They contain a hidden anthropocentricity. So also do tenses. On the other hand, the concepts of ‘earlier’, ‘simultaneous’, and ‘later’ are impeccably non-anthropocentric. I shall argue for a view of the world as a four-dimensional continuum of space-time entities, such that out of relation to particular human beings or other language users there is no distinction of ‘past’, ‘present’, and ‘future’. Moreover, the notion of the flow of time is the result of similar confusions. Our notion of time as flowing, the transitory aspect of time…, is an illusion which precents us seeing the world as it really is. (Smart 1963: 132)

• We come back to this last topic next time.

The Structure of Time

• The B-theory is egalitarian: no moment of time is objectively (‘non-anthropocentrically’) special.

  • Sometimes said to be a spatializing view of time: just as no place is objectively special, likewise B-theories say no time is either.

• According to the B-theory, there are many times, each of which tells us how things are a specific point in time, and the whole truth about reality over time is just the totality of these truths about particular times.

• The A-theory is inegalitarian. While A-theories can agree that there are many times, the totality of facts about what is true according to these times leaves something out – namely, which of them is now, and hence which of them is right about how things are.

  The essence of the A-theory is the objectivity of the distinction between past, present, and future. What is presently true is true, simpliciter, not merely true relative to a time or utterance or situation. (Zimmerman 2005: 431; see also Zimmerman 2008: 212)

What makes a Moment ‘Special’?

• This way of characterising the debate between the A-theory and the B-theory relies on the idea of an objectively special or privileged moment.
• There’s a prima facie worry here, namely, that there are special moments even according to the B-theory; and that the present moment isn’t amongst them.
• For example, if the Big Bang occurred, the moment at which it occurred is very special, an objectively distinguished moment from all others.
• By contrast with the moment of the Big Bang, the current moment is not very distinguished; it is pretty ordinary, all things considered, and not too different from the previous moment or the subsequent on in terms of what happens at it.
• Therefore the present cannot be privileged in terms of what’s happening at it; rather, the present moment is privileged in itself.
• We’ll come back later to the potential sources of this privilege.

Maps and Perspectives

• Think of a map in a shopping mall, which shows the locations of all the shops in space. In the mall itself these maps will often have a useful You are here arrow pointing to the represented location of the map on the map itself.
• This arrow indicates a ‘special’ point: the point at which the map itself is located. But it is obviously not objectively special: another similar map, located in a different part of the mall and with its arrow pointing to a different location, could also be equally true and accurate.
• The arrow points to a perspectivally special point. Each point in space is special ‘according to itself’ in that sense, but it cannot be that one of the two places is really here and the other is not. (That’s not how the word here works!)
• The B-theory says that now is like here: it picks out a perspective on the series on moments, but nothing objectively special.
• The A-theory says now isn’t like here; which moment is present isn’t just a matter of our perspective.

Now, Absolute and Indexical

• Both A- and B-theory of course have the word now.
• Both agree that there is an indexical use of now, on which it means something like the moment of utterance.
  • So I am writing now could mean something like I am writing on August 4, 2022.
• But the A-theorist also think there is an absolute sense of now: the sense in which I am writing now is true iff I am writing.
• In this sense, now denotes a property, that of absolute presentness, rather than referring to a specific time.
• The A-theorist endorses the idea that there is a property of absolute presentness; the B-theorist rejects it.

Translation revisited

• Recall the translation schemes between the A-series and the B-series. To understand past in terms of earlier than, we used the word now.

• But if now has two senses, that translation was ambiguous:

  1. \(t\) is past iff \(t\) is earlier than the time which is absolutely present; and
  2. \(t\) is past iff \(t\) is earlier than the time of utterance.

• The A-theorist endorses the (1) account of pastness, making pastness an absolute notion, not a relative one.

• The B-theorist endorses only the (2) account; is past is an indexical expression.

• These two senses won’t come apart in simple cases (for if I say I am writing now and it is August 4, 2022, then both I am writing and I am writing on August 4, 2022 are true.)

• But they can diverge – when Churchill said ‘Now this is not the end’ after El Alamein, he said something true in the indexical sense (i.e., that November 1942 is not the end of WWII, which was and remains true), but something which was true but is now false in the absolute sense (that WWII isn’t over).

Actuality

• One parallel is with the modal adverb actually.

• Actually seems primarily to have an absolute use, as in examples like

  3. I could have been taller than I actually am.
  • Here actually is about the actual, real world – we are comparing my absolutely real height with a merely possible height I could have had.

• But there might also be indexical uses of actually (Stalnaker 1976: 69). Consider in a work of science fiction; if a character says Actually, faster-than-light travel has already been invented, we don’t understand that use of actually as denoting our actual world, but rather as referring to the ‘world of the fiction’.
  

• These dual roles are – according to the A-theory — parallel in the word now (and the even closer parallel with the adverb presently).

• By contrast, here has no absolute use, being merely indexical.

Absolute Presentness, Temporary Truth

• A proposition is what is said by a particular utterance of a sentence.
• The indexical treatment of now in entails that any sentence involving past, analysed along the lines of (2), expresses a permanently true proposition.
  • If I say World War II is past, I express on this analysis the proposition that World War II is earlier than 2022, which is true always if it is ever true, because it is about the relations between two times in the manifold.
  • Utterances of those words on different occasions express different propositions, e.g., ‘WWII is earlier than 2023’, etc.
• By contrast, if now denotes absolute presentness, as on the analysis in (1), what is expressed by World War II is past is only temporarily true.
  • Every utterance of World War II is past expresses the proposition that WWII has the property of absolute pastness – a property it now has, but lacked at every moment before 1945.

Temporalism and Eternalism

• The thesis that some propositions can be temporarily true is known as temporalism (Richard 1981).
• The A-theory appears to require temporalism: the present moment is absolutely objectively privileged, but soon won’t be (it will soon be one of the many moments that are absolutely past). So the proposition that 2022 is absolutely present cannot be always true; since it is true, it must be temporarily true.
  • Indeed, it can be argued that temporalists about propositions should be A-theorists. The present moment is special because it is the unique moment at which all the temporally variable propositions are true. (See however Fine (2006: 401–2).)
• The rival view to temporalism is eternalism, the view that no propositions change their truth value over time.
  • ‘Eternalism’ is, unfortunately, also the name of another view, about temporal ontology, that we’ll discuss below.

Against Temporalism

• Consider these examples (cf. Richard 1981: 4):

4. In 1970, I said ‘Nixon is up to no good in the White House’, and I still believe what I said.
5. Nixon is up to no good in the White House.

• If propositions vary in truth value over time, the same proposition is expressed by every utterance of (5) – the 1970 one, and the present one.
• If so, then (1) entails that (5) could be used to express Mary’s current belief; but in English (4) does not entail that Mary believes that Nixon is still up to no good in the White House.
• The proposition that Mary believes, expressed by a Nixon-presidency-simultaneous utterance of (5), is accordingly not the same proposition as a present utterance of (5) expresses; apparently contra temporalism.
  • Another example with the same sort of structure is given by van Inwagen (1983: 32–33).

Variable truth or context-sensitivity?

• Eternalists don’t deny that some sentences change their truth value – those including temporal indexicals like ‘past’ or ‘now’ do.
• But they achieve this by expressing different propositions at different moments: they are context-sensitive.
• So, in a slogan: the eternalist thinks a sentence like World War II is past is context-sensitive, but each of the propositions it can express are permanently true; the temporalist thinks that sentence expresses just one tensed proposition, but that proposition itself has its truth values impermanently.
• B-theorists are eternalists: the ‘block universe’ of the B-theory is just a record of all the eternal truths about what things are like at all the various points of space and time.

‘Taking Tense Seriously’

• The A-theory is sometimes said to be a view that ‘takes tense seriously’ (Zimmerman 2005). This might prompt an objection:

  Tense is a feature of linguistic expressions; but why should the obligatoriness (or otherwise) of tense marking in natural language indicate anything, one way or another, about the structure of time?

• Response. The temporalist view ‘takes tense seriously’ because temporary propositions themselves are have features that resemble tenses.

  • So yesterday the proposition that it is sunny used to be true. But that entails that a different proposition – that it was sunny — is presently true. The relationship between the past truth of the proposition about how things are, and the present truth of the proposition about how things were, mirrors that between the past truth of the present tense sentence it is sunny and the present truth of the past tense sentence it was sunny.

• The B-theorist does not accept that there are propositions which behave like this; nothing analogous to the surface grammar of tense appears in the propositions that the B-theorist takes natural language sentences to express.

The A-theory

• The A-theory then names a cluster of views: tense is fundamental; tense is ineliminable; truth is temporary; the present is privileged; pastness and futurity are absolute….
• Opt for any one of these, and the others come in its wake. We could try to figure out what the ‘real’ source of the A-theory is, but why bother? Orthodox A-theorists endorse them all, and B-theorists deny them all.
• So far we’re just trying to understand what the A-theory is. Why accept it? is another question.

A-theoretic Temporal Ontology: Presentism and its Rivals

The Source of Privilege

• According to the A-theory, the present moment – the one indicated by a standard use of now – is special. What makes it special?
• Different A-theories give different answers (Zimmerman 2008: 212–14):
  • The growing block view says that the past is real, but the future is not; hence the present is special in being the last existing moment (Broad 1923; Tooley 1997);
  • The moving spotlight view says that the present is special just because it alone is accurate in what is true according to it (Cameron 2015; Skow 2015; Deasy 2017), or because it alone is concrete (Williamson 2002);
  • Priority presentism says that the present is special because it is fundamental, and past and future moments are derivative (Baron 2014);
  • But by far the most popular view is existence presentism, the view that the present is special because only present things exist (Bigelow 1996; Zimmerman 2008).

Two Issues in the Metaphysics of Time: Ontology and Tense

• The existence of these many varieties of A-theory show that we should distinguish two questions:

  1. Are past (and future) events and things real in the same way as present things? (Alternatively: do they exist as presently existing things do?) Eternalists (in the ontological sense!) say yes; presentists (and some others) answer no.
  2. Is the totality of how things are temporary (temporalists/A-theorists) or permanent (eternalists/B-theorists)?

• Taking Lewis’ (1976) model of time literally answers both questions yes: the block universe includes all of reality – past, present and future – and the totality of facts (true propositions) in the block universe doesn’t vary from moment to moment.

• The moving spotlight, etc., views show that we aren’t required to answer these questions the same way – ‘spotlighters’ answer the first question yes and the second no.

Temporal Ontology

• Note however that the no/yes combination (a presentist B-theory) is pretty unappealing.
  • That would be the view that time is like a four-dimensional manifold that just happens to lack any extent. All our claims about the past/future will just be false.
• So the viable options look like the doubly eternalist B-theory favoured by Lewis (1976), and various kinds of A-theory that differ over their views on temporal ontology, over which past and future things exist.
• Before we can decide on the overall question of the A-theory or the B-theory, it seems like we need to decide on the question: which A-theory?

Deflationism: Is there a real dispute over ontology?

• Before turning to that, a preliminary objection draws our attention.

  Is there a real dispute between A-theorists and eternalists? I can only make sense of the eternalist claim ‘past events are real’ in two ways:

  1. ‘are real’ is present-tensed; in which case eternalism says that, e.g., dinosaurs are presently real, and that is just false.
  2. ‘are real’ uses the atemporal present – like the occurrence of ‘are’ in ‘people are selfish’, where it means something like ‘are or were or will be’. (Or maybe it’s more akin to ‘always, like charges repel’.) But then eternalism is trivially true, saying, e.g., that dinosaurs are or were real.

• Response (Smart 1963: 137–38). Past events are real is like two is prime, or numbers are real. These are not disjunctions of tensed claims, but rather not tensed at all – they concern entities where a temporal perspective is inappropriate. And when we discuss the overall contents of the block universe, a temporal perspective (from within the block) is likewise inappropriate.

In Favour of Presentism

• Zimmerman (Zimmerman 2008: 212–14) considers various views on A-theoretic temporal ontology.

• He makes two objections to non-presentist views:

  Neither [growing block nor moving spotlight] can explain why we care so much about whether things are present or past. If a pain is just as intrinsically painful when it has the spotlight upon it,… why should the passage of the spotlight … change our attitude towards it? And even if we did care about these rather obscure changes, how could we ever know when they have occurred? (Zimmerman 2008: 214)

First objection: Pain and Existence

• Mere changes in presentness, if they aren’t accompanied by other changes, aren’t things we should care about. Existing pain is painful; since what I care about is avoiding pain, that it is existing and also past is no consolation.

• For the presentist, by contrast, a past pain is nothing, and ipso facto not a painful thing. This fits with our experience; and with our attitudes of relief and anticipation (Prior 1959).

  • We’ll come back to this when we look more closely at temporal experience and the attitudes.

• An alternative? Sophisticated moving spotlight, changes in presentness accompanied by other changes:

  Doubtless, in some sense Trajan no longer exists. Specifically, he is no longer anywhere; he lacks spatial location. Although atoms which once composed him may still be spatially located, he is not identical with those atoms. More generally, we may say that he is no longer concrete. But he still counts for one when we ask ‘How many Emperors of Rome were there?’ (Williamson 2002: 245).

Does This Moment Denote the Present Moment?

From my current perspective I know that Caesar is in the objective past. But do I have any reason to believe that I am in the objective present? What if the objective present is in 2004, when you, dear reader, are reading this paper? … there is no reason on the [growing block] view to think that the objective present is not located at any particular point in some volume of space-time that may lie in the future direction from us. … So we should regard the hypothesis that the current moment is present as only one among very many equally likely ones. (Braddon-Mitchell 2004: 200–201)

The Caesar Argument Unpacked

6. Only one moment is present;
7. If there are many existing moments, each of them appears to be present to its denizens;
8. If there are many existing moments, then almost all moments appear to be present but are not. (From 6, 7)
9. If there are many existing moments, then for all we know, this moment appears to be present but is not. (From 8)
10. We know that this moment is present;
11. So there is only one existing moment, the present moment. (From 9, 10)

• The reasoning at step (11) is modus tollens: from ‘if \(A\), \(B\)’ and ‘not-\(B\)’, conclude ‘not-\(A\)’.
• The B-theorist rejects premise (6) (all moments are present in the indexical sense); the presentist accepts the conclusion.
• The problem for other A-theorists is the other premises seem attractive.

The Argument from ‘Commonsense’

Why be an A-theorist presentist?

• Zimmerman argues that if you are going to be an A-theorist, then you should be a presentist.
• But why be an A-theorist? Zimmerman’s strategy:
  • Show that the A-theory is the theory of commonsense; and that commonsense is at least the default position.
  • Accordingly, we are entitled to believe our commonsense theories without any special evidence for them, as long as we don’t have good evidence against them.
• This second step appeals to a kind of doxastic inertia: that it is rational to retain your beliefs unless you are given a reason to change them.
  • This might derive from an epistemology that focuses on rational changes of mind (Harman 1986).
  • It contrasts with a demanding epistemology which says that you shouldn’t believe without conclusive evidence (Clifford 1876); such an epistemology would say that we should start out with no beliefs at all.

Presentism and Platitudes

• Zimmerman thinks the A-theory’s distinctions between past, present, and future, and the view there is a absolute fact of the matter about which moment is present, are platitudes.

• No special evidence accrues from their platitudinous status; but these claims

  seem obviously true to most sane human beings… these are truisms denied by a relatively small group of people … who have become accustomed to using spatial metaphors to understand temporal notions. (Zimmerman 2008: 221–22)

• Zimmerman isn’t denying the utility of these spatializing metaphors; but when you start interpreting metaphorical claims as if they are literal assertions, you’re in trouble.

Why Should Commonsense be Believed By Default?

• The threat: if platitudes aren’t epistemically specially reliable (aren’t conceptual truths), then why think they are true?

  we must allow that it is reasonable to believe things that seem obviously true, in the absence of special reasons to doubt them; and we must allow this even if the beliefs are admittedly not certainties, and cannot be “proven” in any interesting sense of the word. … if some particular example of an obvious truism is part of commonsense, then it is widely held; and so, assuming most people are well placed to have an opinion about its subject matter, it has passed a further test of reasonableness (Zimmerman 2008: 222)

• But why think ordinary people are ‘well placed’ for their naive opinions to be reasonable? Why trust untutored judgements over the considered opinion of B-theorists?

The Point of Philosophical Argument

• If I commonsensically believe \(p\), I’m entitled to keep believing it even if I can’t answer non-commonsensical philosophical arguments to the contrary. If those arguments persuade you of the B theory, fine; but don’t expect that philosophical argument will persuade everyone.

  Philosophical theories are never refuted conclusively. … The theory survives its refutation – at a price. [And] what we accomplish in philosophical argument [is]: we measure the price.

  [After doing so] we still face the question which prices are worth paying, which theories are on balance credible, which are the unacceptably counterintuitive consequences…. (Lewis 1983: x)

• For Zimmerman, the B-theory is unacceptably counterintuitive; it does injustice to widely accepted platitudes that he finds no compelling reason to give up.

Prior on Tense and Temporal Reality

Talking About Existence

• There is a way of talking which, Prior says, is misleading (1970: 24). We sometimes say things like this:

  12. Centaurs exist in some possible world,

  13. Raskolnikov exists in Crime and Punishment,

  14. Black swans exist in Australia.

• The obvious account of the last sentence that it is existence-entailing: when (14) is truly said, black swans exist.

• Since (12) and (13) are grammatically parallel to (14), and are both true (at least when (12) is taken to paraphrase the true sentence It is possible that centaurs exist) should we conclude that possible worlds or Raskolnikov exist?

• It is at least not obvious that we should.

Tense Operators and the A-theory

To say that there are possible worlds in which there are centaurs is just to say that it could be that there are centaurs. In general, to say that \(X\) could be the case in some non-real world is just to say ‘\(X\) is the case’ with some modifying prefix…. (Prior 1970: 246)

• How to take Dinosaurs exist at some moment in the past? Prior says: not like (14), but more like (12): There were dinosaurs (Prior 1970: 247).

• So Prior thinks that the B-theorist, who takes the past to be ‘[an]other region… in which other things happen’ (Prior 1970: 246), is mislead by the surface form of their language.

• Many B-theorists propose to explain tense away:

  (WAS-PAST)

  It was the case that \(\phi\) iff it is the case that \(\phi\) at some moment in the past.

  Prior accepts this, but thinks the direction of explanation goes from left to right: we understand the modifier in the past in terms of the more basic tense operator was.

Presentism and the Real

• Prior’s distinctive additional thesis is this: To be real is to be truly said to exist without a qualifying modifier.
• Prior claims: it was the case that is a qualifying prefix.
• If was is a qualifying prefix, then past entities and events are not real.
• By contrast, present entities and events are real, since they can be said truly to exist using an unprefixed existence claim: ‘To say that my lecture is present is just to say I am lecturing – flat, no prefixes’ (Prior 1970: 247)
• What about (14): isn’t that said with a qualifying modifier, namely, in Australia, but also black swans are real?
• This isn’t a qualifying prefix: for \(\phi\) in Australia entails \(\phi\).
  • Compare: John is singing in the garden entails John is singing (Nam 1995: 34).
  • Actually things are a little more complex: the prefix In Australia might be a qualifier, since In Australia, every spider is dangerous doesn’t entail Every spider is dangerous (Thomason and Stalnaker 1973: 205)

The Grammar of Tense

‘I was having my breakfast’ is related to ‘I am having my breakfast’ in exactly the same way as ‘I am allegedly having my breakfast’ is related to it, and it is only an historical accident that we generally form the past tense by modifying the present tense, e.g., by changing ‘am’ to ‘was’, rather than by tacking on an adverb (Prior 2005: 136)

• Prior’s idea: the most plausible account of natural language shows that, implicitly, it is committed to an A-theoretic metaphysics.
• The language in which temporal reality ought to be represented thus includes the temporal modifiers it was the case that and it will be the case that.
• These expressions are studied by tense logic, and while the mathematical models of tense logic include past and future times (Sider 2001: 16), we are not required to take those entities in the models seriously – just as we aren’t required to believe in frictionless planes or possible worlds, even though they also feature in useful models.

Prior on A- and B-languages and Presentism

• There is here an argument for the A-theory, and presentism in particular.

  15. The B-theory cannot give an adequate account of tense operators like it was the case that \(\phi\).
  16. The A-theory can give an adequate account of tense operators. (This is part of what it means to say the A-theory takes tense seriously.)
  17. was \(\phi\) is true iff \(\phi\) is in the past. (WAS-PAST)
  18. The best analysis of in the past is as a qualifying modifier which is not existence entailing.
  19. The best analysis of was \(\phi\) is not existence entailing. (from (17) and (18))
  20. Therefore we should adopt a presentist A-theory. (from (16) and (19))

Can the B-theory explain the tense operators?

• The key premise (15) says that the B-theory cannot explain tenses.

• Why not? Consider Smart (1963: 137): ‘“now” is equivalent to “simultaneous with this utterance”’ – what’s wrong with that, or the related view that was means earlier than this utterance?

• There is a flat-footed objection, that someone (a child, perhaps) might know what now means without knowing what an utterance is, or what simultaneous means.

• But set that aside; this approach faces a dilemma:

  1. If this utterance is understood to name the token utterance time (say, 13:42 on August 7, 2011), the sentence is permanently true, unlike the A-sentence it is supposedly synonymous with.
  2. If this utterance is understood to describe a time, which (like descriptions generally) may apply to different objects when used at different times, then the sentence varies in truth value correctly, but now we need to explain in turn how this sentence should be assigned a tenseless B-theoretic equivalent.

Resisting Premise (15)

• Two conceptions of an ‘adequate account’: We have successfully given an adequate account of a sentence \(S\) involving some purportedly problematic expression \(X\) if
  1. We have given another sentence \(S'\) not involving \(X\) that can be truly uttered iff \(S\) can truly uttered.
  2. We have given truth conditions for \(S\) such that for every utterance of \(S\) in some circumstance \(c\), there is a sentence \(S_{c}\) not involving \(X\) that says the same thing as that use of \(S\).
• Premise (15) presupposes that the first conception is correct.
• But why think that? Consider this parallel case: The party is that way and The party is to the south.
• These are not synonymous, so the second cannot be an adequate account of the first according to the first conception.
• But we could run a parallel argument that that way operators must be basic, etc. – and this doesn’t seem plausible.

Indexicals

• Rather: even if we cannot produce a synonymous sentence, we can in every circumstance say the same thing without using that way.
• Each utterance of that way \(\phi\) says the same thing as some sentence about a particular direction, but in such a way that which direction is involved depends on the circumstances of the utterance.
• This is the standard picture of indexicals (Kaplan 1989): relative to a circumstance, a sentence expresses a particular proposition, but perhaps a different proposition at each circumstance.
  • As long as we can produce another sentence which expresses the same proposition, we have analysed the original claim, even if the first sentence depends on the circumstance and the second one doesn’t.

Temporal indexicals and the B-theory

• Likewise, according to the B-theory, every utterance of an A-truth has B-theoretic truth conditions.
  • An utterance of It was raining at \(t\) expresses the same proposition as a simultaneous utterance of it rains before \(t\), which is purely B-theoretic.
  • But those sentences can be used to say different things (the first one is sensitive to the time of utterance, the second one is not), so are not synonymous.
  • Smart’s ‘token reflexive’ account of now is also context-sensitive, and so it succeeds only if the proposition expressed is a B-one – the token reflexivity isn’t doing the work, it is the B-theoretic truth conditions underlying it.
• That is, the A-notions (past, present, future, now, was, will be, …) are like indexicals, and not fundamental features of reality – though they are ineliminable from language, and cannot be analysed away in the first sense (Perry 1979).

The Argument for Presentism

• So Prior’s argument for presentism will not persuade the committed B-theorist; they will simply reject the opening premise (15).

• But what of the A-theorist who accepts that premise?

• There are two spots in the argument where a proponent of the growing block or moving spotlight theory might want to resist:

  1. They might want to question the key premise here is (18), that in the past is a non-existence entailing qualifying prefix.
  2. They might want to question the inference from (19) to (20).

• The second issue can be dealt with swiftly. Prior’s argument seems to rest on a claim like this:

  21. Ceteris paribus (‘other things being equal’), we ought to adopt the smallest ontology consistent with our evidence (Occam’s razor).

• We can all agree that presentism has a smaller ontology - less stuff. But we need to see whether other things are equal – see below.

Are the tense operators non-factive?

• Still, there is a dispute internal to the A-theory about whether it was the case that is a qualifying modifier, as Prior’s argument requires.
• If \(\mathcal{O}\) is a modifier, it is factive iff \(\mathcal{O}p\) and not-\(p\) is self-contradictory.
• Since there were dinosaurs but there aren’t dinosaurs is not self-contradictory, it seems safe to conclude that it was the case that is non-factive.
• But note this isn’t yet conclusive against the eternalist A-theorist. Think of Prior’s own example: allegedly is non-factive, but that doesn’t prevent an allegation being true!
• All that this shows is that A-theoretic eternalists (and growing blockers, et.) need some other reason to think that facts about what exists are permanent, a reason that does not derive from any purported factivity of tense.
• This might be because of some advantage of eternalism (so Williamson (2002) argues the tense logic of permanent existence is preferable); or some disadvantage of presentism – to this second suggestion we now turn.

Against Presentism

Problems for Presentism

• Presentism might be the natural starting point, the folk theory of temporal ontology.
• But it might still be that other parts of our belief system, whether folk or informed by science, are in tension with presentism.
• The cost-benefit analysis might favour eternalism overall, despite the prima facie implausibility of claiming that there is some sense in which dinosaurs exist expresses a truth.
• Sider (2001: 25–52) offers three main problems for the presentist: problems from cross-time relations; problems from truthmakers; and problems to do with relativity.

Against Presentism: Cross-time ontology

• Consider There were two kings named Charles (Lewis 2004). Can this be rendered using the standard tense operators?
  1. It was the case that (there are two kings named Charles)? (False)
  2. It was the case that (there is a king named Charles) and It was the case that (there is another king named Charles)? (Problem: this another smuggles in the cross-time relations we want to understand.)
  3. It was the case that (there is a king named Charles and It was the case that (there is another king named Charles))? (problem: infinitely many kings named Charles cannot be expressed by any sentence of Priorean tense logic, though it can be expressed easily in English.)
• Span operators: It HAS been that \(p\) which (informally) means There was a past time interval at which \(p\).
• We offer the analysis: It has been that (there exist two kings named Charles).
  • Objection: isn’t this just not what the original sentence claimed? Answer: maybe we should have given truth conditions for was that mentioned intervals originally.

Span Operators and Presentism

Presentists do not think that it merely happens to be the case now that only present things exist. They think that it is always the case … that only (then-) currently existing objects exist.… Presentists cannot admit, therefore, that there were once exceptions to presentism. But they would have to admit just this, if they accepted the span operators. (Sider 2001: 27)

• Since there never were simultaneously two kings named Charles, the presentist cannot admit that ever there were two kings named Charles: problem.
  • Also: won’t it be true that ‘It HAS been that I am sitting and standing’; but contradictions are always false too.
• The upshot: span operators are only ideologically acceptable to non-presentist A- and B-theorists, and their use is implicitly in tension with presentism. If we need to use them, we ought not be presentists (but see Brogaard 2007).

Cross-time spatial relations

• So if span operators are off the table, the presentist faces a problem in understanding cross-time relations using tense operators that are ‘instantaneous’.
• This is a big problem, because notions like acceleration seem to require cross-time relations – we need to have facts such as that \(x\) has moved more in the past second than in the one before to ground the fact that \(x\) is accelerating.
• The eternalist can just say: \(x\)’s trajectory (the sequence of spacetime points occupied by \(x\)’s stages) isn’t linear. According to the eternalist, all of these stages exist, so there is no problem with them standing in spatiotemporal relations like \(y\) is not co-linear with \(x\) and \(z\).
• The presentist can’t do this. Perhaps they can appeal to places: e.g., the places \(x\) occupies over time are not co-linear.
  • This is roughly how we handle cross-time comparisons of height, for example.
• But such enduring places are not standard parts of physical ontology (Sider 2001: 28–31).
• It remains a puzzle how presentists can construct cross-time relations from instantaneous snapshots (Sider 2001: 32–35).

Against Presentism: Truthmakers

Truthmaking

For every true proposition \(p\), there exists something \(x\) that necessitates its truth (Armstrong 2004).

• What about past tense claims like there were dinosaurs? What – if not a past dinosaur – makes this true? And mustn’t past dinosaurs thus exist?

• Following Bigelow (1996), this location presently has this property: previously containing dinosaurs. Nothing more to say – that basic state of affairs is a present existing thing which necessitates the truth in question. Is this acceptable?

  The point of the truth-maker principle… is to rule out dubious ontologies.… a proper ontology should invoke only categorical, or occurrent, properties and relations. … Whether the world has the property previously containing dinosaurs is not a matter of what the world itself is like, but point beyond itself, to the past (Sider 2001: 40–41).

Against Presentism: Special Relativity

• In special relativity, there is no absolute and objective physical notion of simultaneity.
• But presentism is the thesis that there is an absolute and objective set of present events; and if so, we could define: \(x\) is simultaneous with \(y\) iff necessarily (\(x\) is present iff \(y\) is present).
• So presentism says there is an absolute notion of simultaneity, (apparently) contradicting STR (Eagle 2021).
• Zimmerman says: while STR doesn’t mention absolute simultaneity, must STR entail the non-existence of absolute simultaneity: ‘we all believe in lots of distinctions physics “can’t see”’ (Zimmerman 2008: 219).
• More on this later in the course.

References