Branching time (x-post from TnT)

I've recently discovered some really interesting papers on how to think about belief in a future with branching time. Folks are interested in branching time as it (putatively) emerges out of "decoherence" in the Everett interpretation of standard Quantum mechanics.

The first paper linked to above is forthcoming in BJPS, by Simon Saunders and David Wallace. In it, they argue for a certain kind of parallel between the semantics for personal fission cases and the semantics most charitably applied to language users in branching time, and argue that this sheds lights on the way that beliefs should behave.

Now, lots of clever people are obviously thinking about this, and I haven't absorbed all the discussion yet. But since it's really cool stuff, and since I've been thinking about related material recently (charity-based metasemantics, fission cases, semantics in branching time) I thought I'd sit down and figure out how things look from my point of view.

I'm sceptical, in fact, whether personal fission itself (and associated de se uncertainty about who one will be) will really help us out here in the way that Saunders and Wallace think. Set aside for now the question of whether faced with a fission case you should feel uncertain which fission-product you will end up as (for discussion of that question, on the assumption that it's indeterminate which of the Lewisian continuing persons is me, see the indeterminate survival paper I just posted up). But suppose that we do get some sense in which, when you're about to fission, you have de se uncertainty about where you'll be, even granted full knowledge of the de dicto facts.

The Saunders-Wallace idea is to try to generalize this de se ignorance as an explanation of the ignorance we'd have if we were placed in a branching universe, and knew what was to happen on every branch. We'd know all the de dicto truths about multiple futures---and we would literally be about to undergo fission, since I'd be causally related in the right kind of ways to multiple person stages in the different futures. So---they claim---ignorance of who I am maps onto ignorance of what I'm about to see next (whether I'm about to see the stuff in the left branch, or in the right). And that explains how we can get ignorance in a branching world, and so lays the groundwork for explaining how we can get a genuine notion of uncertainty/probability/degree of belief off the ground.

I'm a bit worried about the generality of the purported explanation. The basic thought there is that to get a complete story about beliefs in branching universes, we're going to need to justify degrees of beliefs in matters that happen, if at all, long after we would go out of existence. And so it just doesn't seem likely that we're going to get a complete story about uncertainty from consideration of uncertainty about which branch I myself am located within.

To dramatize, consider an instantaneous, omniscient agent. She knows all the de dicto truths about the world (in every future branch) and also exactly where he is located---so no de se ignorance either. But still, this agent might care about other things, and have a certain degree of belief as to whether, e.g. the sea-battle will happen in the future. The kind of degree of belief she has (and any associated "ignorance") can't, I think, be a matter of de se ignorance. And I think, for events that happen if at all in the far future, we're relevantly like the instantaneous omniscient agent.

What else can we do? Well---very speculatively---I think there's some prospect for using the sort of charity-based considerations David Wallace has pointed to in the literature for getting a direct, epistemic account of why we should adopt this or that degree of belief in borderline cases. The idea would be that we *mimimize inaccuracy of our beliefs* by holding true sentences to exactly the right degrees.

A first caveat: this hangs on having the *right* kind of semantic theory in the background. A Thomason-style supervaluationist semantics for the branching future just won't cut it, nor will MacFarlane-style relativistic tweaks. I think one way of generalizing the "multiple utterances" idea of Saunders and Wallace holds out some prospect of doing better---but best of all would be a degree-theoretic semantics.

A second caveat: what I've got (if anything) is epistemic reason for adopting certain kinds of graded attitude. It's not clear to me that we have to think of these graded attitudes as a kind of uncertainty. And it's not so clear why expected utility, as calculated from these attitudes, should be a guide to action. On the other hand, I don't see clearly the argument that they *don't* or *shouldn't* have this pragmatic significance.

So I've written up a little note on some of these issues---the treatment of fission that Saunders-Wallace use, the worries about limitations to the de se defence, and some of the ideas about accuracy-based defences of graded beliefs in a branching world. It's very drafty (far more so than anything I usually put up as work in progress). To some extent it seems like a big blog post, so I thought I'd link to it from here in that spirit. Comments very welcome!

Update: Oh, and worldle abstract:

Indeterminate survival: in draft (x-post from TnT)

Update: I posted this over at Theories and Things, but I feel for it's MV posting I should give the Wordle Abstract for the draft paper:

On with the post:

So, finally, I’ve got another draft prepared. This is a paper focussing on Bernard Williams’ concerns about how to think and feel about indeterminacy in questions of one’s own survival.

Suppose that you know that you know there’s an individual in the future who’s going to get harmed. Should you invest a small amount of money to alleviate the harm? Should you feel anxious about the harm?

Well, obviously if you care about the guy (or just have a modicum of humanity) you probably should. But if it was *you* that was going to suffer the harm, there’d be a particularly distinctive frisson. From a prudential point of view, you’d be compelled to invest minor funds for great benefit. And you really should have that distinctive first-personal phenomenology associated with anxiety on one’s own behalf. Both of these de se attitudes seem important features of our mental life and evaluations.

The puzzle I take from Williams is: are the distinctively first-personal feelings and expectations appropriate in a case where you know that it’s indeterminate whether you survive as the individual who’s going to suffer?

Williams thought that by reflecting on such questions, we could get an argument against account of personal identity that land us with indeterminate cases of survival. I’d like to play the case in a different direction. It seems to me pretty unavoidable that we’ll end up favouring accounts of personal identity that allow for indeterminate cases. So if , when you combine such cases with this or that theory of indeterminacy, you end up saying silly things, I want to take that as a blow to that account of indeterminacy.

It’s not knock-down (what is in philosophy?) but I do think that we can get leverage in this way against rejectionist treatments of indeterminacy, at least as applied to these kind of cases. Rejectionist treatments include those folks who think that characteristic attitudes to borderline cases includes primarily a rejection of the law of excluded middle; and (probably) those folks who think that in such cases we should reject bivalence, even if LEM itself is retained.

In any case, this is definitely something I’m looking for feedback/comments on (particularly on the material on how to think about rational constraints on emotions, which is rather new territory for me). So thoughts very welcome!

Primitivism about indeterminacy: a worry (x-post from TnT)

I’m quite tempted by the view that it is indeterminate that might be one of those fundamental, brute bits of machinery that goes into constructing the world. Imagine, for example, you’re tempted by the thought that in a strong sense the future is “open”, or “unfixed”. Now, maybe one could parlay that into something epistemic (lack of knowledge of what the future is to be), or semantic (indecision over which of the existing branching futures is “the future”) or maybe mere non-existence of the future would capture some of this unfixity thought. But I doubt it. (For discussion of what the openness of the future looks like from this perspective, see Ross and Elizabeth’s forthcoming Phil Studies piece).

The open future is far from the only case you might consider—I go through a range of possible arenas in which one might be friendly to a distinctively metaphysical kind of indeterminacy in this paper—and I think treating “indeterminacy” as a perfectly natural bit of kit is an attractive way to develop that. And, if you’re interested in some further elaboration and defence of this primitivist conception see this piece by Elizabeth and myself—and see also Dave Barnett’s rather different take on a similar idea in a forthcoming piece in AJP (watch out for the terminological clashes–Barnett wants to contrast his view with that of “indeterminists”. I think this is just a different way of deploying the terminology.)

I think everyone should pay more attention to primitivism. It’s a kind of “null” response to the request for an account of indeterminacy—and it’s always interesting to see why the null response is unavailable. I think we’ll learn a lot about what the compulsory questions the a theory of indeterminacy must answer, from seeing what goes wrong when the theory of indeterminacy is as minimal as you can get.

But here I want to try to formulate a certain kind of objection to primitivism about indeterminacy. Something like this has been floating around in the literature—and in conversations!—for a while (Williamson and Field, in particular, are obvious sources for it). I also think the objection if properly formulated would get at something important that lies behind the reaction of people who claim *just not to understand* what a metaphysical conception of indeterminacy would be. (If people know of references where this kind of idea is dealt with explicitly, then I’d be really glad to know about them).

The starting assumption is: saying “it’s an indeterminate case” is a legitimate answer to the query “is that thing red?”. Contrast the following. If someone asks “is that thing red?” and I say: it’s contingent whether it’s red”, then I haven’t made a legitimate conversational move. The information I’ve given is simply irrelevant to it’s actual redness.

So it’s a datum that indeterminacy-answers are in some way relevant to redness (or whatever) questions. And it’s not just that “it is indeterminate whether it is red” has “it is red” buried within it – so does the contingency “answer”, but it is patently irrelevant.

So what sort of relevance does it have? Here’s a brief survey of some answers:

(1) Epistemicist. “It’s indeterminate whether p” has the sort of relevance that answering “I don’t know whether p” has. Obviously it’s not directly relevant to the question of whether p, but at least expresses the inability to give a definitive answer.

(2) Rejectionist (like truth-value gap-ers, inc. certain supervaluationists, and LEM-deniers like Field, intuitionists). Answering “it’s indeterminate” communicates information which, if accepted, should lead you to reject both p, and not-p. So it’s clearly relevant, since it tells the inquirer what their attitudes to p itself should be.

(3) Degree theorist (whether degree-supervaluationist like Lewis, Edgington, or degree-functional person like Smith, Machina, etc). Answering “it’s indeterminate” communicates something like the information that p is half-true. And, at least on suitable elaborations of degree theory, we’ll then now how to shape our credences in p itself: we should have credence 0.5 in p if we have credence 1 that p is half true.

(4) Clarification request. (maybe some contextualists?) “it’s indeterminate that p” conveys that somehow the question is ill-posed, or inappropriate. It’s a way of responding whereby we refuse to answer the question as posed, but invite a reformulation. So we’re asking the person who asked “is it red?” to refine their question to something like “is it scarlet?” or “is it reddish?” or “is it at least not blue?” or “does it have wavelength less than such-and-such?”.

(For a while, I think, it was was indeterminate, one couldn’t know p (think of parallel discussion of “minimal” conceptions ofassumed that every series account of indeterminacy would say that if p vagueness—see Patrick Greenough’s Mind paper). If that was right then (1) would be available to everybody. But I don’t think that that’s at all obvious — and in particular, I don’t think it’s obvious the primitivist would endorse it, and if they did, what grounds they would have for saying so).

There are two readings of the challenge we should pull apart. One is purely descriptive. What kind of relevance does indeterminacy have, on the primitivist view? The second is justificatory: why does it have that relevance? Both are relevant here, but the first is the most important. Consider the parallel case of chance. There we know what, descriptively, we want the relevance of “there’s a 20% chance that p” to be: someone learning this information should, ceteris paribus, fix their credence in p to 0.2. And there’s a real question about whether a metaphysical primitive account of chance can justify that story (that’s Lewis’s objection to a putative primitivist treatment of chance facts).

The justification challenge is important, and how exactly to formulate a reasonable challenge here will be a controversial matter. E.g. maybe route (4), above, might appeal to the primitivist. Fine—but why is that response the thing that indeterminacy-information should prompt? I can see the outlines of a story if e.g. we were contextualists. But I don’t see what the primitivist should say.

But the more pressing concern right now is that for the primitivist about indeterminacy, we don’t as yet have a helpful answer to the descriptive question. So we’re not even yet in a position to start engaging with the justificatory project. This is what I see as the source of some dissatisfaction with primitivism – the sense that as an account it somehow leaves something unimportant explained. Until the theorist has told me something more I’m at a loss about what to do with the information that p is indeterminate

Furthermore, at least in certain applications, one’s options on the descriptive question are constrained. Suppose, for example, that you want to say that the future is indeterminate. But you want to allow that one can rationally have different credences for different future events. So I can be 50/50 on whether the sea battle is going to happen tomorrow, and almost certain I’m not about to quantum tunnel through the floor. Clearly, then, nothing like (2) or (3) is going on, where one can read off strong constraints on strength of belief in p from the information that p is indeterminate. (1) doesn’t look like a terribly good model either—especially if you think we can sometimes have knowledge of future facts.

So if you think that the future is primitively unfixed, indeterminate, etc—and friends of mine do—I think (a) you owe a response to the descriptive challenge; (b) then we can start asking about possible justifications for what you say; (c) your choices for (a) are very constrained.

I want to finish up by addressing one response to the kind of questions I’ve been pressing. I ask: what is the relevance of answering “it’s indeterminate” to first-order questions? How should I alter my beliefs in receipt of the information, what does it tell me about the world or the epistemic state of my informant?

You might be tempted to say that your informant communicates, minimally, that it’s at best indeterminate whether she knows that p. Or you might try claiming that in such circumstances it’s indeterminate whether you *should* believe p (i.e. there’s no fact of the matter as to how you should shape your credences on the question of whether p). Arguably, you can derive these from the determinate truth of certain principles (determinacy, truth as the norm of belief, etc) plus a bit of logic. Now, that sort of thing sounds like progress at first glance – even if it doesn’t lay down a recipe for shaping my beliefs, it does sound like it says something relevant to the question of what to do with the information. But I’m not sure about that it really helps. After all, we could say exactly parallel things with the “contingency answer” to the redness question with which we began. Saying “it’s contingent that p” does entail that it’s contingent at best whether one knows that p, and contingent at best whether one should believe p. But that obviously doesn’t help vindicate contingency-answers to questions of whether p. So it seems that the kind of indeterminacy-involving elaborations just given, while they may be *true*, don’t really say all that much.

Wordles

Via Robbie, I've discovered the genius source of amusement that is Wordle.

Update: Okay, I've become completely addicted. Here are the ones I've saved so far.

Truthmaking for Presentists

The Open Future

Truthmakers and Ontological Commitment

The Contingency of Composition

Turtles All the Way Down

Truthmakers, Realism and Ontology

On The Source Of Necessity

And here is Elizabeth's: Ontic Vagueness

Quantification, Naturalness, Ontology

I’ve posted a draft of a paper ‘Quantification, Naturalness, Ontology’; this is slated for the volume New Waves on Metaphysics, edited by Allan Hazlett – but there’s a while until the deadline, so any comments on it would be really helpful. Here are some of the main themes, on which I’d be grateful to hear thoughts. (These are here condensed and presented without much argument; for further info, obviously, see the paper.)

Thesis 1: As in previous work, I’m concerned with defending a distinction between what there is and what there really is. Following Sider, in order to resist neo-Carnapianism we should insist that there’s a unique most natural existential quantifier: one that carves the world along its quantificational joints. But, there’s no need to say that the ordinary quantifiers of English are this natural quantifier. Naturalness is a reference magnet, to be sure, but it can be trumped by use. But we can introduce a quantifier (‘there really is . . .’) stipulated to be the most natural quantifier. As long as you’re happy with the naturalness talk in the first place, there’s now no mystery in saying that what there is might come apart from what there really is.

Thesis 2: I defend a two-dimensionalist approach to sentences like ‘there is a table’. Considering the universalist world as actual, this sentence requires a table as a truthmaker, and so considering other worlds as counterfactual, we should only judge the sentence to be true at those worlds if they contain certain complex objects, namely tables. But considering the nihilist world as actual, the charitable thing to say is not that that sentence is false but that it requires for its truth only the existence of simples arranged table-wise, and so considering other worlds as counterfactual, we should judge the sentence to be true at a world iff it contains simples arranged table-wise. An attractive consequence is this: assuming (which I hope is the case) that the nihilist world is actual, we have a nice explanation for what many people think is a necessary truth, the necessity of which otherwise looks mysterious, namely: if there are simples arranged table-wise then there is a table.

Thesis 3: It’s right to take Moorean truths about what there is as inviolable. What’s wrong, however, is to read the ontology straightforwardly off of them. The truth of ‘Here is a hand’ is indeed on a stronger footing than any conjunction of premises that entails its falsity. But that doesn’t mean that, e.g., compositional nihilism is false. Compositional nihilism, properly understood, is the claim that no complex objects really exist, and that is compatible with the claim that there are complex objects like hands. The proper methodology is to ask what are needed as the ontological grounds for the Moorean truths. There are no Moorean truths about what there really is.

Thesis 4: The problem of the many is easy. There’s a unique cat on the mat. But asking which collection of particles is the cat, is a bad question. There isn’t really a cat. You can only ask, which collection of particles grounds the fact that there is a cat? Answer: all of them (i.e. all the collections which the universalist thinks are candidates for being the cat). But that doesn’t mean that there are many cats, of course – the one sentence can have multiple grounds.

Thesis 5: Since the ontological commitments of a sentence are its ontological grounds, it’s an open possibility that there are true sentences that lack ontological grounds and hence carry no commitments. I suggest that the truths of mathematics are like this. It’s true that there is a prime number between 8 and 12; but it’s a mistake to think that this is ontologically committing to numbers. (And no ‘paraphrase’ of the sentence into something not quantifying over numbers is necessary to say this.) Mathematical claims are trivial in the sense that they make no demands, a fortiori no ontological demands, on the world. (Cf. what I say here to what Agustin Rayo says in his defence of mathematical trivialism in this excellent paper.)

Thesis 6: Actually not a thesis. I tentatively speculate that one could reduce necessity in the following way: p is necessary iff p lacks an ontological ground. Obviously, not everyone’s going to think this is extensionally adequate, since some think contingent negative existentials lack a ground, and others think everything has a ground, including necessary truths. But I think it looks quite hopeful, and would like to hear whether or not anyone else does.

In other news, Elizabeth and my paper (“Elizabeth and my” – is that right? It sounds terrible, but I can’t think what else it should be.) on the open future has been accepted by Phil Studies. But we’d still appreciate any comments on it, as it’s an issue we’re hopefully going to keep working on.

Metaphysics postdoc at Leeds

Leeds will be hiring a one-year research postdoc in metaphysics (broadly construed) for the academic year 08-09. The post is partially sponsored by the Centre for Metaphysics and Mind.

To apply on line please visit http://www.leeds.ac.uk and click on ‘jobs’, then 'research' (it will be listed as being in the school of humanities, not the department of philosophy). Alternatively, go here. Or application packs are available via email recruitment@admin.leeds.ac.uk or tel+44 (0)113 343 5771. The closing date for applications is August 6th, and interviews will be held in the week beginning Aug 25th.

For US readers: postdocs in the UK are not like in the US. They are a nice gig. There are very minimal teaching or admin duties, so you've basically got a year of research on a decent salary.

Please forward the details on to any potentially interested parties.

PhD studentship in Theoretical Philosophy

PhD studentship available at Leeds: please pass on to any potentially interested parties:

__________________________________
The Department of Philosophy, University of Leeds, intends to offer a Studentship in Theoretical Philosophy to a suitably qualified candidate for its full-time or part-time PhD programme. The studentship is tenable for 3yr (f-t) or 6yr (p-t) from October 2008 and has both tuition and maintenance components: the tuition component will be equivalent to the full EU PhD fee (currently £3.3k p.a. f-t) and the maintenance component will be equivalent to that of the AHRC Doctoral award (currently £12.6k p.a. f-t).The award is conditional on successful application for admission to study for PhD in the Department. However, applicants need not apply for admission prior to application for this studentship. Renewal of the studentship each year is subject to satisfactory progress towards PhD completion.

The successful applicant will undertake a PhD project in the area of Theoretical Philosophy broadly construed and will be supervised by Dr.Robert Williams, Reader in Theoretical Philosophy (http://www.philosophy.leeds.ac.uk/Staff/JRGW/index.html). For a range of preferred research topics, see link there to Dr.Williams' personal home page.

The Department operates a professional training and development scheme for postgraduates: as part of this scheme, successful applicants are often given the opportunity to undertake teaching, which is paid at an hourly rate. The Department also offers its PhD students financial support for conference attendance.

Applications should consist in 6 copies of a CV which includes a 500 word PhD-proposal: applicants should also arrange for 2 academic referees to submit references directly to the Department.

All applications and references should be marked Studentship in Theoretical Philosophy, and addressed to Ms Jenneke Stevens, Postgraduate Secretary, Department of Philosophy, University of Leeds, Leeds LS2 9JT, UK email j.m.stevens@leeds.ac.uk tel 0113 343 3263 fax 0113 343 3265.

Closing date 15 August 2008.

The University of Leeds promotes excellence in teaching, learning and research.

We welcome applications from all sections of the community.

All information is available in alternative formats - please contact 0113 343 5771.

Presentism and Relativity

Familiarly, presentism faces an objection from special relativity. According to special relativity, so the objection goes, there is no such thing as absolute simultaneity: events that are simultaneous according to some reference frame are not simultaneous according to another. As a result, what counts as the present is different from one reference frame to another. If presentism is true, then, what exists must vary from one reference frame to another. But this is uncomfortable. Let us spell this argument out in a bit more detail.

1) There is no such thing as absolute simultaneity. (Premise from special relativity.)
2) Only the present time exists. (Premise from presentism.)
3) Only presently existing things exist, and only presently occurring events are occurring. (From 2.)
4) The present time is the time that includes all and only what is simultaneous with your reading of this . (Analytic of ‘the present time’.)
5) What is simultaneous with this utterance varies from one reference frame to another. (From 1.)
6) What things exist, and what events are occurring, varies from one reference frame to another. (From 3, 4 and 5.)

Presentism looks unacceptable then insofar as special relativity and what we might call ontological absolutism – the claim that what things exist, and what events are occurring, is absolute and not relative to anything; a fortiori it is not relative to a reference frame – are both acceptable.

What does the presentist need to do to meet this objection? A sufficient condition for meeting it, presumably, is that they give some reason for privileging one reference frame over any other; for in that case they can claim simply that what exists is what is simultaneous with your reading of this according to the privileged reference frame. What is simultaneous with your reading of this according to non-privileged reference frames is neither here nor there: there is no pressure to think these things exist unless they are simultaneous with your reading of this according to the unique privileged reference frame.

But how can the presentist have a reason for thinking that one reference frame is privileged (without resorting to claiming that God smiles upon one and not the others)? What could ground the privileged status of one reference frame over another, given that the physical facts don’t appear to distinguish between them?

I hear that question as a question about truthmakers. What we need is a truthmaker for the claim that some reference frame is privileged. If there is some ontological ground for distinguishing one reference frame from the others – some thing or things that mark to pick out one reference frame – then we can, without being arbitrary, take that reference frame to be the privileged one: the one that reveals what there is. So what might the truthmaker be for the fact that some reference frame is the privileged one?

Remember that, for the presentist, to exist is to be present. So consider all the events that exist – they are all and only the presently occurring events. So surely the privileged reference frame is just that one according to which exactly these events are simultaneous. In that case the truthmaker for the fact that this is the privileged reference frame is just what makes it true that those events exist – namely, those events.

So the thought is this. Everyone in this debate agrees that there is a unique set, S, which is the set of the existing entities. (That just follows from the assumption of ontological absolutism, and if you reject that then there is no problem in the first place.) This lets us single out a unique reference frame: the unique reference frame according to which exactly the members of S are simultaneous. And so, if we’ve got good reason to think that everything that exists is present then we’ve got good reason to think that this frame is the privileged reference frame. Since everything in S exists then everything in S is present; so they had better be simultaneous; so the reference frame that says they are simultaneous (and that nothing outwith S is simultaneous with any of them) is obviously the privileged one.

I imagine that seems way too quick. But ask yourself what the demand against the presentist is. It’s not that they must be able to discover what is present. The preceding remarks do not help the presentist do that. It may be in principle impossible for the presentist to know what exists because it is in principle impossible for them to know if their reference frame is the privileged one. But the objection against the presentist wasn’t epistemic, it was ontological. The objection wasn’t that discovering what is present, and hence what exists according to the presentist, is made difficult because there is no absolute simultaneity; the objection was that there is no absolute fact of the matter as to what is present, and hence no absolute fact of the matter as to what exists according to the presentist, because there is no absolute simultaneity. That is what I think is answered by the preceding remarks: insofar as we have reason to think that there is an absolute fact of the matter as to what exists, the presentist has reason to think that there is an absolute fact of the matter as to what is present, since granting the presentist that there is a unique set of existing entities allows them to uniquely specify a reference frame – the reference frame according to which they are all only the present things. What other reference frame could be a candidate for being privileged, given that the presentist thinks that to exist is to be present?

(And the epistemic objection doesn’t seem too worrying to me in any case. It seems to reduce to: you can’t know what exists, because you can’t know if you’re in the privileged reference frame. But why is that any better than any of the myriad sceptical challenges that aim to undermine your knowledge by showing that there are empirically equivalent possibilities where you get it wrong?)

I think the objection against the presentist has seemed more forceful than it is due to the assumption that the presentist should be able to pick out a unique reference frame independently of picking out the class of existing entities. But why hold that assumption? It’s not as if those entities exist in virtue of that reference frame being privileged. If that were the case then it may well be objectionably circular to presuppose their existence in an explanation of why that reference frame is privileged. But existence facts are, plausibly, brute: when it is true that a exists it is true solely in virtue of a. So the existence of the members of S can be taken for granted in any metaphysical explanation we choose to give - indeed, if the truthmaker theorist is right, all explanation comes to a halt when, and only when, we reach propositions concerning what the members of S are.

The members of S don’t exist because they are all present according to the privileged reference frame; rather, it is that reference frame that is privileged because it is the one according to which all and only the members of S are present. All of us, presentist and non-presentist alike, have to simply accept as brute the existence of some entities. For the non-presentist, accepting a set of things whose existence is brute does not serve to privileged one reference frame, but that is precisely because they don’t accept that to exist is to be present. For the presentist, however, these entities must be present, because everything is present, and so it follows immediately that only a reference frame according to which all and only these things are simultaneous is one that gets things right. Since we are sure of at least one thing that it is present – namely the reading of this sentence – and since there is a unique reference frame according to which that event is simultaneous with exactly the members of S, we know that that reference frame is the privileged one.

The argument from relativity might have force against other versions of the A-theory – such as the moving spotlight or growing block views – that postulate a privileged present without saying that what it is to exist is to be present. Such views require a privileged frame of reference but can’t say that it is the frame of reference according to which all the existing things co-exist: that frame of reference would get things wrong since both views admit the existence of past entities as well as present ones. And so they need another answer as to what grounds the privileged status of the reference frame that gets things right, and it’s not clear what they can say. But presentism, I think, faces no problem: and so this is one reason to think that presentism is the best version of the A-theory available.