In my two previous posts, I have explained the notion of ‘truth at a time’ and argued that for a (contingent) proposition to be true at T it must supervene upon what exists at T. In short, truth at T requires a truthmaker at T.
A question that remains concerns accessibility relations among times. If a proposition is true at some earlier time, is it necessary that it be true at all later times that it was true at that earlier time? And if a proposition is true at some later time, is it necessary that it be true at all earlier times that it will be true at that later time? In common tense logical notation, these questions concern the theses:
- p → FPp
- p → PFp
(1) says that if p is true at some time, say T, then it will be true at all times subsequent to T that p was true at T. (2) says that if p is true at T, then it has been true at all times prior to T that p will be true at T.
I believe that (1) is true and (2) is false. In other words, I believe that earlier times are accessible to later times, but I don’t think that later times are accessible to earlier times. This antisymmetry means that I take S4 and not S5 to be the right system of modal logic as far as times are concerned.
S4 ensures reflexivity and transitivity among times. Reflexivity means that each time is accessible to itself. Hence, if it is true at T that p, then it is true at T that it is true at T that p, etc. Transitivity means that if T1 is accessible to T2, and T2 is accessible to T3, then T1 is accessible to T3. Hence, if it is true at T1 that p, and if it is true at T2 that it is true at T1 that p, then it is true at T3 that it is true at T1 that p.
To reflexivity and transitivity, S5 adds symmetry. This means that if T1 is accessible to T2, then T2 is accessible to T1. Hence, if it is true at T1 that p, then it is true at T2 that it is true at T1 that p, and it is true at T1 that it is true at T2 that it is true at T1 that p, etc.
Now, if S5 is right, then both (1) and (2) have to be accepted – what’s true at any time is mirrored at all times. If S4 is right, however, then we cannot accept both (1) and (2), for that would violate antisymmetry. The questions, then, are whether we should accept antisymmetry or not and, if so, whether we should go with (1) or (2).
My argument turns on the relation between time and causality and on the falsity of determinism. Earlier events can cause later events, but not vice-versa (or so most of us think). That motivates antisymmetry, but to establish it we have to appeal to the idea that what’s true at a time depends upon what exists at that time. Suppose event E1 at T1 indeterministically causes event E2 at T2. It is true, therefore, at T2 that E2 is occurring. Given symmetric accessibility between T1 and T2, it is true at T1 that it is true at T2 that E2 is occurring. But this is false if the causal relation between E1 and E2 is indeterministic, for in that case we do not have a truthmaker at T1 for “E2 is occurring at T2”.
If determinism is true, then a unique sequence of later times is implied by earlier times. It can be true at T1, therefore, that “E2 is occurring” will be true at T2. Hence, T2 is implicitly accessible from T1. But if determinism is false, then no unique sequence of later times is implied by earlier times. Let p represent the occurrence of some event that is causally contingent from the perspective of T1 (e.g., “E2 occurs at T2”). From that perspective, it may be that p is true at T2, and it may be that p is false at T2. Moreover, there is nothing at T1 sufficient for making it true either that p will be the case at T2 or that p will not be the case at T2. Since what’s true at T1 depends on what exists at T1, it cannot be true at T1 either that p will be true at T2 or that p will not be true at T2. Given indeterminism, therefore, it follows that (2) is false. If, for example, there being a sea battle at T2 is causally contingent at T1, then even if a sea battle does occur at T2, it does not make “A sea battle will occur at T2” true at T1, contrary to (2).
But what about (1)? It would be very counterintuitive if (1) were false. It’s falsity would allow, for example, that “Caesar crossed the Rubicon” might be true in, say, 1000 A.D., but not true in 2000 A.D. So I want to insist that (1) is true, but I emphasize that it’s truth is not a mere matter of logic. If we accept that truth supervenes on being, then (1) commits us to a substantive metaphysical position. Since what’s (contingently) true at T2 depends upon what exists at T2, for it to be true at T2 that some event E occurred at T1, there must be something at T2 sufficient for making that true. E’s occurring at T1 is not enough. There must also be something that carries E’s occurring at T1 forward in time and that constitutes at T2 E’s having occurred at T1. As to what that “something” is, I refer the reader to this forthcoming paper of mine.
In summary, if determinism is false, as I believe, then (2) is false. (1), however, is true – it would be intuitively quite odd (to say the least) if it weren’t – though it comes at what some will regard as an unacceptable metaphysical price. Those folks either have to deny that truth supervenes on being or reject (1). I think either is a much bigger price to pay.
Hi Alan, you’re assuming presentism here, right? I don’t see how 2 could plausibly be false otherwise (well, I guess you could have a growing block view, but in that case I don’t see any need to have anything “carrying forward” what happened at one time into the next).
Hi Ian,
No, I’m not assuming presentism here. (At least, I don’t think I’m smuggling it in the back door.) Instead, I contend that neither (1) or (2) is analytically true. Each makes a substantive claim about truth-accessibility relations among times, and each incurs non-trivial metaphysical commitments.
Now, if my argument’s right, then what it shows is that non-presentists are no better off than presentists when it comes to providing truthmakers for truths about non-present times. But that’s not a proof of presentism.
But if you reject presentism and the growing block theory, there is no more problem with providing truth makers, right? The truthmaker for “There will be sea battle tomorrow” will simply be the sea battle that exists simpliciter and whose temporal position happens to be tomorrow. Unless we reject an existing future and maintain that all truthmaking must be done in the present, I don’t see what determinism has much to do with anything – it could be entirely undetermined by what exists now that there is a sea battle tomorrow but if the sea battle exists simpliciter and is located tomorrow, we have our truthmaker (consider the spatial analogue – I don’t think truths about other places are plausibly thought of as dependent on what exists in my current location).
Hi Alan. I still am deeply uncomfortable with the basis assumption behind all of this, which I summarise in my blog here.
http://ocham.blogspot.com/2009/01/snow-in-london.html
Hello again Alan,
I’ve read your “Presentism, Truthmakers, and God” paper and I find I’m a bit surprised that the Presentist throws in the towel so soon on page 1. My understanding is that “Presentism is the view that only present objects exist.” (from the SEP article on Time), but you say “For her [the Presentist], past facts don’t exist.” Does this mean that you see facts as objects in some sense? I wonder if you could spare some time to clarify this for us? It may underlie our disagreements. Regards, DB
Hi Alan. Re what that ‘something’ is, why not God, rather than God’s memories?
A presentist would naturally think of God as a continuant: God exists, and it’s his nature (as omnipotent) to be able to change and so (of course) his identity persists through those changes; i.e. what he was like is a truth about him as he was, and who he is is identically who he is now and who he was then, whence what he was like is a truth about him even as he is now.
My problem with it being God’s memories is (as I mentioned in my naive post on that paper) just that God is omnipotent and so (prima facie) he could create a creature who was so independent of himself that not only its future but also its present was unknown to him.
Incidentally, I’ve just noticed something that might affect how you regard my theodicy (and my Cantorian argument for open theism), which is now my second comment on your post on God knowing that he’s uniquely (or triunely) divine. (?)
I don't see how S4 or S5 have much to do with rejecting (2) p → PFp. For (2) to be true, all we need is that, for any true p, it was the case that it will be the case that p. (2) commits you to no view whatsoever about future contingents. So, we can hold (2) true and deny that any future contingent proposition is true. In that case, certainly you'd want to say that for any true p (i.e., redundantly, for any true past or present p) it was the case that it will be the case that p. We can make this more precise. If p is true at time t (and not true at any earlier time) then it is also true at t that it was the case at t-n that it will be true at t that p. This is because, for any time t at which p is true, (2) entails that it was the case at all earlier times that it will be the case that p at t. But, importantly, (2) does not entail that it was the case that it will be the case that p until p is true.
Hi Mike,
You're right that (2) by itself doesn't commit one to any particular view about future contingents. One could accept (2) and either accept or deny the existence of future contingents. My argument, however, was that (2) is incompatible with the conjunction of future contingency (anti-determinism) and the thesis that what is true at a time depends on what exists at that time.
YIn your last sentence you say, “(2) does not entail that it was the case that it will be the case that p is true until p is true” (my emphasis). But that adds something to (2). It renders it a temporally relative thesis, whereas (2) itself, as least as I read it, purports to be a necessary, and thus temporally invariant, thesis.
Your reading of (2) allows that “there will be a sea battle tomorrow” is today non-true prior to the battle and today true after the battle. That's right in line with John MacFarlane's notion of relative truth, but it's not what proponents of (2) (i.e., Ockhamists) have generally wanted to say, which is that in virtue of tomorrow's sea battle it always has been true that there was going to be a sea battle on that date.