Friday, July 22, 2022

Should the A-theorist talk of tensed worlds?

For this post, suppose that an A-theory of time is true, so there is an absolute present. If we think of possible worlds as fully encoding how things can be so that:

  1. A proposition p is possible if and only if p holds at some world,

then we live in different possible worlds at different times. For today a Friday is absolutely present and tomorrow a Saturday is absolutely present, and so how things are is different between today and tomorrow (or, in terms of propositions, that it’s Saturday is false but possible, so there must be a world where it’s true). In other words, given (1), the A-theorist is forced to think of worlds as tensed, as centered on a time.

But there is something a little counterintuitive about us living in different worlds at different times.

However, the A-theorist can avoid the counterintuitive conclusion by limiting truth at worlds to propositions that cannot change their truth value. The most straightforward way of doing that is to say:

  1. Only propositions whose truth value cannot change hold at worlds

and restrict (1) to such propositions.

This, however, requires the rejection of the following plausible claim:

  1. If (p or q) is true at a world w then p is true at w or q is true at w.

For the disjunction that it’s Friday or it’s not Friday is true at some world, since it’s a proposition that can’t change truth value, but neither disjunct can be true at a world by (2).

Alternately, we might limit the propositions true at a world to those expressible in B-language. But if our A-theorist is a presentist, then this still leads to a rejection of (3). For on presentism, the fundamental quantifiers quantify over present things, and the quantifiers of B-language are defined in terms of them. In particular, the B-language statement “There exist (tenselessly) dinosaurs” is to be understood as the disjunction “There existed, exist or will exist dinosaurs.” But if we have (3), then worlds will have to be tensed, because different disjuncts of “There existed, exist or will exist dinosaurs” will hold at different times. A similar issue comes up for growing block.

So on the most popular A-theories (presentism and growing block), we have to either allow that we inhabit different worlds at different times or deny (3). I think the better move is to allow that we inhabit different worlds at different times.


Unknown said...

Amateur A-theorist and presentist here, and I affirm that different times are different possible worlds. (This was a conclusion I had already arrived at before reading your blog post.) I don't find this to be unintuitive.

ASBB said...
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ASBB said...

What about this? (I'm writing this on the fly so there's bound to be some shortcomings, but hopefully it gestures to something ultimately workable) A-Theorists can identify worlds as maximal sets of pairs [w,t] where w is a world understood as a maximal proposition including propositions which change truth value ('it is now Friday', WAS(q), etc.) and t is a time (perhaps a maximal present tense proposition, so 'it is now Friday', but no WAS(q) etc.).

Then, a possible world is just such a set where each w could be true in a sequence given by the order placed on the t's. So W = {[w1,t1], [w1,t2]} (with t1 < t2) is not possible if, say, w1 includes WAS(p) and w2 includes ~WAS(p).

Finally, a world is maximal just in case it is not a subset of a larger world. This is to rule out worlds containing just the temporal slices of the last 100 years, say. This shouldn't cause any problems with pairs of worlds otherwise alike except for the second world being 1 second longer, because the final element of the former world will include ~WILL(p) whereas the penultimate element of the latter will include WILL(p) for some p.

What does this mean for (3)? It probably renders (3) ill-formed. Perhaps the fundamental locution should be: p is true at t in W. Then of course, p is true at t in W iff p is a conjunct of some w such that is an element of W. Suitably amended, (3) should come out true. We also don't have the problem of living in different worlds at different times. (I'll leave it to open futurists to amend this to make sense on their model).

Brandon said...

All of the counterintuitiveness seems to arise from taking the term 'possible worlds' as a literal description rather than a label that became attached to a certain kind of logical object due to the history of the field. However:

(1) Nothing actually requires that possible worlds be literally worlds; if something can be represented by consistent sets of truth-valued propositions, you can apply possible worlds semantics to it, even if you are not dealing with worlds.

(2) We don't live 'in' possible worlds but in the actual world, which is always at every point represented at the level of possibilities by many, many different possible worlds. Thus what really changes across time is not what possible world one 'lives in', but what possible worlds are accessible in the manifold of all possible worlds. This is, so far from being counterintuitive, exactly the principle by which one represents temporal modalities in possible world semantics.

Zsolt Nagy said...

And how does this all comply with relativity theory or with our observed and measured empirical data?
"Does the Past Still Exist?" by Sabine Hossenfelder

It's not like, that beating a dead horse in any instance would or could be reasonable. But then again if "that" dead horse is so incomprehensible to understand our current "comment sense" of "that" horse being dead, then I guess, that it's only natural and rational to explain "that" dead horse again and again and again, why "that" horse is dead, till "that" dead horse finally gets "it".

Zsolt Nagy said...

"Should the A-theorist talk of tensed worlds?"
Maybe. Maybe the A-theorist should rather talk about events with space-time coordinates in the 4 dimensional space-time continuum, such that any other rational being living apparently in that 4 dimensional space-time continuum can actually understand anything, what that A-theorist might want to convey about time.

I wonder: Does any A-theorist know, what proper time is or is supposed to be?
Maybe the A-theorist should talk more about proper time of (inertial) reference frames.
Just sayin.