Sunday, March 18, 2012

Two presentist ways of seeing worlds

If presentism is true, then right now, call it t2, the proposition B that Bucephalus exists is false, but it once was true, namely at t1. Now, at every time a token of the following sentence expresses a truth:

  1. For all p, a proposition p is true if and only if it is true at the actual world.
Now, let's imagine ourselves at t1. Then Bucephalus exists. Thus, B is true. Moreover, (0) expresses a truth, and so B is true at the actual world. So at t1 the sentence
  1. B is true at the actual world
expresses a truth. But now let's return to our time. B is false. But (0) expresses a truth, and so the sentence
  1. B is not true at the actual world
does expresses a truth. Thus, (1) expresses a truth when said at t1 but expresses a falsehood when said at t2. This shows that either:
  1. "The actual world" refers to different worlds at different times
  1. The proposition that p is true at w can change in truth value, even if "p" and "w" refer rigidly to a proposition and a world, respectively.

Thus, the presentist has two ways of understanding possible worlds. Either possible worlds are tensed, so that at every time we inhabit a different possible world (that's option (3)) or else the "true at" relation is tensed, so that we inhabit the same world at different times, or when we say at t that p is true at w, we say something true if and only if p is true at t at w.

I think there is a problem for (4). Let p be the proposition that horses do or do not exist. Let t be the actual present time. Then p is true at every world, since it's a necessary truth. Now consider a world w where the time sequence does not include t. There are several options for this. Maybe in w, time comes to an end in 2011. Maybe time is discrete in w while in our world it is continuous, and so w either includes no times from our world or else w "skips over" t. Or maybe for some other reason the time sequence in w is radically different from our world's time sequence. Then p is true at w. But on (4), when we say that p is true at w, that is true if and only if p is true at t at w. But nothing is true at t at w, since t isn't a time at w.

Here's a slightly different way to see the point. When p is true at w, it is true either because there are or because there are not horses at w (this is an uncontroversial case of disjunctive grounding). Suppose it's true because there are not horses at w. But at which time are the horses not there at w? After all, w could have horses at some but not other times. Presumably, the relevant time is the present time. On proposal (3), every world comes along with its own present time, and this is fine. But on proposal (4), a world's relevant present time is our present time, and w doesn't have our world's present time.

One could try to solve this with counterpart theory for times. But one can suppose w won't have a counterpart to our time.

Here's a bolder move to defend (4) against our argument: The accessibility relation between worlds differs between times. The proposition p isn't true at all worlds, but only at all accessible worlds (this may or may not involve a denial of S5—S5 does not say that all worlds are accessible, but only that accessibility is an equivalence relation). And a world is only accessible if it includes the present time (or a counterpart to it?). This has the implausible consequence that what is metaphysically possible changes with time. For instance, if in w the time sequence comes to an end with 2011, then the proposition that w is actual was possible in 2011, but is no longer possible. But it's implausible that what is metaphysically possible changes with time.

If this is right, then the presentist should embrace (3). But is (3) plausible? Do we really live in different worlds at different times?

The presentist's other move is simply to abandon talking about worlds, and instead talk about, say, abstract times (in the Crisp sense).


Jonathan D. Jacobs said...

Why is it implausible that what is possible changes?

And if the presentist is also a dispositionalist about possibility, then she might think, as I'm inclined to, that there are no possible worlds, and hence a problem that rests on possible worlds talk is a pseudo-problem. Does the present problem require possible worlds to even make sense?

Alexander R Pruss said...


I think metaphysical possibility is the widest non-arbitrary kind of possibility (strictly logical possibility is arbitrary, as it depends on which rules of inference and axioms you include). If the metaphysically possible changes, then there is a wider non-arbitrary kind of possibility: possibility-at-some-time-or-other.

Yeah, the present problem requires possible worlds to make sense.

Jonathan D. Jacobs said...

But the presentist won't think that the widest and most non-arbitrary kind of possibility is possibility-at-some-time-or-other, since she thinks there's only one time. So she will think that her possibility *is* the widest non-arbitrary kind.

What am I missing?

Alexander R Pruss said...

"Was possible, is possible or will be possible" sounds like a non-arbitrary, or not very arbitrary, form of possibility.

Alexander R Pruss said...

The presentist who takes this route also has to say, implausibly, "It is impossible for time to come to an end in 2011" or "It is impossible for time to be discrete" (if, as is plausible, a world where time is discrete has no times in common with our world).

Alexander R Pruss said...

There are two kinds of changes in what is possible. One kind of change is due to a change in what propositions exist. A non-haecceitist presentist will have to allow for such change. Another kind of change is where a proposition exists at two times, but at one it is metaphysically impossible and at the other it is metaphysically possible. That's the kind that bothers me.