## Tuesday, October 30, 2007

### Distinguishing the A- and B-theories

It is not so easy to state a clear distinction between the A- and B-theories of time. One says things like: "According to the A-theory, there is an objective past, present and future". But although I've used formulations like this, I've cringed when doing so, because of various problems.

So, let me propose a different characterization: The A-theorist holds that at different times we inhabit different possible worlds, while the B-theorist denies this.

This formulation makes the A-theory seem implausible--according to the A-theory, interworld travel is possible, since if we wait, we will end up in a different world from the one we're in. Nonetheless, I think this formulation is right, follows from the "objective past, present and future" formulation insofar as we can understand it, and the A-theorist should agree with it. Consider that a world includes or encodes everything that is objectively the case, and if something is objectively the case at w1 but not at w2, then w1 and w2 are different worlds. According to the A-theorist, the difference between some event's being future or past is objective. So, if we consider the world we'll be in in ten minutes, there will be objective differences--some events that now are future will then be past. Hence, it's a different world.

Another reason the A-theorist should embrace this is that it allows one to neatly characterize the difference between A-theories with an open future and A-theories without an open future. On A-theories with an open future, for a future time t, there is a minimal set W(t) of worlds such that it is a fact that the world at t will be one of the members of W(t), and typically W(t) has more than one member. On A-theories without an open future, for any future time t, there is a unique world wt such that it is a fact that the world at t will be wt.

There is, however, an alternative to the above approach for the A-theorist. The argument for my characterization of the A-theory depended on the claim that possible worlds do not change. The A-theorist could deny that. But I think it would be an implausible denial. Possiible worlds are like propositions. They are abstracta, not spatiotemporal entities. They do not change. There is change in a possible world, just as there is change in a novel (i.e., in what the world or novel describes), but the world itself does not change, just as a novel itself need not change (it might, if it gets revised or destroyed, but that's a dififerent change from the change in the novel).

Mike said...

So, let me propose a different characterization: The A-theorist holds that at different times we inhabit different possible worlds, while the B-theorist denies this.

Alex, I'm guessing you mean to qualify this in some important ways. Certainly the B-theorist also holds that at different times we are in different worlds (or, as I would rather put it, at different times different worlds are actual, since I may well be worldbound).
Take world w and time t in w, any event that takes place after t (say, at t') is sufficient to actualize another world w' at t'. So, if I raise my left hand at t' I actualize one possible world at t', if I raise my right hand, I actualize another world at t'. B-theorists surely don't deny that. So I'm thinking you want to say something like, the mere passage of time from t to t' is not sufficient to actualize another world for B-theorists, since there is no genuine passage of time. Something like that?

Alexander R Pruss said...

Suppose I am in w1. Simplify to suppose that the hand-raising is the only indeterministic event in the future. If I raise my left hand at t', I actualize w2, and if I raise my right hand instead, I actualize w3. A B-theorist will say that I either will raise the left hand, in which case w2 already is actual and w2=w1, or I will raise the right hand, in which case w3 already is actual and w3=w1. After all, if w1 is neither w2 and w3, what is it? (A world with a hole in the future? But B-theorists don't accept such.)

What your point nicely shows is that open-future A-theorists have two different reasons to assert that a different world is actualized at different times. First, in virtue of the mere passage of time. Second, in virtue of the fact that more things become determinate as possibilities get closed.

Mike said...

A B-theorist will say that I either will raise the left hand, in which case w2 already is actual and w2=w1, or I will raise the right hand, in which case w3 already is actual and w3=w1. After all, if w1 is neither w2 and w3, what is it?

Yes, this is nice. But how is it that at t' I do not actualize possible world w2? You will agree that I could have actualized w3 at t', right? Had I done so, it would have been the case at t that w3 is the actual future of w1. It sounds like you're treating w2 as inevitable, but I might be reading this wrong.

Mike said...

Alex,

I guess the simpler way to put my worry is that if there is no point in time at which I can actualize another world, fatalism quickly follows.

Alexander R Pruss said...

I guess the B-theorist can say that we help to actualize our world. Suppose in fact I will raise my left hand. Then, w2 is actual. But why is w2 actual? In part because of my own choice. So, I have helped to bring it about that w2 is actual. But this does not imply that different worlds are actual at different times. It was always true that w2 is actual, even before I made my choice, but it was true in part because of that choice. When I make my choice, I'll be able to prevent w2 from being actual, but in fact I won't use that ability.

P. M. Rodriguez said...

It seems to me insufficient to say, even given that each objectively exists, that successive moments in the past, present, and future each comprise simply _different_ worlds, so that there need be no necessary connexion between each world--so that they merely lie over or under each other like the pages of a binder, subject, in principle, to re-arrangement.

If X is true now, and X is not true ten minutes from now, it will not be enough for those in the world ten minutes from now to say "X is true"; they should say, "X is true and X _was_ not true". That future world will include our present world, and its own present world, in distinct ways at least corresponding to spoken distinctions in tense--it will include its own present as our present includes itself, and it will include our present in the way that our present includes our past.

But it seems to me that this inclusion cannot be nested or recurive. There cannot ontologically be something like a pluperfect. The past of the past is not distinct from the past of the present. Consider, for example, light writing (or drawing), where some luminous object is used to outline a shape that becomes meaningful only when viewed on a prolonged exposure of film. _How_ that shape exists is a separate question; but its meaningfulness implies that we cannot nest pasts inside pasts: all pasts are one past within which things can exist without existing at any particular moment of the past.