Thursday, August 04, 2005

Narrow Fatalism and Open Actuality

My recent post on the Idle Argument pointed the way to what I will call 'narrow fatalism', based merely on the tautological idea that "what will be, will be". Sure, there are other possible worlds where things unfold differently. But those aren't our (actual) world, so what good is that? Given the facts that obtain in the actual world, we can't make them any different. (They are, after all, a 'given'.) If I will die tomorrow, then I can't make it the case that I will actually survive. For that would be a contradiction. At best we can appeal to hypotheticals: I would have survived if I'd done something differently. Put another way: In that close possible world where I do behave differently, I instead survive. But again, if I can't actually behave differently, then my merely counterfactual survival is small solace. I want to survive in the actual world, not in some other possible world.

I'm not sure whether this is a genuine problem or not. In a way it seems too easy, too trivial. The problem is just that nothing can actually be other than what it is. (Surprise surprise.) Whichever world is the actual world, other worlds aren't. The truth of P guarantees that P isn't false. Surely these truths are too vacuous to justify any great concern -- or indeed any concern at all. Yet still it seems disturbing that we can't actually make some non-actual world, uh, actual. There's a sense in which this sounds like a very serious limitation on our powers. (It makes it sound like we have no power whatsoever!) But such claims are far from vacuous. So it seems we are suffering from some sort of conceptual confusion.

Perhaps the answer is to go Aristotelian, and deny that there are any future (contingent) truths (yet). To apply this to our modal problem, let us name the possible worlds w1, w2, w3, and so on. Each world wn contains a maximal specification of what is true at that world. (For every proposition P, either P is true at wn or P is false at wn.) So these worlds are definite, determinate, and immutable. However, perhaps it is indeterminate which of these worlds is actual. Perhaps all past events up to the present are consistent with a large set of worlds S = {w5, w6, ..., w9999, etc.}, and it is metaphysically possible that any one of the worlds in S could be(come) actual.

One way to think of it would be to take the entire set S to be "actuality". As time passes, more and more worlds are excluded from S, as they become inconsistent with newly past events.

This could help explain why there are no contingent future truths. After all, it is not determinate within S whether the future contingent P is true or false. (Perhaps it is true in w5, but false in w6, etc.) A proposition P is actually true iff it is true in all of actuality (i.e. all the worlds of S). I am pleased to note that this leads to a rejection of classical logic. For the disjunction "P or not-P" is true in all S-worlds, and thus actually true, even though the same cannot be said of either disjunct ("P" in isolation, or "not-P" in isolation). We can no longer infer from the truth of a disjunction to the truth of one or other disjuncts. This is a result I'm very happy with.

To clarify: Suppose that P is the claim that I will rob a bank tomorrow. As of now, there are worlds in S where P is true, and other worlds in S where P is false. So it is actually indeterminate whether I will rob a bank tomorrow. Suppose I do go and rob a bank tomorrow. Then I will have made it the case that P is true, so all worlds where P is false will get expunged from the set S. As actuality narrows, it becomes more determinate: more propositions become specified as true, or specified as false.

Perhaps at the end of time, all the alternatives will be excluded at last, and we will be able to identify actuality with a single world: w42, say. Because P is true in w42, it has always been impossible that anybody could make P false in w42, for that would yield a contradiction. But this need not yield fatalism unless we rigidly identify actuality with w42. If you did that, then it would be actually impossible for me to make P false. It would be actually impossible for me to not rob the bank tomorrow. This is problematic.

I want to avoid such fatalism. We can achieve this by insisting that actuality, at any moment, encompasses the entirity of set S at that time. So it is not today the case that w42 is the actual world. It is, rather, indeterminate which world will end up actualized: it really could be any of the members of S. By making the appropriate choices, we might instead actualize w5, or w6, or w9999, or whatever. Thus even narrow fatalism may be avoided.

2 comments:

  1. Your proposal seems similar to one proposed by Storrs McCall in his book:
    A Model of the Universe: Space-Time, Probability, and Decision.

    Instead of using a traditional possible worlds approach, he models the universe as a four dimensional branching structure. The present is the lowest branching point, and the past is the trunk. As the present 'moves' along from one branch point to another only one path is taken and the other branches 'fall away.'

    ReplyDelete
  2. Yeah, that's a nice metaphor.

    ReplyDelete

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