## Wednesday, March 29, 2006

### Indeterminate Worlds

It's possible for the future to be indeterminate. Consider a world where this is so. For ease of exposition, I will pretend that it is the actual world '@'. I'm wondering how we should describe this scenario in terms of "possible worlds" talk. Is the world '@' one where, relative to each moment, the future is indeterminate? Or should we instead say that while worlds are given a fully determinate specification, it is (as a matter of "extra-worldly" or "meta-modal" fact) indeterminate which world is actual?

Consider the idea that possible worlds explicate our intuitive notion of 'ways a world might be'. If the future is indeterminate, then we want to say that there are multiple ways it could turn out. Each 'way' should then correspond to a distinct (dynamically possible) world. The problem is then to make sense of the idea that, at present, there is exactly one "way the world is". This suggests that actuality should be identified with one possible world. Given that possible worlds are intrinsically static entities, these two conclusions are in conflict. We cannot be one world at present if we could be any of several worlds in future.

Which appearance should we reject? Suppose we reject the idea of multiple future worlds. There is just the one, presently actual, world, in which more facts will become determinate as time progresses. But then we no longer have the apparatus required to speak of the various possible futures, at least not within the 'possible worlds' framework. So this seems a bad option. We should instead take possible worlds to be maximally complete specifications of 'a way a world might be'. Then indeterminacy is an extra-worldly fact, rather than something one finds within a world. Faced with two options, we should say "it's indeterminate whether we're in world w1 or w2", rather than "in world w, it's indeterminate whether 1 or 2 is true".

This may commit us to denying that there is exactly one way the world is. But that is not so counterintuitive once we consider the future as being part of this 'way'. If the future is genuinely open, then we will want to say that it's indeterminate what 'way' the world is, in this broad, future-including, sense.

How are we to make sense of this? My post Narrow Fatalism and Open Actuality proposed that we identify actuality (at any given moment) with the set of dynamically possible worlds. (I use the term 'dynamically possible' to denote those that remain 'open' possibilities at the given time.) We may even continue to speak of "the way the world is", if we understand this as referring to the set of dynamically possible worlds rather than any one world in particular. We want "actuality" and "the way the world is" to co-refer, after all. It just requires some departure from the idea that 'ways' and 'worlds' are one and the same thing. Some ways are worlds, but others - we now find - are instead sets or pluralities of worlds.

Some might not like this picture -- perhaps due to a conviction that actuality must be exactly one possible world -- and so be led to conclude that this strong sort of "indeterminism" is strictly impossible. (I suspect that's what most philosophers would say. But I hope to claim the common folk on my side!)

Such philosophers might still leave room for a weaker sense of 'indeterminism'. While they think that the actual world (and hence, actual future) is "metaphysically fixed" -- that we are in possible world #42 whether we like it or not -- they can note that there are other possible worlds that have identical histories to ours, but divergent futures. So they can honestly say that past events alone do not determine our future. Our history is consistent with various possible futures. But there is an extra, metaphysical fact which does determine our future. I'm not entirely clear on what that means, but it sounds ominous.

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