Assume open futurism, so that, necessarily, undetermined future tensed “will” statements are either all false or all lack truth value. Then there are possible worlds containing me such that it is impossible for it to be true that I am ever in that world. What do I mean?
Consider possible worlds where I flip an indeterministic fair coin on infinitely many days, starting with day 1. Among these worlds, there is a possible world wH where the coin always comes up heads. But it is impossible for it to be true that I am in that world. For that I ever am in that world entails that infinitely many future indeterministic fair coin tosses will be heads. But a proposition reporting future indeterministic events cannot be true given an open future. So, likewise, it cannot be true that I am ever in that world.
But isn’t it absurd that there be a possible world with me such that it is impossible that it be true that I am in it?
My presence is an unnecessary part of the above argument. The point can also be put this way. If open futurism is true, there are possible worlds (such as wH) that can’t possibly ever be actual.
Alex
ReplyDeleteIf the future is both open and infinite, that also means that the future cannot ever be complete. If the future is infinite, there is no last coin. Your wH is only possible in the sense that theoretically for every coin X flipped it is possible that the next coin Y comes up heads.
wH cannnot ever be actual if actual infinities are impossible, but that has nothing to do with open futurism.
Another way to put this point. Everybody agrees that
ReplyDelete(A) For all future coin flips, it is possible that they will come up heads.
But most people would infer, while the open futurist is committed to denying, that
(B) It is possible that, for all future coin flips, they will come up heads.
Good point, I think if one says this, one has to say that which possible world we are in changes with time. On day n, we are in a possible world that has exactly n coin toss results in it.
ReplyDeleteI was thinking that possible worlds are transtemporal, and include truths about all times.
Here is the lesson, I think. The open futurist has to either say:
1. There are possible worlds that cannot be actual and there is never a fact of the matter as to which world we inhabit, or
2. Every day we inhabit a different possible world.
An unfortunate consequence approach of (2) is that then there is no possible world where the limiting frequency of heads is 1/2, and it's hard to make sense of the strong law of large numbers except as a purely mathematical fact.