Given a time t and a world w, possible or not, say that w is t-possible if and only if there is a possible world wt that matches w in all atemporal respects as well as with respect to all that happens up to and including time t. For instance, a world just like ours but where in 2027 a square circle appears is 2026-possible but not 2028-possible.
Here is an interesting and initially plausible metaphysical thesis:
- The world w is possible iff it is t-possible for every finite time t.
But (1) seems false. For imagine this:
- On the first day of creation God creates you and promises you that
on some future
day a butterfly will be created ex nihilo. God never makes any other promises. God never makes butterflies. And nothing else relevant happens.
I assume God’s promises are unbreakable. The world described by (2) seems to be t-possible for every finite time t. For the fact that no butterfly has come into existence by time t does not falsify God’s promise that one day a butterfly will be created. But of course the world described by (2) is impossible.
(It’s interesting that I can’t think of a non-theistic counterexample to (1).)
So what? Well, here is one applicaiton. Amy Seymour in a nice paper responding to an argument of mine writes about the following proposition about situation where there are infinitely many coin tosses in heaven, one per day:
- After every heads result, there is another heads result.
She says: “The open futurist can affirm that this propositional content has a nearly certain general probability because almost every possible future is one in which this occurs.” But in doing so, Seymour is helping herself to the idea of a “possible future”, and that is a problematic idea for an open futurist. Intuitively:
- A possible future is one such that it is possible that it is true that it obtains.
But the open futurist cannot say that, since in the case of contingent futures, there can be no truth about its obtaining. The next attempt at accounting for a possible future may be to say:
- A future is possible provided it will be true that it is possible that it obtains.
But that doesn’t work, either, since any future with infinitely many coin tosses (spaced out one per day) is such that at any time in the future, it is still not true that it is possible that it obtains, since its obtaining still depends on the then-still-future coin tosses. The last option I can think of is:
- A future is possible provided that for every future time t it is t-possible.
But that fails for exactly the same reason that the t-possibility of worlds story fails.
Here is one way out: Deny classical theism, say that God is in time, and insist that God has to act at t in order to create something ex nihilo at t. But God, being perfect, can’t make a promise unless he has a way of ensuring the promise to come true. But how can God make sure that he will one day create the butterfly? After all, on any future day, God is free not to create it then. Now, if God promised to create a butterfly by some specific date, then God could be sure that he would follow through, since if he hadn’t done so prior to the specified date, he would be morally obligated to do so on that day, and being perfect he would do so. So since God can’t ensure the promise will come true, he can’t make the promise. (Couldn’t God resolve to create the butterfly on some specific day? On non-classical theism, maybe yes, but the act of resolving violates the clause “nothing else relevant happens” in (2).)
This way out doesn’t work for classical theism, where God is timeless and simple. For given timelessness, God can timelessly issue the promise and “simultaneously” timelessly make a butterfly appear on (say) day 18, without God being intrinsically any different for it. So I think the classical theist has reason to deny (1), and hence has no account of “possible futures” that is compatible with open futurism, and thus probably has to deny open futurism. Which is unsurprising—most classical theists do deny open futurism.
2 comments:
You write:
> “[...] Seymour is helping herself to the idea of a ‘possible future’, and that is a problematic idea for an open futurist.”
I agree that open futurists must be precise about what “possible future” means, but couldn't the open-futurist ground that phrase in the measure-theoretic sense without committing to a single settled timeline?
Open futurists translate “infinitely many heads” into a schema of finite, open propositions: for every natural n, WILL: “there are at least n heads.” Each instance is contingent but can successively acquire a truth‑value; their infinite conjunction need never do so.
This move respects open futurism’s ban on presently true contingent futures, while still allowing talk of “almost every possible future” in a mathematically rigorous sense.
For instance, the open-futurist could quantify over outcome-sequences rather than “settled” world-histories, no? We can say: in the space of all infinite coin-toss sequences, the subset in which “after every heads there is another heads” has measure 1. Secondly, there isn't a requirement that each sequence be currently true. Probability-1 in this space does not make the corresponding proposition true now in your world; it merely shows that the set of sequences where it fails is of measure 0.
Am I overlooking anything?
Since the infinite conjunction on open futurism will never, and can never, be true, I don't see how the infinite conjunction is a *possible* future. Note, too, that even apart from open futurism one can have an infinite sequence of propositions q1,q2,... such that the conjunction of any finite number of number is possible, but the conjunction of the whole is impossible. (E.g., qn = "The number of stars in the universe is finite but bigger than n.") And indeed this is what looks like is happening in this open futurist case: any finite number of the propositions is compossible, but their infinite conjunction is impossible, and impossible things should get possibility zero.
Maybe, though, your suggestion is not to worry about possibility, but simply to consider infinite outcome sequences regardless of whether they are possible or not. No infinite coin-toss sequence is, on open futurism, possible since it is not possible that it ever be true that the sequence obtains. But no worries! We can still assign non-trivial probabilities to the abstract space of sequences, regardless of their impossibility.
I guess this seems wrong to me.
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