The infinite future problem for causal accounts of metaphysical possibility

Starting with my dissertation, I’ve defended an account of metaphysical possibility on which it is nothing other than causal possibility. I would try to define this as follows:

• p is possible₀ iff p is actually true

• p is possible_n + 1 iff things have the causal power to make it be that p is possible_n.

• p is possible iff p is possible_n for some n.

I eventually realized that this runs into problems with infinite future cases. Suppose a coin will be tossed infinitely many times, and, as we expect, will come up heads infinitely many times and tails infinitely many times. Let p be the proposition that all the tosses will be heads. Then p is false but possible. Moreover, it is easy to convince oneself that it’s not possible_n for any finite n. Possibility_n involves n branchings from the actual world, while p requires infinitely many branchings from the actual world.

This has worried me for years, and I still don’t have a satisfying solution.

But yesterday I realized a delightful fact. This problem does nothing to undercut the basic insight of my account of metaphysical possibility, namely that metaphysical possibility is causal possibility. All the problem does is undercut one initially plausible way to given an account of causal possibility. But if we agree that there is such a thing as causal possibility, and I think we should, then we can still say that metaphysical possibility is causal possibility, even if we do not know exactly how to define causal possibility in terms of causal powers.

(There is one danger. Maybe the true account of causal possibility depends on metaphysical possibility.)