Powers or Dispositions Accounts of Possibility: A Puzzle

                On dispositional accounts of possibility, for ◊P at t to be true is just for something to have the power to bring it about, at t, that P (i.e., that ◊P just in case something has the power to bring it about, at t, that P). As Brian Leftow notes in his God and Necessity (note: while I disagree with Leftow was to *why* dispositional account of possibility go wrong, I should note that I do agree with him *that,* in fact, there is some difficulty with them, the point of which I bring up so not to misrepresent Leftow's own view) (pg. 68), which is the inspiration for my present discussion and from which I here partly borrow, such an account does not require that anything cause it that P if it just happens that P (for it doesn't require that causes that make it that ◊P actually bring it about that P). But if there neither is nor has been such a power, ~◊~P.
                Since □P just in case ~◊~P, any P that just happens (i.e., without being caused to happen) will also turn out necessary. But, now departing from Leftow's own criticism of powers accounts, this seems odd to me. For surely actually P → ◊P (i.e., actually P only if possibly P). But ◊P at t is true just in case it is also true that something has the power to bring it about, at t, that P. And so it follows that ◊P → something has the power to bring it about that P. But, recall, the assumption was that there is not anything that either has or has had such a power. And if this is true, it will just be false that ◊P.
                But assume for the sake of argument that something does have such a power or that there has been something that has had such a power. Then it will be true, however, that there is not anything that causes it at t that P and that something has the power to bring it about, at t, that P. And while not contradictory perhaps, the conjunction of these two claims seems odd. 
                For then, or so it will seem, the fact that something has the power to bring it about (at t) that P has no connection with the fact that actually P (at t). And thus it's hard to see how the fact that something has the power to bring it about, at t, that P explains the possibility of P at t. But then, on the dispositional account of possibility, there is nothing that explains that ◊P at t. But this is inconsistent with the claim that ◊P at t just in case something has the power to bring it about, at t, that P. So a dispositional account of possibility is true only if 'it just happens that P' is impossible, which is a problem. For it is difficult to say what it would not be possible. (Considering that this account is one that I'm currently interested in, I actually hope what I say here is wrong. But it also isn't easy for me to see how it can be true.)