So I’ve been thinking about this objection I made to the Possible Worlds account of counterfactuals as an undergraduate, and I’m curious whether anyone has read something which deals with this problem (or whether anyone has a rough-and-ready rejoinder).
The objection goes like this: Possible Worlds Semantics (PWS) claims to give an account both of our notion of counterfactual dependence and our notion of possibility. These are, roughly, the notions we express with the English constructions “If…had been the case, then…would have been the case,” and “It might/could be/have been the case that…” PWS explicates these notions by saying that the former is true iff the closest world (on some contextually-defined similarity metric) in which the antecedent is true is a world where the consequent is true also. The later is true iff there is some world accessible to the world of evaluation at which ‘…’ is true.
However, things seem to go screwy when we stick these two notions together. So, suppose that I say to you:
(1) If I had been in Washington D.C. in 1789, I might have seen George Washington’s inaugural address.
It seems to me that this is an appropriate thing to say, that we regularly use sentences of this form (If…had been the case, then…could/might have been the case’), and that someone could understand this sentence using only our ordinary concepts of counterfactual dependence and possibility. That is, it seems to me that this sentence invokes no concepts over and above the ordinary, familiar notion of counterfactual dependence and the ordinary, familiar notion of possibility (with the possibility claim embedded in the consequent of the counterfactual). However, it’s not clear (to me) how to translate (1) into the language of modal logic in a way that gets the truth-value right. One first guess might be the following:
(1′) ‘I am in Washington D.C. in 1789’ > ◊(‘I see GW’s inaugural address’)
(1′) can’t be right, because PWS tells us that, in evaluating (1′), we go to the closest possible world in which I am in Washington D.C. in 1789 (call it ‘A’), and check to see whether or not ‘◊(‘I see GW’s inaugural address’)’ is true at that world. however, ‘◊(‘I see GW’s inaugural address’)’ will be true at A just in case there is a world, accessible from A, in which ‘I see GW’s inaugural address’ is true – and it seems intuitively clear that there is such a world. So, PWS tells us that (1′) is true.
However, this can’t be a good translation of (1), because, intuitively, (1) is false. GW’s inauguration didn’t take place in Washington D.C. It took place in New York City. Pre-theoretically, I want to say that, in light of this information, something like the following is true:
(2) If I had been in Washington D.C. in 1789, then it is not the case that I might have seen GW’s inauguration.
And, again, I don’t see any clear way of translating (2) into the language of modal logic such that PWS is going to make it true (and such that it’s going to allow us to give a uniform account of counterfactuals and possibility).