I've read somewhere that sentences of the form "If P were the case, then Q would be the case" should be interpreted in the following way (I write P>Q to abbreviate the counterfactual conditional).
P>Q is true in w iff in the closest possible world in which P is true, Q is true.
Then it is usually said that this formulation is equivalent to
P>Q is true in w iff the material conditional P-> Q is true in w.
Why is the truth of that conditional equivalent to being true in the closest possible world?
Edit: to be more precise, my question stems from a section of Yablo's "Non-catastrophic presuppostion failure", in which Yablo tries to argue (and later reject) the view that the real asserted content S of a sentence, when a presupposition is false, is true iff the simple sentence S is true in the closest possibile world where the presupposition P holds.
From the paper: "S is true (false) in w iff S is true (false) in the world closest to w where π holds."
then Yablo goes on and says:
"This simplifies matters, because for S to be true (false) in the world closest to w where π holds is, on standard theories of conditionals, precisely what it takes for a conditional π → S to be true (false) in w."
"S is true (false) in w iff π → S is true (false) in w." "Note 22: I assume that π→S is false iff π→~S is true."
This looks to me as Yablo is putting forth the fact that "being true in the closest possible world where π is true" can be identified with π → S being true in the world of interest (where the evaluation takes place, so to speak) - but it is not clear to me why it should be so.