My recently expressed unease with possible worlds was clarified somewhat by the latest issue ofThe Reasoner (issue 2, the article about counterpossible antecedents (also this reply)): I shalln't delve into details (so this post is mostly a memo to myself) but in mathematics we don't want the vacuous truth of boththat if Goldbach's conjecture were false (or true, whichever is not the case) then X would be the caseandthat if thatthen not-X would, which we would get on some analyses of subjunctive conditionals, as that case would have no possible worlds. We clearly don't want epistemic possibilities, as the truth and falsity of Goldbach's conjecture are both epistemic possibilities at present, as is constructivism of course, whence I wonder whose metaphysics would yield the literal meaning of 'would'? The background presumptions of the particular communicants would surely give us something too subjective for the literal meaning, but the wider linguistic community is surely going to have too vague an intersection of its various presumptions (which would include those of people like Pythagoras, Cantor, Brouwer and Quine).
I am old; in 2003, at the age of 40, I was published in the British Journal for the Philosophy of Science, but since then I've done little. Blogging since 2007, my main involvement was via the Philosophers' Carnival, which moved to Facebook.