Friday, June 01, 2007

Good Reasoning

My recently expressed unease with possible worlds was clarified somewhat by the latest issue of The 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 both that if Goldbach's conjecture were false (or true, whichever is not the case) then X would be the case and that if that then 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).

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