Mathematical structuralism and the Identity of Indiscernibles

Abstract

context from the antecedent to the consequent which would be required for the utterance to express a falsehood.5 If there were some deep theoretical or intuitive reason to identify propositions with sets of possible worlds, perhaps it would be worth trying to learn to live with such aberrations. But I can see no such reason, even from Lewis's point of view. The impression that sets of possible worlds are 'just right' for a version of the proposition role seems to be due to the thought that, by encapsulating the information about what has to be the case for them to be true, they allow for an especially simple and natural way to analyse modal claims about truth and falsity. Once we realize that these claims will have to be given a counterpart-theoretic treatment in any case (given counterpart theory for individuals), this apparent advantage of sets of possible worlds over 'singular propositions' disappears. I conclude that, for the counterpart theorist, singular propositions outperform sets of possible worlds across the board as candidates to be cast in the proposition role, even on the narrowest conception of what that role might amount to.