 There is no denying that a proposition determines a set of possible worlds – namely, the worlds at which the proposition is true. And for a good many semantic purposes – in particular, for giving the truth-conditions of sentences containing only extensional operators – treating propositions as sets of worlds suffices. But there are well known problems with this account when it comes to propositional attitudes. The most famous problem is the problem of equivalence. Intuitively, the proposition that arithmetic is incomplete is distinct from the proposition that 2+2=4. Most 5-year-olds know the latter but can’t even entertain the former. As both propositions are true in exactly the same set of worlds – namely, all, assuming the necessity of mathematical truths – unstructured-propositionalism entails that they are the same proposition. Indeed, unstructured propositionalism entails that there is exactly one necessary proposition. This is problematic, as it seems to entail that anyone believes that 2+2=4 just in case he believes that arithmetic is incomplete.