Full Idea
It is well known that when a proposition is identified with the set of possible worlds at which it is true, a region in the space of possible worlds, cognitively significant distinctions are lost.
Gist of Idea
It is known that there is a cognitive loss in identifying propositions with possible worlds
Source
Timothy Williamson (Vagueness [1994], 7.6)
Book Reference
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.211
A Reaction
Alas, he doesn't specify which distinctions get lost, so this is just a pointer. It would seem likely that two propositions could have identical sets of possible worlds, while not actually saying the same thing. Equilateral/equiangular.