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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 Ref
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.
| 23486 | Pictures are possible situations in logical space [Wittgenstein] |
| 4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| 9654 | A proposition is a set of entire possible worlds which instantiate a particular property [Lewis] |
| 15736 | A proposition is the property of being a possible world where it holds true [Lewis] |
| 15738 | Propositions can't have syntactic structure if they are just sets of worlds [Lewis] |
| 7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
| 21624 | It is known that there is a cognitive loss in identifying propositions with possible worlds [Williamson] |
| 18001 | Are there partial propositions, lacking truth value in some possible worlds? [Magidor] |