Are Propositions Sets of Possible Worlds?

A familiar objection to the theory that propositions are sets of possible worlds is psychological: propositions so conceived are too coarse-grained to be the objects of our cognitive attitudes. I raise an objection which is ontological: propositions so conceived are ontologically dependent on objects to which they seem unrelated. I argue, in the form of a reductio, that if propositions are sets of possible worlds then, for instance, the qualitative proposition that someone is wise is ontologically dependent on Socrates, which is obviously false. The theory that propositions are sets of possible worlds is vulnerable to the reductio because it is essential to a set that it have the members that it actually has. To avoid the reductio, I reverse the order of analysis and define possible worlds in terms of propositions: possible worlds are maximal consistent propositions. I offer a theory of propositions in which, roughly speaking, a proposition is the disjunction of the maximal consistent propositions that entail the proposition. The theory avoids the reductio because, in it, it is inessential to a maximal proposition that it be maximal, so it is inessential to a proposition that it be entailed by the maximal propositions that actually entail it.