I'm trying to learn about modal logic and the metaphysics of modality, and there's something that has been bugging me about what I've read so far: are there set-theoretical issues with supposing we can refer to every possible world? I'm not worried about models with finitely many worlds, but some of the modal metaphysics I've read defines the set of possible worlds (i.e, W) as something like "a set that contains all and only the maximally consistent sets of propositions". This makes me nervous for two reasons:
Reason 1: If w is a possible world then, for every subset s of w, the proposition "s is a subset of w" is true (and therefore should be an element of w). This makes it seem like w contains an element for every subset of itself. But if that were true, then the power set of w would have a cardinality equal to or less than w, which is impossible.
Reason 2: It seems like it would be possible for the world to consist of a point particle in R^3.Because the point particle exists in a real number space, there are an uncountable number of places such a particle could be. Does this imply that the set of possible worlds is uncountable? And, if it is uncountable, is that a problem?
Any clarification of these issues would be greatly appreciated. Thanks.