Abstract:

The paper argues, varying Cantor’s well-known set-theoretic reasoning, that the principle “(It is possible that p) iff (in some possible world, p)” leads to a paradoxical conclusion regarding how many possible worlds there are. The argument justifies some scepticism about whether there are possible worlds in any of the philosophical senses of the term (as opposed to the sense in which we talk about possible worlds in modal logic and which is minimally laden from a metaphysical viewpoint).