Possible worlds and paradoxes

Abstract

Robert Adams' definition of a possible world is paradoxical according to Selmer Bringsjord, Patrick Grim and, more recently, Cristopher Menzel. The proofs given by Bringsjord and Grim relied crucially on the Powerset Axiom; Christoper Menzel showed that, while this continued to be the case, there was still hope for Adams' definition, but Menzel he undusted an old russellian paradox in order to prove that we could obtain the same paradoxical consequences without appealing to any other set theory than the Axiom of Separation. Nevertheless, Menzel's result only showed that there was no actual world. In this paper we try to generalize Russell's paradox to arbitrary possible worlds without introducing an irreducible modal component in the discussion.