Logically Impossible Worlds

Abstract

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan (with his collaborators) introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds.