Inconsistency without Contradiction

Abstract

Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that `in so-and-so world' is a restricting modifier which passes through the truth-functional connectives. The outcome is a sort of subvaluational semantics which makes a contradiction 'A and not-A' false even when both 'A' and 'not-A' are true, just as supervaluational semantics makes a tautology 'A and not-A' true even when neither 'A' and 'not-A' are.