Abstract

Saul Kripke’s work on the semantics of non-normal modal logics introduced the idea of non-normal worlds, worlds where certain connectives behave differently from the way in which they behave in the worlds of normal modal logics. Such worlds may be thought of as impossible worlds, though Kripke did not, himself, talk of them in this way. Since Kripke’s invention, the notion of an impossible world has undergone much fruitful development and application. Impossible worlds may be of different kinds—or maybe different degrees of impossibility; and these worlds have found application in many areas where hyperintensionality appears to play a significant role: intentional mental states, counterfactuals, meaning, property theory, to name but a few areas. But what, exactly, is an impossible world? How is it best to characterise the notion? To date, the notion is used more by example than by definition. In this paper I will investigate the question, and propose a general characterisation, suitable for all standard purposes and tastes.