27 A Classically-Based Theory of Impossible Worlds Modal Propositional Calculi’, in The Theory of Models

The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of ‘worlds ’ in order to study various philosophical and logical phenomena. The literature contains discussions of ‘non-normal worlds’,1 ‘non-classical worlds’,2 ‘non-standard worlds’,3 and ‘impossible worlds’.4 These atypi-cal worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) to solve the problems associated with propositional attitude contexts, inten-tional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphys-ical theory of such atypical worlds tend to move too quickly from philo-sophical characterizations to formal semantics. For example, one of the best attempts to develop such a theory can be found in Priest [1992]. I