The logic of metaphysical modality

Abstract

This chapter provides some background explanations: first, of what is meant by metaphysical modality, and second, of the basic ideas of the logic of modality and alternative modal logics. It presents some arguments for the view that the logical principles governing metaphysical necessity and possibility are those of the strongest normal modal logic. In the model-theoretic semantics for modal logics developed in the late 1950s and early 1960s, an interpretation is based on a set of indices—usually called ‘(possible) worlds’. Modern texts usually present modal logics as natural deduction or tableaux systems, in part because they make the construction of proofs easier than it is in axiomatic systems, but comparison of different systems is simpler if they are presented axiomatically. The chapter deals with alethic modalities—that is, roughly, with modalities having to do with the kind or mode of truth attaching to propositions.