Metaphysical Necessity in a Formal System

Abstract

AbstractThis chapter gives attention to some of the more formal aspects of the proposed account and formulation of metaphysical necessity and possibility. The chapter presents definitions of metaphysical necessity and metaphysical possibility that could be added to a formal modal logical system for metaphysical modality. It is considered how, in such a system, we might accommodate the conjunction property: that if it is metaphysically necessary that A, and metaphysically necessary that B, then it is metaphysically necessary that A and B . The chapter defends the result that, strictly speaking, metaphysical necessity and possibility are not duals in the system, and shows how this interacts with our understanding of absolute necessity. It is considered whether we should endorse the validity of familiar modal schemas such as T, 4 and 5, and it is discussed in general what to make of iterated metaphysical modalities. The chapter also considers the extent to which it is justified to continue using a possible worlds semantics for this modal logical system in spite of also endorsing a non-worlds modal metaphysics.