Summary

Abstract

What is the relation between modal logic and modal metaphysics? As a technical discipline, modal logic is in effect a branch of applied mathematics that studies extensions of standard formal languages by additional sentence operators, independently of any particular interpretation of those operators. Modal metaphysics studies the nature and extent of possibility and necessity, where those terms are understood in a strong non-epistemic ‘metaphysical’ sense: something is necessary just in case it would have obtained no matter what, and possible just in case it does not necessarily not obtain. Informally, metaphysicians can read the operators □ and ◊ of modal logic as expressing such necessity and possibility, although that reading plays no official role in the technical development. When the modal language also contains quantifiers, metaphysicians will naturally read them as unrestricted. That metaphysical reading of the modal operators and quantifiers will be assumed in what follows. Metaphysicians want to know which formulas of the modal language are metaphysically universal , in the sense of being true on every interpretation of the non-logical constants and free variables in them. The metaphysically universal formulas, whichever they are, constitute the core metaphysical theory of the most general structure of modal reality. We can use modal logic as a technical aid in studying that theory.