A topos-theoretic approach to reference and modality

Abstract

This paper presents an approach to modal logic based on the notion of kind or interpretation of a count noun as a prerequisite for reference. It gives a mathematical formalization of this notion in the context of a locally connected topos 8 (thought of as a universe of variable sets) over a topos S (thought of as a universe of constant sets). In this context, modal operators are intrinsically definable and the resulting formal system is described in some detail. © 1991, Duke University Press. All Rights Reserved.