Topos Modeling of Social Conflict: Theory and Methods

Abstract

Category theory and, more specifically, topos categories provide a more expressive type of mathematical modeling and, thereby, open the door to social models that are both rigorous and expressive. The present analysis draws upon four views of topos categories to construct a rich model of a logic based on recognition theory. The topos initially provides support for: (1) set theory (and classical logic), (2) topological regions dualism. The resulting structures support: (3) a local intuitionist logic that can vary by situated circumstances and actor types, and (4) the specification of regions that are defined by finely-differentiated classifiers. These tools construct an integrated topos category of social recognition that supports diverse forms of local logic. The latter are then explored regarding their contributions to a mathematical model of social conflict. Categorial analysis of historical patterns, as well as a complementary simulation model, is used to illustrate the advantages of such an approach.