Individuating Logics: A Category-Theoretic Approach

This paper addresses a recent debate as to whether logical anti-exceptionalists should understand logical theories in syntactic or semantic terms. In Wigglesworth (2017), I propose a purely semantic approach, while Woods (2018) has argued in favor of a purely syntactic approach. Here, I argue that neither of these approaches is satisfactory, as both treat arguably distinct logics as equivalent logical theories. I argue instead for an approach that combines syntactic and semantic components. The specific approach to a combined account of logical theories is based on the category-theoretic notion of an institution.