Unifying classicality and non-classicality

This project aims to bring together the study of classicality and non-classicality within the fields of mathematical logic and philosophy of logic. The project is divided into two parts. First, we will unify classical and non-classical foundations of mathematics within a set-theoretic framework. Moreover, our approach is distinctive from previous attempts of such unification. We believe only an algebraic approach has sufficient generality for such a task. Secondly, we will extend our reconciliation of classicality and non-classicality to the area of philosophy of logic and philosophy of set theory. In particular, we plan to unify the study of set-theoretic and logical pluralism. We believe this will allow us to gain new insights into both fields of study.