Lee, Chanwoo
(2025)
Category Theory as an Explanatory Foundation.
[Preprint]
Abstract
Can category theory be a foundation of mathematics? While category theory is taken to organize the body of mathematical knowledge and practice, its status as a foundational theory has been disputed. I argue that category theory can serve as a foundation of mathematics especially in an explanatory sense. The explanatory sense of foundation is both historically situated and philosophically motivated; I examine its historical uses by some of the pioneering figures as well as its theoretical ramifications across several philosophical topics. Then what makes category theory explanatory in the relevant sense? I argue that the explanatory nature of category theory can be understood as its capacity to offer abstract explanation. To support this, the case studies on mathematical explanation through Galois theory and category theory will be considered, which will be tied in with more traditional accounts of category theory’s foundational status. Thus, I argue that category theory’s foundational status can be supported through the lens of mathematical explanation, which demonstrates a successful interplay between the two traditions in philosophy of mathematics, i.e., the foundation-oriented tradition and the practice-oriented tradition.
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Category Theory as an Explanatory Foundation. (deposited 08 Dec 2025 13:50)
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