Philosophy of Mathematics seminar

Jonathan Kirby (University of East Anglia)

Up with categories, down with sets; out with categories, in with sets!

I will compare practical approaches to the notions of subsets and extension sets, coming from broadly set-theoretic and category-theoretic traditions of mathematics. I will argue that the set-theoretic approach (more precisely, the element-based approach) is the most practical for “looking down” or “in” at subsets and the category-theoretic approach (more precisely, the function-based approach) is the most practical for “looking up” or “out” at extensions, and I will suggest some guiding principles for using these approaches without recourse to either category theory or axiomatic set theory.