Hope Duncan (University of Leeds) – What do we want a foundation to do?

Abstract: Set theory is often accepted as a foundation of mathematics because of our ability to embed mathematical objects as sets, and prove classical theorems from the axioms of set theory. However, this answer does not examine what ‘job’ we want a foundation of mathematics to do, what it is that makes a theory foundational. We will discuss the response of the philosopher Penelope Maddy to this question, and time permitting also discuss category theory and homotopy type theory through this lens.