Character and Object: Frege-Dedekind Fest 2016

(Joint work with Jeremy Avigad)

In this talk I will discuss issues of mathematical design, as reflected in the work of Dedekind and Frege. More precisely, I will consider Dedekind’s work on the development of the notion of character and Frege’s foundational logical system. While Dedekind and Frege were focused on quite different projects (Dedekind with extending our knowledge, Frege with securing our foundations), both faced similar pressures. In particular, I will argue that both Dedekind and Frege had to balance the desire for flexibility and uniformity in their mathematics alongside the necessity of rigor. Finally I will use these case studies to draw some conclusions about how we ought to design our mathematics.