CEFISES Seminar: Stéphanie Ponsar, « What is a foundation of mathematics? »

Livestream https://youtube.com/live/d4Sqq8jbK4w

Series: Work-in-Progress

Speaker: Stéphanie Ponsar (UCLouvain)

Title: « What is a foundation of mathematics? »

Abstract

The need for a solid foundation in mathematics emerged at the turn of the 20th century. During this period, mathematics faced an existential crisis, partly due to paradoxes in Frege’s formulation of set theory. To address these issues and establish a robust basis for mathematics, Hilbert proposed a program consisting of 23 problems to be solved. Meanwhile, Zermelo took on the task of axiomatizing set theory. Today, the Zermelo-Fraenkel axiomatization is widely accepted as a foundational theory in mathematics.

With the rise of category theory, there is now a diverse range of views among philosophers about what the foundations of mathematics should entail. This analysis will explore the requirements for the foundations of mathematics as they relate to both set theory and category theory. These requirements will be examined from logical, semantic, ontological, and epistemological perspectives. The goal is to highlight the differences between the foundational approaches of set theory and category theory.