Speaker: Colin Rittberg, VUB

Title: Philosophy in mathematical practice

Commentary : Aleksandra Samonek, UCLouvain

Venue: Collège Mercier first floor, salle Jean Ladrière, Place Cardinal Mercier, Louvain-la-Neuve

Time: 24th of April 2019, 15:00-17:00

Abstract:

In this talk I argue that there are avenues for fruitful interaction between the metaphysical views mathematicians hold and the mathematics they practise. To do so I engage with the contemporary debate in set theory. My focus will be on the recent argument by Hugh Woodin for a unique set-theoretic universe, which he calls “Ultimate-L”. Roughly, I argue that Woodin’s metaphysical views shape his research project and I show how he sets up his research project such that the formal results it promises to produce can influence, shape, and guide his metaphysical views. As an indication that such dialectical interplay between metaphysical views held and mathematics performed is not a single-case phenomenon, I will briefly discuss the interactions of Joel David Hamkins’ metaphysical views and his research projects. The upshot of my talk is the insight that to understand a mathematical practice, we need to understand the philosophical positions of its practitioners.