Methodological and Ontological Structuralism in Mathematics: A Husserlian Take

Logic Café Lecture
The Philosophy Department and the Institute Vienna Circle are jointly organizing a series of talks this term

Date: 05/06/2023

Time: 16h45-18h15

Meetings are usually held on Mondays from 16:45 to 18:15 in Raum 3F (D0313), 3. floor Department of Philosophy

Abstract:

Methodological structuralism and ontological structuralism in mathematics offer separate, yet related, accounts of structuralism in mathematics. The former captures certain structuralist ways or methods of practicing mathematics, while the latter concerns questions about the nature of mathematical structures. However, exactly how these two are related is not clearly accounted for in the literature. In this talk, I offer a solution to this problem by following Husserl's teleological view of scientific practice.

On Husserl's teleological view of science, we have the intersubjective practitioners who form a community of empathy. The structuralist ways or methods are characterised by the empathic relationship within the community. This community aims at a goal or goals, but what the nature of these goals are can vary. So, I suggest that, following this Husserlian view, ontological structuralism is concerned with the structures which are aimed at by the community and its practice.