On the Contemporary Practice of Philosophy of Mathematics

Abstract

In this paper I propose to reflect on contemporary philosophy of mathematics. i argue that the impartiality to methodology that is present in the current practice of philosophy of mathematics is an intellectual vice of our research community because it leaves our philosophical methods to engage with mathematics implicit. This hides difficulties our research community faces, difficulties our students can reasonably expect to learn about and which we need to engage with to overcome them. to be virtuously open-minded about methodology is not to be impartial about methodology but rather to critically assess the proposals on offer in a public debate.

Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free

“…There is an ongoing debate about the right methodology for Philosophy of Mathematical Practice(s), see f.i. (Rittberg 2019) or the many programs mentioned by Carter (2019). One can see a parallelism between the development of PMP and certain events in Philosophy of Science.…”