The overarching theme of this masterclass is the analysis of a ‘practical turn’ in the philosophy of mathematics. Is this turn analogous to the practical turn in philosophy of sciences? Should it be? What is the exact role of the empirical studies of mathematical practice (e.g. mathematics education, sociology of mathematic, etc.)? How should these interact with the philosophy of mathematics? In particular, we want to encourage work in the following three areas:
- We want to draw attention to the seminal work of Imre Lakatos: a) he was a key figure in developing early themes after the practical turn in the philosophy of physics in form of his idea of ‘research programmes’. b) His work in the philosophy of mathematics was a turning point for the discipline. Lakatos particularly aimed at transferring insights from his work on the philosophy of science to the philosophy of mathematics. However, he did not have enough time to develop these ideas before his early death.
- Additionally, we want to encourage work on the interplay of the philosophy of mathematics and the philosophy of science. One might tackle questions such as: should philosophy of science conferences have tracks for philosophy of mathematics? What was the role of Tarski when the two disciplines split up? How close should the philosophy of mathematics community be to the logic community? What should we make of the growing community of philosophers of mathematical practice as well as the cooperation with other disciplines (such as ethno-mathematical studies, mathematical education, cognitive sciences, etc)?
- Another possible string of investigation is the analysis of new scientific methodologies in the philosophy of mathematics. To what extent are they philosophically significant? How can they inform a philosopher of mathematics? An analogous problem has already arisen for philosophy of science in relation to science studies.