Empirical Research and The Philosophy of Mathematics

Markus Pantsar (Helsinki) gives a talk at the MCMP Colloquium titled "Empirical Research and The Philosophy of Mathematics". Abstract:In the philosophy of mathematics, one of the most fundamental questions concerns how mathematical methods help us get knowledge of the world. In this, mathematics with its apparent a priori character seems to be radically different from the empirical methods we otherwise rely on in science. This relation between the mathematical and the empirical has received extensive treatment from the likes of Quine, Putnam and Kitcher. In this talk, however, I want to focus on a different approach: what can we learn empirically about mathematical thinking and, in particular, what relevance does this have in philosophy? For this purpose, I will present some examples of results from psychology, animalstudies, sociology and the study of mathematical practice, and evaluate their philosophical importance. While such results are often inconclusive or irrelevant, I will contend that there are numerous studies concerning primitive mathematical thinking that we should take seriously in philosophy. In addition, I will formulate the outlines of an epistemological theory that can retain the special character of mathematical knowledge while not making it empirically unfeasible.