Toward a Methodology for the Philosophy of Mathematical Practice

Practice-based approaches to philosophy of mathematics have gone mainstream over the past several decades. As the paradigm has grown in popularity, however, there’s been little sustained meditation—and still less any explicit consensus—on what precisely it means for philosophy to take practice seriously. The field’s lack of a clear common methodology has begun to make itself felt in slowed and uncertain progress on core problems. Here I review the methodological situation and propose five canons to guide future research. I focus throughout on the study of explanation in mathematics as a guiding example.