ABSTRACT
I. INTRODUCTION Jean Paul Van Bendegem proposes a mapping of the “major approaches” that constitute the relatively new “philosophy of mathematical practice”, gives insights about the relation between this new trend and “traditional philosophy of mathematics” and makes suggestions to build “bridges” between the two. A mapping of the different constitutive trends of practicebased studies of mathematics is especially welcome, since even a quick glance at the works susceptible to be viewed as instances of practice-based studies of mathematics is enough to convince that the corresponding studies have diversifi ed and heterogeneous objects, aims, and methods. In our commentary, we focus on this diversity. We start with an overview of Van Bendegem’s cartography considered as a whole (Section II). Next we attempt to specify further what it means to study mathematical practices, following fi rst the philosophical approaches listed by Van Bendegem (Section III), and then, more briefl y, the other approaches of his repertory (Section IV). Along the path, we compare some aspects of the philosophy of mathematical practice and the practice-based philosophy of natural sciences.
