Abstract

For some time now part of the philosophy (and related studies) of mathematics has been referred to as ‘the philosophy of mathematical practice’. Although a number of contributions have offered characterisations of this new area, it is still not entirely clearly defined. Moreover, a number of similar terms, such as ´mathematical philosophy’ and the ‘philosophy of mathematics as practiced’, have been used to refer to related areas within the philosophy of mathematics. The talk will present and discuss some of these characterisations. I shall start by giving a brief account of mathematical philosophy as coined by Russell and as part of scientific philosophy at the beginning of the 20th century. The second part will discuss two quite different accounts of the philosophy of mathematical practice, offered by Paolo Mancosu (2008) and Jean-Paul Van Bendegem (2014). In the final part I propose a characterisation of the philosophy of mathematics as practiced as the part of philosophy that actively engages with the actual practice of mathematics – past and present. This means, for example, that philosophical questions are based on mathematics itself, or the activities of mathematicians. Furthermore, answers to philosophical questions may draw on mathematical tools or (historical) case studies. The ‘activities of mathematicians’ could, for example, include what mathematicians say or write about their work or how they go about finding new results. This part will propose some questions that could be relevant to contemporary mathematical practice and presents some illustrative examples.

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