Enquête sur les modes d’existence des êtres mathématiques

Abstract

This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world [Latour 2012]. An answer to this question is put forward with the aid of the work of Reviel Netz on the emergence of Greek mathematics [Netz 1999], and of Charles Sanders Peirce on the diagrammatic dimension of mathematical practice [Peirce 1933-1958], [Peirce 1976], in the framework of an empiric conception of mathematics based on the notion of experience according to William James [James 2007], and inspired by certain aspects of Per Martin-Löf’s philosophy [Martin-Löf 1987]. It provides a way of describing the firm certainty with which proofs endow theorems, while invalidating the interpretation of this certainty as the mark of a direct access to an absolute and transcendental truth.