Practice, Constraint, and Mathematical Concepts

Philosophia Scientiae 16 (1):15-28 (2012)

Abstract
Dans cet article je propose d'exprimer et de défendre une conception des pratiques et du domaine de discours mathématiques qui soit sensible, d'une part, au pluralisme des relations entre pratiques inférentielles et intérêts, et d'autre part, à la structure objective et déterminante des concepts mathématiques. J'ébauche tout d'abord une caractérisation générale des pratiques, pour ensuite préciser certains phénomènes propres aux pratiques mathématiques. Suit un recensement des idées qui se dégagent des arguments pluralistes, et de celles qui sont à retenir. Mais je défends par la suite la nécessité d'une forme de réalisme mathématique, qui toutefois ne peut être le réalisme d'objets que prônent les partisans de l'argument d'indispensabilité. Je défends plutôt un réalisme des concepts, soutenu par ce que je baptise l'« argument de la contrainte ».In this piece I articulate and defend a conception of mathematical practice and mathematical subject-matter, which is responsive both to a sensible pluralism concerning the connection between inferential practices and guiding interests, on the one hand, and to the objective content-determining structure of mathematical concepts on the other. I begin by sketching a general characterization of practices themselves, and by specifying some of the unique features of mathematical practices. An examination of inferential pluralism follows, and some insights of pluralist arguments are retained. But I argue further for the requirement of some form of mathematical realism, though the object-realism of the indispensability argument is assessed and rejected. My positive proposal argues for a form of concept-realism, which is established by what I call the "argument from constraint."
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DOI 10.4000/philosophiascientiae.710
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