Practice, Constraint, and Mathematical Concepts

Practice, Constraint, and Mathematical Concepts

Blog Article

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 diamond painting strand en zee 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 here argues for a form of concept-realism, which is established by what I call the "argument from constraint.".