Structuralism and the applicability of mathematics

Jairo J. Da Silva

pp. 229-253

in: Essays on non-empiricist rigorous philosophy, Axiomathes 20, 2010.

Abstract

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.