Structuralism and the Applicability of Mathematics - da Silva, Jairo Jose [UNESP] (Springer, 2010)
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.
Keywords: Structuralism; Philosophy of applied mathematics; Phenomenology of mathematics; Ontology of mathematics; Epistemology of mathematics