The (reasonable) effectiveness of mathematics in empirical science

Abstract

I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains -mathematical domains in particular- whose formal structures bear relevant formal similarities with them. I also discuss the consequences to the ontology of mathematics and empirical science of this structuralist approach.