Realism in the Contemporary Philosophy of Mathematics

Abstract

Probably no term in the philosopher's lexicon has had more distinct uses than `realism'. In this article we attempt at explaining how this term works within the scope of contemporized standpoints of the philosophy of mathematics. In order to attain this we accept differentiation of the philosophy of mathematics from the theory of the foundamentals of mathematics, and then in the first one we distinguish epistemology, ontology, semantics, methodology, and pragmatics. The realistic attitude is presented here both in the traditional, and contemporized approach. The traditional realism represented by K.Gödel and G.Frege have been recently contemporized by the discussions, which arose with regard to the attitudes of M.Resnik, M.Steiner, and S.Shapiro. In the article we present all this options.