Abstract

The aim of this paper is to explicate and evaluate Resnik's structuralism in the philosophy of mathematics, and especially to show some difficulties in his theory. Firstly I clarify his main arguments concerning mathematical realism and structuralism. His position has some merits from the points of ontology and epistemology. Then I point out the philosophical implications of his interpretation of mathematical patterns as merely epistemological devices for philosophical explication. By using indispensability argument as a means of justification of mathematical realism, he admits the degree of our commitment to the existence of mathematical objects. Finally I will show that he fails to explain patterns and positions of mathematical structures in category theory.