Structuralizm versus Object Realism – A Genuine Argument?

Abstract

In the article, I discuss the differences between mathematical structuralism and object realism. I argue that they are partly only a matter of formulation and that some basic theses of both standpoints can be translated into the opponent’s language.

I also indicate some problems of both these standpoints. From the point of view of mathematical structuralism, object realism has to face the problem of reference of mathematical terms. From the point of view of mathematical realism, mathematical structuralism relies on quite strong metaphysical assumptions. I also claim that structuralism also violates our intuitive understanding of some mathematical