Strukturalizm jako alternatywa dla platonizmu w filozofii matematyki

Abstrakt

The aim of this paper is to analyze structuralism as an alternative view to platonism in the philosophy of mathematics. We also try to find out if ontological and epistemological problems of platonism can be avoided by admitting the principles of structuralism. Structuralism claims that mathematical objects are merely positions in structures and have no identity or in general any important features outside these structures. Such view allows to avoid problems of the nature of numbers and other mathematical objects. But the chief motivation of structuralism is in fact epistemological. It offers a nice way of explaining how one can get the knowledge of mathematical objects by the process of abstraction. On the other hand, there are many problems connected with mathematical structuralism. Some of them are analyzed in the paper. We come to the conclusion that mathematical structuralism, up to now, can't express the whole truth about mathematics.