2008•Logique et analyse/Logique et analyse. Nouvelle sérieRequires access

Structuralism and category theory in the contemporary philosophy of mathematics

Izabela Bondecka-Krzykowska, Roman Murawski

Abstract

The set-theoretical (Bourbaki-style) and category-theoretical approach to structuralism in the philosophy of mathematics are compared. Advantages and disadvantages of those approaches are indicated. We come to the conclusion that category theory can be the language of mathematical structuralism but one should be careful to claim that it can serve as a foundation for the whole of mathematics.

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Key concepts: Structuralism (philosophy of science), Category theory, Foundations of mathematics, Philosophy of mathematics, Foundation (evidence), Mathematics, Set theory, Epistemology