The philosophical structuralism and the foundations of mathematics: the Hellman-Awodey controversy
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In the framework of the philosophy of contemporary mathematics, Hellman and Awodey both hold an interesting discussion on the role of Zermelo-Fraenkel Set Theory and Category Theory in the perspective of a good foundation for mathematics. For Hellman, neither Set Theory nor Category Theory constitutes a good foundational framework for mathematics and, in addition, Categories does not achieve a strong autonomy regarding Sets. Awodey's claim is that Category Theory is a best option in the frame of a new way of understanding what a foundation of mathematics means. In this sense, the aim of this paper is to highlight the philosophical main features of this discussion, to establish some related positions and to show some interesting consequences for the philosophy of mathematics.
- Structuralism
- Structure
- Foundation of mathematics
- Category theory
- Set theory
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Accepted 2018-02-01
Published 2017-07-15
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