The Last Mathematician from Hilbert's Gottingen: Saunders Mac Lane as Philosopher of Mathematics |
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| Authors: | McLarty Colin |
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| Institution: | Department of Philosophy, Case Western Reserve University, Cleveland, OH, USA 44106 |
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| Abstract: | While Saunders Mac Lane studied for his D.Phil in Göttingen,he heard David Hilbert's weekly lectures on philosophy, talkedphilosophy with Hermann Weyl, and studied it with Moritz Geiger.Their philosophies and Emmy Noether's algebra all influencedhis conception of category theory, which has become the workingstructure theory of mathematics. His practice has constantlyaffirmed that a proper large-scale organization for mathematicsis the most efficient path to valuable specific results—whilehe sees that the question of which results are valuable hasan ineliminable philosophic aspect. His philosophy relies onthe ideas of truth and existence he studied in Göttingen.His career is a case study relating naturalism in philosophyof mathematics to philosophy as it naturally arises in mathematics.- Introduction
- Structures and Morphisms
- Varieties of Structuralism
- Göttingen
- Logic: Mac Lane's Dissertation
- Emmy Noether
- Natural Transformations
- Grothendieck: Toposes and Universes
- Lawvere and Foundations
- Truth and Existence
- Naturalism
- Austere Forms of Beauty
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