Journal Article

The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics

Colin McLarty

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 58, issue 1, pages 77-112
Published in print March 2007 | ISSN: 0007-0882
Published online February 2007 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axl030
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics

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While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most efficient path to valuable specific results—while he sees that the question of which results are valuable has an ineliminable philosophic aspect. His philosophy relies on the ideas of truth and existence he studied in Göttingen. His career is a case study relating naturalism in philosophy of 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

Journal Article.  14399 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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