Authors
Colin McLarty
Case Western Reserve University
Abstract
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.
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DOI 10.1093/bjps/axl030
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References found in this work BETA

Introduction to Metamathematics.Stephen Kleene - 1952 - Princeton, NJ, USA: North Holland.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.

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Citations of this work BETA

Foundations as Truths Which Organize Mathematics.Colin Mclarty - 2013 - Review of Symbolic Logic 6 (1):76-86.
Categories Without Structures.Andrei Rodin - 2011 - Philosophia Mathematica 19 (1):20-46.
Mathematics as a Love of Wisdom: Saunders Mac Lane as Philosopher.Colin McLarty - 2020 - Philosophical Problems in Science 69:17-32.

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