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

@article{McLarty2007TheLM, title={The Last Mathematician from Hilbert's G{\"o}ttingen: Saunders Mac Lane as Philosopher of Mathematics}, author={Colin McLarty}, journal={The British Journal for the Philosophy of Science}, year={2007}, volume={58}, pages={77 - 112} }

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…

## 15 Citations

Saunders Mac Lane: From Principia Mathematica through Göttingen to the Working Theory of Structures

- Philosophy
- 2020

Saunders Mac Lane (1909– 2005) attended David Hilbert’s weekly lectures on philosophy in Göttingen in 1931. He utterly believed Hilbert’s declaration that mathematics will know no limits: Wir müssen…

A Forgotten Theory of Proofs ?

- MathematicsLog. Methods Comput. Sci.
- 2019

This essay attempts to revive the idea of an algebra of proofs, place MacLane’s thesis work and its vision in a new framework and try to address his original vision.

Mathematics as a Science of Non-abstract Reality: Aristotelian Realist Philosophies of Mathematics

- PhilosophyFoundations of Science
- 2021

There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy…

Anti-Foundational Categorical Structuralism

- Philosophy
- 2012

The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the…

MATHEMATICAL RIGOR AND PROOF

- Philosophy, MathematicsThe Review of Symbolic Logic
- 2019

Abstract Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowledge, a mathematical…

Introduction to Representation Theory

- Mathematics
- 2011

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to…

FOUNDATIONS AS TRUTHS WHICH ORGANIZE MATHEMATICS

- PhilosophyThe Review of Symbolic Logic
- 2012

The article looks briefly at Feferman’s most sweeping claims about categorical foundations, focuses on narrower points raised in Berkeley, and asks some questions about Feferman’s own foundations.…

Categories without structures

- Mathematics, Philosophy
- 2009

A non-structuralist interpretation of categorical mathematics is developed and its consequences for history of mathematics and mathematics education are shown.

Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics

- PhilosophyBetween Logic and Reality
- 2012

The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.

Recent publications

- Physics
- 2007

I was a Lecturer, Reader, and then Professor, at Bristol from 1985 to 2001. I moved to University of Warwick, and retired in 2014, returning to Bristol. In addition to my position here, I retain…

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