# 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={C. 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… Expand

#### 15 Citations

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

- 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… Expand

A Forgotten Theory of Proofs ?

- Mathematics, Philosophy
- Log. 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. Expand

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

- 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… Expand

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… Expand

MATHEMATICAL RIGOR AND PROOF

- Mathematics
- 2019

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 proof must be… Expand

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… Expand

FOUNDATIONS AS TRUTHS WHICH ORGANIZE MATHEMATICS

- Computer Science, Mathematics
- The 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.… Expand

Categories without structures

- Computer Science, Mathematics
- 2009

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

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

- Sociology, Computer Science
- Between 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. Expand

Recent publications

- 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… Expand

#### References

SHOWING 1-10 OF 93 REFERENCES

The Rising Sea : Grothendieck on Simplicity and Generality

- 2003

In 1949, Andre Weil published striking conjectures linking number theory to topology and a striking strategy for a proof [Weil, 1949]. Around 1953, Jean-Pierre Serre took on the project and soon… Expand

Philosophy of mathematics : structure and ontology

- Mathematics
- 2004

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively… Expand

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

- Mathematics
- The Mathematical Gazette
- 2000

This book, written from the point of view of a historian of logic, painstakingly plots the gradual emergence of the axiomatic theory of sets as an independent study from the time when the set concept… Expand

The Category of Categories as a Foundation for Mathematics

- Mathematics
- 1966

In the mathematical development of recent decades one sees clearly the rise of the conviction that the relevant properties of mathematical objects are those which can be stated in terms of their… Expand

Labyrinth of thought: a history of set theory and its role in modern mathematics

- Mathematics
- 2007

Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of… Expand

Recensioni/Reviews-Modern Algebra and the Rise of Mathematical Structures

- Mathematics
- 1996

The notion of mathematical structure is among the most pervasive ones in twentieth century mathematics. "Modern algebra and the rise of mathematical structures" describes two stages in the historical… Expand

Mordell’s review, Siegel’s Ietter to Mordell, diophantine geometry, and 20th century mathematics

- Mathematics
- 1994

In 1962, I published Diophantine Geometry. Mordeil reviewed this book (Mor 1964](note 1) , and the review became famous. Immediately after the review appeared, in that same year, Siegel wrote a… Expand

Topology and logic as a source of algebra

- Mathematics
- 1976

Introduction. Each President of the American Mathematical Society is required to present a retiring presidential address. By custom, this address is not in any way directed to the examination of the… Expand

Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt

- Mathematics
- 2001

ed from its qualitative aspects. It is useful to think of the views of Weyl and Brouwer in connection with the phenomenology of the consciousness of internal time because Husserl probably invested… Expand

Mathematics. A Science of Patterns?

- Philosophy, Computer Science
- Synthese
- 2004

It is shown that it is possible to construct a realist philosophy of mathematics which commits one neither to dream the dreams of Platonism nor to reduce the word 'realism' to mere noise. Expand