nLab philosophy of mathematics

Idea

The philosophy of mathematics.

Related concepts

• pluralism, reductionism

• Platonism

• finitism, ultrafinitism

• constructivism, predicative mathematics

• structuralism

• philosophy of science

  • philosophy of physics

• history of mathematics

• epistemology of mathematics

References

• Stanford Encyclopedia of Philosophy, Philosophy of Mathematics

• Wikipedia, Philosophy of mathematics

• Albert Lautman, Mathematics, ideas and the physical real, 2011 translation by Simon B. Duffy; English edition of Les Mathématiques, les idées et le réel physique, Librairie Philosophique, J. VRIN, 2006

• Fernando Zalamea, Filosofía sintética de las matemáticas contemporáneas, (Spanish) Obra Selecta. Editorial Universidad Nacional de Colombia, Bogotá, 2009. 231 pp. MR2599170, ISBN: 978-958-719-206-3, pdf. Transl. into English by Zachary Luke Fraser: Synthetic philosophy of contemporary mathematics, Sep. 2011. bookpage. Some excerpts here.

• David Corfield, Towards a philosophy of real mathematics, Cambridge University Press, 2003 (doi:10.1017/CBO9780511487576, gBooks)

• Roland Omnès, Converging Realities – Toward a common philosophy of physics and mathematics, Princeton University Press, 2005

• Saunders MacLane, Mathematics, form and function, Springer-Verlag 1986, xi+476 pp. MR87g:00041, wikipedia

• George Lakoff, Rafael E. Núñez, Where mathematics comes from, Basic Books 2000, xviii+493 pp. MR2001i:00013

• Yuri I. Manin, Mathematics as Metaphor:

  Selected Essays of Yuri Manin, Amer. Math. Soc. 2007

• Michael D. Potter, Set theory and its philosophy: a critical introduction, Oxford Univ. Press 2004

• Ralf Krömer, Tool and object: A history and philosophy of category theory, Birkhäuser 2007

• Jean-Pierre Marquis, From a geometrical point of view: a study of the history and philosophy of category theory, Springer, 2008

• Ian Hacking, Why is there philosophy of mathematics at all?, Cambridge University Press 2014

• William Bragg Ewald, From Kant to Hilbert, From Kant to Hilbert: Readings in the Foundations of Mathematics, 2 vols. (original readings in English translation)

• Paolo Mancosu, Philosophy of mathematics and mathematical practice in the seventeenth century, OUP, 1996.

• Imre Lakatos, Proofs and refutations, in J. Worrall & E. Zahar (Eds.), The logic of mathematical discovery. Cambridge University Press 1978

• Hermann Weyl, Philosophy of Mathematics and Natural Science, Princeton University Press, 2nd edition, Princeton University Press, 1950 (ISBN:9780691141206)

• Jacques Hadamard, Psychology of invention in the mathematical field, Princeton University Press 1945

The role of Heraclitus:

• Joachim Lambek, The influence of Heraclitus on modern mathematics, In Scientific Philosophy Today: Essays in Honor of Mario Bunge, edited by Joseph Agassi and Robert S Cohen, 111–21. Boston: D. Reidel Publishing Co.