Philosophy of mathematics
Philosophy of math mainly studies the ontology and epistemology of mathematics. It focuses heavily, perhaps excessively, on foundations of math, to which I dedicate a separate page.
Literature
General
- Linnebo, 2017: Philosophy of Mathematics, in Princeton Foundations of Contemporary Philosophy (NDPR )
Topics in mathematics
- Potter, 2004: Set Theory and its Philosophy (NDPR )
- Landry, ed., 2017: Categories for the Working Philosopher
- nCat Cafe: announcement and discussion of John Baez’s contribution (1 ,2 )
Contemporary mathematics
A fledgling movement is trying push philosophers of math away from traditional foundational subjects (logic, set theory, elementary number theory) and towards contemporary math in all its diversity.
- Rota, 1997: Indiscrete Thoughts
- A call to action, at most—not a systematic philosophy of contemporary math
- Reviewed on my blog
- Corfield, 2003: Towards a philosophy of real mathematics
- Reviews: AMS Notices , Math Intelligencer, NDPR
- Zalamea, 2012: Synthetic philosophy of contemporary mathematics (nForum )
- Review: Giuseppe Longo
- Short review: some intriguing passages, but crippled by vagueness, unexplained jargon, and above all an obscure, continental writing style
- The most useful part is the literature review in Ch. 2: “Advanced mathematics in the tracts of mathematical philosophy: A bibliographical survey”