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What is the best way to get started with the philosophy of mathematics? Given that I know (from university) the basics that are discussed (Set theory, Russell's paradox, Axiom of Choice, ...) what is the optimal strategy to start??

Should I start with the history of mathematics and then gradually switch to philosophy? Are there any must-read books on the subject for the beginner? What should one know (crucial mathematical or philosophical ideas/theories) before starting?

Also, it seems that almost all of the subject is written in english, and while i can fluently read/understand/translate written english, it is not my first language. Do you know of any reference in Spanish??

Thanks in advance

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  • For some kickass modern philosophy of mathematics written in Spanish, check out Fernando Zalamea. He goes way beyond the traditional Frege-Russell stuff from the 1900's, and gets to the heart of modern (post-1950's) math. He's the first postmodernist who ever made sense to me. urbanomic.com/book/…
    – user4894
    Mar 27, 2019 at 20:59
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    There is no universal "best way", it depends on your background, inclinations, interests, etc. Which "not really mathematical" philosophy are you an avid reader of? What, more specifically, attracts you within philosophy of mathematics (formal theories/logic, metaphysics of abstract objects, nature of proof, connections to practice and applications, etc.)? Philosophical circles are not that numerous, and the English is currently lingua franca, even for native Spanish speakers, so to stay current you'll have to get on board with that.
    – Conifold
    Mar 27, 2019 at 21:31
  • I would suggest The Philosophy of Mathematics by Auguste Comte (c1851) archive.org/details/philosophymathe02comtgoog/page/n4 and A Philosophy of Mathematics by Louis Osgood Kattsoff (c1948) archive.org/details/philosophyofmath00katt
    – Bread
    Mar 28, 2019 at 0:30
  • SEP's entries (there are many) like : Philosophy of Mathematics with biblio.
    – Mauro ALLEGRANZA
    Mar 28, 2019 at 7:15
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    You're welcome to the logic chat-room if you want to have a mathematically-informed discussion about philosophy of mathematics.
    – user21820
    May 17, 2019 at 17:33

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I have a principled argument for why this book should exist. I have no such argument for why it contains just what it contains. The principles are these:

• You cannot understand philosophy of mathematics without understanding mathematics.

• You cannot understand mathematics without doing mathematics.

[...]

I have taught undergraduates for three decades. In the 14 times I taught philosophy of mathematics, I discovered again and again that some important text was opaque to my students largely because they lacked some particular bit of mathematical background. Most of the missing bits came from a handful of subject areas: Primitive Recursive Arithmetic, Peano Arithmetic, Gödel’s theorems [...]

The readers most likely to benefit from this book are exactly those most likely to benefit from a philosophy of mathematics course. Those readers will have some background in formal logic, they will find mathematics engaging and nonthreatening, they will understand basic properties of the natural and real numbers, and they will see the point of asking ‘‘why’’ and ‘‘how’’ questions that emerge from mathematical experience, but cannot be answered by just producing more mathematics. I would describe this last trait as ‘‘philosophical inclination’’ — and it is the inclination, rather than any particular philosophical training, that is likely to be most important here.

Pollard, S. (2014). A Mathematical Prelude to the Philosophy of Mathematics. Springer.

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