I want to know a lot about the Philosophy of Math. What books

>>9846314

Russell's IMP.

Hardy's Apology (easy read, touches on aesthetics, a branch of philosophy).

>>9846314
Question: is a map indespensable to our best navigation of a territory, or is it only tangential?

>>9846314
I'm currently reading Thinking About Mathematics by Shapiro. Definitely worth checking out.

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>>9846314
Read Laws of Form - It'll blow your mind, and it certainly gave Russell (Bertrand) a proper shake

I very much enjoyed this:
http://ndpr.nd.edu/news/phenomenology-logic-and-the-philosophy-of-mathematics/

I find that the vast majority of philosophy of math is in earnest but misses the forest for the trees. It's either a shallow skim of some perennial (er, in the last 150 years) issues, like platonism vs. conventionalism, or it engages with a very narrow but very deep knowledge of some specific area within analytic philosophy.

The problem in my opinion is that the people who are most interested in the philosophy of math are likely to be either mathematicians, or analytic philosophers. Neither is well-versed in transcendental philosophy of any kind. Unfortunately, the problem of math is the problem of (a) how an objective, self-disclosing logical system can exist, and (b) how that system can relate to an "external" world. Those questions absolutely require some kind of transcendental and metaphysical commitments, and it's absolutely necessary to be self-conscious about making those commitments and working with them.

Luckily there's been a resurgence of interest in the mathematically and scientifically minded neo-Kantians around the late 19th century.

You should also look into Wittgenstein's philosophy of mathematics, which is an extension of his philosophy of language and is conventionalist.

>>9846314
Frege, Russell, Wittgenstein, Quine, Godel, Putnam, Husserl, Peirce, Carnap, maybe even Badiou if you don't mind continental bullshit. It's a huge branch of philosophy, just about every worthwhile philosopher has something to say about it

>>9846928
The answer is that it's neither objective nor relates to external facts directly. Reality doesn't operate on ZFC+infinite cardinals. If we have a choice between saying that data conforms exactly to hypothesis xyz and saying that it's a good enough approximation we pick the former for convenience's sake every time.

>>9846314
If you don't have a handle on logic and set theory first, I would definitely study them in-depth before trying to jump right into phil of math as many, if not most, of the philosophers in that area are analytic philosophers or mathematicians themselves. After that, you could delve into the authors >>9846931 mentions. I would add in there Benacerraf and Resnik as well.

there was a dog that had two bones

>>9848427
gee, bill, two bones?

>>9846314
>I'm semi-mathematically literate (up to calc III)

As a math major I don't want to rain on your parade, but if you have not been introduced to proofs (preferably in an academic setting) then you do not understand mathematical reasoning. You should at least pick up some proof based number theory before moving on to the philosophy of math.

>>9846931
I would just add Whitehead as well. Excellent philosopher.

>>9846342
>>9846889
>>9846903
>>9846928
>>9846931
>>9848423
Thanks, this has given me a lot to start with.

>>9848461
I read How to Prove It this summer and I'm taking an intro to proof kind of course next semester anyway