requesting a book recommendation

Would anyone here be willing to recommend me a decent book on different philosophies of mathematics (eg formalism, intuitionism, etc)?  I've been searching amazon and I'm having a difficult time distinguishing what's worth the purchase.  I'm looking for something relatively rigorous in its details.

I have some background in predicate calculus (mathematical logic - I've read through the proofs of Gödel's theorems and briefly touched on second-order logic), set theory (I'm familiar with ZFC as well as basic ordinal and cardinal arithmetic), and a tiny bit of category theory (products, equalizers, duality, etc).  I wouldn't mind reading something that reviews those things, as long as the main subject is the philosophy and it's aimed at someone with an undergraduate background in math.

Thanks to anyone who bothered to read this.

>>9
Ok, can you cite any - fucking - thing that defines "long-division" that way?

And can you explain why "jumping different levels of math to form one formula to create an algorithm" is called long-division?  And why [whoever the fuck came up with that name] didn't say "hey, that's a retarded thing to name the process of formulating an algorithm, let's give it a name that makes sense and isn't also the name of an elementary arithmetic procedure"?  I'd love to know the answer to that one.


Oh my god, why am I so easy to troll? :<