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.

It sounds like you are looking for physics (tangible proofs) and metaphysics (intangible proofs) -intuition- mathematics.

Though, I wonder if predicate calculus, logic, Gödel's theorems, second-order logic, and set theory are enough. You may want to look into long-division. A math book that reviews a number of contemporary maths that I do have is called, Topics in contemporary mathematics, though I'm not sure that is practical for what you are talking about. You also may want to check out Chaos mathematics (the study of math) to get an understanding that our math system is fundamentally imperfect which is the reason for theorems and other equations to equalize or get close to as real an answer as possible. Like the use of Pi.

Other than that, I would look into a list of mathematics philosophers and see where they left off and research what maths we've come up with since then with regards to the subjects and topics they were proving. I believe there is a list on Wikipedia to get started with.

Good luck!

>>2
You may want to look into long-division.
What does this mean?  I thought long division was just an arithmetical procedure.

>>3
>>just an arithmetical procedure.
I lol'd.

Long division has a little to do with procedure, but it also has a lot to do with condensing maths into a simpler form to explain something complex. If you have this, especially with philosophy math, you'll easily be able to represent something complex in a simple way to those that understand long-division. And no, this is not something you learned in grade school.

you know how 3.1415926535897932384626433832795 = π?
That's long-division only you also begin to condense whole equations into symbols. There's more to it than that, but that ought to get you started. You know any show or program that you may have seen some math professor writing out a really long equation on the board and you couldn't make heads nor tails of it? That's long-division, for the most part.

If you wanted to explain something like intention in a mathematical process, you couldn't exclude choice, you couldn't exclude reason, you couldn't exclude rationality, you couldn't exclude emotion at that moment, you also couldn't exclude any other mental or physical attributes that may contribute to intention. Best way to explain something complex in simple form? Long-division. E=MC^2 <--Long division.

I have no idea what you're talking about.

>>5
Seconded.

>>5
>>6
it's simple...if you don't know...find out. Look for information that leads to what this is. Even if the information reveals something entirely different, at least you found the answers you were looking for instead of living the rest of your lives not really knowing what I'm talking about.

How am I supposed to tell you guys that mathematics is flawed because humans are flawed? We have to use something like Pi in order to find out dimensions of a circle. This "patch" in mathematics is used in order to bi-pass a fundamental missing-link in mathematics which is the closest thing we have to what could be considered a working equation; πr^2.

If you want to know what profession deals with problems in mathematics, you are looking for a Chaotician. Chaos Theory, deals with the smallest matters that create the greatest errors. There is a hypothesis that our numbering system is fundamentally flawed which is what gives us these errors. The larger the problem, the solution becomes further from the truth.

Of course this is something you haven't generally heard of, what person in their right mind wants to destabilize a system that has been used over and over by many different fields of study and practice? It would be tantamount to overthrowing the traditions of religion as a WHOLE. Nobody would be spared.

>>7
Ok, I looked high and low for any definition of "long division" that didn't refer to the arithmetic procedure (ie. http://en.wikipedia.org/wiki/Long_division ) ...  and there is nowhere to be found a definition that fits your fucktardedly glorious definition where E=MC^2 is long-division or any of that crap you were gibbering about.

So please, enlighten the ever-living fuck out of us.

It's more about algorithms. Equations that utilize other equations within variables, going numerous depths for the purposes of simplifying what would otherwise be complicated and arduous computer work.

You might notice that we no longer utilize binary, but something called C++ or compiler code.

Long-division is the process of jumping different levels of math to form one formula to create an algorithm.

And no, it's not what you've learned in grade-school.

>>7
There is a hypothesis that our numbering system is fundamentally flawed which is what gives us these errors.
No shit, we don't have an effective way of expressing arbitrary irrationals (especially e and pi) that a computer can understand.  It does not mean mathematics needs to be overthrown, or that there would even be anything to overthrow it to for that matter.
It's really not anything profound.  Chaos theory is simply the study of ill-conditioned systems.  If you're obsessed with chaos theory then what I would recommend doing is actually learning it, not preaching about it on some messageboard when you don't actually understand the first thing about it.

OP here.  I ended up purchasing this:
http://www.amazon.com/gp/product/0195148770/
Hopefully it will be good.  I'm still open to other recommendations though.

>>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? :<

>>11
Oooh, Good one, OP! Btw, did you buy it new or used?
Used it's only about half price. :3

I think that will be a grand place to start from! You will have a treasure trove of questions in your studies after reading this book! :3

TOTAL WIN!

>>12
How would I know, I'm just quoting what my uncle told me. He even told me that he's not sure that it is actually called long-division, but the part of reducing large equations to small equations in a condensing manor is used by chaoticians that study the fundamentals of math itself is accurate. Just because I don't have the name right, doesn't mean it doesn't exist, it just means I don't have the name right. :/

Of course, if it really mattered to you, you'd ask mathematicians and chaoticians to find out the answer...if you DARE! HAHAHAHAHAHA!!!!! Oooooh, spooooky. :3

And as for why you are so easy to troll?
You don't think you will get trolled on 4chan. :/
Srsly, wtf did you THINK would happen? Get a straight answer?
XD AHAHAHAHAHAHAHAHA!!!!!!

>>13
I bought it new from a third-party seller for $53 plus shipping.  Looks like I got the last one by that seller.  Unfortunately, my semester seems to be picking up so I may not be able to really get into it until summer.

Principles of Physical Cosmology by Peebles -- it's astrophysics at its finest.

>>15
awesome book, below retail cost = INFINIWIN!

http://www.iwantapal.com/