I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way.

Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.