What well-written introductory books are there about a mathematical point of view on the philosophy of mathematics and its different school of thought?
By this I mean a book that has some mathematical treatment of the subject, for example it might describe the mathematics of constructivism, rather than just the broad ideas behind it. I'm also looking for an introductory book, as my background in philosophy is quite shallow.
Edit: I'm looking for a book that presents the philosophical ideas alongside the mathematical theories. @oneguy has linked notes about the (mathematical) foundations of constructivism, but they lack a philosophical discussion.
All of what I found about the philosophy of mathematics is very mathematically shallow, or on the other extreme (mathematical texts about logic and set theory). It would be nice to find something in between and less specialized.
The french book « Penser les mathématiques » has a few articles that fall into what I'm looking for. (http://www.amazon.fr/MATHEMATHIQUES-S%C3%A9minaire-philosophie-math%C3%A9matiques-sup%C3%A9rieure/dp/2020060612)
Edit 2: The Stanford Encyclopedia of Philosophy has very good articles on the subject, with a proper mathematical level and references (http://plato.stanford.edu/entries/mathematics-constructive/).