First and foremost I should say that I am not educated in Philosophy; I study Mathematics.
Essentially, the job of a mathematician is to prove theorems by logical deduction from axioms, which are statements considered to be true in advance. The axioms themselves are essentially up to the mathematician, in that so long as they don't contradict each other any statements could be treated as axioms for some system. In the experimental sciences, similarly, what is taken as absolute truth is observation: what nature is seen to do.
My question is this: in philosophical arguments, what is taken to be true? Is there an equivalent to what I've described above?