I think a key challenge with music theory is that it is tackling some of the same problems as in linguistics.

You have a somewhat formal system that follows some sort of methodology. However, while there is a system, it seems nearly impossible to actually describe the axioms of this system formally.

With language or music, how do you determine some bases from which all other concepts are composed? I suspect that there is probably no such bases since new concepts seem to be able to be spontaneously created from human experience and often have circular relations.