Axiomatization

Axiomatization, or development of a set of ideas from first principles, is certainly a popular technique in mathematics and to some extent in areas like physics, etc. The irony is that across my humanities classes, few want it in any of them, even philosophy.

It is true some fields of endeavor don't lend themselves to it particularly well (the study of natural languages comes to mind--most languages have rules but they also have exceptions, etc). On the other hand, an axiom by definition is something which is true by assertion and so whenever something is simply asserted as true, that is an axiom. At the same time, whenever one says "these are the conclusions desired", it automatically forces them to build an argument in support of them with certain premises which in term have premises and sooner or later one hits axioms. The difference is merely they are enumerated last.

Meaningful discourse can certainly be had without explicit axiomatization, but axioms are the logical foundation of discourse (along with a specified system of logic which is itself axiomatic). Thus to fully understand the other and the foundation of their argument, one must understand--at least implicitly--their axioms.