Maths is a self-consistent and closed system. From that point of view, the nature of axioms is irrelevant. You can have an unlimited kinds of axiomatic systems, each consistent and each explanatory in its own way. What is a theorem in one system can be treated as an axiom in the next as long as the system itself leads to no contradictions.
Given that human knowledge encompasses more than one axiomatic system, it would be foolish to endow a system designed to replicate human knowledge with an immutable set of axioms.
Given that human knowledge encompasses more than one axiomatic system, it would be foolish to endow a system designed to replicate human knowledge with an immutable set of axioms.
Please watch this presentation of Richard Feynman on the nature of maths and physics: http://www.feynmanphysicslectures.com/relation-of-mathematic...