Note that I am not talking perse, about the definition of axioms. I know what that is, their these 'self-evidently true' statements which are the building blocks of all reasoning, meaning there untraceable.
This makes sense, because you can't have an infinite regress where reason after reason, you justify yourself perpetually. However, given the nature of axioms, how do we know when we have one? How do we know that something is 'self-evident' enough (though some may argue it need not be) and that it cannot be proven by any other truths?
I think that a good place to start is answering such questions, is by looking at their use. Since you can't just say 'this is an axiom' but 'this is not an axiom', maybe we can look for signs that we have obtained one in their deployment. Particularly in the fact that their untracable: Is there a solid method to prove that an axiom is the ultimate starting point in our reasoning?
Just to make clear, am speaking of axioms as being independent of what we think. Axioms are discovered, not created.