I think you’re speaking in ignorance here. Aristotle, for example, never tried to prove any axiom. And how does Hoppe try to prove any axiom for that matter?
Proof refers to logical deduction. By definition one can’t prove an axiom (i.e., via logical deduction). Aristotel knew that. I think Hoppe knows that too.
Philosophers have never learned that lesson, so I hope that my emphatic statement doesn’t rub you the wrong way–odds are good that you too are trying to derive morality from nothing. References to eudaimonia virtually prove it: I’m willing to bet that at the bottom of your ethics is the notion that “morality” consists in fish being fully fish, humans being fully human, and so on. The iron law will nail you every time: down deep in your discourse, your definition of being “true to one’s humanity” will include the NAP. That’s the spot where you’re assuming what you’re trying to prove.
This is all mistaken and confused.
The NAP is not an axoim, btw; it is a conclusion derived from a long chain of reasoning. It simply can’t be a philosophically satisfactory starting point.
I don’t try to prove the NAP, because I know it can’t be done. Any argument I use will lead back to the most basic assumptions, one of which is guaranteed to be the NAP (or a disguised equivalent). Instead I try to convince people, by appealing to their desire not to be aggressed against.
This is mistaken in a number of ways. And I think it’s based on mistaken assumptions about metaphysics, epistemology, and ethical theory. Yes, any argument in favor of the NAP will lead back to discussions of metaphysics and epistemology because the NAP is not an axiom. And no, the NAP will not be at the base of all premises.
Your approach may be good for persuading people, good rhetorically, but it doesn’t suffice for providing a philosophical defense of the NAP.