The Non-Aggression Principle, or NAP, is in one sense trivial, because aggression is really defined as a violation of a legitimate property boundary, so it all depends on what property boundaries are legitimate. Everyone supports "non-aggression", except that libertarians and non-libertarians have a different idea of what constitutes aggression, because they assign property rights according to different principles. In this sense, NAP is a fairly useless term, as it is simply a re-statement of the task of political philosophy: to give meaning to aggression, to explain what constitutes aggression, to say what property boundaries are legitimate.
In another sense, if we take the A of "NAP" as meaning specifically the libertarian idea of aggression, then it is simply a restatement of the libertarian principles for assigning property rights. To "prove the NAP" (in this second sense) would be to "prove the libertarian principles of homesteading and voluntary exchange for assigning property rights".
Can this be proved? To prove it would mean to say that homesteading and voluntary exchange, as principles for assigning property rights, are not just a preference (subjective), but that they are the objectively correct principles for assigning property rights. Hans Hoppe's Argumentation Ethics is one attempt to do this.
What argumentation ethics actually proves, in my opinion, is different. I do not believe it "proves the NAP" or "proves libertarian ethics" which is what I believe it sets out to do. I think the clearest explanation of argumentation ethics comes from Stephan Kinsella: here.
So the question is, does Hoppe's theory establish that the libertarian view of rights, as opposed to competing views, is the correct one?
Hoppe starts by noting that if any proposed theory of rights is going to be justified, it has to be justified in the course of an argument (discourse).
The problem is right here at the start. Is a theory of rights something that can be justified through argumentation? Is there a correct view of rights? Does that question even make sense?
Libertarian rights can be argued for because they are good (they appeal to our human senses of right/wrong) and beneficial (breed prosperity). But this is a justification of libertarianism as a means for already existing ends. It is not justifying them as an end, saying "this is the correct theory of rights, anyone supporting any other theory of rights is incorrect." It is saying "if you think initiating coercion is unethical, or if you just prefer prosperity to poverty, then libertarian ethic is the correct ethic for you".
The rest of Hoppe's argumentation ethics may be (and, I think, is) sound, but what I think it proves is if there is such a thing as objective ethics, i.e. if it is possible to show that one ethic is correct and all others are incorrect, then the libertarian ethic is the only correct and true theory of ethics.
So if a socialist says "I support socialism because it is correct and libertarianism is incorrect", then we could show that he is making a performative contradiction and what he says is not true. If there is such a thing as a correct ethic, libertarianism is it.
But most socialists don't claim that their ethic is correct, just that (they think) it is good and beneficial. The way to counter this is 1) to show that the libertarian ethic is actually the most beneficial ethic (using Austrian economics) and 2) by appealing to their personal ethical values, their sense of justice, of right and wrong, and helping them to see that the socialist ethic is really not one that any good person should be in favor of.
It does not make sense to talk about correctness/incorrectness, and hence of proofs, in the realm of ethics. Ethical values are values; they are subjective. We can appeal to non-libertarians' personal ethical values (showing they conflict with their political ethical values), and we can show them their political ethical values, when implemented via laws, have bad consequences; but we cannot present them with any proof that they are incorrect to hold to the political ethical values that they do. Political philosophy is simply not a subject which has objectively correct and incorrect answers, except as a means of achieving a particular goal.
Note: this is a copy of a post I made at the Mises forums: here.