NAPs Are for Babies
Baby humans need frequent naps. Also, baby libertarians need NAPs (Non-Aggression Principles). In libertarian lore, the Non-Aggression Principle says something like this:
NAP: It is always wrong to initiate force against other people.
Variations on that are known as NAPs. NAPs are good for baby libertarians, because they help bring some statists into libertarianism, once you see that almost all government policies initiate force against people.
But it's really only baby libertarians who need NAPs, because NAP is an oversimplified and blunt instrument. As written above, it is obviously false. One can qualify it to make it not obviously false, but once one adds enough qualifications, it can't (plausibly) be used anymore to construct the sort of simple deductive proofs that baby libertarians desire.
Of course, one can still appeal to NAp, the Non-Aggression presumption, which merely requires that one have a good moral reason for initiating coercion against others.
Now, since some of my audience are libertarians, and some of those are probably toddler libertarians who are ready to do less NAPing, let me say more to help them get beyond their NAPs.
Qualified NAPs
Actually, there is a simpler moral theory to which NAP represents a qualified version. So let's start with the simplest view in the neighborhood:
NAP0 (a.k.a. "pacifism"): It is always wrong to use force against others.
That's obviously false, and almost no one (including libertarians) believes it, because there are cases of justified self-defense and defense of innocent third parties involving use of force. So we make our first qualification, resulting in:
NAP1: It is wrong to use force against others, unless doing so is necessary to stop someone else from using force against others.
But in fact, almost no one, not even libertarians, believes NAP1 either. It too is obviously false. There are many examples showing this.
Example 1: I promise to mow Ayn Rand's lawn in exchange for her grading some of my papers. Rand grades the papers, with copious helpful comments (pointing out where students are evading reality, hating the good for being the good, etc.), but then I don't mow the lawn. I also refuse to do anything to make amends for my failure. Haha.
Almost everyone, including libertarians, thinks that the state can force me to mow the lawn or otherwise make amends (e.g., pay the money value of a mowed lawn).
Example 2: I start deliberately spreading false rumors that Walter Block is a Nazi. This causes him to be ostracized, lose his job, and be blacklisted by the SJW culture that is academia.
Almost everyone, including most libertarians, agrees that Walter should be able to sue me for defamation in court, and collect damages, coercively enforced, of course.
Example 3: Hans-Hermann Hoppe owns a large plot of land around his house. One day, when he emerges from his house to collect his copy of Reason, he sees me sleeping peacefully in a corner of his lawn. Though I haven't hurt anyone and (being very thin and meek) pose no physical threat to anyone, Hans is nevertheless irritated, and demands that I get off his lawn. I just plug my ears and go back to sleep.
Almost everyone (especially Hans) thinks that Hans can use force to expel me from his lawn.
Example 4: I have become seriously injured by a hit-and-run driver, and I need to be taken to the hospital immediately. The only available car is Murray Rothbard's car, but Murray is not around to give permission. (I am also not sure he would authorize saving me.)
Almost everyone thinks it is permissible for me to break into Murray's car (thus initiating force against his property?) to get to the hospital.
Example 5: Powerful space aliens are going to bomb the Earth, killing 3 billion people, unless you deliver to them one recently-plucked hair from the head of Harry Binswanger. Harry, unfortunately, cannot be persuaded to part with the hair for any amount of money. (He really wants to live up to his name, you see.)
Almost everyone thinks it is permissible to forcibly steal the hair.
Of course, all of these examples are easily accommodated: we just have to add appropriate qualifications and clarifications to our NAP. Once we add the needed qualifications, we arrive at:
NAP6: It is wrong to use force against others, unless:
(i) Doing so is necessary to stop them from using force against others (unless: (a) their force was itself justified by one of the conditions listed herein, in which case it is still wrong to use force against them), or
(ii) It is necessary to enforce a contract, or
(iii) It is necessary to force someone to pay compensation for defamation, or
(iv) It is necessary to stop someone from using someone's property without the property owner's consent (unless: (b) the use of the property is necessary, in an emergency situation, to prevent something much worse from happening, in which case it is still wrong to use force against that person), or
(v) It is necessary to prevent some vastly greater harm from occurring.
We've added five main qualifications ((i)-(v)) and two meta-qualifications ((a) and (b)). Is NAP6 true at last? Well, it's hard to say whether we've included all needed qualifications and sub-qualifications. At least this latest NAP is no longer obviously false. But it's so complex that it's hard to claim that it's obviously true either, and it's really unclear why someone else cannot propose another qualification, say, "... or (vi) it is necessary to stop the poor from going without health care."
Libertarians will disagree with qualification (vi), but they don't have a good reason to resist it, if their libertarianism just rests on a NAP. We added (i)-(v) and (a) and (b) in order to accommodate our ethical intuitions (as rationality demands), but then why can't a leftist add (vi) to accommodate their intuitions?
In other words, NAP6 might be true, but you don't establish anything interesting by appealing to it, since someone with different starting intuitions can just as reasonably modify NAP6 to fit those intuitions.
Time for Desperate Rationalizations?
Now, I am aware that some toddler libertarians are going to claim that the NAP isn't really so complicated, because (they will claim) one or more of the qualifications I have included in NAP6 are really redundant or wrong. For example, maybe some doctrinaire libby will say that (iii) should be deleted because defamation is actually okay.
Another unreasonable person will claim that (v) is wrong because actually we should just let the aliens do their worst.
Another desperate person will try to claim that (ii) and (iv) aren't needed because contract breaches and sleeping on someone's lawn are "really" a form of force, and thus we won't really be "initiating force" in examples 1 and 3.
I don't want to spend time debating those sorts of claims, because I find it silly and tedious. Therefore, I am simply going to report my own reaction before moving on, which is that
Those moves are silly on their face. You wouldn’t think of any of those things if you were just trying to faithfully describe reality. You’d only think of them if you’re trying to cling to the initial verbal formulation of an ideological position.
If you're going to do things like that -- like expanding the concept of "force", or making radically implausible normative assertions -- then that's really no better than statists who do similar things, such as claiming that poverty is a form of coercion, claiming that there's nothing prima facie wrong with theft, etc.
Liberty without NAPs
You know what I'm going to say next, so I'll just say it quickly so we can all go home. We don't need some sweeping, absolutist moral theory. The rational way of evaluating possible government policies is to (i) start by noting the prima facie moral reasons against them, (ii) examine the reasons for the policies, according to those who support them, then (iii) apply moral common sense to judge whether the latter reasons are good enough to justify the bad or wrong-making aspects of government policies.
E.g., it’s usually wrong to take people’s money without their consent. Q: is it a good enough reason for doing so that one can help the poor by giving the money to them? Think about how we’d react if I decided to go out and mug people, then send the money off to UNICEF. This wouldn’t go over very well in most circles. So no, not a good enough reason.
Rationalism Is for Robots
If you're trying to "prove" a political conclusion by deriving it from some axioms, then you may have succumbed to an intellectual disorder sometimes called “rationalism”. (The disorder that, e.g., Spinoza famously suffered from.) This disorder causes you to think that the way people find out stuff about the world is by sitting in an armchair, pronouncing the first sweeping, simplistic generalization that occurs to them that sort of seems vaguely plausible for the first ten seconds that you think about it, robotically deducing consequences from that, and then dogmatically embracing every absurd consequence that comes out of it.
That isn’t a way to understand the actual world. That almost never works. And by the way, I’m not deducing that it doesn’t work from an axiom; I’m saying that in practice, in actual cases that we observe, that approach almost never goes well. Virtually 100% of the time, the sweeping generalization that seems plausible to you at first glance is wrong. (That happens because reality is actually complex. Orders of magnitude more complex than a typical human’s typical thoughts. I found that out by having many years of experience with reality.)
The rationalist approach is a way to go spectacularly wrong and wind up saying all sorts of ridiculous things. (Examples: almost every philosopher in history.) It’s also, secondarily, a way of convincing other people that you’re crazy. Normal people then tend to just ignore your insane "proof"s.