TL;DNR: Certain forms of, principally wealth-emphasising, libertarianism, appear to be contradictory.
(Sorry; this argument will be as simple as I can make it).
Non-left libertarianism hinges on the Non-aggression Principle, a “concept in which ‘aggression’ – defined as initiating or threatening any forceful interference with either an individual or their property, or agreements (contracts) – is illegitimate and should be prohibited.” Hereafter called “NAP”; this dispensed with, that form of libertarianism falls. We refute it thus – that, whereas Thomas Hobbes’ authoritarian “Leviathan” state is absurd, since if there were “Bellum omnium contra omnes”, how to come together to establish a state… without some impulse to collaborate, and, with such an impulse, how could there ever have been universal war? That is absurd.
Conversely, for the NAP, unless humans had a conflictual impulse, what need would there be for the Principle? Whereas, if that conflictual impulse exists, how can it be overcome, to enforce the principle, without a contradictory force?
Now, differences are resolved and decisions made, either based on objective reason, or else by subjective convention and arbitrary agreement. If the NAP is based on the former, it is unnecessary, since by assumption there are objective facts including in ethics. Conversely if there are not objective rules of conduct then again the NAP is arbitrary and conventional.
But if the NAP is arbitrary and conventional, but is a first principle, then it utilises reasoning methods (including logics) likewise merely conventional (for if not, those methods derive certain conclusions which are no longer merely conventional). That is, the NAP presupposes a Hilbertian formalist vantage of reasoning and deduction. All this is true also of “argumentation ethics”, as either reasoning is objective and violence never necessary, therefore NAP redundant – or argumentation qua argumentation is conventional, only, and its reasoning rules formalist.
So, as merely social principles, we may observe both the NAP and “Argumentation Ethics” to have ratiocinative Hilbertian formalism their necessary conditions; for "Argumentation Ethics," presumes that arguments have no inherent suasion, but we must additionally agree not to aggress one another if our arguments do not sway them (and presuming this conventional “argumentation” to take the form of reasoning, per von Mises’ “action-axiom”, concluding with action-determining consensus conclusion; else the “argumentation” ends in non-consensual action, i.e., is aggression, contra-principle).
But Gödel’s theorems falsify formalism as incomplete; and the similar Tarski’s theorem falsifies the omni-reliability of more general formalist ratiocinative systems; that so, so too must be NAP and “AE” incomplete, so unworthy of being a guiding principle of action for all cases. We can represent this in zeroth-order logic (provably complete even in formalism), where “Argumentation Ethics” is “AE” (representing NAP also, since both social, have formalism as their necessary condition), the fact of Gödel’s theorems is G, the reliability of formalism for all deduction is F:
[G → (¬F)] ; ["AE" → F] ; G ∴ ¬("AE")
1) [G → (¬F)] | Premise
2) ["AE" → F] | Premise
3) G | Premise
4) [(¬ F)] | 1), 3) Modus Ponens
5) [¬ ("AE")] | 2), 4) Modus Tollens
So we conclude that [“AE” → ⊥]; that is, “Argumentation Ethics” is false. This is tellingly simple a proof.
And so: either the NAP is at best a convenience without logical suasion, in which case there is no reason to obey it, if one is strong enough. Or it is derived from a more basic principle, in which case that forbids violence from its axiomatic self, and the NAP is unnecessary.
One can refrain from force knowing that the universe is rational, that one is correct by rational analysis – a Platonist, or intuitionist, e.g., knows their argument is correct by reason, and violence is redundant; in reason is victory-inevitable, that most human discourse is spurious.
Also, were NAP derived from a force of reason – but if the NAP is deducible from another principle, it is not a first principle, and for reasoning we begin only with absolutely most basic principles. And then we ought to discover and obey what enables the NAP. Which, if what is objective supersedes NAP, that should be adopted in its place. If NAP is merely conventional, so from formalism, then the NAP is not logically guaranteed, not fit for adoption.
For the latter point, if there be no objective reason the NAP must be adopted, then there is no logical suasion in favor of the principle, and it is enacted only with adequate force to ensure non-aggression – but that is contrary to the principle itself.
Moreover, corporations and stock companies by definition do not parcel capital revenues only into equivalent shares given to each employee in one-to-one correspondence. Therefore, some employee must have more than another – and so, has the ability to suborn the will of who has less (if only by buying up all the resources the latter needs, with a reserve still to supply one’s own needs), who in turn has no ability to ameliorate this condition, without directly aggressing against the better-resourced, which even libertarianism forbids.
Therefore: corporations are inherently hierarchical, at least as greater capital-owner above lesser owner; this holds to in any situation where one's capital is not lent out or sold consensually – and “ancap” as anti-authoritarian, yet permitting such capital hoarding and hierarchy, is thus definitely contradictory. Doubly so, since a monopolist, particularly of necessities, can deprive customers of their revenues at will, which plainly interferes with an individual’s property. “Ancap” permits corporate hierarchies that violate its own “non-aggression principle,” and violates its supposed anti-authoritarianism. “Ancap,” backhanded libertarianism, is a cruel, contradictory absurdity.
All this appears to be correct.
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