The first, initially outlined by Rothbard, proceeds via an argumentum a contrario. If, contrary to the principle of first or original appropriation, a person A were not considered the owner of his visibly (demonstrably, and intersubjectively ascertainably) appropriated body and the standing room and places originally (prior to everyone else) appropriated through him by means of his body, then only two alternative arrangements exist. Either another later-coming person B must be recognized as the owner of A's body and the places originally appropriated by A, or both A and B must be considered equal co-owners of all bodies and places.
(The third conceivable alternative, that no one should own any body and originally appropriated place, can be ruled out as an impossibility. Acting requires a body and standing room and we cannot not act; hence, to adopt this alternative would imply the instant death of all of mankind).
In the first case, A would be reduced to the rank of B's slave and subject of exploitation. B is the owner of the body and places originally appropriated by A, but A in turn is not the owner of the body and places so appropriated by B. Using this ruling, two categorically distinct classes of persons are constituted: slaves such as A and masters such as B, to whom different "laws" apply. Hence, while such a ruling is certainly possible, it must be discarded from the outset as a human ethic, equally and universally applicable for everyone qua human being (rational animal). For a rule to aspire to the rank of a law--a just rule--it is necessary that it apply equally and universally to everyone. The rule under consideration manifestly does not fulfill this universalization requirement.
Alternatively, in the second case of universal and equal co-ownership the universalization requirement is apparently fulfilled. However, this alternative suffers from another, even more severe deficiency, because if it were adopted all of mankind would perish immediately, for every action of a person requires the use of scarce means (at least his body and its standing room). However, if all goods were co-owned by everyone, then no one at any time or place would be allowed to do anything unless he had previously secured everyone else's consent to do so. Yet how could anyone grant such consent if he were not the exclusive owner of his own body (including its vocal chords) by means of which this consent would be expressed? Indeed, he would first need others' consent in order to be allowed to express his own, but these others could not give their consent without first having his, etc. Thus, only the first alternative--the principle of original appropriation--is left. It fulfills the universalization requirement and it is praxeologically possible.
The second argument, first advanced by this author [i.e., Hans-Hermann Hoppe] and yielding essentially the same conclusion, has the form of an impossibility theorem. The theorem proceeds from a logical reconstruction of the necessary conditions of ethical problems and an exact definition and delineation of the purpose of ethics.
First, for ethical problems to arise conflict between separate and independent agents must exist (or must at least be possible); and a conflict can only emerge in turn with respect to scarce means or "economic" goods. A conflict is possible neither with respect to superabundant or "free" goods such as, under normal circumstances, the air that we breathe, nor with respect to scarce but non-appropriable goods such as the sun or the clouds, i.e., the "conditions," rather than the "means," of human action. Conflict is possible only with respect to controllable ("appropriable") means such as a specific piece of land, tree or cave situated in a specific and unique spatio-temporal relation vis-à-vis the sun and/or the rain clouds.
Hence, the task of ethics is to propose rules regarding the "proper" versus the "improper" use of scarce means. That is, ethics concerns the assignment of rights of exclusive control over scarce goods, i.e., property rights,in order to rule out conflict. Conflict, however, is not a sufficient prerequisite for ethical problems, for one can come into conflict also with a gorilla or a mosquito, for instance, yet such conflicts do not give rise to ethical problems. Gorillas and mosquitoes pose merely a technical problem. We must learn how to successfully manage and control the movements of gorillas and mosquitoes just as we must learn to manage and control the inanimate objects of our environment.
Only if both parties to a conflict are capable of propositional exchange, i.e., argumentation, can one speak of an ethical problem; that is, only if the gorilla and/or the mosquito could, in principle, pause in their conflictuous activity and express "yes" or "no," i.e., present an argument, would one owe them an answer.
The impossibility theorem proceeds from this proposition in clarifying, first, its axiomatic status. No one can deny, without falling into performative contradictions, that the common rationality as displayed by the ability to engage in propositional exchange constitutes a necessary condition for ethical problems because this denial would itself have to be presented in the form of a proposition. Even an ethical relativist who admits the existence of ethical questions, but denies that there are any valid answers, cannot deny the validity of this proposition (which accordingly has been referred to also as the "a priori of argumentation").
Second, it is pointed out that everything that must be presupposed by argumentation cannot in turn be argumentatively disputed without getting entangled in a performative contradiction, and that among such presuppositions there exist not only logical ones, such as the laws of propositional logic (e.g., the law of identity), but also praxeological ones. Argumentation is not just free-floating propositions but always involves also at least two distinct arguers, a proponent and an opponent, i.e., argumentation is a subcategory of human action.
Third, it is then shown that the mutual recognition of the principle of original appropriation, by both proponent and opponent, constitutes the praxeological presupposition of argumentation. No one can propose anything and expect his opponent to convince himself of the validity of this proposition or else deny it and propose something else unless his and his opponent's right to exclusive control over their "own" originally appropriated body (brain, vocal chords, etc.) and its respective standing room were already presupposed and assumed as valid.
Finally, if the recognition of the principle of original appropriation forms the praxeological presupposition of argumentation, then it is impossible to provide a propositional justification for any other ethical principle without running thereby into performative contradictions.
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