Take a person, who, to this day, has never left the territory of Nebraska. What does that person do when she claims: "I am not in Nebraska, today." She commits what linguists and philosophers of language call a performative contradiction, i.e. her actual circumstances, being in Nebraska, contradict the statement she makes.
In the above video, the gentleman tries to apply the concept to the task of justifying Anarcho-Capitalism, or indeed derive it irrefutably from first principles.
00:51: "This axiom of action is axiomatic because you cannot not act."
I cannot go into the properties of axiomatic systems too deeply here, but whatever they are, they are not designed to deal with, let alone decide issues of the empirical world. That is to say, you do not make an axiom - the beginning of your reasoning - depend on a prior empirical finding. In their natural habitat of formal systems, axioms tend to be fitted after the fact, to attain the desired overall outcome of formal consistency. In axiomatics, it is not that a starting point gives you a system. It is rather that a (gradually developed) system eventually selects a starting point.
Moreover, proposing a non-contradictory statement does not suffice to establish an axiomatic system.
01:04: "We have a firmly established starting point from which all of economic theory is derived."
Well, it is simply not true that "all of economic theory is derived" that way. No one ever embarked on such a project, including Ludwig von Mises who only made claims to that effect, among any number of contradicting and retracting statements. The least thing to heed in building an axiomatic system is the need to lay out carefully all steps in its derivation, something von Mises never so much as began to attempt.
The above statement reveals the by now archaic and obsolete belief that for knowledge to have validity or for a chain of reasoning to be sound it must be grounded in an ultimate starting point of indubitable truth. No such basis is required, nor does the speaker establish an indubitable base from which apodictically true conclusions can be drawn, as we shall see further below.
We seem to witness a hankering after the old, naive Platonic dream, in whose vision The Ultimate is a fixed structure like a three dimensional grid. Discovering Ultimate Truth is like linking up with the Platonic grid; once you get to grip the base, you can feel your way up and eventually grasp the entire structure. It is the epistemology of the control freak, who likes to think of knowledge and truth as a complete set of something that belongs to him; to him managing truth is like pulling out a drawer to ensure none of your toys are missing.
I have spent at least the early part of my life looking at the world from the point of view of a believer in the flatness of the earth (and still sometimes think it must be turtles all the way down). Millions before me took the same stance, but man has gradually learned to improve the flawed conjecture of a disk-like world by working out better, yet still flawed conjectures.
Aprioristic Praxeology - Between Religious Deontology and Agnostic Consequentialism
The speaker - more guardedly: the type of argument espoused by him - seems to take a middle seat between religious deontology and agnostic consequentialism.
Religious deontology vests the authority to determine ultimate moral value in God. The most elegant version of which, in my view, is the Christian notion that God has created in man a being whose life has a purpose. That which is in accord with this purpose (reflecting God's will) is thereby morally authenticated and valuable, while that which stands in the way of the pursuit of man's purpose is ipso facto morally dubious or immoral. For more see Natural Ends and Prudential Judgement.
The agnostic consequentialist relies on some functional reconstruction of morality (or law, for that matter). He does not make the assumption that moral values or criteria of moral correctness must be issued by an authority, they may have evolved spontaneously, i.e. without the intervention of a designer of the overall outcome. The trick is to find out what functions certain phenomena of moral interest actually serve, and whether the functions are useful or not (in ways to be carefully qualified; an issue I cannot go into here). Private property is conducive to x, y, z. hence it is morally defensible, whether or not this quality of being moral can be retraced to the will of an authority or stringently deduced from first principles. For the consequentialist moral behaviour can be simply an adaptation to the challenges of an environment that by itself has no moral quality. Thus, for instance, infanticide or senicide may represent moral behaviour in an environment where such practices ensure a community's best adaptation to the environment.
Heir to religious deontology, the (type of argument offered by the) speaker represents a form of secularised rationalistic deontology. For him God is not good enough; he trusts no authority but himself, his own reasoning. Therefore, he endeavours to build a theory with which to justify what is supposed to be the only true and valid ethics - his own ethics, the ethics brought into life courtesy of his own mind's incorrupt acuteness. For this reason not only does he reject religious deontology, replacing God by his own intellectual powers, but also agnostic consequentialism, as the latter allows patterns of origination and genesis in moral phenomena that are not under the control of his reasoning, his choice of premises.
We will see that his reasoning is in fact entirely arbitrary and groundless, which makes one wonder, is he setting up a show of apodictic veracity to cover the arbitrariness of his reasoning or is he reasoning arbitrarily to appear to be in possession of absolute truth?
Fundamentum Inconcussum and Performatice Contradiction
01:28: "We cannot deny that we can argue, engage in a discussion with each other, because if we would deny this then we would already be engaged precisely in argumentation."
Now, this argument is susceptible to a number of objections.
First, the validity of the proposition is semantically contingent. Change the meaning of "action" and the performative contradiction disappears.
For certain purposes, one might wish to exclude particular "actions" from the meaning of action/acting. Say, Paul turns in his sleep and starts muttering things unconsciously, for instance: "I am not acting". In the newly defined vocabulary, muttering unconsciously is not acting. So, by definition, Paul is indeed not acting, and the performative contradiction does not apply.
This lays bear one substantial weakness of aprioristic praxeology: the more or less explicit assumption that there can only be one valid concept of action, rather than a set of different approaches, both competitive and complementary, right and wrong, incomplete and open-ended as true science tends to be.
No Connect between "Axiom" and Its Supposed Derivations -- Man Acts - A Proposition with no Unique Consequent
Second, there is no connect whatsoever between using a non-contradictory statement as the supposedly axiomatic foundation of one's philosophy and the provability or empirical validity of (the hypotheses of) a theory built on that statement.
Man acts. So what.
"Man acts." The proposition has no unique consequent. Any number of theories can be derived from it, and only with the indispensable help of further auxilliary propositions. We could just as well start with the proposition: "A black cat is a black cat."
When hard pressed to deal with this lacuna, aprorists/praxeologists soon embark on a reputation-saving rhetorical strategy. Having failed at pulling you sufficiently far into their maze of faith, and getting into trouble defending their far-reaching claims, they typically resort to qualifications that effectively contradict the more ambitious insinuations of their theory of axiomatically derived indubitable knowledge. Quite in the tradition of von Mises himself, the unctuous promises of axiomatic rigour are never followed up by a neat exposition of the assumptions and theorems used to set up the deductive structure.
The qualifications (certainly those adduced by von Mises), however, require rather an advanced command of complicated issues in the theory of science and knowledge, so at least it looks as if the praxeologist's "axiomatic theory" is a matter of great depth and complexity, rather than a ruse in the service of rationalistic conceit.
The speaker's argument is reminiscent of and as bad as Descartes' cogito, ergo sum. In his search for the fundamentum inconcussum (the unshakable basis) of valid reasoning, Descartes ingeniously proposes a statement that he thinks is irrefutable: for even if I doubt, Descartes argues, I must be thinking. So it is clear from my doubting that I think, and hence I am indubitably alive - I think, therefore I am.
Descartes contends that he has found the fundamentum inconcussum, which will serve as the cast-iron grounding for absolutely certain knowledge. But like the speaker above, Descartes fails to establish a compelling link between his fundamentum inconcussum and the insights that are supposed to follow from it. Descartes goes on to argue incongruously, that if a human being probes matters to the best of his doubting abilities, then what he finds out must be true, as God would not play tricks with a man acting in good faith. Well, that is an auxiliary argument wholly unconnected to and in no way following from the argument establishing an instance of indubitability. It is a ruse, plain and simple.
Obsolete Concept of Truth
The speaker's preoccupation with absolute truth belongs to a bygone age when it was not yet understood that the advancement of our knowledge does not depend on absolutely certain knowledge. In fact, the incompleteness and fallibility of our knowledge is what forces man to become the most successful producer of ever improving knowledge among all species.
However, the greed for absolute knowledge is inexhaustible and a great magnet for the authoritarian type, often a deeply insecure person, who craves inviolability in the know-all's figment of finally established truth.
Obsoletely, the speaker will do virtually anything (at least in the world of argumentation) so as to appear to have access to what does not exist, indubitable knowledge.
Anarcho-Capitalism has nothing to do with the defence of freedom. Ironically, it is deeply involved in a performative contradiction, being a badly thought through recommendation of conditions that would lead to civil war. In addition, its oblique "axiomatic" way of reasoning does untold damage to the intellectual dignity of liberty. Finally, it is a pointer to the dogmatism that stifles other branches of the liberty movement, diverting and alienating it from its original purpose.
See also More Geometrico, A Philosophical Weekend - The A Priori in Science, The Great Fiction (2/3), The Elementary Errors of Anarchism (1/2), The Classical Conception of Natural Rights. Classical Liberalism vs. Anarchism (1/3).