At the core of praxeology lies the incontrovertible proposition that humans act. Action is the purposeful employment of means to achieve ends in accord with the actor's values. The existence of action is axiomatic; the very attempt to deny it will result in its affirmation.

Here, I defend this validation of the action axiom — a validation that has been criticized as a self-referential statement. Both the assertion and the attempted denial of the action axiom are indeed self-referential statements, but that does not in itself place them in the same category or deny the truth-value of the former.

Self-referential statements are admissible in argument so long as they are non-contradictory. The action axiom meets this criterion, while its attempted denial does not — as it entails a contradiction. In making this distinction, I refute the positivists' unjust characterization of all self-referential statements as useless for gaining knowledge about reality.

Action as A Priori Synthetic

If one were to merely observe the behavior of humans in the external world, one would not be able to induce the existence of purposive action from it; all one would observe would be certain outward movements of human bodies. Sensory observation of others alone does not allow one to conclude that action exists.

Nor is formal logic sufficient to arrive at a proof that action exists. While it is necessary to reason logically about action to derive praxeological insights from it, there is no set of starting premises from which action can be strictly deduced. Rather, any logical analysis of action already presupposes its existence.

External observation is not necessary to conclude the existence of action, and logical analysis is not sufficient. Nonetheless, any thinking human knows that action exists and that he acts. How can this be? It is so because the fact that humans act is an a priori synthetic proposition. While it cannot be proved from more fundamental starting premises, it can be validated beyond possibility of refutation. Every attempt to refute a fundamental a priori synthetic proposition implicitly confirms its validity. This is so because every attempted refutation is itself a demonstration of the fact being denied. Professor Hans-Hermann Hoppe explains this in his treatise, Economic Science and the Austrian Method:

[T]he proposition that humans act ... fulfills the requirements precisely for a true synthetic a priori proposition. It cannot be denied that this proposition is true, since the denial would have to be categorized as an action — and so the truth of the statement literally cannot be undone.

This also implies that the action axiom is a statement about a fact of reality. Even though an individual might try to deny the axiom, his real behavior attests to its existence. Action is the deliberate employment of means for attaining ends. In this case, the actor's end is the denial of the action axiom. His attempted means is the statement, "Humans do not act." While his endeavor is bound to fail, he still acts so long as he thinks that the means he employs will arrive at the end he seeks.

Self-Referential Statements

A criticism leveled at this validation of the action axiom is that it necessarily uses a self-referential statement — a statement that asserts its own truth-value. Some self-referential statements are paradoxical and problematic. The classic example — "This statement is false" — results in absurdity. If the statement is true, then it is true that the statement is false. If the statement is false, then it is false that the statement is false — and so the statement must be true, in which case it is true that the statement is false, etc. There is no way to resolve this contradiction either way; the statement's basic construction is flawed.

A more complex self-referential statement might be found at the beginning of a book composed entirely of false propositions — for example, of incorrect mathematical equalities like 2+3=7. The introductory statement is, "Every statement in this book is false." It is a self-referential statement in its implication that it is also false. Yet the ramifications of this statement extend beyond itself. For if the introductory statement is false, then it follows that at least one statement in the book is true, and this might be some statement other than the introductory one. Yet, if we know that every other statement was indeed constructed to be false, this will imply that some statement in the book will have to be true and false at the same time — an absurdity. If the introductory statement is true, then it is also false — also an inadmissible contradiction.

Many positivists have used these examples to deny the validity of self-referential statements altogether. Because some self-referential statements lead to absurdity, they claim, such statements have no place at all in obtaining valid knowledge about reality. The positivists use this assertion to challenge the foundation of praxeology: the action axiom.

The action axiom is itself a self-referential proposition; the statement, "Humans act," constitutes an action. The goal of the action is the positive assertion of the action axiom; the means is the statement. The positive assertion of the action axiom can be read thus: "This assertion of the action axiom is itself an action." It is thus a self-referential statement. The attempt to deny the action axiom is also self-referential. It amounts to stating, "Action does not exist; therefore, this statement is not an action." Yet the positivists are wrong to discard both of the statements. The statement that humans act — while self-referential — differs in essence from the statement that action does not exist.

Non-Contradiction: The Distinguishing Criterion

Non-contradiction is one criterion for true knowledge. No datum of knowledge about reality ought to contradict any other; if it does — at least one of the data must be wrong. If any assertion necessarily entails a contradiction, it is a falsely constructed assertion and ought to be thrown out altogether.

The problem with some types of self-referential statements is not that they are self-referential; rather, their irrelevance to real knowledge lies in their contradictory natures. Consider the case, "This statement is false." If one wishes to express real knowledge with that statement, then one implicitly considers the asserted statement to be true. Thus, stating, "This statement is false" is tantamount to claiming, "This statement, which I contend is true, is false." The contradiction is built into the entire expression — and thus it cannot confer knowledge about anything real. Truth cannot be falsehood.

But what would happen if the statement were reformulated? Instead of, "This statement is false," it might become, "This statement is true." While it remains self-referential, the statement ceases to be contradictory. It now merely states, "This statement, which I contend is true, is true." This statement does not give us any indication of the truth of anything outside itself, but it is also non-contradictory. We can consistently assert the truth of such a statement. While it confers no knowledge about anything outside it, it does impart some knowledge about itself — namely, that it is true. The positivists cannot claim that this self-referential statement is a bad formulation. The best they can do is ask, "So what?" and classify it as "mere analytic knowledge."

The situation changes, however, if the statement also refers to any element of reality outside itself. The case of "Every statement in this book is false" is a contradiction, because it amounts to the assertion, "This statement about every statement in the book, which I contend is true, is false." However, this contradiction can easily be avoided if we reformulate the statement thus: "This statement is true, and it asserts that every other statement in the book is false." The statement is indeed self-referential. We cannot assume that its assertion about every other statement in the book can be correct unless the statement itself is also correct. A false statement cannot assert the truth of anything — as we have seen with prior cases of contradictory self-referential statements. Yet the statement is also true: it is true that every other statement in the book is false; the book was deliberately written that way. It is also true that any assertion about the falsity of every other statement in the book is true.

The statement, "This statement is true, and it asserts that every other statement in the book is false" is also different from the mere claim, "This statement is true," in that it is not only relevant to its own truth-value. It can convey definite knowledge about facts outside itself. This is also the case with the action axiom.

Consider the statement, "Humans act," in a more detailed reformulation: "This statement, which asserts that all humans act, is itself an action." There is no contradiction here. If indeed all humans act, then the statement itself — pronounced by a human being — might well be an action. If it fits the definition of an action — which it does — then the statement can make true assertions about its status as such. The statement is both self-referential and true. The action axiom is self-referential, but its referents extend far beyond the statement itself. The action axiom refers to both itself and every other human action.

However, any denial of the action axiom is both self-referential and contradictory. The statement, "Humans do not act," is a contradiction because statements qua statements fit the definition of action; they employ means for the pursuit of ends. The contradictory claim can be reformulated thus: "This statement, which is itself an action, asserts that humans do not act."

We know that genuine knowledge is non-contradictory. If there is a contradiction in the very formulation of a statement, the statement must be thrown out. Since any denial of the action axiom is a contradiction, it cannot confer knowledge about reality. Thus, we can conclude that any denial of the action axiom is false. This can only imply that the contrary, the existence of the action axiom, must be true.

Every true statement is in part self-referential.

I have shown that the positivists' denial of the action axiom on the grounds of its self-referential nature is unwarranted. Now I shall refute the very basis for their use of a statement's self-referential nature as the grounds for discarding that statement. While not every self-referential statement is true, every true statement is necessarily self-referential. If we assert something real, the assertion itself must by implication be true.

Even a purely empirical statement, such as, "This cat is black," is self-referential. If we did not implicitly acknowledge the truth of the assertion, it would have no meaning. In order to assert that the cat is black, we must assert, "This statement, which claims that the cat is black, is true." If it were anything but true, we would again be mired in an irreconcilable contradiction. To claim, "This statement, which claims that the cat is black, is false," is but an amplified version of, "This statement is false."

Thus, a statement's self-referential nature can do nothing to demonstrate its falsehood; quite the contrary, it is necessary for any statement to be true. The genuine criterion for truth is non-contradiction; the action axiom meets this criterion, whereas its denial does not. Because the action axiom cannot be contradicted, it is irrefutably true. Furthermore, its formulation encompasses facts beyond the statement itself; thus, it is true about actions other than its own assertions.

This article originally appeared on Mises.org.

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, The Autonomist, Le Quebecois Libre, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. His newest science fiction novel is Eden against the Colossus. His latest non-fiction treatise is A Rational Cosmology. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.