The “unuseful” tautology
A tautology is a law of logic, part of a law of logic, or a definition. Some people do not think that tautologies tell us anything useful, pointing out that if someone inquires about the weather, to be told, “Either it’s raining or it’s not raining,” is not very helpful.
Ludwig von Mises disagrees with this view. He would readily acknowledge that there are useless tautologies, but he suggests in Human Action that there are also useful tautologies. (Whether he changed his mind on the status of the propositions of praxeology in works written after Human Action isn’t a topic that will be addressed in this article).
Mises says:
“Aprioristic reasoning is purely conceptual and deductive. It cannot produce anything else but tautologies and analytic judgments. All its implications are logically derived from the premises and were already contained in them. Hence, according to a popular objection, it cannot add anything to our knowledge.
All geometrical theorems are already implied in the axioms. The concept of a rectangular triangle already implies the theorem of Pythagoras. This theorem is a tautology, its deduction results in an analytic judgment. Nonetheless nobody would contend that geometry in general and the theorem of Pythagoras in particular do not enlarge our knowledge. Cognition from purely deductive reasoning is also creative and opens for our mind access to previously barred spheres. The significant task of aprioristic reasoning is on the one hand to bring into relief all that is implied in the categories, concepts, and premises and, on the other hand, to show what they do not imply. It is its vocation to render manifest and obvious what was hidden and unknown before.”
Mises proceeds to give an example of useful tautologies in praxeology. He says:
“In the concept of money all the theorems of monetary theory are already implied. The quantity theory does not add to our knowledge anything which is not virtually contained in the concept of money. It transforms, develops, and unfolds; it only analyzes and is therefore tautological like the theorem of Pythagoras in relation to the concept of the rectangular triangle. However, nobody would deny the cognitive value of the quantity theory. To a mind not enlightened by economic reasoning it remains unknown. A long line of abortive attempts to solve the problems concerned shows that it was certainly not easy to attain the present state of knowledge.
It is not a deficiency of the system of aprioristic science that it does not convey to us the full cognition of reality. Its concepts and theorems are mental tools opening the approach to a complete grasp of reality; they are, to be sure, not in themselves already the totality of factual knowledge about all things. Theory and the comprehension of living and changing reality are not in opposition to one another.”
What is the explanation for the fact that the tautologies of praxeology are useful and not useless? In a fascinating passage, which would have to be unpacked to understand its full meaning, Mises finds the answer in an affinity between action and thinking:
“The real thing which is the subject matter of praxeology, human action, stems from the same source as human reasoning. Action and reason are congeneric and homogeneous; they may even be called two different aspects of the same thing. That reason has the power to make clear through pure ratiocination the essential features of action is a consequence of the fact that action is an offshoot of reason. The theorems attained by correct praxeological reasoning are not only perfectly certain and incontestable, like the correct mathematical theorems. They refer, moreover with the full rigidity of their apodictic certainty and incontestability to the reality of action as it appears in life and history. Praxeology conveys exact and precise knowledge of real things.
The starting point of praxeology is not a choice of axioms and a decision about methods of procedure, but reflection about the essence of action. There is no action in which the praxeological categories do not appear fully and perfectly. There is no mode of action thinkable in which means and ends or costs and proceeds cannot be clearly distinguished and precisely separated. There is nothing which only approximately or incompletely fits the economic category of an exchange. There are only exchange and nonexchange; and with regard to any exchange all the general theorems concerning exchanges are valid in their full rigidity and with all their implications. There are no transitions from exchange to nonexchange or from direct exchange to indirect exchange. So experience can ever be had which would contradict these statements.”
In the space remaining, I’d like to elucidate the very interesting ideas Mises suggests about why the tautologies of praxeology are useful. I take him to be arguing in this way: if a proposition is really a tautology, then its truth can’t be questioned, though its usefulness might be. But maybe some of the propositions of praxeology aren’t really tautologies, contrary to appearance. Maybe they contain vague or fuzzy terms; if so, we can’t be sure that future testing of them won’t falsify them. But, Mises suggests, the terms in praxeology aren’t vague or fuzzy. Either they apply or they don’t, and this is immediately evident.
If you study Human Action, you will always find new insights that you missed. I have certainly found this to be true in my sixty years of reading the book.
Originally Posted at https://mises.org/
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