Deduction, Necessary Truth and the Real World

Consider this categorical syllogism:

Major premise: All bachelors are unmarried.

Minor premise: John is a bachelor

Conclusion: Therefore John is unmarried.

If valid and sound, the conclusion has necessary truth.

But that necessary truth is arguably de dicto necessity: a necessity that is a property of the argument being an analytic a priori system, where “John” is merely a hypothetical person who is a bachelor by definition. It follows that even the conclusion must be understood as analytic a priori.

But once we assert “John is a bachelor” of a real and specific person in the world, suddenly something important happens: the minor premise “John is a bachelor” becomes synthetic a posteriori, and can only be proved a posteriori, or by experience, empirical evidence and inductive arguments. The truth of the minor premise therefore becomes contingent, not necessary. It can never have apodictic truth, because there must always be some small doubt about its truth: for example, if John says he is unmarried, then he might be lying or delusional (e.g., perhaps he is mentally ill). If public records say John is unmarried, they may be in error or fraudulent. If John’s friends say he is unmarried, then they may also be mistaken or taken in by John’s lies, and so on.

There is no way to obtain absolute and apodictic truth in propositions known a posteriori.

The consequence of this is that the deduction above only has necessary truth when it is strictly understood as an analytic a priori argument and where the logical necessity is de dicto necessity.

When asserted of a real person, the minor premise and the argument can never be proved in the sense of being absolutely true, because we cannot have apodictic truth about a synthetic a posteriori proposition (the minor premise).

The belief that the syllogism has necessary and absolute truth about any concrete real world person is an illusion that arises by merely assuming the world conforms exactly to the assumptions and requirements of analytic a priori argument: we are using words to abolish uncertainty and effectively imposing an unempirical argument on the real world that can only be known a posteriori. In short, we are conflating (1) the analytic a priori with (2) the synthetic a posteriori, when they are strictly separate.

It has become fashionable in modern analytic philosophy to admit the existence of a second type of necessity: de re necessity. Here it is conceived that the possession of a property y by a certain thing x is logically necessity for it to be identified as a certain kind or type x (a type of essentialist argument).

For example, water is necessarily H₂O: for a thing to be the substance we call water, it must be by necessity have the property of being physically H₂O.

But one can wonder whether this new view that there are necessary a posteriori truths and metaphysical/ontological necessity has gone too far.

Consider the proposition:

Statement 1: water is necessarily H₂O.

Conceived as an analytic a priori statement, it has necessary truth.

But let us consider this statement:

Statement 2: This specific real world sample of water is necessarily H₂O.

Here we face the skeptical challenge and Hume’s problem of induction: how can you be absolutely certain that what you are looking at is water at all? You may have made some error. It might be something that looks like water but is not physically H₂O. Even a scientific analysis of the substance that seems to show that it is chemically H₂O could in theory be mistaken or fraudulent. Or a more elaborate sceptical challenge would be: how can you be absolutely certain that anything you have seen now or in the past that you call water really is H₂O and not some elaborate trick by Descartes’ demon?

Statement 2 above asserted of a real world thing must simply abolish uncertainty by begging the question and assuming all epistemological problems and challenges can be countered, in much the same way that the original syllogism above when asserted as absolutely and necessarily true of any concrete real world person simply abolishes uncertainty and renders the argument analytic a priori.

One could argue, then, that modern metaphysical (essentialist) necessity remains a property of analytic a priori systems.

An Observation on Deduction

Consider the following syllogism:

Major Premise: All elephants are grey.

Minor Premise: Nellie is an elephant.

Conclusion: Therefore Nellie is grey.

This is a formally valid syllogism, but it is unsound. The reason why it is unsound is that the major premise is false: while most elephants are grey, some albino elephants exist. If Nellie were a real life elephant that we have never seen before, there is the possibility that Nellie is an albino elephant, and not grey.

But how do we interpret the epistemological status of major premise?:

All elephants are grey.

If this is meant to assert information about the real world (that is, real world elephants), it must be synthetic a posteriori. We can establish its truth by experience, empirical evidence and inductive arguments.

In this case, as we saw, it is false, because albino elephants exist, and it is also logically possible, though improbable, that a genetic mutation might occur which makes an elephant some colour other than grey or white.

Nevertheless, one could also take “all elephants are grey” as an analytic a priori proposition. We can assert it as true, but only as an empty and hypothetical statement where elephants are arbitrarily defined as having the property “grey.” In this case, we do not care about real world elephants, because they are irrelevant to a purely tautologous proposition we have devised that asserts something merely as an imaginary definition, true by stipulation.

One could even claim that asserted of purely imaginary elephants that are grey by definition, even the conclusion is true, and the argument has necessary a priori truth in our imaginary world of purely grey elephants.

But, of course, what has happened is that we have rendered all the propositions and the whole argument vacuous, empty and tautologous, so that it says nothing necessary of the real world. The propositions and inference would be all true by arbitrary definition of terms, and necessary truth is a purely verbal construct.

And once applied to real world elephants, it all collapses and empirically we know the argument is unsound.

But we can even apply a similar type of analysis to a syllogism that is both valid and sound:

Major premise: All humans are mortal.

Minor premise: Socrates is a human.

Conclusion: Socrates is mortal.

Here both the major and minor premises are synthetic a posteriori and true in the sense that we can construct a set of inductive arguments, from empirical evidence, to the effect that it is extremely probable that all human beings are mortal, and it is extremely probable that the historical person we know as Socrates was human.

The conclusion is necessarily true, but only if the premises are true.

But, when the conclusion is applied to the historical person we know as Socrates as a synthetic a posteriori statement about him, the necessary, apodictic truth is not preserved. Why? The reason is that both the major and minor premises are synthetic a posteriori, and can only ever be highly probable but still fallible.

In order to question the truth of the premises, we have to think of some possibilities that are ridiculous or highly improbable, but nevertheless they are logically possible. Suppose it is possible for a genetic mutation to make a human being immortal in the sense of living without aging. Say Socrates was such a person. Say, his death was staged and he still lives to this day.

Suppose, as an even more outlandish idea, that Socrates was secretly visited by aliens or humans from the far future. Using science, they made him immortal and his death was only staged, so that he still lives.

Of course, these are all either outrageous or extremely unlikely possibilities, but the fact remains that synthetic a posteriori propositions can never be apodictically true: some doubt must remain.

When the syllogism above asserts that “Socrates is mortal” as its conclusion, one can speak of this truth as necessary, only if the premises are taken to be absolutely true.

But, just as in the first case above, we can see how this creates a necessary truth that is ultimately a logical construct (or de dicto necessity) because it banishes all doubt about the truth of the empirical premises and renders them analytic a priori.

Of course, these days, after the work of Putnam and Kripke, analytic philosophers are willing to recognise the existence of certain metaphysical (or de re) necessities, such as (1) identity statements involving proper names or definite descriptions and (2) scientific essences of certain natural kind phenomena, but I do not think this is inconsistent with my comments above on deduction.

Mises’s Flawed Deduction and Praxeology

A breath-taking assertion is made by Mises in his book Human Action about praxeology:

“The scope of praxeology is the explication of the category of human action. All that is needed for the deduction of all praxeological theorems is knowledge of the essence of human action. It is a knowledge that is our own because we are men; no being of human descent that pathological conditions have not reduced to a merely vegetative existence lacks it. No special experience is needed in order to comprehend these theorems, and no experience, however rich, could disclose them to a being who did not know a priori what human action is. The only way to a cognition of these theorems is logical analysis of our inherent knowledge of the category of action. We must bethink ourselves and reflect upon the structure of human action. Like logic and mathematics, praxeological knowledge is in us; it does not come from without.

All the concepts and theorems of praxeology are implied in the category of human action.” (Mises 2008: 64).

The problem with this, not to put too fine a point on it, is that it is all utter rubbish!

When we look carefully through the first few chapters of Human Action, we will not detect any formal deduction going on, by which Mises’s inferences are carefully and painstakingly deduced from the human action axiom.

Even after inspecting Mises’s own informal method of “verbal deduction” does not help in identifying how inferences are formally “deduced” from the action axiom either (see Barrotta 1996: 61–65 for a similar critique).

First, the statement that all human action by non-mentally-ill human beings aims at ends and is, in this sense, purposeful is undoubtedly synthetic a posteriori, not synthetic a priori as I have shown here. For Mises cannot even establish a clear definition and criteria for (1) what constitutes a non-mentally-ill human being or (2) what constitutes conscious human action in the first place, without recourse to a vast amount of empirical scientific evidence about human behaviour, medicine, psychology and biology.

Secondly, the statement

(1) all human action by non-mentally-ill human beings aims at ends and is, in this sense, purposeful

asserts only what it asserts and nothing else. Naturally, it implies things if by means of syllogisms we derive inferences, but even here what one derives will be trivial and already contained in the axiom.

It cannot be used to imply by deduction any other assertions unless a vast amount of additional empirical knowledge and inductive arguments are used. To see this we need only ask: what kind of deductive axiomatic system can proceed with only one axiom?

Mises’s epistemological statement above fails, and we can look at his discussion of the notion of fundamental uncertainty to see an example of this:

“The uncertainty of the future is already implied in the very notion of action. That man acts and that the future is uncertain are by no means two independent matters. They are only two different modes of establishing one thing.

We may assume that the outcome of all events and changes is uniquely determined by eternal unchangeable laws governing becoming and development in the whole universe. We may consider the necessary connection and interdependence of all phenomena, i.e., their causal concatenation, as the fundamental and ultimate fact. We may entirely discard the notion of undetermined chance. But however that may be, or appear to the mind of a perfect intelligence, the fact remains that to acting man the future is hidden. If man knew the future, he would not have to choose and would not act. He would be like an automaton, reacting to stimuli without any will of his own. Some philosophers are prepared to explode the notion of man's will as an illusion and self-deception because man must unwittingly behave according to the inevitable laws of causality. They may be right or wrong from the point of view of the prime mover or the cause of itself. However, from the human point of view action is the ultimate thing. We do not assert that man is ‘free’ in choosing and acting. We merely establish the fact that he chooses and acts and that we are at a loss to use the methods of the natural sciences for answering the question why he acts this way and not otherwise.

Natural science does not render the future predictable. It makes it possible to foretell the results to be obtained by definite actions. But it leaves unpredictable two spheres: that of insufficiently known natural phenomena and that of human acts of choice. Our ignorance with regard to these two spheres taints all human actions with uncertainty. Apodictic certainty is only within the orbit of the deductive system of aprioristic theory. The most that can be attained with regard to reality is probability.” (Mises 2008: 205).

In fact, that “all human action by non-mentally-ill human beings aims at ends” implies nothing necessary about uncertainty or the unknowability of the future.

It would be possible for beings fully aware of the consequences of all future action to still act with a purpose when they act. The action axiom by itself does not establish or imply anything necessary about the nature of the future or non-calculable probability.

Just to establish the existence of a world where humans face an uncertain future in the sense of (1) being unable to perfectly predict the future, and (2) being unable to provide objective probability scores for future outcomes or events in certain processes requires many inductive arguments and a great deal of empirical evidence.

Mises’s statement above already requires that he must use all the evidence of the natural sciences to distinguish systems where (1) deterministic forces can be scientifically identified and objective predictions made from (2) complex systems where stable long-run relative frequencies for outcomes do not exist.

In his attempts to distinguish (1) class probability from (2) case probability (Mises 2008: 107–115), Mises has tacitly relied on the vast empirical knowledge of the relative frequency theory of probability and the inability of this process to yield objective results in cases where long-run relative frequencies cannot be found (e.g., in many areas of the social and economic world).

In short, the very idea that “all praxeological theorems” can be produced by “deduction” from “the essence of human action” fails in the first few chapters of Human Action.

And an astute critic of Mises called George J. Schuller knew this soon after the book was published:

“Acceptance of Mises’ stated axioms does not necessarily imply acceptance of the ‘principles’ or ‘applications to reality’ which he has drawn from them even though his logic may be impeccable. When a logical chain grows beyond the limits set by stated assumptions, it uses unstated assumptions. The number of unstated assumptions (axioms, postulates, or other) in Human Action is enormous. If Mises denies this, let him try to rewrite his book as a set of numbered axioms, postulates, and syllogistic inferences using, say, Russell’s Principia” (Schuller 1951: 188).

BIBLIOGRAPHY
Barrotta, P. L. 1996. “A Neo-Kantian Critique of von Mises’s Epistemology,” Economics and Philosophy 12: 51–66.

Mises, L. von. 2008. Human Action: A Treatise on Economics. The Scholar’s Edition. Mises Institute, Auburn, Ala.

Schuller, G. J. 1951. “Mises’ ‘Human Action’: Rejoinder,” American Economic Review 41.1: 185–190.

Limits of the Human Action Axiom

The foundational idea for the Austrian praxeology of Mises and Rothbard is the human action axiom. This proposition is that all human action is rational because all action is by definition purposeful. First, one should note that this is a peculiar re-definition of the term “rational.” But let’s accept the definition for the moment.

Some vulgar or “pop” Austrians make truly absurd claims on the basis of this axiom, such as that all inferences of Austrian economics must be true because they follow from the human action axiom. Not even Mises believed such rubbish:

“Every theorem of praxeology is deduced by logical reasoning from the category of action. It partakes of the apodictic certainty provided by logical reasoning that starts from an a priori category. Into the chain of praxeological reasoning the praxeologist introduces certain assumptions concerning the conditions of the environment in which an action takes place. Then he tries to find out how these special conditions affect the result to which his reasoning must lead. The question whether or not the real conditions of the external world correspond to these assumptions is to be answered by experience. But if the answer is in the affirmative, all the conclusions drawn by logically correct praxeological reasoning strictly describe what is going on in reality” (Mises 1978: 44).

In other words, praxeology relies on deduction and requires premises that are sometimes synthetic propositions, not ones true a priori.

The human action axiom says that all voluntary human action (by sane, non-mentally ill humans, of course!) is “purposeful,” and this is used in the early deductions of praxeology.

Can anyone see the problem here? I think it is very clear.

The human action axiom is a trivial observation that can also be held by Marxists, communists, Keynesians, neoclassicals, monetarists, or any other economist you care to name. And there is nothing significant you can deduce from it without other premises, since the most simple, useful deductive argument like the syllogism requires 2 premises to infer anything.

Moreover, as even Mises noted, once you get into praxeological arguments they quickly come to use synthetic propositions – either present or hidden – that can only be verified empirically (see “Mises’ Praxeology: A Critique,” October 1, 2010). Thus empirical evidence becomes very relevant indeed.

The “apodictic certainty” claimed for praxeology actually vanishes like a puff of smoke, if there is doubt about the truth of its synthetic stated and hidden assumptions or premises. And there certainly is. One example I have dealt with before is the argument for free trade by comparative advantage (see “Mises on the Ricardian Law of Association: The Flaws of Praxeology,” January 25, 2011).

The correct response to Austrians making idiotic claims about the human action axiom is this: you tell us what you can deduce from only one axiom. Do tell us - we’re fascinated...

Yet another problem with praxeology should be clear to anyone who has read Mises’ Human Action: it is a long, rambling book where it often unclear which arguments are Mises’ ranting and which ones are supposed to be praxeological arguments with apodictic certainty arrived at by deduction. Mises uses informal verbal arguments to lay out his deductions. If he were really a first-rate logician, then Mises would have set his arguments out formally, as was pointed out a long time ago by George J. Schuller:

“Acceptance of Mises’ stated axioms does not necessarily imply acceptance of the “principles” or “applications to reality” which he has drawn from them, even though his logic may be impeccable. When a logical chain grows beyond the limits set by stated assumptions, it uses unstated assumptions. The number of unstated assumptions (axioms, postulates, or other) in Human Action is enormous. If Mises denies this, let him try to rewrite his book as a set of numbered axioms, postulates, and syllogistic inferences using, say, Russell’s Principia or, closer home, Von Neumann’s Theory of Games as a model” (Schuller 1951: 188).

Addendum: Quine’s Philosophy is a Disaster for Praxeology
Another point is that any Austrian who adopts Quine’s idea that there is no meaningful distinction between analytic or synthetic propositions has destroyed the basis for the a priori status of the human action axiom. For Quine believed that no proposition is immune from possible revision of its truth by the test of experience and that there is in fact no real a priori knowledge of reality.

BIBLIOGRAPHY

Mises, L. 1978 [1962]. The Ultimate Foundation of Economic Science: An Essay on Method (2nd edn, Sheed Andrews & McMeel, Kansas City.

Schuller, G. J. 1951. “Mises’ ‘Human Action’: Rejoinder,” American Economic Review 41.1: 185–190.