Irrational facts?

I suppose you all know what an irrational number is. And I trust you don’t take the existence of such numbers as an assault on rationality or an injunction against using reason when dealing with mathematics.

Now I came across this in Ludwig von Mises’ Theory and history:

The human search for knowledge cannot go on endlessly. Inevitably, sooner or later, it will reach a point beyond which it cannot proceed. It will then be faced with an ultimate given, a datum that man’s reason cannot trace back to other data. In the course of the evolution of knowledge science has succeeded in tracing back to other data some things and events which previously had been viewed as ultimate. We may expect that this will also occur in the future. But there will always remain something that is for the human mind an ultimate given, unanalyzable and irreducible. Human reason cannot even conceive a kind of knowledge that would not encounter such an insurmountable obstacle. There is for man no such thing as omniscience. […] It is customary, although not very expedient, to call the mental process by means of which a datum is traced back to other data rational. Then an ultimate datum is called irrational. No historical research can be thought of that would not ultimately meet such irrational facts. (P. 183f; italics mine.)

Now wait a minute. Facts are neither rational nor irrational. They are just facts. The terms “rational” and “irrational” pertain to what we do in our minds with the facts. It is a misnomer and an equivocation to call the facts rational or irrational.

Or does he mean that reason cannot deal with those “ultimate givens”, just because it cannot trace them back to something even more ultimate? But this is ridiculous. If reason encounters an ultimate given that cannot be traced further back, it simply accepts it as an ultimate given. There is nothing irrational about that.

Apart from this objection (and some others I may come to think of later),Theory and History is a book I heartily recommend.

Irrational ends?

(Added May 16.)

The following quote is more troublesome:

All ultimate ends aimed at by men are beyond the criticism of reason. Judgments of value can be neither justified nor refuted by reasoning. The terms “reasoning” and “rationality” always refer only to the suitability of means chosen for attaining ultimate ends. The choice of ultimate ends in this sense is always irrational. (P. 167.)

And if you know your Mises, you know that this idea is repeated over and over in his works.

Obviously, Mises never considered Ayn Rand’s explanation of the link between “life” and “value” (or if he did, he might have considered it “irrational” and “beyond reason”).

But her derivation is fact-based. To take some high-lights: That living organisms require a specific course of action to remain alive is a fact. For lower organisms this is automatic, but for man it involves deliberation and choice, and that is a fact. And it is a fact in the sense of an “ultimate given”, because it can hardly be traced back to even more basic facts. To choose life, and the preservation and enhancement of one’s life, is certainly the rational thing to do.

A couple of pages later Mises writes:

… there is a far-reaching unanimity among people with regard to the choice of ultimate ends. With almost negligible exceptions, all people want to preserve their lives and health and improve the material conditions of their existence. (P. 269f.)

True enough. Very few people, I would venture to guess, deliberately act to harm their lives, their health, their well-being. There are exceptions, but most people, when they harm themselves, do it because of some error in their reasoning. They find the wrong means, means not suitable the end sought, to use Mises’ way of expressing it.

But an appeal to majority is not a good argument. Majorities are sometimes wrong. And on Mises’ own reasoning and with his terminology, the majority here is as irrational as the small minority that does not take life and health as their ultimate goal.

There is a similar quote in the very beginning of the book:

Judgments of value […] express feelings, tastes or preferences of the individual who utters them. With regard to them there cannot be any question of truth and falsity. They are ultimate and not subject to any proof or evidence. (P. 19.)

That values or value judgments have no “truth value” and are just expressions of feelings or tastes is something we are taught by virtually every philosopher who is not an Objectivist. It is as common and ubiquitous as the closely connected idea that one cannot (and must not) try to derive an “ought” from an “is” – and as wrong.

Mises uses the example of someone preferring Beethoven to Lehar (or vice versa). This is a value judgment. The person who says it is saying that Beethoven, to him, is a higher value than Lehar (or vice versa). And here it is OK to talk about a difference in taste, and there is no point in trying to dispute it.

But there are so many issues where this would be nonsensical. If we prefer capitalism to socialism, this is not a matter of taste. Neither is it a matter of taste whether we prefer life to death, health to illness, happiness to misery or wealth to poverty. Such an issue can only come up when a man is so ill, or so disappointed, that he loses his taste for life. (Situations where Immanuel Kant would demand that he continues to live out of duty.)

Closely connected is the idea, so often repeated by Mises, that economics (and science in general) should be value-free (or wertfrei; for some reason Mises retains the German word). But this idea is contradictory on the face of it. It says that a theory should be “value-free” rather than “value-laden” – i.e. that such a theory is better than other theories – i.e. that is more valuable.

Now, I have not said anything about the very good things to be found in Theory and History. That will have to wait for another time.

(See also Is Action an A Priori Category?, Is Life Worth Living?, On the Objectivity of Values, and Objectivism versus “Austrian” Economics on Value. Also Ayn Rand and Böhm-Bawerk on Value.)


PS 2016: It would make some sense to call facts “pre-rational”, since all reasoning has to start with facts. And by the same token, it would make some sense to call the value of life a “pre-rational” value. We do not originally choose to be alive – that choice was made by out parents and all their ancestors before them: the choice to have children. But the bottom line of all other values we choose is remaining alive and make the best possible of our lives.

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7 Responses to Irrational facts?

  1. Good point. What about the phrase “facts of reality”?

  2. In fact (if you’ll excuse the pun), it makes as much or as little sense to talk about “irrational numbers” as to talk about “irrational facts”. Of course, there a reason for the term “irrational number”, although I know too little to say what this reason is. I have filed this under the heading “linguistic oddities”. (In earlier times, those numbers were called “surds”, but I don’t know the origin of this term either.)

    • Not sure what the Greek term for “irrational” number was, but in older English translations (See e.g. Thomas Heath’s translations) these numbers were called “incommensurable.” “Commensurable” is actually not an adjective, but a preposition; it describes the relationship between two numbers. The Greeks didn’t understand numbers as possibly unitless values the way we do – that was actually a nontrivial leap in understanding of mathematics that took some time to achieve widespread acceptance. Therefore their idea of a number was always a line segment *in relation to* a given fixed line segment (so for example giving a line segment arbitrarily the value “1” then “2” would be the line segment obtained by drawing the first one twice following the construction in Euclid’s Elements for copying lines). For them the idea that you could find a line segment “incomensurable” to a prescribed line segment was absurd, maybe that is where rational/irrational comes from. It is a speculation but based on similar controversies in math today I would guess the issue comes from the fact that the existence of irrational numbers suggests a certain level of incomputability from the point of view of working with pure integers (e.g. how does one multiply two irrational numbers? how do we know if two irrational numbers are equal to each other? No finite algorithm can answer these questions in general, and the whole Greek mathematics program was based on finite algorithms).

  3. Actually, I mentioned irrational numbers only because I thought it was a good way to start the blog post.

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