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Review of Fuerle’s Pure Logic of Choice


In his 1986 book, Fuerle includes a chapter titled “Free Will” in which he asserts, basically, that people have free will. I see no evidence that, in 1986, he felt that the existence of free will precluded the use of mathematics in economics. Except for occasionally invoking geometric proofs (such as the one about the interior angles of a triangle summing to 180°) as an ideal for economic theory to emulate, The Pure Logic of Choice is silent on the subject of mathematics in economics.

In a recent e-mail, Richard Fuerle has expanded on his views of free will, specifically stating his opposition to the use of mathematics in economics.


As you know, the Austrians argue that mathematics cannot be applied to economics because economics deals with entities, e.g., prices and quantities bought and sold, that can change arbitrarily and unpredictably. Mathematical modeling requires the world that is modeled to behave rationally and predictably… But values, which determine prices, can jump all over the place, even though the usually don’t. That is, there is no underlying law that determines the value that people place on things… There is no underlying law because people have free will. An attempt to apply mathematics to values, i.e., to epistemically correlate a mathematical model with people’s economic decisions, will be highly approximate, especially at times of stress.


That is quite an indictment. My theory fails during times of stress? I had better be careful not to let myself get stressed out about this e-mail or I might see my entire theory collapse around me.

Actually, if prices and quantities bought and sold were really arbitrary and unpredictable, that would preclude application of any economic theory, regardless of how much or how little math it employed. All economic theories, from Human Action, which eschewed all mathematics, to the latest article in the Journal of Economic Theory, claim to make meaningful statements about prices. If prices are really arbitrary and unpredictable, then a lot of people have been wasting their time writing about them.

Part IV of Fuerle’s book describes many “laws” of economics and, specifically, of prices. This is difficult to reconcile with his later claim that prices and quantities bought and sold are arbitrary and unpredictable. For instance, Fuerle writes:


Prices are the bits of knowledge that influence individuals to coordinate their plans. To the extent that the conditions of the Law of Quantity Demanded apply, a higher price for good A will influence individuals to alter their plans by foregoing purchasing good A, and perhaps instead purchasing good B. Under these same conditions, to the extent that the conditions that the Law of Supply and Demand apply, sellers will ask a higher price for good B, which will influence other individuals to alter their plans by foregoing purchasing good B and instead perhaps purchasing good C, and so on. Like dropping a pebble into a pond, the effect ripples through the economy, each person voluntarily altering his plans so as to coordinate them with the plans of others. In this way, a “spontaneous order” arises, which was the result of purposeful behavior, yet which no single mind conceived and planned. This is the miracle of the free market (p. 132).


Miraculous indeed if prices are actually arbitrary and unpredictable! Or perhaps prices are only arbitrary and unpredictable when I am watching them, but they behave themselves under Fuerle’s stern glare.

All economists, from every school except socialism, have observed the “spontaneous order” of the free market. It is arrogant for one school, the Austrians, to lay claim to the very concept of spontaneous order and, like Procrustes, attempt to fit their every critic into the mold of Oskar Lange.

Modern Austrians are like a boy who clears level one of his video game but then is quickly killed by the tougher monsters in level two and, afraid to repeat that bad experience, he just keeps restarting his game at the beginning until he can clear level one in record time. But, though he now goes through level one at a dead run and shoots monsters the moment they stick their heads up, the boy cannot be said to have mastered his video game because he still gets killed just as quickly as ever in level two and it is a six-level game. In the same way, the Austrians want to keep re-fighting their battle with Lange while refusing to admit that they have new enemies now – like me. 1

Fuerle prefaces the invoking of one of his laws (above) by writing, “To the extent that the conditions of the Law of Quantity Demanded apply,…” And, in general, all of his laws require that certain conditions be met before the law can be applied. This is no different than an axiomatic system like mine except that all of my theorems have the same conditions, namely the three axioms which define my theory. Fuerle’s theory is also axiomatic except that each of his twenty laws have their own set of conditions. This is a weakness. It is better if all of one’s results are derived from a single, unified set of assumptions, as my theorems are. It gives one’s book a sense of cohesion.

Thus, I would deny Fuerle’s claim that “there is no underlying law that determines the value that people place on things.” In fact, there are three underlying laws, or axioms, as I call them:

1) One's value scale is totally (linearly) ordered:
  i) Transitive; p q and q r imply p r
  ii) Reflexive; p p
  iii) Anti-Symmetric; p q and q p imply p = q
  iv) Total; p q or q p
2) Marginal (diminishing) utility, u(s), is such that:
  i) It is independent of first-unit demand.
  ii) It is negative monotonic; that is, u'(s) < 0.
  iii) The integral of u(s) from zero to infinity is finite.
3) First-unit demand conforms to proportionate effect:
  i) Value changes each day by a proportion (called 1+j, with j denoting the day), of the previous day's value.
  ii) In the long run, the j's may be considered random as they are not directly related to each other nor are they uniquely a function of value.
  iii) The j's are taken from an unspecified distribution with a finite mean and a non-zero, finite variance (1999, pp. xxiii-xxiv).

If Richard Fuerle or anyone else wishes to argue that these three axioms are inapplicable to the real world, they are welcome to do so. I feel that my axioms are wisely chosen and I would be interested in hearing why they are not. However, to argue that prices are arbitrary and unpredictable and there are no underlying law that determines the value that people place on things is absurd. Such an assertion belies the existence of Fuerle’s own theory, which claims to make meaningful statements about prices.

There is no direct way to counter such nihilism. Arguing with a nihilist is like lecturing a teenager, who responds to every assertion with “whatever.” One can only observe that Fuerle, Mises, Keynes, this author and many others have written books about the behavior of prices. We would not have made the effort if we thought that prices were arbitrary. Hopefully, the weight of tradition will preserve the existence of economics as a legitimate field of inquiry against the attacks of the nihilists.

1 A good example is Robert Murphy’s recent article (QJAE, 9 (2), pp. 3-11), in which he digs up Lange’s moldering remains, sticks another knife in its skeletal ribs and then re-buries it.

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