The great libertarian philosopher and economist, Murray Rothbard, student of Ludwig von Mises, wrote extensively about an axiomatic approach to understanding economics.The idea is that sound (i.e., true) economic principles are logically deducible from a small set of axioms (perhaps just one) in the same way that true theorems about geometry can be deduced from a small set of axioms (do I need to reference Euclid?). Mises called this deductive method, praxeology, and the method characterizes the Austrian school of economics. Here’s a quote from Rothbard taken from the praxeology.net web site:

Praxeology rests on the fundamental axiom that individual human beings act, that is, on the primordial fact that individuals engage in conscious actions toward chosen goals. This concept of action contrasts to purely reflexive, or knee-jerk, behavior, which is not directed toward goals. The praxeological method spins out by verbal deduction the logical implications of that primordial fact. In short, praxeological economics is the structure of logical implications of the fact that individuals act. This structure is built on the fundamental axiom of action, and has a few subsidiary axioms, such as that individuals vary and that human beings regard leisure as a valuable good. Any skeptic about deducing from such a simple base an entire system of economics, I refer to Mises’s Human Action. Furthermore, since praxeology begins with a true axiom, A, all the propositions that can be deduced from this axiom must also be true. For if A implies B, and A is true, then B must also be true.

I want to take issue with the method. I do so on two grounds. The first is the famous incompleteness theorem of Kurt Gödel. In this work, Gödel proved that, in any complex axiomatic mathematical system there are propositions (theorems) that cannot be proved or disproved within the axioms of the system. He also demonstrated that the consistency of the axioms (i.e., whether or not they are contradictory) cannot be proved. His work, by the way, ended a century of attempts to find the axioms which would put the whole of mathematics on an axiomatic basis.

The second ground is more practical: What appear to be perfectly logical steps in trying to demonstrate something, may be incorrectly applied and lead to a false conclusion.

Let me first illustrate the second ground. The following diagram represents an attempt to prove something patently false, namely, that an acute angle equals a right angle. We use Euclid’s axioms and theorems.

diagram

Let’s start by constructing the right angle, ABC. We then construct the acute angle, BCF, at the end of the line, BC. We then measure off equal distances (using a compass) BD and CE and draw a straight line from D to E. Using our compass, we then construct the perpendicular bisectors of BC (shown in green) and DE (shown in red). Since DE is not parallel to BC, these bisectors meet at a point, O. Then we draw the straight lines, DO, BO, CO and EO.

Since the point, O, is on the perpendicular bisector of the line, DE, then DO = EO. This is indicated by the short, single, purple mark on these 2 lines. Similarly, since O is on the perpendicular bisector of BC, then BO = CO and this is shown by the double mark on these lines. BD = CE by construction; triple purple mark on these lines.

We have now demonstrated, by one of Euclid’s theorems, that triangle DOB is congruent to, or equals, triangle EOC. Maybe they don’t look quite congruent, maybe our drawing technique is off a little, but that is logically the case. Since the corresponding parts of congruent triangles are equal, angle ABO = angle FCO (green). Since triangle OBC is an isosceles triangle, angle OBC = angle OCB (red), again by a Euclidian theorem (base angles of an isosceles triangle are equal).

And now the punchline. Axiom: if equals are added to equals, the results are equal. So, if we add angle ABO to angle OBC, the result must be equal to adding angle FCO to angle OCB. But, if we add angles ABO and OBC, we get angle ABC, a right angle. And, if we add angles FCO and OCB, we get angle FCB, an acute angle. Therefore, an acute angle equals a right angle. QED.

“BFD”, I hear you say. Hmmmm. Well, OK. But we (Isn’t it cute how I have insinuated that “we” in here; now you’re complicit in this stuff, too!). Where was I? Oh, yes … we have used the axiomatic method, quite properly, and wound up with a result which is obviously false. There is no mistake in the axioms or the logic. So how is this possible? Can this type of fallacy arise in trying to deduce economic principles from the praxeological axiom of action?

———- to be continued ———–