December 30, 2014

Who is afraid of axioms?

Joint comment on ‘Proper use of math in economics’ and ‘The failure of economics is due to the use of axiomatic method’


With the example of general equilibrium theory directly before their eyes heterodox economists seem to have settled on the opinion that a theory is a logical exercise which is based on arbitrary assumptions called axioms that have no empirical content whatsoever. It is therefore important to recall briefly what a theory is.

“A theory consists of a number of assumptions which logically function as axioms. Through specification and by introducing initial conditions, we may deduce predictions from them. If the predictions prove to be valid we may also say that the assumptions are realistic.” (Klant, 1994, p. 75)

Contrary to the impression received from orthodox economics, a theory is not a self-contained fictional construct but refers to reality. And exactly here comes the ambiguity in. As a matter of fact, equilibrium theory has explicitly cut the tie to reality.

“Allegiance to rigor dictates the axiomatic form of the analysis where the theory, in the strict sense, is logically entirely disconnected from its interpretations.” (Debreu, 1959, p. x)

This is true for mathematics proper. It is completely false when axiomatization is applied outside mathematics.

“Formal axiomatic systems must be interpreted in some domain ... to become an empirical science.” (Boylan and O'Gorman, 1995, p. 198)

The assessment that orthodox economics is not much more than a formalized shell game with economic terms is therefore fully justified.

“... GE theory is explicitly defended as a purely formal presentation of the determination of economic equilibrium in a decentralized competitive economy, having no practical value except as a benchmark ...” (Blaug, 1994, p. 126)

By consequence, equilibrium economics is not a theory in the proper sense.

“Suffice it to say that, in my opinion, what we presently possess by way of so-called pure economic theory is objectively indistinguishable from what the physicist Richard Feynman, in an unflattering sketch of nonsense ‘science,’ called ‘cargo cult science’.” (Clower, 1994, p. 809)

The fundamental defect of orthodox economics does not consist in axiomatization but in applying the WRONG axioms.

“Much of economic theory is based on three questionable assumptions: (1) the world is deterministic; (2) decision makers act as if they know the values of all relevant parameters; and (3) consumers and firms respectively, act as if they were maximizing utility and profit.” (Stigum, 1991, p. 29)

The first task of Heterodoxy is therefore to formulate a theory that is based on a different set of axioms. Axioms, though, do not follow simply from looking at what appears as reality.

“Indeed, there is no such thing as an uninterpreted observation, an observation which is not theory-impregnated.” (Popper, 1994, p. 58)

Therefore, the old induction/deduction chestnut has to be put aside.

“... there is not and cannot be any fundamental opposition between ‘theory’ and ‘fact finding,’ let alone between deduction and induction.” (Schumpeter, 1994, p. 45)

Heterodox economists are mistaken to think that because the orthodox axioms are false axiomatization is dispensable.

“It would be a mistake to lower the level of analysis and clarification. The only way possible is a thorough reexamination of the theory’s basic hypotheses, i.e., a true paradigmatic revolution.” (Ingrao and Israel, 1990, p. 362)

And this brings us directly to J. S. Mill's Starting Problem.

“What are the propositions which may reasonably be received without proof? That there must be some such propositions all are agreed, since there cannot be an infinite series of proof, a chain suspended from nothing. But to determine what these propositions are, is the opus magnum of the more recondite mental philosophy.” (Mill, 2006, p. 746)

Based on good methodological reasons, I propose to move from subjective to objective axiomatic foundations (see here).

To my knowledge there is presently no superior set of axioms available.

Egmont Kakarot-Handtke

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