January 1, 2015

The axiomatic method is impeccable

Comment on 'Debreu and the Bourbaki delusion of deductive-axiomatic economics'


Alan Kirman gives an excellent overview about how Debreu et al. led general equilibrium theory ad absurdum. I agree with all of it except for the somewhat implicit conclusion that the axiomatic-deductive method is inapplicable in economics, which is expressed in the title. It is logically incorrect to argue from the fact that someone has crashed an airplane into the ground that it is a delusion that airplanes can fly.

A minor point is that Bourbaki cannot be made accountable for the neoclassical structure-without-application: “..., it was the von Neumann perspective that shaped general equilibrium theory ..., and thus reconstituted economic theory.” (Weintraub, 2002, p. 78).

For a suggestive collection of statements about axiomatization see also the AXEC website.

The axiomatic-deductive method is impeccable. It is a sad fact that economists either cannot apply it correctly or do not understand what J. S. Mill, perhaps the greatest methodologist among them (Popper, 1980, p. 19), already clearly understood and taught.

Misapplication of the axiomatic method is ultimately responsible for the failure of Orthodoxy. But worse, lack of understanding is also the most important cause for the failure of Heterodoxy.

A paradigm shift consists in replacing the hitherto existing set of axioms by a better one. Keynes famously demanded to throw over the classical axioms (Keynes, 1973, p. 16). New axioms define a new paradigm. Heterodox economists were hitherto incapable of formulating an alternative set of axioms. It seems that they did not even understand that this is their constructive task. Only for lack of a convincing alternative the obsolete Arrow-Debreu-McKenzie axioms still stand.

To resume with Clower: “My opinion continues to be that axiomatics, like every other tool of science, is no better than its user, and not all users are skilled.” (1995, p. 308)

After the neoclassical misapplication it is high time that the axiomatic-deductive method is skillfully and successfully put to work in economics (see the AXEC Project).

Egmont Kakarot-Handtke

Clower, R. W. (1995). Axiomatics in Economics. Southern Economic Journal,
62(2): 307–319. URL
Keynes, J. M. (1973). The General Theory of Employment Interest and Money.
The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke:
Macmillan. (1936).
Popper, K. R. (1980). The Logic of Scientific Discovery. London, Melbourne,
Sydney: Hutchison, 10th edition.
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham,
NC, London: Duke University Press.