Comment on Lars Syll on ‘The Bourbaki-Debreu delusion of axiomatic economics’
Blog-Reference
“... but when the road ends at a coal-pit, he [the traveler] doesn’t need much judgment to know that he has gone wrong, and perhaps to find out what has led him astray.” (Hume)
It is known for a long time now that Orthodoxy is a degenerate research program. The problem is (i) that Heterodoxy spotted a myriad of faults and flaws but never the crucial foundational defect, and (ii), that Heterodoxy never inaugurated an independent and self-reliant PROGRESSIVE research program.
So traditional Heterodoxy followed as the at all times critical sidekick faithfully behind the orthodox Rocinante towards the end of the coal pit. To the quite natural question of what has gone wrong, the Malmö branch of traditional Heterodoxy answers that axiomatics had been the original sin of economics: “Mathematical axiomatic systems lead to analytic truths, which do not require empirical verification, since they are true by virtue of definitions and logic. It is a startling discovery of the twentieth century that sufficiently complex axiomatic systems are undecidable and incomplete.” (Asad Zaman)
This is as far beside the point as one can get because every methodologist knows that: “Formal axiomatic systems must be interpreted in some domain ... to become an empirical science.” (Boylan et al., 1995, p. 198)
And: “... a theory should be accurate within its domain, that is, consequences deducible from a theory should be in demonstrated agreement with the results of existing experiments and observations.” (Kuhn, quoted in Redman, 1993, p. 3)
Exactly at this critical juncture Debreu’s foundational error/mistake is located, viz. the complete DISCONNECT from the economic domain: “Allegiance to rigor dictates the axiomatic form of the analysis where the theory, in the strict sense, is logically entirely disconnected from its interpretations.” (1959, p. x)
Debreu’s application of axiomatics lacks a deeper understanding of the scientific method. There is some irony/absurdity in the fact that the great heterodox economist Georgescu-Roegen had been quite clear about the relationship between axioms and reality: “What particular reality is described by a given theory can be ascertained only from that theory’s axiomatic foundation.” (1966, p. 361)
It is pretty obvious that Debreu missed the crucial point of Bourbaki’s axiomatics. “From the axiomatic point of view, mathematics appears thus as a storehouse of abstract forms — the mathematical structures; and it so happens — without our knowing why — that certain aspects of empirical reality fit themselves into these forms, as if through a kind of preadaptation. ... It is only in this sense of the word ‘form’ that one can call the axiomatic method a ‘formalism’.” (Bourbaki, 2005, p. 1276)
It was quite clear to Bourbaki that NOT ALL mathematical structures incorporate ‘certain aspect of empirical reality’, which means, that there is a “... whole crop of monster-structures, entirely without application” (Bourbaki, 2005, p. 1275, fn. 9).
Hence, Debreu’s axiomatization of Walrasian General Equilibrium is a monster-structure that is due to Debreu’s misunderstanding of Bourbaki. It is NOT the axiomatic-deductive method that is wrong, it is the neo-Walrasian axioms that are false.#1
“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.” (Clower, 1995, p. 308)
‘Unskilled’ needs here be taken as a euphemism for utter scientific incompetence. It is this incompetence that brought Orthodoxy and its sidekick traditional Heterodoxy to the end of the coal pit.
Let us leave them there in their hopeless darkness.
Egmont Kakarot-Handtke
References
Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Volume II, 1265–1276. Oxford, New York: Oxford University Press. (1948).
Boylan, T. A., and O’Gorman, P. F. (1995). Beyond Rhetoric and Realism in Economics. Towards a Reformulation of Economic Methodology. London: Routledge.
Clower, R. W. (1995). Axiomatics in Economics. Southern Economic Journal, 62(2): 307–319. URL
Debreu, G. (1959). Theory of Value. An Axiomatic Analysis of Economic Equilibrium. New Haven, London: Yale University Press.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter Economic Theory and Agrarian Economics, 359–397. Cambridge: Harvard University Press.
Redman, D. A. (1993). Economics and the Philosophy of Science. New York, Oxford: Oxford University Press.
#1 The whole theoretical superstructure of Orthodoxy is based upon this forever unacceptable set of hardcore propositions a.k.a. axioms:
HC1 There exist economic agents.
HC2 Agents have preferences over outcomes.
HC3 Agents independently optimize subject to constraints.
HC4 Choices are made in interrelated markets.
HC5 Agents have full relevant knowledge.
HC6. Observable economic outcomes are coordinated, so they must be discussed
with reference to equilibrium states. (Weintraub, 1985)
The mission of constructive Heterodoxy is to fully REPLACE this set with a superior set, i.e. to perform the Paradigm Shift.
Related 'From Orthodoxy to Heterodoxy to Sysdoxy' and 'Economists and the economy ― a nonstarter since 200 years' and 'How incompetent are economic methodologists? Very!' and 'Macroeconomics: Economists are too stupid for science' and 'The canonical macroeconomic model'.
