February 21, 2016

Causa finita

Comment on Barkley Rosser and Lars Syll on ‘How could “testing axioms” be controversial?’

Blog-Reference

Barkley Rosser writes “Curiously, they [Lucas and Sargent] did not seem to care whether the assumption was actually true, because it was ‘an axiom,’ something that is assumed and cannot be tested …” (See intro)

The first methodological idiotism consisted in Lucas’/Sargent’s idea of what an axiom is; the second idiotism consisted in the rest of the profession swallowing the first idiotism hook, line and sinker.

Every half-witted economist can know from the founding fathers that an axiom is defined by its ROLE in a consistent set of propositions, a.k.a. theory: “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)

To receive a proposition for the time being without proof never meant that any green cheese assumption is acceptable as axiom.

As a rule, the proof of axioms is in the deductively derived conclusions. If what the theory says should be the case is actually the case, then the axioms are indirectly corroborated. If not, they are refuted qua modus tollens. “Whether an axiom is or is not valid can be ascertained either through direct experimentation or by verification through the result of observations, or, if such a thing is impossible, the correctness of the axiom can be judged through the indirect method of verifying the laws which proceed from the axiom by observation or experimentation. (If the axiom is deemed to be incorrect it must be modified or instead a correct axiom must be found.) (Morishima, 1984, p. 53)

All this is well-known since Newton: “Could all the phaenomena of nature be deduced from only thre [sic] or four general suppositions there might be great reason to allow those suppositions to be true.” (quoted in Westfall, 2008, p. 642)

Not only physicists but mathematicians, too, have tested their axioms: “One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean.” (Brown, 2011, p. 565)

No mathematician will ever accept the rational expectations assumption as premise of economic theory as Lucas/Sargent could have known from history: “Walras approached Poincaré for his approval. ... But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. ... He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge ‘perhaps requires a certain reserve’.” (Porter, 1994, p. 154)

What Walras and his neoclassical followers simply never understood was that the expression ‘... perhaps requires a certain reserve’ is a code among mathematicians which translates into ‘do not bother me with your brain-dead garbage’.

So here is how to deal with economics from Walras to DSGE: “As with any Lakatosian research program, the neo-Walrasian program is characterized by its hard core, heuristics, and protective belts. Without asserting that the following characterization is definitive, I have argued that the program is organized around the following propositions: HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to  equilibrium states.
By definition, the hard-core propositions are taken to be true and irrefutable by those who adhere to the program. ‘Taken to be true’ means that the hard-core functions like axioms for a geometry, maintained for the duration of study of that geometry.” (Weintraub, 1985, p. 147)

To begin with, no one with an iota of scientific instinct will ever accept HC1 to HC6 as axioms. All the more so, as after the “duration of study”, that is, after more than 140 years of pointless model bricolage, even the dullest economist has now realized that this approach has failed in all methodological dimensions. The duration of acceptance of HC1 to HC6 is a simple metric for scientific incompetence.

Walrasian axioms have never been acceptable and will never be. They have to be fully replaced.*

Egmont Kakarot-Handtke


References
Brown, K. (2011). Reflections on Relativity. Raleigh, NC: Lulu.com.
Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, volume 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund. URL
Morishima, M. (1984). The Good and Bad Use of Mathematics. In P. Wiles, and G. Routh (Eds.), Economics in Disarry, pages 51–73. Oxford: Blackwell.
Porter, T. M. (1994). Rigor and Practicality: Rival Ideals of Quantification in Nineteenth-Century Economics. In P. Mirowski (Ed.), Natural Images in Economic Thought, pages 128–170. Cambridge: Cambridge University Press.
Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.

*See 'How economics finally became a science'