Comment Lars Syll on 'Proper use of math in economics'
Blog-Reference
In my post of Dec 22 I introduced the Prophets of Preemptive Vanitization. More often than not, these prophets populate the social sciences, and from all theorems that have ever been developed in mathematics or physics, the impossibility theorems are closest to their hearts because they are equally good for both inhibition and excuse.
So, one cannot mention the word axiom in the social sciences without the Pavlovian reflex: Oh, you know, Gödel has proved that a complete and consistent set of axioms is impossible (see Wikipedia). Yes, and now? Is Newtonian physics wrong because the Euclidean axioms are incomplete? And, by the way, one can always expand a set of axioms if necessary, so Gödel is not of practical concern at all outside mathematics.
For a snail, it is irrelevant that it cannot, in principle, surpass the speed of light. By the same token are the impossibility theorems from cutting-edge physics and logic irrelevant to economic methodology. By no stretch of the imagination can Gödel's proof be used to argue against axiomatization. Heterodox economists could know this from one of the great heterodox economists.
“Lest this position is misinterpreted again by some casual reader, let me repeat that my point is not that arithmetization [= axiomatization] of science is undesirable. Whenever arithmetization can be worked out, its merits are above all words of praise. My point is that wholesale arithmetization is impossible, that there is valid knowledge even without arithmetization, and that mock arithmetization is dangerous if peddled as genuine.” (Georgescu-Roegen, 1971, p. 15)
We easily can agree on this. Thus, to argue against axiomatization amounts for all practical purposes to the conservation of manifest logical and conceptual defects in the theoretical edifice of economics. And there are many of them. Economists are known as sloppy thinkers.
“The truth is, most persons, not excepting professional economists, are satisfied with very hazy notions.” (Fisher, quoted in Mirowski, 1995, p. 86)
This goes some way in explaining the secular stagnation of economics. “I think it is the lack of quite sharply defined concepts that the main difficulty lies, and not in any intrinsic difference between the fields of economics and other sciences.” (von Neumann, quoted in Mirowski, 2002, p. 146 fn. 49)
The arguments of the Prophets of Preemptive Vanitization against axiomatization have always been far off the mark. Axiomatization is a very effective tool and the fact that it is not exactly 100 percent effective is no argument against it. How effective is the Verstehen of the so-called social sciences?
This said, my key argument is not so much methodological but indeed very practical. In order to replace the neoclassical approach, which is axiomatized, Heterodoxy must replace the axiomatic foundations of neoclassical theory. Hence, there is no urgent need to discuss axiomatization in the abstract. According to well-established scientific practice, there is no other way.
“The moral of the story is simply this: it takes a new theory, and not just the destructive exposure of assumptions or the collection of new facts, to beat an old theory.” (Blaug, 1998, p. 703)
And each theory is built upon some clearly stated premises. It is as straightforward as this.
“When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” (Resume of Aristotle's Analytica).
It has often been argued that scientists do not proceed axiomatically in their research. This, of course, is well-known in the history of science. But clearly, the moment they apply some piece of mathematics they do so indirectly. And in the end, the whole theoretical edifice must be logically coherent. This goes without saying.
“I am of the opinion that, certainly, for the purposes of research it is always necessary to combine the intuition with the axioms.” (Felix Klein, quoted in Weintraub, 2002, p. 25), see also (2013, Sec. 6).
From the fact that physics is at the moment not completely axiomatized does not logically follow that economics cannot or should not be axiomatized.
“Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced.” (Feynman, 1992, p. 50)
Asad Zaman correctly remarks that all methodology, in the end, boils down to empirical testing: “For example, Egmont keeps arguing that his axiomatization is better than others, and that others are wrong while his is correct. To me, it seems that this requires demonstration on practical grounds ...”
This, indeed, is the all-decisive argument.
As it happens, this argument has already been answered on this blog and elsewhere. For example, see my comment 'Going beyond error and distortion' of Dec 12.
In this comment, I have refuted the Keynesian I=S and presented the correct formula which is testable. See also my refutation of Keen's profit theory (2013). The fact of the matter is that all logical implications of the structural axiom set are testable because the axioms contain only measurable variables. And this is why structural axioms are methodologically superior to the behavioral axioms of Orthodoxy.
To answer Asad Zaman's key argument: there are as many testable propositions available as one could wish. See the working papers on SSRN.
See also the comment of Dec 21 above: “If anybody thinks that the structural axiom set is false, he is invited to refute one proposition that follows deductively from it.”
From the structural axioms follows the Profit Law. And this makes it possible to empirically refute other approaches, e.g. (2011).
My claim is that the objective-structural axiom set is superior to the familiar formal starting points of economic analysis. This claim is open to scrutiny according to the criteria of formal and material consistency. One is not obligated to apply the structural axiom set provided one possesses already the correct formal foundations, which is improbable given the unacceptable state of orthodox and heterodox economics.
Axiomatization means clearness. As self-defined social scientists, economists traditionally prefer the twilight zone where “.. nothing is clear and everything is possible.” (Keynes, 1973, p. 292). And after they have muddled everything up to the point of inconclusiveness they invariably excuse the mess with the complexity of the subject matter. This goes already for a while. Here we have Duhem-Quine:
“Knight accuses the positivists of overlooking the complexity and uncertainty of testing in all sciences and argues at length that positivist views of science are particularly inappropriate to economics, which, like all sciences of human action, must concern itself with reasons, motives, values and errors, not just causes and regularities.” (Hausman, 1989, p. 118)
With regard to methodology, Asad Zaman stands firmly in the neoclassical tradition.
“Post-Kuhnian understanding of science and axiomatics is rather complex, with no obvious and simple theory of knowledge attached.”
After Kuhn's schematic account of a paradigm shift, the Prophets of Preemptive Vanitization tried hard to get back into their natural habitat, the twilight zone of human all too human messiness. However, nobody needs a theory of knowledge to convince himself that BOTH Orthodoxy and Heterodoxy do not satisfy scientific standards.
It is not a big issue when Asad Zaman does not understand the merits and chances of axiomatization. It is, though, of utmost importance that he refrains from silly statements like: “The failure of economics is due to the use of axiomatic method.” or, even worse: “Thus, any axiomatization can only make a LIMITED set of claims. For example, Egmont’s axioms may provide an explanation for the role of money, but have nothing to say about the global financial crisis. Indeed, since so far the best explanation come from behavioral finance, while Egmont’s axioms bypass behavior, it would seem that his axiom CANNOT say anything about this crisis.”
This looks pretty much like an impossibility assertion out of thin air. It is obvious that Asad Zaman prefers to stay in the woods of psychology and sociology. This personal decision has to be accepted. But it cannot be accepted that he ignores facts. These are:
(i) From the fact that behavioral assumptions (like utility maximization) are denied the status of an axiom does not logically follow that no behavioral assumptions can be applied. Just the contrary: structural axiomatization is compatible with ANY behavioral assumption, that is, it is fully compatible with behavioral finance.
(ii) From the structural axiom set indeed follows quite a lot about financial crises. For those who can read and think it is all on SSRN.
Asad Zaman is right, axiomatization makes only limited claims ― grandiose vacuousness is left to the so-called social sciences ― yet these claims are as certain as can be. The first important result of structural axiomatization is:
Neither Classicals, nor Walrasians, nor Marshallians, nor Marxians, nor Keynesians, nor Institutionalists, nor Monetary Economists, nor Austrians, nor Sraffaians, nor Evolutionists, nor Game theorists, nor Econophysicists, nor RBCers, nor New Keynesians, nor New Classicals ever came to grips with profit. Hence, they fail to capture the essence of a capitalist market economy.
In its present state, Heterodoxy is unacceptable according to scientific criteria. The options are: move on or move out.
Egmont Kakarot-Handtke
References
Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University Press, 5th edition.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge: Cambridge University Press.
Hausman, D. M. (1989). Economic Methodology in a Nutshell. Journal of Economic Perspectives, 3(2): 115–127. URL
Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–15. URL
Kakarot-Handtke, E. (2013a). Crisis and Methodology: Some Heterodox Misunderstandings. SSRN Working Paper Series, 2083519: 1–25. URL
Kakarot-Handtke, E. (2013b). Debunking Squared. SSRN Working Paper Series, 2357902: 1–5. 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.
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.
Mirowski, P. (2002). Machine Dreams. Cambridge: Cambridge University Press.
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.