Blog-Reference
I came across David Glasner's post of 16 July 2014 'Modern macroeconomics ― obscurantist axiomatization' on this blog.
This post also deserves a comment in the present context. I will ignore the counterproductive resentments (snobbishness, pedantry, etc.) against axiomatization and focus on some pivotal historical facts.
Glasner writes: “Before discussing the situation in economics, I would note that axiomatization did not become a major issue for mathematicians until late in the nineteenth century (though demands ― luckily ignored for the most part ― for logical precision followed immediately upon the invention of the calculus by Newton and Leibniz) and led ultimately to the publication of the great work of Russell and Whitehead, Principia Mathematica whose goal was to show that all of mathematics could be derived from the axioms of pure logic.”
Axiomatization became already a major issue for mathematicians with Euclid around 300 BC. Among heterodox economists, it seems that only Georgescu-Roegen understood the significance of this unique event.
“We are therefore justified in saying that with Euclid's Elements the causa materialis of geometry underwent a radical transformation; from a more or less amorphous aggregate of propositions it acquired an anatomic structure. Geometry itself emerged as a living organism with its own physiology and teleology,... And this true mutation represents not only the most valuable contribution of the Greek civilization to human thought but also a momentous landmark in the evolution of mankind comparable only to the discovery of speech or writing.” (1966, p. 9)
Axiomatization then became a major issue for physicists with Newton.
The Principia starts with the famous 'Axioms, or the Laws of motion' and the role of Euclidean geometry for Newtonian physics cannot be overestimated. So impressive were the accomplishments of Newtonian physics that eighteenth-century philosophers, including the founders of political economy, jumped on the bandwagon.
And so it became an issue in the so-called social sciences with Hume. “Like most of his fellow moral philosophers, Hume thought it was worth a try to make all sciences as rigorous as Newtonian physics ...” (Redman, 1997, p. 111)
Finally, this is how axiomatization became a major issue in economics around 1800: “To Senior belongs the signal honor of having been the first to make the attempt to state, consciously and explicitly, the postulates that are necessary and sufficient in order to build up … that little analytic apparatus commonly known as economic theory, or to put it differently, to provide for it an axiomatic basis.” (Schumpeter, 1994, p. 575)
So Glasner got it not quite correct: “The fetish for axiomatization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium.”
The traces go even back before Adam Smith. In fact, the first attempts to axiomatize human behavior can be traced back to Hutcheson, Hume's and Smith's celebrated teacher (Redman, 1997, p. 116).
Glasner got it, again, not quite correct with: “The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science.”
Exactly the opposite is true: “But it was a second and more important quality that struck readers of the Principia. … For readers of that day, it was this deductive, mathematical aspect that was the great achievement.” (Truesdell, quoted in Schmiechen, 2009, p. 213)
The rest of Glaser's argumentation is not much better (for the refutation of the awkward Gödel argument see here).
The conclusion is obvious. Heterodoxy is right, the neoclassical axioms have to be rejected. This, though, does not mean that axiomatization has to be rejected. On the contrary. In order to replace neoclassical economics, Heterodoxy has to replace the neoclassical axioms with heterodox axioms. There is no way around this.
“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 foundational premises as already J. S. Mill made abundantly clear. As a matter of fact, cutting-edge physicists take their inspiration from an economist.
“... but underneath the complexities [of string theory] is a modern version of John Stuart Mill's desideratum of fundamental physics: a unified description of all fundamental interactions.” (Farmelo, 2009, p. 436)
Heterodoxy does not have one good reason to reject axiomatization yet many to apply it. The best reason is indeed that correct axiomatization ends confusion, of which is plenty among both orthodox and heterodox economists (2013).
The outrageous fact, written in stone for all future methodologists, is that to this day the representative economist cannot tell the difference between income and profit.
Egmont Kakarot-Handtke
References
Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University Press, 5th edition.
Farmelo, G. (2009). The Strangest Man. The Hidden Life of Paul Dirac, Quantum Genius. London: Faber and Faber.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions for the Economist, pages 92–129. Cambridge: Harvard University Press.
Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL
Redman, D. A. (1997). The Rise of Political Economy as Science. Methodology and the Classical Economists. Cambridge, London: MIT Press.
Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, volume 1. Norderstedt: Books on Demand, 2nd edition. URL
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.
***
