Comment on Lars Syll on 'Proper use of math in economics' with special reference to Asad Zaman
Blog-Reference
You write: “Math and Science have ENTIRELY different methodologies which are suitable to them.”
True. And it is exactly one of the great wonders how in the end this fits together so nicely: “I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with what is going on in the original thing.” (Feynman, 1992, p. 171)
A famous paper by Wigner is titled ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’ (1979). And this led Velupillai to wonder about ‘The Unreasonable Ineffectiveness of Mathematics in Economics.’ (2005)
One possible answer could be that the cause of this unreasonable ineffectiveness lies in the scientific incompetence of economists. This hypothesis has been advanced by a well-known representative of the real sciences. See: ‘The Farce That Is Economics: Richard Feynman On The Social Sciences’ More here.
Not only physicists have wondered about unreasonable effectiveness but mathematicians, too:
“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)
You write: “The scientific method involves making observations about nature and then GUESSING at laws which generate the observed patterns — that is induction.”
This is simply false and inductivists should know this by now. The real question is this: “If then it is the case that the axiomatic basis of theoretical physics cannot be an inference from experience, but must be a free invention, have we any right to hope that we shall find the correct way?” (Einstein, 1934, p. 167)
You write: “Consider the Pythagorean Theorem. It would make no sense to draw triangles and measure their sides to verify it, or to attempt to find a counterexample to the law.”
This is simply false.
“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)
You write: “As Popper put it, if there is no potential observation which could conflict with the law, then it is not a scientific law.”
True. And this is why theoretical economics deals only with testable propositions. And this, in turn, is the reason why the structural axiomatic paradigm is superior to both the orthodox and heterodox approaches (2014).
You write: “The observational and empirical aspect of science means that it cannot be axiomatic.”
This, again, is simply false.
“But the axioms Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought” ... (Einstein, quoted in Clower, 1998, p. 409)
You write: “GREAT progress in science resulted PRECISELY from dropping the axiomatic methodology and switching to an observational and inductive process which led to scientific laws which could never be proven, UNLIKE mathematical laws.”
Exactly the opposite is true.
“It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them which give us the key to the understanding of the phenomena of Nature. Experience can, of course, guide us in our choice of serviceable mathematical concepts; it cannot possibly be the source from which they are derived; experience, of course, remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics. In a certain sense, therefore, I hold it to be true that pure thought is competent to comprehend the real, as the ancients dreamed.” (Einstein, 1934, p. 167)
You write: “The failure of economics is due to the use of the axiomatic method, which is eminently unsuitable for natural science, as was proven in the course of history.”
The incorrectness of this conclusion is unsurpassable.
The fact of the matter is that economics is a failed science because Orthodoxy got the axiomatic foundations wrong and Heterodoxy has none at all.
The absurdity of the situation consists in the plain fact that Orthodoxy at least understands the crucial importance of axiomatization while heterodox economists do not even see the task before them.
At first sight, it looks tragic, but then it is only a slapstick: All those who are marching to the tunes of Marshall's Burn-Hymn are directly going over the scientific cliff.
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, Vol. II, 1265–1276. Oxford, New York: Oxford University Press. (1948).
Brown, K. (2011). Reflections on Relativity. Raleigh: Lulu.com.
Clower, R. W. (1998). New Microfoundations for the Theory of Economic Growth? In G. Eliasson, C. Green, and C. R. McCann (Eds.), Microfoundations of Economic Growth, 409–423. Ann Arbour: University of Michigan Press.
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the History of Science. Cambridge, London: MIT Press.
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics. Cambridge Journal of Economics, 29: 849–872.
Wigner, E. P. (1979). Symmetries and Reflections, chapter The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 222–237. Woodbridge: Ox Bow Press.