Blog-Reference and Blog-Reference on Mar 9
Orthodox and heterodox economists are talking much at cross purposes about the relationship between economics and mathematics: “Noah Smith — like so many other mainstream economists — obviously has the unfounded and ridiculous idea that because heterodox people like yours truly often criticize the application of mathematics in mainstream economics, we are critical of math per se.” (See intro)
The bottom line is, as always in economics, that BOTH sides are wrong. It is long known that economists are unable to tap the ‘unreasonable effectiveness of mathematics’: “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)
The original methodological blunder of economists is, as Poincaré immediately noticed, to apply mathematics to NONENTITIES like utility. Worse, economists have built these NONENTITIES right into the foundations of the whole analytical edifice. The Walrasian framework is given with this verbalized axiom set: “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.” (Weintraub)
The representative economist has not realized it but methodologically these premises are forever unacceptable. It should be pretty obvious that the Walrasian axiom set contains three NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every model that contains a NONENTITY is a priori false.
What economists do not understand since Jevons/Walras/Menger is that mathematics simply does not work with NONENTITIES. Calculus is pointless when applied to utility and elementary arithmetic does not work when applied to determine the number of dancing angels on a pinpoint.
But elementary mathematics should be applicable, for example, for determining the fundamental macroeconomic relationships, which are very real and measurable with the precision of two decimal places. However, economists cannot even apply the elementary mathematics of accounting. Keynes is a case in point.
The formal basis of the General Theory is given with: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (p. 63)
This syllogism is conceptually and logically defective because Keynes did not come to grips with profit: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end, he gave up and discarded the draft chapter dealing with it.” (Tómasson et al.)
In other words, Keynes could not determine the total monetary profit for the economy as a whole which is the foundational magnitude of all economics. Neither could the Post Keynesians or the Anti-Keynesians in the past 80+ years.
As a political busybody, Keynes lacked a deeper understanding of mathematics but Lars Syll maintains: “With his profound knowledge of mathematics, Keynes realized the limits of its applicability to the real world — and that it was certainly not enough for a relevant social science to prove things about thought up worlds.” (See intro)
The question of the limits of the applicability of mathematics to the real world is absurd in the context of economics because economists can not even determine the total monetary profit of the business sector of a national economy which is given as the sum of profits and losses of all firms that constitute the economy. There is nothing more empirical and mathematical than total monetary profit. Yet, with the simple task of calculating it, economists are already at their intellectual limit.
Heterodoxy is by no means more competent than Orthodoxy. All heterodox profit theories are provably false.#1
Economists not only lack a proper understanding of the role of mathematics in science but of science, in general.#2 Lars Syll, the methodological spokesperson of Heterodoxy maintains: “As social scientists we should never equate science with mathematics and statistical calculation. All science entail human judgment, and using mathematical and statistical models don’t relieve us of that necessity. They are no substitutes for doing real science.”
What Heterodoxy overlooks is that economics is NOT a social science. All Human-Nature issues are the subject matter of other disciplines (psychology, sociology, anthropology, biology/Darwinism, political science, social philosophy, history, etcetera) and are taken in from these by way of multi-disciplinary cooperation. NOT human behavior is the subject matter of economics but the behavior of the economy. Economics is not a social science but a systems science.
Economics is not only in need of a Paradigm Shift from false Walrasian microfoundations but also from false Keynesian macrofoundations. The whole of economics has to be put on objective (= behavior-free), consistent and measurable macrofoundations.#3 This is the precondition for the productive application of mathematics.#4
Economics is still at the stage where Bagehot found it in 1885 with orthodox folks restlessly building models out of NONENTITIES on the one side and clueless heterodox realists on the other exchanging their idiotic arguments about mathematics and science: “It [Political Economy] is an abstract science which labours under a special hardship. Those who are conversant with its abstractions are usually without a true contact with its facts; those who are in contact with its facts have usually little sympathy with and little cognisance of its abstractions. Literary men who write about it are constantly using what a great teacher calls ‘unreal words’ — that is, they are using expressions with which they have no complete vivid picture to correspond. They are like physiologists who have never dissected; like astronomers who have never seen the stars; and, in consequence, just when they seem to be reasoning at their best, their knowledge of the facts falls short. Their primitive picture fails them, and their deduction altogether misses the mark — sometimes, indeed, goes astray so far, that those who live and move among the facts boldly say that they cannot comprehend ‘how any one can talk such nonsense.’ Yet, on the other hand, these people who live and move among the facts often, or mostly, cannot of themselves put together any precise reasonings about them.”
Economics, that is, Walrasianism, Keynesianism, Marxianism, and Austrianism, is still at the stage of vacuous and confused blather where Bagehot found it in 1885. The scientific incompetence of economists borders on idiocy.
Egmont Kakarot-Handtke
#1 Heterodoxy, too, is proto-scientific garbage
#2 For details of the big picture see cross-references Math/Mathiness
#3 For details of the big picture see cross-references Paradigm Shift
#4 See the First Economic Law on Wikimedia AXEC06
