November 14, 2016

Heterodoxy’s popular but silly math denial

Comment on Lars Syll on ‘Formalized economics bordering on the insane’


It is well known that orthodox economics is misapplied math (Mirowski). The abuse has been criticized under the label mathiness but in fact, has a wider methodological dimension. The problem with economists is that they are cargo cult scientists: “... they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential.” (Feynman) What is missing is a deeper understanding of science and mathematics and the relation between the two.

Metaphorically speaking, scientists put first their trousers on and then their boots, economists do it the other way round: “The mathematical language used to formulate a theory is usually taken for granted. However, it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. ... The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein)

In the same vein: “Surely it would be considered absurd, bordering on the insane, if a surgical procedure was implemented because a tool for its implementation was devised by a medical doctor who knew and believed in topological fixed-point theorems?” (Velupillai, see intro)

The absurdity began with economists borrowing the tool ― calculus ― from physics and making a behavioral axiom out of it: “HC2 agents individually optimize subject to constraints.” (Weintraub) This has been the fundamental methodological mistake: the tool came first and the pivotal behavioral assumption was tailored to the tool.

Walras’s determination of general equilibrium was found wanting by mathematicians: “You know, Oskar, if those books are unearthed sometime a few hundred years hence, people will not believe they were written in our time. Rather, they will think that they are about contemporary with Newton, so primitive is their mathematics. Economics is simply still a million miles away from the state in which an advanced science is, such as physics.” (von Neumann) And this critique led eventually to the fixpoint theorem.

However, the formal rectification left Walras’s conceptual root structure unchanged: “It seems clear that Debreu intended his Theory of Value to serve as the direct analog of Bourbaki's Theory of Sets, right down to the title. ... But this required one very crucial maneuver that was nowhere stated explicitly: namely, that the model of Walrasian general equilibrium was the root structure from which all further scientific work in economics would eventuate.” (Weintraub)

Walras’s root structure is defined with this 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)

Two things should be obvious: (i) the axiom set contains three nonentities (HC2, HC4, HC5) and is therefore forever unacceptable, and (ii), when the conceptual root structure is false then it does not help much to express it in set-theoretical terms. Formalization does not make a false behavioral assumption like utility maximization true.

When the elementary framework of concepts consists of economic nonentities then no amount of formalization helps and math cannot unfold its specific strength. Physics took off not until the foundational concepts of energy, mass, force, velocity, acceleration, etcetera were clearly defined and properly understood.

Economics is still at the proto-scientific level and the representative economist cannot even tell the difference between profit and income.#1 In order to get out of utter confusion and to put economics on firm ground formalization is indispensable: “I mean by this that formalization eliminates provincial and inessential features of the way in which a scientific theory has been thought about. ... Formalization is a way of setting off from the forest of implicit assumptions and the surrounding thickness of confusion, the ground that is required for the theory being considered. ... In areas of science where great controversy exists about even the most elementary concepts, the value of such formalization can be substantial.” (Suppes)

Orthodoxy has misapplied formalization and traditional Heterodoxy has never been able to put it to good use. With incompetent scientists, it is no wonder that economics is a failed science. As long as Heterodoxy insists on storytelling and is unable to apply the enormous leverage of mathematics it will not get out of its proto-scientific burrow.

With regard to mathiness holds: from the misapplication of Orthodoxy does not follow the non-application of traditional Heterodoxy but the proper application of constructive Heterodoxy.#2

Egmont Kakarot-Handtke

#1 Profit and the collective failure of economists
#2 For the complete and consistent set of foundational equations see cross-references Paradigm Shift.

For details of the big picture see cross-references Heterodoxy and cross-references Math/Mathiness.