March 21, 2017

How economists shoot themselves non-stop in the methodological foot

Comment on Lars Syll on ‘The man who crushed the mathematical dream’

Blog-Reference and Blog-Reference on Mar 24

Heterodoxy tells the world that Orthodoxy is unacceptable. In this general sense, Heterodoxy is absolutely right. What is annoying about Heterodoxy is that it rejects Orthodoxy mostly for the wrong reasons and, worst of all, that it has never developed a superior alternative: “… we may say that … the omnipresence of a certain point of view is not a sign of excellence or an indication that the truth or part of the truth has at last been found. It is, rather, the indication of a failure of reason to find suitable alternatives which might be used to transcend an accidental intermediate stage of our knowledge.” (Feyerabend)

One of the most idiotic arguments against Orthodoxy is that it applies the axiomatic-deductive method. The fault in this argument consists in the fact that not the method is false but that the orthodox axioms are false. Standard economics is built upon this set of hard core propositions: “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)

This set of behavioral axioms consists of three NONENTITIES (HC2, HC4, HC5) and the simple fact of the matter is that a theory/model that is based on a nonentity is a priori false. So, Orthodoxy is axiomatically false, which is the death sentence for a paradigm.

Now, Lars Syll argues “any such deductive-axiomatic economics will always consist of some undecidable statements. When not even being able to fulfill the dream of a complete and consistent axiomatic foundation for mathematics, it’s totally incomprehensible that some people still think that could be achieved for economics.”

Gödel tells us something about the limits of mathematical axiom sets. These limits are irrelevant for economics just as it is irrelevant for a snail to learn that it cannot surpass the speed of light. The problem of economists is that they cannot apply elementary mathematics correctly. And it is an absurdity of sorts when people who cannot put 2 and 2 together invoke Gödel’s theorem.#1

Economists need elementary arithmetic and algebra and for these bread-and-butter applications Gödel’s theorem is absolutely irrelevant.

From the indisputable fact that both orthodox and heterodox economists do not apply the axiomatic-deductive method correctly does NOT follow that the method is defective but that both orthodox and heterodox economists are scientifically incompetent.

The situation in economics is this: the false Walrasian microfoundations and the false Keynesians macrofoundations have to be replaced by true macrofoundations.#2 The first methodological rule of economics says: If it isn’t macro-axiomatized, it isn’t economics.

Egmont Kakarot-Handtke

#1 See also ‘Economics, Gödel, and a would-be field day for math-Luddites’ and ‘The insignificance of Gödel’s theorem for economics’ and ‘It's all over — but for whom?’ and ‘Still in the woods
#2 See cross-references Axiomatization

Related 'From Hilbert’s hotel to Hilbert’s method' and 'The irrelevance of economics' and 'Switching into constructive gear' and 'What engine?' and 'At the Robinson Line' and 'The father of modern economics and his imbecile kids' and 'Where economics went wrong' and 'The end of traditional Heterodoxy in the Malmö coal pit'

COPY of Blissex's post

March 27, 2017 at 12:58 am
«no matter what system is chosen, there will always have to be other axioms to prove previously unproved truths»
Oh please this is a decades old huge misunderstanding: Gödel two theorems don’t state anything like that, or anything of wider philosophical importance, they are just narrow technicalities, that say more or less that a mathematical system cannot be used as its own own proof theory to prove that all its own true theorems are provable in it (completeness) and that none of its own false theorems are provable in it (consistency). It is a technicality of interest only for the historical purpose of discussing Hilbert’s programme, and in particular Hilbert’s hope that finitary (in the induction sense, not the size of proof sense) proofs of arithmetic would be possible.
The two subsequent theorems by Gentzen are far more interesting on the topic of the difference between logical provability and logical truth, even if still fairly technical, and they much generalize Gödel two theorems by showing that to prove the completeness and consistency of a mathematical system is possible but only using a system with strictly higher order induction. That has nothing to do with «other axioms to prove previously unproved truths» even if there is a vague similarity.
The Gentzen theorems while quite interesting pose no wider philosophical questions or have any implications like «such deductive-axiomatic economics will always consist of some undecidable statements».
PS A very little noticed detail about Gödel and Gentzen’s theorems is that they are about whether consistency and completeness of a mathematical system can be proven, not whether the mathematical system is in fact complete and consistent