June 21, 2017

Morons on math

Comment on Lars Syll on ‘Simpson’s paradox’


A theory is the humanly best mental representation of reality. A theory is fundamentally different from a commonsensical description of reality.

A theory must satisfy two criteria in order to be accepted to the corpus of scientific knowledge: material and formal consistency. Logical consistency is secured by applying the axiomatic-deductive method and empirical consistency is secured by applying state-of-the-art testing.

For the refutation of a theory, it suffices to demonstrate that it is either logically or empirically inconsistent. We know by now that economics is both. The current state is this: the four main approaches ― Walrasianism, Keynesianism, Marxianism, Austrianism ― are mutually contradictory, axiomatically false, materially/formally inconsistent, and all got profit wrong. With the pluralism of provably false theories economics sits squarely at the proto-scientific level.

Economics is a failed science and this proves first of all that BOTH orthodox and heterodox economists are incompetent scientists. They do not even understand what science is all about. Feynman called these people cargo cult scientists.

Cargo cult scientists are easy to spot because they talk often about methodology, i.e. how to do science properly, and what they say is glaring nonsense. Paul Romer is a case in point: “Math cannot establish the truth value of a fact. Never has. Never will.”

No, because scientific truth is defined by material AND formal consistency, and math is supposed to guarantee formal consistency. And this is what it has done so admirably throughout history ― except in economics. This, though, is not the fault of math but of economists.

Scientists know that math works but they are not sure why: “At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” (Einstein, 1921), see also (Wigner, 1979), (Velupillai, 2005)

“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)

“The method of reasoning by chains of syllogisms is nothing but a transformation mechanism, applicable just as well to one set of premises as to another; it could not serve therefore to characterize these premises. In other words, it is the external form which the mathematician gives to his thought, the vehicle which makes it accessible to others, in short, the language suited to mathematics; this is all, no further significance should be attached to it.” (Bourbaki, 2005)

Genuine scientists know how to use math to their advantage, economists=cargo cult scientists don’t. In very general terms it can be said that economists fail because of the Fallacy of Insufficient Abstraction. What economist have not yet understood is that the subject matter of economics is not Human Nature/behavior/action but the behavior of the economy. Economics is NOT a social science but a system science.

The economy, i.e. the subject matter of economics, is an abstraction that has to be clearly defined by a set of premises, a.k.a. foundational propositions, a.k.a. axioms. Without clear premises all conclusions are for the waste basket, the whole argument is scientifically worthless, and economic policy guidance has no sound scientific foundation.

When the premises are not correctly defined mathematics cannot work its magic and as a collateral damage econometrics becomes a senseless exercise. When utility maximization is put into the premises no testable proposition ever results. Economists do not understand this elementary methodological fact since 140+ years.

It is not so that mathematics or standard statistical methods are inapplicable in economics. The failure of economics is uniquely and exclusively caused by the scientific incompetence of economists. The ultimate reason why economics never rose above the proto-scientific level is that it is built upon false premises. As Aristotle put it: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.”

In the last 200+ years, neither orthodox nor heterodox economists have produced scientific knowledge of their thing. They do not even understand the elementary mathematics of accounting.*

Egmont Kakarot-Handtke

* See for example ‘The final implosion of MMT’ and ‘How Keynes got macro wrong and Allais got it right

For details of the bigger picture see cross-references Math/Mathiness