January 21, 2016

Full methodological illiteracy

Comment on Asad Zaman on ‘Axiomatic economics — the Bourbaki-Debreu delusion’

Blog-Reference

Asad Zaman interprets the history of science thus: “The scientific method arose as a rejection of the axiomatic method used by the Greeks for scientific methodology. It was this rejection of axiomatics and logical certainty in favour of empirical and observational approach which led to dramatic progress in science.”

Zaman’s understanding of methodology is substandard, to say the least. It is a widely known fact that modern physics is unthinkable without the prior move from Euclidean to non-Euclidean axioms. The following quotes speak for themselves and they say exactly the opposite of Zaman.

“This seemingly pre-established harmony between the mathematics and the subsequent physics has been a cause for puzzlement among historians and philosophers of science. One example of such a coincidence is the relationship between the mathematics of Hilbert space and the formulation of Quantum Mechanics. Another very good example is the development of Riemannian Geometry prior to the emergence of GTR. It was as if Gauss, Riemann, Ricci and Levi-Civita had Einstein in mind when constructing their non-Euclidean geometries.” (Zahar, 1980, p. 4)

“A complete system of theoretical physics consists of concepts and basic laws to interrelate those concepts and of consequences to be derived by logical deduction. It is these consequences to which our particular experiences are to correspond, and it is the logical derivation of them which in a purely theoretical work occupies by far the greater part of the book. This is really exactly analogous to Euclidean geometry, except that in the latter the basic laws are called ‘axioms’; and, further, that in this field there is no question of the consequences having to correspond with any experiences. But if we conceive Euclidean geometry as the science of the possibilities of the relative placing of actual rigid bodies and accordingly interpret it as a physical science, and do not abstract from its original empirical content, the logical parallelism of geometry and theoretical physics is complete.” (Einstein, 1934, pp. 164-165)

“Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced.” (Feynman, 1992, p. 50)

For anyone who can read, this does not sound like a ‘rejection of axiomatics’ by cutting-edge physics. Neither did Einstein ever reject ‘the axiomatic method used by the Greeks’. Just the contrary!

“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)

For ancients read ancient Greeks, the inventors of science and the axiomatic-deductive method: “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. (Aristotle, Posterior Analytics).

With Zaman’s methodology, Heterodoxy will not produce any scientific knowledge of anything.

Egmont Kakarot-Handtke


References
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.
Zahar, E. (1980). Einstein, Meyerson and the Role of Mathematics in Physical Discovery. The British Journal for the Philosophy of Science, 31(1): 1–43. URL

Related 'Axiomatics — the heterodox bugbear' and 'Bagehot’s wisdom and the silliness of modern economists' and 'Economists’ slapstick methodology' and 'Lousy scientists'

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REPLY Heterodoxy methodology — back to the future, comment on Bruce Wilder on Jan 22

You propose “to grant broad assent to Alan Kirman.” Since Kirman gives a condensed version of the well-researched history of General Equilibrium Theory (Ingrao et al., 1990) there cannot be anything other than assent.

The point is, what are the conclusions of the demise of GET? Basically we have two:
(i) Paradigm shift: “There is another alternative: to formulate a completely new research program and conceptual approach. As we have seen, this is often spoken of, but there is still no indication of what it might mean.” (Ingrao et al., 1990, p. 362)
(ii) To abandon the axiomatic-deductive method because “It was this rejection of axiomatics and logical certainty in favor of empirical and observational approach which led to dramatic progress in science.” (Zaman)

It should be clear to everyone by now that there is no such thing as a choice or trade-off between logical and material consistency. Science requires always both “Research is in fact a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant, 1994, p. 31)

Since the axiomatic-deductive method guarantees logical consistency it cannot be abandoned. But alone it is insufficient. The results of axiomatic-deductive operations must be observable (=material consistency).

By the way, has Zaman ever heard that the concept of Atom goes back to the ancient Greeks and does he think that they derived it from observation? Or does he think that Plank saw a Quantum under the microscope? Galileo did not figure out the Law of the Falling Bodies empirically by jumping off the tower of Pisa but by first studying Euclid.

Zaman’s naive realism/empiricism is not a tenable methodological position. It is outdated since more than 2500 years.*

Conclusion: The demise of GET (and by consequence RBC, DSGE etc) makes a paradigm shift, i.e. a replacement of the axiomatic foundations of economic theory, necessary. That is the proper task of Heterodoxy.


References
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the History of Science. Cambridge, MA, London: MIT Press.
Klant, J. J. (1994). The Nature of Economic Thought. Aldershot, Brookfield, VT: Edward Elgar.

* See ‘Bagehot’s wisdom and the silliness of modern economists

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REPLY Comment on Silwyson of Jan 27

You comment on my post: “You have glossed over an important part of your Einstein quote: “experience of course remains the sole criterion of the serviceability of a mathematical construction ...”

Be sure that I have chosen this quote exactly because Einstein clarifies here in one brief statement the relationship between empiricism and formalism.

For more details about the correct understanding of methodology see ‘How to restart economics

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REPLY Comment on Silwyson of Jan 30

You say “Economists do not understand science.” Yes, indeed, but this includes Zaman and you. You cite Aristotle and Galileo, so let us look closely into the matter.

Roughly speaking, Aristotle put the Law of Motion thus: every body moves to his natural place of rest. Then he took a stone and threw it skywards. The stone came down some meters away. Never in the history of mankind had a law better been empirically tested and confirmed without exception.

Against this, Galileo said, roughly, every body moves in a straight line until eternity. An empirical proof could not be given until space flight was possible.

Nevertheless, this counter-intuitive assertion reappears as the first axiom of motion in Newton’s Principia. (Axiomata Sive Leges Motus, Wikipedia)

And this is what Galileo told naive empiricists and commonsensers and brain-dead realists about the essence of science: “I shall never be able to express strongly enough my admiration for the greatness of mind of these men who conceived this [heliocentric] hypothesis and held it to be true. In violent opposition to the evidence of their own senses and by sheer force of intellect, they preferred what reason told them to that which sense experience plainly showed them ... I repeat, there is no limit to my astonishment when I reflect how Aristarchus and Copernicus were able to let conquer sense, and in defiance of sense make reason the mistress of their belief.” (quoted in Popper, 1994, p. 84)


References
Popper, K. R. (1994). The Myth of the Framework. In Defence of Science and Rationality., chapter Science: Problems, Aims, Responsibilities, pages 82–111. London, New York, NY: Routledge.