## Deductivism — the original sin in economics

2 February, 2016 at 10:27 | Posted in Economics | 2 CommentsMathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for

possible realities …This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics. Researchers involved with mathematical projects in economics could, for the time being at least, postpone the day of interpreting their preferred axioms and assumptions. There was no longer any need to seek the blessing of mathematicians and physicists or of other economists who might insist that the relevance of metaphors and analogies be established at the outset. In particular it was no longer regarded as necessary, or even relevant, to economic model construction to consider the nature of social reality, at least for the time being …

The result was that in due course deductivism in economics, through morphing into mathematical deductivism on the back of developments within the discipline of mathematics, came to acquire a new lease of life, with practitioners (once more) potentially oblivious to any inconsistency between the ontological presuppositions of adopting a mathematical modelling emphasis and the nature of social reality. The consequent rise of mathematical deductivism has culminated in the situation we find today.

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Incompetence — the original sin in economics

Comment on ‘Deductivism — the original sin in economics’

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Tony Lawson summarizes: “This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics.”

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This is not quite accurate, the mathematization of economics started before Hilbert’s general axiomatization of mathematics: “… economists have long been mathematicians without being aware of the fact. The unfortunate result is that they have generally been bad mathematicians, and their works must fall. Hence the explicit recognition of the mathematical character of the science was an almost necessary condition of any real improvement of the theory.” (Jevons, 1871, PS. 13)

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The axiomatization of economics started even earlier “To Senior belongs the signal honor of having been the first to make the attempt to state, consciously and explicitly, the postulates that are necessary and sufficient in order to build up … that little analytic apparatus commonly known as economic theory, or to put it differently, to provide for it an axiomatic basis.” (Schumpeter, 1994, p. 575)

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Where Tony Lawson is right is that economists messed the whole thing up, and this resulted in the ongoing ridiculous mathiness discussion.

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The key of formalization, axiomatics, or mathiness is “Formal axiomatic systems must be interpreted in some domain … to become an empirical science.” (Boylan et al., 1995, p. 198)

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Now, Debreu did explicitly the very opposite, that is, he disconnected “Allegiance to rigor dictates the axiomatic form of the analysis where the theory, in the strict sense, is logically entirely disconnected from its interpretations.” (Debreu, 1959, p. x)

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It is well-known from where Debreu got his methodological inspiration “It seems clear that Debreu intended his Theory of Value to serve as the direct analogue of Bourbaki’s Theory of Sets, right down to the title.” (Weintraub, 2002, p. 121)

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Now, it is pretty obvious that Debreu missed the crucial point of Bourbaki’s axiomatics. “From the axiomatic point of view, mathematics appears thus as a storehouse of abstract forms — the mathematical structures; and it so happens — without our knowing why — that certain aspects of empirical reality fit themselves into these forms, as if through a kind of preadaptation. … It is only in this sense of the word ‘form’ that one can call the axiomatic method a ‘formalism’.” (Bourbaki, 2005, p. 1276)

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It was quite clear to Bourbaki that NOT ALL mathematical structures incorporate ‘certain aspect of empirical reality’, which means, that there is a “… whole crop of monster-structures, entirely without application” (Bourbaki, 2005, p. 1275, fn. 9).

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Hence, Debreu’s axiomatization of Walrasian General Equilibrium is a monster-structure that is due to Debreu’s misunderstanding of Bourbaki. It is NOT the axiomatic-deductive method that is wrong, it is neoclassical economics that is wrong.

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Generally, it can be said that the so-called social scientists cannot get their head around the essentials of the scientific method. Tony Lawson is one of them. It is quite obvious that no genuine scientist ever abused the axiomatic-deductive method by declaring green-cheese assumptions like constrained optimization and equilibrium as axioms. In marked contrast, economists never had any scruples to make fools of themselves: “most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point” (Krugman).

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Einstein explained in a short paragraph what the so-called social scientist do not understand until this very day “The basic concepts and laws which are not logically further reducible constitute the indispensable and not rationally deducible part of the theory [= axioms]. It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” (Einstein, 1934, p. 165)

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Note that Einstein treats axioms and experience as two sides of the same coin — just like Bourbaki — no disconnect here!

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The fact of the matter is that both orthodox and heterodox economists have not been very skilled users of the scientific method up to now. This explains why economics is a failed science since more than 200 years.

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Egmont Kakarot-Handtke

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References

Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From

Kant to Hilbert. A Source Book in the Foundations of Mathematics, volume II,

pages 1265–1276. Oxford, New York, NY: Oxford University Press. (1948).

Boylan, T. A., and O’Gorman, P. F. (1995). Beyond Rhetoric and Realism in Economics. Towards a Reformulation of Economic Methodology. London: Routledge. Debreu, G. (1959). Theory of Value. An Axiomatic Analysis of Economic Equilibrium. New Haven, London: Yale University Press.

Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science,

1(2): 163–169. URL http://www.jstor.org/stable/184387.

Jevons, W. S. (1871). The Theory of Political Economy. Library of Economics and

Liberty. URL http://www.econlib.org/library/YPDBooks/Jevons/jvnPE.html.

Schumpeter, J. A. (1994). History of Economic Analysis. New York, NY: Oxford

University Press.

Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, NC, London: Duke University Press.

Comment by Egmont Kakarot-Handtke— 2 February, 2016 #

Just to point out a small ‘sin’ of Lawson’s. What he calls ‘mathematical deductivism’ is deductivism that employs what Keynes calls ‘pseudo-mathematics’. It might be better to call it ‘pseudo-mathematical deductivism’. In defense of Hilbert, it is also worth noting that he was trying to develop an alternative to sloppy deductivism. It would be good to know how his work got so badly mis-interpreted.

Comment by Dave Marsay— 2 February, 2016 #