Blog-Reference and Blog-Reference on Feb 5 and Blog-Reference on Jul 23, 2019
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.”
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)
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)
Where Tony Lawson is right is that economists messed the whole thing up, and this resulted in the ongoing ridiculous mathiness discussion.
The key to 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)
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)
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 analog of Bourbaki’s Theory of Sets, right down to the title.” (Weintraub, 2002, p. 121)
Now, it is pretty obvious that Debreu missed the crucial point of Bourbaki’s axiomatic: “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)
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)
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.
Generally, it can be said that the so-called social scientists cannot get their heads 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).
Einstein explained in a short paragraph what the so-called social scientists do not understand to 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)
Note that Einstein treats axioms and experience as two sides of the same coin — just like Bourbaki — no disconnect here!
The fact of the matter is that both orthodox and heterodox economists have not been very skilled users of the scientific method to this day. This explains why economics is a failed science for more than 200 years.
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, 1265–1276. Oxford, New York: 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
Jevons, W. S. (1871). The Theory of Political Economy. Library of Economics and Liberty. URL
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.
***REPLY to Calgacus on Jul 23, 2019
You say: “The logical faintness of these damns amounts to praise of neoclassical economics. So they have nothing to worry about from this kind of both overblown and inadequate critique.”
Frank Hahn was always very happy with the incompetent critics of the neoclassical research program: “The enemies, on the other hand, have proved curiously ineffective and they have very often aimed their arrows at the wrong targets.”
Related 'The stupidity of Heterodoxy is the life insurance of Orthodoxy.'