October 21, 2016

Wicksell’s misplaced critique of mathematics

Comment on Lars Syll on ‘On the proper use of mathematics in economics’


Wicksell had no qualms to apply: (i) marginalism, (ii) the supply-demand-equilibrium cross, (iii) the equalization of saving and investment.

All these concepts are provable false#1 and from this follows that Wicksell was one of the many incompetent scientists who tried their luck in economics but only piled up the heap of rubbish.

Wicksell argued: “It is, by the way, evident that the economic aspects must be the determining ones everywhere: economic truth must never be sacrificed to the desire for mathematical elegance.”

This is trivially true. Nonetheless, as it is framed, the argument is misleading because it suggests that economists already had the true theory and mathematicians gave it away for elegance. Clearly, this never happened. Economists in general and Wicksell in particular never had the true theory. What the mathematical economists in fact did was to formalize false theories with unsuitable mathemathics.

It is a bit surreal to observe that Wicksell, who applied all his life the logically defective concepts (i)/(iii), is nowadays presented as a forerunner of the mathiness critique which identifies math as the ultimate cause of all that is wrong with economics.

What exactly went wrong with the fusion of economics and mathematics? The mathiness blunder occurred because economists realized the analytical power of calculus and its pivotal role in physics and translated it into a behavioral axiom, i.e. “Agents independently optimize subject to constraints.” (HC2 in Weintraub, 1985). This, indeed, is the WRONG sequence.

“The mathematical language used to formulate a theory is usually taken for granted. However, it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. ... The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein, in Schmiechen, 2009, p. 368)

In other words, economics has to develop its own mathematical tools and not to grab them from other disciplines. The scientific incompetence of economists consists of the MISapplication of mathematics. More specifically, both Walrasian microfoundations and Keynesian macrofoundations are conceptually defective#2 and because of this mathematics cannot unfold its ‘unreasonable effectiveness’.

There is NO such thing as a Wicksellian trade-off between factual truth and mathematical elegance or, more generally, between relevance and rigor.

Egmont Kakarot-Handtke

#1 See ‘How Wicksell and the rest got inflation/deflation wrong
#2 For details see ‘From Orthodoxy to Heterodoxy to Sysdoxy