December 30, 2014

What engine?

Fourth comment on 'Proper use of math in economics'

Blog-Reference

The utilitarist's view of mathematics:
“Use mathematics as a short-hand language, rather than as an engine of inquiry.” (Marshall, see intro)

The scientist's view of mathematics/formalization/axiomatization:
“Formalisation was not to be merely a mechanical check on the integrity of scientific reasoning, but through the process of axiomatisation, mathematics was to be an engine of discovery.” (Weintraub, 1998, p. 1844), see also (Suppes, 1968, p. 653)

Having declined the tried and tested ‘engine of inquiry’ it does not come as a surprise that Marshall discovered nothing of scientific value but instead became the hero of those who are enthusiastic about the Cambridge methodology of common sense and loose verbal reasoning.

What Marshall took home from the Tripos was that mathematics is good for saving ink. This is as far beside the point as can be. The whole question is about methodology and the point of mathematics/formalization/axiomatization is:

“The procedure of the axiomatic method, as it is expressed here, amounts to a deepening of the foundations of the individual domains of knowledge – a deepening that is necessary for every edifice that one wishes to expand and to build higher while preserving its stability.” (Hilbert, 2005, p. 1109)

I, too, agree with Paul Schächterle. Those who do not intend to build higher but are happy in the scientific slums do not need any mathematics/formalization/axiomatization. All others are indeed happy that they do not get out there but gather around the Marshall monument.

Egmont Kakarot-Handtke


References
Hilbert, D. (2005). Axiomatic Thought. In W. Ewald (Ed.), From Kant to Hilbert. A
Source Book in the Foundations of Mathematics, volume II, pages 1107–1115.
Oxford, New York, NY: Oxford University Press. (1918).
Suppes, P. (1968). The Desirability of Formalization in Science. Journal of
Philosophy, 65(20): 651–664.
Weintraub, E. R. (1998). Controversy: Axiomatisches Mißverständnis. Economic
Journal, 108(451): 1837–1847. URL