The fault line of axiomatization: Walras' linkage of physics with economics

Abstract

Economists have often aligned the field of economics with physics; in the process seeking to enhance the rigor of economics by mathematizing it. In the late nineteenth century there was no more ardent champion of this view of what economics should become than Leon Walras. His own writings, though, betray a tension between comprehending this mathematization as proceeding in parallel with physics or through a metaphorical analogy with physics. The limitations in Walras' ability to axiomatize economics reveal a flawed effort to establish the foundations of economics by analogy; this difficulty has persisted through the twentieth century.

Keywords:

• Leon Walras
• neo-classical economic thought through 1925
• economic methodology
• economic equilibrium
• relation of economics to other disciplines

Notes

1 See, for example, Paul Krugman's column depicting rent control as attempting to defy the law of gravity, that is, the laws of supply and demand; The New York Times, 7 June 2000.

2 Charles Lyell's Principles of Geology, which first appeared in 1830, emphasized the great length of time over which the earth had changed, hence giving geology a history and making it subject to historical law. Darwin, for his part, relied upon Lyell's contention in advancing the notion of natural selection; see Darwin (1998: 127).

3 In the tradition of, say, P.-S. Laplace's (1824) highly popular recasting of his own work in astronomy, Exposition du Système du Monde, which then proved to be quite influential across a broad intellectual community. Walras' use of the term, ‘system of the world’, to characterize the scope of general economic equilibrium may well have been drawn from Laplace, even if its ultimate source was Newton.

4 See Mirowski 1988, Mirowski and Cook 1990.

5 Paul Samuelson (1983) 1947. Foundations of Economic Analysis. The motto reads: ‘Mathematics is a Language’. See also Samuelson's adaptation of LeChatelier's principle in physical chemistry to economics, which he validates in the following footnote: ‘This is a purely mathematical theorem’, p. 38.