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

The Mathematical Turn in Economics: Walras, the French Mathematicians, and the Road Not Taken

“…As for Walras, it is well known that he clung to Poinsot’s Statics as his vade mecum to physics throughout his entire adult life (Turk 2006, pp. 200–201).…”

“…Darboux, Tannery, Poincare, and Picard. As to Borel, Walras expressed some concern that Borel had not yet written to him, but took him to be approving as well, on the basis of Renard's own opinion. And, to the extent that a framework for mathematics might be applied to economics, Walras' own comprehension of the uses of mathematics in mechanics inclined him to view it as offering up an axiomatic structure, even though that structure and its primitives were actually dependent upon an analogy with classical mechanics (Turk 2006). And, to the extent that a framework for mathematics might be applied to economics, Walras' own comprehension of the uses of mathematics in mechanics inclined him to view it as offering up an axiomatic structure, even though that structure and its primitives were actually dependent upon an analogy with classical mechanics (Turk 2006).…”

“…The inclination not to modify the program of economics may reflect as well a seemingly commonsensical understanding about the nature of science and the role of mathematics in it, where mathematics, whether in physics or economics, was grasped intuitively as serving as a medium, whereby number, and hence quantification, in words enshrined by Tobias Dantzig, became “the language of science” (Dantzig 1930). And, to the extent that a framework for mathematics might be applied to economics, Walras’ own comprehension of the uses of mathematics in mechanics inclined him to view it as offering up an axiomatic structure, even though that structure and its primitives were actually dependent upon an analogy with classical mechanics (Turk 2006). This was quite distant and distinct from the conventionalism that characterized Poincare’s mathematical thought, where experience and imagination shaped mathematical concepts rather than being shaped by idealized principles and primitives, and influenced the choice of hypotheses that might be fitted to a given set of facts (Heinzmann and Nabonnand 2008).…”