Money, Banks and Finance in Economic Thought

Axiomatizing economics in action: John von Neumann, 1928-1937

Carvajalino Juan, Université Paris 8, Vincennes-Saint-Denis

This is a project on the history of the axiomatic method as brought into economics by John von Neumann during the mid-1930s with an emphasis on his 1937 paper A Model of General Economic Equilibrium. In that paper, von Neumann constructed a system of linear equations and inequalities, which characterized the equilibrium of a continuously growing economy. The mathematical aspects of that paper were only accessible to professional mathematicians. Despite this, in the postwar period, it had a tremendous influence in the development of certain branches of economics and, more generally, in the rise of mathematical economics. Von Neumann’s paper also became an emblematic expression of the axiomatic method in economics, which is often described as a method of pure mathematical formalism, as opposed to (economic) meaning. Heavily based on archival material that has remained unexplored by commentators of von Neumann’s work in economics, this project aims at reconstructing the set of practices that led von Neumann to build his growth model paper. For this purpose, the notes and drafted models found in his archives, which anteceded the publication of his 1937 paper, are discussed in length and taken as reflections of his evolving practices in mathematical economics, and hence as reflections of his axiomatic method in economics in action. As a result, the standard divide attached to von Neumann’s axiomatic method in economics between formalism and meaning is nuanced. It is claimed that while the end product appears as a mathematical piece where emphasis definitely lays on the structural makeup of mathematical forms, the process of axiomatizing reveals a much greater emphasis on economic meaning.

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Keywords: John von Neumann, practice, axiomatic method, meaning, formalism