Axiomatics in the proofs of existence of a general equilibrium, by Arrow and Debreu.

Summary This work attempts to show that the 1940s and 1950s witnessed a profound epistemological revolution in economics, at least as important as the "Keynesian revolution". This revolution led to the emergence of an axiomatic style of thinking. The integration of the axiomatic method in economics leads to the separation of the logical structure of the theory from its possible interpretations, Debreu's monograph (1959) constituting the canonical model of this separation for the discipline of economics. From this separation, two different points of view emerge within general equilibrium models: an economic point of view and an axiomatic (or mathematical) point of view. Each of these points of view is linked to its own development logic. The logic of axiomatic development pushes us to reduce the number of hypotheses or, at least, to weaken them, in order to propose the most general theorems possible. The logic of economic development, on the other hand, leads to the search for realistic hypotheses that reinforce the economic relevance of the model. This double logic leads to a permanent tension in the economist's theoretical activity. Indeed, the mathematical generalization of theorems leads, in some cases, to interpretations that are not in line with economic intuition, or may contribute to obscuring their economic meaning. We lose in understanding what we gain in extension. The example of the 1954 article by Kenneth Arrow and Gérard Debreu illustrates this essential tension in the axiomatic style of thinking in economics.