The Existence Paradigm and the Antinomy of the Liar in Mathematical Economics

Abstract

Early contributions in Walrasian general equilibrium analysis led to logical problems that are remnants of the foundations debate in mathematics. The problem of existence of equilibrium in a competitive economy was at the core of this research program. This was however a loaded question since it admits different methodological approaches and interpretations. By tracing back the problem to the foundations of mathematics this paper aims to identify logical implications of the existence paradigm in Walrasian theory. Grounded on a bird’s eye overview of the history of ideas in early mathematical economics, the distinction is made between different interpretations of the question in relation with axiomatics and models of competitive economies. This leads to the conclusion that in general equilibrium theory, the problem set to provide consistency or existence proofs entails logical implications about the antinomy of liar and the rationale of doctrines in economics.