Varieties of Mathematics in Economics

Abstract

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics have come to be used in the formalization of mathematics in more recent years. These other varieties, I claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper I discuss aspects of the way real analysis dominates the mathematical formalizations of economic theory and the prospects for overcoming this dominance.