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Varieties of Mathematics in Economics- A Partial View

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  • K. Vela Velupillai
  • Shu G. Wang

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, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.

Suggested Citation

  • K. Vela Velupillai & Shu G. Wang, 2010. "Varieties of Mathematics in Economics- A Partial View," ASSRU Discussion Papers 1015, ASSRU - Algorithmic Social Science Research Unit.
  • Handle: RePEc:trn:utwpas:1015
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    1. Domenico Delli Gatti & Mauro Gallegati & Hyman P. Minsky, 1994. "Financial Institutions, Economic Policy, and the Dynamic Behavior of the Economy," Economics Working Paper Archive wp_126, Levy Economics Institute.
    2. Roger Sandilands, 2009. "Hawtreyan Credit Deadlock or Keynesian Liquidity Trap? Lessons for Japan from the Great Depression," Working Papers 0904, University of Strathclyde Business School, Department of Economics.
    3. Hyman P. Minsky, 1992. "The Financial Instability Hypothesis," Economics Working Paper Archive wp_74, Levy Economics Institute.
    4. K. Velupillai, 1988. "Some Swedish Stepping Stones to Modern Macroeconomics," Eastern Economic Journal, Eastern Economic Association, vol. 14(1), pages 87-98, Jan-Mar.
    5. Ferri, Piero & Minsky, Hyman P., 1992. "Market processes and thwarting systems," Structural Change and Economic Dynamics, Elsevier, vol. 3(1), pages 79-91, June.
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