The unreasonable ineffectiveness of mathematics in economics

In this paper, I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalisations imply non-constructive and uncomputable structures. A reasonable and effective mathematisation of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilities. In the face of this, I conjecture that an economics for the future will be freer to explore experimental methodologies underpinned by alternative mathematical structures. The whole discussion is framed within the context of the celebrated Wignerian theme: The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Copyright 2005, Oxford University Press.

[1]  Hassan Masum.  Review of a new kind of science , 2002, SIGA.

[2]  Roberto Tamborini,et al.  The monetary transmission mechanism in Italy: the credit channel and a missing ring , 2001 .

[3]  Anil Nerode,et al.  The Introduction of Non-Recursive Methods into Mathematics* , 1982 .

[4]  J. Keynes.  The Economic Possibilities of Our Grandchildren , 1987 .

[5]  Jack Schwartz,et al.  The Pernicious Influence of Mathematics on Science , 1992 .

[6]  Yiannis N. Moschovakis,et al.  Notes On Set Theory , 1994 .

[7]  Heinz D. Kurz,et al.  Sraffa and the Mathematicians: Frank Ramsey and Alister Watson , 2000 .

[8]  Herbert E. Scarf,et al.  Mathematical Programming and Economic Theory , 1990, Oper. Res..

[9]  Luitzen Egbertus Jan Brouwer.  An intuitionist correction of the fixed-point theorem on the sphere , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  John Maynard Keynes,et al.  The economic consequences of Mr. Churchill , 1925 .

[11]  Marco Bee,et al.  FIRMS' BANKRUPTCY AND TURNOVER IN A MACROECONOMY , 2004 .

[12]  Charles S. Peirce,et al.  Reasoning and the Logic of Things. The Cambridge Conferences Lectures of 1898 , 1994 .

[13]  L. Bonatti,et al.  Profit versus Nonprofit Firms in the Service Sector: A Formal Analysis of the Employment and Welfare Implications , 2005 .

[14]  Ralph E. Gomory,et al.  INTEGER PROGRAMMING AND PRICING , 1960 .

[15]  F. S.,et al.  A Mathematician's Apology , 1941, Nature.

[16]  K. Velupillai.  ECONOMICS AND THE COMPLEXITY VISION: CHIMERICAL PARTNERS OR ELYSIAN ADVENTURERS? , 2003 .

[17]  P. Sraffa.  Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory , 1960 .

[18]  H. Putnam,et al.  Reasoning and the Logic of Things. The Cambridge Conferences Lectures of 1898. , 1993 .

[19]  S. Burr.  The Unreasonable Effectiveness of Number Theory , 1993 .

[20]  Matteo Ploner,et al.  The Financial Markets and Wealth Effects on Consumption: an Experimental Analysis , 2003 .

[21]  Giulia Felice,et al.  Dinamica strutturale e occupazione nei servizi , 2003 .

[22]  E. Hobson.  The Theory of Functions of a real Variable. , 1922 .

[23]  S. Smale.  Dynamics in General Equilibrium Theory , 1976 .

[24]  G. Hardy,et al.  What is Mathematics? , 1942, Nature.

[25]  K. Arrow,et al.  General Competitive Analysis , 1971 .

[26]  Peter D. Lax,et al.  From Cardinals to Chaos: Reflections on the Life and Legacy of Stanislaw Ulam , 1989 .

[27]  W. Bean.  Personal Knowledge: Towards a Post-Critical Philosophy , 1961 .

[28]  U. S. Naval.  The Art of Probability FOR SCIENTISTS AND ENGINEERS , 2003 .

[29]  D. Laugwitz,et al.  Eine Erweiterung der Infinitesimalrechnung , 1958 .

[30]  Roberto Tamborini,et al.  From Kuwait to Kosovo: what have we learned; reflections on globalization and peace , 2000 .

[31]  J. Thomison,et al.  Compared to what? , 1990, Journal of the Tennessee Medical Association.

[32]  P. Howitt,et al.  The Transactions Theory of the Demand for Money: A Reconsideration , 1978, Journal of Political Economy.

[33]  M. Shubik.  Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing , 1962 .

[34]  K. Vela Velupillai,et al.  Effectivity and constructivity in economic theory , 2002 .

[35]  E. Wigner.  The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint) , 1960 .

[36]  J. Schwartz.  Lectures on the Mathematical Method in Analytical Economics , 1961 .

[37]  Hubert Gabrisch,et al.  WHY IS TRADE BETWEEN THE EUROPEAN UNION AND THE TRANSITION ECONOMIES VERTICAL , 2002 .

[38]  E. Wigner.  Events, Laws of Nature, and Invariance Principles. , 1964, Science.

[39]  M. Polanyi.  Personal Knowledge: Towards a post-critical philosophy , 1959 .

[40]  R. Hamming.  The Unreasonable Effectiveness of Mathematics. , 1980 .

[41]  Newton C. A. da Costa,et al.  Gödel incompleteness in analysis, with an application to the forecasting problem in the social sciences , 1994 .

[42]  M. Shubik.  The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits , 1984 .

[43]  Gian-Carlo Rota,et al.  Discrete thoughts: Essays on mathematics, science, and philosophy , 1986 .

[44]  M. Leffler.  Bush's Foreign Policy , 2004 .

[45]  Richard W. Hamming,et al.  The Art of Probability for Scientists and Engineers , 1991 .

[46]  Is our mathematics natural? The case of equilibrium statistical mechanics , 1988 .

[47]  M. Pugno.  Under Tertiarisation and Unemployment , 2000 .

[48]  The Service Paradox and Endogenous Economic Growth , 2003 .

[49]  Arthur M. Lesk,et al.  The unreasonable effectiveness of mathematics in molecular biology , 2000 .

[50]  M. Pugno,et al.  The Underground Economy and the Underdevelopment Trap , 2002 .

[51]  Giuseppe Espa,et al.  Mappe di probabilità di sito archeologico : un passo avanti , 2003 .

[52]  H. Uzawa.  WALRAS' EXISTENCE THEOREM AND BROUWER'S FIXED-POINT THEOREM , 1962 .

[53]  Robin Gandy,et al.  The confluence of ideas in 1936 , 1988 .

[54]  J. Barkley Rosser,et al.  DYNAMICS OF MARKETS : ECONOPHYSICS AND FINANCE , 2006 .

[55]  Leslie Elliott Armijo,et al.  Compared to What? , 2006 .

[56]  Newton C. A. da Costa,et al.  The Incompleteness of Theories of Games , 1998, J. Philos. Log..