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The unreasonable ineffectiveness of mathematics in economics

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  • K. Vela Velupillai
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Oxford University Press in its journal Cambridge Journal of Economics.

    Volume (Year): 29 (2005)
    Issue (Month): 6 (November)
    Pages: 849-872

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    Handle: RePEc:oup:cambje:v:29:y:2005:i:6:p:849-872

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    1. Riccardo Fiorentini & Roberto Tamborini, 2001. "The Monetary Transmission Mechanism in Italy: The Credit Channel and a Missing Ring," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 60(1), pages 1-42, June.
    2. Tamborini Roberto, 2006. "Il contratto della docenza universitaria. Un problema multi-tasking," Rivista italiana degli economisti, Società editrice il Mulino, issue 1, pages 3-26.
    3. Maurizio Pugno, 2003. "The service paradox and endogenous economic growth," Department of Economics Working Papers 0301, Department of Economics, University of Trento, Italia.
    4. Marco Bee & Giuseppe Espa & Roberto Tamborini, 2002. "Firms’ bankruptcy and turnover in a macroeconomy," Department of Economics Working Papers 0203, Department of Economics, University of Trento, Italia.
    5. Matteo Ploner, 2003. "The financial markets and wealth effects on consumption - an experimental analysis," Department of Economics Working Papers 0306, Department of Economics, University of Trento, Italia.
    6. Roberto Tamborini, 2002. "One "monetary giant" with many "fiscal dwarfs": The efficiency of macroeconomic stabilization policies in the European Monetary Union," Department of Economics Working Papers 0204, Department of Economics, University of Trento, Italia.
    7. Hubert Gabrisch & Maria Luigia Segnana, 2002. "Why is trade between the European Union and the transition economies vertical?," Department of Economics Working Papers 0207, Department of Economics, University of Trento, Italia.
    8. Kumaraswamy Velupillai, 2003. "Economics and the complexity vision: chimerical partners or elysian adventurers," Department of Economics Working Papers 0307, Department of Economics, University of Trento, Italia.
    9. Giulia Felice, 2003. "Dinamica strutturale e occupazione nei servizi," Department of Economics Working Papers 0304, Department of Economics, University of Trento, Italia.
    10. Maria Rosaria Carillo & Maurizio Pugno, 2002. "The underground economy and the underdevelopment trap," Department of Economics Working Papers 0201, Department of Economics, University of Trento, Italia.
    11. Giuseppe Espa & Roberto Benedetti & Anna De Meo & Salvatore Espa, 2003. "Mappe di probabilità di sito archeologico: un passo avanti," Department of Economics Working Papers 0302, Department of Economics, University of Trento, Italia.
    12. Roberto Tamborini, 2004. "The economic consequences of Mr. G.W. Bush's foreign policy. can the us afford it?," Department of Economics Working Papers 0402, Department of Economics, University of Trento, Italia.
    13. Maurizio Pugno, 2000. "Under Tertiarisation and Unemployment," Department of Economics Working Papers 0004, Department of Economics, University of Trento, Italia.
    14. Luigi Bonatti & Carlo Borzaga & Luigi Mittone, 2005. "Profit versus Nonprofit Firms in the Service Sector: A Formal Analysis of the Employment and Welfare Implications," Rivista di Politica Economica, SIPI Spa, vol. 95(3), pages 137-164, May-June.
    15. Roberto Tamborini, 2000. "From Kuwait to Kosovo: what have we learned; reflections on globalization and peace," Department of Economics Working Papers 0002, Department of Economics, University of Trento, Italia.
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    Cited by:
    1. Guglielmo Chiodi, 2012. "On Richard Goodwin’s Elementary Economics from the Higher Standpoint," ASSRU Discussion Papers 1219, ASSRU - Algorithmic Social Science Research Unit.
    2. K. Vela Velupillai, . "Remembering Krishna Bharadwaj," ASSRU Discussion Papers 1209, ASSRU - Algorithmic Social Science Research Unit.
    3. C. P. Kwong, 2009. "Mathematical analysis of Soros's theory of reflexivity," Papers 0901.4447, arXiv.org.
    4. Kakarot-Handtke, Egmont, 2011. "Primary and secondary markets," MPRA Paper 32996, University Library of Munich, Germany.
    5. Luc LAUWERS, 2009. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Center for Economic Studies - Discussion papers ces09.05, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
    6. K. Vela Velupillai, 2006. "Variations on the Theme of Conning in Mathematical Economics," Working Papers 112, National University of Ireland Galway, Department of Economics, revised 2006.
    7. Lukáš Kovanda, 2011. "The Future of Economics: Four Possible Scenarios," Politická ekonomie, University of Economics, Prague, vol. 2011(6), pages 743-758.
    8. Lukáš Kovanda, 2010. "Critical Realism as an Ontological Basis of Post-Keynesianism," Politická ekonomie, University of Economics, Prague, vol. 2010(5), pages 608-622.
    9. Bartholo, R.S. & Cosenza, C.A.N. & Doria, F.A. & de Lessa, C.T.R., 2009. "Can economic systems be seen as computing devices?," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 72-80, May.
    10. K. Vela Velupillai, 2012. "The Relevance of Computation Irreducibility as Computation Universality in Economics," ASSRU Discussion Papers 1212, ASSRU - Algorithmic Social Science Research Unit.
    11. K. Vela Velupillai, 2008. "Uncomputability and Undecidability in Economic Theory," Department of Economics Working Papers 0806, Department of Economics, University of Trento, Italia.
    12. Dusek, Tamás, 2012. "A Debreu-féle neowalrasi általános egyensúlyelmélet antiempirista axiomatizmusa
      [The anti-empirical axiomatism of neo-Walrasian general equilibrium theory]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 988-1004.
    13. Kakarot-Handtke, Egmont, 2012. "The rhetoric of failure: a hyper-dialog about method in economics and how to get things going," MPRA Paper 43276, University Library of Munich, Germany.

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