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The unreasonable ineffectiveness of mathematics in economics

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  • K. Vela Velupillai

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.

Suggested Citation

  • K. Vela Velupillai, 2005. "The unreasonable ineffectiveness of mathematics in economics," Cambridge Journal of Economics, Oxford University Press, vol. 29(6), pages 849-872, November.
  • Handle: RePEc:oup:cambje:v:29:y:2005:i:6:p:849-872
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    File URL: http://hdl.handle.net/10.1093/cje/bei084
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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. 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.
    3. 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.
    4. Lukáš Kovanda, 2010. "Kritický realismus: ontologická báze postkeynesovské ekonomie
      [Critical Realism as an Ontological Basis of Post-Keynesianism]
      ," Politická ekonomie, University of Economics, Prague, vol. 2010(5), pages 608-622.
    5. K. Vela Velupillai, 2012. "The Relevance of Computation Irreducibility as Computation Universality in Economics," ASSRU Discussion Papers 1212, ASSRU - Algorithmic Social Science Research Unit.
    6. C. P. Kwong, 2009. "Mathematical analysis of Soros's theory of reflexivity," Papers 0901.4447, arXiv.org.
    7. 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.
    8. Lauwers, Luc, 2010. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 32-37, January.
    9. K. Vela Velupillai, "undated". "Remembering Krishna Bharadwaj," ASSRU Discussion Papers 1209, ASSRU - Algorithmic Social Science Research Unit.
    10. Lukáš Kovanda, 2011. "Ekonomie budoucnosti: čtyři možné scénáře
      [The Future of Economics: Four Possible Scenarios]
      ," Politická ekonomie, University of Economics, Prague, vol. 2011(6), pages 743-758.
    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. Kakarot-Handtke, Egmont, 2011. "Primary and secondary markets," MPRA Paper 32996, University Library of Munich, Germany.
    13. K. Vela Velupillai, 2007. "Variations on the Theme of Conning in Mathematical Economics," Department of Economics Working Papers 0703, Department of Economics, University of Trento, Italia.

    More about this item

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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