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Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics

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  • K. VELA VELUPILLAI

    ()
    (Department of Economics, University of Trento, Via Inama, 5, 381 00 Trento, Italy; Girton College, Cambridge CB3 0JG, UK)

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    Abstract

    The emergence of non-constructivities in economics is entirely due to the unnecessary and inappropriate formalization of economics by means of 'classical' mathematics. I have made similar claims for the emergence of uncomputabilities and undecidabilities in economics in earlier writings. Here, on the other hand, I want to suggest a way of confronting uncomputabilities, and remedying non-constructivities, in economics, and turning them into a positive force for modeling, for example, endogenous growth, as suggested by Stefano Zambelli. 107,108 In between, a case is made for economics to take seriously the kind of mathematical methodology fostered by Feynman and Dirac, in particular the way they developed the path integral and the δ-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way Gödel thought incompleteness and its perplexities should be interpreted and resolved, is also outlined, albeit briefly, in the concluding section.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 01 ()
    Pages: 5-51

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:01:p:5-51

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    Related research

    Keywords: Constructive mathematics; mathematical economics; computability; computable economics; Busy Beaver functions;

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    References

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    1. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, December.
    2. Herbert E. Scarf, 1977. "The Computation of Equilibrium Prices: An Exposition," Cowles Foundation Discussion Papers 473, Cowles Foundation for Research in Economics, Yale University.
    3. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
    4. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, January.
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    Cited by:
    1. David Colander, 2009. "“What is so Austrian about Austrian Economics?”," Middlebury College Working Paper Series 0910, Middlebury College, Department of Economics.
    2. K. Vela Velupillai, 2008. "Uncomputability and Undecidability in Economic Theory," Department of Economics Working Papers 0806, Department of Economics, University of Trento, Italia.

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