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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, National University of Ireland, Galway)

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    Abstract

    It is natural to claim, as I do in this paper, that the emergence of non-constructivities in economics is entirely due to the formalizations 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 modelling, 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 modelling fostered by Feynman and Dirac, in particular the way they developed the path integral and the ?- 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 in the concluding section.

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    Bibliographic Info

    Paper provided by National University of Ireland Galway, Department of Economics in its series Working Papers with number 0128.

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    Date of creation: 2007
    Date of revision: 2007
    Handle: RePEc:nig:wpaper:0128

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    1. Mount,Kenneth R. & Reiter,Stanley, 2002. "Computation and Complexity in Economic Behavior and Organization," Cambridge Books, Cambridge University Press, number 9780521800563.
    2. 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.
    3. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    4. Herbert E. Scarf, 1977. "The Computation of Equilibrium Prices: An Exposition," Cowles Foundation Discussion Papers 473, Cowles Foundation for Research in Economics, Yale University.
    5. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521319867.
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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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