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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)

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.107,108In between, a case is made for economics to take seriously the kind ofmathematical methodologyfostered by Feynman and Dirac, in particular the way they developed thepath integraland theδ-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way Gödel thoughtincompletenessand its perplexities should be interpreted and resolved, is also outlined, albeit briefly, in the concluding section.

Suggested Citation

  • K. Vela Velupillai, 2012. "Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 5-51.
    • Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:01:n:s1793005712400017
    DOI: 10.1142/S1793005712400017
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    References listed on IDEAS

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    1. Mount,Kenneth R. & Reiter,Stanley, 2007. "Computation and Complexity in Economic Behavior and Organization," Cambridge Books, Cambridge University Press, number 9780521037891, September.
    2. K. Vela Velupillai, 2008. "Sraffa's mathematical economics: a constructive interpretation," Journal of Economic Methodology, Taylor & Francis Journals, vol. 15(4), pages 325-342.
    3. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    4. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, April.
    5. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, September.
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    Cited by:

    1. Sundar Sarukkai, 2012. "Mathematics In Economics: Reducibility And/Or Applicability?," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 81-93.

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