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Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics

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  • K. Vela Velupillai

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 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 uncomputabilites, 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 methodology fostered by Feynman and Dirac, in particular the way they developed the path integral and the delta-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way G�del thought incompleteness and its perplexities should be interpreted and resolved, is also outlined in the concluding section.

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  • K. Vela Velupillai, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Department of Economics Working Papers 0722, Department of Economics, University of Trento, Italia.
    • Handle: RePEc:trn:utwpde:0722
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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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