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

K. Vela Velupillai
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K. Vela Velupillai: Department of Economics, National University of Ireland, Galway

No 128, Working Papers from National University of Ireland Galway, Department of Economics

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.

Date: 2007, Revised 2007
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