Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
Velupillai, K. Vela
Velupillai, K. Vela
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2007
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Working Paper
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Velupillai, K. V., (2007) "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics" (Working Paper No. 0128) Department of Economics, National University of Ireland, Galway.
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. 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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National University of Ireland, Galway
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Attribution-NonCommercial-NoDerivs 3.0 Ireland