Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
AbstractIt 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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Bibliographic InfoPaper provided by National University of Ireland Galway, Department of Economics in its series Working Papers with number 0128.
Date of creation: 2007
Date of revision: 2007
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Other versions of this item:
- 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.
- 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.
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