Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics
AbstractThe 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. 107,108 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 δ-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, albeit briefly, in the concluding section.
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.
Volume (Year): 08 (2012)
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Other versions of this item:
- 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.
- K. Vela Velupillai, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Working Papers 0128, National University of Ireland Galway, Department of Economics, revised 2007.
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