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, University of Trento, Via Inama, 5, 381 00 Trento, Italy;

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 01, 5-51

Abstract: The 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.107,108In between, a case is made for economics to take seriously the kind ofmathematical methodologyfostered by Feynman and Dirac, in particular the way they developed thepath integraland theδ-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way Gödel thoughtincompletenessand its perplexities should be interpreted and resolved, is also outlined, albeit briefly, in the concluding section.

Keywords: Constructive mathematics; mathematical economics; computability; computable economics; Busy Beaver functions (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712400017

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