Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
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.
|Date of creation:||2007|
|Date of revision:||2007|
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- Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, March.
- Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
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"Applying General Equilibrium,"
Cambridge University Press, number 9780521266550, November.
- Scarf, Herbert E., 1993.
"The computation of equilibrium prices: An exposition,"
Handbook of Mathematical Economics,
in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 21, pages 1007-1061
- Herbert E. Scarf, 1977. "The Computation of Equilibrium Prices: An Exposition," Cowles Foundation Discussion Papers 473, Cowles Foundation for Research in Economics, Yale University.
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