Reflections On Mathematical Economics In The Algorithmic Mode
AbstractNon-standard analysis can be harnessed by the recursion theorist. But as a computable economist, the conundrums of the Löwenheim-Skolem theorem and the associated Skolem paradox, seem to pose insurmountable epistemological difficulties against the use of algorithmic non-standard analysis. Discontinuities can be tamed by recursive analysis. This particular kind of taming may be a way out of the formidable obstacles created by the difficulties of Diophantine Decision Problems. Methods of existence proofs, used by the "classical" mathematician — even if not invoking the axiom of choice — cannot be shown to be equivalent to the exhibition of an instance in the sense of a constructive proof. These issues were prompted by the fertile and critical contributions to this special issue.
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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)
Issue (Month): 01 ()
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Other versions of this item:
- K. Vela Velupillai, 2010. "Reflections on Mathematical Economics in the Algorithmic Mode," ASSRU Discussion Papers 1016, ASSRU - Algorithmic Social Science Research Unit.
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- Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
- K. Vela Velupillai & Stefano Zambelli, 2012. "Computability and Algorithmic Complexity in Economics," ASSRU Discussion Papers 1202, ASSRU - Algorithmic Social Science Research Unit.
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