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 InfoPaper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1016.
Date of creation: 2010
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Other versions of this item:
- K. Vela Velupillai, 2012. "Reflections On Mathematical Economics In The Algorithmic Mode," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 139-152.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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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