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Reflections on Mathematical Economics in the Algorithmic Mode

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  • K. Vela Velupillai
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    Abstract

    Non-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 Info

    Paper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1016.

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    Date of creation: 2010
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    Handle: RePEc:trn:utwpas:1016

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    1. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
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    Cited by:
    1. 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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