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Reflections On Mathematical Economics In The Algorithmic Mode

  • K. VELA VELUPILLAI

    ()

    (Department of Economics, University of Trento, Via Inama 5, 381 00 Trento, Italy)

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    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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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 01 ()
    Pages: 139-152

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:01:p:139-152
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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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