In this paper we interpret a characterization of the Gödel speed-up phenomenon as providing support for the ‘Nagel-Newman thesis’ that human theorem recognizers differ from mechanical theorem recognizers in that the former do not seem to be limited by Gödel's incompleteness theorems whereas the latter do seem to be thus limited. However, we also maintain that (currently non-existent) programs which are open systems in that they continuously interact with, and are thus inseparable from, their environment, are not covered by the above (or probably any other recursion-theoretic) argument
Keywords Logic  Machine  Mathematics  Mind  Science
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DOI 10.1093/bjps/45.2.549
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Some Remarks on the Undecidability Results.Kurt Gödel - 1972 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Kurt Gödel: Collected Works Vol. Ii. Oxford University Press. pp. 305--306.

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2004 Annual Meeting of the Association for Symbolic Logic.Sergei Artemov - 2005 - Bulletin of Symbolic Logic 11 (1):92-119.

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