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The Limits of Human Mathematics

Noûs 35 (s15):93 - 117 (2001)

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  1. Minds and Machines.Hilary Putnam - 1960 - In Sidney Hook (ed.), Dimensions Of Mind: A Symposium. NY: NEW YORK University Press. pp. 138-164.
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  • Extensions of some theorems of gödel and church.Barkley Rosser - 1936 - Journal of Symbolic Logic 1 (3):87-91.
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  • Minds, Machines and Gödel.J. R. Lucas - 1961 - Etica E Politica 5 (1):1.
    In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: therefore, for (...)
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