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  1. Minds, Machines, And Mathematics A Review of Shadows of the Mind by Roger Penrose. [REVIEW]David J. Chalmers - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2:11-20.
    In his stimulating book SHADOWS OF THE MIND, Roger Penrose presents arguments, based on Gödel's theorem, for the conclusion that human thought is uncomputable. There are actually two separate arguments in Penrose's book. The second has been widely ignored, but seems to me to be much more interesting and novel than the first. I will address both forms of the argument in some detail. Toward the end, I will also comment on Penrose's proposals for a "new science of consciousness".
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  • Shadows of the Mind: A Search for the Missing Science of Consciousness.Roger Penrose - 1994 - Oxford University Press.
    Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and ..
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  • Penrose's new argument.Per Lindström - 2001 - Journal of Philosophical Logic 30 (3):241-250.
    It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new (...)
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  • Mechanism, truth, and Penrose's new argument.Stewart Shapiro - 2003 - Journal of Philosophical Logic 32 (1):19-42.
    Sections 3.16 and 3.23 of Roger Penrose's Shadows of the mind (Oxford, Oxford University Press, 1994) contain a subtle and intriguing new argument against mechanism, the thesis that the human mind can be accurately modeled by a Turing machine. The argument, based on the incompleteness theorem, is designed to meet standard objections to the original Lucas-Penrose formulations. The new argument, however, seems to invoke an unrestricted truth predicate (and an unrestricted knowability predicate). If so, its premises are inconsistent. The usual (...)
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  • Beyond the doubting of a shadow.Roger Penrose - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2:89-129.
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