Penrose's new argument

Journal of Philosophical Logic 30 (3):241-250 (2001)
Abstract
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 argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive
Keywords Gödel's proof  formal system  human mathematical reasoning
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Reprint years 2004
DOI 10.1023/A:1017595530503
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Proving That the Mind Is Not a Machine?Johannes Stern - 2018 - Thought: A Journal of Philosophy 7 (2):81-90.
Mechanism, Truth, and Penrose's New Argument.Stewart Shapiro - 2003 - Journal of Philosophical Logic 32 (1):19-42.
Remarks on Penrose's New Argument.Per Lindstrom - 2006 - Journal of Philosophical Logic 35 (3):231-237.

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