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.
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Lindström, P. Penrose's New Argument. Journal of Philosophical Logic 30, 241–250 (2001). https://doi.org/10.1023/A:1017595530503
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DOI: https://doi.org/10.1023/A:1017595530503