Philosophia Mathematica 14 (2):229-254 (2006)

In his 1951 Gibbs Lecture Gödel formulates the central implication of the incompleteness theorems as a disjunction: either the human mind infinitely surpasses the powers of any finite machine or there exist absolutely unsolvable diophantine problems (of a certain type). In his later writings in particular Gödel favors the view that the human mind does infinitely surpass the powers of any finite machine and there are no absolutely unsolvable diophantine problems. I consider how one might defend such a view in light of Gödel's remark that one can turn to ideas in Husserlian transcendental phenomenology to show that the human mind ‘contains an element totally different from a finite combinatorial mechanism’.
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DOI 10.1093/philmat/nkj008
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On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
What is Cantor's Continuum Problem?S. C. Kleene - 1948 - Journal of Symbolic Logic 13 (2):116-117.
Is Mathematics Syntax of Language?Kurt Gödel - 1953 - In K. Gödel Collected Works. Oxford University Press: Oxford. pp. 334--355.

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