Mathematical truth may evolve
Iintuitionism holds that mathematical truth evolves. If so, there's no reason to believe that the Gödel sentence generated by system will still be that system's own Gödel sentence when the sentence is later evaluated.
Penrose assumes that all mathematicians agree on a shared and immutable notion of mathematical truth. But a major school of mathematics, intuitionism, holds that mathematical truth involves is instead.

Jon Doyle (1990).
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Artificial Intelligence »Artificial Intelligence
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
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No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
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Mathematical insight is non-algorithmic »Mathematical insight is non-algorithmic
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Mathematical truth may evolve
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