Lucas can believe his Whiteley sentence
The claim that Lucas can't believe the Whiteley sentence is incorrect. Lucas can recognise Whiteley sentence is true, as there's a point of view from which he can understand how the sentence tricks him.
From this point of view Lucas can appreciate that he can't assert the sentence-and consequently he can recognise its truth.

J. E. Martin and K. H. Engleman (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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Lucas tricks machines into contradicting themselves »Lucas tricks machines into contradicting themselves
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Lucas can believe his Whiteley sentence
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