The super-mechanist
Even if Lucas in Gödelize any machine that a mechanist can develop, that ability doesn't entail that he can Gödelize any machine whatsoever. A superhuman mechanist might be able to design a machine that exceeds Lucas's Gödelizing ability.
Paul Bernacerraf (1967).
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
Argument from Gödel's theorem is dialectical »Argument from Gödel's theorem is dialectical
A machine can play Lucas's game »A machine can play Lucas's game
The super-mechanist
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