Self-referential machines
A self-referential machine can evaluate Gödel sentences for itself. Such a machine may evade the Lucas argument.

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Artificial Intelligence »Artificial Intelligence
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
Improved machines »Improved machines
Self-referential machines
Gödelizing operator can defeat Lucas's argument »Gödelizing operator can defeat Lucas's argument
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