Informal proof
A machine could, in principle, construct an informal proof of the truth of the Gödel sentence. So long as the machine doesn't regard such informal persuasions as proof proper, introducing them into its system won't lead to inconsistency.
So a, self-referential machine may recognise the truth of its own Gödel sentence without using a Gödelizing operator.


Paul Benacerral (1967).
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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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Improved machines »Improved machines
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Self-referential machines »Self-referential machines
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Gödelizing operator can defeat Lucas's argument »Gödelizing operator can defeat Lucas's argument
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A self-Gödelizing machine can still be out-Gödeled »A self-Gödelizing machine can still be out-Gödeled
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Informal proof
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Machine isn't capable of informal proof »Machine isn't capable of informal proof
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