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