Inconsistency without explosion of belief
Lucas's argument depends on the assumption that if humans were inconsistent, they would be committed to believing anything and everything. But this conclusion follows from a rule of propositional logic we have no reason to believe holds for humans.
It is quite possible for minds to be both inconsistent and coherent.

Douglas Hofstadter (1978).
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Inconsistency without explosion of belief
Douglas Hofstadter »Douglas Hofstadter
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