The halting problem has a structural similarity to the Goodman/Kripke paradox insofar as the fact that the machine has not yet halted cannot count as evidence that it will not halt.
Also, the demonstration that a human mind is like a general cognitive engine - a Turing machine - would have to include a demonstration that it was following the rules of such a machine, and Kripke has shown that this demonstration cannot be conclusively constructed.
So, curiously, it seems that if my mind is like a Turing machine, there is no finite way in which I could demonstrate this. It would not be a computable issue.
The proposal that the mind is a kind of Turing machine can only ever be a kind of assumption of cognitive science - a 'false heuristic'? - and not part of a deductive cognitive theory.
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