Nonintelligent procedures can be noncomputable
There are possible procedures that don't require intelligence to carry out, yet that are noncomputable.
Imagine that some part of the brain receives electrochemical pulses, and emits pulses in such a way as to instantiate the busy beaver function. The noncomputability of the busy beaver function shows that some psychological procedures may not be computable.

Selmer Bringsjord, 1992.
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Nonintelligent procedures can be noncomputable
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The busy beaver function »The busy beaver function
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