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    Lucas and Penrose extended this: if human cognition is no... — Carmelics
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    Challenges→Anything that can be computed can also be computed by the universal Turing machine.

    Lucas and Penrose extended this: if human cognition is not Turing-computable, then 'computable' in the claim smuggles in an unjustified restriction to formal-mechanical processes.

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    1 reason for
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    Reasons For

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    • 1.Human mathematical insight (e.g., Gödel's incompleteness) appears to transcend formal systems, suggesting non-algorithmic cognition.
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    • 2.Defining 'computable' narrowly as Turing-computable presupposes computationalism without independent justification from cognitive science.
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    • 3.If human minds access truths unprovable in formal systems, they operate beyond mechanical rule-following, requiring broader ontology.
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    Reasons Against

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    • 1.No empirical evidence demonstrates humans actually solve Gödelian tasks non-computationally; intuition about cognition is unreliable.
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    • 2.'Turing-computable' already encompasses vast logical space; calling non-Turing processes 'real' cognition just relabels confusion without explanation.
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    • 3.Lucas-Penrose arguments commit logical fallacy: from 'minds aren't provably formal' they conclude 'minds aren't formal'—a gap remains.
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    Related

    'Turing-computable' already encompasses vast logical space; calling non-Turing p...Anything that can be computed can also be computed by the universal Turing machi...Defining 'computable' narrowly as Turing-computable presupposes computationalism...Human mathematical insight (e.g., Gödel's incompleteness) appears to transcend f...
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    If human minds access truths unprovable in formal systems, they operate beyond m...Lucas-Penrose arguments commit logical fallacy: from 'minds aren't provably form...No empirical evidence demonstrates humans actually solve Gödelian tasks non-comp...

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