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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Anything that can be computed can also be computed by the universal Turing machine.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Gödel argued that human mathematical intuition allows recognition of truths no formal system can prove, suggesting minds exceed Turing-machine capacities.
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    • 2.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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    • 3.The claim is therefore either trivially true by definitional fiat or false if 'computable' tracks a mind-independent, broader notion of effective procedure.
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    Reason for 2 of 2
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    • 1.Hypercomputation models (e.g., Zeno machines, oracle Turing machines) can solve the halting problem, which no standard Turing machine can.
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    • 2.If physically realizable processes exceed Turing-computable functions, the Church-Turing thesis describes a subset of computation, not its totality.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The universal Turing machine can compute what any other Turing machine computes.
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    • 2.The Turing machine notion fully captures computability (Church-Turing thesis).
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