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    Anything that can be computed can also be computed by the... — Carmelics
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    Home/Truth & Knowledge
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    Anything that can be computed can also be computed by the universal Turing machine.

    Truth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Related

    Gödel argued that human mathematical intuition allows recognition of truths no f...Hypercomputation models (e.g., Zeno machines, oracle Turing machines) can solve ...If physically realizable processes exceed Turing-computable functions, the Churc...Lucas and Penrose extended this: if human cognition is not Turing-computable, th...
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    The Turing machine notion fully captures computability (Church-Turing thesis).The claim is therefore either trivially true by definitional fiat or false if 'c...The universal Turing machine can compute what any other Turing machine computes.

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    The universal Turing machine can compute what any other Turing machine...92%The universal Turing machine can compute everything that is computable...88%Using T_decide and the universal Turing machine, one can construct a m...81%Any problem not computable by the universal Turing machine is uncomput...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: turing-machine
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    The universal Turing machine which was constructed to prove the uncomputability of certain problems, is, roughly speaking, a Turing machine that is able to compute what any other Turing machine computes. Assuming that the Turing machine notion fully captures computability (and so that Turing’s thesis is valid), it is implied that anything which can be “computed”, can also be computed by that one universal machine. Conversely, any problem that is not computable by the universal machine is conside
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit