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    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Whether the second machine class properly extends the fir... — Carmelics
    Home/Skepticism
    HistoryEditSee Inverse

    Whether the second machine class properly extends the first machine class is currently an open problem

    Modality & Possibility
    ?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.Demonstrating formally that the second machine class is not realistic would require proving separation results for complexity classes
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    • 2.Those separation results are currently unresolved
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Mathematical openness does not entail epistemic equipoise: asymmetric evidence can rationally favor one resolution over another.
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    • 2.The overwhelming failure of proposed hypercomputation models to escape physical realizability constraints constitutes strong inductive evidence against proper extension.
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    • 3.Epistemic humility about formal proof is distinct from genuine uncertainty about the underlying mathematical fact, which may already be determinate.
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    Reason against 2 of 2
    ?
    • 1.Turing's original Church-Turing thesis, interpreted as a physical hypothesis by Deutsch and others, constrains what machine classes are genuinely possible.
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    • 2.If the physical Church-Turing thesis is correct, the second machine class is not physically realizable, dissolving the openness as philosophically significant.
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    Topics

    SkepticismModality & Possibility

    Connections

    2 topics

    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Demonstrating formally that the second machine class is not realistic would requ...Epistemic humility about formal proof is distinct from genuine uncertainty about...If the physical Church-Turing thesis is correct, the second machine class is not...Mathematical openness does not entail epistemic equipoise: asymmetric evidence c...
    +3 moreShow less
    The overwhelming failure of proposed hypercomputation models to escape physical ...Those separation results are currently unresolvedTuring's original Church-Turing thesis, interpreted as a physical hypothesis by ...

    Similar

    It is currently an open problem whether the second machine class prope...96%It is currently an open problem whether the second machine class prope...95%Demonstrating formally that the second machine class is not realistic ...75%Any problem complete for a class that properly extends P cannot be in ...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    On the other hand, if \(x \not\in X\), then all of \(N\)’s computations from \(C_0(x)\) are required to lead to rejecting states. Non-deterministic machines are sometimes described as making undetermined ‘choices’ among different possible successor configurations at various points during their computation. But what the foregoing definitions actually describe is a tree \(\mathcal{T}^N_{C_0}\) of all possible computation sequences starting from a given configuration \(C_0\) for a deterministic mac
    Extraction notes

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

    Details

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