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    It is currently an open problem whether the second machin... — Carmelics
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    It is currently an open problem whether the second machine class properly extends the first machine class

    Skepticism
    ?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.Formally demonstrating that second machine class models are unrealistic would require proving complexity class separation results
      ?

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    • 2.The relevant complexity class separation results are currently unresolved
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The 'openness' of a mathematical problem is an epistemic fact about human knowledge, not an ontological fact about machine class relations.
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    • 2.Epistemic uncertainty about whether P≠NP does not entail metaphysical indeterminacy in the extensional relationship between the classes.
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    • 3.Therefore, the claim conflates our ignorance of the answer with the answer itself being genuinely unsettled in reality.
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    Reason against 2 of 2
    ?
    • 1.Lakatos's philosophy of mathematics shows that 'open problems' exist within fallible proof-practices, not as brute features of mathematical reality.
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    • 2.If the second machine class in fact properly extends the first, the problem is not open but merely unsolved by current methods.
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    • 3.Characterizing the separation problem as 'open' smuggles a verificationist assumption—that truth tracks proof availability—into a realist mathematical domain.
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    Topics

    SkepticismTruth & Knowledge

    Connections

    1 topic

    Proof of definition segments1 linked

    Related

    Characterizing the separation problem as 'open' smuggles a verificationist assum...Epistemic uncertainty about whether P≠NP does not entail metaphysical indetermin...Formally demonstrating that second machine class models are unrealistic would re...If the second machine class in fact properly extends the first, the problem is n...
    +4 moreShow less
    Lakatos's philosophy of mathematics shows that 'open problems' exist within fall...The 'openness' of a mathematical problem is an epistemic fact about human knowle...The relevant complexity class separation results are currently unresolvedTherefore, the claim conflates our ignorance of the answer with the answer itsel...

    Similar

    It is currently an open problem whether the second machine class prope...99%Whether the second machine class properly extends the first machine cl...95%Demonstrating formally that the second machine class is not realistic ...77%Formally demonstrating that second machine class models are unrealisti...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    1 Deterministic and non-deterministic models of computation According to the Cobham-Edmonds Thesis the complexity class \(\textbf{P}\) describes the class of feasibily decidable problems. As we have just seen, this class is defined in terms of the reference model \(\mathfrak{T}\) in virtue of the assumption that it is a ‘reasonable’ model of computation. Several other models of computation are also studied in complexity theory not because they are presumed to be accurate representations of the c
    Extraction notes

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

    Details

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