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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that If P = NP, then finding a satisfying valuation for a propositional formula is no harder than constructing its truth table, and factoring a natural number would be no more difficult than verifying a given factorization.

    ?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.Computational complexity classes are defined relative to models of computation, and their equivalence is model-dependent, not an absolute metaphysical fact.
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    • 2.The claim conflates extensional equivalence of complexity classes with identity of epistemic difficulty, which are distinct notions even under P = NP.
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    • 3.Even if P = NP, the witnessing polynomial reductions may have constants or degrees rendering them practically intractable, preserving real cognitive asymmetry.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Kripke's distinction between epistemic and metaphysical possibility implies that P = NP being mathematically true does not collapse the epistemic gap between search and verification.
      ?

      Think about whether this reason is strong or weak

    • 2.The asymmetry between finding and checking reflects a constitutive feature of bounded rationality that survives any formal complexity-theoretic collapse.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.P is the class of problems decidable efficiently.
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      Think about whether this reason is strong or weak

    • 2.NP is the class of problems verifiable efficiently given a certificate.
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    • 3.If P = NP, then the difficulty of deciding and verifying coincide (up to a polynomial factor) for all problems in NP.
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.