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    Carmelics

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    Inverse View

    It is not the case that Propositional logic satisfiability is NP-complete

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.NP-completeness is defined relative to deterministic Turing machines, a model whose physical realizability remains philosophically contested (cf. Gandy 1980).
      ?

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    • 2.If alternative computational substrates (e.g., analog or quantum systems) collapse P and NP, SAT's 'hardness' is model-relative, not an intrinsic logical property.
      ?

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    • 3.Claims about propositional satisfiability complexity thus presuppose a contingent choice of computational ontology, not a necessary logical truth.
      ?

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    Reason for 2 of 2
    ?
    • 1.Cook's theorem establishes NP-completeness under polynomial-time many-one reductions, but Buss's bounded arithmetic formalizes this within systems of varying proof-theoretic strength.
      ?

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    • 2.Whether NP-completeness proofs are themselves formalizable without presupposing consistency of strong arithmetical systems is an open foundational question (cf. Krajíček 1995).
      ?

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    • 3.The claim that SAT is NP-complete inherits the epistemic status of the metatheory in which complexity classes are defined, making it a conditional rather than absolute result.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • Cook (1971) and Buss (1987) established that full propositional satisfiability is NP-complete
      ?

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