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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that The absence of known independence proofs for P≠NP reflects our limited proof-theoretic tools, not the intrinsic provability of the statement within PA or ZFC.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.P≠NP has concrete combinatorial content about resource bounds, suggesting it's decidable in principle even if we lack proofs currently.
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    • 2.Absence of independence proofs after decades of serious effort is weak evidence; we should expect real independence to show more structural signs.
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    • 3.Conflating 'unproven' with 'unprovable' commits a fallacy; failed proof attempts reflect human ingenuity limits, not mathematical impossibility.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Gödel's incompleteness theorems show formal systems have inherent limitations; our current proof methods may simply be too weak for P≠NP.
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    • 2.Many hard problems (Goldbach's conjecture, twin primes) remain unresolved despite centuries of effort, suggesting structural barriers, not just technique.
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    • 3.Independence results exist for other major conjectures; independence for P≠NP would fit a pattern of undecidability in foundational mathematics.
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