Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

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

    It is not the case that A proof of P ≠ NP is beyond the reach of currently known proof techniques

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The relativization barrier shows diagonalization alone fails, but does not preclude non-relativizing techniques like arithmetization used in IP=PSPACE.
      ?

      Think about whether this reason is strong or weak

    • 2.Shamir's 1992 proof that IP=PSPACE succeeded precisely by exploiting non-relativizing algebraic methods previously deemed insufficient.
      ?

      Think about whether this reason is strong or weak

    • 3.The existence of successful non-relativizing proofs defeats the inference from 'known techniques fail' to 'proof is beyond reach'.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Epistemic humility about proof techniques is historically unreliable: Fermat's Last Theorem resisted proof for 357 years before Wiles applied unforeseen modular forms machinery.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates current methodological limitations with principled impossibility, committing what Lakatos called 'monster-barring' against nascent proof strategies.
      ?

      Think about whether this reason is strong or weak

    • 3.Geometric Complexity Theory provides a concrete, technically developed research program whose incompleteness does not constitute evidence of fundamental unreachability.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Diagonalization cannot separate P from NP due to the relativization barrier established by Baker, Gill, and Solovay
      ?

      Think about whether this reason is strong or weak

    • 2.Geometric complexity theory and other proposed approaches are still in need of substantial refinement or genuinely new methods will be required
      ?

      Think about whether this reason is strong or weak

    • 3.No existing method has succeeded in yielding the desired separations
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

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