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 If the NP-completeness of BHP is provable only within systems that already assume P≠NP, the conditional 'BHP ∈ P → P=NP' is trivially vacuous rather than informative.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Vacuity requires the conditional to be true in all models; if BHP∈P genuinely implies P=NP in standard models, it's informative regardless of proof methods.
      ?

      Think about whether this reason is strong or weak

    • 2.Many important results are provable only in stronger systems; this doesn't make them vacuous—it reflects genuine logical dependencies, not circularity.
      ?

      Think about whether this reason is strong or weak

    • 3.The conditional's value lies in ruling out a possibility (BHP∈P∧P≠NP), which is meaningful even if the proof strategy presupposes P≠NP's truth.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A conditional is vacuous if its consequent becomes provable only by assuming the antecedent false, making the implication logically uninformative.
      ?

      Think about whether this reason is strong or weak

    • 2.If P≠NP is required to prove BHP∈NP is false, then we cannot derive information about P vs NP from BHP's complexity without circular reasoning.
      ?

      Think about whether this reason is strong or weak

    • 3.Informative theorems should increase knowledge within a fixed framework; conditionals requiring framework-changes provide no substantive insight.
      ?

      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.