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
    The absence of known independence proofs for P≠NP reflect... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→P ≠ NP is unlikely to be independent of strong formal theories such as PA or ZFC

    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.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Gödel's incompleteness theorems show formal systems have inherent limitations; our current proof methods may simply be too weak for P≠NP.
      ?

      Think about whether this reason is strong or weak

    • 2.Many hard problems (Goldbach's conjecture, twin primes) remain unresolved despite centuries of effort, suggesting structural barriers, not just technique.
      ?

      Think about whether this reason is strong or weak

    • 3.Independence results exist for other major conjectures; independence for P≠NP would fit a pattern of undecidability in foundational mathematics.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.P≠NP has concrete combinatorial content about resource bounds, suggesting it's decidable in principle even if we lack proofs currently.
      ?

      Think about whether this reason is strong or weak

    • 2.Absence of independence proofs after decades of serious effort is weak evidence; we should expect real independence to show more structural signs.
      ?

      Think about whether this reason is strong or weak

    • 3.Conflating 'unproven' with 'unprovable' commits a fallacy; failed proof attempts reflect human ingenuity limits, not mathematical impossibility.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Absence of independence proofs after decades of serious effort is weak evidence;...Conflating 'unproven' with 'unprovable' commits a fallacy; failed proof attempts...Gödel's incompleteness theorems show formal systems have inherent limitations; o...Independence results exist for other major conjectures; independence for P≠NP wo...
    +3 moreShow less
    Many hard problems (Goldbach's conjecture, twin primes) remain unresolved despit...P ≠ NP is unlikely to be independent of strong formal theories such as PA or ZFCP≠NP has concrete combinatorial content about resource bounds, suggesting it's d...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit