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
    Baker, Gill, and Solovay (1975) demonstrated that relativ... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→P is a subset of NP

    Baker, Gill, and Solovay (1975) demonstrated that relativized proofs cannot settle P vs NP, suggesting the question resists standard formal methods.

    ?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.Relativization shows that many proof techniques (diagonalization, algebraic methods) provably fail to distinguish P from NP in relativized worlds.
      ?

      Think about whether this reason is strong or weak

    • 2.Multiple decades of failed attempts using standard formal systems suggest fundamental obstacles rather than mere technical difficulty.
      ?

      Think about whether this reason is strong or weak

    • 3.The existence of natural oracles where P=NP and others where P≠NP demonstrates the question transcends relativizable reasoning.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Relativization limitations don't preclude non-relativizing proof techniques; arithmetic circuit lower bounds have bypassed relativization barriers.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates 'standard relativizable methods fail' with 'the problem resists all formal methods,' which is an unwarranted leap.
      ?

      Think about whether this reason is strong or weak

    • 3.Natural proofs and other metamathematical barriers are separate obstacles; relativization alone doesn't establish fundamental unsolvability.
      ?

      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

    Multiple decades of failed attempts using standard formal systems suggest fundam...Natural proofs and other metamathematical barriers are separate obstacles; relat...P is a subset of NPRelativization limitations don't preclude non-relativizing proof techniques; ari...
    +3 moreShow less
    Relativization shows that many proof techniques (diagonalization, algebraic meth...The claim conflates 'standard relativizable methods fail' with 'the problem resi...The existence of natural oracles where P=NP and others where P≠NP demonstrates t...

    Details

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