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
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The system P_1 admits proofs of PHP_n of size polynomial in n.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Polynomial-size proof existence is a syntactic, complexity-theoretic notion that does not track the semantic difficulty of recognizing why PHP_n is true.
      ?

      Think about whether this reason is strong or weak

    • 2.Cook and Reckhow's framework conflates proof length with proof comprehensibility, obscuring that short formal derivations may require exponential search to discover.
      ?

      Think about whether this reason is strong or weak

    • 3.A genuine account of provability must distinguish between the existence of a proof and the feasibility of finding it, as Kreisel's work on proof theory demands.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Buss's proof of PHP_n in P_1 encodes induction over sharply bounded formulas, which presupposes the very combinatorial principles PHP is meant to test.
      ?

      Think about whether this reason is strong or weak

    • 2.A proof system that builds in the resources needed to derive a principle cannot serve as independent evidence that the principle is 'easily provable' in any epistemically meaningful sense.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • Buss (1987) demonstrated that P_1 has polynomial-size proofs of PHP_n.
      ?

      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.
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42