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 Any system requiring an oracle for first-order arithmetic to achieve completeness lacks the self-contained inferential closure definitive of a logic.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Many mathematical logics (second-order, type theory) are standardly considered logics despite requiring semantic resources beyond FOA decidability.
      ?

      Think about whether this reason is strong or weak

    • 2.Oracles are formal mathematical objects; oracle-relative completeness is rigorous and internal to recursion theory—no mysterious external addition.
      ?

      Think about whether this reason is strong or weak

    • 3.Self-containment conflates proof-theoretic completeness with semantic adequacy; they're distinct properties and both can hold with oracles.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Gödel's incompleteness theorems show FOA-complete systems transcend first-order expressiveness, violating closure within a single logical framework.
      ?

      Think about whether this reason is strong or weak

    • 2.Self-contained inference requires the system to justify all completeness-enabling resources internally; external oracles violate this requirement.
      ?

      Think about whether this reason is strong or weak

    • 3.Logics are characterized by decidable proof procedures; oracle-dependence makes completeness verification non-algorithmic and non-logical.
      ?

      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.