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 Weak completeness (every valid formula is provable) is the standard notion of completeness in propositional modal logic, making 'only' misleading.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Strong completeness is provable for K, T, S4, S5 with finite axiomatizations, so 'only weak' undersells what modal logic actually achieves.
      ?

      Think about whether this reason is strong or weak

    • 2.The word 'only' reasonably flags that weak completeness omits finite consistency preservation, a philosophically significant limitation.
      ?

      Think about whether this reason is strong or weak

    • 3.Pedagogically, distinguishing weak from strong completeness clarifies what's proven, even if weak is standard—'only' aids precision, not misleading.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Weak completeness (valid → provable) is achieved by major modal logics K, T, S4, S5, making it the standard in textbooks and research.
      ?

      Think about whether this reason is strong or weak

    • 2.Strong completeness (Γ ⊨ φ → Γ ⊢ φ) fails for infinitary cases in modal logic, so weak completeness is the realistic standard.
      ?

      Think about whether this reason is strong or weak

    • 3.Using 'only' suggests weak completeness is unusual or limited, when it's actually the primary completeness notion modal logicians establish.
      ?

      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