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
    CBF (Converse Barcan Formula) is unprovable in KQML — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    CBF (Converse Barcan Formula) is unprovable in KQML

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.KQML is sound relative to Kripke's semantics for closed formulas
      ?

      Think about whether this reason is strong or weak

    • 2.Soundness guarantees that no invalid formula is provable in a sound deductive system
      ?

      Think about whether this reason is strong or weak

    • 3.CBF is invalid in KQML's semantics
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.KQML's soundness proof applies only to closed formulas, leaving open whether CBF is provable for open formulas under extended interpretations.
      ?

      Think about whether this reason is strong or weak

    • 2.Garson and others have shown that quantified modal logics admit multiple non-equivalent semantics, so 'KQML's semantics' is not a uniquely fixed target.
      ?

      Think about whether this reason is strong or weak

    • 3.If CBF is evaluated under a constant-domain semantics rather than varying-domain Kripke semantics, it becomes valid, making unprovability relative to semantic choice, not absolute.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Timothy Williamson's necessitism entails that every individual necessarily exists, which validates CBF across all possible worlds without exception.
      ?

      Think about whether this reason is strong or weak

    • 2.If necessitism is coherent and CBF follows from it, then a system augmented with necessitist axioms would render CBF provable, undermining the claim's generality.
      ?

      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.

    Topics

    Modality & PossibilityTruth & Knowledge

    Related

    CBF is invalid in KQML's semanticsGarson and others have shown that quantified modal logics admit multiple non-equ...If CBF is evaluated under a constant-domain semantics rather than varying-domain...If necessitism is coherent and CBF follows from it, then a system augmented with...
    +4 moreShow less
    KQML is sound relative to Kripke's semantics for closed formulasKQML's soundness proof applies only to closed formulas, leaving open whether CBF...Soundness guarantees that no invalid formula is provable in a sound deductive sy...Timothy Williamson's necessitism entails that every individual necessarily exist...

    Similar

    BF (Barcan Formula) is unprovable in KQML100%□N is unprovable in KQML98%P1 has been proved unsolvable, meaning no solution of P1 can exist.86%If P1 is proved unsolvable and P1 has been reduced to P2, then P2 must...85%

    Source

    AI-extracted1/3 agreementValid
    SEP: possibilism-actualism
    View source passageHide passage
    With these modifications in place, Kripke is able to demonstrate that his deductive system KQML is sound and complete for closed formulas relative to his semantics. Soundness, in particular, tells us that no invalid formula is provable in the system. Hence, since BF, CBF, and \(\Box\textbf{N}\) are all invalid in KQML, soundness guarantees that they are all unprovable in KQML.
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit