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    BF (Barcan Formula) is unprovable in KQML — Carmelics
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    Home/Modality & Possibility
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    BF (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
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    • 2.Soundness guarantees that no invalid formula is provable in a sound deductive system
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    • 3.BF is invalid in KQML's semantics
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.KQML's semantics presupposes variable domains across worlds, but this choice is a philosophical commitment, not a logical necessity.
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    • 2.If one adopts a constant-domain semantics (as Barcan Marcus originally did), BF is not merely provable but a theorem of the resulting system.
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    • 3.The unprovability of BF in KQML thus reflects a semantic stipulation favoring actualism, not an intrinsic logical feature of quantified modal logic.
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    Reason against 2 of 2
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    • 1.Soundness of KQML relative to its own semantics is a metalogical result internal to that semantic framework and does not establish BF's broader modal invalidity.
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    • 2.David Lewis and Timothy Williamson argue that necessitism—the thesis that necessarily everything necessarily exists—provides independent metaphysical grounds for BF's truth across all modal systems.
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    • 3.If necessitism is correct, the invalidity of BF in KQML's semantics indicates a defect in that semantics' metaphysical adequacy, not a proof of BF's unprovability in all legitimate modal logics.
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    Modality & PossibilityTruth & Knowledge

    Related

    BF is invalid in KQML's semanticsDavid Lewis and Timothy Williamson argue that necessitism—the thesis that necess...If necessitism is correct, the invalidity of BF in KQML's semantics indicates a ...If one adopts a constant-domain semantics (as Barcan Marcus originally did), BF ...
    +5 moreShow less
    KQML is sound relative to Kripke's semantics for closed formulasKQML's semantics presupposes variable domains across worlds, but this choice is ...Soundness guarantees that no invalid formula is provable in a sound deductive sy...Soundness of KQML relative to its own semantics is a metalogical result internal...The unprovability of BF in KQML thus reflects a semantic stipulation favoring ac...

    Similar

    CBF (Converse 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...86%

    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