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    Carmelics

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    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 BF (Barcan Formula) is unprovable in KQML

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

    Reasons For

    2 perspectives
    Reason for 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 for 2 of 2
    ?
    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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    Strongest counterpoint
    Explore the most compelling reason on the other side.