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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 The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.SQML's constant domain assumption—that every individual exists in every possible world—is a substantive metaphysical commitment, not a logical truth.
      ?

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    • 2.Once variable domains are permitted (as in Kripke's 1963 semantics), the universal instantiation axiom fails and BF is no longer valid.
      ?

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    • 3.The validity of BF in SQML therefore reflects a built-in possibilist ontology, not a discovery about modal logic as such.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Kripke argued that BF's converse entails that actually existing individuals are necessarily possible, but BF itself entails that possible individuals actually exist—a commitment many find ontologically profligate.
      ?

      Think about whether this reason is strong or weak

    • 2.If modal logic is to serve as a neutral framework for metaphysical inquiry, its theorems should not prejudge first-order disputes about what exists across worlds.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.In the model theory of SQML, the possibility operator ◇ is literally an existential quantifier ranging over all possible worlds
      ?

      Think about whether this reason is strong or weak

    • 2.In evaluating an existentially quantified formula ∃νφ at a possible world w, the quantifier ∃ν ranges unrestrictedly over all individuals
      ?

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    • 3.When two existential quantifiers range over independent domains, switching their order does not alter the truth value of the formula
      ?

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