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    Once variable domains are permitted (as in Kripke's 1963 ... — Carmelics
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    Challenges→The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)

    Once variable domains are permitted (as in Kripke's 1963 semantics), the universal instantiation axiom fails and BF is no longer valid.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.In variable domain semantics, a quantified formula true at world w may quantify over objects not existing at w, breaking standard instantiation.
      ?

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    • 2.Universal instantiation assumes the domain is constant; when domains vary across worlds, substituting a name risks referring to non-existent objects.
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    • 3.Barcan formula's validity requires that whatever exists in accessible worlds already exists in the current world—variable domains explicitly reject this.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Variable domain semantics can preserve universal instantiation if restricted to objects in the actual domain of the evaluating world.
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    • 2.The failure of BF may reflect defects in Kripke's 1963 semantics rather than a principled problem with variable domains themselves.
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    • 3.Some philosophers argue variable domains should be combined with actualist quantification, which restores universal instantiation validity.
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    Related

    Barcan formula's validity requires that whatever exists in accessible worlds alr...In variable domain semantics, a quantified formula true at world w may quantify ...Some philosophers argue variable domains should be combined with actualist quant...The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)
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    The failure of BF may reflect defects in Kripke's 1963 semantics rather than a p...Universal instantiation assumes the domain is constant; when domains vary across...Variable domain semantics can preserve universal instantiation if restricted to ...

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