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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Perspectives
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The formula ◇∃x Bx entails ∃x◇Bx (where B represents the predicate 'is Bergoglio's child')

    ?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.The quantifier swap in P2 is only valid if the domain of quantification is held fixed across all possible worlds.
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    • 2.On variable domain semantics (Kripke 1963), individuals may exist in some worlds but not others, so ∃x ranges over different objects world-by-world.
      ?

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    • 3.Therefore ◇∃xBx may be made true by a merely possible individual that falls outside the actual domain, blocking the inference to ∃x◇Bx.
      ?

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    Reason for 2 of 2
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    • 1.Actualists following Prior and Fine deny that merely possible individuals are genuine values of bound variables in actual-world quantification.
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    • 2.If ∃x in ∃x◇Bx ranges only over actual existents, the entailment requires Bergoglio's possible child to actually exist, which begs the question against actualism.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.◇∃x Bx means: some world and some individual are such that, in that world, that individual is Bergoglio's child
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    • 2.Saying 'some world and some individual are such that P' is equivalent to saying 'some individual and some world are such that P'
      ?

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    • 3.Therefore the formula can be rewritten as ∃x◇Bx without change in truth value
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.