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    The formula ◇∃x Bx entails ∃x◇Bx (where B represents the ... — Carmelics
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    Home/Modality & Possibility
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    The formula ◇∃x Bx entails ∃x◇Bx (where B represents the predicate 'is Bergoglio's child')

    Modality & Possibility
    ?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.◇∃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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Topics

    Modality & Possibility

    Connections

    1 topic

    Philosophy of Language2 linked

    Related

    Actualists following Prior and Fine deny that merely possible individuals are ge...If ∃x in ∃x◇Bx ranges only over actual existents, the entailment requires Bergog...On variable domain semantics (Kripke 1963), individuals may exist in some worlds...Saying 'some world and some individual are such that P' is equivalent to saying ...
    +4 moreShow less
    The quantifier swap in P2 is only valid if the domain of quantification is held ...Therefore the formula can be rewritten as ∃x◇Bx without change in truth valueTherefore ◇∃xBx may be made true by a merely possible individual that falls outs...◇∃x Bx means: some world and some individual are such that, in that world, that ...

    Similar

    The formula 'possibly there exists an x such that x is a child of Berg...80%The formula 'there exists an x such that x is possibly a child of Berg...79%◇∃x Bx means: some world and some individual are such that, in that wo...76%FM entails Value Definiteness (VD).76%

    Source

    AI-extracted1/3 agreementValid
    SEP: possibilism-actualism
    View source passageHide passage
    That is, informally, if there could be something satisfying any given description \(\varphi,\) then there is something that could satisfy that description, a thing that is possibly \(\varphi.\) The validity of BF in SQML rests on two facts: first, that in the model theory of SQML (as in all varieties of possible world semantics), the possibility operator \(\Diamond\) is literally an existential quantifier ranging over all possible worlds; and second, that, in evaluating an existentially quan
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit