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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Adams necessarily exists — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Adams necessarily exists

    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.For any property F, by GSA (Generalized Substitution Axiom) and Nec, necessarily Adams has F only if Adams exists: □(Fa → E!a)
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    • 2.Identity is a relation, so identity statements are atomic formulas governed by GSA
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    • 3.By GSA, Adams is self-identical only if Adams exists: a=a → E!a
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Self-identity (a=a) is a logical truth only for terms that successfully refer, but names of contingent beings may fail to refer in worlds where those beings don't exist.
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    • 2.If 'Adams' is a rigid designator that presupposes its referent's existence, then (a=a) is not a pure logical truth but a metaphysically loaded one, making the derivation of necessary existence question-begging.
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    • 3.Kripke's framework for rigid designation does not entail that a designator refers in worlds where its bearer is absent, so GSA applied to contingent beings smuggles in existential presuppositions.
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    Reason against 2 of 2
    ?
    • 1.On a free logic interpretation, atomic predications including identity are false (not true) when the subject term lacks a referent in a given world.
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    • 2.If free logic governs quantified modal logic, then (a=a) fails in worlds where Adams does not exist, breaking the derivation at P5 without any contradiction in the remaining premises.
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    Topics

    Modality & Possibility

    Connections

    1 linked claim · 2 topics

    Philosophy of Language5 linkedTruth & Knowledge2 linked
    Numbers necessarily exist

    Related

    Adams accepts the standard laws of identity (Id1 and Id2)Adams is self-identical (a=a) is a logical truthBy GSA, Adams is self-identical only if Adams exists: a=a → E!aFor any property F, by GSA (Generalized Substitution Axiom) and Nec, necessarily...
    +7 moreShow less
    Identity is a relation, so identity statements are atomic formulas governed by G...If 'Adams' is a rigid designator that presupposes its referent's existence, then...If free logic governs quantified modal logic, then (a=a) fails in worlds where A...Kripke's framework for rigid designation does not entail that a designator refer...

    Similar

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    Source

    AI-extracted1/3 agreementValid
    SEP: possibilism-actualism
    View source passageHide passage
    Thus, in particular, for any property \(F,\) by GSA and Nec we have that, necessarily, Adams has \(F\) only if he exists: \(\Box(\sfF\sfa \to \sfE!\sfa)\). The problem here is that Adams (reasonably) considers identity to be a relation; identity statements are thus simply a variety of atomic formula and, hence, it is also an instance of GSA that Adams is self-identical only if he exists, \(\sfa=\sfa \to \sfE!\sfa\). As Adams accepts the usual laws of identity Id1 and Id2, we appear to have the
    Extraction notes

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

    Details

    Numbers necessarily exist
    On a free logic interpretation, atomic predications including identity are false...
    Self-identity (a=a) is a logical truth only for terms that successfully refer, b...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit