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    Within a single fixed language for which Leibniz's Law is... — Carmelics
    Home/Personal Identity
    HistoryEditSee Inverse

    Within a single fixed language for which Leibniz's Law is defined, Relative Identity and Leibniz's Law are incompatible.

    Modality & PossibilityPersonal Identity
    ?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.Identity relations are assumed to be equivalence relations.
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    • 2.The underlying propositional logic is assumed to be classical.
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    • 3.Given these assumptions, RI and LL cannot both hold in the same framework.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Wiggins demonstrates that a sortal-relativized reading of LL—'x and y are the same F only if they share all F-relevant properties'—remains consistent with RI.
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    • 2.The incompatibility claim assumes LL must range over all properties unrestricted, but a sortal-restricted LL is not logically weaker in any objectionable sense.
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    • 3.Since the restricted LL still grounds all legitimate individuation practices, the alleged incompatibility is an artifact of an unnecessarily strong formulation of LL.
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    Reason against 2 of 2
    ?
    • 1.Geach argues that all identity is sortal-relative, so 'absolute identity' required by Leibniz's Law is not a coherent predicate but a philosophical fiction.
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    • 2.If no language can coherently define absolute identity, then LL's presupposition fails, and the incompatibility dissolves rather than refuting RI.
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    Topics

    Personal IdentityModality & Possibility

    Connections

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    Truth & Knowledge1 linked

    Related

    Geach argues that all identity is sortal-relative, so 'absolute identity' requir...Given these assumptions, RI and LL cannot both hold in the same framework.Identity relations are assumed to be equivalence relations.If no language can coherently define absolute identity, then LL's presupposition...
    +4 moreShow less
    Since the restricted LL still grounds all legitimate individuation practices, th...The incompatibility claim assumes LL must range over all properties unrestricted...The underlying propositional logic is assumed to be classical.Wiggins demonstrates that a sortal-relativized reading of LL—'x and y are the sa...

    Similar

    Measurements of P and Q are incompatible.82%□N is invalid in KQML's semantics77%CBF is invalid in KQML's semantics77%BF is invalid in KQML's semantics77%

    Source

    AI-extracted1/3 agreementValid
    SEP: identity-relative
    View source passageHide passage
    It may seem, then, that RI is simply incoherent. These arguments, however, are a bit too quick. On analysis, they show only that the following three conditions form an inconsistent triad: (1) RI is true (for some fixed predicates \(F\) and \(G)\). (2) Identity relations are equivalence relations. (3) The relation x and y are the same F figuring in (1) satisfies LL. For suppose that the relation x and y are the same G, figuring in (1), is reflexive and that \(x\) is a \(G\). Then \(x\) is the sam
    Extraction notes

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

    Details

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