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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Identity relations are assumed to be equivalence relations. — Carmelics
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    Home/Personal Identity
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    Supports→Within a single fixed language for which Leibniz's Law is defined, Relative Identity and Leibniz's Law are incompatible.

    Identity relations are assumed to be equivalence relations.

    Modality & PossibilityPersonal Identity
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    Related propositions within the same area of thought.
    Given these assumptions, RI and LL cannot both hold in the same framework.The underlying propositional logic is assumed to be classical.Within a single fixed language for which Leibniz's Law is defined, Relative Iden...

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    Any equivalence relation presupposes identity84%RI, the claim that identity relations are equivalence relations, and t...79%By Leibniz's Law applied to the same-F relation, since x and y are the...78%Not all equivalence relations can be drafted to do the job of identity...77%

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    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

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