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    By Leibniz's Law applied to the same-F relation, since x ... — Carmelics
    Home/Personal Identity
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    Supports→RI, the claim that identity relations are equivalence relations, and the claim that the same-F relation satisfies Leibniz's Law form an inconsistent triad.

    By Leibniz's Law applied to the same-F relation, since x and y are the same F, they must share the property of being the same G as x.

    Modality & PossibilityPersonal Identity
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    Personal IdentityModality & Possibility

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    By RI, x and y are not the same G.RI, the claim that identity relations are equivalence relations, and the claim t...Suppose RI is true for fixed predicates F and G, so x and y are the same F but n...Suppose the same-G relation is reflexive and x is a G, so x is the same G as x.

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    This contradicts the claim that x and y are not the same G.

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    Suppose the same-G relation is reflexive and x is a G, so x is the sam...88%If x is assumed to be vaguely identical to y, then by Leibniz's Law, x...86%Given Supersubstantivalism+, x is identical to y.85%By Leibniz's Law, if x and y differ in a property, then x and y are ab...82%

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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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