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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Relative identity is logically untenable because it entails a contradiction under Leibniz's Law.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Geach argues Leibniz's Law presupposes absolute identity, which begs the question against relative identity theories.
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    • 2.On relative identity, 'a = b' is always sortal-relative (a is the same F as b), so cross-sortal substitution in Leibniz's Law is simply ill-formed.
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    • 3.A logically ill-formed inference generating contradiction reveals a category error in the argument, not a contradiction in the target theory.
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    Reason for 2 of 2
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    • 1.Wiggins's work shows that identity statements require a covering sortal concept, and predicates like 'is G' inherit their extension from sortal-relative criteria of application.
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    • 2.If 'is G' applies relative to a sortal kind, then 'a is G' and 'b is not G' need not be contradictory when a and b fall under distinct covering sortals.
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    • 3.The appearance of contradiction in relative identity cases thus reflects equivocation in the application of predicates across sortals, not a genuine violation of substitutivity.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.If relative identity were allowed, one could reach a situation where a is G, a = b, and b is not G.
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    • 2.For 'a is G' and 'b is not G' to be contradictory, 'is G' must be univocal across both occurrences.
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    • 3.Leibniz's Law requires that if a = b, then whatever is true of a is true of b.
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