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    Relative identity is logically untenable because it entai... — Carmelics
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    Home/Consciousness & Mind
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    Relative identity is logically untenable because it entails a contradiction under Leibniz's Law.

    Consciousness & Mind
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Consciousness & Mind

    Related

    A logically ill-formed inference generating contradiction reveals a category err...For 'a is G' and 'b is not G' to be contradictory, 'is G' must be univocal acros...Geach argues Leibniz's Law presupposes absolute identity, which begs the questio...If 'is G' applies relative to a sortal kind, then 'a is G' and 'b is not G' need...
    +5 moreShow less
    If relative identity were allowed, one could reach a situation where a is G, a =...Leibniz's Law requires that if a = b, then whatever is true of a is true of b.On relative identity, 'a = b' is always sortal-relative (a is the same F as b), ...The appearance of contradiction in relative identity cases thus reflects equivoc...Wiggins's work shows that identity statements require a covering sortal concept,...

    Similar

    A proof against relative identity works by showing that allowing relat...80%Type-type identity theory is false (or at least not widely tenable)79%If type-identity is impossible, token-identity must be justified on gr...79%The utter certainty of the logical law of identity (A = A) is grounded...75%

    Source

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    More importantly, that there are no ad hoc sortals is essential to the significance of the formal proof that there is no such thing as relative identity. In logic and in the application of Leibniz’s Law, ‘a is F’ is normally equivalent to ‘a was, is or will be F’, otherwise the Law would not apply to such accidental properties as ‘is brown’. This is also the way phase sortals work: a human being is, was, or will be a baby. The argument against relative identity works by arguing that, if one allo
    Extraction notes

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

    Details

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