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Single Idea 16497
[filed under theme 9. Objects / F. Identity among Objects / 2. Defining Identity
]
Full Idea
The principle of Leibniz's Law marks off what is peculiar to identity and differentiates it in a way in which transitivity, symmetry and reflexivity (all shared by 'exact similarity, 'equality in pay', etc.) do not.
Clarification
Leibniz's Law here is the Indiscernibility of Identicals
Gist of Idea
Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity
Source
David Wiggins (Sameness and Substance [1980], 1.2)
Book Ref
Wiggins,David: 'Sameness and Substance' [Blackwell 1980], p.21
The
14 ideas
with the same theme
[whether identity can be defined - and how]:
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22322
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You can't define identity by same predicates, because two objects with same predicates is assertable
[Wittgenstein]
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17594
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We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy'
[Quine]
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10797
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Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all
[Marcus (Barcan)]
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9848
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Content is replaceable if identical, so replaceability can't define identity
[Dummett, by Dummett]
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9842
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Frege introduced criteria for identity, but thought defining identity was circular
[Dummett]
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11831
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The formal properties of identity are reflexivity and Leibniz's Law
[Wiggins]
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16497
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Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity
[Wiggins]
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16498
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Identity cannot be defined, because definitions are identities
[Wiggins]
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16502
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Identity is primitive
[Wiggins]
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16015
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Problems about identity can't even be formulated without the concept of identity
[Noonan]
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16017
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Identity is usually defined as the equivalence relation satisfying Leibniz's Law
[Noonan]
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16016
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Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular
[Noonan]
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16020
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Identity can only be characterised in a second-order language
[Noonan]
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6053
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Identity is as basic as any concept could ever be
[McGinn]
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