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Single Idea 22322
[filed under theme 9. Objects / F. Identity among Objects / 2. Defining Identity
]
Full Idea
Russell's definition of identity [x is y if any predicate of x is a predicate of y] won't do, because then one cannot say that two objects have all their properties in common
Gist of Idea
You can't define identity by same predicates, because two objects with same predicates is assertable
Source
Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5302), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 53 'Ident'
Book Ref
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.358
A Reaction
[The Russell is in Principia] Good. Even if Leibniz is right that no two obejcts have identical properties, it is at least meaningful to consider the possibility. Russell makes it an impossibility, rather than a contingent fact.
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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16020
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Identity can only be characterised in a second-order language
[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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16017
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Identity is usually defined as the equivalence relation satisfying Leibniz's Law
[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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