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Single Idea 17594
[filed under theme 9. Objects / F. Identity among Objects / 2. Defining Identity
]
Full Idea
For general terms write 'if Fx then Fy' and vice versa, and 'if Fxz then Fyz'..... The conjunction of all these is coextensive with 'x=y' if any formula constructible from the vocabulary is; and we can adopt that conjunction as our version of identity.
Gist of Idea
We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy'
Source
Willard Quine (Word and Object [1960], §47)
Book Ref
Quine,Willard: 'Word and Object' [MIT 1969], p.230
A Reaction
[first half compressed] The main rival views of equality are this and Wiggins (1980:199). Quine concedes that his account implies a modest version of the identity of indiscernibles. Wiggins says identity statements need a sortal.
The
14 ideas
with the same theme
[whether identity can be defined - and how]:
22322
|
You can't define identity by same predicates, because two objects with same predicates is assertable
[Wittgenstein]
|
17594
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We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy'
[Quine]
|
10797
|
Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all
[Marcus (Barcan)]
|
9848
|
Content is replaceable if identical, so replaceability can't define identity
[Dummett, by Dummett]
|
9842
|
Frege introduced criteria for identity, but thought defining identity was circular
[Dummett]
|
11831
|
The formal properties of identity are reflexivity and Leibniz's Law
[Wiggins]
|
16497
|
Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity
[Wiggins]
|
16498
|
Identity cannot be defined, because definitions are identities
[Wiggins]
|
16502
|
Identity is primitive
[Wiggins]
|
16015
|
Problems about identity can't even be formulated without the concept of identity
[Noonan]
|
16017
|
Identity is usually defined as the equivalence relation satisfying Leibniz's Law
[Noonan]
|
16016
|
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular
[Noonan]
|
16020
|
Identity can only be characterised in a second-order language
[Noonan]
|
6053
|
Identity is as basic as any concept could ever be
[McGinn]
|