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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 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]