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9. Objects / F. Identity among Objects / 2. Defining Identity

[whether identity can be defined - and how]

13 ideas
We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine]
Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]
Content is replaceable if identical, so replaceability can't define identity [Dummett on Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins]
Identity cannot be defined, because definitions are identities [Wiggins]
Identity is primitive [Wiggins]
Problems about identity can't even be formulated without the concept of identity [Noonan]
Identity can only be characterised in a second-order language [Noonan]
Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
Identity is as basic as any concept could ever be [McGinn]