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Full Idea
In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers.
Clarification
His middle period is 1891-1906
Gist of Idea
Frege introduced criteria for identity, but thought defining identity was circular
Source
Michael Dummett (Frege philosophy of mathematics [1991], Ch.10)
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.113
A Reaction
The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria.
| 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] |