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Full Idea
Numerical identity is usually defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the indiscernibility of identicals, where everything true of x is true of y.
Gist of Idea
Identity is usually defined as the equivalence relation satisfying Leibniz's Law
Source
Harold Noonan (Identity [2009], §2)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
Noonan says this must include 'is identical to x' among the truths, and so is circular
Related Ideas
Idea 10104 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman]
Idea 16016 Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
Idea 11831 The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
| 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] |