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 Reference
'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]