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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]
| 16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [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] |
| 16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
| 16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
| 16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
| 16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |