more from Harold Noonan

Single Idea 16017

[catalogued under 9. Objects / F. Identity among Objects / 2. Defining Identity]

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


Harold Noonan (Identity [2009], 2)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [], 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]