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

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]**