more from Harold Noonan

Single Idea 16016

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

Full Idea

Identity can be circularly defined, as 'the relation everything has to itself and to nothing else', …or as 'the smallest equivalence relation'.

Gist of Idea

Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular


Harold Noonan (Identity [2009], §2)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [], p.2

A Reaction

The first one is circular because 'nothing else' implies identity. The second is circular because it has to quantify over all equivalence relations. (So says Noonan).

Related Ideas

Idea 10104 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman]

Idea 16017 Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]