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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
Source
Harold Noonan (Identity [2009], §2)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], 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]
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| 16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
| 16020 | Identity can only be characterised in a second-order language [Noonan] |
| 16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
| 16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
| 16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
| 16018 | Indiscernibility is basic to our understanding of identity and distinctness [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] |