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Single Idea 11831

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

Full Idea

The formal properties of identity are the reflexivity of identity, and Leibniz's Law (if x is the same as y, then whatever is true of one is true of the other).

Gist of Idea

The formal properties of identity are reflexivity and Leibniz's Law

Source

David Wiggins (Sameness and Substance Renewed [2001], Pr.2)

Book Ref

Wiggins,David: 'Sameness and Substance Renewed' [CUP 2001], p.4

A Reaction

Presumably transitivity will also apply, and, indeed, symmetry. He seems to mean something like the 'axiomatic formal properties'.

Related Idea

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

The 14 ideas with the same theme [whether identity can be defined - and how]:

22322 You can't define identity by same predicates, because two objects with same predicates is assertable [Wittgenstein]
17594 We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine]
10797 Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]
9848 Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
9842 Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
11831 The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
16497 Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins]
16498 Identity cannot be defined, because definitions are identities [Wiggins]
16502 Identity is primitive [Wiggins]
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]
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]
6053 Identity is as basic as any concept could ever be [McGinn]