- Real identity in the world is defined in terms of coincidence of properties: objects are identical if they both determinately have and determinately lack the same properties, and they are distinct if one determinately has a property that the other determinately lacks.
- If neither of these holds, then it is indeterminate whether the objects are identical.
- It is an empirical matter whether there is any indeterminacy at all, and an empirical matter whether such indeterminacy, if it exists, extends to identity.
- This explanation of identity validates Leibniz's Law2: From 'a = b' and 'φa' one can infer 'φb'.
- But it does not validate the contrapositive form of this law: one might have 'φa' and '¬φb' both true without '¬a = b' being true; this can happen if 'φx' does not express a property.
- The identity discussed here is not "relative identity3" because relative identity4, unlike genuine identity, does not validate Leibniz's Law5.
- The four identity puzzles are reviewed; in each case in which the identity is indeterminate, there is a property determinately possessed by one object that is not determinately possessed by the other, but there is no property for which they determinately disagree.
Footnote 1: Taken from "Parsons (Terence) - Indeterminate Identity: Analytical Table of Contents".
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