Identity |
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Parsons (Terence) |

Source: Parsons - Indeterminate Identity, 2000, Chapter 3 |

Paper - Abstract |

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__Analytic TOC_{1}__

- 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 Law
^{2}: 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 identity
^{3}" because relative identity^{4}, unlike genuine identity, does not validate Leibniz's Law^{5}. - 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.

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