METAPHYSICS – AN OVERVIEW : Identity and Persistence

Two Important Preliminary Distinctions:  (1) Qualitative identity versus numerical identity;  (2) Numerical identity versus the unity relation.

The Definition of Numerical Identity:  (1) Numerical identity is a purely logical relation; (2) Numerical identity can be defined via introduction and elimination rules. 

A Potentially Misleading Way of Talking:  "synchronic identity" versus "diachronic identity".  Identity is not a cross-temporal relation.

Realist versus Reductionist Accounts of the Synchronic Unity Relation:  (1) What makes it the case that two property instances that exist at the same time belong to one and the same thing?  (2) Is the synchronic unity relation unique and unanalyzable, or is it analyzable?  (3) Is it reducible, for example, to nomological connections between property instances?  (4) Or does the synchronic unity relation have to be analyzed in terms of causal relations to property instances that exist at earlier times?

Realist versus Reductionist Accounts of the Diachronic Unity Relation:  (1) What makes it the case that two property instances that exist at different times belong to one and the same persisting thing?  (2) Is the diachronic unity relation unique and unanalyzable, or is it reducible, for example, to causal connections of an appropriate sort?  (3) Causal connections as a necessary condition of the presence of the unity relation:  Armstrong's annihilation/creation case.  (4) Are all questions of identity settled once all causal relations are settled?  (5) The issues raised by fission and fusion cases.

The Diachronic Unity Relation and the Definition of Persisting Entities:  (1) The diachronic unity as a relation not between temporal parts, but between property instances existing at different times;  (2) Fission and fusion cases show that the diachronic unity relation cannot be both symmetric and transitive, whereas identity is;  (3) Can one define a persisting entity ("identity over time") in terms of property instances that are related via a non-branching unity relation?