The Counterpart Relation
The counterpart relation (hereafter C-relation) differs from the notion of identity. Identity is a reflexive, symmetric, and transitive relation. The counterpart relation is only a similarity relation; it needn’t be transitive or symmetric. The C-relation is also known as genidentity (Carnap 1967), I-relation (Lewis 1983), and the unity relation (Perry 1975).
If identity is shared between objects in different possible worlds then the same object can be said to exist in different possible worlds (a trans-world object, that is, a series of objects sharing a single identity).
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