Full Idea
The outstanding technical objection to counterpart-theoretic semantics concerns its handling of the logic of identity. In quantified S5 (the orthodox semantics) a = b → □(a = b) is valid, but 'a' must not attach to two objects.
Gist of Idea
Counterpart theory is not good at handling the logic of identity
Source
Graeme Forbes (The Metaphysics of Modality [1985], 3.5)
Book Reference
Forbes,Graeme: 'The Metaphysics of Modality' [OUP 1985], p.66