Many philosophers and linguists have been attracted to counterpart theory as a framework for natural language semantics. I raise a novel problem for counterpart theory involving simple declarative sentences with proper names. To resolve this problem, counterpart theorists must introduce the notion of a counterpart in the semantics of the non‐modal fragment of language. I develop my preferred solution: a novel theory of proper names as counterpart‐theoretic individual concepts. The resulting view highlights a hitherto unnoticed fact: counterpart theorists should formulate (...) their theory, not by modifying the standard semantics for modal operators, but by modifying the standard semantics for names and variables. (shrink)