His name is Socrates because that’s what he’s called: A model-theoretic account of name-bearing

Abstract

The notion of name-bearing, and its relation to the use of proper names to refer to individuals, has long remained mysterious in linguistics. In the present paper, I provide a novel semantics for proper names as variable expressions that enforce restrictions on their syntactic indexation, in order to give a precise model-theoretic definition of name-bearing that explicitly depends on the notion of reference to individuals using proper names.