2007, The Philosophical Quarterly
Singular-term semantics has been intractable. Frege took the referents of singular terms to be their semantic values. On his account, vacuous terms lacked values. Russell separated the semantics of definite descriptions from the semantics of proper names, which caused truth-values to be composed in two different ways and still left vacuous names without values. Montague gave all noun phrases sets of verb-phrase extensions for values, which created type mismatches when noun phrases were objects and still left vacuous names without values. There is a single type of value for all noun phrases that dissolves the difficulties which have beset singular-term semantics. I. RUSSELL'S DIVISION Ever since Bertrand Russell made definite descriptions vanish on analysis into existential generalizations, and contrasted them with simple symbols that directly designate individuals, many theorists have divided singular terms into two semantic types. There are genuine singular terms which take individuals as their semantic values; 1 and there are quantified noun phrases, which on Russell's view have no 'meaning in isolation'. Russell analysed definite descriptions using the unrestricted quantifiers of standard predicate logic, which operate on propositional functions (formulae with free variables) to yield sentences. When sentences are translated into logical notation by means of unrestricted quantifiers, there are no constituents identifiable as noun phrases. Logical analysis eliminates definite descriptions. Recently, many semantic theorists have modified Russell's analysis while preserving his division between genuine singular terms and quantified expressions. Quantified noun phrases are analysed as restricted quantifier phrases that have sets of verb-phrase extensions for semantic values. The current view is not that descriptions lack meaning in isolation but rather that 1 By 'semantic value' I mean the extension that an expression has when it is evaluated with respect to a circumstance. The semantic value of a sentence is its truth-value.