With this discussion of some of the philosophical background for a typed theory of lexical meaning, I now turn to examining some precursors of the theory to be proposed here. All of these precursors take some sort of stand concerning the representation of lexical meaning and the sort of phenomena that are the focus of this book—various forms of predication both at the clausal and morphological levels, copredication, and coercion.

A basic issue concerning lexical representation is lexical ambiguity. Some people distinguish between monomorphic and polymorphic languages, which correspond to two different ways of thinking about ambiguity. A monomorphic language (or lexicon for a language) is one in which each word has a unique type and syntactic category. Ambiguous words on this view are analyzed as words with the same orthography but each with a different sense. This is the view found in Montague Grammar or even in HPSG, and it corresponds to an approach to ambiguity according to which ambiguous expressions are represented by the set of their disambiguations. A polymorphic language (or lexicon for a language) is one in which each word may have multiple types or underspecified types that may be further specified during the composition process. Underspecification is a tool or method devised by linguists working on ambiguity in sentential and discourse semantics.