A Single-Type Semantics for the PTQ-Fragment

Abstract

In (Montague, 1970), Montague defines a formal theory of linguistic meaning which interprets a small fragment of English through the use of two basic types of objects: individuals and propositions. In this paper, I develop a comparable semantics which only uses one basic type of object (hence, single-type semantics). Such a semantics has been suggested by Partee (2009) as a ‘minimality test’ for the Montagovian type system, which challenges the need for a bi-partitioned ontology. The proposed semantics captures the propositional interpretation of proper names, unifies Montague’s semantic ontology, and yields insight into the apparatus of types in formal semantics.