My goal in this paper is to present and defend a semantics for demonstrative phrases like ‘that dog’. There are several semantic proposals currently on offer for demonstratives, but only a handful attempt to capture the full range of uses of these phrases. Among these are Jeffrey King’s quantificational semantics for demonstratives, and Paul Elbourne’s semantic treatment of demonstratives as definites in a situation semantics. The theory I defend here also captures the full range of uses of demonstrative phrases, but in a very different way from either King’s or Elbourne’s theories. Where those theories assume that there must be a unified semantic account of the full range of uses of demonstratives, I shall instead defend a view according to which demonstratives exhibit a special kind of ambiguity. The central contention of what I call the Pragmatic Ambiguity Theory is that the rules governing the use of demonstratives in English distinguish between those uses that are acts of speaker reference, and those that are not. For those uses of demonstratives that are acts of speaker reference, the semantic function or role of the demonstratives is to exploit speaker reference for semantics. These uses are directly referential. For those uses of demonstratives that are not acts of speaker reference, the semantic function or role of the demonstratives is the same as that of definite descriptions.