Since the late 1970s, the orthodox view of complex 'that' phrases (e.g., 'that woman eating a granola bar') has been that they are contextually sensitive devices of direct reference. In Complex Demonstratives, Jeffrey King challenges that orthodoxy, showing that quantificational accounts not only are as effective as direct reference accounts but also handle a wider range of data.
After providing arguments against direct reference accounts of 'that' phrases and developing a quantificational theory of them, King looks at the interaction of 'that' phrases with modal operators, negation, and verbs of propositional attitude. He argues for evidence of scope interaction between 'that' phrases and other scoped elements. King also addresses semantic properties of 'that' and other determiners, and the possibility of extending the semantics of 'that' phrases to 'that' as a syntactically simple demonstrative. Finally, he argues against what he calls ambiguity approaches, theories that hold that the various uses of 'that' phrases cannot be treated by a single semantical theory.