4 - Some empirically significant properties of quantifiers and determiners

Summary

An important benefit of generalized quantifier theory is that it enables one to discover and study semantic properties of empirical significance. Some of these properties are useful in expressing descriptive generalizations and in replacing inferior generalizations stated in pre-theoretical terms or with reference to morphology. The best-known examples are the properties involved in the characterization of what noun phrases occur in existential sentences or license certain negative polarity items. Other properties, like conservativity and extension, offer valuable clues to learnability and to the working of the syntax/semantic interface. Yet others are useful building blocks in understanding scope behavior and the ability to be associated with existential closure or exceptive phrases.

Another benefit is that the theory offers a simple insight into how complex quantifiers can be obtained by Boolean operations. This solves an important portion of the compositionality questions arising in the noun phrase domain, although other questions remain, as will be seen in Chapter 5 and in the subsequent chapters.

Finally, in many cases the theory enables us to state the claims in such a way that they are not restricted to quantifiers or to the nominal domain but transcend category boundaries. Monotonicity properties and Boolean combinations are prime examples.

This book strictly follows the terminology that generalized quantifiers are the denotations of full noun phrases like every dragon and more than two dragons. Expressions like every and more than two denote semantic determiners. The discussion will proceed in two stages.