I argue that English modal auxiliaries have an array of logical types: they function as sentence operators, as predicates, and as variable binding operators. Chapter One introduces the root/epistemic distinction and earlier treatments of it in the literature of generative grammar and model theoretic semantics. An extensive descriptive section in Chapter Two establishes precisely the empirical characteristics of the distinction, which are confined to the semantics. I then account for these characteristics by positing two semantic types for modal auxiliaries: the first type is that of a sentence operator and is at work in the interpretation of modal sentences with an epistemic sense and for those with a deontic 'ought-to-be' sense; the second type is that of a relation between a property and an individual and it is at work in the interpretation of modal sentences expressing ability, disposition, rights and obligations (traditionally, the root interpretations.) The link between the interpretive class of the modal sentence and the type of the modal expression in Intensional Logic is not drawn in the lexicon, but is accounted for by native speakers' intuitions about what sort of notions make sense as modal properties and what as modal propositions. In Chapter Three, I turn to another class of interpretations of modal sentences, exemplified by the sentence 'A basketball player can be short'. After demonstrating that the modal auxiliary functions as a variable binder in such sentences, I go on to expand the inventory of types associated with modal auxiliaries to include the type associated with variable binding operators.
