Homework 4: The definite article

At the end of class yesterday, we started talking about the meanings of verbs, adjectives, nouns and prepositional phrases in predicate position. We ended up saying that the denotation of a verb like smoke is a function from individuals to propositions; that is, a function from individuals to a function from possible worlds to truth values. Specifically, the verb smoke denotes the function smoke' which is defined as follows:

• For any individual x, smoke'(x) = { w | x smokes in w}.

ASSUME that nouns like doctor, semanticist, etc. have meanings of the same sort as intransitive verbs like smoke. So doctor, for example, denotes the function doctor' which is defined as follows:

• For any individual x, doctor'(x) = { w | x is a doctor in w}.

YOUR JOB: Given this denotation for the noun doctor, propose a denotation for the determiner the that correctly captures its use in a sentence like:

• The doctor smokes.