Five experiments investigated the interpretation of quantified noun phrases in relation to discourse structure. They demonstrated, using questionnaire and on-line reading techniques, that readers in English prefer to give a quantified noun phrase in (VP-external) subject position a presuppositional interpretation, in which the noun phrase limits or restricts the interpretation of an already available set, rather than giving it a nonpresuppositional or existential interpretation, in which it introduces completely new entities into the discourse. Experiment 1 showed that readers prefer a presuppositional interpretation of three ships over the existential interpretation in Five ships appeared on the horizon. Three ships sank. Experiment 2 showed longer reading times in sentences that are disambiguated toward the existential interpretation than in sentences that permit the presuppositional interpretation. Experiment 3 suggested that the presuppositional preference is greater when the phrase three ships occurs outside the verb phrase than when it occurs inside the verb phrase. Experiment 4 showed that Korean subjects marked with a topic marker received more presuppositional interpretations than subjects marked with a nominative marker. Experiment 5 showed that German subjects in VP-external (but nontopic) position received more presuppositional interpretations than VP-internal subjects. The results suggest the syntactic position of a phrase is one determinant of its interpretation, as expected according to the mapping hypothesis of Diesing (1992).