This research investigates the second language (L2) acquisition of a quantificational phenomenon that involves the interplay of multiple levels of linguistic analysis. The interpretation of English sentences containing negation and the quantifier phrase "every NP" in subject (e.g., Every horse didn't jump over the fence) and object (e.g., Mary didn't eat every meal) position can be scopally ambiguous and occurs at the syntax-semantics-pragmatics interface. Not much is known about how L2 learners deal with such scope ambiguities, and the present study examines how this interface phenomenon is acquired in L2 acquisition. 15 native speakers of English and 38 L1-Korean L2 learners of English participated in an Acceptability Rating Task in which the subjects read short passages and rated the target sentence as an acceptable or unacceptable description in the context of the story. The results suggest that L2 learners of lower proficiency can be interfered by L1 transfer while learners of advanced proficiency can access native-like interpretations. The study finds evidence for L2 indeterminacy in the interpretation of sentences that occurs at the syntax-pragmatics-semantics interface, but also finds support for the Full Transfer/Full Access Hypothesis. In sum, the interpretation of scope ambiguities seems to be a UG-driven developmental problem that can be overcome with increasing proficiency in L2 acquisition.