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Does every sentence like this exhibit a scope ambiguity

We think recent work in linguistics tells against the traditional claim that a string of words like (1) Every girl pushed some truck has two readings, indicated by the following formal language sentences (with restricted quantifiers): (1a) [!x:Gx]["y:Ty]Pxy (1b) ["y:Ty][!x:Gx]Pxy. In our view, (1) does not have any b-reading in which 'some truck' has widest scope. 1 The issue turns on details concerning syntactic transformations and terms like 'every'. This illustrates an important point for the study of natural language: ambiguity hypotheses are indeed hypotheses—i.e., theoretical claims to be justified in light of various considerations, not theses whose truth can be directly observed by speakers. Correlatively, strings that appear to be similar may differ with respect to scopal possibilities. While the object cannot take scope over the subject in (1), we hold that in (2) Some girl pushed every truck 'every truck' can take scope over 'some girl'. But showing that (2) is truth-conditionally ambiguous is hard, especially if natural language involves tacit quantification over events. (A string can be structurally ambiguous without having truth-conditionally distinct readings; consider [[α & β] & γ] as opposed to [α & [β & γ]].) Other cases are clearer. The subject in (3) Two girls pushed six trucks can be distributive or collective. Indeed, we use facts about plural constructions like (3) and (4) Both girls pushed six trucks to support the claim that (1) is truth-conditionally unambiguous. Finally, we argue that (5) Ralph believes that the richest man is happy has no reading in which 'the richest man' has scope over 'believes'. Our particular conclusions are less important, though, than the methodological moral. Linguistic meaning is constrained in ways that ambiguity hypotheses must respect. It can be hard to know how many readings a string of words has, especially when the scope of quantifiers is at issue. Far from being paradigms of ambiguity in natural language, (1-2) are complicated cases.