Does every Sentence Like This Exhibit a Scope Ambiguity?Paul Pietroski and Norbert Hornstein, Univ. of MarylandWe think recent work in linguistics tells against the traditional claim that a string of words like(1) Every girl pushed some truckhas 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 ondetails concerning syntactic transformations and terms like ‘every’. This illustrates an important point forthe study of natural language: ambiguity hypotheses are indeed hypotheses—i.e., theoretical claims to bejustified 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 ishard, especially if natural language involves tacit quantification over events. (A string can be structurallyambiguous 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 truckscan be distributive or collective. Indeed, we use facts about plural constructions like (3) and (4) Both girls pushed six trucksto support the claim that (1) is truth-conditionally unambiguous. Finally, we argue that(5) Ralph believes that the richest man is happyhas no reading in which ‘the richest man’ has scope over ‘believes’. Our particular conclusions are less important, though, than the methodological moral. Linguisticmeaning is constrained in ways that ambiguity hypotheses must respect. It can be hard to know howmany readings a string of words has, especially when the scope of quantifiers is at issue. Far from beingparadigms of ambiguity in natural language, (1-2) are complicated cases.21. It is a familiar point that the inference from (1b) to (1a) is valid, while the inference from (1a) to(1b) is not. Correspondingly, (1a) is true in each of the siutations below:123 123 # # # $#%abc abcwhere letters represent girls, numbers represent trucks, and each arrow represents a pushing of therelevant truck by the relevant girl. Since (1b) is false in the first situation and true in the second, (1a) and(1b) have different truth conditions. It does not follow, though, that (1) is ambiguous. Given that (1) canbe verified by either situation, (1) cannot have (1b) as its sole reading. But if (1) has (1a) as its solereading, (1) is still true in both situations; and one cannot infer that a string of words has two readings,just because it is true in two different situations. After all, (1a) is true in many situations, including123 123 123 # $#%## #% $ $ #abc abc abcIt does not follow that (1) is many ways ambiguous. A quantified expression can be true in varioussituations on a single reading. Indeed, this is the case with (1a), which is true in all five situations above.Similarly, (1b) is true in a plurality of situations, since the truck pushed (by all three girls) can vary. This helps explain what we mean by ‘ambiguity’. If a string of words is ambiguous, it is by virtueof its association with alternative underlying forms. Consider(6) You cannot stop a philosopher with a thesis. Here the prepositional phrase can modify the direct object, as in ‘stop [a philosopher (with a thesis)]’; orthe verb phrase, as in ‘[stop (a philosopher)][with a thesis]’. This is, like the ambiguity of ‘duck’, a caseof homophony. In a natural language, distinct expressions can sound alike: the sound of ‘duck’corresponds to more than one word; the string of words in (6) corresponds to more than one sentence. We3return to the thought that a single English sentence can have two meanings—say, by virtue of itsassociation with distinct sentences of some other language (like Mentalese); and of course, a sentencemight be used to “convey a thought” that is not a grammatically possible meaning of the sentence. But inour view, questions about ambiguity turn on whether the word-string in question is associated withdifferent syntactic structures. So we want to focus on—and criticize—the common view that (1) isassociated with a syntactic structure in which ‘some truck’ has scope over ‘every girl’.Facts about usage are at best evidence of underlying structure. But if a string of words can beused veridically in a disparate range of situations, that is indeed evidence of ambiguity. Consider(7) Meg found Bob a challengewhich can be true if Meg found Bob to be a challenge, or if Meg found a challenge for Bob. But torepeat, any situation that verifies (1b) will also verify (1a); on its a-reading, (1) applies—unambiguouslyand nondisjunctively—to every situation that can verify (1) on any alleged reading. So the relevantplurality of situations does not divide into subcases in a way that suggests multiple readings.2In thinking about the range of situations that verify (1), a speaker may distinguish various specialcases: each girl pushing her own truck; or all three girls pushing the same truck. Speakers familiar withformal logic may attend to such distinctions habitually. But an expression can call different situations tomind without being ambiguous. When we think of (1a), which is unambiguous, we tend to think of thefirst two special cases depicted above. Hearing (1) might also prompt thought of other sentences, like(8) There is a truck that every girl pushed(9) Some truck was pushed by every girl.But theorists cannot just assume that (1) has a reading with the truth conditions of (8), shared by (9).One might claim that competent speakers of English would say—or can be led to say—that (1)has an interpretation on which it is false in all but one of the five situations indicated above; and thismight be construed as support for the claim that (1) has a reading indicated by (1b).3 Yet even if one can4extract the relevant judgments about falsification conditions, it is not clear what this would show. Anyspeaker sophisticated enough to provide such judgments might be conjecturing that (1) is ambiguous, andthen letting this conjecture drive her “intuitions”.