Like my own theory, the theory proposed in Sauerland et al. (2005) takes bare plurals to be number neutral. In contrast to me, however, they argue that the atomicity of singulars is not part of their denotation, but rather a presupposition which must be satisfied locally. This presupposition plays an important role in their calculation. The contrast between the singular and the plural, according to Sauerland et al., is not a scalar one. Rather, the singular and the plural compete based on a pragmatic prin- ciple calledmaximize presupposition, which was first introduced in Heim (1991). This principle says that when choosing between two different morphological forms, the one with stronger presuppositions must be chosen, as long as that will not lead to a presupposition violation. Given their argument that the singular presupposes atomicity, while the plural has no presupposition, the principle of maximize presup- position entails that if the singular form can be used without presupposition failure, it must be used. This, in turn, means that if the plural was used, it is possible to infer that the singular could not have been used in that context. This inference is a conversational implicature, but not a scalar one.
based on any of the original Gricean maxims10, but rather on a different principle,
that of maximize presupposition. Unlike traditional scalar implicatures, the resulting implicature is not based on the idea that the negated alternative is false. Rather, it assumes that the negated alternative lacks truth value, as using it would result in a presupposition failure.
Thus, in the case of (311), it is presupposed that the subject refers to an atomic dog (and not to a sum). If a single dog is barking, this presupposition is satisfied. Thus, if I say (310), I am in violation of maximize presupposition. On the other hand, if two dogs were barking, uttering (311) would lead to presupposition failure, while (310) can be uttered safely. Thus, the use of (310) implies that, given the assumption that the the speaker is being cooperative, he must believe that more than one dog barked.
(310) Dogs are barking.
(311) A dog is barking.
Sauerland et al. also propose an explanation of why this implicature does not arise in downwards entailing sentences. Since this is not a scalar implicature, scale reversal
pre se is not involved. However, they note that a sentence which says “there is no atom x such that φ(x)” is inherently weaker than saying “there is no X such that
φ(X)”, when X is number neutral. Choosing the sentence with the presupposition, thus, leads to a weaker utterance. They posit that maximize presupposition only applies when it strengthens the utterance, not when it weakens it. Thus, if a negated plural is uttered, it cannot be inferred that this was because the presupposition fails, and there is no implicature.
Sauerland et al. limit their attention to sentences with just a bare plural, and do not discuss sentences where there is any other plural involved. However, they do 10At least not as originally formulated. The principle that presuppositions must be maximized
discuss sentences with an every subject, such as (312) below, which they contrast with (313):
(312) Every boy should invite his sisters to the party.
(313) Every boy should invite his sister to the party.
Their argument is that in (313), the atomicity presupposition of his sister is dis- tributed over by the subject, so that (313) presupposes that every boy has a single sister. They point out that in a situation where at least one boy has more than one sister, (313) cannot be used and (312) must be used instead. This is indeed correct. However, their theory states that this is because (313) must be used whenever it can be; i.e. when each boy has exactly one sister. Unfortunately, according to my infor- mants both (312) and (313) are acceptable if that is the case. That means that the explanation for why (312) can be used in a scenario where most boys have one sister cannot be derived from an inference over maximize presupposition.
The data is further complicated by the fact that (312) contains the modal should, which, I have argued in chapter 2, creates an environment in which plurals do not denote ‘more than one’. Indeed, comparing (312) with (314) shows that the latter displays the pattern familiar to use with every sentences:
(314) Every boy invited his sisters to the party.
Unlike (312), (314) can only be used if each boy has at least two sisters. But Sauerland et al. cannot predict that either; for them, there is no difference between (314) and (312), and thus they predict that (314) would be usable as long as any boy has more than one sister, even if all the other boys have only one each.
A similar problem occurs once sentences which get dependent readings are con- sidered. Take the following two sentences:
(316) All my friends own a nice car.
Sauerland et al. do not discuss what happens to the atomicity presupposition of a nice car under all. But since (316) can only be used if each of my friends owns a single car, then it appears that the presupposition is distributed over by the subject, just like in (313). But that creates the exact same expectation as before: that (315) could only be used if I have at least one friend who owns more than one nice car. However, as we know, (315) can be used even if no such friend exists, as long as more than one car is owned overall. Thus, assuming that the presupposition is distributed over by all gives the wrong result.
A different possibility is that (316) involves some process of presupposition ac- commodation, and that it does not presuppose that each of my friends owns a single car, but rather asserts it11. If this is the case, maximize presupposition does not hold;
(315) can thus be used without any implicatures. But we have also seen this to be the wrong result. Dependent plurals are not completely number neutral, but rather have an overall multiplicity condition, which this suggestion leaves unexplained.
Overall, then, it appears that while the proposal in Sauerland et al. (2005) can de- rive the multiplicty condition of bare plurals that are not in the scope of another plural or every, it cannot explain the behavior of dependent plurals, and it provides truth conditions which are too weak for bare plurals in the scope of every. Furthermore, the account of why multiplicity is not implied in downwards entailing environments invokes scalar reasoning which is otherwise absent from their proposal. Thus, though they may be correct that singular NPs presuppose atomicity rather than assert it, it does not seem that such a presupposition offers a better explanation of the behavior of bare plurals compared to the scalar analysis proposed above.
11Sauerland et al. (2005) do not discuss accommodation in this context, but they do argue that
presuppositions associated with NPs inside indefinite DPs are accommodated, thus showing that the process exists in their system.