Presuppositional effects of strong determiners: a processing account

Barwise and Cooper (1981) observe that it is difficult to use NPs with strong determiners (like 'every', 'most', 'both', etc.) improperly. Sentences containing such an NP are generally regarded as undefined when the set denoted by its common noun is empty. However, NPs with weak determiners (such as 'some', 'no', 'five', etc.) can be used naturally when they receive an improper interpretation. De Jong and Verkuyl (1987) suggest that existential presuppositions be incorporated into the semantic interpretations of strong determiners in order to account for this distinction. We argue that the classical semantics of strong determiners should not be modified to deal with the fact that they yield judgments of anomaly on improper readings of the NPs in which they occur. We propose an alternative analysis in terms of the assessment procedures which speakers use to evaluate sentences with weak and strong NPs. These procedures are determined by the semantics of weak and strong determiners, respectively. We show that this analysis provides a principled account of the relevant differences between weak and strong NPs on improper uses, while avoiding the difficulties that beset the presuppositional approach. Sentences such as (la) and (Ib) pose a problem for truth-conditional semantics. (1) a. All American Kings lived in New York, b. Every cosmonaut at our party got drunk. Given that there have never been any American Kings (that is, a King of America) and that no cosmonauts attended out party, speakers of English do not generally react to these sentences in the way one would expect, given their semantic analysis. On the interpretations assigned to these sentences in classical logic, they are both true. Sentences with universally quantified NP subjects are represented as containing implications within Linguistics 26 (1988), 1021-1037 0024-3949/88/0026-1021 $2.00 © Mouton de Gruyter, Amsterdam 1022 S. Lappin and T. Reinhart the scope of the universal quantifier. If the antecedent is false for every value of the variable (for example, 'American King' is not satisfied by any element of the domain), the entire implication is true. In fact, speakers tend to regard such sentences as undefined. This suggests that they are instances of presupposition failure, and that use of the subject NP presupposes that the extension of the common noun of the subject NP is nonempty. The difficulty which these sentences create is similar to the problem raised by Grice (1975). How do we explain the discrepancy between the classical interpretations of logical expressions and the way in which these expressions are actually used in natural language? Some well-known examples of such discrepancies are given in (2a) and (2b). (2) a. Lucie is a linguist or a pianist, b. Lucie is not both. (3) a. Some linguists voted for Reagan, b. Not all linguists voted for Reagan. (4) a. Lucie has a daughter. b. Lucie does not have more than one daughter. In normal circumstances of utterance, speakers assume that if the (a) sentences are true, then the (b) sentences are, also. However, the (a) sentences do not logically entail the (b) sentences. The question is whether, in order to capture these implications in English, it is necessary to modify the classical semantic interpretations assigned to the sentential connectives and quantifiers. Should, for example, Or' be interpreted as exclusive disjunction, and a(n) N'" be understood as 'exactly one'? Although this approach has, on occasion, been adopted (for a recent example concerning the analysis of "'a(n) N'", see Van Eijk 1983), the Gricean view is that these implications do not justify a revision of the classical semantics of logical terms. They can be treated as instances of pragmatic inference and, specifically, as implicatures. The apparent existential entailments of the universal quantifier in (la) and (Ib) pose the same question. As we shall see, at least one analysis of this problem incorporates these entailments into the semantics of the relevant quantifiers. In section 2, we argue that this approach is not well motivated. On the other hand, the presuppositions which seem to hold for (la) and (Ib) cannot be explained as implicatures of the Gricean variety, as the relevant conditions for deriving such implicatures are not satisfied in these cases. We will maintain that no change in the classical interpretation of the universal quantifier is required in order to deal with these sentences. Rather, the presuppositional effects will be seen to follow indirectly from Effects of strong determiners 1023 the classical interpretation. These effects reflect the procedures of empirical assessment through which these sentences are processed. These procedures are themselves sensitive to the semantic properties of quantifiers. 1. (Im)proper interpretations and the weak-strong distinction We will follow Barwise and Cooper (1981; henceforth B&C) in treating NPs as expressions that denote sets of sets. Thus, for example, 'some man' denotes the set of all sets containing at least one man (that is, the set of all sets whose interaction with the set of men is not empty), 'every man' denotes the set of sets each of which contains all men, and 'Mary' denotes the set of sets which contains Mary. On this view, (5) Five linguists came to dinner. is true if and only if the set which is the extension of the VP (the extensional property of coming to dinner) is a member of the set of sets denoted by 'five linguists'. This set is the set of all sets (which may be thought of as properties in extension) containing (at least) five linguists. Consider the case of an NP whose N' (common noun) extension is empty. Depending on the interpretation assigned to the determiner, the NP will denote the set of all subsets of the domain of individuals (the power set of the universe of discourse) or the null set, or it will be undefined. For example, 'every unicorn' denotes the set of all sets of individuals, due to the fact that the extension of 'unicorn' is the null set, which is a subset of every set of individuals. The same is true for 'no unicorn'. On the other hand, 'some unicorn' denotes the null set, as there is no set whose intersection with the null set (the extension of 'unicorn') is not empty. B&C adopt the Strawsonian view of definite descriptions. Within their semantic system, the denotation of'the unicorn' is undefined, as the condition requiring that the extension of the N' to which the 'the' applies contain a unique individual is not satisfied. Let us say that when the extension of the N' of an NP is empty, or does not satisfy the cardinality condition of a definite determiner like 'the', and, consequently, one of these three situations holds, the interpretation of the NP is improper. B&C observe that it is not always easy, or even possible, to use an NP improperly in natural languages. As we have already seen, it is generally not possible to use universally quantified NPs improperly (as in [1] above). This is also true for other NPs. The relevant distinction here is between NPs with weak determiners and those with strong determiners. We will characterize this distinction in section 3. At this point, it is sufficient to note that there are several 1024 S. Lappin and T. Reinhart linguistic environments in which these two types of NP pattern differently. The best known of these is the postcopular NP position in existential 'there' constructions (as Milsark 1977 observes). NPs with weak determiners can occur in this environment, while NPs with strong determiners cannot.