Word count: 10252, including references, notes, acknowledgments, cross-references, and biography; excluding abstract and keywords (NB: counted using the Monterey Language Services free pdf tool. This gave a slightly different (lower by about 40 words) result than pasting the pdf into Word.) Strong and weak nominals Louise McNally Universitat Pompeu Fabra [email protected] Abstract Milsark (1977) introduced the terms weak and strong to distinguish (respec- tively) the nominals that could appear in English there-existential sentences (e.g. some trees, cf. There are some trees in the garden) from those that puta- tively could not (e.g. most trees, cf. ??There are most trees in the garden). Since then, the strong/weak distinction has played a role in the analysis of a wide va- riety of phenomena in many languages. This contribution reviews the different characterizations of the distinction that have appeared in the literature, as well as the most important phenomena in which it has been argued to intervene: Existential constructions, the individual-level/stage-level predicate distinction, certain aspects of information structure, case marking, and so-called semantic incorporation. We also review the application of the distinction to subclassify definite descriptions. Keywords: quantifiers, bare plurals, (in)definiteness, existential sentences, incorpo- ration, individual-level predicate, stage-level predicate, thetic/categorical distinction 1 <A> Introduction Milsark (1977) introduced the terms strong and weak to distinguish (respectively) the nominals1 that putatively could not appear in English there-existential sentences from those that clearly could, as illustrated with representative examples in (1)-(2).2 (1) strong a. ??There is the/each/every solution. b. ??There are two of the/most/both solutions. (2) weak a. There is a solution. b. There are some/two/many/few/no solutions. Since then, the strong/weak distinction has played a role in the analysis of a wide variety of phenomena in many languages. This chapter reviews the different charac- terizations of the distinction that have appeared in the literature, as well as the most important phenomena in which it intervenes. These include (roughly in the chrono- logical order they were first discussed in the literature) existential constructions in various languages (including existential have in English, see e.g. Keenan 1987, Par- tee 2004), the individual-level/stage-level predicate distinction (see Carlson 1977 and references cited below for this terminology), certain aspects of information structure, case marking, so-called semantic incorporation (see e.g. Van Geenhoven 1996), and the semantic subclassification of definite descriptions. <A>The history of the strong/weak distinction Very generally speaking, one can group definitions of the strong/weak distinction ac- cording to whether they first define strength and characterize weak as \not strong", or rather define weakness and characterize strong as \not weak". No analysis gives fully independent definitions of both notions. Thus, a very basic question is whether only one of the two classes of nominals is fully homogeneous. The definitions also split according to whether they are grounded in a strictly truth-conditional or logical property of determiners or nominals, or rather in their presuppositions. <B> The origin of the distinction Milsark (1977) used the strong/weak distinction to classify determiners and by exten- sion, the terms came to classify nominals as well. Though he did not provide formal semantic definitions, Milsark proposed that the difference between strong and weak determiners was that the former are interpreted quantificationally, while the latter are interpreted nonquantificationally, as cardinality predicates. However, Milsark's work predated the popularization of formal semantic analyses that treat definite nominals nonquantificationally (e.g. Kamp 1981, Heim 1982). Thus, while his definition clearly treats weak determiners as a natural class (defined in terms of cardinality), it is less clear that it crucially treats strong determiners as a natural class. 2 Milsark's proposal was deeply bound up with his interpretation rule for existential sentences, shown in (3) (Milsark 1974: 206), where Q NP is the postverbal nominal constituent (e.g. a storm in There was a storm in the Atlantic), Q standing for the determiner (e.g. a in a storm); and X is any secondary predicate that might accompany the nominal (e.g. in the Atlantic). (3) E Rule: there AUX (have-en) be Q NP X is interpreted: the class C denoted by NP has at least one member c such that P(c) is true, where P is a predicate and P is the reading of X and the set of such members c is of cardinality Q. Some determiners clearly do not contribute cardinality predicates, such as every, while others, such as the numerals, clearly do, as the contrast in (4) indicates.3 (4) His objections were ??every/two. Nonetheless, in order for the definitions to make clear predictions in more complex cases (for example, to account for the putative unacceptability of partitives, as shown in (1b)), Milsark's characterization required an independent definition of cardinality predicate. Milsark did not provide any such formal definition. Though ultimately incomplete as a characterization of the conditions under which nominals can appear in existential sentences (see section <B> Existential and re- lated constructions below), Milsark's characterization of the strong/weak distinc- tion contained the important idea that a positive definition could be given for weakness; this idea has survived in one of the definitions discussed in section <B> Definitions of the distinction grounded in semantic type. <B> The distinction as a semantic property of determiners The first attempt to define strong and weak in formal semantic terms appears in Bar- wise and Cooper (1981). Like Milsark, Barwise and Cooper considered strength and weakness to be properties of determiners. However, they took the approach of provid- ing a definition for strong determiners, and then defined weak determiners negatively as those that are not strong.4 Barwise and Cooper's definition of strong is reproduced in (5) (where a quantifier is the denotation of what, following Abney (1987), is now usually referred to as a DP; A corresponds to the set denoted by the nominal complement to the determiner { typically called its restriction; E stands for the domain of entities in the model, and [[D]] stands for the denotation of D). The definition is quite technical, arguably because it was designed to cover both true proportional determiners like every and not obviously proportional expressions like two of the.5 (5) A determiner D is positive strong (or negative strong, respectively) if for every model M =< E; [[]] > and every A ⊆ E, if the quantifier [[D]](A) is defined then A 2 [[D]](A). (Or A 62 [[D]](A), resp.). If D is not (positive or negative) strong, then D is weak. A strong (weak) NP is then an NP headed by a strong (weak, respectively) determiner. (Barwise and Cooper 1981: 182) 3 Quantifiers, on this analysis, denote sets of sets: every dog denotes the set of all sets that contain every dog (or, alternatively, the set of properties that every dog has), two dogs denotes the set of all sets that contain two dogs, etc. For Barwise and Cooper, strong determiners come in two types: positive strong (e.g. each, most, both, the, and partitive phrases such as two of the) and negative strong (e.g. neither). Positive strong determiners form quantifiers that necessarily contain their restriction as an element; negative strong determiners never do. What this definition amounts to in operational terms is that when a positive strong determiner appears in a sentence of the form in (6a), the result is a tautology (6b, c). With negative strong determiners, the result is a contradiction (6d). (6) a. Det N is an N. b. Every dog is a dog. c. Two of the dogs are dogs. d. Neither dog is a dog. The condition \if the quantifier [[D]](A) is defined” in the definition is needed to dis- tinguish examples such as (6c, d), with strong determiners, from those in (7), which contain weak determiners on their analysis (like Milsark's). (7) a. Two dogs are dogs. b. No dog is a dog. The crucial case arises when there are no dogs. In such a case, they argue, the interpretation for two of the dogs and neither dog will not be defined because these phrases presuppose the existence of dogs. In other words, it is anomalous to talk about two of the dogs or neither dog if there are no dogs. If the quantifier is not defined, then it will be impossible to compute the semantics for the entire sentence. We therefore ignore those cases; in all the rest, the sentences are either tautological or contradictory, depending on the determiner. In contrast, they claim, two dogs and no dog do not carry any presupposition concerning the existence of any dogs. Any time there are two or more dogs, (7a) will be true and (7b), false; however, according to Barwise and Cooper's intuitions, if there are no dogs, (7a) will be false, and (7b), true. Thus, the sentences in (7) (and all others with weak determiners) are neither tautological nor contradictory. Barwise and Cooper's definitions improved upon Milsark's in precision; in addition, the crucial role given to presupposition (manifest in their definedness condition) and the identification of symmetry as a relevant property of determiners (see footnote 4) foreshadow future developments in the analysis of strength and weakness. However, their definitions did not lead directly to a convincing account of the existential sentence facts that the strong/weak distinction was originally intended to explain, as will be discussed in section <A> Manifestations of the distinction (see Keenan and Stavi 1986 for an early critique). In addition to a number of technical problems pointed out by Keenan and Stavi, we will see that the basic descriptive problems are that, first, like Milsark, Barwise and Cooper defined strength and weakness as properties of determiners, rather than as properties of nominals as a whole; and second, they 4 arguably erred in taking strength as basic and defining weakness negatively.