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Strong and weak nominals Louise McNally Universitat Pompeu Fabra [email protected]

Abstract Milsark (1977) introduced the terms weak and strong to distinguish (respectively) 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 putatively 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 variety 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, incorporation, individual-level predicate, stage-level predicate, thetic/categorical distinction

1 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 characterizations 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 chronological 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.

The history of the strong/weak distinction

Very generally speaking, one can group definitions of the strong/weak distinction according 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.

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 Existential and related constructions below), Milsark’s characterization of the strong/weak distinction 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 Definitions of the distinction grounded in semantic type.

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 ∈ [[D]](A). (Or A ̸∈ [[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 distinguish 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 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.

Definitions of the distinction grounded in semantic type The popularization of nonquantificational semantics for definite and indefinite nominals in the early 1980s, including those in Kamp (1981) and Heim (1982), together with the theory of type shifting in Partee (1987), eventually led to new definitions of strong and weak based on semantic type. The crucial innovation was that nominals could, as a rule, be assigned to not just one semantic type but rather to a family of types. The three basic semantic types between which Partee argued that nominals routinely shift (hence the term type-shifting; see Type shifting) are the generalized quantifier type (in notation used in an extensional version of Montague Grammar, type ⟨⟨e, t⟩, t⟩), the property type (⟨e, t⟩), and the entity type (e). This more sophisticated nominal semantics yielded both proposals to define strong as strictly quantifier-denoting (as opposed to entity- or property-denoting) and proposals to define weak as strictly property-denoting (leaving a broader definition for strength). De Hoop 1992 exemplifies the first option. She argues based largely on data involving the interpretations of nominals with different kinds of case marking (see section Case below) that strength and weakness are not essentially properties of determiners, but rather are better understood as properties of interpretations of determiners and nominals. As a result, nominals containing “Barwise and Cooper weak” determiners can have strong interpretations, as can, indeed, nominals without any determiner at all. She equates strong interpretations with quantifier-type denotations, which may arise either due to the lexical semantics of the determiner (for example, in the case of every N, where she takes every to be of type ⟨⟨e, t⟩, ⟨⟨e, t⟩, t⟩⟩) or via type-shifting, induced by what she refers to as strong case, from the entity type (for example, in the case of strongly-interpreted indefinites, where indefinites are initially analyzed non-quantificationally as “e-type variables”). In contrast, on de Hoop’s analysis weak nominals are not necessarily all of the same semantic type. She proposes that some weak nominals are entity-denoting, while others function as verb modifiers (i.e., are of type ⟨⟨e, t⟩, ⟨e, t⟩⟩). De Hoop offers as an example of an e-type weak nominal the sort of definite found in phrases such as do the laundry. Common to all weakly interpreted nominals is the intuition that they form “part of the predicate” (de Hoop 1992: 109ff.), something that generalized quantifiers cannot do presumably because they must undergo quantifier raising in order to be interpreted (see Quantifier scope). We will return to de Hoop’s analysis in sections Case and (Semantic) Incorporation below, and we will revisit the sort of definites she treated as weakly interpreted in section Strong and weak definites. The second option for a type-based account of the strong/weak distinction was first explicitly suggested, though not formalized, in Ladusaw (1994). Ladusaw proposed that weak nominals denote “descriptions”; McNally and Van Geenhoven (1997) subsequently formalized Ladusaw’s notion of description by assigning weak nominals property-type denotations. On this view, even though strong nominals lack a uni- fied semantic type (they can be either entity-denoting or quantificational), they share 5 the characteristic that, in theories such as Kamp’s and Heim’s, they both introduce discourse referents, represented as variables in the logical representation for the nominal. In contrast, weak nominals do not introduce discourse referents, but rather only descriptive content. Any inference that there is an individual fitting the description provided by the weak nominal is due to entailments from elsewhere in the sentence in which the weak nominal appears, typically the verb with which the nominal com- bines. This perhaps somewhat abstract idea will be illustrated in the discussion of incorporation in section (Semantic) Incorporation. Finally, it should be noted that Diesing (1990) proposes a fundamentally syntactic account of strong vs. weak readings closely connected to the analyses grounded in semantic type that have just been introduced. Her analysis builds on what she referred to as the Mapping Hypothesis, which establishes a connection between syntactic structure and a syntactic logical form (LF) of the sort proposed in Heim (1982); this LF, in turn, maps onto a logical representation in which quantificational determiners are interpreted as relations between open propositions (see Rooth 1987 for comparison of this semantics to the semantics for determiners in Barwise and Cooper’s generalized quantifier approach). According to this hypothesis, on which clauses are assigned a structure consisting of an inflectional phrase (IP) nesting a verb phrase (VP), ver- bal arguments, including the subject, typically originate within VP.6 Following Heim, Diesing posits that necessarily quantificational nominals, such as every N, cannot be interpreted in situ but rather must undergo quantifier raising and adjoin to IP; the determiner then moves out of the noun phrase to form a tripartite structure in which it is sister to the rest of the nominal from which it originated as well as to the rest of the clause, as in (8a). This maps onto a logical representation with the adjoined nominal contributing the restriction on the quantificational determiner, and the rest of the clause forming what Heim called the determiner’s nuclear scope, as represented informally in (8b).

(8) a. [IP everyx [NP dogx][IP [VP x barked]]] b. Everyx [x is a dog] [x barked] Now, with an indefinite, one of two things can happen: it can raise, like a necessarily quantificational nominal, or it can stay within the VP. If the indefinite ends up outside of the VP, it will always map into the restrictive clause of the LF. Since Diesing assumes, following Kamp and Heim, that indefinites are not inherently quantificational, if the indefinite raises it will get its quantificational force from an operation that Heim called text-level existential closure, as illustrated for (9a) in (9c) (existential closure is indicated by placing the existential operator in parentheses).

(9) a. Robin played a sonata. b. [IP [NP sonatax][IP [VP Robin played x]]] c. (∃)x [x is a sonata] [Robin played x]

Diesing further proposes that all restrictive clauses, whether contributed by necessarily quantificational nominals as in (8) or by indefinites when they are outside VP, carry the presupposition that at least one individual satisfies the restriction; this she takes 6 as crucial to the existence of a strong interpretation. Alternatively, if the indefinite remains within the VP, it is mapped into the nuclear scope of the LF. The variable associated with the nominal is then bound by existential closure at the level of the VP. If there is no other quantifier in the sentence, there will be no restrictive clause, only a nuclear scope. Diesing posits that when the descriptive content of the indefinite appears in a nuclear scope there is no presupposition that any individual will satisfy that descriptive content, and correspondingly the nominal will have a weak interpretation. This is shown in (10) for (9a).

(10) a. [IP [VP Robin played a sonata]] b. (∃)x [Robin played x ∧ sonata(x)]

Diesing’s proposal thus connects strength and weakness to presupposition. However, the question of interest here is whether it makes any claims about the relation between strength, weakness, and semantic type. Unfortunately, this question is impossible to answer because Diesing failed to provide a full semantics for her logical forms and because, despite the superficial similarities between the role of Every x in (8b) and existential closure in (9c) and (10b), existential closure differs in crucial ways from other sorts of quantification, including any existential quantification that might be explicitly introduced a determiner.7 However, Diesing does explicitly assume that weak nominals contribute (along with descriptive content) a variable that is bound by existential closure at the VP level. This would suggest that she takes weak nominals to denote entities, rather than properties, and thus that her analysis is closer to de Hoop’s than to Ladusaw’s in terms of the mapping between strong/weak and semantic type.8 Over time, the definition of weak as property-denoting has arguably proven to be more successful in accounting for some of the classic data motivating the strong/weak distinction than has been de Hoop’s proposal to define strength narrowly as quantifier- denoting. However, de Hoop’s work stands out for making the first and, as we will see, highly relevant connection between weakness and verb modification.

Discourse-semantic characterizations of the distinction The final sort of definition of strong and weak that one finds in the literature is grounded in presupposition (see, e.g., in addition to the proposal in Diesing 1990, discussed above, Geurts and van der Sandt 1999 and Moltmann 2005). Though discussing the technical variations in the different proposals is beyond the scope of this article, we can at least point to subtle differences between the proposals in the nature and sources of these presuppositions. As mentioned at the end of the previous section, Diesing associated all nominals raised out of VP with the presupposition that some individual satisfies the nominal description – in other words, with a domain presupposition. However, her analysis in principle allows the presupposition to arise for more than one reason. On the one hand, it could be due to the fact that the speaker knows (and wants to communicate) that a referent exists for the nominal in question. This is the case, for example, of so-called referential or specific indefinites. In the case of partitives, the presupposition 7 is due to the presupposition associated with the definite article in the complement to of in the partitive (however the presuppositions of definites are best characterized). Finally, Diesing assumes, unlike Barwise and Cooper, that all quantifiers – not just some, such as neither – presuppose a nonempty restriction. That is, she maintains that speakers do not use expressions such as no dogs quantificationally in situations in which there are no dogs (see e.g. Partee 1987 for more on this point). She also makes the connection in the opposite direction: If one uses e.g. no dogs in a context where the existence of a set of dogs is not presupposed (as in There were no dogs), that use must be weak, i.e. it will be given a nonquantificational semantics on which no functions as a cardinality predicate. Moltmann (2005), in contrast, essentially grounds the presupposition in the pro- portionality associated with certain determiners. Like Barwise and Cooper and unlike Diesing, she does not assume that all quantifiers presuppose a nonempty restriction (or domain, as she refers to the restriction) over which they quantify. However, she notes that in order for a determiner to yield a proportional quantifier, it is first necessary to identify the set over which the proportion is being measured. This presupposition underlies the determiners each, every, most, both, and the definite and demonstrative articles. Neither, because it is restricted to quantifying over sets with exactly two members, will also carry a presupposition on its domain. Moltmann does not discuss partitives with weak determiners. However, we might expect that she would classify the nominals as strong to the extent that they carry a presupposition on their domain due to the presence of the definite article in the complement to of. Presuppositional definitions of the strong/weak distinction tap into an important insight, perhaps most noticeably in the account of the interpretation of nominals with individual- vs. stage-level predicates, as will be shown in section Individual- and stage-level predicates. Relatedly, domain presupposition has also played a key role in some accounts of the restrictions on nominals in existential sentences (see Comorovski 1991, Zucchi 1995 and section Existential and related constructions). However, the extent to which presupposition-based definitions of strength/weakness succeed on their own or can be correlated with definitions in terms of semantic type is difficult to determine because, as we will now see, the facts that the distinction was developed to explain are complex and have been the subject of some disagreement.

Manifestations of the distinction

Having reviewed the different definitions of strength and weakness that have been proposed, we now turn to the different sorts of data that the distinction has been used to explain. We present these data roughly in the chronological order in which they appeared in the literature. While additional research would be necessary to determine whether all of the data share any one single property, some aspect of information structure, and in particular the sensitivity of the construction in question to the way in which discourse referents are introduced, is arguably relevant in all cases.

8 Existential and related constructions The restriction on the distribution of nominals in there-existentials that Milsark wanted to explain is widely (if inaccurately) known as the definiteness restriction or definiteness effect. Definiteness effects were subsequently identified in other constructions (see Reuland and ter Meulen 1987 for an overview), such as the so-called existential have construction in English (Keenan 1987, Partee 2004; see (11)), as distinguished from the ordinary possessive have construction, which carries no such restriction (see (12)).9

(11) a. Mary has ??the/??every/a/no sister. b. Mary has ??most/??both/??some of the/two/many sisters. (12) a. Mary has the/every/a/no piece of paper. b. Mary has most/both/some of the/two/many pieces of paper.

Milsark’s account of this restriction in there-existentials, though not formalized, was essentially semantic. He took there be to contribute an existential operator that quan- tifies over the set denoted by the postverbal nominal. If the postverbal nominal does not denote a set, but rather is itself quantificational, the existential operator will not be able to carry out its function. It therefore follows that only those determiners that can be interpreted as cardinality predicates, rather than as quantifiers, can appear in the construction; any other expression creates problems for the semantic composition process because it will not be of the appropriate semantic type to combine with a quantificational operator.10,11 In contrast, Barwise and Cooper (1981) argued that the effect arose because, on their analysis, which took there be to be equivalent to the verb exist, existential sentences containing strong determiners were tautologous and therefore uninformative. Crucial to their account was the assumption that any phrase following the noun (the X in Milsark’s E Rule in (3)) formed part of the postverbal nominal, as in (13a); only on this analysis is the sentence equivalent to the tautologous (when there are apples) (13b). If in the basket does not form part of the nominal, then the sentence is not tautologous (see (13c)).

(13) a. There was [DP every apple in the basket]. b. Every apple in the basket existed. c. Every apple was/existed in the basket.

Keenan (1987) criticized this account on the grounds that tautologous sentences are not usually anomalous; the syntactic analysis in (13a) was also later argued to be untenable (see McNally 1992 and references cited there).12 However, Keenan, like Barwise and Cooper (and see also Zucchi 1995), maintained that the definiteness effect is not due to a problem of semantic types. Though discussing his and Zucchi’s works in detail would take us too far afield, they both effectively exclude strong nominals from existentials on the existence assertion reading because these nominals presuppose the existence of a non-empty set of individuals fitting the nominal description, and this presupposition is, for different reasons, incompatible with the felicity conditions 9 on the existence-assertion use of existential sentences. McNally (1992), drawing on observations in Lumsden (1988) and elsewhere, argued that the definiteness effect in there-existentials is not, in fact, a unitary phenomenon, but rather has independent type-theoretic and presuppositional components. The evidence for this view is of various sorts. First, strong determiners are licensed in the construction if they quantify over kinds or types of entities, as opposed to token-level entities, as in (14).

(14) a. There was every reason to leave. b. Students will be able to compute how many days during the week there was each type of weather. (http://jillianraleigh.weebly.com/uploads/2/4/7/0/24702135/weather graphing.pdf )

Second, nominals marked specifically with definite determiners can appear in existential sentences without any sort of special interpretation just in case the nominal as a whole does not have a unique denotation, even if the nominal itself clearly describes a token entity rather than a kind-level entity. For example, in (15), though the definite article signals that there is a unique lid for each Cool-Whip container, the fact that there is potentially more than one individual that satisfies the description a Cool-Whip container allows for the possibility that more than one object satisfies the description the lid to a Cool-Whip container.

(15) [M]y dad had some trouble slicing the pumpkin pie, and we ﬁnally discovered that there was the lid to a Cool-Whip container in the pie underneath the ﬁlling! (http://forums.welltrainedmind.com/topic/331079-this-is-just-plain-weird)

Finally, the restriction on partitives in existential sentences is less strict than Milsark maintained; examples such as (16) have been cited in the literature:

(16) ...Ida wondered if there was some of the marines’ homebrewed engine juice around. (http://www.tor.com/stories/2014/01/the-burning-dark-excerpt-adam- christopher)

Moreover, there are clearly languages where the restriction on definites and partitives in existential sentences does not apply; see e.g. de Hoop (1992) and Hoeksema (1989) for relevant Dutch data involving partitives, Comorovski (1991) on partitives in En- glish,Ward and Birner 1995 and Abbott 1997 for many other sorts of examples of definites and demonstratives in existentials, and McNally (1992) on definite nominals in Catalan existential constructions.13 The acceptability of definites and partitives in principle is expected if, in order to appear in the construction, the postverbal nominal has to denote a property, since under Partee’s theory of type-shifting both types of nominals can shift to the property type. This suggests that any restriction on these nominals in existentials, to the extent that one exists, is due to the oddness of asserting the existence of an individual whose 10 existence is presupposed, rather than to a clash in semantic type. In contrast, Partee’s theory does not postulate the possibility of a well-behaved property-type denotation for certain strong determiners such as each. However, it would be unsurprising to find quantifiers such as those in (14) if some kind of connection could be made between kind or type-level individuals and properties – that is, quantification would be expected to be possible if the determiner were to quantify over properties. Adapt- ing the property-theoretic semantics of Chierchia and Turner (1988), McNally (1992) proposed to analyze the nouns in examples like (14) as describing entity correlates of properties: the entity guise properties have when they appear in argument positions.14 On this account, the strong determiners in (14) could be interpreted in the usual way, as quantifying over a variable of the sort that the existential construction selects for in the “pivot” nominal position following the verb be. Though the nature of the definiteness restriction in existentials has continued to be the subject of debate (see e.g. Zamparelli 1995 and Francez 2007 for criticisms of McNally’s analysis, and see McNally 2011 for a recent general overview), the facts do clearly indicate that, if they are to be characterized in terms of strength and weakness, these notions must be defined as properties of nominal interpretations, rather than fundamentally as properties of determiners.

Individual- and stage-level predicates Milsark (1977) used the strong/weak distinction not only to account for there-existential sentences but also to capture the inverse correlation he observed between the acceptability of nominals in existentials and their compatibility with individual-level predicates, such as intelligent.15 This inverse correlation is illustrated in (17)-(18) (sm stands for the unstressed pronunciation of some; examples adapted from Milsark, and judgments are those he would have assigned).16

(17) a. *There was every/the man in the room. b. Every/the man was intelligent. (18) a. There were sm people in the room. b. *Sm people were intelligent.

Milsark further observed that individual-level predicates are blocked as the secondary predicate (also called the coda) in the construction, while stage-level predicates such as drunk are licensed:

(19) a. *There were sm people intelligent. b. There were sm people drunk.

Since Milsark proposed that existential sentences were derived by transformation from copular sentences, it followed that if an individual-level predicate required a subject that was blocked from existential sentences, the individual-level predicate would also be blocked in existential sentences. In other words, (19a) was blocked because the source sentence (18b) was unacceptable. A related manifestation of this inverse correlation is that bare plurals and mass 11 terms were claimed to have only non-generic interpretations in existential sentences, and only generic interpretations as the subjects of individual-level predicates (contrast (20a-b), from Milsark 1977). Unsurprisingly, then, the individual-level predicate tasty is blocked in (20c).

(20) a. There is coffee on the stove. [non-generic reading only] b. Coffee is tasty. [generic reading only] c. *There is coffee tasty.

However, Milsark did not have a deeper explanation for why weak nominals would not be compatible with individual level predicates. On Diesing’s (1990) account, the requirement that individual-level predicates such as intelligent have strong subjects, while stage-level predicates such as in the room do not, followed from a claimed difference in argument structure between the two. Fol- lowing Kratzer (1995) (which was circulating in manuscript form in the late 1980s), Diesing posited that the external argument of stage-level predicates was a (typically implicit) spatio-temporal variable, while that of individual-level predicates was the bearer of the individual-level property in question. Given her Mapping Hypothe- sis, this entailed that the subject of individual-level predicates was always generated outside VP and would eventually be given a strong interpretation (see section Definitions of the distinction grounded in semantic type, above). This account of the difference between individual-level and stage-level predicates has been controversial (see e.g. Condoravdi 1992, McNally 1994 for early criticisms). However, there is an important insight underlying this proposal, later articulated in Ladusaw (1994) (although in slightly different terms from those used here; see McNally 1998b): The use of an individual-level predicate presupposes the individuation of an entity to which it is ascribed or a set of potential ascribees that are quantified over, whereas stage-level predicates can be used without any such presupposition. Ladusaw characterized this condition in terms of the contrast between categorical and thetic judgment types (drawn from the work of Franz Brentano and Anton Marty, and popularized in modern linguistics by Kuroda 1972 and Sasse 1987, among others). A categorical, or double, judgment, involves first recognizing some entity and then affirming or denying some predication over that entity; a thetic, or single, judgment, is not so divided. Individual-level predicates, by hypothesis, can only be attributed via the former type of judgment. If the use of a weak nominal to represent the ascribee of an individual-level predicate is inconsistent with the above-mentioned presupposition, or alternatively, cannot be used to refer to the subject of a categorical judgment, then it will follow that weak nominals are incompatible with that class of predicates. Ladusaw argues that this is exactly what we should expect of weak nominals if they denote properties.

Informationally-marked syntax Diesing (1990) brought to the fore a variety of syntactic data that interact with the strong/weak distinction (and with the distribution of individual- and stage-level predicates as well). One example is the restrictions on the acceptability and interpretation 12 of nominals in diﬀerent subject positions in embedded clauses in German ((21)-(23)). Diesing argues that there are both VP-internal and VP-external subject positions, distinguished by their relative ordering with respect to sentence-modifying particles such as ja doch ‘indeed’. The subjects of individual-level predicates can appear only in VP- external position, while those of stage-level predicates can appear in either position. Relatedly, Diesing claimed that VP-external bare plural subjects have a necessarily generic reading, while VP-internal ones are existentially interpreted.

(21) (Diesing 1990: 59) a. ...weil Wildschweine ja doch intelligent sind. since wild boars “indeed” intelligent are ‘since (in general) wild boars are intelligent.’ b. *?...weil ja doch Wildschweine intelligent sind. since “indeed” wild boars intelligent are (22) (Diesing 1990: 58) a. ...weil Professoren ja doch verf¨ugbar sind. since professors “indeed” available are ‘since (in general) professors are available.’ b. ...weil ja doch Professoren verf¨ugbar sind. since “indeed” professors available are ‘since there are professors available.’ (23) (Diesing 1990: 56) a. ...weil Linguisten ja doch Kammermusik spielen. since linguists “indeed” chamber music play ‘since (in general) linguists play chamber music.’ b. ...weil ja doch Linguisten Kammermusik spielen. since “indeed” linguists chamber music play ‘since there are linguists playing chamber music.’

Diesing argued that additional evidence for these two positions could be found in the restrictions on the so-called was-f¨ur split (see (24)) and so-called split topicalization (see (25)), on the theory that extraction from within nominals is possible only from within VP-internal argument positions. Thus, it would appear that weak nominals license the was-f¨ur and split topicalization, while strong nominals do not.

(24) (Diesing 1990: 62) a. *Was sind für Leguane intelligent? what are for iguanas intelligent b. Was sind für Leguane verfügbar? what are for iguanas available ‘What kind of iguanas are available?’ (25) (Diesing 1990: 64) a. *Wildschweine sind viele intelligent wild boars are many intelligent 13 ‘(In general) wild boars are intelligent.’ b. Wildschweine sind viele verfügbar. wild boars are many available ‘As for wild boars, many are available.’

Some of these facts have subsequently been questioned; for example, J¨ager(2001) claims that universal nominals such as in (26) (his (61a)) can appear in the VP- internal position:

(26) weil ja alle Studenten Englisch k¨onnen because prt all students English know ‘because all students know English’

Jägerargues that, as a result, the simplest version of the Mapping Hypothesis cannot be maintained. Instead, he claims that the VP-external position is a topic position, where what it means to be a topic is very close to the notion of subject of a categorical judgment. He characterizes topics as “anaphoric or discourse linked in a broad sense and, if they are indefinite, they can be bound by superordinate operators” (p. 114). The distribution of quantificational nominals such as that in (26), he claims, is determined by factors independent of topicality. Jägerdoes not explicitly address the formal definition of weak vs. strong nominals, and the facts he discusses do not depend crucially on one particular definition of the distinction as long as it follows that weak nominals cannot be discourse linked or bound by superordinate operators. Summarizing this brief discussion, Jägerand Diesing differ over what makes a strong nominal strong. For Diesing, strong nominals are interpreted as such in virtue of where they appear in the syntax. For Jäger,particular syntactic positions are associated with particular discourse functions that are compatible only with strong nominals and not with weak ones, but the strong or weak interpretation as such is not reducible to a particular syntactic configuration.

Case de Hoop (1992) uses the terms strong and weak to characterize the sorts of case alter- nations illustrated in (27)-(29). Accusative in Finnish and Turkish, and nominative in West Greenlandic,17 are examples of strong case; partitive in Finnish and instrumental in West Greenlandic are examples of weak case.18

(27) Finnish (de Hoop 1992: 67) a. Ostin leivän. bought.1sg bread.acc ‘I bought the bread.’ b. Ostin leipää. bought.1sg bread.part ‘I bought (some) bread.’ (28) Turkish (de Hoop 1992: 68)

14 a. Ali kitabı okudu. Ali book.acc read ‘Ali read the book.’ b. Ali kitap okudu Ali book read ‘Ali read a book.’ (29) West Greenlandic (de Hoop 1992: 70) a. Jaaku-p arnaq tuqut-p-as Jacob.erg woman.nom kill.ind.3sgerg/3sgnom ‘Jacob killed the woman’ b. Jaaku-p arnaq tuqut-si-v-uq Jacob.nom woman.ins kill.ap.3sgnom ‘Jacob killed a woman’

De Hoop argues that case is correlated with interpretation: Nominals bearing strong case have strong interpretations; those bearing weak case have weak interpretations. As noted above, she associates strength with a generalized quantifier denotation. Though she does not assign a single semantic type to weak case nominals, she makes a crucial claim about their function: “An object that bears weak case is interpreted as part of the predicate” (p. 99). Support for this claim comes in large part from the observation that weak case objects typically do not behave like the objects of ordinary transitive verbs. For instance, she observes that weakly interpreted objects in Dutch cannot become subjects under passivization. In addition, she points to a close relationship between weak case nominals and noun incorporation in a variety of languages, including West Greenlandic and Hungarian. As a result, de Hoop proposes that at least some such objects function as predicate modifiers, i.e. are expressions of type ⟨⟨e, t⟩, ⟨e, t⟩⟩. The proposal that nominals can have this predicate modifier type does not fit well within the general theory of nominal type shifting proposed in Partee (1987) because Partee argues that the three basic types she assigns to nominals and the functions that shift between them have a “naturalness” to them that simply does not extend in an obvious way to include the ⟨⟨e, t⟩, ⟨e, t⟩⟩ type.19 However, subsequent work on incorporation, to which we now turn, has offered alternatives that preserve de Hoop’s insight.

(Semantic) Incorporation Van Geenhoven (1992, 1996) developed an analysis of noun incorporation in West Greenlandic on which the incorporating verb lexically selects for a property-type nominal. The argument for lexical selection comes from the fact that some verbs in West Greenlandic are obligatorily incorporating, others have both incorporating and non- incorporating variants, and still others do not allow for incorporation at all. Intereset- ingly, the existential predicate is one of the obligatorily incorporating predicates, in line with analyses of the English existential that treat the pivot nominal as property- denoting (e.g. McNally (1998a)). 15 Van Geenhoven’s lexical semantics for an incorporating verb is illustrated in (30) (some details simpliﬁed; note that w is a variable over possible worlds). As the representation indicates, incorporating verbs combine directly with property-type nominals. This seems like an obvious analysis when one considers that the incorporated nominal is a bare noun, lacking any determiner or other morphology.

(30) a. -tur-puq ‘ate.3sg.ind’: λP λwλx∃y[eatw(x, y) ∧ Pw(y)] b. ipili ‘apple’: apple c. ipili-tur-puq ‘ate.3sg.ind an apple (lit. ‘apple-ate’)’: λwλx∃y[eatw(x, y)∧ applew(y)] Note that the verb, and not the nominal, introduces an existentially quantified variable over the sort of individual that is described by the object. Thus, this analysis differs from de Hoop’s in that it is the verb, and not the nominal, that has an unexpected semantic type. What empirical differences there might be between these two options and which option is preferable is a question that remains for future research. Van Geenhoven (1995) and McNally (1995) independently proposed the same analysis for verbs combining with bare plural objects in (respectively) German and Spanish (see e.g. (31) for an example of the latter) despite the fact that these constructions were not morphosyntactically incorporating.

(31) Marta compr´o manzanas. Marta bought apples ‘Marta bought apples.’

Later, McNally and Van Geenhoven (1997) used these and other data to argue for the property-type analysis of weak nominals. These works initiated a long line of research on semantically incorporated and bare existential nominals in which several different alternative compositional mechanisms have been proposed for the verb and nominal (e.g. Farkas and Swart 2003, Chung and Ladusaw 2004, Dayal 2003, Dayal 2011, Espinal and McNally 2011; see also Noun Incorporation). In the course of this research, the notions of strength and weakness have ceased to play anything other than a descriptive role, perhaps because the incorporation literature has largely come to assume that incorporated nominals are property or modifier type expressions. The notions of weakness and strength independently of semantic type offer little in the way of extra traction in addressing the specific analytical problems posed by incorporation.

Strong and weak definites Recall that in section Definitions of the distinction grounded in semantic type we noted that de Hoop (1992) classified definite descriptions such as the laundry in do the laundry as weak (and e-type). Her intuition was that these definites shared with other weak nominals the characteristic of forming “part of the predicate.” Such definites were not analyzed in detail in de Hoop (1992), but have received considerable attention since the work of Carlson and Sussman (2005) and Carlson et al. (2006). 16 Carlson et al. (2006) used the term strong to identify definites with typically unique and familiar referents, as in (32).

(32) (Carlson and Sussman 2005: example (2)) a. Mary went to the desk. b. I’ll read the book when I get home. c. Open the cage, will you please? d. Fred listened to the Red Sox over the headphones.

They used the term weak to refer to deﬁnites that do not have unique or discourse familiar referents.20 For instance, (33a) has an interpretation which is satisﬁed if Mary went to any store whatsoever, rather than a necessarily unique or familiar one. Similarly (33c) can be understood as a request to open any window, not necessarily a unique or familiar one.

(33) (Carlson and Sussman 2005: example (1)) a. Mary went to the store. b. I’ll read the newspaper when I get home. c. Open the window, will you please? d. Fred listened to the Red Sox on the radio.

The ability of (apparently singular) weak deﬁnites to license discourse anaphora to plural nominals (see (34), adapted from Carlson et al. 2006) further supports the view that they lack unique reference:

(34) Jacqueline took the train from Paris to Moscow...they were all clean and ran right on time.

Carlson and Sussman use a variety of diagnostics to distinguish weak deﬁnites from strong ones. For example, only weak deﬁnites license a sloppy reading in VP anaphora (contrast (35a-b)).

(35) a. Fred went to the store, and Alice did, too. (OK as diﬀerent stores) b. Fred went to the desk, and Alice did, too. (must be the same desk)

Based on these diagnostics, Carlson et al. (2006) suggest that weak definites denote properties, in the spirit of McNally’s (1995) analysis of bare plurals in Spanish (see also Puig-Waldmüller2008). However, more recently Aguilar-Guevara and Zwarts (2010) have argued that in fact they denote kind-level entities of the sort posited by Carlson (1977) for the analysis of generics. If Aguilar-Guevara and Zwarts’s argumentation is correct, it suggests that kind terms and weak nominals, if not identical, share some features related to their referential properties. This would not be surprising under the analysis of weak nominals as property denoting, given that the notions of property, entity correlate of a property, and kind appear to be deeply intertwined (see e.g. Chierchia 1998 and McNally 2009 for discussion; see also the discussion around example (14) in section Existential and related constructions). Neverthe- less, how best to capture the similarities and differences between weak definites, other 17 weak nominals, and kind terms remains a question in need of additional research.

Conclusion

Though it was a topic of recurrent discussion in the twenty or so years following the publication of Milsark (1977), the question of how best to deﬁne strong and weak nominals was always closely connected to the analysis of very speciﬁc facts, whether it involved the restriction on nominals that can appear in there-existentials, constraints on the interpretations of nominals bearing certain case marking, or any of the other phenomena discussed in the previous section. It is fair to say that as our understand- ing of these phenomena has grown richer and the proposed accounts for them have become more sophisticated, the notions of strength and weakness themselves have become less important, other than as loose descriptive terms for types of readings available to nominals. Nonetheless, the research that developed from Milsark’s original characterization of the distinction has made a lasting contribution in highlighting the ways in which the basic semantic properties of determiners – their entailments and their presuppositions – are intimately related to the semantic types that the nominals containing them eventually can be assigned in theories that postulate type shifting. It is these properties and their manifestations in natural language, and not the terms strong or weak, that ultimately matter.

Acknowledgments

I would like to thank Veerle Van Geenhoven and Bill Ladusaw for their contributions to my thinking about the strong/weak distinction, and to the ICREA Foundation for their support in the form of an ICREA Academia award.

Notes

1Throughout this chapter, I will generally use the term nominal to refer to any phrase whose main descriptive content is provided by a noun, whether the phrase includes a determiner (e.g. a solution, each solution) or not (e.g. solutions, discussion). When a distinction is crucial, I will use Determiner Phrase (DP) for the former and bare nominal (sometimes specifying the type of bare nominal, e.g. bare plural) for the latter. In material published prior to Abney (1987), the term noun phrase (NP) was generally, if not always, used as I use the term nominal here. Note that I have kept the original terminology in all citations. 2The double question marks (??) indicate unacceptability without specifying whether the source is syntactic, semantic or pragmatic. 3How best to define the determiners associated with cardinality has been a matter of some debate, but as a first approximation of Milsark’s intuition, we can cite this description from Keenan (2003: 190): a determiner that contributes a cardinal predicate is “one sensitive to the cardinality of the intersection of its arguments - its value (whatever it is) remains invariant under changes of arguments that preserve that cardinality.” Such a definition rules out determiners like every, for example, because the truth of every N Vs depends not on the number of individuals in the intersection of N and V but rather on the proportion of individuals in N that are also in V. See Keenan (2003) for extensive discussion and formal definitions. 4Though Barwise and Cooper did not offer a separate definition for weak determiners, in the course of their work they identified a class of determiners they called symmetric, which was later 18 refined in work by Keenan (Keenan 1987, Keenan 2003) and renamed existential (and also known as intersective). Though the rather complex technical details need not concern us here, Barwise and Cooper’s strong determiners are not as a rule symmetric, and there is a deep connection between being symmetric and having a possible interpretation as a property, which in turn closely approximates Milsark’s intuition that weak determiners were equivalent to cardinality predicates. See the works cited in this footnote as well as McNally (1992) for definitions and discussion. 5Barwise and Cooper treated as determiners various sorts of expressions that on most syntactic analyses would not be considered constituents, e.g. strings such as two of the in partitives. 6The exception is the subject argument to so-called individual-level predicates, discussed in section Individual- and stage-level predicates. 7Though space precludes a full explanation of this difference, to give the reader one example of how they differ, quantificational determiners introduce subordinated discourse domains and establish conditions that must be satisfied as those domains are dynamically updated. In contrast, existential closure does not introduce a subordinated discourse domain, but rather is simply a reflex of the fact that for any statement expressed usng a free variable to be true, some individual has to satisfy the conditions on that variable. See Kamp (1981), Heim (1982) for details. 8Technically, for the VP-internal indefinite to be interpreted as a property, the variable contributed by the indefinite would have to be lambda-bound in the logical representation for the sentence; however, such a step is never discussed in Diesing (1990). That said, it should be noted that in later work (Diesing and Jelinek 1995), Diesing does explicitly associate VP-internal indefinites with a property-type interpretation. 9Existential have sentences contain a relational noun such as sister, mother, or lid in their direct object position, with have simply serving to identify the subject argument as one participant in the relation the noun denotes; in possessive have sentences, have itself introduces the (possession) relation that holds between the subject and object. See the references cited in the text for further discussion. 10Definite nominals, including proper names, were acknowledged already by Milsark to appear in there-existential sentences with what has come to be known as the “list” interpretation, as in (i) (see e.g. Rando and Napoli 1978).

(i) Who can help us? There’s Mary.

This interpretation was not subsumed under Milsark’s E-Rule. 11 E.g. Herburger (1997) argues that an analysis based on existential quantiﬁcation over a cardinality predicate is problematic when the determiner is monotone decreasing, as in (ia), or non-monotone, as in (ib):

(i) a. There were at most three/few/no cookies left. b. There were exactly three cookies left.

The problem is that if all that the semantics requires is that one be able to find a set satisfying a given cardinality, a sentence containing a monotone decreasing or non-monotone determiner will be true even if there are larger sets in the context satisfying larger quantities. For instance, (ib) will be satisfied by identifying a (sub)set of exactly three cookies within a larger set of four or more cookies. But intuitively in such a context, (ib) should be false. McNally (1998a) proposes to solve this problem by treating at most and exactly as compositionally separate from the accompanying numeral (Krifka 1999), and by giving a decompositional analysis to no and few following Ladusaw (1992) as equivalent to not...a and not...many, respectively. On this approach, at most, exactly, and not function as sentence-level operators that guarantee that it will not be sufficient to identify a set of entities with a particular cardinality in order to satisfy an existential sentence. The reader is referred to these works for further discussion. 12Comorovski (1991) argues that Barwise and Cooper’s account can be preserved under an alternative syntactic analysis in which the final phrase (e.g. in the basket) forms a separate constituent from the postverbal nominal, but doing so requires a not otherwise motivated semantic composition rule for the nominal with that phrase. 19 13One might question whether such sentences are “truly” existential. Keenan (1987) notably argued that any determiner can appear in there-existentials, but that only those determiners that he defined as existential (effectively, his way of capturing the intuition behind Milsark’s notion of weakness) give rise to what he referred to as an existential interpretation – in other words, counted as truly existential. However, aside from risking circularity, attempting to define existential sentences narrowly, in terms of the reading a particular subset of determiners yields, fails to account for the differences in behavior of definite, demonstrative, and partitive vs. necessarily quantificational nominals in the construction in English, and it also sheds no light on the complex cross-linguistic variation in the distribution of determiners in existential constructions documented in Beaver et al. (2005). 14See Chierchia (1984) and the works cited in the text for further details, and Chierchia (1998) for a translation of the intuition behind this analysis into a more familiar set-theoretic semantics. It should be pointed out that a weakness of McNally’s proposal was that it did not clarify in any way exactly how kinds or types (as informally understood) should be related to entity correlates of properties. 15Milsark called these predicates property denoting; the more current individual-/stage-level terminology due to Carlson (1977) is used here. A distribution-independent definition of individual-level and stage-level remains elusive. For Milsark, the former

name some trait possessed by the entity and which is assumed to be more or less permanent, or at least to be such that some signiﬁcant change in the character of the entity will result if the description is altered. (Milsark 1977: 13)

The latter denote states “which are subject to change without there being any essential alteration of the entity.” (ibid, p. 12). See also Generics. 16 Milsark argued that any potential counterexamples to the inverse correlation, e.g. (i), could be explained by positing a strong interpretation for the determiner in the context of an individual-level predicate, and by positing a weak interpretation for the determiner in the context of the existential construction.

(i) a. There were two/few/no men in the room. b. Two/Few/No men were intelligent.

17De Hoop takes these examples from Bittner (1988); in Van Geenhoven (1996) the relevant case is glossed as absolutive. 18However, see Kiparsky (1998) for criticism of de Hoop’s account of partitive case. Other examples where case or similar marking arguably correlates with a distinction very similar to the strong/weak distinction include the genitive of negation in Russian, which Kagan (2007) associate with a property-type interpretation for the nominal, and a marking on direct objects in Spanish, whose absence has been associated with a property-type interpretation (Bleam 2005, López 2012). 19Partee does seem to assume that type ⟨⟨e, t⟩, ⟨e, t⟩⟩ would be a natural shift specifically from the property type ⟨e, t⟩, and indeed this type alternation appears frequently in the literature on modification. Thus, de Hoop’s proposal that weak nominals function as verb modifiers has a very close affinity to the proposal that weak nominals denote properties. 20Despite the apparent coincidence between de Hoop’s class of weak definites and theirs, Carlson et al. (2006) state that they adapt the term from Poesio (1994), who used the term to characterize a different class of definite descriptions, namely those found in examples like (15), above.

SEE ALSO: Bare plurals; Generics; Information structure; Kinds of (non-)specificity; Noun incorporation; Partitives; Quantifier scope; Speaker’s reference; Type shifting; Varieties of definites

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Louise McNally is Professor of Linguistics at Universitat Pompeu Fabra, Barcelona. Her research centers primarily on the interaction between lexical and compositional semantics. She has published on topics such as existential constructions, noun incorporation and related phenomena, the semantics of adjectival and adverbial modiﬁcation, nominalization, and lexical aspect.