Abstract
Schwarzschild (2006, 2011) observes that adjectives like heavy are obligatorily distributive when attributive, but not when predicative. He proposes a non-monotonicity requirement on attributive modification which rules out the collective reading: because the dimension of weight is not allowed to be monotonic on the part–whole relation determined by the noun phrase, and a collective reading of attributive heavy will be monotonic, only the distributive reading is available. Here, we propose that non-monotonicity follows from the independently determined distributivity of certain attributive adjectives. In addition to dimension adjectives like heavy, evaluative adjectives like pretty also result in obligatory distributive readings when in attributive position, while allowing collective readings when predicative, despite the fact that they are non-monotonic on both readings. Other adjectives, e.g., numerous, are collective in attributive position, despite being monotonic. We propose that the requisite distributive reading with attributive heavy (and pretty) stems independently of non-monotonicity, and is due to the particular way the adjective’s comparison class is interpreted in the attributive position; the non-monotonicity of attributive heavy is then a consequence of distributivity.
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Notes
- 1.
From now on, for reasons of brevity, when we say that an adjective is (non-)monotonic, we mean that the adjectival dimension is (non-)monotonic on the part–whole relation in the domain given by the noun phrase.
- 2.
Word order is reversed in two particular constructions (see Ionin and Matushansky 2004; Solt 2007), which differs from (13b) in the presence of an article. Notably, the attributive adjective heavy has a collective interpretation:
The interpretation here is that the collection of boxes is heavy (the sentence is true even in the case where each box is light, but together the boxes weigh 30 lbs.).
Kayne (2005) shows that a similar construction is possible involving both an attributive and a Q adjective in the reverse linear order (again, note the presence of the article):
On Kayne’s account, the adjective modifies a null quantity noun NUMBER, whose pseudo-partitive complement the lexical noun boxes is:
Extending this account to (i) would yield a null AMOUNT OF:
We also observe that higher syntactic placement of the attributive adjective results in the return of the collective/distributive ambiguity for dimension adjectives (Ouwayda 2011).
We take this to be a case of the same type of construction as in (i)—note the contrast in (vi)—and so a parallel structure to that of (iv) would be appropriate, as in (vii):
Such examples are thus not a counterexample to Schwarzschild’s generalization.
- 3.
We note, however, that a search of Corpus of Contemporary American English Davies (2008) reveals several such examples. The presence of the expected worth (e.g., fifty-dollars-worth of gas) is apparently optional.
- 4.
Jessica Rett (p.c.) observes that when (17b) is in the present tense (They are expensive) the distributive reading is the only available reading. We agree that there is a difference between the present and the future in this respect, although the collective reading is not completely ruled out under our intuitions. We don’t know why the future allows a collective reading more easily than the present.
- 5.
We use the term “dimensional” to refer to a subset of relative adjectives. Dimensional adjectives are associated with quantity scales such as length, weight, size. They come in antonym pairs, e.g., tall–short, wide–narrow, heavy–light, and the positive dimensional adjectives can typically be modified by conventional measure phrases: 6 ft tall, 4 cm wide. “Evaluative” adjectives like pretty, expensive, strong, lazy are also relative, but they are linked to quality scales, and often to more than one scale and so they don’t all have single antonyms, and they also are not associated with conventional measure phrases. See Bierwisch (1989).
- 6.
As noted by Partee (1989), in the presence of the (as in (20b)), many only has a cardinal reading. The same is true for several and numeral determiners.
- 7.
It has been argued that absolute adjectives also depend on a comparison class (van Rooij 2011; Toledo and Sassoon 2011) but not of the kind that can be expressed by a for-phrase as the one in (32)–(33). On Toledo and Sassoon’s (2011) account, absolute adjectives have a comparison class comprised of counterparts of the individual of which the adjective is predicated. Such a “counterpart” comparison class is incompatible with the extensional category generally referenced by for-phrases such as for a wine bottle. For-phrases that can co-occur with absolute adjectives have different form, and according to Toledo and Sassoon, reference individual counterparts (see (i) and (ii), Toledo and Sassoon’s 2011: ex. (24), (25)).
- 8.
- 9.
Ludlow (1989) also notes that predicative adjectives can have a comparison class that is more general than the denotation of the NP of the subject of predication. This is particularly clear in cases like (i), which, read generically, cannot limit the comparison class to elephants.
He also notes a contrast with cases when the domain of quantification is restricted: in (ii) the comparison class is most naturally interpreted as being limited to elephants.
What matters to us is that predicative adjectives allow wider settings of their comparison class, as in (i), in contrast to attributive adjectives, where the comparison class is fixed by the modified NP.
- 10.
We do not discuss here nonlocal for-phrases as in (i) (from Schwarz 2010). The challenge with such examples is to determine how the comparison class set by the overt for-phrase interacts with the implicit comparison class associated with the positive attributive adjective.
- 11.
De Clercq (2008) discusses agreement patterns in object-denoting proper names used as common nouns (PUCs), as in (i), which is based on a personal proper name, and (ii), which is based on a brand name.
De Clercq notes that German provides evidence for the underlying presence of a common noun in PUCs as the article varies in gender depending on the gender of the non-overt noun:
In Belgian Dutch the article in such cases is invariably masculine, agreeing neither with the proper name nor with the likely underlying common noun. This complicates the analysis of the morphosyntax of the null expression that De Clercq posits, but for our purposes the details are immaterial, since we are focusing on the semantic effects.
- 12.
In McKinney-Bock (2013) the comparison class is introduced by a deg head that is separate from pos. The advantage of this proposal is that the same pos can be used in combination with relative and absolute adjectives. We have made the simplified move to have a single quantifier, pos. Furthermore, on McKinney-Bock’s account, the covert comparison class-denoting argument is a syntactically complex expression, a for-phrase with an elided NP, whose content is recovered under identity with the attributively modified noun phrase, i.e., it is a case of ellipsis resolution. As our goals in this paper are different, we do not adopt this particular proposal, but we note that it would be compatible with our account of attributive relative adjectives. We also note that there are several counterarguments to the (abstract) pos morpheme (Rett 2015), and our account of attributive relative adjectives does not depend on the existence of the morpheme pos; the formal weight could be carried in another way.
- 13.
We use interval semantics following McKinney-Bock (2013), although this is not crucial for our argument.
- 14.
The lexical entry in (45) is from Heim (1999), updated to work with the interval semantics for gradable adjectives we assume here.
- 15.
A pragmatic restriction to singularities has been suggested by Stateva (2005) for distributive readings of plural superlatives (e.g., the interpretation of John and Bill are the tallest students as Each of John and Bill is taller than any other (relevant) student). Plural superlatives also allow group readings, perhaps less saliently, see Fitzgibbons et al. (2008).
- 16.
The other types of generic sentences are direct kind predications, in which indefinite singulars cannot participate, as in (i)–(ii).
The nominal phrases in direct kind predications (definite singulars and bare plurals) are standardly assumed to denote kinds, while the nominal phrases in characterizing generics (indefinite singulars and bare plurals) are assumed to denote predicates restricting a generic operator. Because definite singulars cannot occur in comparison class denoting for-phrases (e.g., * for the first-grader) we assume that the bare plurals that do occur (e.g., for wine bottles) are characterizing generic nominals rather than kinds. This is important because direct kind predications may express collective generalizations, as in (i)/(ii) and (iii)/(iv):
- 17.
A reviewer notes that prototypicality may not quite be the notion we need, given that not all NPs have prototypes, citing as examples “male nurse”, “non-Methodist”, “resident”. We acknowledge that this is a complex issue, but ultimately it is not essential for us to resolve: whatever notion best captures the semantics of characterizing generics is what is involved in comparison classes of relative adjectives.
Additionally, the same reviewer points out the following intuition.
In this example, the speaker has never had an experience of eating dragon fruit before, and so has no concept of a prototypical dragon fruit. The reviewer suggests that the comparison class in the above example is not restricted to the denotation of the NP, but instead to the speaker’s experience of eating foods (other than dragon fruit).
We agree with the intuition in (i). At first, this appears to challenge Higginbotham’s generalization that attributive adjectives are interpreted relative to the head noun, but we believe this is not the case. Given the context in (i), the sentence is only felicitous when the adjective has a pitch accent/ is focused. Adjectives with focus are interpreted relative to other comparison classes than the default, possibly because they are in higher position within the nominal phrase (McKinney-Bock 2013, see also footnote 1), and so for focused adjectives like heavy the collective reading returns.
- 18.
Since pos presupposes that its individual argument is a member of the comparison class, see (48), prototypicality will be ascribed to that argument by the presupposition.
- 19.
The for-phrases that appear with numerous are of the type that are licensed with absolute adjectives as well, as we discussed in footnote 7. Consider (i) and (ii).
- 20.
Numerous predicates only over pluralities, and to the extent that it allows distributive readings it distributes to sub-pluralities that are non-atomic. Champollion (2015) claims that sum predicates have distributive readings with numerous (a judgment that is not shared by several speakers who we consulted):
Additionally, a Google search returns several hits that contain both many and possibly distributive numerous.
However, several other results show that numerous can co-occur with many in a context that is clearly not distributive.
Here, numerous seems to be modifying a dimension of density or frequency (according to our intuitions about these sentences). The stores are both many in number and numerous because they occur in clusters (and the same for nests in trees, or waterfalls along a hiking track).
- 21.
- 22.
Although, plentiful and sparse can also appear in a pseudo-partitive structure, as revealed in the following examples.
This raises the possibility that there is an analysis of numerous as well where it realizes a pseudo-partitive structure with a null NUMBER (a la Kayne 2005).
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Acknowledgements
The inspiration for this work was Roger Schwarzschild’s widely influential paper on the syntax of measurement (Schwarzschild 2006). Many thanks to Roger for his insights, on paper and in conversation. We are also indebted to Jim Higginbotham for discussion over the years, without which our understanding of adjectives would not be the same. Thanks to Jessica Rett and an anonymous reviewer for insightful comments. An early version of this work was presented at SALT 2012.
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McKinney-Bock, K., Pancheva, R. (2019). Why Is Attributive “Heavy” Distributive?. In: Altshuler, D., Rett, J. (eds) The Semantics of Plurals, Focus, Degrees, and Times. Springer, Cham. https://doi.org/10.1007/978-3-030-04438-1_5
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