Since Carlson (1977)’s seminal work, genericity has been one of the topics that are widely discussed in semantics. Although generic readings are conveyed through diverse forms of noun phrases (NPs), research has centered on characterizing generic readings of bare plurals. NPs with (in)definite determiners, demonstratives, or numerals have not drawn much attention. Kind-denoting interpretations are also treated as a secondary topic, compared with characterizing generic ones. This study will address a topic which is worth getting more academic attention: kind readings of NPs with numerals.
NPs with numerals show different patterns in their interpretations, occurring with predicates which take either an object or a kind as their argument.
The sentences in (1) are distinct only in the selection of the nouns in their subject positions, and the predicate
To account for different preferences between object and kind readings, I will briefly summarize diverse categories of readings in generic sentences, giving a focus on kind readings of numeral NPs. I will critically review previous analyses on kind readings of numeral NPs and argue that none of the analyses provide satisfactory accounts for the different preferences. I will revise an interpretation domain for the interrelatedness of an object domain and a kind domain and propose a lexical restriction on the semantics of numerals.
Sentences may assert specific events or states that are restricted by time and space. For instance, (3a) asserts the event of discovering
(3a) is called an ‘episodic’ sentence due to its specificity, and
bare plurals occur with a predicate of general property, they are conducive to generic readings.
According to Krifka et al (1995), there are predicates which take only kind-referring terms in their argument positions. For example, the subject argument of
Kind-referring terms are understood to denote kind individuals that are generated from the maximal sets of entities. Whether they are of bare plural forms or singular NPs with the definite article, kind NPs denote unique individuals that are abstract away from objects. Occurring with the kind-taking predicate
Here is a taxonomic hierarchy which shows that the species of whale is further divided into several subkinds such as blue whale, dolphin, fin whales, etc.
Just as individuals are summed to make a larger entity, subkinds are conflated into a higher entity of kind. Taking a number of subkinds in its denotation, the kind
All the NPs with
Subkind readings are not limited to count nouns. Mass nouns occurring in a count noun context typically get taxonomic readings.
1One of the important features of characterizing generics is that they admit exceptions in their denotations. The existence of some dinosaurs that were nothuge does not make a difference in the truth of (3b) as far as they make a miscellaneous set of entities. 2Characterizing generic sentences include generalizations over events as well as generalizations over objects as in (3b). For example, (i) conveys a habitual reading of John’s activity. (i) John smokes a cigar after dinner. (i) is not about one instance of John’s smoking a cigar. It is about John’s habit, which is a generalization over the events of John’s smoking after dinner. For more argument about the habitual readings of generics, see Krifka et al (1995) and Pelletier et al (1997).
To derive subkind readings, Krifka (1995) notes that kind terms and proper names show close similarities and argues that kind terms denote names of kind individuals. An interpretation domain is divided into two structures, one for objects and the other for kinds. The structure of kinds makes a taxonomic hierarchy as in (4). Krifka also discusses the fact that kinds are ontologically prior to objects because all languages which allow bare NPs use them to refer to kinds.
Krifka posits two functions to derive object and subkind readings: realization relation R and taxonomic relation T. In the intensional framework, R and T depend on a possible world i. Then, if k is a kind, λx.Ri(x,k) applies to objects of k in a world i and λx.Ti(x,k) applies to subkinds of k in a world i. RT is the union of these two relations: RTi (x,y) = Ri(x,y) ∨ Ti (x,y).
Given the relations, Krifka argues that classifier and non-classifier languages show distinction in the interpretations of kind terms with numerals. In classifier languages, classifiers distinguish the selection of objects and kinds whereas in non-classifier languages numerals include unit readings which encompass both objects and kinds. For example, Chinese, a classifier language, adopts distinctive classifiers to deliver object or kind readings.
Krifka suggests two operators OU and KU for numeral readings. For each possible world, OU takes a kind and yields a measure function that measures the number of objects of that kind, and KU takes a kind and yields a measure function for the number of subkinds of that kind. Then, the classifiers
Taking a kind y in each possible world i,
Although the selection between objects and kinds is specified by classifiers in classifier languages, non-classifier languages cannot make use of this strategy. Hence, Krifka argues that measuring functions are incorporated in the semantics of numerals, which includes OKU, the union of OU and KU. For instance, the numeral
Since a non-classifier language like English does not have classifiers to encode the measuring functions, the semantics of numerals incorporates the conflated function OKU. Taking a kind y in each possible world,
Krifka’s argument for the distinctive semantics between classifier and non-classifier languages has inspired much following research. The notion of the measuring functions is also understood as useful to derive numeral readings. Despite these merits, his analysis does not have a clue for the different preferences of subkind readings between human and nonhuman nouns as pointed out in section 1. He postulates a taxonomic hierarchy which is not affected by semantic feature like humanness, andthus there is no theoretical ground to distinguish the kinds of book and student in numeral readings.
To account for kind readings cross-linguistically, Chierchia (1998) adopts a lattice-theoretic structure for the interpretation domain of individuals and kinds, following Link (1983) and Landman (1989).3 In their analysis, singular and plural entities are equally postulated as entities, which are defined by the join operation ‘+’ and the part-of relation ‘≤’ in a join semi-lattice structure. Suppose that a world w has only three individuals d1, d2, and d3 for
Given the lattice structure of individuals, Chierchia argues that objects and kinds make separate structures and that they are mapped to each other by operators.4 The properties of the three
In Chierchia’s analysis, kinds do not make a taxonomic hierarchy as in (4). Kinds are individuals that make a lattice structure and they are mapped to objects by the operators. Hence, kinds are not restricted to biological ones or ‘well-established’ ones. Chierchia argues that artifacts (like chairs or cars) or complex things (like intelligent students or spots of ink) may also make kinds as far as they show sufficiently regular behaviors. He further adds that what counts as kind is not set by grammar but by the shared knowledge of a community of speakers. Thus, the structure of kinds varies with the context to a certain degree and remains somewhat vague. Chierchia concerns himself with the semantics of characterizing generics, which is discussed to be derived from kinds. Hence, the concept of kinds is broad enough to include all instances of characterizing generics.
Chierchia’s analysis provides a satisfactory account for the typological aspects of NPs. As for the current topic of subkind readings, kind entities are assumed to be determined by the shared knowledge of language users and may be affected by contexts. At first glance, this appears to leave room where human and nonhuman nouns are distinctively assigned kind entities. However, Chierchia claims that all lexical nouns are mapped to kinds and that complex nouns may or may not. Hence, his framework does not provide a structure in which human and nonhuman nouns have different biases towards subkind readings.
In the analyses of Krifka (1995) and Chierchia (1998), a single structure is postulated for kind entities although the shape of the structure is distinguished. Krifka’s structure is more oriented to the taxonomic hierarchy, and Chierchia’s to the lattice-theoretic structure. This leads to the difference that kind entities of Krifka’s analysis are defined narrowly to include natural kinds or well-established ones while those of Chierchia’s are broad enough to encompass all entities that are mapped to sums of objects.
Nomoto (2010) follows the previous analyses in that individuals consist of two basic sorts, i.e., object and kind individuals, which are distinctly typed.5 He also adopts a lattice-theoretic domain of individuals in the sense of Link (1983) & Landman (1989). What deviates from the earlier approaches is that he posits two structures for kinds: a taxonomic one and a lattice-theoretic one. Following Dayal (2004), Nomoto argues that a taxonomic hierarchy is a list of names that denote natural kinds as exemplified in (4). Kinds used in generic sentences are not restricted to natural kinds, so a taxonomic hierarchy is just part of the kind structure.
Kinds are individuals like objects. They are only distinguished in their types. Hence, kinds also constitute a lattice-theoretic structure like objects. For instance, the kinds and subkinds of mammals and whales are represented as in (11).
Nomoto argues that an atomic kind individual like whale is a group derived from its subkinds by the group formation function ‘↑’.6 In a world w, where there only three kinds of whales such as blue whales, dolphins, and sperm whales, these three kinds make a lattice structure as in (11b). The supremum of these three kinds, i.e. Blue Whale+Dolphin+Sperm Whale, is mapped to a group ↑(Blue Whale+Dolphin+Sperm Whale), which is identified as the kind whale. Then, the kind whale is again makes a lattice structure with other mammals as in (11a). In this domain, a taxonomic hierarchy is understood as the structure consisting of group entities of kinds without including sums of kinds.
Nomoto further argues that subkind readings are derived by the application of the member specification function ‘↓’ and the type-shifting function ‘Ident.’7
According to Chierchia (1998), the property of objects is mapped to a kind individual by ∩. Since this kind is assumed to be a group of subkinds in Nomoto’s analysis, ↓ is needed to map it to a sum of its subkinds. Finally, Ident takes a sum of subkinds and yields a set of subsums. Bare nouns are type-shifted to derive subkind readings.
A type-shifted subkind reading is exemplified by
The kind whale is a group of the three kinds of whales as in (13a). The subkind reading of whales is type-shifted as in (13b). First, ↓ applies to the group to yield a sum of the three species. Then, Ident turns a sum of the species into a set of subsums. In this set, the subkind reading of
In the lattice-theoretic domain, where kinds and subkinds are related with the group formation function, the semantics of numerals is uniformly defined regardless of whether they combine with objects or kinds. After being type-shifted, bare nouns in subkind readings denote a set of sums just like bare nouns in object readings. Hence, the semantics of numerals simply restricts the number of atoms in the sums that are selected.
In spite of the convincing argument for the group denotations of kinds, Nomoto’s analysis is not equipped with a mechanism for the distinct preferences of subkind readings. Although a nonhuman NP like
When the kind book is member-specified and makes a set of sums by the functions, it is mapped to a sum of subkind like Book A and Book B. Likewise, since taxonomic kinds are the results of group formation of subkinds, human kinds like student are also related with their subkinds by the functions. When the type-shifting procedure applies to the kind student, it yields a set of subkinds of students such as elementary school students and middle school students. Hence,
3Although Chierchia (1998) follows Link (1983), he does not accept nonatomic properties of materials for mass nouns. Chierchia assumes that mass nouns are plural by themselves. 4Chierchia (1998) assumes that properties and kinds are of different types. Properties are of type
> and kinds of type e. Hence, they do not make a single structure. 5Object individuals are of type eo, and their properties
For the proper treatment of subkind readings, we will consider howsubkind readings are affected in sentences. First, as noted in the previous analyses, the lexical properties of predicates are crucial in determining kind or subkind readings.
The whole species of a kind cannot be buried in some place in most cases. Thus,
In addition to the lexical properties of predicates, I argue that those of nominal arguments also play a crucial part in determining subkind readings. As noted in section 1, not all nouns can make subkind denotations even in the cases that they occur with predicates with kind arguments.
A scrutiny with more examples shows that the semantic feature of nouns indeed functions as a decisive factor in the selection of object and subkind readings.
Just as be
English is classified as a language which does not have classifiers in its grammar. Hence, subkind readings of NPs with numerals are affected only by the lexical properties of predicates and nouns. In contrast with non-classifier languages like English, classifier languages have further mechanisms that affect subkind readings, i.e., classifiers.9 Various language show different patterns of object and kind readings of numeral NPs.
In Chinese, classifiers are mandatory to numeral NPs, so nouns cannot combine with numerals without the occurrence of a classifier. For numeral readings, distinct classifiers may be used to denote objects and kinds as discussed by Krifka (1995).
Unlike Chinese, classifiers in Malay yield only object readings. (cf. Nomoto 2010)
In contrast with the obligatory use of classifiers in Chinese, classifiers are optional in numeral NPs in Malay. Hence, two forms of NPs are available as in (19) to deliver numeral readings. Interestingly, numeral NPs without classifiers have an ambiguity between object and kind readings. The NP without the classifier
Although Korean is a classifier language where classifiers are optionally used in numeral NPs, subkind readings show a pattern that parallels with that of English. NPs that are highly ordered in the animacy hierarchy do not freely denote subkind readings while those in lower positions are easy to have subkind readings.
Subkind readings affected by the animacy hierarchy are also observed in Malay. (cf. Nomoto 2010)
As noted above, numeral NPs without classifiers are supposed to have subkind readings in Malay. However, nouns show different degrees of acceptability even in bare numeral structures. Nomoto observes that the ease of an object reading is higher in the following order:
Chinese, Malay, and Korean are all classifier languages, in which the use of classifiers is either mandatory or optional in numeral NPs. However, classifiers carry different functions in these languages. Distinct classifiers may be used for object and subkind readings, or the use of classifiers has the effect of blocking subkind readings. Or classifiers may license both object and kind readings. The idiosyncrasy of classifier functions shows that selectional restrictions between objects and kinds need to be encoded in the semantics of classifiers.10 Furthermore, subkind readings are highly affected by the animacy hierarchy of nouns in English, Korean, and Malay. The easiness of subkind readings for NPs of lower animacy is cross-linguistically prevalent. Hence, the animacy degrees of nouns should be reflected in the semantics of numerals or classifiers.
For the proper treatment of subkind readings, I argue that the interpretation domain proposed by Nomoto (2010) needs to be further elaborated. Nomoto assumes that the domain of objects is separate from that of kinds. Objects make a lattice structure by the join operation and the group formation function, and kinds make another lattice structure by the same operation and function. However, an interrelated relation between the two domains is not considered in his analysis.
To see why an interrelated relation is needed between the two domains, let us consider the denotations of the proper names in the following:11
Before going into the details of the problem, it needs to be considered whether this is a question worth pursuing. This problem arises because a group and a kind share many properties. Both of them are abstract atoms and represent a number of objects which may be located in disconnected times and places. In other words,
I argue that the unworthy selectional problem is attributed to the disconnectedness of the domains of objects and kinds. I propose that the grouping of objects by ↑ yields the group of the objects, which again corresponds to the kind of the objects. In other words, a group of objects makes a kind on the lowest level in the kind domain.
When all the copies of some book like Book A are grouped to a group like ↑(Book A1+Book A2+Book A3), it is understood as a group of the copies. This group is also used as the title of the book, which is the kind BOOK A. The domains of objects and kinds are intertwined by the functions ↑ and ↓. Since a group of objects and a kind on the lowest level are not distinguished in this new domain, the selectional problem of the NPs in (22) is not an issue any more.
Kind and subkinds are relative concepts. Thus, once kinds on the lowest level are made by the grouping of objects, these kinds are grouped together to make another kind on the upper level. Suppose that copies of the book titled Book A make the kind BOOK A and that other book kinds such as BOOK B and BOOK C are made in the same fashion. In the situation that BOOK A, BOOK B, and BOOK C constitute an exhaustive set of books in the world w, BOOK A, BOOK B, and BOOK C are grouped to make the higher kind BOOK. A hierarchical structure of the kind domain is produced in the repeated grouping of kinds in this way.
In the lattice-theoretic domain of Link (1983), materials for mass terms make a separate lattice structure from that of objects for count terms. Although materials and objects are distinct in their atomicity, they constitute the same structure. In a lattice structure, materials are joined to make sums and also grouped to make groups. When groups are made by ↑, they serve to make a kind domain. Although materials are non-atomic and non-countable, kinds of materials are countable like kinds of objects. Hence, mass terms occur freely in count noun contexts, and the same subkind readings are available for mass terms. Hence,
Bare plurals in English are construed in two ways, namely indefinite object readings and kind readings. To deal with the ambiguity of bare plurals, two basic approaches are adopted in literature. One is to assign only kind readings to bare plurals and derive indefinite object readings from the kind denotations when necessary (cf. Carlson 1977, 1989; Chierchia 1998). The other is to accept the ambiguity of bare plurals and postulate both object and kind readings for them (cf. Wilkinson 1991, Diesing 1992, Gerstner & Krifka 1993, and Kratzer 1995).
Nomoto (2010) adopts the former approach, which is kinds-based. Bare plurals uniformly refer to kinds, which are defined by ∩, the nominalization operation of properties. Occurring with kind-level predicates like
In the latter approach, bare plurals are ambiguous between objects and kinds. Object-level predicates combine with object-denoting bare plurals and kind-level predicates with kind-denoting bare plurals. If we adopt this ambiguity approach, not only predicates but also numerals should be distinguished in their arguments. Unlike predicates, most numerals yield either object or kind readings. Hence, I argue that numerals should be ambiguous between object-level numerals and kind-level numerals.
Numerals other than the singular
The object numeral
When the object-denoting bare plural
The two possible approaches to the semantics of bare plurals naturally lead to the two analyses for numeral readings. To see which one is more appropriate to deal with subkind readings, we will compare them closely. According to Nomoto (2010), the interpretations of
The bare plural
In contrast, the current proposal follows the ambiguity approach of bare plurals and postulates the ambiguities of numerals. Here are the interpretations of
In Nomoto’s analysis, the kind domain is not connected with the object domain. On the other hand, the current analysis assumes that the kind domain is intertwined with the object domain because kinds on the lowest level are equal to groups of objects. This revised domain provides a more efficient framework for the interpretations of proper names.
Proper names and kinds are discussed to share many semantic properties, so they are assumed to denote atoms. (cf. Krifka et al. 1995) Although proper names denote atomic entities of kinds like bare plurals, they are not used as nominal predicates. Then, the up operation does not apply to proper names according to Nomoto’s analysis. This means that since the object reading of
Another problem to consider in comparing the two analyses is the different preferences of subkind readings depending on the properties of nouns. As noted in section 3.3., the empirical problem with Nomoto’s analysis is how to block the subkind readings of human NPs with numerals.
There are basically two conceivable ways for the blocking effect. One is to revise the interpretation domain so that kinds of human nouns are not connected with subkinds. To achieve this purpose, a quite ad hoc stipulation will be needed. Conceptually, the kind student may be divided into smaller kinds such as elementary school and middle school students, and kind terms like
Another way to achieve the blocking effect is to attribute lexical properties to nouns or numerals to restrict the application. Since numerals are not assigned separate interpretations depending on their argument categories, this lexical approach is not made used of in Nomoto’s analysis. Object readings are open to all bare plurals, so numerals cannot have lexical properties targeting human arguments. Unlike Nomoto’s analysis, the current analysis posits the ambiguities of numerals so that only kind numerals may have a lexical restriction as to human nouns. Hence, I propose that although object numerals are not restricted in taking their argu-ments, kind numerals do not take human nouns as their arguments.13 Then, the semantics of kind numerals is revised as in (31a).
Taking an argument x which is not part of the kind human, the kind numeral
As observed in section 4.2, classifiers in the classifier languages carry diverse functions intra-linguistically and cross-linguistically. The diversity of the functions provides a theoretical ground to lexical restrictions on classifiers as discussed by Krifka (1995) in section 3.1. It is not easy to assume that nouns have significantly different meanings between classifier and non-classifier languages. Then, it is natural to postulate that semantic roles of classifiers are partly transferred to numerals in nonclassifier languages.14 If we assume that the selection between objects or kinds is described in the semantics of classifiers, we can also assume that numerals in non-classifier languages may be restricted in their argument entities between objects and kinds. The parallel restrictions on classifiers and numerals are further supported by the fact that human nouns are less likely to have subkind readings in Korean and Malay as well as in English. In view of the fact that predicates in English are lexically restricted in their argument categories between objects and kinds, the lexical restriction on numerals is not quite unexpected.
8I follow the animacy hierarchy discussed by Corbett (2000). (i) Animacy Hierarchy speaker > addressee > 3rd person > kin > human > animate > inanimate Personal pronouns denoting a speaker, addresses, and 3rd persons take the highest position. Other human nouns including kinship terms take the next positions. Finally, animate nouns have higher animacy than inanimate nouns. Corbett argues that the singular-plural distinction in a given language must affect a top segment of the Animacy Hierarchy. Just as the degree of animacy affects the plurality of nouns, it also affects subkind readings. 9The semantic roles of classifiers in general are not discussed in this study. Some researchers argue for the counting function of classifiers and others for expressing semantic categories of nouns. 10Nomoto (2010) argues that classifiers uniformly block subkind readings cross-linguistically. However, widely used subkind readings of classifier NPs in Korean make explicit counterarguments against Nomoto. See Kwak (2012) for more details. 11The corelatedness between kinds and proper names is well discussed by Krifka et al. (1995). 12Whether the kind Prius is on the lowest level or not depends on contexts. In the context of (28), there are no subkinds under the kind Prius. However, in other contexts as in (i), the specificity of the kind domain is further refined, and the kind Prius may consist of its subkinds which are divided by years. (i) The magazine tested
Although generic readings are delivered through diverse forms of NPs in English, previous research on genericity is highly focused on the semantics of bare plurals. Additionally, characterizing generic sentences are widely discussed, but kind sentences do not draw as much attention. Hence, I have concentrated on subkind readings of NPs with numerals in this study.
As for kind interpretations, Krifka (1995) and Chierchia (1998) provide interesting analyses. However, they do not go into the details of subkind readings. Adopting the kinds-based approach of Chierchia, Nomoto (2010) argues that kinds are groups of subkinds and suggests a refined interpretation domain for kinds and subkinds in a lattice-theoretic structure.
I have pointed out that subkind readings are not available to all NPs with numerals. Human nouns are not allowed to have subkind readings even when they occur with predicates taking kind entities. The different preferences for subkind readings are not confined to English. The same preferences are observed in classifier languages like Korean and Malay.
In Nomoto’s analysis, numerals are not ambiguous whether they take objects or kinds as their arguments. Hence, the different preferences for subkind readings are not easy to be fit in his framework because object readings are open to all categories of nouns.
For the proper treatment of subkind interpretations, I have revised the interpretation domain suggested by Nomoto although I have accepted the group readings of kinds. The separate domains of objects and kinds are neither conceptually convincing nor empirically useful, especially in the semantics of proper names. In the revised domain, I have followed the ambiguity approach as to the semantics of bare plurals and proposed separate interpretations of kind-level numerals. Unlike object-level numerals, I have proposed that kind-level numerals are under a lexical restriction which states that arguments for numerals are not part of the kind human in the kind domain. By this restriction, nonhuman nouns freely occur with numerals to have subkind readings while human nouns do not.
This lexical restriction is not idiosyncratic to English. Classifiers in classifier languages carry diverse functions as to kind readings, which need to be lexically restricted. If we assume that part of the roles of classifiers are transferred to numerals in non-classifier languages, a similar lexical restriction is also naturally expected in non-classifier languages like English.