Deriving four generalizations about nominals in three classifier languages

Abstract

This squib presents a set of facts concerning nominal structures in Bahnar, Mandarin, and Vietnamese. It proposes an account of these facts which reduces them to cross-linguistic differences with respect to the availability of particular syntactic configurations involving the bare noun and its extended projection. These differences, in turn, are derived from cross-linguistic variations with respect to the availability of items in the functional lexicon.

Résumé

Cette notule présente un ensemble de faits concernant les structures nominales en bahnar, en mandarin et vietnamien. Elle propose une explication de ces faits qui les réduit à des différences interlinguistiques par rapport à la disponibilité de configurations syntaxiques particulières impliquant le nom nu et sa projection étendue. Ces différences, à leur tour, sont dérivées de variations interlinguistiques en ce qui concerne la disponibilité d’éléments du lexique fonctionnel.

1. Classifier languages and parametric variation

One fact about linguistic variation is that nouns which intuitively denote the same concept can have different combinatorial properties in different languages. In English, the noun dog can combine directly with the numeral one, as in John has one dog.¹ In Vietnamese, on the other hand, the noun chó ‘dog’ cannot combine directly with the numeral một ‘one,’ but requires the mediation of a “classifier” (CL).²

1. (1) John cómột *(con) chó

   John have one  cl  dog

   ‘John has one/a dog’

This difference between English and Vietnamese is representative of the contrast between “number-marking” languages such as English, French, and German, and “classifier” languages such as Chinese, Vietnamese, and Japanese. It has been noted that variation exists among languages of both types. For example, bare nouns can be definite in Chinese but not in Vietnamese, while classifier-noun combinations can be definite in Vietnamese but not in Chinese (see Cheng and Sybesma 1999, Trinh 2011). Among number-marking languages, some, such as English and German, allow bare plurals to be arguments but others, such as French and Italian, do not. Such facts call for an account of the variation at both the macro level between classifier and number-marking languages, and at the micro level between languages within each group. This requires analysis and comparison of particular languages of both types. A fair amount of work has been devoted to the semantics of nominals in number-marking languages (see Link 1983, Pelletier and Schubert 1989, Barker 1992, Schwarzschild 1992, Krifka 1999, among others). Also, concrete proposals have been made to account for the macro-variation between classifier and number-marking languages, as well as for the micro-variation among the latter (see Krifka 1995; Chierchia 1998, 2010; Dayal 2004). Analyses of classifier languages, however, have been fewer and less explicit, and this is true to an even greater extent for the micro-variation between them. Works in this direction, to the best of our knowledge, tend to be heavily syntactic in nature, with semantic considerations playing a secondary role (see Cheng and Sybesma 1999, 2005; Saito et al. 2008; Wu and Bodomo 2009; Watanabe 2010, among others). This squib is an attempt at balancing the situation. Our objective is to show that given appropriate formalization of certain concepts, several facts about the syntax and semantics of nominals in three classifier languages – Bahnar, Chinese, and Vietnamese – can be made to follow from independently motivated assumptions about the building blocks of semantic representations, as well as plausible hypotheses about linguistic variation.

The general framework we adopt will be the “principles and parameters” theory (see Chomsky 1993, 1995, 1998, 2004). This theory seeks to find out what is common to all languages (i.e., the principles), and what are the ways in which languages can vary (i.e., the parameters). An influential view, which is sometimes called the “Borer-Chomsky conjecture,” holds that parametric variation is to be reduced to the lexicon, in particular the functional lexicon.³

For example, it has been proposed that whether wh-movement exists depends on C (see Huang 1981, 1982), whether V-raising exists depends on T (see Pollock 1989, Chomsky 1991), and whether N-raising exists depends on D (see Longobardi 2001, Cinque 2005). Of course, there is no a priori reason to assume that functional items are restricted to those of categories C, T, and D, or that variation is restricted to the ability to trigger movement. The term “functional category” is not definitional, and its extension is to be determined based on considerations of empirical adequacy as well as theoretical economy and elegance. In the same way, the possibility must be kept open that functional categories may differ not only with respect to their featural make-up, but also with respect to their availability: the functional lexicon of one language may contain a certain item which is absent from the functional lexicon of another language (see Manzini and Wexler 1987, Bǒskovíc and Gajewski 2011). In this squib, we will argue that our three-way comparison of Bahnar, Chinese, and Vietnamese shows that differences of precisely this kind exist.

Before we end this introduction and get to the main discussion, we will address the question of the grammatical status of classifiers. While it is quite uncontroversial to assume that elements such as definite articles, demonstratives, or silent type-shifting operators are functional items, it is less so with classifiers. As classifiers seem to indicate the “class” of the nouns, which is a cognitive notion, one might feel that classifiers should be considered subtantives. Our assumption in this squib will be that they are functional items. We will now provide some justification for this assumption, using, without loss of generalization, examples from Vietnamese for illustration.⁴

One criterion for some lexical item to be considered “functional” is that it can be omitted without affecting the intended meaning: (2) will be understood as saying the same thing as (1), even though it will be perceived as an ungrammatical sentence.⁵

1. (2) *John có  một chó

   John have one dog

   (‘John has one/a dog’)

Thus, classifiers do not add semantic content to the sentence.⁶ Related to this observation is the fact that there is a degree of arbitrariness in the relation between a noun and the classifier that it requires. Take the classifiers con and cái in Vietnamese, for example. The first typically combines with nouns which denote animals, and the second typically combines with nouns which denote inanimate objects. However, the noun thuyền ‘boat’ may combine with both con and cái, and there is a strong preference, in standard Hanoi dialect at least, for combining the noun dao ‘knife’ with con rather than with cái.

1. (3)

   1. a. John nhìn thấy một con/cái thuyền

      John see one cl boat

      ‘John sees a boat’

   2. b. John cầm một con/^??cái dao

      John hold one cl knife

      ‘John is holding a knife’

Thus, the dependency between a noun and its accompanying classifier is, to some degree, similar to that between a noun and its grammatical gender in such languages as German and French.⁷

Another way in which noun-classifier dependency resembles grammatical gender is that combining a noun with a “wrong” classifier, just like inflecting a noun with a “wrong” gender, results in a grammatical error, not in a different meaning. Thus, the classifier to go with chó ‘dog’ is con, not cái, and the grammatical gender of Haus ‘house’ is neuter, not masculine, but combining chó ‘dog’ with the classifier cái, and Haus ‘house’ with a masculine determiner, will still convey the intended meaning, even though the sentence is perceived as formally deviant.

1. (4)

   1. a. *John có một cái chó

      John have one cl dog

      (‘John has one/a dog’)

   2. b. *John hat einen Haus

      John have one.masc house

      (‘John has one/a house’)

Last but not least, classifiers show two properties which have been considered distinctive of functional items. First, they are a closed class: while it is imaginable a company might invent a new noun to name a new product, it is unimaginable for it to invent a new classifier to count items of that new product. Second, classifiers has a “world independent” semantics: their denotation stays constant across different states of affairs. This will become clear in the discussion below. At this point, we take these considerations to be sufficient reasons for assuming that classifiers are functional items.

2. Four generalizations about Bahnar, Mandarin, and Vietnamese

Bahnar and Mandarin are similar to Vietnamese in being “classifier languages” of the East Asian variety: nouns can only combine with numerals through the mediation of a classifier, as has been illustrated for Vietnamese in the previous section. Let us now turn to the discussion of demonstratives, argumenthood, and definiteness in these three languages.⁸

In Mandarin and Vietnamese, a demonstrative requires a classifier but does not require a numeral, as shown in (5a) and (5b), repectively.

1. (5)

   1. a. nei (liang) zhi gou

      dem two cl dog

      ‘those two dogs’

   2. b. (hai) con chó đó

      two cl dog dem

      ‘those two dogs’

In Bahnar, on the other hand, a demonstrative requires both a classifier and a numeral, as shown in (6).

1. (6) *(ʔbal) tɔʔ kɔʔ nej

   two cl dog dem

   ‘those two dogs’

Let us state the first generalization.

1. (7) Generalization 1

   DEM can combine with CL-NP in Mandarin and Vietnamese, but not in Bahnar

Regarding argumenthood, bare classifier phrases (i.e., those of the form CL-NP) can be verbal arguments in Vietnamese, as shown in (8).

1. (8) con chó muốn sang đường

   cl dog want cross road

   ‘The dog wants to cross the street’

In contrast, this does not hold for Bahnar and Mandarin, as shown in (9a) and (9b), respectively.

1. (9)

   1. a. *tɔʔ kɔʔ waʔ kwa tɤrɔŋ

      cl dog want cross road

   2. b. *zhi gou yao guo malu

      cl dog want cross road

      Let us state the second generalization.

2. (10) Generalization 2

   CL-NP can be verbal arguments in Vietnamese but not in Bahnar or Mandarin

We take the semantic type of intransitive and transitive verbs to be 〈e, t〉 and 〈e, 〈e, t〉〉, respectively. For example, $[ [ {{\rm smokes}} ] ] = [ \lambda x\colon x\in D_e\,\;x\,{\rm smokes}] $ and $[ [ {{\rm loves}} ] ] = [ \lambda y\colon y\in D_e\,\cdot [ \lambda x\colon x\in D_e\cdot x\,{\rm loves}\,y] ] $ (see Heim and Kratzer 1998, and see footnote 11 below for an explanation of the lambda notation). When we say that a nominal is an argument of a verb, what we mean is that the nominal or its trace is interpreted as an argument to the function denoted by the verb, which entails that only nominals which are of type e or have traces of type e can be arguments. This is the sense in which Chierchia (1998) uses the term “argumental” in classifying nominals (see e.g. Chierchia 1998: 344). Now, it has been proposed that nominals of type 〈e, t〉, when they are in object position, can compose with the verb via the rule of Restrict (see Chung and Ladusaw 2004, Trinh and Sudo 2009, Trinh 2011). What Restrict does can be described informally as making a new verb out of a verb and a nominal. This means that nominals which compose with verbs via Restrict are not verbal arguments, in our terminology. Since subjects cannot compose with verbs via Restrict, the fact that a nominal cannot be subject can be considered evidence that it is not of type e (i.e., that it cannot be a verbal argument). Thus, the subject position provides a more reliable diagnostic for argumenthood than the object position. For this reason, we will disregard the object position in our discussion on argumenthood. Note that in other discussions, say one on whether numerals can combine directly with nouns, the position of the relevant nominal will play no role. Thus, examples (1), (2) and (3) all have the nominal in object position. This does not affect anything which we have just said regarding argumenthood.⁹

Regarding definiteness, bare numeral phrases, that is, those of the form Num-CL-NP, can be definite in Bahnar and Vietnamese, as shown in (11a) and (11b), respectively.

1. (11)

   1. a. ʔbal tɔʔ kɔʔ waʔ kwa tɤrɔŋ

      two cl dog want cross road

      ‘The two dogs want to cross the road.’

   2. b. hai con chó muốn sang đường

      two cl dog want cross road

      ‘The two dogs want to cross the road.’

This does not hold for Mandarin, as shown in (12).

1. (12) *liang zhi gou yao guo malu

   two cl dog want cross road

   (‘The two dogs want to cross the road.’)

Let us state the third generalization.

1. (13) Generalization 3

   Num-CL-NP can be definite in Bahnar and Vietnamese, but not in Mandarin

Also regarding definiteness, bare nouns can be definite in Bahnar and Mandarin, as shown in (14a) and (14b), respectively.

1. (14)

   1. a. kɔʔ waʔ kwa tɤrɔŋ

      dog want cross road

      ‘The dog(s) want(s) to cross the road.’

   2. b. gou yao guo malu

      dog want cross road

      ‘The dog(s) want(s) to cross the road.’

In Vietnamese, however, bare nouns cannot be definite, as shown in (15).

1. (15) chó muốn sang đường

   dog want cross road

   *‘The dog(s) want(s) to cross the road.’

Let us state the fourth generalization.

1. (16) Generalization 4

   Bare NP can be definite in Bahnar and Mandarin, but not in Vietnamese

Table 1 summarizes the facts about Bahnar, Mandarin and Vietnamese which we have just discussed.

Table 1: Four generalizations about Bahnar, Mandarin, and Vietnamese

As we can see, three typologically similar languages can display subtle, intricate and quite puzzling distinctions in distribution and interpretation with respect to the nominal domain. We will propose an account of the four generalizations established above which derives these distinctions from the sort of parametric variations mentioned in the introduction, namely differences in terms of availability of items in the functional lexicon.

3. Deriving the generalizations

Our analysis of the facts just presented extends the proposal made in Trinh (2011) for the differences between Mandarin and Vietnamese to include Bahnar. The definitions below, save that of K₂ in (22b), are taken from that work, barring notational differences which are not substantial. The section will start with some theoretical groundwork and ends with the derivation of the four generalizations stated above, in the form of informal proofs.

3.1 Theoretical groundwork

This section lays out some assumptions and terms that underlie our analysis. It should be noted that most, if not all, of these assumptions have been motivated elsewhere, in particular in Chierchia (1998) and Trinh (2011) as well as in works cited therein.

3.1.1 Bare nouns

Following Chierchia (1998) and several others, bare nouns will be assumed to denote atomic predicates (i.e., sets of singularities) in number-marking languages, and to denote cumulative predicates (i.e., sets of both singularities and pluralities) in classifier languages. Thus, suppose a, b and c are the only dogs in world w, then the English word dog denotes, in w, the set {a, b, c}, while the denotation in w of its Vietnamese counterpart, chó, is the set ${ {a, \;b, \;c, \;a\oplus b, \;a\oplus c, \;b\oplus c, \;a\oplus b\oplus c} } $, where $x\oplus y$ is the plurality consisting of x and y.¹⁰ The lexical entries for dog and chó are given in (17b).¹¹

1. (17)

   1. a. $[[ {{\bf dog}}]]^w = [ \lambda x.\,\,x\,{\rm is\ a\ singular\ dog] } = {\rm { \ }a, \;b, \;c \ }$

   2. b. $[[{{\bf ch {o^{\!\!'}}}} ]]^w = [ \lambda x.\,x\,{\rm is\ a\ singular\ dog\ or\ a\ plurality\ of\ dogs] } = { \ }a, \;\,b, \;\,c{\rm , \;}\,\,a\;\oplus b, \;\,\,a\oplus c, \;\,\,b\oplus c, \;\,\,a\oplus b\oplus c $

Let ‘x ⊏ y’ mean x is a proper part of y and ‘$x{\rm \sqsubseteq }y$’ mean that x is a part of y, i.e. is a proper part of or identical to y. Thus, a ⊏ $a\oplus b$ and $a\oplus b{\rm \sqsubseteq }a\oplus b$, but $a\oplus b \;\;$ ̸⊏ $a\oplus b$.

3.1.2 Numerals

For the semantics of numerals, the function sup is defined as one which maps a predicate P to the “supremum” of P, which is to say, that entity which has all and only members of P as (proper or non-proper) part.

1. (18) $x\sqsubseteq sup( P ) \Leftrightarrow _{{\rm def}}\forall y( {y\in P\leftrightarrow y\,{\rm \sqsubseteq }x} ) $

Suppose $P = { {a, \;b, \;c, \;a\oplus b} } $, then $sup( P ) = a\oplus b\oplus c$.¹² Counting requires uniformity: only individuals with the same number of atomic parts can be counted (Ionin and Matushansky 2006).¹³ Uniformity is defined in (19), where n is a variable ranging over natural numbers and x _P is the number of parts of x that are P.¹⁴

1. (19) $P\,is\ uniform\Leftrightarrow _{{\rm def}}\exists n( \forall x( P( x ) \to \vert x\vert _P = n) ) $

To illustrate, the lexical entry for the numeral two is given in (20), where ℘ (P) is the power set of P, i.e. ℘ (P) = {Q|Q ⊆ P}.

1. (20) $[[{{{\bf two}}}]]^w( P ) = [ \lambda x.\,\exists y( y\in \wp ( P ) \wedge \vert y\vert _P = 2\wedge x = sup( y ) ) ] $ if P is uniform, undefined otherwise

Thus, numerals are of type 〈〈e, t〉, 〈e, t〉〉, that is, the type of restrictive modifiers. Suppose P = {a, b, c}, then $[ [ {{{\bf two}}} ] ] ^w( P ) = { {a\oplus b, \;a\oplus c, \;b\oplus c} } $. However, if $P = { {a, \;b, \;a\oplus b} } $, then $[[{{{\bf two}}}]]^w(P)$ will be undefined, as P is not uniform.

3.1.3 Classifiers

From what has just been said, it follows that numerals cannot combine with bare nouns in classifier languages, since these nouns denote cumulative predicates which are not uniform. This is why mediation of the classifier is required. The function at is defined as one which maps any cumulative predicate P to a subset of P whose members have no proper parts that are P.

1. (21) $x\in at( P ) \Leftrightarrow _{{\rm def}}x\in P\wedge \neg \exists y( {y\in P\wedge y }$ ⊏ x)

We are now ready to propose meanings for the classifier. Anticipating the discussion which will come presently, we define two types of classifiers, K₁ and K₂¹⁵

1. (22)

   1. a. [[K1]]^w = [λP.at(P)] $[ [ {{\rm KIND\;NP}} ] ] ^w = [ \lambda w$

   2. b. [[K2]]^w = [λn:n ∈ D〈〈e, t〉, 〈e, t〉〉[λP.n(at(P))]]

As we can see, K₁ maps a predicate to a predicate, while $[ [ {{\rm K}_2} ] ] $ maps a numeral and a predicate P to a predicate. This means we have two different bracketings for numeral phrases of the surface profile [Num K noun].

1. (23)

   • 

   • 

Both of these structures have been argued to exist. Specifically, it has been proposed that Chinese opts for (23a) and Japanese for (23b) (see Saito et al. 2008). We will argue that Chinese and Vietnamese opt for (23a) while Bahnar opts for (23b).

3.1.4 Definiteness and kind reference

A silent morpheme the is defined which has roughly the same meaning as the English definite article the. Specifically, $[ [ {{\rm \tf="Times-RomanSC (Screen)" the}} ] ] ^w$maps a P to the “maximal” entity in P if there is one, undefined otherwise. This captures both the existence and uniqueness presuppositions of definiteness (see Heim 1991).

1. (24) $[ [ {{\rm \tf="Times-RomanSC (Screen)" the}} ] ] ^w( P ) = sup( P ) $ if sup(P) ∈ P, undefined otherwise

Suppose P = {a}, then $[ [ {{\rm\tf="Times-RomanSC (Screen)" the}} ] ] ^w( P ) = a$. If $P = { {a, \;b, \;a\oplus b} } $, then $[ [ {{\rm \tf="Times-RomanSC (Screen)" the}} ] ] ^w( P ) = a\oplus b$. However, if P = {a, b} or $P = \emptyset $, then $[ [ {{\rm \tf="Times-RomanSC (Screen)" the}} ] ] ^w( P ) $ will be undefined. This is the same THE as in Trinh (2011).

Among the individuals in the universe of discourse, there are kinds, which are functions from properties to individual concepts (see Chierchia and Turner 1988; Chierchia 1998). A silent morpheme kind is defined which turns nouns into names of kinds in (23), where ${\oplus} P$ is the ${\oplus} $-closure of P, i.e. ${\oplus} P = { sup( Q ) \vert Q\subseteq P} $.¹⁶

1. (25) $[ [ {{\rm \tf="Times-RomanSC (Screen)" kind\;NP}} ] ] ^w = [ \lambda w $.$sup( {{[ [ {{\rm NP}} ] ] }^w} ) ] $ if $[ [ {{\rm NP}} ] ] ^w = {\oplus} [ [ {{\rm NP}} ] ] ^w$ and $\exists w\colon \vert {{[ [ {{\rm NP}} ] ] }^w} \vert > 1$, undefined otherwise

Thus, $[ [ {{\rm \tf="Times-RomanSC (Screen)" kind}} ] ] ^w$maps each cumulative predicate P into the function from each world w to $[ [ {{\rm \tf="Times-RomanSC (Screen)" the\;NP}} ] ] ^w$. Note that this definition of kind entails that neither [CL NP] nor [Num CL NP] can combine with kind, as these are not cumulative predicates.

In addition to the operator kind, the inverse of kind is also defined. It is ext, which is also a silent morpheme and which maps kinds into the plurality which instantiate them in each world.¹⁷

1. (26) $[ [ {{\rm \tf="Times-RomanSC (Screen)" ext\;}[ {{\rm \tf="Times-RomanSC (Screen)" kind\;NP}} ] } ] ] ^w = [ [ {{\rm \tf="Times-RomanSC (Screen)" kind\;NP}} ] ] ^w( w ) $

In addition, we propose the following preference principle. At this point we will have to assume that this is a primitive of natural language grammar.¹⁸

1. (27) The kind-over-the principle

   If both $[ [ {{\rm [ \tf="Times-RomanSC (Screen)" kind\;}\alpha ] } ] ] ^w$ and $[ [ {{\rm [ \tf="Times-RomanSC (Screen)" the\;}\alpha ] } ] ] ^w$ are defined, use [kind α] instead of [the α]

In other words, when it is possible to use kind, it is not possible to use the.

3.2 Accounting for the facts

We are now in the position to derive the generalizations established in section 2. Our proposal concerns only the functional lexicon, and is quite simple. Specifically, we assume that Mandarin and Vietnamese differ in the way proposed by Trinh (2011), and add Bahnar to the list. Our addition results in the following: (i) Bahnar has K₂ but not K₁, while the opposite holds for Mandarin and Vietnamese; (ii) Bahnar and Vietnamese have the but Mandarin does not; (iii) all three languages have kind; (iv) Bahnar and Mandarin have ext but Vietnamese does not. Table 2 summarizes this cross-linguistic distribution of the functional morphemes K₁, K₂, the, kind and ext.

Table 2: Functional elements in nominal structures

This distribution of functional items across Bahnar, Mandarin, and Vietnamese have consequences for the availability of syntactic structures among these three languages. It turns out that these consequences match the generalizations established in section 2 precisely. Let us now derive these.

First, consider generalization 1, repeated below as (28).

1. (28) Generalization 1

   DEM can combine with CL-NP in Mandarin and Vietnamese, but not in Bahnar

Proof – There are two possible parses for the DEM-CL-NP string: either [DEM [CL NP]] or [[DEM CL] NP].¹⁹ Under the standard assumption that demonstratives, just like definite and indefinite articles, take predicates (i.e. expressions of type 〈e, t〉) as arguments, [[DEM CL] NP] is excluded, since neither K₁ nor K₂, our options for CL, is of type 〈e, t〉.²⁰ Thus, [DEM [CL NP]] is the only possible parse. Given that NP is a predicate, hence of type 〈e, t〉, CL in the DEM-CL-NP string must be of type 〈〈e, t〉, τ〉 where τ is some arbitrary type. As K₁ is of type 〈〈e, t〉, 〈e, t〉〉 and K₂ of type 〈〈〈e, t〉, 〈e, t〉〉, 〈〈e, t〉, 〈e, t〉〉〉, CL in the DEM-CL-NP string must be K₁ and cannot be K₂. Since Bahnar has K₂, not K₁, while Mandarin and Vietnamese have K₁, not K₂, the DEM-CL-NP string can be generated in Mandarin and Vietnamese but not in Bahnar. QED.

Next, consider generalization 2, repeated below as (29).

1. (29) Generalization 2

   CL-NP can be verbal arguments in Vietnamese, but not in Bahnar or Mandarin

Proof – Verbal arguments are of type e (Heim and Kratzer 1998). By hypothesis, [K₁ NP] is of type 〈e, t〉 and [K₂ NP] is a type mismatch, that is, uninterpretable. This means that for a language to have CL-NP as verbal argument, it must have K₁ and it must have a silent operator which maps [K₁ NP] into an expression of type e. From the inventory of silent operators postulated above, only the fits the description of such an operator, which means that among the three languages under discussion, only Vietnamese fits the description of such a language: it is the only language to have both K₁ and the in its functional lexicon. QED.

Next, consider generalization 3, repeated below as (30).

1. (30) Generalization 3

   Num-CL-NP can be definite in Bahnar and Vietnamese, but not in Mandarin

Proof – By virtue of the definition of K₁ and K₂, the Num-CL-NP string is parsed as [[Num CL] NP] in Bahnar and as [Num [CL NP]] in Mandarin and Vietnamese. Both of these structures, however, are expressions of type 〈e, t〉. Thus, the only way for a language to have Num-CL-NP interpretable as definite is for it to have a silent operator which maps expressions of type 〈e, t〉 into definite descriptions. Again, the is the only item among those postulated above which can do this. As it is available in Bahnar and Vietnamese but not in Mandarin, generalization 3 holds. QED.²¹

Finally, consider generalization 4, repeated below as (31).

1. (31) Generalization 4

   Bare NP can be definite in Bahnar and Mandarin, but not in Vietnamese

Proof – From the definition of the, kind and ext, it follows that there are two parses of NP, which results in a definite description: either [the NP] or [ext [kind NP]]. Given the kind-over-the principle, [the NP] is unavailable in Bahnar and Vietnamese, since these languages have both the and kind. By hypothesis, Mandarin does not have the, so [the NP] is not available in Mandarin either. Thus, the only way for a bare NP to be definite in Bahnar, Mandarin, or Vietnamese is to be parsed as [ext [kind NP]]. As Bahnar and Mandarin have ext, while Vietnamese does not, bare NPs can be definite in the first two, but not in the last. QED.

4. Conclusion

We have established four generalizations about the syntax and semantics of nominal structures in three classifier languages – Bahnar, Mandarin, and Vietnamese – which show an intricate pattern of cross-linguistic variation. We developed an analysis which derives these generalization purely in terms of differences among the three languages with respect to their functional lexicon. Specifically, we defined pieces of formal meaning which have been given empirical motivation in other works, and advanced a proposal as to which piece is realized as a functional item in which language. We then showed that syntactic and semantic consequences of our proposal match the four generalizations we established in a precise manner.²² The set of facts we discussed is admittedly compact, but its small size allows a fully explicit account to be formulated which forces puzzling stipulations such as the kind-over-the principle to be manifest and which makes it possible to execute exact computations of the meaning of syntactic structures. In addition, it invites expansion of the data base which we hope to pursue in future work.