3.1 Numerals

Kaingang is a non-classifier language, i.e., numerals can combine with individual-denoting nouns without any intervening classifier, as illustrated in (9) and (10).

Like in familiar non-classifier languages, Kaingang numerals are compatible with substance nouns when the latter are coerced to refer to conventional packages, as in (11), or in subkind/taxonomic interpretations, as in (12).

Nevertheless, Kaingang departures from familiar non-classifier languages by allowing numerals to combine directly with substance nouns even when they are interpreted as referring to non-conventionalized portion-units. This is laid out in (13–16).

In (13), the counted portions are puddles of water. In (14) and (15) the units are by drops and puddles of blood, respectively, while in (16) they constitute portions of sand. In all cases the portions are contextually supplied and don’t correspond to conventionalized units. Furthermore, the portions counted in a situation can vary in shape, size, and containers, as in Context A (17), depicted in Figure 1. Together with the possibility of directly counting (non-)conventional units, (17) indicates that the ‘unitizing’ semantics of Kaingang nouns should be extremely general.²

In sum, the data above show that in Kaingang numerals directly modify individual and substance nouns. The availability of substance noun+numeral constructions in contexts that supply non-conventional portions constitutes one piece of evidence that substance nouns in Kaingang can be interpreted as referring to individuated portions.

3.2 Quantity words

In many mass/count languages there are quantity words which select for particular types of nouns. For instance, in English, (a) little, less and much combine only with mass nouns, whereas (a) few, many, and several require count nouns. The availability of this distinction in the distribution of quantity words is often used as one diagnostic test for the existence of the mass/count distinction in a language (Bloomfield 1933; Doetjes 1997; 2012).

Kaingang has at least five quantity words: kar ‘all’, ũ ‘some’ e ‘many’, pipir ‘few’, and mẽ ‘more’. All these terms are compatible with individual and substance nouns, as illustrated by the minimal pairs in (18–22), where the quantity words immediately follow the nouns.

The quantity expression e ‘many’ always preserves its cardinal interpretation of a large number of units, irrespective of the noun it combines with. When combined with a substance noun the large number will be of portions, as exemplified in (23). The infelicity of the sentence in (23) in context B results from the fact that this scenario doesn’t provide multiple portion-units for e to quantify over.

To describe a context like B, the adjective mág ‘big’ is used instead.

Note that due to the number neutrality of the noun kyvénh, (24) can also mean that Fógtẽ saw more than one big puddle of blood. As expected, the adjective mág isn’t in complementary distribution with e. Both can occur in the same nominal construction, always triggering the meaning of a large number of big individuals or portions:

The same pattern is displayed by pipir ‘few’. Whether it combines with individual nouns, as in (27), or with substance nouns, as in (28) and (29), it consistently means a small number of individuated units.

To describe a situation where a small portion of blood dripped, the count adjective sĩ ‘small’ is used instead.

The sentence in (30) can also be used to describe a situation with small units of blood, due to the number neutrality of the noun. Like e ‘many’ and mág ‘big’, pipir is not in complementary distribution with sĩ. Pipir can participate in a noun phrase headed by a noun already modified by sĩ, as in (31) and (32).

Summarizing, the data in this subsection demonstrate that quantity words in Kaingang are compatible with individual and substance nouns, triggering the same interpretation with both types of nouns. Particularly, they show that the quantity terms e ‘many’ and pipir ‘few’ are associated with a cardinality interpretation even when combined with substance nouns.

3.3 Count adjectives and reciprocals

As already foreshadowed in subsection 3.2, substance nouns can occur with adjectives which hold of each singularity in the extension of a noun. In other words, Kaingang substance nouns can also be modified by adjectives which denote properties of individuated entities, such as mág ‘big’, sĩ ‘small’, and ror ‘round’. Because these adjectives mostly select for count nouns, Deal (2017) refers to them as ‘count adjectives’, whereas Schwarzschild (2011) calls them ‘stubbornly distributive adjectives’. Consider the minimal pairs below:

In addition, these adjectives can also appear as predicative adjectives in constructions whose subjects are bare substance nouns:

In (36) and (37), the properties of being round and big distribute to each portion-unit of blood referred to by the bare noun.

Furthermore, like individual-denoting bare nouns, as in (38), bare substance nouns can be the antecedents for reciprocals, as in (39–41).

The constructions with substance nouns above involve the application of their reciprocal vps to a plurality containing unitized portions of a substance, each of which bears the reciprocal relation of being similar to all the others. The felicity of (39–41) shows that their subject bare nouns are interpreted as denoting sets of contextually salient portion-units of water, clay, and flour, respectively.

3.5 Quantity comparisons

3.5.1 Mẽ ‘more’

In languages that encode the mass/count distinction, count nouns are primarily compared based on cardinality, whereas substance mass nouns are evaluated based on volume/weight (Barner & Snedeker 2005). In English, for instance, the comparative sentence (42a) asserts that the cardinality of Pedro’s children is greater than the cardinality of Roberta’s children. In contrast, sentence (42b) means that the overall volume of flour that Roberta has is greater than the overall volume of flour that Pedro has.

1. (42)
1. a.

1. Pedro has more children than Roberta.

1.  
1. b.

1. Roberta has more flour than Pedro.

Accordingly, depending on the noun replacing N in comparative constructions of the type X has more N than Y, speakers will privilege judgements along the number or volume dimensions.

The Kaingang data laid out so far support the thesis that all nouns can be interpreted as count nouns and as such denote sets of counting units. This gives rise to the prediction that speakers will privilege number-based interpretations of all nouns in comparative constructions. To test this prediction, Barner & Snedeker’s (2005) quantity judgement tasks were applied. The consultants were shown pictures of real-world objects and substances. Each picture contained a collection of one or two objects or portions of a substance side-by-side with another collection of multiple objects of the same category or portions of the same substance. The quantities on the left side of the pictures were presented as belonging to one person and those on the right side to another one. Importantly, the total volume of the objects/portions on the left always exceeded those on the right, whereas the objects/portions on the right outnumbered those on the left. After showing these stimuli pictures to each consultant, they were asked the target comparative question in (43a) containing the quantity expression mẽ ‘more’, where N was replaced by an individual or substance noun, and then requested to provide one of the two possible answers in (43b).

1. (43)
1. a.

1. Ũ
2. indef
1. nỹ
2. q
1. tỹ
2. sbj
1. N
2. N
1. mẽ
2. more
1. nĩ?
2. asp
1. ‘Who has more N?’

1.  
1. b.

1. Pakój/Maria
2. Pakój/Maria
1. vỹ
2. nom
1. N
2. N
1. mẽ
2. more
1. nĩ
2. asp
1. Maria/Pakój
2. Maria/Pakój
1. ve kỹ.
2. than
1. ‘Pakój/Maria has more N than Maria/Pakój.’

Stimuli were designed with six nouns of each type, as listed in (44). The pictures were presented in a random order.

1. (44)

1. Individual-denoting nouns:
2.  
3. Substance-denoting nouns:
4.  
1. gĩr ‘child’, kasor ‘dog’, ka ‘tree’, kakanẽ ‘fruit’, kur
2. ‘clothes/clothing’, nĩgja ‘bench/chair/stool’.
3. goj ‘water’, kyvénh ‘blood’, rénhte ‘milk’, venh kuri ‘flour’,
4. kur ‘fabric’,³ vãfe ‘string’

Note that although the nouns kur ‘fabric’ and vãfe ‘string’ do not denote substances, I heuristically include them in the substance nouns category because cross-linguistically they are often treated as mass nouns compared in terms of volume/size (Deal 2017). Figures 2, 3, 4, 5, 6, 7 display six instances of the visual stimuli provided in the comparative tasks.

Figure 2

rénhte ‘milk’.

Figure 3

venh kuri ‘flour’.

Figure 4

nĩgja ‘bench’.

Figure 5

kakanẽ ‘fruit’.

Figure 6

vãfé ‘string’.

Figure 7

kur ‘fabric’.

In accordance with the prediction, speakers systematically compared all nouns along the number dimension. Namely, even in scenarios containing substances, like in Figure 2, and a target question like (45), there were no volume-based interpretations.

1. (45)

1. Ũ
2. indef
1. nỹ
2. q
1. tỹ
2. sbj
1. rénhte
2. milk
1. mẽ
2. more
1. nĩ?
2. asp
1. ‘Who has more milk?’

Although the volume of the portion of milk on the left of Figure 2 is larger than the total volume of the three drops on the right, the speakers without hesitation counted the number of portions. That is, in a context where the portion of milk on the left edge belongs to Pakój, while all the other portions to Maria, the three consultants, when asked (45), responded that Maria had more milk. As a result, these findings offer further supporting evidence that all nouns in Kaingang are interpreted as count nouns.

3.5.3 Mág ‘big’

If substance nouns denote sets of portion-units and mág ‘big’ is a count predicate, it falls out naturally that in quantity tasks mág will be interpreted as a property assigned to individual- or portion-units. This diagnostic test was first proposed by Lima (2014a; b), as part of her study of countability in Yudja. To investigate this prediction, I again used the number neutral nouns in (44). The visual stimuli were constituted by pictures containing on the left side one big object or portion of a substance and on the right side multiple objects of the same category or portions of the same substance. Below is the question employed, followed by the two opposing responses.

1. (47)
1. a.

1. Ũ
2. indef
1. nỹ
2. q
1. N
2. N
1. mág
2. big
1. nĩ?
2. asp
1. ‘Who has a big N?’

1.  
1. b.

1. Pakój/Maria
2. Pakój/Maria
1. vỹ
2. nom
1. N
2. N
1. mág
2. big
1. nĩ.
2. asp
1. ‘Pakój/Maria has a big N.’

For illustration, I lay out in Figures 8, 9, 10, 11 four samples of the pictures used as stimuli.

Figure 8

venh kuri ‘flour’.

Figure 9

kur ‘fabric’.

Figure 10

kakanẽ ‘fruit.

Figure 11

kyvénh ‘blood’.

The prediction that mág primarily would be attributed to the single object or portion on the left side of each picture was confirmed. Therefore, this result offers further evidence in support of the thesis that, like individual nouns, substance nouns in Kaingang provide units for counting. So much so that even in a scenario where the total volume of the multiple portions of a substance exceeds the volume of the single portion on the left edge of the picture, speakers compared the sizes of individuated portions, not their overall volume. For instance, in a situation where the portion of milk on the left edge belongs to Pakój, while all the other portions to Maria, as displayed in Figure 12, the default response of the consultants, when asked (47a), was that Pakój had a big unit of milk.

Figure 12

rénhte ‘milk’.

3.6 A brief note on container words

Kaingang allows for the optional use of container phrases in constructions with numerals and substance nouns. In such configurations container words like runja ‘bucket’ and kej ‘basket’ are complements of a locative, like in Yudja (Lima 2014; 2016), or of a postposition of instrument. For example, the container noun runja ‘bucket’ in (48c) is the complement of the same postpositions as in (48a–b).

Note that in (48c) the container phrase runja ki/tỹ ‘in/with bucket(s)’ doesn’t occur between the numeral régre ‘two’ and the substance noun rỹnhrỹj ‘sand’. A construction in which the container phrase intervenes between the numeral and the noun is ruled out in Kaingang, as illustrated in (49).

Thus, the syntactic configuration in (48c) and the consultants’ rejection of (49) suggest that container phrases in Kaingang are adjuncts.

Like in English, in Kaingang and Yudja container phrases can be interpreted as providing the units for counting. However, as opposed to English, in Kaingang and Yudja container phrases can also have a locative meaning. That is, sentences like (48c) can be interpreted as referring to locations where already individuated units are placed.⁴ Consider sentence (50) and the three contexts below depicted in Figures 13, 14, 15.

The construction in (50) is felicitous in all the three scenarios above. One crucial element common to all of them is that the quantity of water carried can be mapped onto two concrete portions of water. In context A, the two portions are individuated by two buckets, i.e., units and buckets coincide. In context B, although the quantity of water carried isn’t individuated inside the bucket, it can be traced back in time to two concrete bottles that partitioned the quantity into two counting units. As for context C, in it the container phrase is interpreted as just indicating the receptacle where the concrete counting units individuated by the two bottles are placed, i.e., the bucket is neither used to individuate nor to measure the portions.

The felicity of the sentence in (50) in context c, hence, shows that Kaingang container phrases can also have a locative interpretation, i.e., one that indicates where concrete counting units are located. Thus, the fact that Kaingang container phrases are adjuncts, that they cannot intervene between numerals and (substance) nouns, as well as the fact that the interpretation of constructions like the one in (50) doesn’t always associate the units with the receptacles denoted by the container nouns, are quite compatible with an analysis of Kaingang substance nouns as count nouns that denote portion-units.

Summarizing, this section provided a list of morphosyntactic and semantic pieces of evidence showing that individual and substance nouns in Kaingang pattern alike in the counting system of the language, i.e., there are no morphosyntactic or semantic features that distinguish them in this domain. These findings support the hypothesis that all nouns in Kaingang are interpreted as count. Like individual nouns, substance nouns denote counting units not only when combined with numerals and other quantity words, or in comparative constructions, but also when they appear bare, as evidenced in the examples with reciprocals and count adjectives. As a result, the individuating mechanism involved in the count interpretation of Kaingang nouns cannot be attributed to numerals and quantity expressions. The only thesis that seems to be borne out by the facts is that the operation supplying the individual- or portion-units must already be encoded in the nouns themselves. The conclusion is that all nouns are inherently count in Kaingang, i.e., they enter derivations already vested with a count meaning. In section 4, I provide a semantic analysis of this lexical property shared by all Kaingang nouns.

4.1 Theoretical background: Krifka’s approach

Krifka (1989; 2007; 2008) claims that the mass/count distinction is grounded in two semantic properties of predicates: quantization and cumulativity. A predicate P is quantized if and only if whenever P applies to both x and y, y cannot be a proper part of x, as formally stated in (51). In contrast, a predicate P is cumulative if and only if whenever it holds of two entities it also holds of their sum, as defined in (52).

Prototypical examples of a quantized predicate in mass/count languages such as English are constructions formed by the combination of numerals with count nouns. The constituent one child, for example, expresses a quantized predicate that is true of each individual child, but not of their sums. As for cumulative predicates, their paradigmatic instances are substance mass nouns like blood, which denote a set closed under sum formation, i.e., a join-semilattice structure.⁵ Crucially, (51) and (52) are mutually exclusive.

Count nouns are modeled by Krifka as two-place predicates which contain a measure function defined on a domain of entities structured by a complete join-semilattice. In this approach, the “built-in modes of dividing reference” (Quine 1960: 91) encoded by count nouns are accomplished by an additive measure function from entities to numbers (Krifka 1989), which provides a unit of measurement. Additive measure functions can also be expressed by classifiers or measure terms such as head-of, kilo-of, litter-of, etc. Formally, Krifka defines an additive measure function as follows:

The definition in (53) states that a measure function μ is additive whenever the application of the function to the concatenation of two non-overlapping entities is identical to the sum of the application of the function to each entity. As Filip & Sutton (2017) put it, “an additive measure function tracks the part structure of the entities it measures” (Filip & Sutton 2017: 343). It follows from (53) that “if two objects have a weight of 2 and 3 kg respectively, then their concatenation has the weight of 5 kg” (Krifka 1989: 79). Similarly, a measure function like head-of is additive because the concatenation of two head of cattle and four head of cattle results in six head of cattle. Further examples of additive measure functions are pounds, meters, calories, etc. In contrast, there are also non-additive measure functions. Take degrees Celsius, for instance. If objects a and b have a temperature of 20 and 30 degrees Celsius, respectively, their concatenation doesn’t result in a temperature of 50 degrees Celsius.

Thus, Krifka treats counting as a special type of measuring, one whose units of measurement are concrete individuals or portions of a substance. In classifier languages, the additive measure function that provides concrete units is denoted by sortal classifiers, which must apply to cumulative nouns in order to derive countable constructions. As for mass/count languages, count nouns are lexically born with this counting function, while mass nouns lack them.

Krifka names the built-in counting function of count nouns nu, standing for ‘natural-unit’ (1989; 2003; 2007; 2008), or ou, standing for ‘object-unit’ (1995). It is modeled as an additive function μ that expresses a relation between quantities of P and a number n, as given in (54). nu measures P in terms of concrete units of counting.

Mass nouns like blood are treated as one-place predicates, namely, as functions of type ⟨e,t⟩ that lack a built-in measure function, as illustrated in (55a). In contrast, count nouns like child are treated as two-place relations between numbers and entities, i.e., as functions of type ⟨n,⟨e,t⟩⟩, as shown in (55b).

Under this approach, numerals are arguments for nouns containing bult-in measure functions, saturating the n variable introduced by them. So, when (55b), a function from a number to a predicate, applies to a numeral like four, the result is a set of pluralities of children with cardinality 4.⁶

In languages that allow semantically plural bare nominals, like English, plural markers in bare nouns signal the existential closure of the number argument n, creating cumulative reference, as in (57).

As for the selection of singular or plural forms of nouns when combined with numerals, it is enforced by syntactic agreement, since cardinals can only form a constituent with predicates containing an unsaturated number variable. So, while the plural -s in bare plurals in English has a semantics, its role in numeral+plural noun configurations is strictly syntactic.⁷

4.2 The semantics of Kaingang nouns

Based on the number neutrality and pervasive count meaning of Kaingang bare nouns, it can be tempting, at a first blush, to analyse individual and substance nouns in the language as cumulative atomic predicates, i.e., as exhibiting join-semilattice denotations with atoms at the bottom. In a mereology semantics, atoms can be defined absolutely, as given in (58), or relative to a predicate P, as defined in (59).

Given (58) and (59), an atomic predicate can be defined as in (60).

Note that atomic(p) is true of both non-cumulative and cumulative atomic predicates. In other words, atomic(p) applies to nouns that denote sets of atoms, namely, (prototypical) singular nouns, as well as those that denote sets of atoms and their sums, i.e., plural nouns. As a result, on the assumption that atomicity is sufficient for nouns to be countable, an analysis of Kaingang nouns as cumulative atomic predicates would explain their count interpretation.

Nevertheless, it turns out that there is compelling crosslinguistic evidence indicating that atomicity is not the defining property of count nouns (Krifka 2007; Rothstein 2010; 2017). One piece of evidence comes from the so-called object mass nouns like furniture, luggage, kitchenware, jewellery, clothing, etc. Although these nouns have atoms in their denotations, and thereby can pattern in certain ways with count nouns – by allowing cardinal-based evaluations in comparative constructions and combining with count adjectives (Barner & Snedeker 2005) – this isn’t sufficient for them to be vested with the morphosyntax of count nouns. For example, in English and Brazilian Portuguese object mass nouns can neither inflect for number nor directly combine with numerals and other count quantity expressions.

Barner & Snedeker (2005) and Bale & Barner (2009), based on experimental tests, argue that the availability of cardinality-based readings of object mass nouns in quantity comparisons is evidence in support of an analysis of object mass nouns as semantically count, but morphosyntactically mass. The authors go further and claim that this class of nouns always triggers cardinality-based interpretations. But some studies have challenged this view (Rothstein 2016, 2017; Rothstein & Pires de Oliveira 2016). They demonstrate that object mass nouns can also be interpreted along other dimensions, such as weight and volume, and that this flexibility is context dependent. For instance, if (61a) is stated “in the context of choosing a moving truck, the volume of the furniture is relevant and not the number” (Rothstein 2017: 122). As such, (61a) can be true in a scenario where Bill has five pieces of furniture and John just three pieces, provided that the totality of John’s pieces of furniture occupy more space in a truck than Bill’s. Importantly, this is not the case with (61b), which is judged false in a scenario such as the one above. This indicates, observes Rothstein (2017), that pieces of furniture, as opposed to furniture, always forces a number-based reading.

These cases hence reveal that the semantics of object mass nouns and singular count nouns differ. The cardinality-based evaluation of object mass nouns in comparisons seems to be favored by perceptual salience of the objects in their denotations. However, due to their mass meaning, they don’t impose any measuring dimension, leaving it for the context to arbitrate (Rothstein 2017). I believe Krifka’s theory (1989; 2007) offers a neat explanation of this flexible behavior of object mass nouns. They share atomicity with English prototypical count nouns and cumulativity with substance nouns. But, by lacking the quantized nature of count nouns, the cardinality dimension can’t be the only one available for them in comparison tasks (see Rothstein 2016 for a crosslinguistic perspective on object mass nouns).

A second piece of evidence, as Rothstein (2010; 2017) points out, involves count nouns such as rope, fence, wall, bouquet, table, etc. These nouns are non-atomic. Subparts of a rope can still be ropes, a fence or wall can be constituted by parts that are also fences or walls, and two bouquets or tables can be joined to form one bouquet or table. What counts as one fence or wall is context-sensitive, i.e., it can vary across utterance contexts. Without further specification, linking the count semantics of this class of nouns to atomic reference would be highly problematic, for it falls short of explaining their malleability regarding what constitutes one unit in their denotations.⁸

Accordingly, motivated by the crosslinguistic evidence above, I consider Krifka’s (2007) emphasis on the quantized/cumulative opposition better suited for explaining the semantics of the count/mass distinction than the atomic/non-atomic one. This is embedded in the machinery of his theory, which offers, I hope to demonstrate, an efficient toolbox for dealing with a language like Kaingang, where all nouns exhibit a count meaning.⁹

I thus propose to analyse the generalized counting strategy in Kaingang as a direct effect of the lexical meaning of nouns. Kaingang nouns are predicates that come from the lexicon already equipped with a context-sensitive built-in additive function à la Krifka (1989; 2007; 2008) which maps entities (individuals or portions) into numbers. Because all nouns have this quantizing function as part of their lexical meaning, they are already born quantized, which means that Kaingang root nouns are specified as being count. I assume that nouns give semantic information on the type of units in their denotations (Quine 1960). This is modeled as encoded in the counting functions of nouns. To indicate this information, I label the counting function of individual nouns iu_C (individual-units), given in (62a), whereas the one of substance nouns is tagged pu_C (portion-units), given in (62b).

Taking gĩr ‘child’ and kyvénh ‘blood’ as illustrative nouns, the following lexical entries are assigned to Kaingang root nouns.¹⁰

Individual root nouns such as (63a) denote sets of individual-units, whereas substance root nouns like (63b) denote sets of portion-units. Their inherent counting function expresses a relation between quantities and a number, represented by the free variable n (see on the next page a detailed discussion of n as a free variable). The subscripted variable c in iu/pu encodes the context-dependence of what counts as one unit (Krifka 2007; Rothstein 2007; 2010). Under the analysis advanced here, the value of the variable c is conceived of as being pragmatically determined. The idea is that c provides the partition of the noun denotation by supplying the contextually salient individuals or portions to be accessed by the counting function iu/pu. The incorporation of c into the counting function allows us to represent the crucial role of utterance contexts in deriving the sets of portion-units in the denotation of substance nouns, which easily varies across contexts. For instance, if the sentence in (17), repeated here in (64), is uttered in context A, depicted in Figure 16, the set of units in the denotation of quantized goj will include the individuated portions (which are distinct in size and shape) in the gallon, in the glass, and forming the puddle, but exclude their proper parts. As a result, only the three (spatially) salient portions will be counted.

The representation of pu_C as context-sensitive, hence, neatly captures the instability of substance count noun denotations, for portions are entities counted as contextual units. Moreover, by incorporating c into the built-in quantizing functions of count nouns, we show that it is the “context dependence of count nouns [that] explains the apparent non-quantization of nouns like fence, wall, hedge, bouquet” (Krifka 2007: 35), as well as of substance count nouns in Kaingang. As for count nouns that denote sets of stable individuals, like gĩr ‘child’ and fóg ‘non-indigenous person’, the sets of individuals will be constant for every value of c.¹¹

Notice that in (63a–b) the number variable n is left free. I treat its value as contextually supplied, rather than saturated by a number argument. This departure from Krifka’s analysis not only allows cumulative and quantized predicates to be of the same type, i.e., ⟨e,t⟩, but it also prevents quantized nouns from gaining a cumulative denotation in an early stage of the derivation via existential closure of n at the n(p) or nump level, i.e., before they are converted into bare noun arguments.

This analysis shows that Kaingang bare nouns can be used to refer to pluralities selected from the denotation of quantized nouns, which indicates that plural interpretations of bare nouns uninflected for number don’t need cumulative reference at the n(p) or nump level.¹²

To implement my analysis, I represent Kaingang indefinite bare nouns in argument position as existentially bound choice functions.¹³ In prose, a choice function f maps a non-empty set onto one of its elements, which means that it’s a function of type ⟨⟨e,t⟩,e⟩. For instance, f applies to a quantized substance bare noun like kyvénh ‘blood’ and selects one of the portion-units that consist of blood. Let us take context A in (65) as an example. The salient drops of blood in this context have cardinality 3. Given that I treat contexts of utterance as supplying the value of the free variable n, in context A n turns out to be 3. That is, under this analysis, the n variable can be saturated by the cardinality of the portion-units that are contextually salient. As a result, the bare noun kyvénh in (65) denotes a quantized set with pluralities of cardinality 3 as elements, as given in (66a). Therefore, if, in context A, the choice function picks out the salient plurality of portions of blood with cardinality 3, e.g., the one that is encircled in (66a) and represented in (66b), then the sentence in (65) will be true.

In (67), I provide a compositional semantics of the truth conditions of the sentence in (65), abstracting away from tense.

Note that the analysis implemented in (65–67) accounts for the plural interpretation of Kaingang bare nouns without associating it with a cumulative denotation. The contextual saturation of the n variable allowed us to demonstrate that in principle plural interpretations of bare nouns are not incompatible with assigning them a quantized denotation. In this regard, it is easy to see how the same analysis can be extended to contexts in which Kaingang bare nouns get a singular interpretation. In such scenarios the salient individual or portion is a singularity. As a consequence, the n variable will be saturated by 1. Thus, in the analysis illustrated in (65–67), by the time that a Kangang bare noun is type-shifted to an argument, it expresses a predicate which contains an unbound variable n, and hence is quantized relative to any contextual assignment of a value to n.

Alternatively, if we assume that the number-neutral meaning of Kaingang bare nouns necessarily relies on cumulative reference, this idea can be implemented by existentially binding the free variable n. This resource, as Krifka (1989) shows, gives rise to a cumulative interpretation. However, this is accomplished not at the root or np/nump level, but at a higher syntactic level after the quantized noun is inserted in the syntactic derivation. For concreteness, let us assume that this existential closure takes place at the level of the clause. By contrast, in languages that contain plural bare nouns, such as English, it’s the plural morpheme on the noun itself that introduces ∃-closure. Given that the number neutrality of Kaingang bare nouns isn’t associated with plural morphology, it can be assumed that the number variable n is unselectively bound by the existential operator that also binds the choice function variable f. Namely, the cumulative reading of Kangang bare nouns arises whenever the structure in (68) occurs at the clausal level (where ‘μ_C’ stands for the contextual measure function, either iu_c or pu_c).

Thus, the approach proposed above envisages two possible ways of resolving the free variable n of Kaingang bare nouns, namely, contextual saturation or existential closure. Each of these mechanisms brings about its own semantic effects. The former always gives rise to a quantized bare noun with a contextually specified cardinality, while the latter leads to cumulative reference at the clause level (but not at the root level). Thus far both mechanisms are equally consistent with the Kaingang data. Only further research on the semantics of Kaingang bare nouns may provide supporting evidence to decide between the two strategies.

One immediate consequence of treating quantized nouns as predicates of type ⟨e,t⟩ is that numerals in Kaingang cannot denote arguments for the n variable, for whenever they combine with a noun n represents a free variable. To tackle this, I propose to model Kaingang numerals as predicate modifiers with a cardinality presupposition whose satisfaction depends upon the contextual value of the number variable n within quantized predicates. To illustrate this, (69) gives the lexical entry of the numeral tãgtũ ‘three’.

Under this theoretical solution, the cardinality presupposition targets the number within the measure function. It introduces the condition that the predicate modified by a numeral must display a certain contextual cardinality. The idea is that a numeral is only defined if its presupposition is satisfied by the contextually supplied number for the n variable of the noun it combines with. Given the lexical entry (69), hence, one-place quantized predicates become arguments of numerals. By functional application of the denotation of a numeral to a quantized predicate another quantized predicate is then created, but now with a cardinality presupposition passed on by the numeral. The schematic tree in (70) illustrates this procedure with the constituent kyvénh tãgtũ ‘three (portions of) blood’.

In (70) the np denotation encodes the quantized nature of the noun, along with its ⟨e,t⟩ type, and as such it is ready to be the argument of the numeral, which, as a predicate modifier, i.e., an expression of type ⟨⟨e,t⟩,⟨e,t⟩⟩, applies to the NP and generates another predicate. At this stage, the presupposition of the numeral is projected into the derived predicate.¹⁴

The analysis outlined in (69) and (70) obviously does not intend to be an exhaustive account of numerals in the language. It was set forth in this paper, first and foremost, to show that it is in principle possible to provide a compositional treatment of a noun+numeral constituent in Kaingang when quantized nouns are represented as predicates of type ⟨e,t⟩ containing in their internal structure a counting function modeled along the lines of Krifka.

To summarize, the analysis advanced here treats all nouns in Kaingang as lexically count. Nouns express quantized predicates of type ⟨e,t⟩ containing a built-in counting function that measures quantities in terms of individual- or portion-units. The context-dependence of what counts as a unit is incorporated into the function via a contextual variable c, as in Krifka (2007). This guarantees that the units are evaluated relative to the utterance context. Further, the number variable of the counting function is left free, allowing its value to be contextually supplied and ensuring that the root noun is quantized, rather than cumulative (unlike English plural count nouns). This solution entails that individual and substance nouns in Kaingang can still be quantized at the point at which they are converted into bare noun arguments with an indefinite interpretation. This is so even when bare nouns denote pluralities. By representing indefinite bare nouns as introducing a silent choice function, I showed that pluralities can be selected from the extension of quantized nouns whenever their contextual cardinality is > 1. Finally, I also suggested that the number-neutral meaning of bare nouns can be analysed as arising at the clause level from the option of unselectively binding the number variable via the existential operator that also binds the choice function variable.