In this section, I introduce the basic assumptions on the domain of individuals and the semantics of common noun denotations. First of all, I take the domain of entities D_e to be closed under the sum operation ‘+’ and partially ordered based on the sub-part relation ‘⊑’ (Link 1983: et seq). When an individual has no sub-part other than itself, this individual is atomic or an atom.

I call this notion of atomicity mereological atomicity, but I primarily use the term “atom” to refer to mereological atoms.

Two entities overlap if there is an entity which is a mutual part of these entities. I use the symbol ◦ to model the overlap relation following the convention.

I define the notion of generalised sum following Champollion (2017).

The closure of a property under sum is defined in (14) (Link 1983).

I assume that plural nouns denote sets of atoms which are closed under sum (Link 1983).

In the original analysis of Link (1983), denotations of plural nouns lack the atoms, e.g., ⟦cats⟧ = {cat₁+cat₂, cat₂+cat₃, cat₁+cat₃, cat₁+cat₂+cat₃}. However, more recent analyses assume that denotations of plural nouns include atoms and the multiplicity inference comes from pragmatic inferences (Sauerland et al. 2005; Spector 2007; Zweig 2009; Križ 2017: to note a few). This choice does not matter for the purpose of this paper: I am only concerned with cases in which the multiplicity inference is obligatory and thus one can replicate the discussion based on the assumption that plural nouns do not include atomic parts.

Two higher-order properties, cumulative reference (Quine 1960) and quantised reference (Krifka 1989), distinguish denotations of singular nouns and denotations of plural nouns.

Singular nouns are quantised, whereas plural nouns are cumulative. For example, cat is quantised and non-cumulative: cat₁ ∈⟦cat⟧ and cat₂ ∈⟦cat⟧, but cat₁+cat₂ ∉⟦cat⟧ as shown in (15a), while cats is cumulative and non-quantised: cat₁+cat₂ ∈⟦cats⟧, cat₂+cat₃ ∈⟦cats⟧ and cat₁+cat₂+cat₃ ∈⟦cats⟧ as shown in (15b).

I assume that count nouns and mass nouns take their denotations in the same domain.11 One can assume either a single non-atomic domain (Krifka 1989) or a single atomic domain (Gillon 1992; Chierchia 1998). Unless I explicitly mention it, I assume a single atomic domain of individuals. On this assumption, one can assume that singular count nouns and mass nouns are distinguished based on plurality: singular count nouns denote sets of atoms, whereas mass nouns denote sets of atoms which is closed under sum.12 In this sense, mass nouns are inherently plural as exemplified in (17).

Mass nouns such as water have atomic parts, but their denotations are not related with a set of atomic parts, which serves as a counting unit (Chierchia 1998).

On this assumption, one cannot distinguish plural nouns and mass nouns.13 To distinguish plural nouns and mass nouns, one can adopt another notion of atomicity. For example, the notion of P-atom (Krifka 1989) defines atoms relative to predicates.

(18) can distinguish plural nouns and mass nouns: the denotation of a plural noun includes P-atoms and the denotation of a mass nouns does not, while both are still sets of mereological atoms that are closed under sum. Note that this definition of P-atom is quite coarse-grained. Indeed, there are more elaborated versions of atomicity in the market (Rothstein 2010; Chierchia 2010; to note a few) and they are motivated to make more fine-grained distinctions among different types of nouns. However, it is beneficial for me to adopt a coarse-grained definition because my primary aim is to examine whether there is any indication of a count-mass distinction and/or a singular-plural distinction at all in Japanese. If it turns out that one needs at least a coarse-grained definition of atomicity to describe Japanese data, then one can proceed to the next step and ask if finer-grained definitions of atomicity are also motivated there.

Summing up, the two notions of atomicity make two different distinctions. The mereological atomicity distinguishes singular count nouns from plural nouns and mass nouns. The P-atomicity distinguishes singular count nouns and plural nouns from mass nouns. These two notions become relevant at different sections in this article. The mereological atomicity plays the central role in §4 and the P-atomicity plays the central role in §5.

In this section, I introduce the notion of measurement monotonicity and show that this semantic property plays a crucial role in restricting the syntactic distribution of measure phrases in English. Monotonicity is defined as a property of measurement such that it traces the part-whole structure of noun denotations (Krifka 1989; 1992; Schwarzschild 2002; 2006; Nakanishi 2008; Wellwood 2015). ‘⊏’ is a proper part relation, ‘<’ is a total order relation relative to the measurement dimension and μ is a function from individuals to degrees.

For example, litre-measurement is monotonic: part of an entity necessarily has a smaller volumes in litres than the whole. However, temperature-measurement is non-monotonic: part of an entity need not have a lower temperature than the whole. Schwarzschild (2002; 2006) shows that this property correlates with the syntactic distribution of measure phrases in English: pseudo partitives allow only monotonic measure phrases as shown in (20), but measure attributives14 only allow non-monotonic measure phrases as shown in (21).15

Pseudo partitives are sensitive to noun denotations as well: plural nouns and mass nouns can occur in a pseudo partitive structure as repeated in (22a) and (22b), but singular count nouns cannot as shown in (22c). This suggests that monotonic measure phrases select non-quantised noun denotations (Krifka 1989; Filip & Sutton 2017).

However, note that (22c) may allow a reading in which “book” is coerced to a mass noun. Champollion (2017) notes that (22c) can be used in a situation in which the books are sold by weight or five pounds of pulp that results from shredding books.

On the other hand, measure attributives allow singular count or mass nouns, but disallow plural nouns. For example, “seven pound babies” has two theoretically possible ways of parsing as shown in (23a) and (23b).

The structure (23a) offers a reading in which there are multiple babies each of who weighs 7 pounds. On the other hand, the structure (23b) offers a reading in which there are babies that collectively weigh 7 pounds. However, the reading associated with the structure (23b) is not attested, suggesting that measure attributives cannot attach to plural NPs.16 Schwarzschild (2002; 2006) concludes that measure modifiers are lexical modifiers which occur inside an NP as shown in (24a), but pseudo partitives are functional modifiers which occur at the specifier of a functional head Mon⁰, which occurs at the middle field of nominal functional projection as shown in (24b).

This Mon⁰ is responsible for the monotonicity constraint and the selectional constraint.

Despite its typological distance from English, Japanese also exhibits syntax-monotonicity correlation. Nakanishi (2008) notes that the postnominal measurement construction requires monotonic measurement, but prenominal numeral quantifiers are ambiguous as exemplified in (25) and (26).17

These data suggest that Japanese postnominal measurement constructions impose a monotonicity constraint, just like English pseudo partitives. It raises a question of whether the postnominal measurement construction has a selectional constraint on noun denotations which is analogous to the one with English pseudo partitives. I will tackle this question in the next section.

In this section, I discuss the range of readings that are allowed in Japanese measurement constructions. First of all, I introduce the terminology for the relevant readings. As a disclaimer, I primarily describe them in a theory-neutral way to avoid committing to any particular notion of atomicity.

An individual reading entails existence of discrete individuals.18 There are two types of individual readings: singular readings entail existence of one individual and plural readings entail existence of more than one individual. Plural readings are furthre classified into two types: distributive plural readings attribute the measure phrase to each individual and cumulative plural readings attribute the measure phrase to the sum of individuals.19 One may group up singular readings and distributive plural readings: if one pluralises the whole NP under a singular reading, one can obtain a distributive plural reading. In contrast, a substance reading entails absence of discrete individuals.20 If one adopts P-atoms, this means that a substance reading entails absence of P-atoms. On the other hand, if one does not adopt P-atoms, this means that a substance reading entails existence of more than one atom and these atoms are different from those involved in plural readings.

Let me exemplify these readings with some examples. (27) and (28) contain a numeral ni (2), a mensural classifier kiroguramu (CL_Kilogram) and a notional count noun ringo (apple). While (27) allows all the four readings, (28) only allows a cumulative plural reading and a substance reading.21

Cumulative plural readings are not always available. If the relevant discrete individuals are not small enough relative to the measurement degree, a cumulative plural reading is blocked. In such cases, some nouns resort to count-to-mass coercion.22 (29) and (30) use the same noun as (27) and (28), but use a measure phrase with a smaller degree. In (29) and (30), cumulative plural readings are not available: 100 grams is too light for multiple apples.

Now, recall the contrast between the prenominal measurement construction and the postnominal measurement construction with respect to the notional count noun uma (horse) as repeated in (31) and (32). Here, the singular reading and the distributive plural reading require there to be one or more than one horse individual each of which weighs 500 kilograms. In contrast, the cumulative plural reading requires there to be some horse individuals which collectively weigh 500 kilograms and the substance reading requires there to be a portion of horse meat which weighs 500 kilograms.

(33) shows that (31) can be used to express that one or more than one horses run, but (32) cannot be, i.e. it can only describe a strange situation in which horse meat runs in a horse race.

On the other hand, (34) shows that (32) can be used to express that a butcher sold some amount of horse meat in a month while (31) is degraded.

Thus, the individual readings and the substance reading in (31) and (32) describe different types of entities: uma (horse) denotes a set of individual animate entities in the former, whereas it denotes inanimate non-individuated stuff in the latter. The contrast between (31) and (32) suggests that the postnominal measurement construction selects the latter in these cases. The same contrast can be reproduced with smaller animals, e.g., hamusutaa (hamster). Count-to-mass coercion is more surprising in this case, considering that it is even less conventional to eat hamster meat.23

In both cases, a cumulative plural reading is available if the measurement degree is large enough as shown in (37a) and in (37b).24

As shown above, easiness of count-to-mass coercion differs across nouns. For example, ringo (apple) easily allows a substance reading, whereas uma (horse) and hamusutaa (hamster) do not. Count-to-mass coercion is much harder with nouns that denote highly individual objects, e.g., kuruma (car). In (39), a cumulative plural reading is predicted to be unavailable because 2 kilograms is too light for multiple cars. Thus, if count-to-mass coercion is available, (39) should only allow a substance reading. The fact that (39) is degraded suggests that this coercion is quite hard or not possible with kuruma (car).

A cumulative plural reading is fine with kuruma (car) when the measure is large enough to make this pragmatically plausible as shown in (40).

Summing up, a singular reading and a distributive plural reading of a notional count noun are blocked in the postnominal measurement construction, whereas not in the prenominal measurement construction. If a measurement degree is too small to make a cumulative plural reading available, a count-to-mass coercion is triggered.

In this section, I discuss notional mass nouns. Firstly, the postnominal measurement construction is not sensitive to individuation as repeated in (41) and (42). In this case, the singular reading and the distributive plural reading entail that stuff is individuated based on one type of container and the cumulative plural reading entail that this individuation is done based on possibly multiple types of containers. In contrast, substance readings do not entail presence of containers. Both (41) and (42) can be used regardless of presence of a container in a given context.

In (43), a cooler contains several bottles of beer and the speaker report the total weight of those bottles of beer. Thus, beer is individuated based on bottles. In this context, the prenominal measurement construction and the postnominal measurement construction are both acceptable.

On the other hand, beer is not individuated based on containers in (44) and the speaker reports the total weight of beer produced in a brewery in one day. In this context, the prenominal measurement construction and the postnominal measurement construction are both acceptable.

This suggests that the postnominal measurement construction does not require nouns to have non-individuated denotations and the prenominal measurement construction does not require nouns to have individuated denotations. Note that a singular reading is degraded in (42). This reinforces the main point of the observation: the selectional constraint of the postnominal measurement construction is visible in the range of readings available in this environment.

In this section, I have shown the range of readings available in the postnominal measurement construction in Japanese. The observed pattern is summarised in Table 1. The availability of substance readings with notional count nouns depends on the availability of count-to-mass coercion.

The upshot is that the postnominal measurement construction in Japanese seems to impose some semantic restriction on noun phrases it selects. Although it is not visible in the type of nouns it selects, it is visible in the range of readings it allows. In the next section, I argue that this raises a puzzle and discuss two possible solutions to it.

In this section, I discuss a way to modify the definition of measurement monotonicity so that it can predict the range of readings available in the postnominal measurement construction in Japanese.

Champollion (2017) proposes a higher-order property stratified reference, which is a general constraint which applies to pseudo partitives, for-adverbials and the adverbial each. Since the main focus of this paper is on the semantics of monotonic measurement, I adopt a particular version of stratified reference for pseudo partitives which is defined in (47).

The stratified measurement reference plays the role of measurement monotonicity and non-quantisation requirement at the same time. Moreover, it restricts an entity x so that it can be sub-divisible into smaller pieces each of which has a smaller degree with respect to the measure function μ. Putting aside the compositional details for now, I will show how it accounts for the unavailability of a singular reading in the postnominal measurement construction.

Firstly, (47) correctly predicts that pseudo partitives select nouns with non-quantised denotations. (48) and (49) exemplify the denotations of pseudo partitives with mass nouns or plural nouns.

(48) denotes a set of stuff which is water and weighs 30 pounds, on the presupposition that those amounts of water satisfy the stratified measurement reference with respect to ⟦water⟧ and weight. Thus, for x ∈ ⟦thirty pounds of water⟧ to hold, x has to be sub-divisible into smaller entities y such that y is still water and is lighter than x. Otherwise, it results in presupposition failure. Similarly, (49) requires that x is sub-divisible into smaller entities y such that y is still books and is lighter than x. Since denotations of plural nouns and mass nouns are closed under sum (see Section 2.1), this sub-divisibility requirement is satisfied in these cases. Thus, it correctly predicts that plural nouns and mass nouns are felicitous in pseudo partitives.

The stratified measurement reference correctly predicts that singular count nouns cannot occur in pseudo partitives, too. Take (50) as an example.

The underlined part says that x is partitioned into parts each of which is a book and lighter than x. However, ⟦book⟧ is a set of atoms. Thus, this sub-divisibility requirement is not satisfied, i.e. a book is an atom and cannot be sub-divided further. Thus, it correctly predicts that singular count nouns are infelicitous in pseudo partitives.

Now, let’s see if the stratified measurement reference can correctly block a singular reading in the postnominal measurement construction. The point is that the stratified measurement reference can block a singular reading even if Japanese common noun denotations are inherently cumulative. I start with a case with a substance reading.

(51c) requires that x is sub-divisible into smaller entities y such that y is still beer and is lighter than x. Since Japanese common noun denotations are inherently cumulative by assumption, this sub-divisibility requirement is satisfied. In this case, the stratified measurement reference makes the same prediction for pseudo partitives in English and the postnominal measurement construction in Japanese. Note that the same result can be obtained with the non-quantisation requirement.

Difference between the stratified measurement reference and non-quantised reference becomes visible when a notional count noun occurs in the postnominal measurement construction. Note that the denotation of ringo (apple) is closed under sum by assumption, i.e. ⟦ringo⟧ = λx[*apple(x)].

In this case, (52c) is stronger than the non-quantised reference: it requires that each member of ⟦ringo 2-kiroguramu⟧ can be sub-divisible into smaller pieces so that those pieces are still members of ⟦ringo⟧. This precludes a singular reading: if x is an atom, it violates (52c), i.e. the set of x which satisfies (52c) is equivalent to the exclusive plural reading of ⟦ringo⟧.25 Thus, the stratified measurement reference correctly rules out a singular reading in the postnominal measurement construction.26

On this point, note that the proposed semantics does not derive a distributive plural reading. While ⟦ringo⟧ is cumulative, (52b) is not cumulative: it is a set of apple-sums each of whose member is 2 kilograms. For example, 2 kilograms of apples is a member of this set, but 4 kilograms of apples is not. This correctly predicts that (52) does not have a distributive plural reading.27

Count-to-mass coercion is triggered due to an interaction between the stratified measurement reference and the common knowledge. (53) shows the denotation of the postnominal measurement construction with the notional count noun uma (horse).

The underlined part requires that x is sub-divisible into horses each of which is lighter than x. However, this clashes with common knowledge: 500 kilograms is too light for multiple horses. Thus, one cannot satisfy the presupposition without making it contradict with the common knowledge. As a result, (53) is infelicitous. To avoid it, one has to coerce ⟦uma⟧ so that it denotes a set of horse meat so that common knowledge about an individual horse does not matter.28 On this point, one can either assume that (i) some nouns are polysemous, e.g., uma denotes a set of horses in one sense and a set of horse meat in the other sense, or (ii) a general operation of universal grinder shifts the denotation of uma (horse) from a set of horses into a set of horse meat.29

Indeed, Champollion (2017) discusses a similar phenomenon in English: apples is degraded with a sufficiently small measurement degree while apple is felicitous under a substance reading.30

This is expected from the sub-divisibility requirement of the stratified measurement reference: apples cannot be divided into apples which are smaller than 100 grams or one gram. In this sense, I am not the first one who claims that the interplay of the stratified measurement reference and common knowledge makes a cumulative plural reading infelicitous.

Lastly, notional substance mass nouns with mass-to-count coercion block a singular reading: the stratified measurement reference forces an individual portion of stuff to be sub-divisible. For example, imagine a situation in which there is a glass of beer which weighs 500 grams. (55) shows how the stratified measurement reference works in this case. For the notational convenience, I put “*glass of beer” as the product of mass-to-count coercion of ⟦biiru⟧ in (55).31

(55c) requires that each member of ⟦biiru 500-guramu⟧ can be sub-divisible into smaller pieces so that those pieces are still members of *⟦glass-of-beer⟧. As a result, ⟦biiru 500-guramu⟧ does not include individuals which are singular glasses of beer. Thus, the stratified measurement reference blocks a singular reading when stuff is portioned into containers.

For a compositional implementation, I adopt some assumptions on the semantics of numerals and measure phrases. My assumption is essentially the same as the assumptions adopted in Champollion (2017), but this choice is not essential to the main point of this paper. Following Krifka (2008); Rothstein (2013); Sudo (2016; to appear), I assume a numeral of referential type.32

I assume that mensural classifiers denote predicates of type ⟨n,⟨dt⟩⟩. For example kiroguramu (CL_Kilogram) is defined as shown in (57).

The mapping from individuals to degrees is achieved by a covert measurement function. For example, μ_weight maps an individual to a degree.

I assume that the postnominal measurement construction involves Mon⁰ which takes an NP as its complement and the Num-CL complex as its specifier as shown in (59). I assume that the covert mapping operator occurs in the middle field following Champollion (2017). As he notes, this choice does not matter. I assume that case particles are realisations of a nominal functional head Case⁰ and the NP-Num-CL word order is derived by an NP-raising to Spec, CaseP (Watanabe 2006).

I assume that Mon⁰ introduces the stratified measurement reference as presupposition. The denotations of terminal nodes are given in (60).33

Now, the denotation of the postnominal measurement construction is compositionally obtained as shown in (61). I ignore the semantics of Case⁰ and the semantic repercussion of the NP raising.34

Summing up, this section described the first option to explain the range of possible readings in the postnominal measurement construction in Japanese. I showed that the stratified measurement reference (Champollion 2017) correctly predicts that a singular reading results presupposition failure. This explains why a singular reading is blocked in the postnominal measurement construction in Japanese even though common nouns in Japanese are neither marked for singular nor plural. With this option, one can maintain the hypothesis that Japanese common noun denotations are inherently cumulative.

In this section, I discuss a way to modify the common noun denotations of Japanese so that the non-quantisation requirement applies non-trivially.

In a series of papers (Watanabe 2006; 2010; 2017: a.o.), Akira Watanabe proposes that Japanese has #⁰ which is the locus of number specification. In this sense, he commits to the view that Japanese has a syntactic count-mass distinction: common nouns in Japanese are sorted based on number specification and they sometimes enter in an agreement relation with #⁰. Watanabe (2006) proposes that #⁰ hosts an NP in its complement and a numeral on its specifier as shown in (62).35

Watanabe (2006) assumes nominal functional heads Case⁰, Q⁰ and D⁰ above #⁰ and proposes that sortal classifiers occupy the #⁰ position. Now, the distributional patterns of the unit of a numeral and a classifier are derived with massive DP-internal remnant movements. (63a) and (63b) respectively show the structures associated with the NP-Num-CL order and the Num-CL-no-NP order.36

Crucially, Watanabe (2006) makes a syntactic distinction between sortal classifiers and mensural classifiers: sortal classifiers are realisations of #⁰, whereas mensural classifiers are not. Accordingly, #⁰ is covert in the latter case.38 The structure for mensural classifiers are given in (64).

This structural distinction corresponds to a count-mass distinction: (62) accepts count nouns, whereas (64) accepts mass nouns.39 Watanabe (2006) states it as Mass/Count Universal (65).

Watanabe (2017) further argues for a singular-plural distinction in Japanese based on contrast between partitives and reverse partitives.40 Partitives allow both a singular reading and a plural reading as shown in (66a), whereas reverses only allow a plural reading as shown in (66b).

Moreover, Watanabe (2017) shows that reverse partitives trigger mass-to-count coercion as shown in (67b): contaminated water is required to be partitioned based on a contextually salient unit.41

Watanabe (2017) proposes that the reverse partitive structure is derived with an NP raising to Spec, #P driven by agreement based on [-singular] feature. He assumes the base structure given in (68).42

In the next step, the NP ringo (apple) within the DP is raised to Spec, #P, entering an agreement relation with #⁰.43

Lastly, the reverse partitive order is derived when ichibu (part) is raised to Spec, CaseP.44

In this analysis, the reverse partitive structure does not allow a singular reading because the NP has to agree with #⁰ in [–singular] feature.45 Note that Watanabe (2017) assumes that bare NPs are marked with [±singular], i.e. their denotations include atomic as well as non-atomic individuals. In this sense, denotations of bare NPs are inherently cumulative, while denotations of #Ps are not.

Based on the discussion so far, one can suggest that the postnominal measurement construction in Japanese has the structure given in (71) and propose that Mon⁰ takes #P as its complement.46

Crucially, #P distinguishes singular denotations, plural denotations and mass denotations. On this point, I define the denotation #⁰ with a built-in (non-)atomicity condition.47 Here, I sketch one possible implementation. First, I assume that a count noun denotes a set of atoms, whereas a mass noun denotes a set of atoms which is closed under sum. Count nouns are pluralised when it bears [–singular] feature, i.e. if ⟦NP_[+singular]⟧ = P, then ⟦NP_{[–singular]}⟧ = *P. I assume that this pluralisation takes place “off-line” in the lexicon. Thus, the assumption that a bare NP is marked with [±singular] is maintained when an NP occurs in syntactic structures. Second, I assume that #⁰ has different semantics depending on its number specification. Under the assumption that mass nouns are inherently plural, there is no strong motivation to distinguish the semantics of #⁰_[–number] and #⁰_{[+number,–singular]}. Accordingly, a plural-mass distinction is only made in syntax: plural NPs agree with #⁰_{[+number,–singular]} and mass NPs agree with #⁰_[–number]. Importantly, this analysis distinguishes #P with [+number,+singular] and #P with [+number,–singular]. Accordingly, the denotation of #P with [+number,–singular] ends up including only non-atoms due to pragmatic enrichment in parallel with English plurals.48

In this analysis, the non-quantisation requirement of Mon⁰ correctly rules out a singular reading simply because it is incompatible with a #P with [+number,+singular]. On the other hand, a #P with [+number,–singular] feature or [–number,–singular] feature is permitted in the postnominal measurement construction. For a compositional implementation, I assume the denotation of Mon⁰ in (73), which minimally differs from Mon⁰ defined in (60b) with respect to the presupposition.

For example, the composition of the singular reading of ringo ni-kiroguramu (apple 2-CL_Kilogram) is given in (74). I ignore the composition above the CaseP layer here, too.

In this case, the #P bears [+number, +singular] feature and it results in presupposition failure: #P denotes a set of atoms and it is quantised by definition. Thus, a singular reading is blocked. If the #P bears [+number,–singular] feature or [–number] feature, it denotes a set of atoms which is closed under sum. Thus, it meets the non-quantisation presupposition. This explains why the postnominal measurement construction blocks a singular reading while allowing a cumulative plural reading and a substance reading. The unavailability of distributive plural readings follows in the same way as the analysis sketched in Section 4.1: even when ⟦ringo⟧ is cumulative, the denotation of the postnominal measurement construction itself is not cumulative.

This approach treats count-to-mass coercion in the same way as well. (75a) shows that the case in which uma (horse) is combined with #⁰_{[+number,–singular]}. Crucially, since singular #Ps and plural #Ps are distinguished by assumption, the denotation of plural #Ps ends up including only non-atoms due to pragmatic enrichment.

Now, (75a) clashes with common knowledge. (75a) requires there to be plural horses which collectively weigh 500 kilograms, but 500 kilograms is too light for plural horses. On the other hand, uma (horse) with #⁰_[–number] can satisfy the non-quantisation presupposition without clashing with common knowledge. Thus, only the option with count-to-mass coercion can output a felicitous result with uma 500-kiroguramu (500 kilograms of horse).

Summing up, this section described the second option to explain the range of possible readings in the postnominal measurement construction in Japanese. If one wishes to maintain the hypothesis that the semantics of monotonic measurement imposes the non-quantisation requirement, one has to modify the semantics of common noun denotations in Japanese. I claimed that the syntax-semantics interface with #⁰ along with Watanabe (2006; 2017) correctly predicts that a #P with [+number,+singular] violates the non-quantisation presupposition.

So far, I have discussed two possible analyses of the postnominal measurement construction in Japanese. In this section I discuss ways to analyse the prenominal measurement construction.

As I discussed in Section 2.2, the prenominal measurement construction in Japanese allows both monotonic measure phrases and non-monotonic measure phrases. This suggests that either (i) the prenominal measurement construction is underspecified with respect to monotonicity and quantisation or (ii) it is structurally ambiguous between the monotonic structure and the non-monotonic structure. Starting with the underspecification approach, I point out that it has difficulty in deriving distributive plural readings and I argue for the structural ambiguity approach.

Following Schwarzschild (2002; 2006), I assume that the non-monotonic structure involves an NP adjunction as shown in (76).49 If one assumes #⁰, it occurs above the NP.

I assume that no is a morphological linker which is post-syntactically inserted (Watanabe 2006).

I propose that the Num-CL unit in this structure functions as an intersective modifier. I assume a type variant of a covert mapping operator as defined in (77).50

The compositional detail of the prenominal measurement construction ni-kiroguramu-no ringo (2-CL_Kilograms-no apple) is given in (78).51

Since Mon⁰ is absent in this structure, both a monotonic mensural classifier and a non-monotonic mensural classifier can occur in this structure. Furthermore, it does not impose any restriction on ⟦ringo⟧: as long as the total weight of them is 2 kilograms, there can be any number of apples including one. Thus, a singular reading is not blocked in the prenominal measurement construction.

However, distributive plural readings pose a problem for this approach. In the end, I argue for the structural ambiguity approach. There are two options to derive a distributive plural reading: one is to let a measure phrase distributively apply to a noun denotation and the other is to apply pluralisation to the constituent [Num-CL NP]. In the first option, one can modify (77) as (79): this version of μ′ attributes the measure phrase to each atomic parts of an individual x.

The revised version of μ′ can also derive a singular reading when x is an atomic individual. However, (79) does not derive a reading in which the measurement degree is attributed to the sum of atoms. Thus, a cumulative plural reading and a substance reading are not obtained with (79).

The other option is dependent on the #P approach. One can modify the denotations of #⁰_{[+number,–singular]} and common nouns so that #⁰_{[+number,–singular]} pluralises a singular denotation and a common noun denotes a set of atoms. Now, distributive plural readings are obtained when (78) involves #_{[+number,–singular]}. An example with ni-kilogramu-no ringo (2-CL_Kilograms-no apple) is given in (80c).

Here, (80c) includes sums of atomic apples each of which weighs 2 kilograms.52 On this point, it is crucial that the common noun denotation is inherently non-cumulative. Otherwise, it overgenerates. For example, ni-kiroguramu-no ringo (2-CL_Kilograms-no apple) cannot be used to refer to seven apples which collectively weigh 4 kilograms. However, (81) includes such plural individuals, predicting non-attested readings. Thus, this option with the modified denotation of #_{[+number,–singular]} requires the common noun denotations to be inherently non-cumulative.

Although this revised entry of #_{[+number,–singular]} successfully derives a singular reading and a distributive plural reading, it cannot derive a cumulative plural reading: there is no way to pluralise a noun denotation before it is combined with a measure phrase.

So far, I have shown two ways to derive a distributive plural reading in the prenominal measurement construction. However, both analyses do not predict that the non-monotonic structure derives cumulative plural readings and substance readings.53 Here is a dilemma: if one wishes to include a distributive plural reading, then cumulative plural readings and substance readings are excluded. One can solve this dilemma if one assumes that the prenominal measurement construction is structurally ambiguous between the non-monotonic strtucture and the monotonic structure. Recall that the proposed structures for the postnominal measurement construction, i.e. (61) and (71), both involve an NP-movement. If this movement is optional, then the monotonic structure can also derive the Num-CL-no-NP order. This leads to a division of labour: the non-monotonic structure is responsible for a singular reading and a distributive plural reading, while the monotonic structure is responsible for a cumulative plural reading and a substance reading. Since the postnominal order can only be derived with the monotonic structure, it still explains why the postnominal measurement construction does not allow a singular reading nor a distributive plural reading.54

Summing up, I discussed the syntax and semantics of the prenominal measurement construction. I proposed that the Num-CL unit in the non-monotonic structure is an intersective modifier. Although this assumption can derive a singular reading, a cumulative plural reading and a substance reading, it cannot derive a distributive plural reading. It motivates some mechanism for distributive attribution of a measure phrase. However, addition of this mechanism wrongly filters out a cumulative plural reading and a substance reading. To solve this dilemma, I proposed that the prenominal measurement construction is structurally ambiguous between the non-monotonic structure and the monotonic structure. The former derives a singular reading and a distributive plural reading, while the latter derives a cumulative plural reading and a substance reading.

In this section, I discussed two possible ways to explain why a singular reading is blocked in the postnominal measurement construction in Japanese. Essentially, one has to choose to put burden on the theory of monotonic measurement or on the theory of common noun denotations in Japanese. The first option is to modify the analysis of monotonic measurement, while maintaining the assumption that Japanese common noun denotations are inherently plural. I claimed that the stratified measurement reference in Champollion (2017) makes the right predictions even if Japanese noun denotations are inherently cumulative. The second option is to modify the analysis of common nouns in Japanese, while maintaining the assumption that the semantics of monotonic measurement requires a noun to have a non-quantised denotation. I claimed that the #P approach in Watanabe (2006; 2017) makes the right predictions even if the semantics of monotonic measurement just requires a noun to have a non-quantised denotation.

These two approaches roughly converge in the analysis of the prenominal measurement construction: the prenominal measurement construction is structurally ambiguous between the non-monotonic structure and the monotonic structure. In the non-monotonic structure, the Num-CL unit functions as a distributive attributive modifier and it derives a singular reading and a distributive plural reading. In the monotonic structure, it involves the same underlying semantics as the postnominal measurement construction and it derives a cumulative plural reading and a substance reading. This covers all the four possible readings for the prenominal measurement construction.

As I have discussed in Section 2.1, Chierchia (1998) assumes that both count nouns and mass nouns take their denotations in the atomic domain. Furthermore, he reduces a count-mass distinction to a singular-plural distinction: singular count noun denotations are not closed under sum, whereas mass noun denotations are closed under sum.55 Based on this view, Chierchia (1998) proposes that denotations of numeral classifier languages are inherently plural and thus they lack a count-mass distinction. One of the advantages of this analysis is that it naturally captures the generalisation that bare arguments are generally used as a kind-denoting expression. Chierchia (1998) proposes a pair of operators ^∪ and ^∩ as defined in (82a) and (82b). I use k as variable for kinds.

Based on this correspondence between kinds and plural properties, Chierchia (1998) proposes the Nominal Mapping Parameter: languages are parametrised based on two binary features, [±Arg(ument)] and [±Pred(icate)]. [+Arg] feature allows a noun to be mapped to an entity of type e and [+Pred] feature allows a noun to be mapped to a predicate of type ⟨et⟩. This nicely explains the cross-linguistic distribution of bare arguments and kind-denoting expressions.56 See Chierchia (1998) for data and discussion. What is relevant for the discussion here is that Chierchia (1998) proposes that numeral classifier languages are specified with [+Arg, –Pred]. This explains why these languages generally allow bare arguments and lack an obligatory plural morpheme.

This analysis of numeral classifier languages also explains why classifiers are obligatory when a numeral is combined with a noun. In the analysis of Chierchia (1998), a noun denotation is countable if it is associated with a set of atoms. Count nouns are associated with a set of atoms because their denotation only include atoms, whereas mass nouns are not because they are already plural in the lexicon. Chierchia (1998) proposes that a set of atoms serves as a counting unit for numerals and mass nouns cannot be directly combined with numerals because they do not provide a counting unit. This explains the behaviour of numeral classifier languages. Noun denotations in those languages are inherently plural and do not provide a counting unit for numerals. Thus, a classifier is necessary to provide a counting unit for numerals. This makes a prediction that noun denotations in numeral classifier languages are uncountable without help of classifiers.

However, the previous literature has suggested that Japanese has several syntactic environments which only allow notional count nouns, but do not involve an overt classifier. First, Watanabe (2006) shows that distributive universal quantifiers require individuated noun denotations and dono-NP-mo (every NP) in Japanese is illicit with the notional mass noun mizu (water) as shown in (83).57 This is unexpected if Japanese does not have a count-mass distinction.

Furthermore, Japanese has several quasi-cardinal modifiers which do not involve an overt classifier, but sensitive to notional count nouns. (84) shows that nan-byaku-toiu (hundreds of) and tasuu-no (many) require nouns with a specific mode of individuation.

In addition to those count-sensitive quasi-cardinal modifiers, Sudo (to appear) shows that interpretations of proportional quantifiers are sensitive to countability. Hotondo (most) in Japanese is compatible with both notional count nouns and notional mass nouns.

However, hotondo (most) allows different patterns of interpretations for notional count nouns and notional mass nouns. First, consider the situation (86). Sudo (to appear) shows that (85a) can be true only in the count-based situation (86a).

The same is not true for notional mass nouns. Consider the situation (87).

Since the same modifier is used, this difference must be attributed to the semantic difference between hon (book) and mizu (water). Thus, Sudo (to appear) proposes that common noun denotations are sorted into countable nouns and uncountable nouns, if not count nouns and mass nouns.58

In the more recent papers of his (Chierchia 2015; 2021), Chierchia abandons the claim that numeral classifier languages lack a count-mass distinction: nominal properties are sorted into atomic ones and non-atomic ones based on the notion of P-Atom.59 However, he maintains the view that common nouns in numeral classifier languages are kind-denoting and thus their predicative denotations are inherently cumulative since ^∪k is either closed under sum or undefined. In this sense, observations discussed so far in this section suggests that Japanese has at least a lexical atomicity distinction, but these are not enough to show that Japanese has a singular-plural distinction or a syntactic count-mass distinction.

The two analyses of the postnominal measurement construction I proposed have different implications in this regard. The first analysis with the stratified measurement reference does not presuppose a count-mass distinction, but it is compatible with it. In this sense, this analysis neither argues for nor against a lexical count-mass distinction in Japanese. On the other hand, the second analysis with #P acknowledges both a lexical count-mass distinction in NPs and a syntactic count-mass distinction in #Ps. In this sense, the implications of the second approach are stronger than the discussion in this section. Note that both analyses can be made compatible with an analysis in which Japanese common nouns are kind-denoting and thus their corresponding properties are inherently plural. The analysis with the stratified measurement reference is compatible with the assumption that Japanese noun denotations are inherently cumulative. The analysis with #P is conditionally compatible with the inherent cumulativity assumption. Recall that I laid out two possible analyses to derive a distributive plural reading: one with the distributive μ′ operator and the other with the modified version of #_{[+number,-singular]}. The former option is compatible with the inherent cumulativity assumption. However, the latter option requires common noun denotations to be non-cumulative in the lexicon. This is contradictory with the inherent cumulativity assumption. In this sense, both analyses can retain the Chierchia-style explanation for the typological correlation between lack of number specification and generalised bare argument, but it make the distributive μ′ operator the only option to derive distributive plural readings.

So far, I reviewed the analysis of Chierchia (1998) and challenges to his analysis. The tentative conclusion is that Japanese has a lexical atomicity distinction. Then, the next question is if Japanese has a syntactic count-mass distinction.

Watanabe (2017) argues that the distinction between countable nouns and uncountable nouns in Sudo (to appear) can be the one between object mass nouns, e.g., furniture, and substance mass nouns, e.g., water.60 (88) shows that furniture does not require a determiner, disallows a cardinal modifier and allows much. Thus, furniture is syntactically mass.

However, furniture refers to a set of discrete entities unlike water, which refers to substance. Thus, the intuitive notion of individuation and a count-mass distinction do not always match.

Thus, Watanabe (2017) claims that one must check if Japanese makes distinction between count nouns and object mass nouns. Watanabe (2017) shows that counterparts of plural mass nouns funds and assets do not display an interpretive distinction in the reverse partitive structure.

Watanabe (2017) concludes that they are always marked with [-singular]. On the top of it, Watanabe (2017) shows that count-sensitive modifiers do not allow shikin (funds).

This suggests that shisan (funds) is semantically plural, but syntactically mass. This is a piece of evidence for a syntactic count-mass distinction for Watanabe (2017).61

Combining the discussions so far, there are reasons to believe that Japanese has a count-mass distinction both in its lexicon and in its syntax. On this point, one can wonder if it is necessary to encode a count-mass distinction in its lexicon for the first place. Borer (2005) proposes that that every noun root is universally mass and its count-mass status is determined by unambiguous functional structure provided in syntax. More specifically, the functional head (Div⁰, CL⁰ or count⁰) is the locus of individuation. On this view, count nouns are those which acquire their mode of individuation from this functional head and mass nouns are obtained as a default due to the lack of the dividing feature in that head. The relevant functional head is realised either as a classifier or as an article/plural morpheme. In this sense, classifier systems and article systems are two sides of the same coin. One theoretical merit of this approach is that we can avoid redundancy between syntax and the lexicon. As there are different unambiguous functional structures above count nouns and mass nouns, further lexical specification of a count-mass distinction is redundant. This is close to the position taken in Cheng & Sybesma (1999) and Watanabe (2006).

In this paper, I do not aim to make a strong claim on this issue, but let me point out that the postnominal measurement construction provides further material which merits the discussion on a syntactic count-mass distinction in Japanese. As I have shown in Section 3, cumulative plural readings and substance readings have different truth conditions with respect to individuation. However, I claim that those plural readings in the postnominal measurement construction show a ‘mass-like’ property in the sense that they do not make atoms salient for further grammatical operations. Recall that Japanese bare arguments are compatible with an overt distributor sorezore (each) as repeated in (92).

The floating sorezore (each) itself is sensitive to countability in the same way as other count-sensitive environments discussed in Section 5.1.

Imagine a situation in which a server is bringing several glasses of water to a table in which customers are reading books. Now, the server drops these glasses of water and each of these are spilled on two books. However, (93) is still infelicitous in this situation, suggesting that the floating sorezore (each) is sensitive to some notion of atomicity.

Now, let’s see if the floating sorezore (each) is felicitous when it is combined with a cumulative plural reading of the postnominal measurement construction. As a baseline, consider (94).

Now compare it with the postnominal measurement construction as shown in (95): addition of the postnominal measurement construction leads to infelicity. In principle, one can consider a distributive plural reading and a cumulative plural reading in (95). Since a distributive plural reading is unavailable in the postnominal measurement construction, the infelicity of (95) suggests that cumulative plural readings are incompatible with the floating sorezore (each).

Note that the prenominal measurement construction is fine under a distributive plural reading, although it is a bit harder to imagine that several 5 ton cars are running.

Definiteness is orthogonal to this contrast: the contrast retains between (97a) and (97b).

If cumulative plural readings in the measurement constructions make reference to the same type of plural individuals as gakusei (student) in (92) and kuruma (car) in (94), they should have been compatible with the floating sorezore (each). A similar behaviour is observed in English: Rothstein (2011) shows that pseudo partitives with plural nouns are compatible with much, but not with many.

Furthermore, Rothstein (2011) shows that they are incompatible with reciprocals.

In Japanese, a reciprocal adverb koogo ni (alternately) can describe the same situation. Imagine that red books and blue books are standing next to each other. (100) is felicitously true in this context.

In contrast, cumulative plural readings of the measurement constructions are incompatible with koogo ni (alternately). (101) is infelicitous in the situation in which red books and blue books are standing next to each other.62

These observations may suggest that plural readings of the Japanese postnominal measurement construction are mass-like to the same extent as English pseudo partitives with plural nouns.

Rothstein (2011) proposes that (i) the counting structure and the measurement structure are syntactically distinguished, and (ii) count denotations and mass denotations are in one-to-one correspondence with the counting structure and the measurement structure.63 Although more work is needed to make a precise assessment, the observations so far suggest that the same may apply to Japanese. I do not develop a full-fledged analysis in this paper, but let me describe a possible way to implement it with the ingredients discussed so far. First, I minimally modify the monotonic structure so that #⁰ plays the role of Mon⁰ as shown in (102).

Since both types of measurement constructions underspecify atoms, I assume that either (i) the NP-raising to Spec, CaseP is optional or (ii) the remnant #P can be raised to Spec, QP when Q⁰ is introduced to the derivation. This is in line with the structural ambiguity discussed in Section 4.3.

Second, I refine the denotations of #⁰ based on P-atoms. I assume that P-atoms are underspecified in the lexical semantics of common nouns and #⁰ plays a role to specify P-atoms as shown in (103).

Now, this analysis makes a distinction between a set of atoms and a set of P-atoms. If the notion of atomicity relevant for distributivity is P-atom, this correctly predicts that plural readings in the measurement constructions are compatible with neither sorezore (each) nor koogo ni (alternately).

If the discussion so far is on the right track, the fact that cumulative plural readings of the measurement constructions are compatible with neither an overt distributor nor a reciprocal adverb provides a piece of support for a syntactic atomicity distinction in Japanese: the #P layer is necessary to distinguish NP denotations with P-atoms and those without P-atoms. In addition, recall that notional count nouns are compatible with the floating sorezore (each) as shown in (92) and (94), while notional substance mass nouns are not as shown in (93). This suggests that P-atoms can be defined with notional count nouns, but not with notional substance mass nouns.64 Note that this P-atom-based semantics of #_[–number] emulates the effect of the stratified measurement reference. Imagine that P(x) is true. ⟦#_[–number]⟧ (P)(x) presupposes that there is no sub-part of x which is a P-atom. Crucially, x itself cannot be a P-atom. As a result, #⁰_[–number] rules out any readings which imply P-atoms, i.e. singular readings and plural readings. In this sense, #_[–number] triggers count-to-mass coercion whether its complement induces a singular reading or a plural reading. See Rothstein (2011) for a more elaborated analysis of plural-to-mass coercion in pseudo partitives in English. Accordingly, the difference between a singular reading and a cumulative plural reading is attributed to a different notion of atomicity than P-atom nor mereological atomicity, e.g., natural atomicity (Rothstein 2010).65 Although I leave the precise formalisation of the resultant system for future research, this offers a novel material for further discussion on a count-mass distinction in Japanese. The take-home message is that the measurement constructions provide further observations which may suggest that Japanese makes an atomicity distinction both in its lexicon and its syntax.