Quality nouns and other mass nouns

The definition of qualities in Chapter 3 makes two assumptions about their structure. The first is that qualities are partially ordered by a mereological part-of relation. Each quality is a Linkian non-atomic join semi-lattice. The second is that qualities are ordered by the size preorder ≤, which is the main ingredient of the proposed semantics of gradability and comparison for possessive property concept sentences. Being ordered by the total preorder ≤ is what distinguishes qualities from the denotations traditionally assumed for substance mass nouns like water or sand, which are only ordered by the mereological partial order.

This chapter is dedicated to motivating these two assumptions, partly by testing their predictions and partly by demonstrating their explanatory force. The assumption that qualities are mereologically ordered makes the prediction that quality-denoting property concept nouns should pattern morphosyntactically with other nouns that are assumed to be so ordered, namely other mass nouns. We show that this prediction is borne out by a range of morphosyntactic environments that target mass nouns in familiar languages. Furthermore, we argue that making this assumption affords a simple explanation for a corner of the grammar of property concept constructions in Ulwa which would remain mysterious if it were not made.

The assumption that qualities are preordered by size (≤), and that the denotations of other mass nouns are not, predicts the existence of environments in which the two types of noun diverge. If there are such environments, it should be possible to link them in a natural way to the presence of a size ordering. We demonstrate that this prediction is borne out in an interesting way, based partly on novel observations and partly on observations made in the literature, for example by Tovena (2001) for Romance and more recently by Baglini (2015) for Wolof. Tovena and Baglini point out distributional contexts that sharply distinguish property concept nouns from other mass nouns, and propose to account for them in terms of a distinction between intensive and extensive quantity. We argue that those environments that distinguish the two kinds of mass noun are those that select for or are otherwise sensitive to the presence of a size-preordering.

6.1

Qualities are mereologically structured

This section provides motivation for the assumption that qualities are partially ordered by a mereological relation. First, we demonstrate that the prediction made by this assumption, that quality-denoting nouns should pattern with mass nouns in the familiar environments that track mereological structure, is borne out. Second, we show that this assumption provides an elegant account of the semantics of Ulwa possessive constructions in which the possessed noun is formed from a quality-denoting property concept root and the possessive suffix –ka described in Chapter 3.

6.1.1 Patterning with mass nouns

If qualities are mereologically ordered, then all other things being equal, we expect that constructions that are sensitive to this kind of denotation will exhibit this sensitivity also with quality-denoting nouns. Standard mass/count diagnostics (on which see e.g. Pelletier and Schubert 2003; Doetjes 2012 for recent overview discussion) in English and other familiar languages seem to bear this prediction out, in that nouns that are plausibly quality denoting are unambiguously mass. In this section we briefly lay out these facts.1 The discussion makes the presumption, which we take to be fairly intuitive, that English ‘abstract’ mass nouns and nominalizations, words such as courage, beauty, and patience which occur in possessive near-equivalents of property concept sentences, are quality denoting. We do not argue for this presumption here.

One environment usually taken to distinguish count and mass nouns is pluralization—count nouns pluralize, while mass nouns do not, except in reference to either kinds or conventionalized units of the material in question, that is, on a so-called ‘universal packager’ interpretation (see Jackendoff 1991: 24 n. 11 for this term and its intellectual history).

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Technically, this diagnostic is sensitive not to mereological structuring, but rather to atomicity (or lack thereof)—only nouns with an atomic denotation pluralize, while nouns with a non-atomic one do not. However, because only mereologically-structured domains are non-atomic2 (see the axioms in Link 1983), a diagnostic that reveals a denotation to be non-atomic also diagnoses it as mereologically structured. Quality-denoting nouns like those in (3) behave in exactly the same way.

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Much like the nouns in (2), these are well-formed only on a kind-type reading. For example, in a world in which there are different kinds of beauty, one can talk about them with the plural of beauty. In reference to some mass of the quality beauty, however, the plural noun is ill-formed in the same way that ordinary mass nouns are.3

Given the above, it is no surprise that count nouns are acceptable when determined by a numeral, while mass nouns are not, save on a universal packager or kind-type reading.

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This diagnostic, again, probes atomicity, but ultimately picks out nouns with a mereologically structured denotation for the same reasons pluralization does, as discussed above. Our intuition is that the same is true for quality-denoting nouns, to the extent they are acceptable at all. For example, one anger might be one particular kind of anger (quiet, aggressive, etc.), and similarly for one courage.

Also, quantifying determiners such as each and every appear with count nouns (6), but not mass nouns (outside universal packager contexts) (7).

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Again, quality-denoting nouns in English generally pattern with ordinary mass nouns—it is hard even to conceive of contexts in which DPs like those in (8) could be used (though see n. 3).

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Certain determiners that divide nouns into count or mass also group quality-denoting nouns with uncontroversial mass nouns. For example, little and much are acceptable only with mass nouns (save in a universal-grinder context):

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The same is true for quality-denoting nominals:

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As a final point, determination of mass nouns, outside universal packager contexts like those discussed above, normally requires use of the partitive construction (12), while count nouns normally appear in it only with universal-grinder interpretations (13).

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Again, quality-denoting nouns behave like ordinary mass nouns in appearing in the partitive construction.

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In short, the evidence from English is clear that in a range of mass/count diagnostic constructions, quality-denoting nouns pattern with ordinary mass nouns. And the same has already been seen for possessive-predicating nominals in the Bantu language Basaá in §5.2.3. We believe that the same is true quite generally of quality-denoting nominals, and that this is, in fact, quite uncontroversial. We take these facts as evidence that quality-denoting nouns, like ordinary mass nouns, have a mereologically structured denotation. Additional strong evidence for this claim that the denotations of property concept lexemes are so structured comes from an obscure corner of the grammar of Ulwa, which we discuss next.

6.1.2 Ulwa double –ka

The Misumalpan language Ulwa, discussed in detail in previous chapters, has a pattern of double possession with property concept roots, which we have to this point not discussed, which provides a novel argument that property concept roots in the language have a mereologically-ordered denotation. Given the relationship of the Ulwa facts to possessive property concept predication in other languages, we also take this as an argument for the mereological structuring of quality denotations more generally.4

The starting point for the discussion is the fact, discussed extensively in Chapters 2–4, that in Ulwa, predication of property concept lexemes, as in (15a), draws on morphosyntactic material otherwise syncretic with NP-internal possessive marking, as can be seen through comparison with (15b).

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Our analysis of this, discussed extensively in previous chapters, is that Ulwa property concept lexemes are bound quality-denoting roots, to which possessive material suffixes to create a predicate of individuals. A sentence with such a word predicated of an individual a is true if a has some portion of quality ranked high enough in the total preorder of portions of quality denoted by the property concept root from which the predicate is derived.

There are two puzzling constructions of Ulwa that we have not yet discussed to which this analysis does not extend naturally, and the correct truth conditions of which it fails to capture. The first, illustrated by the data in (16), has property concept nouns in –ka occurring in the complement of the possessive verb watah. As (17) shows, the same position can host a bare root. The occurrence of a bare root in this environment is unsurprising on our theory, since watah is a possessive verb and so makes the same semantic contribution as –ka. The occurrence of a derived property concept noun, however, is more surprising, since the presence of the possessive verb watah looks as though it renders –ka semantically redundant (or vice versa).

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As we discuss in Koontz-Garboden and Francez (2010: 235), versions with and without –ka seem to be in free variation in this position, with no clear difference in meaning. The question is how this could be the case.

A related second mysterious construction is one in which property concept nouns in –ka occur as heads of possessive noun phrases, as shown in (18).

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The two constructions in (16) and (18) seem surprising at first in light of the analysis developed in previous chapters, since they each involve two instances of a possessive element. In (16), the possessive morpheme –ka co-occurs with the possessive verb watah ‘have’, and in (18), it co-occurs with another instance of –ka. If possessive semantics is required to turn root-denotations into predicates, what is the role of the second possessive marker? In what follows, we discuss these constructions in more detail. We refer to the construction in (16) as the –ka watah construction, and to the one in (18) as the double-ka construction. The answer we propose to the question why such constructions have double possession, builds directly on the analysis of Ulwa property concept sentences developed in previous chapters, and makes direct appeal to mereological structure in the denotation of Ulwa property concept roots.5 The analysis takes as its point of departure the fact that in ordinary Ulwa possessive noun phrases, the possessive relation contributed by –ka can be a mereological part–whole relation. We show that taking –ka to express the mereological relation-ordering qualities when it combines with property concept roots leads to a correct analysis of both problematic constructions. Under this analysis, the view of the Ulwa pattern as semantically motivated is not only maintained, but strengthened, since the possessive affix –ka emerges as having a range of interpretations that, we show, is natural given what is known about possession in Ulwa and crosslinguistically. These facts thereby constitute a strong argument not only for the general analysis of the Ulwa facts argued for in this book, but more specifically for mereological structuring in quality-denoting lexemes.

6.1.2.1 –ka watah constructions

The –ka watah construction is exemplified in (16) and by the additional data in (19).

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If we naively apply the analysis developed in the previous chapters to these data (ignoring the interval argument, for simplification), –ka and watah have the denotations in (20), –ka denoting a relation between properties and individuals that possess them and watah denoting a relation between individuals standing in the possessive relation to one another.

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Such an analysis, blindly applied to the facts discussed in (19), assigns to the sentence in (21) (a simplified version of (19a), the truth conditions in (22), where thickness is a constant of type p.

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These truth conditions ensure that Jessica’s hair has something thick, but not that is has thickness, that is, not that it is thick (recall that the analysis equates having thickness with being thick). Koontz-Garboden and Francez (2010: 237) conjecture that such examples might be viewed as analogous to English examples like (23a), which is roughly equivalent to (23b).

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However, this is not a particularly illuminating analogy, as the relevant English examples are very limited, as shown by the oddity of (24a,b).6

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Furthermore, the desired equivalence with (23b) cannot be achieved without a prepositional phrase, as shown in (26).

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A better analysis of these constructions would not make them exotic in this way, but rather generate a meaning for them consistent with the ordinary predicational meaning that they seem to have.

6.1.2.2 Double –ka constructions

As shown in (15b), the possessed noun in an Ulwa possessive noun phrase, is affixed with –ka. Since words resulting from affixing –ka to an Ulwa property concept root are, categorially, nouns (see Koontz-Garboden 2007: ch. 6), they too can head a possessive noun phrase, in which case they are again suffixed with –ka. This results in ‘double’ –ka suffixation, as illustrated in (26).

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That this second occurrence of –ka marks possession on the head of a possessive NP is clear from its morphological characteristics. On the head of a possessive noun phrase, –ka agrees with the possessor in person and number, as shown in (27). Precisely the same is true when the possessed noun is made of a root suffixed with –ka, as in double –ka constructions, as shown by the full paradigm in (28) for the root sang– ‘green, alive’ given in Green (1999: 81).7

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Examples (27) and (28) exemplify a well-known prosodic condition on the position of –ka in possessive noun phrases (see e.g. McCarthy and Prince 1998), namely that –ka can be infixed to the leftmost iamb of the host rather than suffixed.8 For example, sang-ki-ka is the first singular possessive form of the word sang-ka.

What meaning does our analysis assign to such double-possessed PC words? The starting point is obviously the denotation for –ka in each of the instances discussed above—as suffix to a property concept root, and as marker of possession on a possessed noun in a possessive NP. These share a common lexical core, namely the possessive relation, but differ type-theoretically, as discussed in Chapter 3 (see there n. 21). For the purposes of this discussion, we assume the denotation for root suffixing –ka in (29), again leaving to the side the interval variable, which is irrelevant for this discussion. The denotation we assume for possessive NP –ka is in (30)—it takes a nominal meaning, and creates a relation between individuals x and y, where y is a member of the set denoted by the noun composed with.9

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With this as background, the meaning our analysis assigns to double –ka marked property concept roots is exemplified in (31), with the example bilam sikamhkaka ‘fish’s stench’.

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Again, this does not correspond to the interpretation that such noun phrases seem to have. Intuitively, the noun phrase bilamh sikamhka should receive an interpretation matching its gloss, that is, it should refer to the fish’s stench (or the set of the fish’s stench portions, or the set of sets containing the fish’s stench portions). Instead, on this analysis, it denotes the set of smelly things the fish has. For example, (26) on this analysis says that something stinky that the fish has alerts me to the fact that Bob has fish, rather than saying that the fish’s stench alerts me of this.

In §6.1.2.3 we show that the problem lies in not fully appreciating the consequences of the mereological ordering of quality denotations and in having an oversimplified understanding of possession. Once we have a more nuanced understanding of possession, it can be shown that these facts are actually predicted by the analysis, particularly when we understand more fully the consequences of the mereological ordering of quality denotations.

6.1.2.3

The alternative analysis

We have argued in the preceding chapters that possessive predicating property concept lexemes, Ulwa property concept roots among them, denote qualities. These are conceptualized as masses, and are modelled on a par with the denotations of mass nouns in the algebraic approach of Link (1983), as discussed in detail in Chapter 3. The key intuition of our analysis is that the possessive material in Ulwa property concept predication is required in order to turn quality-denoting property concept lexemes into predicates of individuals.

The point of departure for a better analysis of –ka watah and double-ka constructions is the observation, made repeatedly in the literature (see inter alia Barker 1995; Jensen and Vikner 1996; Heine 1997; Partee 1997; Vikner and Jensen 2002; Tham 2006 and references therein) that, crosslinguistically, nominal possessive morphology is highly underspecified semantically. In particular, among the relations introduced by English nominal possessive morphology are alienable possession (including ownership) (32), and a range of relations of inalienable possession or integral part/whole relations (33).

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Why it is that possessive morphology functions to introduce these semantic relations, that is, what makes alienable and inalienable possession or integral parthood a natural class, is a very interesting question which we do not attempt to address here. What is important for our purposes is that, unsurprisingly, the same situation obtains also in Ulwa. Examples (34a) and (34b) show that –ka is used to introduce ownership relations and part/whole relations, respectively. Additional part/whole examples are given in (35).

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Of particular interest is example (35c), which clearly demonstrates that among the relations expressible by –ka is that between masses and their mereological parts.

Once it is recognized that the relation ≼, the mereological relation ordering qualities (see Chapter 3 for details), is one of the possible specifications of the underspecified possessive relation π, the correct interpretations are derived by the existing analysis. Portions of a quality bear ≼ to other portions of the same quality, and they bear another possessive relation, for which we use the symbol R, to individuals that bear them. R and ≼ differ from one another at a minimum in the latter being a transitive relation. With this as background, we have the formal tools in place to give a more satisfactory analysis to the two constructions of interest.

6.1.2.4 Reanalyzing –ka watah constructions

We assume the same denotations for –ka and watah, namely the one given in (20) above. Assuming the possessive relation π can be resolved into different more specific relations as discussed at 5.1.2.3, combining –ka with a property concept root can lead to two different interpretations, tied to the realization of π as R or ≼. If π is resolved to R, the possessive relation that holds between individuals and (portions of) qualities they have, the derived property concept noun denotes the set of individuals that have some portion of the quality named by the root. This is the meaning of such nouns in predicative position, as familiar from previous chapters, and as given in (36). The derivation is shown in (37).

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When π is resolved to ≼, the resulting noun denotes the set of things that have a portion of the quality denoted by the root as a mereological part. This is what we suggest happens in –ka watah constructions. As an example consider again (19), repeated in (38).

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Resolving the relation introduced by –ka to ≼ gives the noun tubak-ka the meaning in (39).

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In this case, the semantic effect of –ka affixation is to map the quality contributed by the root to the set of things that have some portion of the quality in question as a ≼-part. However, this set is simply the quality itself, since, by the definition of ≼ as a relation that orders qualities, all and only portions of a quality have portions of that quality as ≼-parts. This is stated in (40), using S as a metavariable for qualities and s, s′ as metavariables for portions.

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Resolving π to ≼ thus leads to an interpretation for the derived noun which is identical to that of the root, namely the quality named by the root. The full derivation of (38) is given in (41).

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Example (41d) says that Jessica’s hair bears the R relation to something that bears the ≼ relation to a portion of thickness. Because anything that bears ≼ to a portion of thickness is itself a portion of thickness, what Jessica’s hair bears R to is a portion of thickness. On this interpretation, then, (38) simply says that Jessica’s hair has a portion of thickness, that is, that it is thick. More generally, constructions in which the complement of watah is a root receive exactly the same interpretation as –ka watah constructions, in which that complement is a noun derived from a root by –ka suffixation.10 This not only yields the desired truth conditions, but nicely derives the observation that there is genuinely free variation between roots (e.g. tubak) and –ka-suffixed property concept nouns (e.g. tubak-ka) in the complement of watah ‘have’, a fact illustrated above by the data in (16) and (17). Furthermore, while the forms are in free variation in contexts in which they can both occur syntactically, they are not generally in free variation. For example, the double –ka construction discussed below features possessive noun phrases in which the possessed noun denotes a quality. Since roots are not nouns and cannot head possessive noun phrases in Ulwa, they are barred in this construction.11

6.1.2.5 Reanalyzing double –ka constructions

All nouns heading a possessive NP are marked with possessive NP –ka (42a). The same is true of the nouns derived from roots by suffixing –ka (42b), giving rise to double –ka constructions. These constructions pose a similar problem to –ka watah constructions, and their semantics similarly becomes straightforward when π is interpreted as ≼ when combining with a root.

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We propose that in the head noun of (42b), sikamh-ka, –ka contributes the relation ≼. In this case, as was shown in (39), the meaning of the derived noun is equivalent to that of the bare root—both denote the quality named by the root. Thus, the noun sikamh-ka simply denotes the set of portions of stench. In combination with the possessor noun bilam ‘fish’, the entire possessive NP denotes the set of portions of stench that the fish bears the relation R to, or in other words, the fish’s stench. Example (43) shows the derivation of (42b).

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The key step in this derivation is (43b), in which the possessive relation contributed by –ka is resolved to ≼. This is what guarantees that the denotation of sikamhka is identical to the root sikamh–, allowing the denotation of the full possessive noun phrase to be, as in (43d), the set of stench portions that the fish has. Thus, our reanalysis of the data now assigns to the sentence (26a) above its most salient reading, namely that the fish’s stench (rather than something stinky that the fish has) alerts the speaker that Bob has fish.12

6.1.2.6 Concluding remarks: Ulwa double possession as evidence for mereological ordering of qualities

In the preceding, we discussed two constructions in Ulwa in which property concept roots are implicated, and whose interpretations, on first blush, seemed rather mysterious, given the analysis we have developed of Ulwa at various points throughout this book. We showed, however, that once one takes seriously both the semantics of the possessive relation, and especially the fact that qualities, the denotations of Ulwa property concept roots, are mereologically ordered, the interpretations that these constructions have fall out as a direct consequence. We take the existence of these constructions and their associated interpretations, as a consequence, as strong evidence in favor of the approach to qualities we have developed in this book—that is, as having a denotation much like mass nouns, and crucially with mereological ordering.

At the same time, on the analysis we have developed, qualities are not exactly like the denotations of mass nouns. In particular, we have argued that they are size-ordered, and that this size-ordering is directly responsible for their gradable behavior. We do not believe that the denotations of ordinary mass nouns, by contrast, are ordered in this way. In §6.2 we discuss empirical arguments for this position.

6.2 Qualities are totally (pre)ordered

This section motivates our assumption that quality nouns differ from other mass nouns in that the qualities they denote, unlike the masses denoted by other mass nouns, are totally ordered by size. The motivation comes from a set of environments, some observed in previous literature and some novel, in which mass nouns and quality nouns do not pattern together. We argue that these environments plausibly involve sensitivity to the presence or absence of a total order, and outline an analysis for each case.

6.2.1

Negative quantifiers in Romance

Tovena (2001), building on observations made in Van de Velde (1996), points out that the nominal complement of certain negative quantifiers is an environment in which there is a contrast between two classes of mass noun in Italian and French. The pattern is the one shown for Italian in (44), from Tovena (the French parallel involves the quantifier aucun ‘no’).

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The generalization pointed to by (44) is that the quantifier nessun selects uniformly against plurals and for singular count nouns, but distinguishes two classes of mass noun. While nouns like vino ‘wine’ are illicit, others, like coraggio ‘courage’ are fine.13

According to Tovena (2001: 568), descriptively speaking, the class of mass nouns that are licit with nessun are ‘abstract mass nouns’, and includes property concept nominals, such as coraggio ‘courage’ in (44b), which is also possessive predicating (Peyronel and Higgins 2006: 31). Tovena proposes an analysis of this pattern according to which it hinges on a contrast between ‘extensive’ and ‘intensive’ quantities, notions that she elaborates in substantial and illuminating, if not fully explicit, detail.

In fact, the empirical picture regarding property concept nouns with nessun (and its variants nessuno and nessuna) seems to us to be fairly unclear. The intuitions of native consultants and the results of searches on Google coincide in indicating that common possessively predicating property concept nouns in Italian, like fame ‘hunger’, sete ‘thirst’, or caldo ‘heat’, are less acceptable with nessun than others, like paura ‘fear’ and coraggio ‘courage’. For example, most of our consultants reported the strong judgments in (45).

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One consultant, however, accepted all three. Google searches clearly show that paura ‘fear’ is far more common in collocation with nessuna than fame or sete. While all three are in fact attested, property concept sentences such as those in (45) with nessuna are practically unattested for fame and sete.14 It therefore seems to us that more detailed empirical work is required in order to establish what precisely is the class of expressions carved out by Tovena’s generalizations, and that property concept nouns do not behave uniformly in the complement of nessun. If this is correct, then any analysis that would derive the pattern from a general semantic feature of property concept nouns would overgenerate.

Nevertheless, for current purposes it is interesting to ask whether our assumption that quality-denoting property concept nouns differ from mass nouns like acqua ‘water’ in being totally ordered by size could account for Tovena’s generalization if it did turn out to apply uniformly to property concept nouns. We propose that it could. Specifically, we propose that nessun is a quantifier that requires a domain of discrete entities, that is, entities that do not overlap. This means that nessun can combine with expressions that denote exclusively in a domain of atom, immediately explaining (in a completely standard way and following Tovena) the restriction against plurals and mass nouns. The acceptability of property concept nouns is explained precisely by the assumption that qualities are totally ordered. The total preorder ≤ induces an equivalence relation on qualities, intuitively thought of as is the same size as, partitioning each quality into sets of portions of the same size. Each such equivalence class is discrete. The mereological partial order on masses does not induce an equivalence relation on parts of masses, because it is antisymmetric. Two distinct parts of water w, w1, for example, can, by definition, not be parts of one another,15 in contrast to two portions of a quality, which can be ‘bigger than or equal to’ each other (i.e. be the same size). Mass nouns, therefore, present no discrete entities for nessun to count.

This kind of explanation allows a simple statement of the semantics of sentences like (45c). This sentence asserts that the speaker stands in the have relation to no equivalence class of portions of the quality fear. It is reasonable to assume, and we do in fact assume this in Chapter 3, that any individual who has any portions of fear has exactly one maximal portion of fear. This maximal portion of fear is in exactly one equivalence class of portions of fear. We posit that an individual a has an equivalence class CQ of portions of a quality Q if and only if there is a portion p ∈ CQ such that π(a,p). The sentence in (45c), then, asserts that the speaker has no equivalence class of fear, and thus entails that the speaker has no portions of fear. From the fact that any individual has one maximal portion of any quantity, it follows that any individual either has one equivalence class of, say, fear, or else she has none. We conjecture that the uniqueness of possessed equivalence classes explains why quality nouns that can occur with nessun cannot occur with any other count quantifiers, such as numerals and other cardinals, as well as the fact, observed by Tovena (but largely mysterious on her analysis), that although mass nouns like coraggio ‘courage’ can be used with singulative quantifiers like nessun, they cannot be used with all singulative quantifiers. For example, corragio is unacceptable as the restriction for qualche ‘some’.

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This follows directly from the fact, discussed, for example, by Crisma (2012), that qualche, even though it combines exclusively with morphologically singular nouns, can be used only with plural reference, as shown in (47). If singulative quantification with quality-denoting nouns is over equivalence classes, and every portion of a quality is in exactly one class, then the domain of quantification for singulative quantifiers with quality nouns never contains a plurality of classes.

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Creation of equivalence classes is not the only way to create discrete meaning from a mass noun. Ordinary mass nouns are somewhat famously known, as discussed in §6.1.1, to allow kind readings in count contexts, as for example in (48).

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Kinds are certainly discrete in the sense that they do not have parts that might overlap. If ordinary mass nouns can be coerced to atomic kind readings, then we might expect that they could occur with nessun on a kind reading. This does seem to be the case, as evidenced by the naturally occurring (49).

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The upshot of this brief discussion of Italian nessun is, first, that much more work is required to establish whether this quantifier indeed distinguishes between different classes of mass noun and what these classes are exactly. Presumably, the same holds of the parallel case in French, though we have not examined the French data in any detail. Second, and more importantly for current purposes, assuming the empirical picture is roughly as proposed by Tovena, and that nessun distinguishes quality-denoting nouns from other mass nouns, our assumption that qualities are totally ordered by size whereas mass nouns are not provides an intuitive explanation of this.

6.2.2 Exclamatives

Another context discussed by Tovena (2001: 573) in which the same two classes of mass nouns emerge is wh-exclamatives. Exclamatives, generally speaking, are sentences used “to express an affective response to what is taken to be a fact” and “convey the speaker’s surprise that some present situation is remarkable” (König and Siemund 2007: 316). As is well known at least since early studies such as Elliot (1974) and Grimshaw (1979), exclamatives are a formally distinguished sentence class, differing from so-called ‘sentence exclamations’ (50) in that rather than taking the form of a declarative sentence, they take some other form, such as that of a question, an inversion structure, or just a noun phrase, as shown by the data in (51) (all from Rett 2011: 412).

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Our focus here is on wh-exclamatives. Aside from the formal difference, they differ from sentence exclamations also in their discursive effects. In particular, they have what Castroviejo Miró (2008) calls an expressive content and a descriptive content, neither of which seems to be asserted, but the exact theoretical status of which is still being negotiated in the literature (for Zanuttini and Portner 2003: 40 and Rett 2011: 414, the descriptive content is presupposed, but Castroviejo Miró (2008) and more recently Chernilovskaya and Nouwen (2012) argue that the discursive effects of exclamatives, regarding both the descriptive and the expressive content, are more complex). For example, (51a) has the descriptive content that the cakes John bakes are delicious to a high degree, and the expressive content that the degree to which these cakes are delicious has some emotive effect on the speaker (such as surprise).

A key property of wh-exclamatives is that their descriptive and expressive contents always involve a gradable notion. This gradable notion can be explicitly mentioned, as in (52a), or it can be left for contextual inference, as in (52b) (Milner 1978; Gérard 1980; Castroviejo Miró 2006; Rett 2011; Chernilovskaya and Nouwen 2012).

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An observation noted for Italian by Van de Velde (1996) (as reported in Tovena 2001) and which holds also for English, is that wh-exclamatives with plural count nouns and ordinary mass nouns cannot generally be associated amount readings. By this we mean that the gradable property involved in their descriptive and expressive content cannot naturally be resolved to cardinality or quantity. For example, (53a) and (53b), featuring plurals, can be used to exclaim that Sandy has very beautiful dogs or that the neighbors have very well-behaved children; they cannot be used to exclaim that Sandy has (surprisingly/impressively … ) many dogs, or that the next door neighbors have (surprisingly/impressively … ) many children.

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Exactly the same is the case for ordinary mass nouns, as demonstrated in (54). While (54a) can be used to exclaim that the Aegean has very pleasant (clean, etc.) water, and (54b) can be used to exclaim that the Plastic Albatros bar has excellent whiskey, these sentences cannot be used to exclaim that there is a lot of water in the Aegean or that the Plastic Albatros has a lot of whiskey.16

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This behavior of mass nouns (and plurals) in wh-exclamatives contrasts sharply with that of quality-denoting property concept lexemes. With such lexemes, the amount reading is by far the most unmarked one, as shown by the sentences in (55). A speaker uttering (55a), (55b), or (55c) is committed to Kim having much courage, much beauty, or much wisdom respectively, and her utterance is paraphrasable as a sentence exclamation that is explicitly about amount.

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The contrast between quality-denoting property concept lexemes and mass nouns comes out particularly clearly with contrastive minimal pairs. The sentences in (56) are truth-conditionally equivalent, whereas the sentences in (57) are not.

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The same observation can be made contrasting what-exclamatives with how much-exclamatives, where an amount is compositionally introduced. With property concept nominals, the two exclamative types are equivalent, and both are further equivalent to a corresponding adjectival how-exclamative if there is one. This is shown in (58). With ordinary mass nouns, however, this equivalence breaks down for most native speakers, as shown in (59).

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These data clearly suggest that there is a contrast in need of explanation.17

The contrast between mass nouns and quality nouns in English and Italian can be replicated in other Romance languages, such as Catalan, and in unrelated languages like Hebrew. For example, in Hebrew, a which-exclamative with a property concept nominal like ko’ax ‘strength’ is truth-conditionally equivalent to a how much-exclamative, as shown in (60). By contrast, a similar pair of sentences with the mass noun mayim ‘water’ is not truth-conditionally equivalent. With eyze ‘which/what’ in (61a), the exclamative gives rise to a property reading, while with kama ‘how much’ as in (61b), the exclamative gives rise to an amount reading.

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Precisely the same pattern is observed in Catalan. A wh-exclamative gives rise to an amount reading with a property concept nominal (62a), but is odd with an ordinary mass noun (62b) (Elena Castroviejo Miró, p.c.).

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The emerging generalization is that wh-exclamatives are an environment that differentiates quality nouns and other mass nouns. While the former are most natural on an amount reading, the latter, when acceptable, only have a contextually determined property extent reading.

While we do not attempt here anything like a worked-out analysis of exclamatives, we do propose that this contrast receives a natural explanation as a consequence of the assumption that qualities are preordered by size whereas mass nouns are not. As mentioned above, the descriptive and expressive contents of wh-exclamatives are always built on a gradation. Quality-denoting property concept lexemes lexically provide a scale, namely the scale created by the preorder ≤. Mass nouns, on the other hand, provide no such scale lexically, and cannot therefore form the source for the descriptive or expressive content of an exclamative. Consider, for example, an exclamative such as (55a) above, repeated in (63).

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Intuitively, this sentence exclaims something about Kim’s courage, which, given the semantics elaborated in Chapter 3, is a portion of courage of a certain ‘size’, that is, with a certain position in the ≤-ordering. The descriptive content is, roughly, that this portion is ranked high on ≤, and the expressive content that it’s ranking on ≤ has an emotive effect on (impresses, surprises, etc.) the speaker. Since position on ≤ is something that all portions of qualities have inherently, the exclamative ‘has access’ to this gradable property.

Non-quality-denoting mass nouns, as discussed in §6.2.1, are partially ordered by a mereological part–whole relation. This partial order does not lend itself to gradability—there is no sense in which certain things are ranked higher than others on the part–whole relation, first and foremost because the ordering is partial, and it is not the case that any two given parts of, say, whiskey, are ordered relative to one another. Furthermore, and consequently, there is no sense in which a part of whiskey’s ‘position’ in the part–whole structure is something that a speaker has any way of perceiving and being impressed by, since nothing about the part of whiskey discloses anything about such a position. In contrast, speakers are, presumably, able to perceive, or at least we speak as if we are able to perceive, a person’s degree of courage (in our terminology, the equivalence class into which a person’s maximal courage-portion falls) from her behavior. Of course, the denotations of mass nouns certainly are measurable, and we convey quantitative information about masses all the time, for example, in sentences like (64).

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Quantities of masses, however, are not given by their part–whole structure inherent in the denotation of mass nouns, but rather imposed externally by such measures as volume, weight, etc. Such measures are not inherent to the lexical entry of a mass noun, and this, we submit, is why wh-exclamatives cannot pick up on amounts of mass substances without explicit contextual cues, and perhaps also a semantic coercion process which maps part of masses to a totally ordered scale of amounts by means of a measure function (as assumed in much of the literature: see, for example, Wellwood 2015 for an extensive discussion).

6.2.3 Behavior under modification

Tovena (2001: 572) observes that there are gradable modifiers that target the same class of Italian mass nouns as can occur with nessun, that is, her class of abstract mass nouns. We show in what follows that this is the case also in English, and that such modifiers, like wh-exclamatives, distinguish between quality nouns and ordinary mass nouns in a way explained by the presence or absence of the size ordering. Our starting point is work by Morzycki 2009; 2012, who observes that much as there are gradable and non-gradable adjectives (see e.g. Bolinger 1972: 21), there are also gradable and non-gradable count nouns, and that the difference is diagnosed by the ability to be modified by gradable modifiers. We show that his observations extend to mass nouns as well, in precisely the way that is expected given what was said in this section thus far: while quality nouns are gradable, mass nouns are not. This fact provides key evidence for our assumption that the two classes differ order-theoretically. Modifiers like those documented by Morzycki are sensitive to the presence of a total order, and quality nouns have denotations that are totally ordered by size, whereas mass nouns do not.

Morzycki documents three classes of adnominal gradable modifiers. We leave to the side what he calls (Morzycki 2012: 191) the prototypicality modifiers real and true, which we believe, along with him, to be doing something other than accessing scale structure in the lexical semantics of a noun. The two classes of modifiers which are relevant here are his big class and utter class. Morzycki argues that the ability of a noun to appear in one class or another is a consequence of its dimensionality, namely whether the noun is gradable along a single dimension or along multiple ones. While we are skeptical of this line of explanation for the contrast, for reasons explained in n. 18, we agree with Morzycki that both classes diagnose gradability in the lexical semantics of nouns. Crucially, both classes distinguish quality nouns from ordinary mass nouns in the way predicted by Morzycki’s claim that these modifiers diagnose gradability, and by our assumption that having denotations ordered by ≤ is what makes quality nouns gradable.

The first class of modifiers includes big, huge, and major. The observation is that, on a property extent reading, distinguished from the irrelevant dimensional reading available for big and huge, some nouns can be modified by these modifiers (65) and others cannot (66).

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As Morzycki’s work and these examples make clear, many nouns that can be modified by this class of modifiers are count nouns. We remain agnostic as to how gradability with count nouns should be formally implemented. Morzycki’s point is that the noun phrase big sportscar in (66b) cannot be used to describe a sportscar that is in some way more of a sportscar than what normally counts as a sportscar. This contrasts sportscar with nouns like disaster or idiot. The phrase big idiot can, and normally would be, used to describe an individual who is more of an idiot than other idiots, and the phrase major disaster would normally be used to describe a disaster which is more disastrous than others.

Alongside this class of modifiers there exists another, consisting of the modifiers utter, complete, absolute, outright, which Morzycki (2012: 194) shows are more restricted in the class of nouns that they modify. This is exemplified in (67) and (68).

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Like the modifiers in the big class, those in the utter class can modify nouns like disaster and idiot, but fail to modify nouns like American and sportscar. Unlike the modifiers in the big class, however, utter modifiers cannot modify nouns such as smoker or basketball fan. Morzycki (2012: 193–4) argues that this contrast, too, has to do with multidimensionality: smoker and basketball fan are multidimensional, whereas nouns like idiot and disaster are not. In relation to idiot, Morzycki claims that “there is really only one property that makes one an idiot: idiocy. This is not to say that idiocy is perfectly indivisible. One can be an idiot about different things, or in view of different things, or to different degrees. But the crucial ingredient, idiocy, remains the same” (Morzycki 2012: 194). Similarly, in relation to disaster, “there are different reasons why something might be a disaster, but the sole criterion for determining whether something is a disaster is unambiguously disastrousness” (Morzycki 2012: 194). As with the big class modifiers, we are skeptical about the multidimensionality line of explanation of why utter modifiers differentiate between count nouns, not least because we are not fully convinced of the unidimensionality of nouns like idiot. What is clear, however, is that both big class and utter class modifiers diagnose gradability in nouns.

With this as background, we observe that the modifiers Morzycki documents also separate quality nouns from mass nouns, in the expected way. Many of those nouns that we claim are quality nouns and that therefore have ≤-ordered denotations are acceptable with both classes of modifiers:18

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Ordinary mass nouns, by contrast, are quite straightforwardly unacceptable:19

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Our proposal is that these modifiers are sensitive to the total ordering in the denotation of the noun they modify. Just like a big idiot is a predicate that holds of an idiot who outranks other idiots in idiocy, so big beauty is a predicate that holds of a portion of beauty that outranks other portions of beauty on the ≤ ordering. Again, it is not crucial here to attempt denotations for all of the relevant modifiers, not least because it is a matter in need of further research how exactly they differ from one another (see n. 18 and discussion earlier in this section). What is clear, however, is that they all require gradability of their modifiand, and that the ≤-relation-ordering qualities makes quality nouns gradable. Essentially, big as a nominal modifier has a semantic effect roughly similar to that of an adjectival intensifier such as very. Something that has big or absolute beauty is something that is very beautiful. We propose (73) as a first pass at a denotation for the gradable modifier use of big, where P≤ is a predicate with a totally ordered extension, and ! is a predicate modifier mapping the extension of any gradable property to a contextually determined subset thereof, consisting only of those elements that are ranked higher than a contextually supplied lower bound on the ordering associated with the modified property.

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Whether a denotation along these lines is ultimately defensible, the facts reported in this section constitute strong evidence in favor of our proposal that quality nouns differ from other mass nouns in having denotations that are totally ordered by size.

6.2.4 A certain modifier

Van de Velde (1996), Tovena (2001), and Hinterwimmer (under review) observe that the modifier certain (and its French equivalent) has special properties when used with certain abstract mass nouns. Hinterwimmer’s observation is that with ordinary mass nouns, as in (74), a certain triggers a kind-type reading.

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The situation is different, Hinterwimmer observes, with abstract mass nouns, his examples of which are property concept nominals, presumably quality denoting.

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Although a kind-type reading is available with these, it is somewhat marked. The unmarked reading is one wherein “a certain makes the resulting statement weaker: In [(75b)] … the speaker is intuitively understood to make a slightly less positive claim about the relevant picture than in the variant with a bare noun, and likewise for [(75b)] … ” (Hinterwimmer, under review: 7–8). That something other than a kind-type reading is available is made clear by the fact that a continuation denying a kind-type reading does not give rise to infelicity, as shown in (76). A similar continuation with a non-quality mass noun leads to contradiction (77).

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Additionally, a continuation specifying a quantity is odd with a mass noun, but fine with a property concept noun (78).

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What these data show is that a certain modification with property concept nominals gives rise to an amount reading that is not available with ordinary mass nouns. This points to exactly the same conclusion as was reached above for Morzycki’s modifiers, namely that property concept nouns are gradable in a way that mass nouns are not, and again this is explained immediately on our assumption that qualities are lexically ordered by ≤ whereas mass nouns are not. Mapping mass nouns to amounts requires a measuring function, which must be supplied compositionally, or introduced, presumably by means of coercion, by an explicit context.

6.2.5 Such

Another modifier that gives rise to amount readings with property concept nouns but not with other mass nouns is French tel/pareil ‘such’, as pointed out by Tovena (2001: 571), and observed first by Van de Velde (1996). The same contrast is found in English for such, and, as expected, it distinguishes property concept nominals from ordinary mass nouns in the same way as the hitherto discussed modifiers do, pointing once more towards our hypothesized order-theoretic difference between qualities and masses. The contrast in English is demonstrated by contrasting (79) with (80).

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Examples (79a,b) are statements about large amounts (of courage, beauty). Both sentences can be paraphrased with so much replacing such. This is not the case for (80), which can be about kinds, but not about amounts. Neither sentence in (80) can be paraphrased with so much replacing such. The contrast is brought out clearly with the minimal pairs in (81). While (81a) is perfectly coherent, (81b) is a contradiction.

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As with the previous cases, this contrast in the availability of amount readings is immediately explained by the assumption that property concept nouns denote qualities and that qualities, unlike masses, are totally ordered by ≤.

6.2.6 Wolof degree modifiers and comparatives

The contrast between property concept nominals and ordinary mass nouns emerges quite saliently in the Niger–Congo language Wolof, in a number of contexts recently noted and documented in Baglini (2015). These contexts include the behavior of gradable modifiers, comparatives, and degree questions. We discuss these areas in turn, drawing on Baglini’s rich empirical observations.

Wolof has two classes of property concept lexemes. The first is a class of non-possessive predicating predicates that behave like intransitive verbs. This can be seen by comparing (82) with (83), an ordinary intransitive verbal sentence. The key observation is that both take verbal inflectional morphology, and lack any copula or possessive morphosyntactic structure (see also discussion in McLaughlin 2004).

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This pattern of predication contrasts with that exhibited by the second class of Wolof property concept lexemes, which are nominals. As shown by (84) and (85), Wolof property concept nominals are possessive predicating.

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The analysis we have developed in previous chapters extends straightforwardly to the Wolof data. We assume that possessive-predicating property concept lexemes in Wolof are quality denoting, and that in virtue of such a denotation trigger possession in predicative constructions. We also assume that like quality-denoting property concept lexemes in other languages, their denotation is ordered by ≤, and that this accounts for their gradable behavior. In the sections that follow we show, drawing on Baglini’s data and empirical argumentation, that Wolof property concept nominals contrast with ordinary mass nouns in precisely this property—while the former exhibit behaviors consistent with having a ‘size’ ordering, the latter do not.

6.2.6.1 Gradable modifiers

The Wolof degree modifier lool can modify property concept verbs (86a) as well as verb phrases headed by the possessive verb am ‘have’ with a quality-denoting complement noun (86b). However, it is unavailable with verb phrases headed by the same verb when the nominal complement is a mass noun (87).

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Our analysis of these facts takes as its point of departure the analysis of quality possession in Ulwa in Chapter 3. A central problem in that discussion was dealing with the contextually sensitive nature of quality possession in sentences such as (88).

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As discussed at length in Chapter 3, in a sentence such as (88) the amount of dirtiness the shirt needs to have to make the sentence true will vary from context to context. In order to capture this, we gave the Ulwa possessive suffix –ka a denotation that resulted in such sentences denoting context-sensitive propositions—functions from intervals of portions to truth-values, as shown for the denotation of (88) in (89).

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The idea is that the context-sensitivity of property concept sentences is captured in terms of intervals of qualities, where such intervals have a lower bound (see Chapter 3 for the details). Different values for the interval variable I in (89) determine different cut-off points in the ≤ ordering, corresponding to minimum standards for dirtiness. Such size-ordered intervals of qualities also figured into our analysis of Ulwa comparatives. On that analysis, an individual x has more of some quality than an individual y if and only if there are more lower-bounded intervals in which x has a portion than there are ones in which y does. As shown in Chapter 3, this is the case if and only if x’s maximal portion of the quality outranks y’s on ≤.

With this as background, we now return to Wolof lool ‘very’. The intuition underlying our analysis of lool ‘very’ is that it manipulates the interval of the quality it modifies. Informally, a verb phrase composed of the possessive verb am and a property concept nominal denotes a relation between individuals and an interval of a quality. For example, am xel ‘have wit’, describes a relation between individuals and intervals of wit, a relation which holds if and only if the individual has a portion of wit that is in the interval, and hence has a portion of wit that is ranked higher on ≤ than the standard set by that interval, that is, the interval’s lower bound. The effect of lool on such a VP denotation is to restrict the intervals involved to those with a lower bound that, in the context, is considered very high, higher than the lower bound for having wit in the context (cf. Wheeler 1972: 325 on English very).

We capture this intuition formally by making reference to the interval argument of a predicate. The VP am xel ‘have wit’ in our analysis has the denotation (90).

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The denotation we suggest for lool based on this proposal is in (91), where α is a variable over relations between individuals and intervals of qualities, and ! is the modifier we used in our semantics for big in §6.2.3, mapping any interval of a quality (including the quality itself) to a subset thereof, the lower bound of which is contextually considered to be very high.

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The derivation in (92) shows the meaning derived for (86b) under this analysis.

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This proposal makes the sentence in (86b) true if and only if Awa has a portion of wit in a subinterval of the wit quality which includes all and only portions that, in the context, are ranked very high on ≤.

This analysis enables a straightforward explanation for why lool modification is restricted to just those VPs it is restricted to. lool modification is restricted to gradable predicates, a requirement which is intuitive, given its translation as ‘very’ and what is generally known about modifiers with that kind of meaning. In the current set-up, being gradable in Wolof means having totally ordered denotations. Specifically, lool operates on pairs of individuals and ≤-interval of a quality, and introduces the modifier !, which raises the lower bound of the input interval. Quality-denoting nouns provide such intervals. Herein lies the explanation for the unacceptability of lool as a modifier of am-VPs with an ordinary mass noun complement, as in (87). Ordinary mass nouns are partially ordered by a mereological order, but not totally ordered by size or any other total order, and do not make intervals available, correctly predicting the unacceptability illustrated by (87).

Wolof lool can also modify verbal property concept lexemes, as illustrated by the data in (86a), and we therefore propose that such lexemes have, as a matter of their lexical meaning, the same denotations as are achieved compositionally with property concept nominals. That is, they denote relations between individuals and intervals.20 A property concept verb such as rafet ‘to be pretty’ has a denotation like that in (93).21

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Further evidence for our analysis of the modifier lool comes from the additional observations made by Baglini in relation to comparatives, which also group Wolof am-VPs with property concept nominals together with property concept stative verbs. Before moving on, we reiterate the main point, which is that the behavior of lool points to the same conclusion as we have drawn on the basis of a range of other facts in other languages discussed in this chapter, namely that what is responsible for the differential distribution and interpretative possibilities available to property concept nouns and other mass nouns is the order-theoretic properties of their denotations. Qualities are ordered by ≤, masses are not.

6.2.6.2 Comparatives

Wolof has two kinds of comparative, both ‘exceed’ comparatives in the typology of Stassen (1985). One is formed with the verb ëpp, while the other is formed with a verb gën. Comparatives with gën are like the gradable modifier lool discussed in §6.2.6.1 in that they group am VPs with a nominal property concept complement with verbal property concept lexemes, to the exclusion of am VPs with ordinary mass noun complements. This is not to say that ordinary mass nouns cannot be used in comparatives; they can, but only with ëpp, which can be used with any mass or plural count noun (Baglini 2015: 140). The observation, then, is that gën, much like lool, seems to be sensitive to lexical gradability, encoded by hypothesis in the denotations of nominal and verbal property concept lexemes in Wolof through the total size preordering on qualities. The facts of both these comparatives are discussed in detail by Baglini (2015: ch. 4). We summarize only the facts related to gën here, since it is gën comparatives that provide evidence for our claim that property concept nominals come with a size ordering while ordinary mass nouns do not.

According to Baglini (2015: 140), comparatives with gën in Wolof are built based on the schema in (94), where stativity of the VP is a necessary (but not sufficient—see below) criterion.

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This schema is exemplified by the data in (95), where the stative VP is headed by a verbal property concept lexeme.

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VPs headed by transitive stative verbs are also found in this construction:

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(97) shows that VPs headed by eventive verbs are unacceptable in the gën comparative.

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As would be expected given this generalization, VPs headed by am ‘have’ with a property concept nominal complement are acceptable in gën comparatives.

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As Baglini shows, however, non-eventivity of the VP alone seems not to be sufficient for use with gën. For example, we see no reason to believe that having rice is any more eventive than having strength in (98). Nevertheless, the VP am ceeb ‘have rice’ cannot be used in a gën comparative.22

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In fact, according to Baglini, ordinary mass nouns, when used as the complement of am ‘have’, generally create VPs that are unacceptable in gën comparatives.

The starting point for our analysis of these facts is recognition that gën comparatives are at least in some cases clearly clausal (Baglini 2014), as evidenced by (100).

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We follow Baglini in generalizing the clausal analysis across all gën comparatives, and assign them the semantics we assigned to Ulwa clausal comparatives in Chapter 3. On that analysis the comparative operator kanas ‘more’ takes two clauses as arguments, each of which is assumed to denote a set of intervals. That clauses denote sets of intervals is a direct result of our semantic analysis of possessive strategies of predication, which, as noted in §6.2.6.1, works the same for Ulwa and Wolof.

A comparative on this analysis, then, compares the sets of intervals denoted by two clauses, and is true if and only if the intervals characterized by the first clause are a superset of the intervals characterized by the second (see the analysis of Ulwa comparatives in Chapter 3 for details). gën has the denotation in (101), where I,J range over sets of intervals of qualities.

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As with Ulwa comparative kanas, a comparative sentence with gën will be true just in case the set of intervals in which the standard has a portion is a subset of the set of domains in which the target has a portion. This is exemplified by the derivation of (102) in (103). Example (102) is shown to be true if and only if the set of intervals in which Binta has a portion of strength is a proper subset of the set of intervals in which Aïda has a portion of strength.

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The crux of the analysis is the same as it was for all other cases distinguishing quality nouns from mass nouns discussed in this chapter, namely that gën requires intervals. While intervals can be supplied by qualities, which are totally ordered by ≤, they cannot be supplied by mass nouns. This analysis correctly predicts, then, that gën is unacceptable with mass nouns.

In discussing the facts surrounding lool, we were led to the conclusion that Wolof property concept verbs have the same type of denotation as do verb phrases composed of the verb am ‘have’ and a property concept nominal, namely relations between individuals and domains of portions. This claim is also supported by the Wolof comparative facts. As shown in (104), gën comparatives can be formed with Wolof property concept verbs. This follows straightforwardly from our analysis if these denote relations between individuals and domains of qualities, as already suggested above. This is exemplified for (104) in (105), assuming the denotation for rafet ‘to be pretty’ independently proposed in the discussion on lool in (93) and the denotation for gën proposed in this section.

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As seen in (96), repeated in (106), it is not only property concept verbs that can be used in gën comparatives, but any stative VP, including ones involving stative transitives.

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Within the theory developed so far, the obvious route for dealing with this fact is to generalize the semantics of quality possession to all stative predicates in Wolof, associating them with denotations that relate individuals to qualities. This is a proposal with a wide (and somewhat forebidding) range of interesting consequences which we cannot explore in the context of this book, but the grammatical cohesiveness of transitive statives, property concept verbs, and am ‘have’ verb phrases with property concept complements makes it prima facie attractive in our view. In order to concretize what taking this route involves, we sketch here a preliminary semantics for stative transitives such as bëgg ‘like’. The proposal is built on the intuition that portions of qualities can stand in different relations to individuals, and that qualities can be directed at something. For example, just as individuals can ‘have’ portions of a quality, they can also be the ‘target’ of a portion of a quality. Presumably, an individual is the target of a portion of liking if the liking is directed at them, or, in other words, if they are the reason for the fact that another individual has that portion of liking.

Formally, a transitive stative verb such as bëgg ‘like’ is assigned as its denotation a function mapping properties (and, presumably, also individuals, propositions, and possibly other types of semantic objects) to relations between individuals and qualities. For example, bëgg maps the predicate jën ‘fish’ to the property of being an individual who has a portion of liking that is directed towards fish. The quality of liking is totally ordered by ≤, like any other quality. Such a denotation is given in (107), where τ is a two-place relation, intended as the ‘target’ relation.

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Among the attractive features of this kind of denotation is that it retains the logic of transitive verbs, that is, captures inference patterns characteristic of such verbs which, presumably, would be valid in Wolof. For example, it would be very surprising if Wolof speakers did not have the intuition that the Wolof equivalent of Ali likes fish entails that Ali likes something, that the Wolof equivalent of Ali likes fish and meat entails Ali likes fish, etc.

Assuming this and the denotation for gën ‘exceed’ given in (101), we derive (108) as the meaning of a sentence like (106).

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More evidence pointing in favor of this route of analysis of stative transitives such as bëgg ‘like’ comes from Baglini’s observation that, like all stative verbs, transitive statives can also be modified by lool, as shown in (109).

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The final question to answer in relation to gën comparatives is why eventive verbs are unacceptable in them, as shown in (97), repeated in (110).

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Without going into a detailed analysis that would tie us to some particular theory of eventivity and its representation at syntax/semantics interface, issues that go far beyond the scope of this book, we conjecture that the answer lies in the nature of eventhood. Standard theories of events treat eventive predicates, like ordinary mass nouns, as being mereologically ordered (Krifka 1992), raising the possibility of ruling out eventive predicates in gën-comparatives on the same grounds as we ruled out verb phrases composed of am ‘have’ and a mass noun, that is, on the grounds of not being totally ordered. Intuitively, however, eating fish more than someone else means eating fish more often, which entails a count of fish-eating events. Such a count, as discussed extensively in the literature, requires a measure function (e.g. Krifka 1989, 1990, and most recently, Wellwood 2015), and no such measure function is supplied by the eventive verb itself. Assuming, as we have been, that lexemes like Wolof gën, unlike English more, do not bring in their own measure functions, but rather rely for their interpretation on a total ordering inherent in their semantic input, it is again not surprising that they cannot modify eventive verbs.

6.3 Concluding remarks

The point of departure for this chapter is the assumption, made in our semantics of quality possession, that qualities, the denotations of possessive-predicating property concept lexemes, share with masses (the denotations of mass nouns) the property of being mereologically ordered, and differ from masses in being totally ordered by a preorder ≤, thought of as a ‘size’ relation. The motivation for assigning to qualities the ≤ ordering was that doing so was an intuitive way to formulate a semantics for possessive property concept sentences, and the motivation for assigning to them mereological structure came from some rough intuitions about what might be required in developing an account of certain patterns of inference with English nominalization. This chapter musters a range of empirical arguments for both these propositions. It shows that standard mass/count diagnostics group property concept nominals with ordinary mass nouns, and that certain puzzling facts about Ulwa possessive noun phrases featuring property concept roots can be made sense of on the assumption that qualities are mereologically structured. At the same time, there are a wide range of contexts which we have pointed to, in Germanic and Romance languages, in Hebrew and in Wolof, in which property concept nominals do not pattern with other mass nouns. These contexts, we argued, are profitably and intuitively linked to the assumption that qualities, but not masses, are inherently ordered by the total order ≤. The arguments in this chapter, then, serve as independent evidence for the model-theoretic assumptions of the transparentist theory of possessive property concept sentences assumed throughout the book.