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<?xml version="1.0" standalone="yes"?> <Paper uid="W96-0307"> <Title>i THE LEXICAL SEMANTICS OF ENGLISH COUNT AND MASS NOUNS</Title> <Section position="1" start_page="0" end_page="0" type="metho"> <SectionTitle> THE LEXICAL SEMANTICS OF ENGLISH COUNT AND MASS NOUNS BRENDAN S. GILLON </SectionTitle> <Paragraph position="0"> The systematic connection between English mass and count nouns has long been known. Those working within lexical semantics have frequently cited such systematic connections as instances which are susceptible of treatment by so-called lexical rules (Leech 1981), lexical inference rules (Ostler and Atkins 1991), or subtype coercion (Pustejovsky 1995). This paper has three aims: to present the principal morphological and semantic properties of the mass count distinction; to formulate, in terms of lexical (inference) rules, the empirical generalizations pertinent to systematic connection between English mass and count nouns; and to show how such rules fit with a syntactic and semantic theory of English common noun phrases.</Paragraph> </Section> <Section position="2" start_page="0" end_page="51" type="metho"> <SectionTitle> 1 The Mass Count Distinction in English </SectionTitle> <Paragraph position="0"> In English, the distinction between mass nouns and count nouns has clear morpho-syntactic criteria. First and foremost, English count nouns admit a morphological contrast between singular and plural; mass nouns do not, being almost always singular. For example, advice is a mass noun (*advices), whereas suggeslion is a count noun (suggestions). Correlated with this are several other criteria: cardinal numerals and quasi-cardinal numerals (e.g., several) modify count nouns, never mass nouns. For example, two drinks is acceptable, since drink is a count noun; but two milks is not, since milk is a mass noun. Moreover, little and much modify mass nouns, never count nouns; whereas few and many modify count nouns, never mass nouns. Mass nouns do not tolerate the indefinite article (*an advice), whereas singular count nouns do (a suggestion). The pronoun one may serve as the antecedent of count nouns, not of mass nouns.</Paragraph> <Paragraph position="1"> (1.1) Mary gave Jill advice and John gave her some/*one too.</Paragraph> <Paragraph position="2"> (1.2) Mary gave Jill a suggestion and John gave her one too.</Paragraph> <Paragraph position="3"> MORPttO-SYNTACTIC CRITERIA: MASS NOUN COUNT NOUN modified by cardinal numerals - + modified by quasi-cardinal numerals - + modified by indefinite article - / modified by many and few - + modified by much and less + -SG/PL contrast - + one antecedent - + While the generalizations underpinning the morpho-syntactic criteria just given have never been questioned, nonetheless they have been ignored by semanticists interested in the semantics of mass nouns: for example, Bunt (1985), Eschenbach (1992), Jackendoff (1991), Link (1983), LC/nning (1987), ter Meulen (1981), Ojeda (1993), Roeper (1983), to mention only a few. Instead, semanticists have tried to distinguish English mass and count nouns on the basis of what they denote. Two criteria have been invoked - namely, cumulativity of reference and divisivity of reference - in spite of the fact that these criteria have long been recognized as utterly inadequate. Quine (1960: p. 91) observed that, if a mass term such as water is true of each of two items, then it is true of the two items taken together; and he dubbed this semantical property of mass terms 'cumulative reference'. This characterization, while apt, does not, however, distinguish mass nouns from count nouns; for, cumulativity of reference also holds of plural count nouns. Just as it is the case that &quot;if the animals in this camp are horses and the animals in that camp are horses, then the animals in the two camps are horses&quot;; so it is the case that &quot;if a is water and b is water then a and b together are water (Link 1991)&quot;. (Also, see Bunt 1985: p. 19.) The second criterion, that of the divisivity of reference, suggested by Cheng (1973: pp. 286-287), states that any part of something denoted by a mass noun is denoted by the same mass noun. However, this criterion is belied by two classes of words. On the one hand, there is a large class of words which pattern morpho-syntactically with mass nouns, yet their denotations have parts which do not fall within the same noun's denotation. On the other hand, there is a large class of words which pattern morpho-syntactically with count nouns, yet their denotations have parts which also fall within the same noun's denotation. The first set of facts had been pointed out by Quine, even before the criterion itself had been first suggested, let alone come into vogue. &quot;... there are parts of water, sugar, and furniture too small to count as water, sugar, furniture. Moreover, what is too small to count as furniture is not too small to count as water or sugar; so the limitation needed cannot be worked into any general adaptation of 'is' or 'is a part of', but must be left rather as the separate reference-dividing business of the several mass terms (Quine 1960: p. 99)&quot;. Indeed, minimal pairs such as the following make it abundantly clear that divisity of reference incorrect:</Paragraph> </Section> <Section position="3" start_page="51" end_page="51" type="metho"> <SectionTitle> COUNT NOUNS MASS NOUNS </SectionTitle> <Paragraph position="0"> The second class of words include the following: stone, rock, ash, string, cord, rope, and tile. These nouns behave both as mass nouns and as count nouns. But even in their guise as count nouns, they satisfy the criterion of the divisity of reference. Suppose, for example, one has an eight foot rope. Cutting it in half, one can be said to obtain two rolSes of four feet each. And cutting each of these ropes in half again, one thereby obtains four ropes of two feet each.</Paragraph> <Paragraph position="1"> The mistake of semanticists is to have confounded what it is for the denotation of a noun to be specified as having no minimal parts and what it is for the denotation of a noun to be unspecified for whether or not it has minimal parts. Semanticists have uniformly opted for specification, whereas the facts call for non-specification.</Paragraph> <Paragraph position="2"> The view advocated here is that of non-specification. In the next section, I shall set out the widely recognized morphological and syntactic facts pertaining to common nouns and the noun phrases comprising them and set out an account of the morphology and syntax which honors a treatment of mass nouns in terms of non-specification.</Paragraph> </Section> <Section position="4" start_page="51" end_page="55" type="metho"> <SectionTitle> 2 The Phrasal Syntax and Semantics of the Mass-Count Dis- </SectionTitle> <Paragraph position="0"> tinction It is useful, to begin with, to recognize that English nouns fall into four Classes: pronouns, proper names, mass nouns, and count nouns. Thes four classes are easily distinguished on the basis of two criteria: first, whether or not the noun in question occurs equally freely in the singular and in the plural; and second, whether or not the noun in question tolerates the full range of determiner. On the one hand, proper names and pronouns do not tolerate determiners , though admittedly the definite article occurs in some proper names; while mass nouns and count nouns do. On the other hand, pronouns and count nouns evince the alternation between singular and plural, even if the alternation is sometimes not morphologically realized, as is the case with many nouns for wildlife (e.g., sheep, deer), whereas proper names and mass nouns do not evince such an alternation.</Paragraph> <Paragraph position="1"> occurs with admits the contrast of a determiner singular and plural proper name -</Paragraph> <Paragraph position="3"> Common nouns, that is, mass nouns and count nouns, are distinguished by the lexical features =kCT, which are assigned to common nouns in their lexical entries. These features serve to constrain the free assignment of the morpho-syntactic features of ~PL. To begin with, any noun with the feature +CT must be assigned exactly one of the features, +-PL; and any noun with the feature -CT must be assigned the feature -PL. The assignment of the features ~PL conforms to certain restrictions. One restriction is lexical.</Paragraph> <Paragraph position="4"> Some nouns have their grammatical number specified lexically. Thus, for example, police, which is a count noun, has the feature +PL specified in its lexical entry. 1 Plural mass nouns ~ all have the feature +PL specified in their lexical entries.</Paragraph> <Paragraph position="5"> The other restrictions are syntactic. The first is the well-known fact that there is agreement between the grammatical number of determiners and the grammatical number of the nouns they modify. Thus, this desk, that oil, and those odds are acceptable, whereas these desk, that oils, and thai odds are not. Another restriction is that inflected verbs agree in grammatical number with their subjects.</Paragraph> <Paragraph position="6"> (2.1) This student is usually meticulous.</Paragraph> <Paragraph position="7"> (2.2) *This student are usually meticulous.</Paragraph> <Paragraph position="8"> (3.1) This oil is viscous.</Paragraph> <Paragraph position="9"> (3.2) *This oil are viscous.</Paragraph> <Paragraph position="10"> (4.1) *Those earnings is insignificant.</Paragraph> <Paragraph position="11"> (4.2) Those earnings are insignificant.</Paragraph> <Paragraph position="12"> Standard treatments of feature can accommodate these two restrictions: the features of a count noun are assigned to its first dominating noun phrase node (i.e., its maximal projection) and the features assigned to a determiner must be consistent with the features of its first dominating noun phrase node. It is also true that a conjoined noun phrase is plural, even if its conjuncts are singular. (5.1) John and Mary are leaving.</Paragraph> <Paragraph position="13"> (5.2) *John and Mary is leaving.</Paragraph> <Paragraph position="14"> (6.1) The wiring and the piping are in the storeroom.</Paragraph> <Paragraph position="15"> (6.2) *The wiring and the piping is in the storeroom.</Paragraph> <Paragraph position="16"> This can be handled by a simple rule: the feature of a conjoined noun phrase is the sum of the features of the conjuncts, where the sum of xPLi is -PL if i = 1 and +PL otherwise (where x ranges over + and and i enumerates the i th conjunct in the conjunction). 3 a This specification is to be distinguished from phonological specifications pertaining to the phonological reafization of the features +-PL. For example, 'mouse' in the plural is realized as 'mice'; 'deer' in the plural is still realized as 'deer'; and 'means' in the singular is still realized as 'means'; etc.</Paragraph> <Paragraph position="17"> The pairs of features ~CT and +-PL impose semantic conditions. To make clear what these conditions are, I shall turn to the introduction of a few mereological and set theoretic concepts. Let an object formed from one or more members of a given background set be an aggregate. For example, let the background set have exactly three distinct elements: a, b, and c. Then, exactly seven aggregates can be formed from its elements: a, b, c, ab , ac , bc , and abc .</Paragraph> <Paragraph position="18"> If a, b, and c are concrete particulars, then so are ab, ac, bc, and abc. In addition, each concrete particular can be seen as a minimal aggregate. In other words, the concrete individual a can be seen as an aggregate a, the smallest aggregate which can be formed from a. Not all aggregates have atomic constituents. Those which do are also known as pluralities. The set of desks in a room can form an aggregate whose atomic constituents are precisely the desks in the room: the aggregate in question here is a scattered object (ep., Indonesia is a scattered object.) The entire volume of space in a room forms an aggregate, but it has no atomic parts.</Paragraph> <Paragraph position="19"> A plurality is not the same as a collective, or a group: a plurality is nothing more than the sum of its atomic constitutents, whereas a collective is more than the sum of its atomic consitutents. The constituency of a collective can change without the collective changing. As is well known, not only can the members of a collective come and go with the collective remaining intact, but the very same people may make up two distinct collectives. What is crucial to collectives is that they are subject to constituting conditions which determine how the members of the collective constitute the collective of which they are members; whereas pluralities do not have such constituting conditions. Indeed, as Simons (1987: ch. 4.4) has pointed out, a plurality can be seen as the limiting case of a collective: a plurality is a collective without conditions governing its constitution.</Paragraph> <Paragraph position="20"> The set of aggregates accruing to the formation of aggregates from elements of a background set has the algebraic structure of a complete join semi-lattice with a unit and without a zero. The relation of being a sub-aggregate is a partial ordering on the set of all aggregates formed from the background set. The elements of the background set are the minimal aggregates in the set of all aggregates; while the aggregate formed from all of the background set's elements is the unique maximal aggregate, that is, the greatest aggregate or unit aggregate.</Paragraph> <Paragraph position="21"> In addition, an aggregation is defined to be a set of aggregates with the requirements that their join yield the greatest aggregate (that is, the unit aggregate) and that it be minimal, in the sense that, no aggregate in the set is a proper sub-aggregate of any other aggregate in the set.</Paragraph> <Paragraph position="22"> When a noun has the feature +CT, its denotation is the set whose members are all and only those minimal aggregates of which the noun is true. In other words, it is the largest subset of the domain of discourse such that the noun is true of each element in the set. The noun 'desk' is a count noun, hence it has the feature +CT. Its denotation is the set of all desks in the universe of discourse. When a noun has the feature -CT, its denotation is the set whose sole member is the greatest aggregate of which the noun is true. The noun 'machinery' is a mass noun, hence it has the feature -CT, so its denotation is the set whose sole element is the greatest aggregate of machinery formed from the universe of discourse.</Paragraph> <Paragraph position="23"> It is well-known that demonstrative noun phrases, quantified noun phrases, and interrogative noun phrases in English exhibit different patterns: interrogative noun phrases form overtly discontinuous structures (i.e., move at S-structure), while demonstrative and quantified noun phrases do not; quantified noun phrases exhibit different scope-like interpretations, while demonstrative noun phrases do not 4. It is not surprising, then, that these different kinds of noun phrases are sensitive to the features =t:PL in different ways. The denotation of a demonstrative noun phrase is the denotation of its ~r, modulo any further restriction imposed on it by its determiner. Now every noun phrase has grammatical number. The semantic import for a demonstrative noun phrase of singular grammatical number is that its denotation be one, while that of plural grammatical number is that its denotation may be be one or greater.</Paragraph> <Paragraph position="24"> It might be asked why the cardinality of a plural demonstrative noun phrases might be allowed to be one. Are there cases where the grammatical number is plural but the denotation is one? Yes, plural mass 4More precisely, singular quantified noun phrases exhibit different scope-like interpretations, while singular demonstrative noun phrases do not. There are cases where plural demonstrative noun phrases and interrogative noun phrases exhibit scope-like interpretations.</Paragraph> <Paragraph position="25"> nouns have a denotation of one, but have the grammatical number of plural. Second, if the cardinality of a plural noun phrase were required to be greater than one, then the following sentences would not be true. (7.1) These men (Mark Twain and Samuel Clemens) are the same man.</Paragraph> <Paragraph position="26"> (7.2) The numbers 22 and vf~ are identical.</Paragraph> <Paragraph position="27"> I now turn from the semantics of demonstrative noun phrases to how they are evaluated with respect to the predicates Of which they are arguments. A predicate is evaluated, not with respect to the denotation of a demonstrative noun phrase which is its argument, hut with respect to the elements in an aggregation constructed from the demonstrative noun phrase's denotation, where the choice of aggregation is determined by one's knowledge of the world and one's context. Such flexibility accounts for why it is that, when different piles of leaves are touching different bundles of wires, the following sentences (due to Lauri Carlson) are true. (8.1) These leaves are touching those wires.</Paragraph> <Paragraph position="28"> (8.2) This foliage is touching that wiring.</Paragraph> <Paragraph position="29"> In the first case, there is a way of assembling the individual leaves into aggregates of leaves and the individual wires into aggregates of wires such that each aggregate of leaves, that is, each pile of leaves, is touching some aggregate of wires, that is some bundle of wires, and each aggregate of wires is being touched by some pile of leaves. In the second case, there is a way of breaking up the largest aggregate of foliage into sub-aggregates of foliage and the largest aggregate of wiring into sub-aggregates of wiring such that each sub-aggregate of foliage, that is, each pile of foliage, is touching some sub-aggregate of wiring, that is, some bundle of wiring, and each sub-aggregate of wiring is being touched by some sub-aggregate of foliage.</Paragraph> <Paragraph position="30"> Having stated and illustrated the principles governing plural demonstrative noun phrases, I turn to those governing plural quantified noun phrases. As always, a denotation is associated with a count noun, namely, the largest subset of the domain of discourse of each of whose members the noun is true. But the quantifier is restricted, not to the count noun's denotation, but to an aggregation built from that denotation. The choice of aggregation is partially constrained by the features :t:PL. If the feature assigned to the noun phrase node of the quantified noun phrase is /PL, then the choice of the aggregation is unconstrained; but if it is -PL, then the choice is constrained to the least aggregation, that is, the set of all the minimal aggregates of the count noun's denotation - which is, of course, just the count noun's denotation. Notice that this is analogous to the constraint imposed by these features on the denotation of demonstrative noun phrases. Next, if the quantifier is universal, then the predicate must be true of each aggregate in the aggregation to which the quantifier is restricted; and, if it is existential, then the predicate must be true of at least one aggregate in the aggregation to which the quantifier is restricted.</Paragraph> <Paragraph position="31"> To see how the principles work, consider this sentence with plural quantified noun phrases.</Paragraph> <Paragraph position="32"> (9) All men in the room endorsed some women.</Paragraph> <Paragraph position="33"> Suppose the denotation of 'men' is ml, m2, m3, m4, ms, m6, and nit the denotation of 'women' is Wl, w2, w3, w4, and ws. Suppose further that the men form committees of various sizes (including committees of one), say, roT, mlra2ma, mlm2m4, and m4msm6, and that the women too form committees, say, wlw~, w4ws, and wl w3. Finally, suppose that there is an endorsement of the female committees by the male committees, as depicted below.</Paragraph> <Paragraph position="35"> The situation certainly renders the sentence in (3) true and that it is so can be derived by any rule which assigns clausal scope to quantified noun phrases. Thus, the quantified noun phrases in the sentence in (9) can be assigned the scopal configuration shown in (10).</Paragraph> <Paragraph position="36"> (10) \[NP All men \]~ \[NP some women \]y Is \[NP Z \] \[YP endorsed \[NP Y \]\]\] Next, the following two sets are aggregations formed from the denotation of 'men' and 'women' respectively.</Paragraph> <Paragraph position="38"> Finally, each aggregate in (11.1) bears the relation of endorsing to some aggregate in (11.2).</Paragraph> <Paragraph position="39"> Quantified count noun phrases range over elements in the aggregation formed from elements in the denotation of the noun phrase's count noun. Quantified mass noun phrases also range over elements in the aggregation formed from the denotation of the noun phrase's mass noun, which is the greatest aggregate in the domain of discourse of which the mass noun is true. In many cases, the choice of aggregation is virtually arbitrary.</Paragraph> <Paragraph position="40"> (12.1) All water is wet.</Paragraph> <Paragraph position="41"> (12.2) All information is valuable.</Paragraph> <Paragraph position="42"> In other cases, the choice is constrained by common knowledge.</Paragraph> <Paragraph position="43"> (13.1) Some footwear in this store sells for under thirty dollars.</Paragraph> <Paragraph position="44"> (13.2) All ammunition found by the police was fifty caliber.</Paragraph> <Paragraph position="45"> (13.3) No livestock in this pasture weighs more than one hundred kilograms.</Paragraph> </Section> <Section position="5" start_page="55" end_page="58" type="metho"> <SectionTitle> 3 The Empirical Generalizations </SectionTitle> <Paragraph position="0"> For sometime, lexical semanticists have been aware of words which satisfy both the mass criteria and the count criteria. Adhering to standard linguistic usage, I shall refer to this correlation as conversion, leaving open whether or not this phenomenon is to be further analyzed as so-called zero derivation. Moreover, I accept the suggestion of the term that the correlation has a directionality to it, though I am aware of the fact, pointed out by Leech (1981: pp. 224-225), that what the directionality should be is not always clear.</Paragraph> <Paragraph position="1"> To my knowledge, no systematic investigation of mass count alternation in English has been carried out, though remarks of individual instances abound and observations of some sub-regularities have been made (for example, Ostler and Atkins 1991). My purpose here is to pull together the observations which have been made and expand the empirical base so as to arrive at a preliminary formulation of the regularity or regularities involved.</Paragraph> <Paragraph position="2"> I divide this discussion into two parts, as suggested by the term conversion. I look first at conversion of mass nouns to count nouns and then at the conversion of count nouns to mass.</Paragraph> <Section position="1" start_page="56" end_page="57" type="sub_section"> <SectionTitle> 3.1 Conversion from Mass Noun to Count Noun </SectionTitle> <Paragraph position="0"> As remarked above, a mass noun is unspecified as to whether or not its denotation has minimal parts. Its conversion to a count noun requires that its denotation must be such that it has minimal parts, or atoms. In the case of a mass noun for concrete things or stuff, its count noun version has as its denotation either units of what the mass noun denotes, or kinds of what it denotes. Here are some well-known examples: coffee, tea, beer, hamburger, cheese, and wheat.</Paragraph> <Paragraph position="1"> The conversion of these nouns to count nouns can fall under any of several types. The most commonly recognized one is that of kinds. This conversion appears with such nouns as breads, cheeses, clays, coffees, salts, minerals, oils, teas, and wheats. Another common conversion is to that of units. Thus, chocolates, beers, and hamburgers may denote servings of the denotation of the underlying mass noun.</Paragraph> <Paragraph position="2"> (14.1) Only two coffees are sold in this store: Ethiopian and Costa Rican.</Paragraph> <Paragraph position="3"> (14.2) Would you care for a coffee? But servings are not the only kind of unit. Surely a unit, different from that of a serving, is invoked in the case of weight. Particularly revealing here are the mass nouns of pizza and cake where two units are possible, one corresponding to a serving and the other corresponding to a unit of fabrication. The former requires the useof a partitive expression, a slice of pizza and a piece of cake, whereas the latter accrues to the count noun conversions of pizza and cake.</Paragraph> <Paragraph position="4"> (15.1) Did you order pizza? (15.2) I ordered a pizza, not a slice of pizza.</Paragraph> <Paragraph position="5"> It would be a mistake to think that units, or servings, and kinds are the only atoms available to mass nouns undergoing conversion to count nouns. Let us begin with mass nouns denoting emotions. Indeed, emotion is a mass noun which converts to a count noun with the correlated shift in meaning of kinds of emotion. Not all words for emotions have a count noun counterpart. For example, anger, disgust, grief, astonishment, and esteem do not. But many do: for example, joy, embarrassment, delight, sorrow, disappointment, anxiety, dislike, love, like, and care.</Paragraph> <Paragraph position="6"> (16.1) Carol feels intense anxiety before every dinner party she gives.</Paragraph> <Paragraph position="7"> (16.2) Carol has two anxieties: her job and her children.</Paragraph> <Paragraph position="8"> The conversions here all denote THAT WHICH GIVES RISE TO THE EMOTION. Indeed, this conversion is true of many mass nouns denoting mental states in general, such as, surprise, wonder, admiration, pleasure, worry, aspiralion, ambition, and desire.</Paragraph> <Paragraph position="9"> (17.1) Bill dots not have much desire to continue working.</Paragraph> <Paragraph position="10"> (17.2) Bill has but one desire: to continue working.</Paragraph> <Paragraph position="11"> One interesting case is fear, which, as a count noun, denotes both kinds of fear and objects of fear. Another sort Of conversion is illustrated by mass nouns denoting virtues. Of course virtues denotes kinds of virtue. And of course many virtues are one of a kind: honesty, bravery, courage, chastity, sincerity, gratitude, and fidelity. Still, some mass nouns for virtues are susceptible of conversion, namely, loyalty and allegiance. As count nouns, they denote those things to which one is loyal and those things to which one owes allegiance.</Paragraph> <Paragraph position="12"> (18.1) How much loyalty does Dan have to his friends? (18.2) How many loyalties does Dan have? Still another sort of conversion is one which was alluded to above in connection with fear. Mass nouns, through conversion, can give rise to count nouns denoting instances of the denotation of the mass noun: complexity, detail, discrepancy, error, effort (instances of the exercise of work), action, activity, exposure, thought, and shortage.</Paragraph> <Paragraph position="13"> (19.1) Elizabeth made many efforts to contact her lawyer.</Paragraph> <Paragraph position="14"> (19.2) How much effort is required to lift this weight? Summarizing, then, we conclude that mass nouns, under conversion, give rise to count nouns with a limited variety of shifts in denotation. They include, but may not be confined to, the following: TO BE A KIND OF, TO BE AN INSTANCE OF, TO BE A UNIT OF, and TO BE A SOURCE OF. This can be formalized as follows 1. ICc(Nm)\[ = {x: 2. ICc(Nm)l = {x: 3. ICc(N,~)l : {x: 4. ICc(Nm)l : {x: is a kind of I(Nm\]} is an instance of \[(Nml} is a unit of \[(Nml} is a source of I(gml} (where 'Nm' denotes a mass noun, 'Co' denotes the morphological operation of conversion from a mass noun to a count noun, and '\] \]' denotes the interpretation function).</Paragraph> <Paragraph position="15"> Moreover, there is evidence that the choice of interpretation is relativized to context. Consider the first sentence: (20.0) I sold you two coffees.</Paragraph> <Paragraph position="16"> (20.1) I sold you two kinds of coffee.</Paragraph> <Paragraph position="17"> (20.2) I sold you two cups of coffee.</Paragraph> <Paragraph position="18"> The sense of the sentence in (20.0) as found in the paraphrase in (20.1) would be appropriate to the situation in which a sales clerk at a store which sells only coffee beans is explaining to a customer why a sales receipt shows two different prices. The second sense, as found in the paraphrase in (20.2), would be salient in the situation in which a waiter at a restaurant is explaining to a customer why the price of a cup of coffee is found twice on a bill.</Paragraph> </Section> <Section position="2" start_page="57" end_page="58" type="sub_section"> <SectionTitle> 3.2 Conversion from Count Nouns to Mass Nouns </SectionTitle> <Paragraph position="0"> The semantic requirement imposed on a count noun in its conversion to a mass noun means that its denotation be the largest aggregate, or mereological sum, of the parts of each atom of the denotation of the count noun, where what constitutes a relevant part may, and typically does, vary from count noun to count noun.</Paragraph> <Paragraph position="1"> Ostler and Atkins (1991) point out two sub-regularities exemplifying this shift. Common nouns for animals which humans eat can be used to denote the largest aggregate of those parts considered suitable for human consumption. They include nouns such as duck, chicken, turkey, and lamb - to mention just a few.</Paragraph> <Paragraph position="2"> (Cp. Ostler and Atkins 1991: p. 89.) Common nouns for plants which humans eat can be used to denote the largest aggregate of those parts considered suitable for human consumption. Among these are such words as potato, turnip, carrot, and rutabaga. (Cp. Ostler and Atkins 1991: p. 91.) Other sub-regularities include the case where common nouns for trees can be used to denote the largest aggregate of those parts considered useful for human use in construction), namely the wood, obtained from them. Examples include oak, maple, birch, cedar- and many, many, others.</Paragraph> <Paragraph position="3"> Leech (1981: p. 216) mentions two examples which do not fall in any of the sub-regularities mentioned so far: an area of table and an inch of cigarette. Indeed, these two examples are instances of still another sub-regularity, namely, common count nouns for products can be used to denote parts which contribute to the enlargement or enhancement of the product. This is exhibited in such expressions as the following: (21.1) Bill got a lot of house for $100,000.</Paragraph> <Paragraph position="4"> (21.2) How much floor did you lay today? Finally, there are many cases where the shift in meaning is almost imperceptible. These are words which were mentioned earlier: stone, rock, ash, string, cord, rope, and tile. What is it that differentiates their mass from their count uses? It is nothing more than whether or not one the denotation must be atomic. 5 Summarizing, then, we conclude that count nouns, under conversion, give rise to mass nouns with the following shift of sense: the denotation of the mass noun is the largest aggregate of the parts of the elements 5However, see Wierzbicka 1988 ch. 10 for interesting subtleties.</Paragraph> </Section> </Section> <Section position="6" start_page="58" end_page="58" type="metho"> <SectionTitle> I </SectionTitle> <Paragraph position="0"> comprising the denotation of the count noun, where what constitutes a part is relative to the kind of object denoted by the count noun. Thus, in the case of animals and plants, the parts are the edible portions; in the case of trees, the parts are the portions of wood; and in the case of stones, rocks, ropes, wires, and so forth, the parts are pieces. This can be formalized as follows (where 'No' denotes a count noun, 'Cm' denotes the morphological operation of conversion from a count noun to a mass noun, '~r' is a function which associates with an object its parts 6 and '1 I' denotes the interpretation function).</Paragraph> <Paragraph position="1"> ICm(Nc)l = for some y E I(Ncl}</Paragraph> </Section> class="xml-element"></Paper>