Polysemy and Syntax Stephen Wechsler, The University of Texas at Austin Course time: Monday/Thursday 9:00-10:50 AM

6. Count and mass nouns ...... 1 6.1. Introduction ...... 1 6.2. Grinding and portioning rules ...... 3 6.3. Theories of Count and Mass ...... 4 6.3.1. Lexical theories ...... 4 6.3.2. Constructional theories ...... 7 6.4. Chinese nouns and classifiers ...... 8

6. Count and mass nouns 6.1. Introduction Common nouns fall into two subcategories, count nouns and mass nouns. suggestion (count) versus advice (mass):

1. plural I got good suggestions. *I got good advices.

2. indefinite article and certain other determiners a good suggestion * a good advice every suggestion *every advice each suggestion *each advice

3. one-anaphora Mary gave me that suggestion, and Sue gave me one too. *Mary gave me that advice, and Sue gave me one too.

4. numerals and classifiers a suggestion, two suggestions *a piece of suggestion, *two pieces of suggestion *an advice, *two advice a piece of advice, two pieces of advice

(*)two waters ~ two drops of water

1 5. more determiners: sg. count pl. count mass the ✓ ✓ ✓ some ✓ ✓ ✓ any ✓ ✓ ✓ no ✓ ✓ ✓ more * ✓ ✓ most * ✓ ✓ a lot of * ✓ ✓ *a lot of suggestion little * * ✓ little advice was given too much * * ✓ too much advice was given Some nouns can be either mass or count: count noun cake: cakes; a cake; every/each cake; Mary baked a cake and John baked one, too. mass noun cake: More cake is/*are on the way. Most cake is/*are good for you Too much cake remained. Little cake remained.

count? mass? advice * ✓ suggestion ✓ * cake ✓ ✓ furniture bean asparagus rice wheat shoe footwear shirt clothing watermelon fruit vegetable virtue fur

Can this be reduced to semantics? Generally count nouns refer to objects that can be readily counted. larger particles: beans, peas, cakes smaller particles: *rices, *wheats, *sands 2 instead use classifiers: kernels of rice/wheat; grains of sand ‘piece’ as default classifier: a piece of advice/ furniture/ mail/ etc.

There is no particle size above which all nouns are count and below which they are mass, and there are many minimal pairs (and triples) within and across languages: garments/clothing/clothes ; job/work ; turds/shit across languages: fennel (mass) / fenouil (French ‘fennel’, count), spaghetti (mass in English, plural in Italian).

6.2. Grinding and portioning rules

We can often convert count nouns to mass nouns:

(1) ‘I really rather prefer that my firewood not have quite so much— chair— in it.’ (Piglet to Tigger, after Tigger threw Piglet’s chair in the fire)

More functions of count/mass alternations:

(2) Animal/meat: a. A lamb is running in the field. b. John ate lamb for breakfast.

(3) Object/Stuff an object is made up: a. There is an apple on the table. b. There is apple in the salad.

(4) Stuff/Kind: a. There was cheese on the table. b. Three cheeses were served.

(5) Stuff/Portions: a. The restaurant served beer, and so b. we ordered three beers. sense extensions: Genuine cases of systematic polysemy, where a class of words productively alternates between systematically related senses (Copestake and Briscoe 1995).

(6) ‘grinding’: count noun => mass noun a. Bus is eating a carrot. (count) b. There’s too much carrot in this cake. (mass)

3 (7) ‘portioning’: mass noun => count noun a. I drank too much beer last night. (mass) b. Would you like a beer? (count)

6.3. Theories of Count and Mass Two types of theory:

• Lexical theories: Common nouns fall into two subcategories, count nouns and mass nouns. Some fall into both, or can be converted from one to the other.

• Constructional theories: There is no lexical distinction between count nouns and mass nouns; instead, the apparent differences arise from elements of the syntactic context of the common noun.

6.3.1. Lexical theories Lexical theories try to predict which common nouns are classified as count versus mass. Two main ideas: 1. minimal units: mass noun denotations cannot be counted because they lack stable atoms: the minimal size is too vague be a basis for counting 2. overlap: mass noun denotations cannot be counted because their units overlap, so there are too many different ways to count.

• Model-theoretic accounts: (Chierchia 1998; Copestake 1995; Landman 2010; Chierchia 2010; Filip and Sutton 2015) • Non-model-theoretic accounts: (Jackendoff 1991; Wierzbicka 1985)

In model theoretic accounts, linguistic denotations are represented as mathematical constructs that provide a partial model of the world. The fit between that model and the world allows for predictions about meaning. Model ontologies generally include individuals, sets, and a part relation holding between individuals (plus times, truth values, etc.).

I. Minimal units. The ‘minimal units’ idea can be stated with the notions quantized and cumulative reference: count nouns are quantized (QUA); mass nouns and plural count nouns are cumulative (CUM) (Copestake 1992:94ff).

Cumulative reference. (CUM) A predicate P has cumulative reference if when P is true of two entities it is true of the sum of the two entities. (also called additive)

Examples: mass nouns like gold’ (gold plus gold gives gold) and plurals like horses’ (horses plus horses gives horses)

4 Quantized reference. (QUA) A predicate P has quantized reference if when P is true of an entity it is not true of any proper part of that entity. (also called indivisible)

Examples: Singulars like horse’ (a part of a horse is not a horse) and measured objects like five ounces of gold’ (a part of five ounces of gold is not five ounces of gold)

8 noun types, classified by CUM, QUA, sg/pl number, and other properties (Copestake 1992:94ff):

A. countable (i) individual: includes most singular count nouns, e.g. rabbit. QUA, sg. (ii) plural: semantically regular plurals, e.g. rabbits, tables, children. CUM, pl. (iii) group: group nouns with plural agreement (in British English), but also certain group properties e.g. This band are great live (Brit.); one of the band smashed her guitar. QUA, sg. (iv) pair: pluralia tantum with bipartite physical structure and pair classifier, e.g. (a pair of) trousers, binoculars, scissors. QUA, pl. (v) complex: These are like individuals, but they have variable sg/pl agreement, e.g. gallows, barracks, work. QUA, (sg/pl) (vi) portion: Conventionally measured amount of a substance, e.g. extended senses of whisky, beer (cp. a whisky, a beer). QUA, sg.

B. uncountable (i) mass: ‘normal’ mass nouns, e.g. gold, sand, fennel. CUM, sg. (ii) collection: mass nouns defined by function, e.g. furniture, clothing, cutlery. CUM, sg.

Some mass nouns trigger plural agreement, e.g. oats, cp. too much oats/ feces/ grits/ mashed potatoes (are/*is) thrown away.

Stated with respect to these noun types, the portioning lexical rule turns a mass noun into a portion noun. E.g. a beer consists of some conventional or contextual measure (one serving) of beer qua mass (cp. too much beer). The grinding lexical rule operates on ‘true individuals’, that is to say, nouns of type individual, group, complex, or pair (but not portion, collection, or mass). Or plural? (how much grits) The grinding lexical rule applies to a ‘true individual’ predicate to yield a mass term.

(Landman 2010; Chierchia 2010): For many entities such as liquids, the minimal elements, if any, are too vague to be suitable for counting. A problem: mass nouns like furniture, kitchenware, and cutlery have clear minimal elements. The ‘overlap’ idea applies to those.

5 II. Overlap. In order to count, one needs a suitable level at which to individuate objects. Some nouns provide this: the set of books on the table. Others do not, because the items in the extension overlap: the set of objects or things on the table might includes the book, the first page of the book, the first word on the first page, etc. Mass nouns allow overlap so they disallow counting. Prototypically count nouns have minimal elements that do not overlap. Nouns that include overlapping entities normally restrict their denotation to eliminate the overlap.

Ex. Four farmers put up a fence structure; we can consider it to be one fence; or four fences— but not normally as five fences.

For counting to work, we ignore any overlap between items. We must do this, because counting is an additive measure (an extensive measure) in that 1+1=2 only holds for 1’s that do not overlap, and in the count domain 1+1 is indeed 2.

(Landman 2010) clothing: suit + vest; etc. kitchenware: mortar and pestle: one or two atoms? teaset (teapot plus four cups and four saucers): how many atoms? furniture: table and chair set: how many atoms? bureau & mirror: one or two atoms? With mass denotations there are too many building blocks.

(Chierchia 1998): A singular count noun denotes a set of individuals. For example, suppose that in a particular possible world w, the extension of cat is this set:

[| cat |]w = { a, b, c }

A plural count noun denotes all the non-singleton, non-null subsets of the set denoted by the singular form of the noun. So in that same world w, the extension of cats is this set:

[| cats |]w = PL([| cat |]w) = {{a, b}, {b, c}, {b, c}, {a, b, c}}

(Technically PL(A) = *A – A, where *A is the closure of A: the set of all subsets of A). Chierchia proposes that a mass noun is neutral between singular and plural.

[| furniture |]w = {a, b, c, {a, b}, {b, c}, {b, c}, {a, b, c}}

For example, suppose we have a table, a desk, and a chair. Then intuitively the table is furniture; the desk is furniture; the chair is furniture; and all combinations are furniture: the table and desk; the table and chair; etc.

6 1. Why mass nouns lack a plural: *the furnitures. The denotation of the mass noun (furniture) already contains all the subsets; so if you remove those, nothing remains.

2. Why a mass noun cannot combine with a numeral: *three furniture. Because, due to the overlap problem, there is no suitable basis for counting. In the ex. above of furniture, are there 7, for all the combinations?

III. Combining the two theories Two properties favor mass nouns: 1. The denotation’s countable units are vague. 2. The possible countable units overlap, making counting impossible.

(Filip and Sutton 2015): • When a noun has both properties 1 and 2, it will be a mass noun. • When a noun has neither property 1 nor 2: it will be a count noun. • When nouns have one property but not the other: they vary between count/mass, within and across languages.

OVERLAP NON-OVERLAP VAGUE mud M oat-s, PL-C lieju M (‘mud’, Finnish) kaura (‘oat’, Finnish) kal M (‘mud’, Bulgarian) oatmeal M blood M kaurhiutale-et, PL-C (‘oatmeal’, Finnish) water M vločky, PL-C (oatmeal, Czech) lentil-s PL-C lešta M (‘lentil’, Bulgarian) čočka M (‘lentil’, Czech) bean-s, PL-C bob M (‘bean’, Bulgarian) NON- furniture M cat C VAGUE meubel-s PL-C (‘furniture’, Dutch) kissa C (‘cat’, Finnish) meubilair M (‘furniture’, Dutch) kat C (‘cat’, Dutch) huonekalu-t PL-C (‘furniture’, boy C Finnish) chair C footwear M jalkine-et PL-C (‘footwear’, Finnish)

6.3.2. Constructional theories

See slides. (Borer 2005)

7 6.4. Chinese nouns and classifiers

Chinese has a system of noun classifiers that precede and introduce common nouns. These are similar to the English use of nouns like piece (of advice) and drop (of water) with mass nouns. Adding piece converts a mass noun into a count NP: advice; mass: *an advice, *two advices, *every advice piece of advice; count: a piece of advice, two pieces of advice, every piece of advice

In Chinese, almost all nouns, even those denoting individual items like ‘book’ or ‘person’, are introduced by classifiers. Inspired by this function of some classifiers, some linguists concluded that Chinese nouns lack the count/mass distinction: that all Chinese nouns are like mass nouns. But there is still a count/mass distinction; it is just more subtle in Chinese.

Chinese classifiers can roughly be divided into two groups (Cheng and Sybesma 1999): • ‘massifiers’ create a unit of measure as in (1) • count-classifiers simply name the unit in which the entity denoted by the noun naturally occurs as in (2)

(1) ‘massifiers’ a. san ping jiu three bottle liquor ‘three bottles of liquor’ b. san ba mi three handful rice ‘three handfuls of rice’ c. san wan tang three bowl soup ‘three bowls of soup’

(2) ‘count-classifiers’ a. san ge ren three CL people ‘three persons’ b. san zhi bi three CL pen ‘three pens’ c. san ben shu three CL book ‘three books’

8 Massifiers and count-classifiers differ syntactically: only massifiers, not count- classifiers, can be optionally followed by de:

(3) a. san bang (de) rou three CL-pound DE meat ‘three pounds of meat’

b. liang xiang (de) shu two CL-box DE book ‘two boxes of books’

(4) a. ba tou (*de) niu eight CL-head DE cow ‘eight cows’

b. jiu gen (*de) weiba nine CL DE tail ‘nine tails’ c. shi zhang (*de) zhuozi ten CL DE table ‘ten tables’

Only massifiers, not count-classifiers, can be modified by a preceding adjective from a small set of allowable ones (da ‘big’, xiao ‘small’, etc.).

(5) a. yi da zhang zhi one big CL-sheet paper ‘one large sheet of paper’ b. na yi xiao xiang shu that one small CL-box book ‘that one small box of books’

(6) a. *yi da zhi gou

one big CL dog b. *yi da wei laoshi one big CL teacher mass nouns: Liquor, rice, and soup lack built-in semantic partitioning; they do not come naturally in bottles, handfuls, or bowls ⟼ The words ping ‘bottle’, ba ‘handful’, and wan ‘bowl’ in (1) create units by which the amount of liquor, rice, and soup is measured.

9 count nouns: Books, people, and pens in (2) provide natural units by which they can be counted: individual volumes, persons (one head, one heart, one spine), and pens. ⟼ The classifiers like ge, zhi, and ben do not create units, they simply name units inherent in the noun.

Massifiers do not occur only with mass nouns. Since they create units of measure, they can also occur with nouns that have a natural partitioning as part of their semantics; cp. a group of people, a pound of beans. The distinction between the two types of classifiers is made with explicit reference to two different types of nouns: count nouns and mass nouns.

References

Borer, Hagit. 2005. Structuring Sense, Volume I: In Name Only. Oxford: Oxford University Press. Cheng, L. L. S, and R. Sybesma. 1999. “Bare and Not-so-Bare Nouns and the Structure of NP.” Linguistic Inquiry 30 (4): 509–42. Chierchia, Gennaro. 1998. “Plurality of Mass Nouns and the Notion of ‘Semantic Parameter.’” In Events and Grammar, edited by Susan Rothstein, 53–103. Dordrecht: Kluwer. ———. 2010. “Mass Nouns, Vagueness and Semantic Variation.” Synthese 174 (1): 99–149. Copestake, Ann. 1995. “The Representation of Group Denoting Nouns in a Lexical Knowledge Base.” In Computational Lexical Semantics, edited by P. Saint- Dizier and E. Viegas, 207–31. Cambridge: Cambridge University Press. Filip, Hana, and Peter Sutton. 2015. “Countability in Probabilistic Mereological Type Theory with Records.” presented at the Semantics and Philosophy in Europe, Cambridge, UK. Jackendoff, Ray S. 1991. “Parts and Boundaries.” Cognition 41: 9–45. Landman, Fred. 2010. “Count Nouns-Mass Nouns, Neat Nouns-Mess Nouns.” Baltic International Yearbook of Cognition, Logic and Communication 6 (1): 12. Wierzbicka, Anna. 1985. “Oats and Wheat: The Fallacy of Arbitrariness.” Iconicity in Syntax, 311–42.

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