Other Noun Categories


Plural NPs and Groups


We have been using a distributive analysis for quantified expressions–the predicate is distributed to each individual:


1. Three cups broke.

    [Three x: CUP(x)] BREAK(x)


      The red cup broke.

      The yellow cup broke.

      The blue cup broke.


The distributive treatment parcels the action over each cup in succession. We can also analyze the predicates in (2) distributively:


2. Everyone saw a Norwegian.

    [A x: NORWEGIAN(x)] ∀y SAW(y,x)


      Harry saw Olaf.

      Ann saw Olaf.

      Rebecca saw Olaf, etc.


   b. ∀y [A x: NORWEGIAN(x)] SAW(y,x)


      Harry saw Olaf.

      Ann saw Sven.

      Rebecca saw Olaf and Sven, etc.



Collective Predication


Collective predication refers to predication involving a group of individuals:


3a. The boys greeted one another on the street.

  b. Sally and Harry met at the beach.

  c. The forest surrounds the castle.


A group collective refers to a group with identifiable members. The members of the group carry out the action collectively. The predications do not apply to a single individual:


4a. The boys greeted one another on the street.

  b. The leaders debated the compensation proposal.


Substance collectives refer to a substance. Although substances like sand or flour have individual particles, we do not recognize their individual identities. Even a crowd of people can form a substance as long as we do not care about the specific individuals who make up the crowd. Predicates like surround and disperse can be applied to substances:


5a. The water surrounded the house.

  b. The crowd dispersed slowly.


Collective predication applies to both group collective predicates and substance collective predicates. The individuals in the group interact with one another in group collective predications, but not in substance collective predications.


The distributive analysis cannot be used for collective predicates with quantified plural NPs:


6. A thousand trees surrounded the castle.

    [A thousand(x): TREE(x)] [The y: CASTLE(y)] SURROUND(x,y)


We can use set theory to introduce a variable that stands for the whole group. This produces a collective interpretation:


7. [A X:|X| = 1,000 & ∀y (y ∈ X —> TREE(y)] [The z: CASTLE(z)] SURROUND (X, z)


Plural NPs may have both distributive and collective readings, depending on the context:


8a. The apples in this barrel weigh at least six ounces.

  b. The apples in this barrel weigh at least sixty pounds.


The English quantifiers every and all also differ in their ability to combine with collective predicates. Every can only be used with distributive predicates. All can have both distributive and collective interpretations:


9a. *Every piece here fits together to make a picture.

  b. All these pieces fit together to make a picture.

  c. The price of all these pieces is $20.00.

  d. The price of every piece here is $20.00.


On p. 130 Kearns provides two interpretations for the sentence Two men lifted the mini:


18a. [Two x: MAN(x)] [THE y: MINI(y)] LIFT(x,y)

    b. [A X: |X| = 2 & ∀x (x ∈ X —> MAN(x)] [THE y: MINI(y)] LIFT(X,y)



Group Collectives and Conjunction


The Scottish philosopher and poet James Beattie (1788) described the effect that collective predicates have on conjunction:

 

So, when it is said, Peter and John went to the temple, it may seem, that the conjunction and connects only the two names, Peter and John: but it really connects two sentences, - Peter went to the temple, - John went to the temple. (p. 346)


But with collective predicates:

 

... as in examples, like the following: Saul and Paul are the same ... For, if instead of the first we say, “Saul is the same - Paul is the same,” we utter nonsense; because the predicate same, though it agrees with the two subjects in their united state, will not agree with either when separate. (p. 347)


It is tempting to analyze group collectives as a collection of their members. Krifka (1991) gives the example of a committee made up of John, Mary and Bill. Krifka defines this committee as a sum individual, i.e. committee(a) and a = j⊕m⊕b, and notes several differences between the group and the sum individual:

 

i) John, Mary and Bill can meet socially apart from their committee duties.


      ii) The committee can also meet without having every member present.

 

iii) If John, Mary and Bill form new committees to address different concerns then we have to keep these committees distinct despite their having the same members.

 

iv) If a new member joins the committee, or an old member leaves the committee, the committee remains the same although its members have changed.

 

v) In some cases, committees lose all of their members so their sum individual disappears, but the committee may continue. These cases create the additional problem of distinguishing between different memberless committees.


Conjoined NPs can produce a group structure that does not contain all of the conjoined NPs, e.g.


      Napoleon and Wellington and Blücher fought against each other.


We know that Wellington and Blücher joined forces to defeat Napoleon, but the conjoined NP structure does not indicate this structure, even when the NPs are re-ordered


      Wellington and Napoleon and Blücher fought against each other.


Krifka notes a difference between idiosyncratic collective objects and groups that contain different subgroup objects. Groups do not allow reciprocals or distributive predicates at the group level. Consider the U.S. Congress which consists of the House of Representatives and the Senate. The following sentences do not apply to these subgroups.


      * The Congress controls each other.

         The Congress received one million letters.


Compare the last sentence with

      John and Mary received three letters.


This sentence is ambiguous, but one of the readings is that John received three letters and Mary received three letters.


Krifka also discusses the example of a farm that raises cows and pigs. Consider the following sentences


      i) The cows and pigs were separated from each other.

      ii) The cows and pigs were separated by age.

      iii) The cows and pigs were separated.


The cows and pigs in this example form a group which is split into different configurations depending on how the separation is carried out.


Krifka notes that the following sentence does not have a satisfactory analysis


      The plates were stacked on top of each other.



Mass NPs


Mass NPs denote an uncountable collection of stuff. Countability varies by language and context. Most English nouns can be used as either mass nouns or count nouns:


Count NPs

      a. Tigger caught seven rats under the shed.

      b. We had a choice of three paints.

      c. There were three cars on the street.


Mass NPs

      d. Tigger’s mouth was full of rat.

      e. We need more paint.

      f. That’s a lot of car for the price.


Mass NPs can be used as nouns or predicates. A semantic theory should be able to account for this ambiguity.



The Homogeneity of Mass Terms


Mass terms refer to homogeneous substances–one part is similar to every other part. A homogeneous predicate is distributive and cumulative. In a puddle of water, every drop of liquid in the puddle is H2O. This claim is only true within certain boundary conditions. An actual puddle of water probably contains some impurities that are not distributed evenly within the puddle. The actual molecules of water may also differ. A small fraction of the molecules may be heavy water. The mass predicate is water contrasts with a nondistributive predicate like is oval:


      That puddle is water.

      That puddle is oval.


Not every portion of the puddle is oval.


Cumulative predicates apply to sums or combinations of substances. If you add a bit of water to another bit of water, you are left with water. The predicate is water is cumulative in this sense. In contrast, the predicate is a ring is not cumulative. You cannot point to a collection of rings and claim This is a ring.



Form and Meaning


Count nouns typically have a plural form (e.g., rats, paints), and mass nouns do not, but this coincidence is not perfect (Allen 1980). Some mass nouns only exist in a plural form (e.g., oats, coffee grounds). The singular form of such nouns sounds odd (?an oat). These nouns cannot be counted even though they have a plural form (?seven oats, ?three coffee grounds).


Another type of mass noun has a singular form typical of mass nouns in English, but lacks the internal homogeneity that is also characteristic of mass nouns. Thus, the words furniture, cutlery and crockery are treated as mass nouns in English even though the furniture, etc. in any house is composed of very different things.


One category of count nouns only exists in a plural form (e.g., scissors, pants, woods). While it is acceptable to use the quantified phrase eight pants, the singular term (?one scissor) is unacceptable.


The last oddity is the set of count nouns that lack plurals. Words like hair can be used to refer to a single hair or the hair on someone’s head, but a phrase like the hairs in the soup sounds odd.


Wierzbicka (1985) attempts to account for these oddities by attributing the potential for plurality to the notion of countability-in-principle rather than internal homogeneity per se. Wierzbicka maintains that items like coffee grounds have pieces, but the pieces are typically not worth counting. The plural form is due to the possibility of counting the separate grounds, while mass follows from the functional irrelevance of the pieces.


Wierzbicka accounts for inhomogeneous mass nouns like furniture by noting the internal differentiation of the items making up the collective. Wierzbicka maintains that countability requires items of the same kind. Since the entities making up furniture are different kinds, the mass term lacks countability-in-principle.


Plural count nouns such as scissors and pants have clearly differentiated constituents and, more importantly, constituents of the same kind. Such objects possess countability-in-principle as well as functionally relevant pieces.


Finally, Wierzbicka accounts for singular count nouns like hair by observing that plurality reflects the functional boundedness of the entity. The boundaries between the separate strands of hair are usually irrelevant to our manipulation of the entity. The referent for hair is bounded and potentially countable, but it is functionally singular.



Definitions for Mass Terms


Distributive predicates can apply to individuals in the universe of discourse. We can apply predicates to substances by using small portions of the substances. The term sum applies to the total amount of a substance, while the term part of applies to a smaller portion of the sum. For example, the water sum is the total supply of water in the universe. Every portion of water is part of this water sum. These terms are defined in (26):


26a. Sum(water) = the entire mass of water in the universe

    b. ∀M(M ≤Sum(water) iff M instantiates water)


We can now provide an account of the distributivity of a mass term like water. Suppose we take a portion M which is part of the water sum. We can then take two smaller portions of M–call them M1 and M2. By (26b) M1 and M2 are part of the water sum iff they are actually water. If they are something else, say gold, then M is not water since we took M1 and M2 from M. But we started by assuming M was water, and therefore we have to assume that M1 and M2 are also water to avoid a contradiction (claiming that M1 and M2 are and are not water). Thus, the water content of M extends to every portion of M such as M1 and M2, and M is distributive.


We can account for the cumulativity of a mass term like water as follows. Suppose we start with two portions of water–M1 and M2. If they are both portions of water then they are part of the water sum. Now put M1 and M2 together to make up a new portion M. M is part of the water sum iff it is water. If M is not water, then each of its portions, including M1 and M2 are not water. So once again we must assume M is water to avoid a contradiction. This, the predicate is water is cumulative.


We can define the predicate water as: WATER(M) iff M ≤ Sum(water). This provides a semantics for the predicate. An example along the lines of (28) shows its use as a predicate.


28a. The stuff Jake drank was water.

    b. [The M: DRINK(j, M)] WATER(M)


The definition above provides an interpretation for (28b)


    c. [The M: DRINK(j, M)] M ≤ Sum (water)


Substances have both NP and predicate expressions. Kearns provides an example of a definite NP form along the lines of (29).


29. Mary gave the water to John.

      [The M: WATER(M)] GIVE(m, M, j)


The translations in (28b) and (29) express the substance as a predicate that holds for some portion of the water sum. This distinguishes mass terms from individuals which only appear as arguments but not predicates. We have added a new type of object to predicate logic - a sum individual.


This distinction creates an ambiguity since objects are made from substances. This muddies the water so to speak. We have to distinguish between an entity and the stuff it is made of since we can apply predicates like is oval to puddles, but not water. Kearns shows one way to do this:


30a. The puddle is water.

    b. [∃M: [The x: PUDDLE(x)] CONSTITUTE(M, x)] WATER(M)


Kearns applies the same treatment to predicates like is yellow, which are not substances. This predicate applies homogeneously in the sentence Custard is yellow. Kearns uses a yellow sum that defined to be homogeneously yellow:


31. ∀M (M ≤ Sum (yellow) iff YELLOW(M))


This sum entity only applies to things that yellow throughout their entirety. Substances like custard and gold are completely yellow, whereas lemons and canaries have non-yellow parts. A sum individual can be defined for any predicate which applies to homogeneous substances. The analysis of the sentence Custard is yellow is then:


32. Sum(custard) ≤ Sum (yellow)



Noun Classes


The distinction between count and mass nouns reflects the structure of quantified expressions in any given language. English requires the use of a plural on nouns that refer to humans, animals and objects, i.e., count nouns. A mass must be divided into countable units before it can be counted (e.g., a cup of, three heads of). In contrast, Japanese only uses a plural on human nouns, and the plural is optional. Japanese requires a numeral classifier to be used for all nouns—human, animal, object and substance. The crosslinguistic study of classifiers provides additional insights into the structure of nominal reference.


Grinevald (2003) identifies four types of classifier systems:

 

      POSS+      CLASS     Numeral+ CLASS     CLASS+Noun      // Verb-     CLASS

                        Genitive                      Numeral    Noun                                       Verbal

                        Classifier                    Classifier  Classifier                                Classifier


The following examples illustrate these different types.


Genitive Classifiers: Ponapean (Rehg 1981:184)

      Kene-i mwenge                            Were-i pwoht

      EDIBLE.CLASS-my food           TRANSPORT.CLASS-my boat

      ‘my food’                                     ‘my boat’


Numeral Classifiers: Ponapean (Rehg 1981:130)

      Pwihk riemen                               Tuhke rioapwoat

      pig 2+ANIMATE.CLASS           tree 2+LONG.CLASS

      ‘two pigs’                                     ‘two trees’


Noun Classifiers: Jakaltek (Craig 1986:264)

      xil naj xuwan no7 lab’a

      saw MAN.CLASS John ANIMAL.CLASS snake

      ‘John saw the snake.’


Verbal Classifiers: Cayuga (Mithun 1986:386-388)

      Ohon’atatke:   ak-hon’at-a:k                               So:wa:s akh-nahskw-ae’

      It-potato-rotten past.I-POTATO.CLASS-eat       Dog      I-DOMESTIC.ANIMAL.CLASS-have

      ‘I ate a rotten potato.’                                          ‘I have a dog.’


Denny (1976:125) observed that nominal classifiers divide into three main semantic categories based on social, physical and functional interaction. Languages commonly distinguish animate entities, and especially humans in the social sphere, by gender and social rank. Interaction with physical objects leads to distinctions based on their physical properties, especially shape and material. Since the physical properties of objects are closely associated with their functional properties, it is a mistake to attribute a classifier’s use to one or the other. Many shape classifiers were historically derived from nominals in the vegetal domain (Adams 1986):

 

      Shape Classifiers        Lexical Origin

      1D: long-rigid             tree/trunk

      2D: flat                       flexible leaf

      3D: round                   fruit


Nominal classifiers can be divided into two further groups. Sortal classifiers distinguish between different categories or sorts of objects based on their shape, material or function. They include such distinctions as “round” oranges, “long rigid” arrows, and “flat, flexible” blankets. Mensural classifiers distinguish between different measures (“handful” of flour, “flock” of geese, “cup” of soda) and configurations (“pile” of books, “line” of geese, “puddle” of soda) of objects. Mensural classifiers often make up the bulk of numeral classifiers, whereas the number of sortal classifiers can be quite small.


Grinevald (2000) suggests that the locus of numeral classifiers shows a curious alignment with their meaning. Shape is the major semantic parameter among numeral classifiers, function is the main semantic parameter for genitive classifiers, and material is the dominant semantic parameter for noun classifiers.


Languages use classifiers to identify and track referents in discourse; their classificatory function is secondary to their discourse function. Thus, nominal classifiers should be properly grouped with restricted quantifiers in that nominal classifiers establish the identity of a referent by establishing a restricted set of individuals.


Ponapean

      Pwihk riemen

      pig 2+ANIMATE.CLASS

      ‘two pigs’

      [2x: ANIMATE(x) & PIG(x)]



Exercises (Kearns p. 143-145)


1. The underlined NP in the following sentences can have either a specific or nonspecific interpretation. Give a logical translation for each sentence and indicate which is specific and which nonspecific.


a. Karen wants to shoot a lion.

b. Eric didn’t meet a reporter.

c. Clive might buy a painting.

d. Every flautist played a sonata.



References


Adams, K. 1986. Numeral classifiers in Austroasiatic. In C. Craig (ed.), Noun Classes and Categorization, pp. 241-263. Amsterdam: John Benjamins.

Aikhenvald, A. Y. 2000. Classifiers: A Typology of Noun Classification Devices. New York: Oxford University Press.

Craig, C. G. 1986. Jacaltec noun classifiers: a study in language and culture. In C. Craig (ed.), Noun Classes and Categorization, pp. 263-293. Amsterdam: John Benjamins.

Craig, C. G. 1987. Jacaltec noun classifiers. A study in grammaticalization. Lingua 71:41-284.

Denny, J. P. 1976. What are noun classifiers good for? In S. Mufwene, S. Walker & S. Steever (eds.), Papers from the Twelfth Regional Meeting of the Chicago Linguistic Society 12:122-132.

Grinevald, C. 2000. A morphosyntactic typology of classifiers. In G. Senft (ed.), Nominal Classification, pp. 50-92. Cambridge: Cambridge University Press.

Grinevald, C. 2003. Classifier systems in the context of a typology of nominal classification. In K. Emmorey (ed.), Perspectives on Classifier Constructions in Sign Languages, pp. 91-110. Mahwah, NJ: Erlbaum.

Mithun, M. 1986. The convergence of noun classification systems. In C. Craig (ed.), Noun Classes and Categorization, pp. 379-397. Amsterdam: John Benjamins.

Rehg, K. 1981. Ponapean Reference Grammar. PALI Language Texts: Micronesia. Honolulu: The University Press of Hawaii.

Rooth, Mats. 1985. Association with focus. Doctoral dissertation, University of Massachusetts at Amherst.