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Plurals and Plurality

PLURALS AND PLURALITY

Plurality falls under the concept of grammatical number. So, one prefaces the discussion of plurality with a brief overview of grammatical number. Since this entry is written in English, one can consider grammatical number in English.

English nouns are either plural or singular, which is usually signaled by the presence or absence of the inflectional ending s. Thus, book (singular) contrasts with books (plural). However, some nouns have peculiar forms for singular and plural. For example, the plural of louse (singular) is lice (plural). Some nouns, like deer, do not take the suffix s, yet behave as both singular and plural. This is shown by the form of its preceding determiner and, should the noun be in the subject position, by the form of the main verb. Thus, in the sentence That deer is crossing the road, deer behaves like a singular noun, while in the sentence Those deer are crossing the road, it behaves like a plural noun. Still other nouns, such as police, behave only as grammatically plural.

While every English noun must appear in either a singular or plural form, not every English noun may appear in both forms. On the contrary, English pronouns have both a singular (e.g., he, she, or it ) and a plural form (they ), which, for the most part, share no stem. In addition, as illustrated earlier, many English common nouns, known as count nouns, occur as both singular and plural nouns. By contrast, English proper nouns appear in the singular or plural form, but not both. The singular proper noun Aristotle does not occur in the plural (in the same relevant sense), nor does the plural proper noun the Andes occur in the singular. Moreover, English common nouns, such as dust and advice, called mass nouns, occur typically only in the singular. This division between nouns that can occur both in the singular and in the plural and those that do not occur is crosscut by words that cannot be preceded by the full range of English determiners and those that can be. Thus, English nouns can be partitioned into four classes. On the one hand, proper nouns and pronouns cannot be preceded by determiners, while common nouns can be; and on the other, count nouns and pronouns occur in both singular and plural forms, while mass nouns and proper nouns do not.

Occurs with a determiner Admits the contrast of singular and plural
Proper name
Pronoun +
Mass noun +
Count noun + +

The contrast between singular and plural forms is signaled by the inflection of the noun, but the distinction applies to the noun phrase containing the noun. This is manifested by the fact that conjoined proper nouns behave as though they are plural. For example, while the sentence Russell and Whitehead was coauthors is unacceptable in English, the sentence Russell and Whitehead were coauthors is not.

Bearing in mind these facts about English grammatical number, one may ask what contribution grammatical number makes to a noun phrase. The commonsensical view, the one of traditional grammar, maintains that a plural noun phrase, such as these books, denotes more than one thing, whereas a singular noun phrase, such as this book, denotes precisely one thing. Matters, however, are not so simple. Some singular noun phrases, such as Pegasus, and some plural noun phrases, such as the Furies, denote nothing at all. Some singular nouns denote more than one thing. The proper noun Benelux denotes Belgium, The Netherlands, and Luxemburg; the collective count noun phrase the team denotes the people making up the team; and this furniture may denote a roomful of furniture comprising, say, two tables and a sofa, each of which is, of course, a piece of furniture. At the same time, plural count nouns such as these pants (compare this pair of pants ) may denote only a single thing. Finally, what single thing, if any, does the singular noun phrase the average Roman legionnaire denote?

Common nouns contrast with pronouns and proper names in that they tolerate being preceded either by almost any determiner or by no determiner. When a common count noun is not preceded by any determiner, it must appear in the plural form. Such noun phrases are known as bare plurals. As Greg Carlson (1977) notes, such noun phrases are liable to different construals. The noun dogs in the sentence dogs are barking can be paraphrased as Some dogs are barking ; however, when it occurs in the sentence dogs bark it is not paraphrased as some dogs bark. Rather, it seems to express a quasi-universal statement, something like almost all dogs bark, often known as the generic construal. Carlson notices that a similar contrast applies to mass nouns in the bare usage. Water is liquid as opposed to water is dripping (see Carlson and Pelletier 1995).

Further questions arise with quantified noun phrases. The singular noun phrase some boy might be thought to contrast with the plural noun phrase some boys because the former pertains to a single boy, while the latter pertains to more than one boy. This contrast does not appear to obtain for the singular noun phrase each boy and the plural noun phrase all boys, nor for the singular noun phrase no woman and the plural noun phrase no women.

An important source of data for the investigation of plural noun phrases is their susceptibility to so-called collective and distributive construals. One useful way to determine what these construals consist in is to use an equivalence between plural noun phrases and conjoined noun phrases, where the conjoined noun phrases contain proper nouns. If the men denotes Bertrand Russell and Alfred Whitehead, then (1.0) is paraphrasable by (1.1):

(1.0) The men wrote a book.

(1.1) Whitehead and Russell wrote a book.

It has long been recognized that sentences such as (1.0) and (1.1) have different construals, distinguishable with the help of adverbs:

(2.0) The men wrote a book.

(2.1) The men wrote a book together.

(2.2) The men each wrote a book.

These are paraphrasable by the following sentences, respectively:

(3.0) Whitehead and Russell wrote a book.

(3.1) Whitehead and Russell wrote a book together.

(3.2) Whitehead and Russell each wrote a book.

The sentences in (1) are true on the collective construal, since Principia Mathematica was written as a collaborative effort of Whitehead and Russell. This construal can be forced by the use of the adverb together, as in (2.1) and (3.1). The sentences in (1) are also true on the distributive construal, since Russell wrote at least one book on his own, for example, An Inquiry into Meaning and Truth, and Whitehead also wrote a book on his own, for example, A Treatise on Universal Algebra. This construal can be enforced by the use of the adverb each, as in (2.2) and (3.2).

As shown by the next example, the susceptibility of plural noun phrases to collective and distributive construals is not confined to collaboration:

(4.0) These two suitcases weigh fifty kilograms.

(4.1) These two suitcases each weigh fifty kilograms.

(4.2) These two suitcases weigh fifty kilograms together.

Moreover, collective and distributive construals seem to be the extremes of a range of construals. If the men denotes Richard Rodgers, Oscar Hammerstein, and Lorenz Hart, it is true to say that

(5) The men wrote musicals.

even though none of them wrote a musical on his own and the three never wrote a musical together. What is true is that Rodgers and Hammerstein wrote musicals and Rodgers and Hart wrote musicals (see Gillon 1987).

Next, it should be noted that susceptibility of collective and distributive construals is not confined to plural noun phrases in the subject position. Every argument position containing a plural noun phrasebe it the subject, object, indirect object, or object of a prepositionis liable to these construals, regardless of whether the noun phrase is an argument of a verb or of a noun (see Gillon 1996).

(6.1) Isabelle gave the girls a cookie.

(6.2) Rick drove through the Redwood trees. (Compare Rick drove through the Redwood tree.)

(6.3) The two suitcases' weight is fifty kilograms.

(6.4) The writing of Principia Mathematica by Russell and Whitehead.

Finally, even singular count nouns give rise to collective and distributive construals. Suppose that someone has two suitcases and says:

(7) This luggage weighs fifty kilograms.

The sentence could be taken to mean that altogether the luggage weighs fifty kilograms or that each piece of luggage weighs fifty kilograms.

Two crucial questions arise for the semantics of plural noun phrases: First, what do plural noun phrases denote? Second, how does one account for the various construals to which they are liable?

One can begin with the first question. According to the earliest researchers to address the question, such as Michael Bennett (1974) and Roland Hausser (1974), plural noun phrases denote sets. This view was roundly criticized by Godehard Link (1983) and Peter Simons (1983), who argued, independently of each other, that plural noun phrases do not denote sets, but what Simons called pluralities. Whereas a set of concrete individuals is an abstract mathematical entity, without spatial or temporal location, a plurality of concrete individuals is a concrete entity, with the spatial and temporal location of its membership. However, for both a set and a plurality, identity is determined by membership.

A plurality, then, is nothing more than the sum of its members. At the same time, a plurality is different from a collective, which may be more than the sum of its members. Thus, while a plurality is identified by its membership, so that if it acquires or loses a member, it becomes a different plurality, a collective is not identified simply by its members, for it can remain the same, even if its membership changes. Thus, an orchestra can remain the same, even though its members change. Inversely, the exact same individuals might constitute two collectives. Indeed, Simons (1982) reports that once the same musicians made up the Chapel Orchestra, the Court Opera Orchestra, and the Vienna Philharmonic. Nonetheless, a plurality can also be seen as the limiting case of a collective: that is, a plurality is a collective without conditions governing its constitution (Simons 1987, chapter 4.4).

The set of pluralities on a finite domain has the structure of a join semilattice. For example, consider three people: Dan, Paul, and Rick. They can form seven pluralities: three improperDan, Paul, and Rick; and four improperDan + Paul, Dan + Rick, Paul + Rick, and Dan + Paul + Rick. The algebraic operation symbolized here by + , is a join operation. It is idempotent (x + x = x ), since there is no difference between Dan and Dan + Dan; it is commutative, since there is no difference between Dan + Paul and Paul + Dan; and it is associative, since Dan + (Paul + Rick) is the same plurality as (Dan + Paul) + Rick. The seven pluralities are all concrete individuals.

The join semilattice just described is isomorphic to the join semilattice obtained by assigning each plurality, proper and improper, a set: An improper plurality is assigned a singleton set. Thus, Dan is assigned {Dan }, a plurality comprised of two people is assigned a doubleton set. Thus, Dan + Rick is assigned {Dan, Rick }. And the plurality comprising three people is assigned a set of three people. The operation on these sets corresponding to + is that of union. Since every join semilattice of pluralities is isomorphic to a join semilattice of sets, a number of semanticists, including Fred Landman (1989a, 1989b), Roger Schwarzschild (1996), and Yoad Winter (2001), are content to treat pluralities as sets.

Link (1983) develops a semantics for a formal notation, designed to simulate singularity and plurality. Like Simons (1983, 1987), Link views the denotations of plural count noun phrases as distinct from the denotations of singular mass noun phrases, the former having their denotation based on individuals, the latter on so-called masses (see the mass noun entry). This distinction in denotation seems implausible, in view of the near synonymy of mass nouns such as footwear, luggage, traffic, and advice, with count nouns such as shoes, suitcases, vehicles, and suggestions. In light of such facts, Gillon (1992) provides a semantics of common nouns whereby a plural noun phrase such as shoes and a singular noun phrase such as footwear may have the same denotation; after all, all shoes are footwear, even if some footwear are not shoes. Another semanticist to provide a uniform domain for the interpretation of mass nouns and count nouns is Almerino Ojeda (1993), who takes all nouns to denote, in the first instance, kinds.

One can now turn to the second question: How are the various construals of plural noun phrases to be explained? A few authors such as Gillon (1987, 1992, 1996) and Schwarzschild (1996) think that the collective and distributive construals are extremes of a variety of construals, which, in their view, is pragmatically determined. However, the preponderance of authors recognize only two construalsthe collective and distributive construals of traditional grammarand take them to be the result of an ambiguity arising from the presence or absence of an unpronounced adverb. For some, like Link (1983), the adverb is essentially a phonetically null version of the English adverb each. For others, like Landman (1989a, 1989b), it is a phonetically null collectivizing operator applying to noun phrases. In fact, each of these views require no less than three kinds of phonetically null operators. Since virtually every plural noun phrase, no matter where it occurs in a sentence, is liable to collective and distributive construals, no fewer than three such phonetically null words are required (see Gillon 1996). Finally, several authors (Schein 1993, Lasersohn 1995, Landman 2000) have tried to develop a theory of events and their parts and participants to account for collective and distributive construals.

See also Generics; Nouns, Mass and Count.

Bibliography

Bäuerle, Rainer, Christoph Schwarze, and Arnim von Stechow, eds. Meaning, Use, and Interpretation of Language. Berlin, Germany: Gruyter, 1983.

Bennett, Michael R. "Some Extensions of a Montague Fragment of English." PhD diss., University of California, Los Angeles, 1974.

Carlson, Greg. "A Unified Analysis of the English Bare Plural." Linguistics and Philosophy 1 (1977): 413457.

Carlson, Greg, and Jeff Pelletier, eds. The Generic Book. Chicago: University of Chicago Press, 1995.

Gillon, Brendan S. "Collectivity and Distributivity Internal to English Noun Phrases." Language Sciences 18 (12) (1996): 443468.

Gillon, Brendan S. "A Common Semantics for English Count and Mass Nouns." Linguistics and Philosophy 15 (6) (1992): 597639.

Gillon, Brendan S. "The Readings of Plural Noun Phrases in English." Linguistics and Philosophy 10 (1987): 199220.

Hausser, Roland. Quantification in an Extended Montague Grammar. PhD diss., University of Texas, Austin, 1974.

Landman, Fred. Events and Plurality: The Jerusalem Lectures. Dordrecht, Netherlands: Kluwer Academic, 2000.

Landman, Fred. "Groups I." Linguistics and Philosophy 12 (5) (1989a): 559606.

Landman, Fred. "Groups II." Linguistics and Philosophy 12 (6) (1989b): 723744.

Lasersohn, Peter. Plurality, Conjunction, and Events. Dordrecht, Netherlands: Kluwer Academic, 1995.

Link, Godehard. "The Logical Analysis of Plurals and Mass Terms." In Meaning, Use, and Interpretation of Language, edited by Rainer Bäuerle, Christoph Schwarze, and Arnim von Stechow, 302323. Berlin, Germany: Gruyter, 1983.

Ojeda, Almerindo. Linguistic Individuals. Stanford, CA: Center for the Study of Language and Information, 1993.

Schein, Barry. Plurals and Events. Cambridge, MA: MIT Press, 1993.

Schwarzschild, Roger. Pluralities. Dordrecht, Netherlands: Kluwer Academic, 1996.

Simons, Peter M. "Class, Mass, and Mereology." History and Philosophy of Logic 4 (1983): 157180.

Simons, Peter. Parts: A Study in Ontology. New York: Oxford University Press, 1987.

Simons, Peter M. "Plural Reference and Set Theory." In Parts and Moments: Studies in Logic and Formal Ontology, edited by Barry Smith, 199260. Munich, Germany: Philosophia (Analytica), 1982.

Smith, Barry, ed. Parts and Moments: Studies in Logic and Formal Ontology. Munich, Germany: Philosophia (Analytica), 1982.

Winter, Yoad. Flexibility Principles in Boolean Semantics: The Interpretation of Coordination, Plurality, and Scope in Natural Language. Cambridge, MA: MIT Press, 2001.

Brendan S. Gillon (2005)

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