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6.2.1. Introduction
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This section discusses some more general semantic and syntactic properties of (noun phrases containing) quantifiers. We will start with a brief discussion of the core meaning of the quantifiers. This will be followed by a discussion of the distinction between what has become known in the literature as weak and strong quantifiers. After that we will briefly discuss the fact that quantifiers display different behavior with respect to the question of what kinds of inference are licensed by using certain quantifiers. We conclude with a brief discussion of the independent use of quantifiers, that is, their use as an argument or a floating quantifier.

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[+]  I.  Core semantics

The easiest way to explain the core meaning of the quantifiers is by using Figure 1 from Section 1.1.2, sub IIA, repeated below, to represent the subject-predicate relation in a clause. In this figure, A represents the set denoted by the subject NP and B the set denoted by the verb phrase. The intersection A ∩ B denotes the set of entities for which the proposition expressed by the clause is claimed to be true. In an example such as Jan wandelt op straat, for example, it is claimed that the set denoted by A, viz. {Jan}, is properly included in set B, which is constituted by the people walking in the street. In other words, it expresses that A - (A ∩ B) = ∅.

Figure 1: Set-theoretic representation of the subject-predicate relation

The quantifiers have a function similar to that of the cardinal numerals, namely, to indicate the size or the cardinality of intersection A ∩ B. They differ from the cardinal numerals, however, in that they do not do this in a very precise manner. An existential quantifier like sommige or enkele'some' in (81a), for example, simply indicates that A ∩ B has a cardinality larger than 1. The degree quantifier veel'many' in (81b) indicates that the cardinality of A ∩ B is larger than a certain contextually defined norm n. And the universal quantifier alle'all' in (81c) expresses that the intersection of A and B exhausts set A, that is, that A - (A ∩ B) = ∅.

Example 81
a. Sommige/Enkele deelnemers zijn al vertrokken.
  some/some  participants  are  already  left
  'Some participants have already left.'
a'. sommige: |A ∩ B| > 1
b. Veel deelnemers zijn al vertrokken.
  many participants  are  already  left
  'Many participants have already left.'
b'. veel: |A ∩ B| > n
c. Alle deelnemers zijn al vertrokken.
  all participants  are  already  left
  'All participants have already left.'
c'. alle: |A ∩ B| > 1 & A - (A ∩ B) = ∅

Since the quantifiers perform a similar function as the cardinal numbers without making the cardinality of A ∩ B precise, some Dutch grammars refer to these quantifiers as “indefinite cardinal numerals”; other grammars, like Haeseryn et al. (1997) divide these quantifiers into “indefinite cardinal numerals” and “indefinite pronouns”.

[+]  II.  Strong and weak quantifiers

The examples in (81) are all “partitive” in the sense that set A is already part of domain D. Quantifiers can, however, also be used in presentational sentences, that is, to introduce new entities into domain D, although it is not the case that all quantifiers can be used in this way: the (a)-examples in (82) show, for example, that the existential quantifiers enkele and sommige differ in that only the former can be used in a presentational expletive construction. This means that the difference between sommige and enkele is similar to that between the weak and the strong form of English some, which are given in the glosses and translations as sm and some, respectively. Like enkele, the degree quantifier veel'many' can be used both in a partitive construction such as (81b) and in a presentational expletive construction such as (82b). As is shown in (82c), the universal quantifier alle'all' cannot be used in presentational sentences. Because the properties of the quantifier in the partitive and presentational constructions correlate with, respectively, the weak and the strong forms of English some, they are often referred to as weak and strong quantifiers.

Example 82
a. Er zijn al enkele deelnemers vertrokken.
  there  are  already  sm  participants  left
  'Sm participants have already left.'
a'. * Er zijn al sommige deelnemers vertrokken.
  there  are  already  some  participants  left
  'Some participants have already left.'
b. Er zijn al veel deelnemers vertrokken.
  there  are  already  many participants  left
  'Many participants have already left.'
c. * Er zijn al alle deelnemers vertrokken.
  there  are  already  all participants  left

The examples in (82) show that noun phrases with weak and strong quantifiers behave like, respectively, indefinite and definite noun phrases. There is yet another way in which this correlation holds. First, consider the two (a)-examples of (83), which show that in noun phrases containing a cardinal numeral the head noun of the primeless example can be left implicit if so-called quantitative er is present (provided, at least, that the content of the noun is recoverable from the discourse or the extra-linguistic context). The contrast between (83a') and (83b') shows, however, that this is only possible if the noun phrase is indefinite.

Example 83
a. Jan heeft drie boeken meegenomen.
  Jan has  three books  prt.-taken
  'Jan has taken three books with him.'
a'. Jan heeft er [DP drie [NPe]] meegenomen.
  Jan has  er three  prt.-taken
b. Jan heeft de drie boeken meegenomen.
  Jan has  the three books  prt.-taken
  'Jan has taken three books with him.'
b'. * Jan heeft er [DP de drie [NPe]] meegenomen.
  Jan has  er  the three  prt.-taken

The examples in (84) show that we find a similar contrast between noun phrases containing a weak quantifier and those containing a strong quantifier: leaving the head noun implicit is only possible in the former case.

Example 84
a. Jan heeft er [DP enkele/*sommige [NPe]] meegenomen.
  Jan has  er sm/some  prt.-taken
  'Jan has already taken some of them (e.g., books) with him.'
b. Jan heeft er [DP veel [NPe]] meegenomen.
  Jan has  er many  prt.-taken
  'Jan has already taken many of them with him.'
c. * Jan heeft er [DP alle [NPe]] meegenomen.
  Jan has  er all  prt.-taken
  'Jan has already taken all of them with him.'
[+]  III.  Logical properties of quantifiers: Valid inference patterns

Quantifiers may differ in the logical inferences that they license. High degree quantifiers like veel'many', for example, allow the semantic implication in (85a), whereas low degree quantifiers like weinig'few' do not allow this inference; the inference instead goes in the opposite direction, in that example (85b') implies (85b).

Example 85
a. Veel kinderen drenzen en schreeuwen. ⇒
  many children  whine  and  yell
a'. Veel kinderen drenzen en veel kinderen schreeuwen.
  many children  whine  and  many children  yell
b. Weinig kinderen drenzen en schreeuwen. ⇏
  few children  whine  and  yell
b'. Weinig kinderen drenzen en weinig kinderen schreeuwen.
  few children  whine  and  few children  yell

Another implicational difference between these two quantifiers is given in (86). If example (86a) with the high degree modifier veel'many' is true, the same thing holds for example (86a'), in which the VP zwemmen'to swim' denotes a superset of the VP in de zee zwemmen'to swim in the sea' in (86a). In contrast, this implication is not valid in (86b&b'), in which the quantifier weinig expresses low degree, since there may be many children swimming in the swimming pool; again, the inference goes in the opposite direction: example (86b') implies (86b).

Example 86
a. Er zwemmen veel kinderen in de zee. ⇒
  there  swim  many children  in the sea
  'Many children swim in the sea.'
a'. Er zwemmen veel kinderen.
  there  swim  many children
b. Er zwemmen weinig kinderen in de zee. ⇏
  there  swim  few children  in the sea
  'Few children swim in the sea.'
b'. Er zwemmen weinig kinderen.
  there  swim  few children

These kinds of implications, which have been extensively dealt with in the formal semantic literature of the last two or three decades, are not limited to quantifiers: example (87) shows, for example, that definite noun phrases behave in essentially the same way as the sentences involving a high degree modifier.

Example 87
a. De kinderen drenzen en schreeuwen. ⇒
  the children  whine  and  yell
a'. De kinderen drenzen en de kinderen schreeuwen.
  the children  whine  and  the children  yell
b. De kinderen zwemmen in de zee. ⇒
  the children  swim  in the sea
b'. De kinderen zwemmen.
  the children  swim

The semantic properties of the quantifiers of the type discussed above have repercussions for, e.g., the licensing of negative polarity elements: a noun phrase containing the quantifier weinig'few' can, for example, license the negatively polar verb hoeven'have to', whereas a noun phrase containing the quantifier veel'many' cannot. Since correlations like these have given rise to a vast amount of literature, which deserves a more extensive discussion than we can give here, we will not discuss the issue any further, but we hope to return to it in future work. For the moment, we confine ourselves to referring to Zwarts’ (1981) pioneering work on this topic.

Example 88
a. Weinig mensen hoeven te vrezen voor hun baan.
  few people  have  to fear  for their job
  'Few people need to fear losing their job.'
b. * De/Veel mensen hoeven te vrezen voor hun baan.
  the/many people  have  to fear  for their job
[+]  IV.  Use as modifier or as independent argument

So far, we have only discussed examples with quantifiers that are used as modifiers of the noun phrase. A quantifier can, however, also be used as an independent constituent, that is, as an argument or a floating quantifier. Examples of these two uses are given in, respectively, the primeless and the primed examples of (89). The following sections will also discuss these independent uses.

Example 89
a. Allen gingen naar de vergaderzaal.
  all[+human]  went  to  the meeting.hall
a'. Ze zijn allen naar de vergaderzaal gegaan.
  they  are  all[+human]  to the meeting.hall  gone
b. Alle zijn uitverkocht.
  all[-human]  are  sold.out
b'. Ze zijn alle verkocht.
  they  are  all[-human]  sold

The examples in (89) show that there are two spellings for the independent occurrences of the quantifiers ending in a schwa: with or without a final -n. The presence of this orthographic -n, which is not pronounced in spoken Dutch, depends on the feature ±human of the referent or associate: the form without -n is used with -human and the form with -n with +human nouns. Note that +human should be understood as “consistently human”: conjunctions which are not consistently human, like mannen en hun autoʼs'men and their cars', take alle, not allen, as their independent quantifier. Note further that the examples in (89) are all formal, and most often found in written language; in colloquial speech, the preferred way of expressing the intended assertions would take the form of the primed examples with allemaal'all' substituted for alle(n)'all': Ze zijn allemaal naar de vergaderzaal gegaan/Ze zijn allemaal verkocht.

References:
  • Haeseryn, Walter, Romijn, Kirsten, Geerts, Guido, Rooij, Jaap de & Toorn, Maarten C. van den1997Algemene Nederlandse spraakkunstGroningenNijhoff
  • Zwarts, Frans1981Negatief polaire uitdrukkingenGLOT435-132
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