The core meaning of quantifiers in prenominal position can be easily explained by using Figure 1 from Section 15.1.2, sub IIA, repeated below. This figure represents the subject-predicate relation in a clause: set A represents the denotation set of the lexical part (i.e. the NP-part) of the subject, and set B represents the denotation set of the verb phrase, where A and B are both contextually determined, i.e. dependent on the domain of discourse (domain D). The intersection A ∩ B denotes the set of entities for which the proposition expressed by the clause is claimed to be true. For instance, in an example such as Jan wandelt op straat, it is claimed that the set denoted by A, viz. {Jan}, is included in set B, which consists of the people walking in the street. In other words, it is expressed that A - (A ∩ B) is empty.

The quantifiers have a function similar to that of the cardinal numerals; they indicate the size or cardinality of the intersection A ∩ B. They differ from the cardinals, however, in that they often do not do this in a very precise way. For example, an existential quantifier like sommige or enkelesome in (175a) simply indicates that A ∩ B has a cardinality greater than 1. The degree quantifier veelmany in (175b) indicates that the cardinality of A ∩ B is greater than the contextually defined norm n. The universal quantifier alleall in (175c) not only expresses that the intersection of A and B has a cardinality greater than 1, but also that it exhausts set A, i.e. that A - (A ∩ B) is empty.

Because quantifiers perform a similar function as cardinals without making the cardinality of A ∩ B precise, some Dutch grammars refer to these quantifiers as “indefinite cardinal numerals”; other grammars, such as Haeseryn et al. (1997), divide these quantifiers into “indefinite cardinals” and “indefinite pronouns” on the basis of their distribution (i.e. as part of the noun phrase or as an independently used constituent). In the following, we will simply use the term quantifier.

The examples in (175) are all partitive in the sense that set A is already part of domain D, but quantifiers can also be used in presentative sentences, i.e. to introduce new entities into domain D. However, not all quantifiers can be used in this way: for instance, example (176a) shows that the existential quantifiers enkele and sommige differ in that only the former can be used in a presentative expletive construction. This means that the difference between sommige and enkele is similar to the difference between the weak and strong forms of English some, which are given in the glosses as sm and some, respectively. Like enkele, the degree quantifier veelmany can be used in both partitive constructions such as (175b) and presentative expletive constructions such as (176b). The universal quantifier alleall in (176c) cannot be used in presentative sentences. Because the properties of the quantifier in the partitive and presentative constructions correlate with the weak and strong forms of English some, respectively, they are referred to as weak and strong quantifiers.

The examples in (176) show that noun phrases with weak and strong quantifiers behave like indefinite and definite noun phrases, respectively. There is another way in which this correlation holds. First, consider the two (a)-examples in (177), which show that in noun phrases with a cardinal numeral, the head noun of the primeless example can be left implicit if so-called quantitative er is present (provided that the content of the noun is recoverable from the discourse or extra-linguistic context). However, the acceptability contrast between the two primed examples in (177) shows that this is only possible if the noun phrase is indefinite.

The examples in (178) show that we find a similar contrast between noun phrases with a weak quantifier and those with a strong quantifier: leaving the head noun implicit is only possible in the former case.

For a more detailed discussion of quantitative-er constructions, we refer the reader to Section 20.3.

Quantifiers differ in the logical inferences they allow. High-degree quantifiers such as veelmany, for example, allow the semantic implication in (179a), whereas low-degree quantifiers such as weinigfew do not; the inference actually goes in the opposite direction, in that (179b') implies (179b).

Another implicational difference between these two quantifiers is given in (180). If example (180a) is true with the high-degree modifier veelmany, then the same holds for example (180a'), where the VP zwemmento swim denotes a superset of the VP in de zee zwemmento swim in the sea in (180a). In contrast, this implication is not valid in (180b&b'), where the quantifier weinig expresses low degree, since there may be many children swimming in the pool; the inference again goes in the opposite direction, in that (180b') implies (180b).

These kinds of implications, which have been treated extensively in the formal semantic literature of the last two or three decades, are not limited to quantifiers: example (181) shows, for example, that definite noun phrases behave in essentially the same way as the sentences containing a high-degree modifier.

The semantic properties of quantifiers of the type discussed above have implications for e.g. the licensing of negative polarity elements: a noun phrase containing the quantifier weinigfew can license the negative-polar verb hoevenneed to, whereas a noun phrase containing the quantifier veelmany cannot. Semantic correlations like these have given rise to a vast literature, which will not be discussed here; cf. Zwarts’ (1981) for pioneering work on this topic in Dutch.

So far we have only discussed examples where quantifiers are used as modifiers of a noun phrase. However, a quantifier can also be used as an independent constituent, i.e. as an argument or a floating quantifier. Examples of these uses are given in the primeless and primed examples of (183). The following sections will also discuss these independent uses.

The examples in (183) show that there are two spellings for the independent occurrences of the quantifiers ending in 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] nouns, and the form with -n is used with [+human] nouns (cf. Section 20.2.4, sub II, for further discussion). Note that the examples in (183) are all formal and typically found in written language; in colloquial speech, the preferred way of expressing the intended assertions would be in the form of the primed examples, with allemaalall substituted for alle(n)all: Ze zijn allemaal naar de vergaderzaal gegaan/Ze zijn allemaal verkocht.

The examples in (184) show that the universal quantifier alle behaves like the cardinal numerals in that it can be modified by an adverb like bijnaalmost; cf. Section 20.1.1.5. Since this adverb takes only the cardinal in its scope, it seems plausible that they form a phrase. If so, it is unlikely that the cardinal is a functional head occupying the head position Num of NumP. We have therefore concluded that the projection of the cardinal is in the specifier position of NumP, and we can apply a similar analysis to the universal quantifier alle, assuming that it occupies the same position as the cardinal; the determiner D in these structures is the (phonetically empty) indefinite article Ø.

Although the two structural representations in the primed examples look quite similar, there may be a non-trivial difference between them, which is related to the categorial status of the modifier. Section 20.1.1.1 has shown that there are good reasons to assume that cardinal numerals are actually nouns, but similar evidence does not seem to be available for alle, which rather seems to be adjectival in nature. One way to resolve to solve this potential problem is to assume that the two representations are in fact identical, in that the quantifier phrase is headed by a silent counterpart of the cardinal, number. If so, the representation in (184b') should be replaced by the one in (185a). An attractive argument for this analysis is that the silent noun number can be replaced by the cardinal tweeënvijftigfifty-two (the actual number of novels that Vestdijk wrote) without any change in the truth value of the sentences.

If viable, the analyses in (185) can easily be extended to cases such as (186a), which would then be assigned the representation in (186b); recall from Section 20.1.1.6, sub V, that Kayne (2003; 2007) also advocates such an analysis for English few (among other cases).

The hypothesis proposed here will be adopted in the following sections. The modification of quantifiers will be discussed in more detail in Section 20.2.5.