Nouns and Noun Phrases - University of Macau Library

6.2. Quantifiers
Numerals and quantifiers 895
This section discusses quantifiers like alle/sommige/vele ‘all/some/many’. We will
begin in Section 6.2.1 with a discussion of some more general properties of, and
notions related to these quantifiers. After that, Sections 6.2.2 to 6.2.4 will discuss
the universal, existential and degree quantifiers in more detail.
6.2.1. Introduction
This section will discuss 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.
I. Core semantics
The easiest way to explain the core meaning of the quantifiers is by using Figure 1
from Section 1.1.2.2.1, 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
like 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) = ∅.
A B
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 (78a), for example, simply
indicates that A ∩ B has a cardinality larger than 1. The degree quantifier veel
‘many’ in (78b) indicates that the cardinality of A ∩ B is larger than a certain
contextually defined norm n. And the universal quantifier alle ‘all’ in (78c)
expresses that the intersection of A and B exhausts set A, that is, that
A - (A ∩ B) = ∅.