Nouns and Noun Phrases - University of Macau Library

680 Syntax of Dutch: nouns and noun phrases
The core function of the determiners is to specify the intersection (A ∩ B) and the
remainder of set A, that is, A - (A ∩ B). The definite article de/het ‘the’ in (6)
expresses that in the domain of discourse (domain D), all entities that satisfy the
description of the NP are included in the intersection A ∩ B, that is, that
A - (A ∩ B) = ∅. The singular noun phrase de jongen ‘the boy’ in (6a) has therefore
approximately the same interpretation as the proper noun Jan in the discussion
above; it expresses that the cardinality of A ∩ B is 1 (for which we will use the
notation: |A ∩ B| = 1). The only difference between the singular and the plural
example in (6) is that the latter expresses that |A ∩ B| ≥ 1.
(6) a. De jongen loopt op straat.
the boy walks in the.street
a′. de/het Nsg: |A ∩ B| = 1 & A - (A ∩ B) = ∅
b. De jongens lopen op straat.
the boys walk in the.street
b′. de Npl: |A ∩ B| ≥ 1 & A - (A ∩ B) = ∅
The semantic contribution of the indefinite articles in (7a&b) is to indicate that
A ∩ B is not empty; they do not imply anything about the set A - (A ∩ B), which
may or may not be empty. The difference between the singular indefinite article een
and the (phonetically empty) plural indefinite article ∅ is that the former expresses
that |A ∩ B| = 1, whereas the latter expresses that |A ∩ B| ≥ 1.
(7) a. Er loopt een jongen op straat.
there walks a boy in the.street
‘There is a boy walking in the street.’
a′. een Nsg: |A ∩ B| = 1 & |A - (A ∩ B)| ≥ 0
b. Er lopen ∅ jongens op straat.
there walk boys in the.street
‘There are boys walking in the street.’
b′. ∅ Npl: |A ∩ B| ≥ 1 & |A - (A ∩ B)| ≥ 0
It is important to note that only parts of the meaning descriptions in the primed
examples of (6) and (7) are inherently linked to the determiner: definite articles
imply that A - (A ∩ B) = ∅, whereas indefinite articles do not. The claims with
respect to the cardinality of the intersection A ∩ B do not come from the articles but
from the number (singular versus plural) marking on the nouns: singular marking
expresses that |A ∩ B| = 1, whereas plural marking expresses that |A ∩ B| ≥ 1. It is
therefore not surprising that the difference between definite and indefinite noun
phrases headed by a non-count like wijn ‘wine’ is that the former refers to a
contextually determined amount of wine, whereas the latter simply refers to an
indeterminate amount of wine.
The meaning that we attribute to the number marking, which is due to Farkas &
De Swart (2008), may come as a surprise. First, the meaning attributed in (7a) to the
singular indefinite noun phrase breaks with the tradition in formal semantics that
translates the indefinite article by means of the existential °operator ∃x, which
implies that the article expresses that the intersection A ∩ B contains at least one