Set-denoting adjectives denote sets of entities in the domain of discourse that possess the property denoted by the adjectives; cf. Section 23.3.2.1. A copular construction such as (3a) expresses that the logical subject Jan of the adjective slechtbad is contained in the denotation set of the adjective, which is expressed in predicate logic as in (3a'). The attributive construction in (3b) expresses that the intersection of the set denoted by the noun jongenboy and the set denoted by the adjective slecht contains at least one entity, which is expressed in predicate logic as in (3b'). The semantic representations in (3) express more or less the same thing as the set-theoretical representations in Figure 2 in Section 23.3.2.1, sub I.

Although these semantic representations are adequate approximations of the meanings of the examples in (3), they do not fully express their meanings. By using (3a), we imply that Jan has a certain place on the implied scale of goodness in (2), as in (4a), while in (3b) we imply that there is at least one boy who has a certain place on the scale, as in (4b); in the case of the plural slechte jongensbad boys, each boy can be in a different place, as long as they are before the neutral zone.

4

Scale of goodness

b.

In other words, scalar adjectives seem to have the additional property of relating entities to certain positions on the scale that they imply. If we assume that the range on the implied scale denoted by a scalar adjective consists of a set of ordered degrees, this can easily be expressed in terms of predicate logic.

Consider the representations in (5), where d stands for degree, i.e. a position on the implied scale. The copular construction in (3a) now gets the semantic representation in (5a), which expresses that there is a degree d that is part of the range on the implied scale of goodness denoted by slecht, such that Jan occupies that position on the scale. The attributive construction (3b) can be represented as in (5b): it expresses that there is an entity x such that x is a boy, and that there is a degree d which is part of the range on the implied scale of goodness, denoted by slechtbad, such that x occupies that position on the scale.

Unlike the semantic representations in (3a') and (3b'), the representations in (5) do take into account that the cases in (3) imply a mapping of entities to specific positions on the implied scale.