This chapter focuses on the pre-determiners al'all' and heel'all/whole' as shown in the primeless examples of (1). They will be discussed in relation to their “inflected” counterparts alle and hele in the nearly equivalent constructions shown in the primed examples.

Before discussing al and heel in detail, we will give a very brief indication of some similarities and differences between these two pre-determiners. The two (and their alternants in the primed examples of (1)) have in common that, in a somewhat extended sense, they act as universal quantifiers. One property of universal quantifiers is that they can be modified by approximative modifiers like bijna'nearly' and vrijwel'virtually'. This is illustrated in (2) for the universal quantifier alles'everything', and the negative existential quantifier niets, which can be also be represented as a universal quantifier followed by negation; cf. the equivalence rule ¬∃x φ ↔ ∀x ¬φ.

The primeless examples in (3) show that the pre-determiners al and heel have the same modification possibilities, and in the primed examples we give similar examples for inflected alle and hele. There are some subtle meaning differences between the two sets of examples. Example (3a), for example, refers to a contextually determined set of books, whereas (3a') may also refer to the set of books in the speakerʼs conception of the universe, that is, to all existing books. Example (3b) refers to the parts that make up a house (living, bedrooms, kitchen, bathroom, attic, etc.), whereas (3b') may also refer to the house as a unit, e.g., the house as seen from the exterior.

      That al'all' is a universal quantifier is of course also clear from its meaning: in terms of Figure 1 from Section 1.1.2, sub IIA, it indicates that all members in denotation set A of the noun phrase are properly included in denotation set B of the verb phrase, that is, that A - (A ∩ B) = ∅; cf. the discussion in Section 6.2.1.

The semantics of heel, which will be discussed more extensively in Section 7.2.1, is somewhat different; as was already mentioned, the noun phrase in (3b) refers to the parts that make up the house in question, and the pre-determiner heel indicates that the predicate schoonmaken applies to all parts of this house. Now if we take set A in Figure 1 to refer to the relevant parts of the house, it will be clear that heel also expresses that A - (A ∩ B) = ∅.
      Related to the fact that al and heel quantify over a different kind of set is that the two pre-determiners are generally in complementary distribution, which we will illustrate here for count nouns: since the pre-determiner al quantifies over a set of entities with a cardinality higher than one, the head noun of the noun phrase it quantifies is normally plural; since the pre-determiner heel quantifies over the parts of some entity, the head noun of the noun phrase it modifies is typically singular.

      With the brief discussion above, we have set the stage for the more exhaustive discussion of al and heel in, respectively, Section 7.1 and Section 7.2. We will conclude in Section 7.3 with a brief note on focus particles, which may also occur in pre-determiner position.