The Semantics of Determiners

2. Definite vs. indefinite Ds and DPs
The semantic distinction between definite and indefinite determiners has been at the heart of work in the philosophy of language and linguistic semantics in the last hundred years. A comprehensive overview would go well beyond the limits of this chapter, let alone the current section. We give here only a glimpse of the issues concerned, from the perspective of this author.¹³ We proceed by first laying out the relevant questions and then discuss some of the answers proposed in the literature. As already mentioned, for reasons of space, we leave the discussion of bare nominals outside the scope of this chapter.

At the level of determiners, the definite/indefinite divide cuts the class of non-quantificational determiners as on the right branch of the tree in Figure 2, repeated below:

definite indefinite
-(u)l ‘the’ acest ‘this’ un ‘a’, un-ul ‘one of’ vreun ‘some’ nici un ‘no’
Figure 4: Definite vs. indefinite determiners

The immediate task that arises is to establish the semantic property responsible for this division, a hotly debated issue. We look below at some of the most prominent answers given without attempting to be exhaustive. In the philosophical and linguistic literature the debate is often reduced to characterizing the difference between the ordinary definite article (English the) and the ordinary indefinite article (English a(n)). We will attempt here to recast it so as to shed light on the other determiners in Figure 4.

Two further questions that have to be answered are: (i) Is the distinction presuppositional or not? (ii) Is the distinction symmetric or not? The first question involves the issue of whether the information concerning definiteness carried by these determiners belongs in the asserted part of the sentences in which DPs with these Ds occur or in the presupposed part. (As mentioned above, the former view was taken by Russell, and the latter by Strawson.) In what follows, we take the presuppositional view without further argument since the field seems to have reached a consensus on this issue. We will not go into the further important questions that involve distinctions between various types of presupposition.

The symmetry question concerns the issue of whether the definite/indefinite contrast involves two properties, one for each side of the divide, or whether we are dealing with a single property, which is shared by the items on one side of the divide and absent in the items on the other side. The symmetric view would have it that definite determiners are marked for the presence of some property that renders them definite, while indefinite determiners are marked for the presence of the opposite property that renders them indefinite. The asymmetric view would have it that the members of one class are marked for the presence of some property P while the members of the other are simply not marked for that property. Thinking of definiteness as a feature, this issue amounts to the question of whether the feature is equipollent or privative. If privative, the question is which side of the divide is marked by the presence of a property and which side is unmarked.

Finally, a question that is often neglected in current discussions is that of how the definiteness contrasts within the D realm connect to definiteness contrasts within the larger DP realm. At the DP level, it is intuitive to group DPs as in Figure 5:

definite indefinite

Proper Names, def. pronouns, DPs with indef. determiners, indef. pronouns
DPs with def. determiners bare singulars and plurals¹⁴

Figure 5: Defnite vs. indefinite DPs

If this grouping is justified, the question that arises is how to generalize the semantic property responsible for the division in Figure 4 to the distinction in Figure 5.

The division in Figure 5 is justified in as much as there are grammatical phenomena that treat the DPs on one side of the divide differently from the DPs on the other. We will not go here into providing a full discussion of the issue but only point to some relevant data and references. A phenomenon relevant to this matter, as well as to Romanian, is

Differential Object Marking (DOM), already mentioned above. Languages that exhibit DOM mark a subclass of direct objects by special morpho-syntactic means. In Romanian, there are two interconnected special markers: clitic doubling and marking by the preposition pe, both mentioned in Section 1. The question of interest for the semanticist is what semantic parameters are relevant to characterizing the class of DOs that are specially marked. The vast literature on this topic has shown that definiteness is among the many factors involved. The data within a language as well as across languages point to hierarchies of DPs depending on how likely they are to trigger DOM. Concentrating on definiteness and abstracting away from the many other factors involved, we find the hierarchy in (24) (slightly adapted from Aissen 2003), where Def DPs are DPs with definite or demonstrative determiners:

(24) Proper Name > Def Pronoun > Def. DP > Partitive DP > Indef. DP

The DP types on the left are more likely to be DOM triggers than the DP types on the right, with individual languages fixing cutoff points at various particular rungs on the scale. The data in Romanian is too complex to be discussed here because the definiteness parameter interacts in complex ways with other factors. For data supporting the hierarchy in (24), the interested reader is referred to Aissen’s excellent paper. The existence of languages that have the cut off point after the third rung can be seen as justifying the division in Figure 5. Further questions arise, however, once we accept (24): why are partitive DPs more definite than non-partitive DPs? Why are Proper Names and definite pronouns more definite than definite DPs? We will come back to these issues briefly below.

Turning now back to the D classification in Figure 4, and to the two stars of the two teams, the ordinary definite -ul/the and the ordinary indefinite un/a(n), the two most prominent answers proposed to the question of what distinguishes them center around uniqueness and familiarity.

According to the uniqueness view, already mentioned above, the definite article presupposes that the DP it heads refers uniquely relative to the context in which it is uttered. For concreteness’ sake let us assume that this information is encoded in a semantic feature [DEF] associated with the definite article. In Montagovian terms, this would mean that the property that functions as the argument of a D with the feature [DEF] is presupposed to be a singleton set. Making this property sensitive to context in this theory is not trivial but not impossible. The question of whether the definiteness distinction is symmetric or not amounts to the question of whether indefinites are associated with a [-DEF] feature requiring them to be non-unique (the symmetric view) or whether they are simply seen as not marked for this feature (the non-symmetric view).

An immediate problem that arises is how to extend the uniqueness view to definite plural DPs such as the students/studenţii. Let us assume that the presence of the plural marker is associated with a requirement that the referent of the DP be chosen from among the sums (or groups) of entities in the denotation of the CN. (For an influential formal treatment of plurality, see Link (1983).) The uniqueness requirement on definites can then be generalized as a maximality requirement: the referent of a definite DP has to be the maximal entity within the denotation of the NP relative to the context. If the DP is singular, the only way the entity can be both maximal and atomic is if it is unique. If the DP is plural, it will refer to the largest sum of relevant entities in the context.

According to the familiarity view, defended in the early works in dynamic semantics, the common denominator of definite Ds is the requirement that the discourse referent they introduce be already present in the input DRS. The [DEF] feature in this view comes with a familiarity presupposition. The class of indefinites on the other hand is either marked with a [-DEF] feature amounting to a novelty requirement under a symmetric view (as in Heim 1982), or unmarked for definiteness/novelty under an asymmetric approach.

To illustrate the familiarity/novelty view, assume that (25) is uttered against the input DRS in (19), which itself was obtained after (18) was processed relative to an empty input DRS.

(25) A student sat down.

Under the assumption that indefinites are marked for novelty, by the end of processing (25) we end up with the DRS in (26), leaving aside all the details concerning tense and temporal interpretation:

( 26)

x y