The Semantics of Determiners

3. Unmarked and marked indefinite Ds
In this section we turn to the indefinite side of the picture. For determiners, this is the branch marked ‘indefinite’ in Figure 2, and for DPs, the right branch of Figure 4. We concentrate here on indefinite determiners and leave issues concerning the interpretation of indefinite pronouns and bare singulars and plurals outside the scope of our discussion.
3.1 Unmarked indefinites
Given what was said about the contrast between definite determiners and the ordinary indefinite article, we take it that un in Romanian just like a(n) in English, is unmarked for definiteness. In Farkas (2007) it was suggested that it is, in fact, unmarked for all other features a determiner may bear and that it is this property that is responsible for the well-known versatility of interpretation of DPs whose D is this determiner. It is, in fact, this versatility that attracted the attention of the field to the semantics of indefinites in the first place.

We turn now to discussing these special properties of ordinary indefinites, contrasting them with universal DPs, definite DPs and, finally, the motley group of what we call here marked indefinites.

As mentioned already, unmarked indefinites, like all other DPs called non-quantificational here, may act as antecedents to discourse pronouns. It has also been noticed, quite early on (see Farkas 1981, Fodor and Sag 1982) that, unlike universal DPs, unmarked indefinites are scopally ‘free’. This means that no matter where they occur in a sentence, their interpretation can be independent of any other item in that sentence (in which case they are said to have widest scope) or their interpretation may be affected by some appropriately placed constituent of the sentence (in which case the DP is said to be ‘in the scope’ of that constituent). Consider the examples in (42):

(42) a. Fiecare student a citit o carte scrisă de Lessing.

every student has read a book written by L.
‘Every student read a book written by Lessing.

b. Fiecare profesor a vorbit cu fiecare student

every professor has spoken with every student
care a citit o carte scrisă de Lessing.
who has read a book written by L.
‘Every professor talked to every student who read a book by Lessing.’

The example in (42a) is susceptible to the following two interpretations: (i) the indefinite may be interpreted outside the scope of the universal, in which case (42a) is true just in case there is a particular book by Lessing (say The Golden Notebook) that every student read; (ii) the indefinite may be interpreted within the scope of the universal, in which case the books and the students may co-vary. These two readings would be represented in a PC language with restricted variables as in (43a), for the wide scope reading, and (43b) for the narrow scope reading, where bwl stands for book written by Lessing:

(43) a. ∃y: bwL(y) ∀x: student(x) read(x,y)

b. ∀x: student(x) ∃y: bwL(y) read(x,y)

The reading in (43a) is called an ‘inverse’ reading because the indefinite scopes over a constituent that is higher in the syntactic representation than the indefinite itself.

In the case of (42b) the possible interpretations get more complex. The indefinite may be interpreted as having widest scope, in which case the book by Lessing does not co-vary with either professors or students. Under this interpretation there must be a book by Lessing such that every professor talked to every student who read it. A second possible interpretation is one where the indefinite has narrowest scope, in which case it may co-vary with the students. Under this interpretation all that the professors cared about is whether students had read a book or other by Lessing. If a student had read a Lessing book or other, the professor talked to him/her. Finally, there is an intermediate scope reading as well, in which case the indefinite co-varies with the professors but not with the students. Under this interpretation, for each professor there is some book by Lessing (not necessarily the same for all professors) and the professor talked to every student who had read that book. For each professor there is a particular book such that the professor talked to every student who read that book. We leave it as an exercise to the reader to write the PC formulas that correspond to each reading. The widest and intermediate scope readings here are instances of ‘inverse’ scope.

Unmarked indefinites contrast with universals with respect to the freedom of interpretation just exemplified. Universals may have ‘inverse’ scope over an indefinite but only as long as the items they have scope over are within the same minimal clause as they are:

(44) a. Un student a vorbit cu fiecare profesor.

a student has spoken with every professor
‘A student spoke with every professor.’

b. Un profesor a spus că fiecare student a trişat la examen.

a professor has said that every student has cheated at exam
‘A professor said that every student had cheated on the exam.’

The sentence in (44a) is scopally ambiguous. Under the ‘inverse’ interpretation, the universal has scope over the indefinite (and therefore the student may co-vary with the professor). Under the ‘direct’ interpretation, co-variation is not possible. In (44b) on the other hand, the indefinite and the universal can only be interpreted in the ‘direct’ scope relation. This sentence cannot be interpreted as describing a situation where the professors co-vary with the students.

So far we have established a contrast between a quantificational DP and an unmarked indefinite. Is this scopal freedom characteristic of definites as well? It is very easy to construct examples with definites having widest scope. Having a definite instead of the indefinite in (42) yields widest scope interpretations out of context.

(45) a. Fiecare student a citit cartea scrisă de Lessing.

every student has read book.Def written by L.
‘Every student read the book written by Lessing.

b. Fiecare profesor a vorbit cu fiecare student

every professor has spoken with every student