Fodor and Sag (1982): Referential and quantificational

standard quantificational reading and a referential (i.e. indexical) reading. Fodor and Sag’s original proposal is based on the availability of long-distance scope readings (wide scope readings with respect to scope islands) of indefinites, exemplified for English a-indefinites and German ein-indefinites below. They illustrate their point by the interaction of indefinites with quantifiers. The classic approach to the contrast between referential and quantificational readings is by means of different scope-taking behavior.

I will now give a brief introduction to scope islands and the scope taking behavior of indefinites with respect to scope islands. This is important as we will investigate the referential behavior of indefinite dieser in examples containing scope islands in section 4.4. Scope islands are constructions which usually do not allow quantifiers to take scope out of them. Syntactic islands, i.e. those constructions which do not allow overt extraction (from them) (cf. Ross 1967) always are also scope islands (Endriss 2009: 8). Since if-clauses or that-clauses are known to be such syntactic islands, they are also scope islands.

(231) Peter will be happy if few movies are shown.

if > few

*few > if

(Endriss 2009: 9)

(231) shows how the if-clause is a scope island, as the sentence can only receive the narrow scope interpretation for the quantifier. It can be paraphrased as:

Peter will be happy if overall few movies (under discussion) are shown. It is impossible to interpret the sentence as saying that, for certain few movies, it holds that Peter will be happy if these movies are shown. That would be the wide scope reading” (Endriss 2009: 9). This impossibility for the quantifier to scope out of

the scope island can be labeled as an island-constraint on the side of the island, prohibiting for the quantifier to scope out of it.

Nevertheless, we know that some indefinites, such as a / some N are not bound to obey this island constraint, as they can take scope out of a scope island.

Endriss (2009: 9) refers to this ability as the exceptional wide scope behavior of indefinites:

(232) Peter will be happy if a / some movie is shown.

if > ∃

∃ > if

(Endriss 2009: 9)

(232), in contrast to (231) above, allows for a wide scope reading of the involved quantifiers, as it can mean, for example, that there is a particular movie (e.g. Lord of the Rings part 1), such that if this movie is shown, Peter will be happy. Such a wide scope reading is impossible in the case of (231).

I have shown in the examples above that scope islands can be created by, for example, if- or that-clauses with lexical heads or conditionals, i.e. linguistic operators which give rise to the so-called islands constraint. This means that quantificational indefinites, in these contexts, cannot “leave the island”. In other words, in these contexts quantificational indefinites usually cannot scope out of the scope island. They must obey to the island constraint and thus cannot receive wide scope. This is exemplified once more in (233) below, where we can see that indefinite noun phrases with the indefinite article can get both exceptional wide or narrow scope with respect to the definite NP the rumor in a scope island, reflecting both the referential interpretation and the quantificational interpretation, respectively. However, the universal phrase each student in (234) cannot receive wide scope, obeying to the island constraint. Thus, the referential reading of a in (233) cannot be described by a wide scope existential quantifier. Fodor and Sag (1982) therefore propose a lexical ambiguity of the indefinite article, claiming that the indefinite article is either interpreted as a referring expression (an indexical) or as an existential quantifier. The referring expression is assumed to be scopeless, like an indexical. That is, it only behaves as if it always has widest scope, as in (233b). The quantificational interpretation, as in (233a), must obey island constraints like other quantifiers and accounts here for the non-specific reading.

(233) John overheard the rumor that a student of mine had been called before the dean.

John hörte das Gerücht, dass einer meiner Studenten zum Dekan gerufen wurde.

a. the rumor > a student b. a student > the rumor (Fodor & Sag 1982: 495)

(234) John overheard the rumor that each student of mine had been called before the dean.

John hörte das Gerücht, dass jeder meiner Studenten zum Dekan gerufen wurde.

a. the rumor > each student b. *each student > the rumor (Fodor & Sag 1982: 495)

Fodor and Sag’s (1982) theory clearly predicts that an indefinite is to be interpreted either as a referential expression which always gives the appearance of widest scope (i.e. is scopally inert), or as an existential quantifier, which has to obey scope island constraints.

This prediction can be tested using examples with two quantifiers (see below). According to Fodor and Sag’s (1982) theory, one would only find a narrow scope reading for the existential interpretation and a wide scope reading for the referential interpretation, but no intermediate reading. However, criticizing their account, von Heusinger (2002b: 126) observes: “while judgments on intermediate readings are quite intricate in general, Farkas (1981) observed for certain examples that intermediate readings are often very natural.”

I will further elaborate on the arguments provided against Fodor and Sag (1982) in Section 5.3.3. Being aware of the fact that Fodor and Sag’s (1982) account is subject to critique (if applied to the indefinite article), I am, at this point, rather interested in the suggested sentence semantics for the referential indefinites by Fodor and Sag in (315) below, than in their original motivation for this semantics.

The lexical entries for the two readings suggested by Fodor and Sag (1982) (i.e. the traditional quantificational reading and the new referential reading) are given below in (235a) and (235b), in a two-dimensional semantics with a context set c and an evaluation point I (following Heim 2011):

(235) a. [[aquantN]] = λQ. ∃x. [N(x) and Q(x)]

b. [[aref α]]^c,i = is defined only if there is a unique individual that the speaker of c has in mind in c, and this individual is in [[α]]^c,c; where defined, [[arefα]]^c,i = this individual.

(Heim 2011: ex. 56)

As an illustration consider the pair of sentences in (236). In (236a) the speaker most likely has a particular referent in mind when she utters a man. This is suggested by the observation that the speaker is clearly aware of the identity of the man who proposed to her, and in fact wants to hide his identity from the hearer. The man’s identity is relevant from the speaker’s point of view. In contrast, the speaker has no particular referent in mind in (236b), where she is concerned simply with the presence of some man or other in the women’s bathroom. For

Fodor and Sag (1982) (236a) contains a so-called “referential indefinite” while (236b) contains a quantificational indefinite.

(236) a. A man just proposed to me in the orangery (though I’m much too embarrassed to tell you who it was).

b. A man is in the women’s bathroom (but I haven’t dared to go in there to see who it is).

(Fodor and Sag 1982: 359)

Crucially, considering Fodor and Sag’s (1982) semantics of referentiality in (235b), the extension of a referential indefinite is defined if and only if the speaker intends to refer to the unique individual in the actual world w which is denoted by the indefinite. Since this semantics mirrors Kaplan’s semantics for demonstratives, the referential indefinite was originally claimed to be an indexical or a demonstrative. Demonstratives, according to Kaplan, are defined as expressions which require an associated demonstration. They refer to that very object that the demonstration points out in the actual utterance situation — the demonstratum, as Kaplan calls it.

This indexical behavior is mirrored in Fodor and Sag’s (1982) semantics for referential indefinites, as their extension is defined if and only if the speaker intends to refer to the unique individual in the actual world w which is denoted by the indefinite. The demonstration required for deictic demonstratives is replaced then by what is labeled “private ostension” (as it is not overt) (Fodor and Sag 1982: 384) for referential indefinites. The important feature that the denotation rules for (deictic) demonstratives and referential indefinite phrases share is that the denotation depends only on the context of the utterance and not on the sentential context in which the phrase appears. Like I, you, here, that and so on, these phrases are thus immune to the usual effects of scoped elements in the sentence.

Fodor and Sag (1982) themselves relate their referential indefinites to the Kaplan-semantics of demonstratives, saying that the pointing gesture required for deictic demonstratives is replaced by “private ostension” (Fodor and Sag 1982:

384):

In fact, the closest analogue to a referential indefinite is a demonstrative phrase accompanied by a pointing gesture which is not visible to the hearer, a ‘private’ pointing gesture within the mind of the speaker. (Fodor and Sag 1982: 381)

A demonstrative phrase carries the presupposition that its descriptive content and its associated ostension are compatible (see Kaplan (ms), on pointing to a man and saying that flower), and that the two together pick out a unique referent. Likewise, a referential indefinite carries the presupposition that its descriptive content is compatible with the speaker’s ‘private ostension’. Its denotation will be the individual the speaker ‘has in mind’, as long as the

descriptive content is true of that individual. Thus a referential indefinite can be regarded as an indexical phrase. (Fodor and Sag 1982: 384)

What we have argued is that a referential indefinite resembles a demonstrative without the associated overt pointing or other public identification of the referent. […] Its denotation will be the individual ‘the speaker has in mind’, as long as the descriptive content is true of that individual. […] …we will set about the task of giving a formal semantics for referential indefinites by adapting Kaplan’s formal treatment of demonstratives. (Fodor and Sag 1982: 384)