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Two approaches to definiteness.

There are two main approaches to definiteness (Lyons 1999; Abbott 2004). The familiarity theory is based on the idea that the referent is known to the addressee. It is generally attributed to Christopherson (1939), but is also adopted by scholars from as diverse theoretical persuasions as Bolinger (1977) and Heim (1983). The example in (1) gives a very simple example of how the familiarity account might be imagined to work.

(1) A cat jumped into my garden ... the cat dug up my new bulbs.

On the familiarity account, the indefinite phrase a cat establishes a referent, and so the familiarity of the cat is signalled in the second use of cat in the phrase the cat. By the second clause, the cat is familiar: we identify the bulb-digging cat as identical with the cat that jumps into my garden. The familiarity theory requires a psychological basis: Heim (1983) discusses the referential identity of the phrases a cat and the cat in terms of "discourse reference". Familiarity is located in the discourse, and not in the reference to a real cat in the world: I can say the sentence in (1) without knowing the cat or who owns it, and you can understand it, even though you have never been near my garden, and do not know whether the cat is a marmalade tom or a tabby queen. Most linguists would agree that these discourse referents are intramental: if I say (1) to you, I create a cat referent in your mind, and reactivate it in the second clause.

The alternative approach is sometimes known as the uniqueness approach (Russell 1905). In Russell's account, a definite description (an NP with the as the determiner) has properties in common with both the universal and the existential quantifier. The sentence in (2a) is analysed using the existential and universal quantifiers in (2b), and (2b) is given a prose translation in (2c).

(2) a. The student arrived.

b. 3x[Student(x) &Vy[Student(y) V3y = x] & Arrived(x)]

c. There is one and no more than one thing which is a student, and that thing arrived.

Russell's theory has particular consequences. For example, Russell claims that the sentence in (3a) asserts each of the propositions in (3b)-(3d). (Or, alternatively, asserts the conjunction of these clauses.)

(3) a. The King of France is bald.

b. There is a King of France.

c. There is only one King of France.

d. This individual is bald.

According to Russell, if any of the propositions in (3b)-(3d) is false, the whole sentence in (3a) is false. Thus, given that in 1905 there was no King of France, the proposition in (3b) is false, and therefore (3a) is false.

There is a challenge to Russell's approach to examples such as (3a). For example, Russell's analysis was attacked by Strawson (1950) who claimed (following Frege) that referring expressions presuppose a reference to something and so the existential clause in (3b) is simply a presupposition. In the terms of this theory, saying (3a) does not assert the existence of the King of France, it simply presupposes it. Therefore for Strawson an utterance of the sentence The King of France is bald does not have a truth value, because the definite description fails to refer. Strawson does not explain what a presupposition is, but there is a substantial body of linguistics literature from the 1970s that attempts to make sense of the notion of presupposition (Gazdar 1979, Kempson 1975, Wilson 1975), and at the very least we might concur that presupposition is likely to be a psychological phenomenon loosely speaking we could say that a presupposition is something that speakers and hearers imagine or expect or believe to be the case about the world. Russell, on the other hand, is making an assertion about the relationship between the sentence itself and the world.

Another challenge to Russell's approach comes from Hawkins (1978). Hawkins observed that there are several meanings of the definite article, and that the uniqueness approach does not really capture them. Hawkins's point can be easily confirmed by taking a look at a pedagogical grammar of English for the speakers of a Slavic language. Such grammars explain not just the several meanings of definite articles, but also their many different contexts of use.

On the other hand, Russell's analysis was defended at length by Neale (1990), who explores the consequences for this theory in terms of the debate with Strawson, the behaviour of scope, substitutivity, and opacity, and the behaviour of definites as antecedents of anaphors. That is to say that where Strawson (1950) took a philosophical view of the debate, Neale (1990) located the debate in terms of how the theory addresses the analysis of particular linguistic data. A simple example can be seen in Milsark's (1977) treatment of definiteness effect phenomena, that is the difference between there's a dog and there's the dog.[1] There is a fundamental difference in interpretation between the two examples: The first sentence expresses the existence of the dog whereas the second is locative and identifies where the dog is. There are quite significant restrictions on the behaviour of definites in existential uses of there. What is more, there is a whole class of quantifiers that behave like the, and which often cannot occur in the postverbal position of an existential sentence. These are the proportional quantifiers.

(4) a. * There are most dogs.

b. * There are all dogs.

If the behaves like a proportional quantifier, then we need a theory that captures that observation, as well as the other generalisations that Neale (1990) identifies.

Now we run into two intimately related problems. The first is to do with the nature of quantification into the world, and the other is to do with the nature of reference. Russell's account, which was represented in (2b) exploits unrestricted quantification into the world: that is, the universal and existential quantifiers quantify over all objects in the world. As we will see in 5, we need a restricted theory of quantification to capture proportional quantifiers such as most which cannot be accounted for using unrestricted quantifiers. The other problem is that we cannot work with quantification into the world in a conceptualist theory, so how is a conceptualist theory to capture the analyses which rely on relations between sentences and the world?

The solution I shall adopt is to argue that cognitive linguistics needs a theory of linguistic reference, and that it needs to have a treatment of the proportional quantifiers such as most. The evidence in (4) suggests that it should be possible to extend the treatment of proportional quantifiers to the, and so the main issue is simply what a cognitive theory of proportional quantifiers looks like. There is the question of whether the familiarity approach is the most obviously compatible with cognitive linguistics. Hudson (1990: 293-302, 2007: 226) assumes that it is, because familiarity is an obviously conceptual notion easily amenable to a cognitive analysis, in Hudson's case exploiting his conceptual binding relation. I argue here that the quantificational approach is equally amenable to a cognitive characterisation.

On the other hand, as I said in 1, Langacker (1991) and Davidse (2004) treat the definite article as a proportional quantifier (which Langacker calls a "relative" quantifier), and the uniqueness criterion can apply to uses of the which appear to be best handled in conceptual terms. If I say the dog is growling, and there isn't a dog immediately nearby, I must mean the dog that I live with. What's more, even if you and I are speaking on the phone, and you don't know that I live with a dog, you would conclude that I mean the dog I live with. The uniqueness criterion applies here (I share my home with 3 humans and only 1 dog) and so arguably we require a conceptual notion of uniqueness.

I shall wrap up this section by pointing out that there are several ways of making an NP definite. Abbott (2004) gives the following list.

- PRO Mary tried PRO to fly

- Pronouns I, you, she, them

- Demonstratives This, that, this chair over here

- Definite descriptions with THE The king of France, the table

- Possessive NPs my best friend's wedding, our house

- Proper names Julia, Julia Child

- Universally quantified NPs Each problem, every apple, all (the) girls

- Generic NPs Pencils are made of wood

Abbott points out that this list, as she's presented it, is untheorized. The words which make NPs definite are not obviously all in a single class. For example, definite articles are known to grammaticalize out of demonstratives which are also a source, diachronically, for relative pronouns. And it is not obvious that all of these different ways of expressing definiteness "mean" the same thing given that the has several meanings or uses, and given that there are several ways of expressing definiteness in Abbott's list, we need to bear in mind that a complete story of the and definiteness will include a wider range of meanings than I tackle in this chapter.

In the next section, I discuss a cognitive theory of reference in order to get to an appropriate account of quantification in a cognitive theory.

  • [1] Although, of course, there can be stressed in the first example, and so receive a locative interpretation as well.
 
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