Uniqueness in Definite Noun Phrases1

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Craige Roberts

The Ohio State University

December, 2000
Uniqueness in Definite Noun Phrases1
There is a long debate about the meaning of English definite descriptions, going back to the exchange between Russell and Strawson, and continuing through the rich linguistic and philosophical literature on the subject that has emerged in the last two decades. One can characterize the main positions in the debate in terms of whether the uniqueness effects often associated with the definite description are deemed to be semantic or pragmatic. Another interesting issue which has emerged in the more recent literature is that of the relationship of definite descriptions to pronouns and other definite noun phrases (NPs). And an alternative theory of definite NPs has been promoted wherein they are said to presuppose familiarity instead of uniqueness. The present paper differs from all of the earlier analyses in some respects. I argue that the uniqueness associated with these expressions is both conventional, in that it is a conventional presupposition, and pragmatic, in that the presupposition alludes not to uniqueness of the definite's denotation in the world, but to its unique status with respect to the overall information of the discourse participants. Further, it is argued that the uniqueness in question, along with a presupposition of familiarity, is part of the meaning of all English definites, including pronouns; however, there are additional factors in the interpretation of pronouns which mask this commonality in most contexts.
The main features of the theory I will propose are as follows:

  • Use of a definite NP presupposes that there is a corresponding discourse referent already in the discourse context, and that this familiar discourse referent is unique among the discourse referents in the context in bearing the property in question. (The first conjunct of this hypothesis is, of course, Heim's (1982) familiarity theory of definiteness.)

  • The notion of familiarity involved is not that more commonly assumed, which I will call strong familiarity, where this usually involves explicit previous mention of the entity in question. Rather, I define a new notion, that of weak familiarity,2 wherein the existence of the entity in question need only be entailed by the (local) context of interpretation, and use this to account for a number of prima facie counterexamples to the familiarity hypothesis.

  • Gricean principles and the epistemic features of particular types of context are invoked to explain the uniqueness effects observed by Russell and others, wherein the use of a definite description appears to entail (or presuppose) the uniqueness of the NP's denotation in the actual world in bearing the property in question. This essentially pragmatic method of deriving uniqueness effects permits an explanation of a novel observation: that there is an inverse relationship between actual (as opposed to accommodated) familiarity of the NP's discourse referent and the likelihood of a semantic uniqueness effect.

  • Pronouns, unlike definite descriptions, carry the additional presupposition that the discourse referent which satisfies their familiarity presupposition is maximally salient at that point in the discourse. This difference will be used to explain the fact that when uniqueness effects arise, they are generally triggered by definite descriptions, not pronouns.

In what follows, §1 is an exploration of some key empirical generalizations about the interpretation of definite descriptions, focusing on uniqueness and familiarity. In §2 I present the theory of informational uniqueness and argue that it accounts for all the kinds of phenomena discussed in the previous sections. §3 addresses the interpretation of pronouns, arguing that the theory proposed in §2 can be extended in a simple fashion to account for these as well. In §4 I compare the theory proposed with the other main proposals for the interpretation of definites. And in §5 I briefly consider some extensions and puzzles, and offer some conclusions.

  1. Empirical generalizations about definite descriptions

1.1 Uniqueness effects

Definite descriptions often seem to display the uniqueness effect illustrated by the following story. (It was told to me as true, though I haven't tried to verify it.) When I took my present position, I thought it odd that the official name of the university is The Ohio State University, since most university names omit an article. Someone explained to me that in the nineteenth century the trustees of this state school were irate when a group in southern Ohio had the temerity to name their new private university Ohio University, since the name might be taken to suggest an official affiliation with the state. So, in 1878, when they changed this institution's name from the Ohio Agricultural and Mechanical College, they included the definite article in OSU's official name to counter the impression that there was any other state university in Ohio. As the story suggests, if we say that this is THE Ohio State University, with focus on the article, it does indeed seem to emphasize that this is the only university of its kind – one which is both in Ohio and an institution of the state. It is this impression, that the speaker is claiming that there is an entity in our world which uniquely satisfies the descriptive content of the definite NP, which I will call the uniqueness effect associated with the utterance of the definite. We need to be able to explain how this arises in such examples, as well as accounting for other evidence of the uniqueness of definite descriptions which we will consider below.
On the analysis of singular definite descriptions offered by Russell (1905), they differ from singular indefinites in entailing uniqueness: In order for the utterance containing a definite description to be true in a model under its Russellian logical form, there must be one and only one individual in the model which truthfully instantiates the existential statement. We see this in the Russellian logical form for The Ohio State University is in Columbus, given in (1), with the uniqueness clause underlined:
(1) The Ohio State University is in Columbus.

(1') $x [state-univ(x,Ohio) & "y (state-univ(y,Ohio)  y = x) & in-Cols(x)]

In an extension of this treatment of singulars, plural definites are also unique, in the sense that an instantiation must be the maximal set satisfying the description, or, in Link's (1983) terms, the supremum of the denotation of the possibly complex remainder of the NP, the CN (Common Noun phrase, including the head noun and any complements or modifiers). I will call the Russellian account for the uniqueness effects noted in such examples a theory of entailed semantic uniqueness.
The examples in (2) - (4) also appear to support Russell's analysis of the definite article:
(2) The Queen of England had a bad year in 1993.

(3) Teacher, giving directions: On the next page, you will find a puzzle. Find the clown in the puzzle.

(4) I found a box in my attic the other day. I opened the lid and pushed the button I found inside. You won't believe what happened. (variant due to Irene Heim, p.c.)
(2) leads us to understand that there is a unique Queen of England in the world. Given the teacher's instructions in (3), native speakers all agree that a child would be justified in assuming that there is only a single clown in the puzzle in question (and also, only a single puzzle on the next page). Similarly, in (4), we may assume that the box the speaker found contained one and only one button.
(5) also displays a uniqueness effect in connection with the definite NP the dashboard, but here the uniqueness is generally taken to involve a relational reading of the definite NP:
(5) This car has a statue on the dashboard.
The hearer will assume that there is a single dashboard in the car in question, but not only one dashboard in the entire world. Many NPs are susceptable to such interpretations, where the head is interpreted as a relation such as 'dashboard of', with an implicit argument contextually given, e.g. the denotation of the salient and relevant this car; this is the phenomenon that Clark (1975) calls bridging. Giving this implicit argument to the 'dashboard of'-denoting head yields an expression which denotes the set of things which are dashboards of the car in question, which is then the argument of the definite determiner. In examples such as (5) the relational interpretation of the definite is preferred on pragmatic grounds, since hearers generally know that a) there is more than one dashboard in the world, and b) there is generally only one per car, so that we take the 'dashboard of' relation to be not just a relation, but also a function. It is the assumption that the head is not only relational but functional which constitutes the uniqueness effect in such examples.
(6) and (7) are examples of what Kadmon (1987) calls "uniqueness under quantification", again involving bridging:
(6) Every car had a puncture in the tire.

(7) Every unicycle had a spoke missing from the wheel.

The uniqueness effects which these examples display depend on relational interpretations, of the tire in (6) and the wheel in (7), but the implicit arguments of these relations are variables bound by the quantificational subjects every car and every unicycle, respectively. Hence, we take it that the truth of (6) involves cars having only a single tire, which results in infelicity, since we know that this is not the case.3 The similar requirement in (7) that unicycles have a single wheel is more reasonable,4 so the example is felicitous.
There are a number of types of examples involving definite descriptions where the uniqueness effect just noted doesn't seem to arise. Consider (8a), an example adapted from Evans (1977,1980):
(8) a) There's a doctor in our little town. The doctor is Welsh.

b) lx[doctor(x)]

c) lx[doctor(x) & in-our-town(x)]
Evans pointed out that if we take into account only the descriptive content of the definite the doctor in (8a), i.e. doctor, this would lead to a too-strong uniqueness claim, that the set denoted by (8b), the set of all doctors, contains only one individual. Instead, to obtain the intended interpretation we must also take into account information about the antecedent given via predication in the prior sentence, so that we consider the uniqueness of the set given in (8c), the set of doctors in our town.
Even when a definite description has no NP antecedent, the uniqueness which it presupposes often obtains partly by virtue of properties which are only given contextually, rather than being fully specified by the descriptive content of the definite (or accompanying deictic act). Consider (9):
(9) Herbs and seasonings are in the cabinet to the right of the stove.
This example is perfectly felicitous in a context in which the definite description of interest, the cabinet to the right of the stove, does not by itself provide sufficient information to indicate the way in which the speaker's intended referent is to be understood as unique. In fact, (9) might reasonably be uttered in a kitchen where there is a whole row of cabinets to the right of the stove; it would probably be taken to mean that the seasonings are in the cabinet immediately to the right of the stove. The standard way of maintaining the Russellian analysis of definite descriptions in the face of such examples is to claim a contextually-given restriction of the set of entities over which the existential operator ranges. Kadmon (1990), following Evans, calls this the liberalization of the descriptive content (that given by the CN) of the definite, whether it pertains to information explicitly given about an antecedent, as in (8a), or to information retrieved in some other fashion, usually via pragmatically based inferences. I will use instead the term pragmatic enrichment of the descriptive content of the Np to describe this phenomenon, and assume that this is just an instance of the pervasive phenomenon of domain restriction in the interpretation of logical operators.5
It is now widely accepted that natural language operators – quantificational determiners, modals, tenses, quantificational adverbs, etc. – generally take two arguments; see the introduction and papers in Bach et al. (1995) for extensive contemporary discussion of this very old idea. The first argument is often called the restrictive term; it restricts which entities of the appropriate type the operator ranges over; its quantificational domain. The second argument, or nuclear scope, tells us what must be true of the appropriate proportion of these entities in order for the utterance to be true. It is also a fact that in most cases domain restriction is at most only partly given explicitly – by the CN of a quantificational determiner, an if-clause for a modal, a subordinate temporal clause for tense, etc. Generally, the Gricean assumption that the speaker is being cooperative, and hence truthful, together with falsity or irrelevance of the utterance if the quantificational domain is taken to be only as explicitly given, lead us to assume that she must intend some pragmatic enrichment of the operator's first argument, and hence a pragmatically restricted quantificational domain. In definite descriptions, under the assumption that they carry a uniqueness entailment, the descriptive content given by the CN must be pragmatically enriched in order to obtain a plausible and relevant intended interpretation in cases where uniqueness appears to fail.6 For (9), we might invoke a quantity implicature: If there are several cabinets to the right of the stove and the speaker knows that and yet apparently feels she has given sufficient information to enable the hearer to find the seasonings, then there must be some sense in which the cabinet in question is exactly to the right of the stove, instead of, say, the third cabinet to the right.
Although pragmatic enrichment of the descriptive content clearly plays an important role in the interpretation of definite NPs, as in quantificational NPs more generally, it doesn't suffice to explain a large class of prima facie counterexamples to Russellian uniqueness. (10) is a variant on an example due to Heim (1982):

(10) A wine glass broke last night. The glass had been very expensive.

Suppose that two glasses were broken and that the only criterion for distinguishing the two wine glasses was that when the first one broke, the speaker of (10) was really shocked, but by the time the second broke, he was numb. Otherwise they were indistinguishable. (10) seems to be both felicitous and true in this kind of circumstance.

Kadmon (1990:282) claims that uniqueness still obtains because the speaker's different reactions serve to distinguish the wine glasses after all, since the first was the only one that "affected [the speaker's] mood". And she claims that it isn't necessary that this criterion for distinguishing the wine glasses (or even the fact that the description given doesn't suffice to do so) be available to hearers: "I agree with Searle, Evans and Donnellan that in some felicitous uses of definites the uniquely identifying information is available only to the speaker." But on a view which denies the necessity of hearer accessibility, I don't see how uniqueness has much content at all. For any object I could imagine and intend to refer to by uttering some definite description, there seems to be some (possibly complex) unmentioned property of it that I could have in mind which would make the NP semantically unique relative to my private information, but which, because it was not mentioned, would not be in the common ground of the interlocutors in the conversation. If this is adequate to satisfy the uniqueness condition, then the condition seems too easy to satisfy, leaving it unclear how any examples could be infelicitous because of a failure of uniqueness. And it would also be unclear how uniqueness conditions could serve any conversational purpose, if they may be "secret".

There is one more piece of evidence which strongly suggests that definite descriptions carry uniqueness presuppositions. This is that when the descriptive content of the NP (its CN) guarantees that its denotation is semantically unique, the definite article is required, the indefinite article leading to infelicity, as we see in (11) and (12):
(11) Last weekend we climbed the biggest mountain in West Virginia.

(12) #Last weekend we climbed a biggest mountain in West Virginia.

Hence, it seems that semantic uniqueness is sufficient to require the use of the definite article in English. What is in question is whether semantic uniqueness is a necessary concommitant of its use. Although there are cases where definite descriptions display clear uniqueness effects, and some examples which might be taken to fail to display these effects can be explained via domain restriction, examples like (10) make uniqueness seem less robust than one would like to see in a supposedly semantic, hence conventionally triggered, phenomenon.

1.2. Familiarity presuppositions

Heim (1982) rejects semantic uniqueness for definite noun phrases, a class which she takes to include pronouns as well as definite descriptions. In her theory, a technical realization of ideas found earlier in Christophersen (1939) and Hawkins (1978), the distinction between definites and indefinites is that definites have familiarity presuppositions, while indefinites do not. Familiarity is determined by whether there is already information about a corresponding discourse referent in the local context of interpretation, the context being a file of information held in common by the interlocutors in the discourse. To realize this contextual information which the interlocutors share, she adopts a modified version of Stalnaker's (1974:199-200, 1979:321) notion of the common ground. Crucial for our purposes, the expanded notion includes the Domain of the discourse, technically a set of indices, each of these considered to be a discourse referent known to the interlocutors.7 Intuitively, a discourse referent is the address for a maximal cluster of information assumed by the interlocutors to bear on a single individual; Heim uses the metaphor of a file card. Note that the common ground, as defined by Stalnaker and Heim, includes not only information which is linguistically given, but also that which is presupposed on the basis of other types of input, perhaps common educational or cultural experience, or sensory input. This is an important feature of the common ground for the theory to be developed here.
In related work, Prince offers empirical support (analysis of texts) for the hypothesis that definiteness is a grammaticization of Hearer-Old status. Though Prince does not make it entirely clear what she means by Hearer-Old, it seems to be related to Heim's familiarity. Prince also argues that definites do not presuppose that their antecedent discourse referents are Discourse-Old, which seems to echo Heim's claims that the discourse referents which satisfy the familiarity presuppositions of definites needn't be introduced by prior mention.
There seems to be a lack of clarity in the literature about what it means to be familiar, leading to some confusion about what constitutes a significant challenge to theories based on that notion.8 In this section, I will begin by clarifying what Heim (1982) seems to have meant by the term familiar and why she proposed that familiarity holds of definites. Then I will argue that this notion should cover a class of cases that Heim would probably not have included; including this class will lead to a notion I call weak familiarity. I conclude that the challenges to the familiarity theory that I know of are all based on a narrower view of familiarity than the one proposed here, or even (in most cases) than Heim's original notion.
Heim (1982) characterized NP familiarity as having a corresponding (co-indexed) discourse referent in the Domain of the common ground for the discourse. In her theory, definites presuppose that there is such a discourse referent in the Domain (familiarity), while indefinites presuppose that there is not (novelty). Here is her Extended Novelty-Familiarity Condition (p. 369):9
(13) The Extended Novelty-Familiarity Condition:

For [a Logical Form] f to be felicitous w.r.t. a context C it is required for every NPi in f that:

(i) if NPi is [-definite], then i Dom(C);

(ii) if NPi is [+ definite], then

(a) i  Dom(C), and

(b) if NPi is a formula, C entails NPi.

In (13), Dom is a function from discourse contexts to sets of indices (elements of the set of natural numbers), each such set being the discourse referents which constitute the Domain of the context in question. Clause (13i) characterizes novelty, while (13iia) tells us what it means to be familiar. Clause (13iib) – the descriptive content condition – tells us that the descriptive content of a definite description (represented by a formula) is presupposed to hold of the discourse referent which satisfies the definite's familiarity presupposition; hence this must be entailed by the context.
Heim offers a number of types of examples to argue that definite NPs carry familiarity presuppositions. We have cited one above, (10), repeated here:
(10) A wine glass broke last night. The glass had been very expensive.
Although, as discussed, the glass arguably doesn't display a uniqueness effect, it does satisfy the presuppositions in (13ii). And insofar as the speaker wants to refer in the second sentence to the wine glass that was broken, it is infelicitous to use the indefinite article instead, as predicted by (13i):
(14) #A wine glass broke last night. A glass had been very expensive.
Heim's formal, recursive definitions of the Context (or "File") Change Potential for a given formula specify how discourse referents are introduced into the Domain of a context in the course of interpreting indefinite NPs. However, she makes it clear that there is another way that a discourse referent can be introduced into the Domain (p.309):
Does the [context] also reflect what is familiar by contextual salience? . . .[contexts] must be able to change, and in particular, must be able to have new discourse referents added, without anything being uttered. For instance, if halfway through a conversation between A and B a dog comes running up to them and draws their attention, then that event presumably makes the [context] increase by a new discourse referent.
Assume that the new discourse referent is 7. A and B would also add to the context the information that this discourse referent is a dog that has come running up to them. Then in the resulting context, A might felicitously say: "It7 is going to bite," interpreted as 'the dog that's just come running up is going to bite'. Heim concludes:
Novelty w.r.t. logical form is a necessary, but not a sufficient condition for novelty w.r.t. the [context].
Heim does not discuss further what it means to be contextually salient, and hence able to non-linguistically trigger the introduction of a discourse referent into the discourse context. The example makes it clear that she would include deixis as a means of making salient. But what about cases in which the context of utterance merely entails the existence of some entity? Could such contextual existence entailments, by themselves, ever trigger the introduction of a discourse referent? Heim's discussion suggests that she would not generally assume that they do. For example, in discussing the role of accommodation in ameliorating prima facie counterexamples to familiarity (1982:390-91), Heim cites the example in (15):
(15) Every motel room has a copy of the Bible in it. In this room, it was hidden under a pile of TV Guides. (Heim 1982)
Her discussion makes it clear that she assumes that the felicity of it in (15) involves accommodation of a familiar discourse referent for a Bible, i.e. that there is not a prior familiar discourse referent.10 However, such examples suggest an alternative hypothesis which Heim does not entertain. The first sentence in (15) entails that in the room indicated in the second sentence there is a Bible. We might assume that examples with existence entailments are like Heim's dog example or deixis in directly licensing the introduction of a familiar discourse referent, which then serves to satisfy the familiarity presupposition of the definite NP without accommodation. In fact, one could argue that Heim's dog example is subsumed under the class of examples where definites' familiarity presuppositions are satisfied by contextual entailment: A and B see the approaching dog, see that they each see it, etc., and introduce the corresponding proposition 'there is a dog approaching' into their common ground. The direct existential entailment of this proposition then licenses the introduction of a discourse referent for the approaching dog.
For convenience, let us say that a discourse referent which is introduced in the course of interpreting a noun phrase is
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