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Definiteness and indefiniteness* Barbara Abbott
1. Introduction
The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an , and singular noun phrases (NPs)^1 determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categories definites have received rather more attention, and more than one researcher has characterized the category of definite NPs by enumerating NP types. Westerståhl (1985), who was concerned only with determiners in the paper cited, gave a very short list: demonstrative NPs, possessive NPs, and definite descriptions. Prince (1992) listed proper names and personal pronouns, as well as NPs with the , a demonstrative, or a possessive NP as determiner. She noted, in addition, that “certain quantifiers (e.g. all , every ) have been argued to be definite” (Prince 1992: 299). This list, with the quantifiers added, agrees with that given by Birner & Ward (1998: 114). Ariel (1988, 1990) added null anaphoric NPs. Casting our net widely, we arrive at the list in Table 1, ordered roughly from most definite or determined in some sense to least.
TABLE 1: Preliminary list of definite NPs NP TYPE MORE DETAILS EXAMPLES
- [NP e ] control PRO; pro; other instances of ellipsis Mary tried e to fly; [on a pill packet] e contains methanol [ = Ariel 1988, ex. 7a]
- Pronouns the personal pronouns I, you, she, them
- Demonstratives demonstrative pronouns; NPs with demonstrative determiners
This, that, this chair over here
- Definite descriptions NPs with the as determiner the king of France, the table
- Possessive NPs NPs with genitive NPs as determiner
my best friend’s wedding, our house
- Proper names a. First name alone Julia b. Full proper name Julia Child
- ∀ NPs NPs with a universal quantifier as determiner a. Each Each problem b. Every Every apple c. All All (the) girls
- [DET Ø ] The null determiner understood generically Pencils [are plentiful/made of wood], beauty [is eternal]
Speaking loosely, we can see that each NP type listed in Table 1 is ordinarily used to refer to some particular and determinate entity or group of entities. Possessive NPs have been included in Table 1 since they are almost universally considered to be definite. However Haspelmath (1999a) argued that possessives are not inherently definite but merely typically so. (See also Barker, to appear.) Turning to indefinites, we can construct a parallel list, going in this case from intuitively least definite to most definite. The ordering here is very rough indeed, and (as with the ordering in Table 1) specific details should not be taken to imply any serious claims.
TABLE 2: Preliminary list of indefinite NPs DETERMINER TYPE COMMENTS EXAMPLES
- [DET Ø ] “Bare” NPs understood existentially
Children [are crying], snow [was piled high]
- Any a. Polarity sensitive any [hardly] any books b. “Free choice” any Any idiot [can lose money]
- No No thought(s), no music
- Most Most (of the) apples, most snow
- A/an A cook, an idea
- Sm, some “ sm ” refers to unstressed occurrences with weak or cardinal interpretation. Some is the strong, or partitive, version (see §4 below).
Sm books, some (of the) space
Notice that in neither case is the NP ( a student , every student ) translated as a constituent.^4 Instead these phrases only receive an analysis in the context of a complete sentence. Definite descriptions (NPs with the as determiner) were the centerpiece of Russell’s analysis. (3) receives the analysis in (4a). (4) The student arrived. a. ∃ x [Student( x ) & ∀ y [Student( y ) → y = x ] & Arrived( x )] b. There is one and no more than one thing which is a student, and that thing arrived. Comparing (2a) with (4a) it is clear that the clause distinguishing the two is the one underlined in (4a), which requires there to be only one student. Thus on this view the definite article expresses the idea that whatever descriptive content is contained in the NP applies uniquely, that is to at most one entity in the domain of discourse. Uniqueness does seem to capture the difference between definite and indefinite descriptions in English when they contrast. This is brought out by examples such as the following: (5) That wasn’t A reason I left Pittsburgh, it was THE reason. [ = Abbott 1999, ex. 2] where the stress on each article brings forward a contrast between uniqueness vs. nonuniqueness. It also explains why the definite article is required when the descriptive content of the NP guarantees a unique referent. (6) The king of France is bald. (7) The youngest student in the class got the best grade. (6) is Russell’s most famous example. Russell’s analysis as given applies only to singular NPs. However it is relatively straightforward to extend Russell’s concept (if not his formalization) to definite descriptions with
plurals or mass heads (e.g. the students , the sand ). In his classic treatment Hawkins (1978) proposed that the crucial concept is INCLUSIVENESS – reference to the totality of entities or matter to which the descriptive content of the NP applies. (Cf. also Hawkins 1991; Hawkins’ analysis is actually more complex than this, in order to deal with the problem of incomplete descriptions. See below, §2.3.) This aligns definite descriptions with universally quantified NPs. Russell’s analysis of definite descriptions stood unchallenged for close to fifty years, but since that time a number of issues have arisen which have caused many to question or to reject it. Here we will mention three, in order of the seriousness of the challenge they present to Russell, from weakest to strongest: presuppositionality, referentiality, and incomplete descriptions.
2.1. The problem of presuppositionality The first challenges to Russell’s theory of descriptions were raised by P. F. Strawson in his classic 1950 article “On referring”. One of the main points of this paper was to take issue with what Russell’s analysis implied about what is asserted in the utterance of a sentence containing a definite description. Consider the Russellian analysis of (6): (6) The King of France is bald. a. ∃ x [King-of-France( x ) & ∀ y [King-of-France( y ) → y = x ] & Bald( x )] b. There is one and only one entity who is King of France and he is bald. Strawson argued that the first and second clauses of Russell’s analysis (underlined in (6b) and (6c)), the clauses which contain the statements of existence and uniqueness of an entity meeting the descriptive content of the NP, have a different status from the baldness clause. He noted that were somebody to make an announcement using (6), we would not respond “That’s false!”, but would point out the speaker’s confusion in making the utterance in the first place. Strawson
this volume). (6f) seems not to presuppose the existence of a king, or not as strongly as (6), and seems to be simply false rather than lacking a truth value. (6) f. Bill had lunch with the King of France last week. See Strawson (1964) and McCawley (1979). See also Atlas (to appear), von Fintel (to appear), and the works cited there for discussion.
2.2. The problem of referentiality The second important critique of Russell’s theory was launched by Keith Donnellan in his 1966 classic “Reference and definite descriptions”. Donnellan argued that definite descriptions have two uses, one of which, called by him the ATTRIBUTIVE use, corresponds to Russell’s analysis but the other of which, termed REFERENTIAL, does not. Donnellan’s most famous example is given in (9): (9) Smith’s murderer is insane. As an example of the attributive use of the description in (9), consider a situation in which the police detective first views the crime scene where Smith, the sweetest and most lovable person imaginable, has been brutally murdered. The utterance in that case conveys ‘Whoever murdered Smith is/must be insane’, and the particular description used, Smith’s murderer , is essential to the propositional content of the utterance, just as Russell’s analysis suggests. However we can imagine quite a different scenario, say at the trial of Jones, whom everyone is convinced is the one who murdered Smith. Suppose that Jones is behaving very strangely while on trial – muttering constantly under his breath and throwing spitballs at the judge. A spectator might utter (9), perhaps with a nod in Jones’s direction, in order to make a claim that the individual Jones is insane. This would be an example of Donnellan’s referential use. While on the attributive use
one says something about whoever or whatever fits the description used, on the referential use the description used is just a means to get the addressee to realize which entity is being spoken about, and in principle any other description or term which would have that result would do as well. Thus in the courtroom scenario the speaker might have said, instead of (9), That guy is insane or He [pointing] is insane. Donnellan hedged a good bit on whether the distinction he was pointing out was semantic or pragmatic. One of his more controversial claims was that one could use a definite description referentially to make a true statement about somebody or something who did not fit the description – for instance in the example above, were Jones innocent of Smith’s murder but insane. Kripke (1977) used this controversial claim in a rebuttal many have found persuasive. Kripke distinguished semantic reference from speaker’s reference and argued that Donnellan’s referential use was simply the latter and thus a purely pragmatic affair. On the other hand many of Donnellan’s defenders who have believed in the semantic relevance of his distinction have discarded this controversial aspect (cf. Kaplan 1978, Wettstein 1981, Wilson 1991, Reimer 1998b; cf. also Dekker 1998). Burge (1974) assimilated referentially used definite descriptions (as well as pronouns and, interestingly, tenses) to the category of demonstrative phrases. According to Burge what they all have in common is that they are used to “pick out an object without uniquely specifying it” (206f.). Burge proposed an analysis of demonstrative phrases according to which reference is determined, in part, by an act of referring on the part of the speaker, which accompanies the utterance of the demonstrative phrase. However the descriptive content of the NP must also apply to the referent on his account. (See Neale 1990 and Bach, to appear, for extensive discussion of Donnellan’s referential-attributive distinction, and see Carlson, this volume, on reference in general.)
Strawson did not address the problem of how determinate reference is secured in the case of incomplete descriptions, but many others have. One possibility that might suggest itself is that incomplete definite descriptions are always used referentially, in Donnellan’s sense. If that were so then an analysis such as that proposed by Burge and sketched above, for example, might solve this problem. However it has long been clear that this is not the case. Peacocke (1975:
- proposed the example of “two school inspectors visiting an institution for the first time: one may say to the other, on the basis of the activities around him, ‘the headmaster doesn’t have much control over the pupils.’”. Here the description is clearly being used attributively in Donnellan’s sense, although it is incomplete. In Peacocke’s example, how to fill in the missing constituent ( the headmaster [of this school] ) is fairly straightforward. If all cases of attributively used incomplete descriptions were of this type (as was suggested by Wettstein 1981), then the problem of incomplete descriptions might again be solved. However, Blackburn (1988) used one of Donnellan’s own examples to argue that this hope too is forlorn. [I]n ‘Reference and Definite Descriptions’, Donnellan imagines a speaker at a Temperance Union meeting saying ‘The man drinking a martini, whoever he is, is breaking the rules of our club’. This is a Russellian [i.e. attributive] use of an incomplete description. … but…[t]he speaker may be unable to say whether he means ‘the man at this meeting who is drinking a martini’ or ‘the man in our club who is drinking a martini’, or ‘the man in this house who is drinking a martini’. (Blackburn 1988: 276; emphasis in original.) Blackburn suggested that a person using an incomplete definite description is actually tacitly alluding to a vague class of propositions determined by various ways of completing the incomplete description, and what she says is true if all of these, or perhaps a “weighted majority” (271), are true.
Neale (1990), citing a number of predecessors including Sellars (1954), Sainsbury (1979) and Davies (1981), argued that the problem of incomplete descriptions is not confined to definite descriptions but is faced equally by (other) quantified NPs. Consider (11): (11) Everyone was sick. uttered by Neale in response to a question about how his dinner party the previous night had gone. Clearly I do not mean to be asserting that everyone in existence was sick, just that everyone at the dinner party I had last night was. … Similar examples can be constructed using ‘no’, ‘most’, ‘just one’, ‘exactly eight’, and, of course, ‘the’…. Indeed, the problem of incompleteness has nothing to do with the use of definite descriptions per se ; it is a quite general fact about the use of quantifiers in natural language. (Neale 1990: 950; emphasis in original) Neale’s main concern was to defend Russell’s quantificational analysis of definite descriptions and it sufficed for that end to argue that the incompleteness problem is general. In addition, however, following Sellars (1954) and Quine (1940), Neale supported an approach on which incomplete NPs are seen as elliptical for some fuller expression or expression content. There have been many variations on this theme: see Stanley & Szabó (2000) and the works cited there for examples. The main drawback has been discomfort at the fact that the elided content must often be indeterminate, for both speaker and addressee. There are several other general lines of approach to the problem of incompleteness currently on offer. One very popular one is to shrink the domain of evaluation of the NPs in question, so that the descriptive content is satisfied uniquely as intended. Barwise & Perry (1983) spoke in terms of RESOURCE SITUATIONS, Westerståhl (1985) introduced CONTEXT SETS,
definite descriptions which are used to refer to entities which are typically or always NOT the only entity to which the descriptive content of the NP applies, even in a restricted domain of evaluation. Consider the examples in (13): (13) a. Towards evening we came to the bank of a river. [from Christophersen 1939: 140] b. The boy scribbled on the living-room wall. [ = Du Bois 1980, ex. 86] c. John was hit on the arm. [ = Ojeda 1993, ex. 1] Rivers always have two banks, rooms have more than one wall, and people have two arms, and there seems to be no reasonable way to reduce the context so as to exclude the other items falling under the description used without also excluding essential entities such as the river, the living- room, and John, in the examples given. As pointed out by Birner & Ward (1994), in each of these examples the definite description gives a location. In other types of sentences these NPs are infelicitous: (14) a. # The bank of the Thames is the personal property of the Queen. b. # Mary painted the living room wall. (Of course the sentences in (14) would improve if placed in a context in which one particular bank of the river, or one particular wall of the room, were made salient in some way.) Why are definite descriptions used in sentences like (13)? Du Bois made the interesting observation that in these cases, despite the nonuniqueness of potential referents, use of the indefinite article would be odd. Cf. (15): (15) # He scribbled on a living-room wall. [ = Du Bois 1980, ex. 88] Du Bois pointed out that (15) “gives the impression of being unnaturally precise” (Du Bois 1980: 233), and seems to carry the unwanted implication that the hearer might care which wall was being scribbled on.^6
3. Familiarity The chief competitor for the uniqueness approach to capturing the essence of definiteness has been an approach in terms of FAMILIARITY, or KNOWNNESS to use Bolinger’s term (Bolinger 1977). The locus classicus of this approach within the tradition of descriptive grammars is Christophersen 1939: “Now the speaker must always be supposed to know which individual he is thinking of; the interesting thing is that the the -form supposes that the hearer knows it too” (Christophersen 1939: 28). The concept of familiarity which Christophersen had in mind in this passage seems quite similar to Prince (1992)’s concept of HEARER-OLD information, which she aligned with the idea of information which is “in the permanent registry” (Kuno 1972), or “culturally copresent” (Clark and Marshall 1981). (Prince contrasted Hearer-old information with the narrower category of DISCOURSE-OLD information, which includes only entities that have been mentioned in the previous discourse.) Prince noted that the category of definite NPs, defined in terms of form, correlates well with conveyers of Hearer-old information, but that the correlation is not perfect: some NPs which are definite in form can introduce entities not assumed to be known to the addressee at the time of the utterance. She gave the examples in (16) (= Prince 1992, ex. 5). (16) a. There were the same people at both conferences. b. There was the usual crowd at the beach.^7 c. There was the stupidest article on the reading list. The role of existential sentences, like those in (16), as a diagnostic for indefiniteness will be explored below in §4.
definitely not correct. But if we use sometimes an existential quantifier and sometimes a universal, we suggest an ambiguity in indefinite NPs which is not felt. Heim’s elegant solution to this problem involved a novel approach to semantic interpretation called FILE CHANGE SEMANTICS. Drawing on prior work by Karttunen (1969, 1976), Heim took mini-discourses like that in (18) as illustrating prototypical uses of indefinite and definite NPs: (18) A woman sat with a cat on her lap. She stroked the cat and it purred. On this view a major function of indefinite NPs is to introduce new entities into the discourse, while definite NPs are used to refer to existing discourse entities. Heim analyzed both indefinite and definite NPs as nonquantificational; instead their interpretation involves only a variable, plus whatever descriptive content may reside in the remainder of the NP. Following Karttunen (cf. also Du Bois 1980), Heim likened a discourse to the building up of a file, where the variables in question are seen as indexes on FILE CARDS representing discourse entities and containing information about them. The difference between indefinite and definite NPs was expressed with Heim’s NOVELTY and FAMILIARITY conditions, respectively. Indefinite NPs were required to introduce a new variable (corresponding to the act of getting out a new blank file card). On the other hand definite NPs were required to be interpreted with a variable which has already been introduced, and (in the case of a definite description as opposed to a pronoun) whose corresponding file card contains a description congruent with that used in the definite NP. This explicates the idea that definite NPs presuppose existence of a referent, together with the idea that presuppositions are best seen as background information or the common ground assumed in a discourse (see Stalnaker 1974, 1978; cf. Abbott 2000 for a contrary view).
On this approach an example like (2) (A student arrived) would receive an interpretation as in (2d): (2) d. Student( x ) & Arrived( x ) The existential quantification needed for this example is introduced by a general discourse level rule, requiring that file cards match up with actual entities for the discourse to be true. However if indefinite NPs fall within the scope of a quantified NP, as happens in donkey sentences, the variable they introduce is automatically bound by that dominating NP’s quantifier. Thus Heim’s File Change Semantics yielded an interpretation for (17) which is equivalent to that in (17b), but without requiring two different interpretations for indefinite NPs.^8
3.2. Unfamiliar definites & accommodation The familiarity approach to the definiteness-indefiniteness contrast seems to imply that any definite description must denote an entity which has been explicitly introduced into the discourse context or is common knowledge between speaker and addressee, but of course that is not always the case. Consider her lap in (17) (assumed to be a definite description). This possessive denotes an entity that has not been specifically introduced. Heim’s solution for this kind of case relied on a principle introduced in David Lewis’s classic paper “Scorekeeping in a language game” (Lewis 1979). In this paper Lewis compared the process of a conversation to a baseball game. One major DISanalogy is the fact that, while the score in a baseball game can only be changed by events on the field, the “conversational scoreboard” frequently undergoes adjustment just because the speaker behaves as though a change has been made. The relevant principle in this case is Lewis’s RULE OF ACCOMMODATION FOR PRESUPPOSITIONS:
(20) a. What’s wrong with Bill? Oh, the woman he went out with last night was nasty to him. [ = Hawkins 1978, ex. 3.16] b. If you’re going into the bedroom, would you mind bringing back the big bag of potato chips that I left on the bed? [ = Birner & Ward 1994, ex. 1b] c. Mary’s gone for a spin in the car she just bought. [ = Lyons 1999, ex. 18, p. 8] One could argue that these are simply cases of accommodation, and point out that in each case the intended referent bears some relation to an entity which has already been introduced into the discourse context, but nevertheless they seem contrary to at least the spirit of the familiarity type of approach.
3.3 Attempts at a synthesis In a sense the uniqueness and familiarity theories of definiteness are odd foes. Uniqueness of applicability of the descriptive content, as explicated in Russell’s analysis, is a strictly semantic property while the assumption of familiarity to the addressee is discourse-pragmatic in nature. A priori one might have supposed the two to be complementary rather than at odds, and indeed, there have been attempts to derive each from the other. Accepting both as correct in some sense, the idea of deriving familiarity from uniqueness is likely to strike one first since we generally suppose semantic properties to be arbitrary and pragmatic ones to be natural (if not inevitable) consequences of semantic facts plus the exigencies of the conversational situation. This was the approach sketched in e.g. Hawkins (1984) and Abbott (1999). However, with the development of “dynamic” theories like Heim’s that embed sentence semantics into analyses of discourse, this old distinction became blurred. Heim raised familiarity to a principle of semantics, making it
possible to suggest instead that the uniqueness requirement could be derived from it (cf. Heim 1982: 234ff.). Szabó (2000) and Roberts (2002) have also taken this approach to unification. Just as some have assumed that both uniqueness and familiarity are correct, others have argued in effect that neither is. Birner & Ward (1994) presented problematic examples for both approaches, some of which have been cited above, and concluded that neither gives a correct account of definite descriptions. Lyons (1999), too, reviewed existing theories in both camps and concluded that neither is synchronically correct. Examples like those in (19) and (20) have led other authors to abandon familiarity (which implies prior acquaintance) in favor of a concept of IDENTIFIABILITY. The idea is that use of the definite conveys to the addressee that they ought to be able to determine a unique referent from the description used plus contextual or background information, whether or not they had prior acquaintance with it. Birner & Ward (1998) pointed out that the term “identify” suggests that an addressee is able to pick the referent out in the world at large. They argued instead that “what is required for felicitous use of the definite article (and most uses of other definites) is that the speaker must believe that the hearer is able to individuate the referent in question from all others within the discourse model” (Birner & Ward 1998: 122; italics in original). This is an idea that many have found attractive.
On the other hand Lyons (1999) argued that definiteness is a GRAMMATICALIZED category: originally definite NPs were understood to denote identifiable entities, but as a consequence of the category’s becoming grammaticalized have acquired other uses. This is another way to attempt a synthesis between these two approaches, although there is a drawback in loss of ready formalizability.
