What is Definiteness?

I have to read a number of works to better understand definiteness and indefiniteness, which can’t be decided purely by the presence or absence of certain words or their arrangements. So here’s a summary to lay out the defining characteristics of (in)definiteness. I have quoted heavily from these works which are all publicly viewable, and in no way would like to show having originality of these ideas.

Definiteness is signalled (from Heusinger) thru:

  1. Proper nouns or names – “refers to exactly one individual, namely the bearer of the name. The reference is purely conventional since no internal part of the expression points or gives any relation to its bearer. proper names are highly context dependent.” This is marked differently in Philippine languages.
  2. Personal pronouns -  “either as deictic or as anaphoric. In the absence of any linguistic context, the pronoun refers to an object that must be in some way prominent in the context or “easy to access”. This deictic interpretation of the pronoun is licensed if the pronoun is accompanied by a demonstration or if the non-linguist context contains some prominent or salient object. Background knowledge may play an important role, too. A pronoun is interpreted anaphorically, if it refers to an object that has been already introduced into the discourse.”
  3. Possessive constructions – “denotes exactly the object that fulfills the property that is expressed by the common noun and that further stands in a certain relation to the object that is denoted by the modifier. This relation can be determined by the lexical material of the head noun if it is a functional concept. If the head noun does not denote a functional concept, but rather a sortal one, the relation is usually the possessor relation.” John’s car is that object that is a car and has a certain relation to John, which is
    probably the car that John owns.
  4. Demonstratives – “refer to an object only if the linguistic utterance is accompanied by a non-linguistic demonstration or ostension. They identify their referent by combining a demonstrative action with descriptive information about the referred object.”
  5. Definite NPs – signalled in English by the articles a, the, and zero article. “They refer to their objects not by convention but due to their descriptive content and further information, like our shared background knowledge or contextual information about the place and time of utterance.” Has the following usage:
    1. Anaphoric linkage – the definite NP refers to an object that is explicitly introduced by the linguistic context. Thus, definiteness is based on the principle of coreference.””Once upon a time, there was a king, … and the king …”
    2. Relational Dependency – “the definite NP refers to an object due to another already mentioned object in the discourse. It establishes a relation to a mentioned object in discourse. Since nothing else than the relation is expressed the relation itself must unequivocally determine exactly one object. The relational concept of an definite NP must be lexically determined.” “I bought a new car. I had to change the motor.”
    3. Situational Salience – “the situation or the non-linguistic context delivers additional information to single out the referent.  This non-linguistic context can consist in the shared background knowledge or in the actual circumstances.” “The train left two minutes ago.
    4. Uniques – “nouns whose lexical content is such that only one object can fit it.  A unique can consist in a noun that expresses a functional concept, i.e. a concept that gives exactly one value for each argument, like “the sun”, “the time”. It can also consist in a complex nominal expression that due to its meaning refers only to one object (in the relevant context) like the first man on the moon.”

We will refer to various studies already done to summarize the distinction between the two with respect to so-called articles in English (a, the, zero article), like:

  1. Uniqueness Theory – According to Russel, definiteness marking (a) asserts the existence of the NP, and (b) this NP is not more than one, like the center of the solar system. Russell’s example “The king of France is bald” is found to be nonsensical and uninterpretable. Another example provided by Abbott: “That wasn’t a reason I left Pittsburgh, it was the reason.
    • This is refuted by Strawson who pointed out that existence is merely presupposed and not asserted.
    • Donnellan also refuted that the definite is quantificational but rather either referring or non-referring (attributive).
    • Hawkins also pointed out the problem of incomplete description, where  the descriptive content of the definite NP [ e.g. “the glass” (on the table) ] is insufficient to identify a truly unique referent and not existing in other entities on a universal scale, so he tried to remedy this using “pragmatic sets” or a pragmatically reduced context in which referents are to be evaluated for their uniqueness, but Lewis provided a counter-example “The dog got in a fight with another dog. – I’ll have to see to it that the dog doesn’t get near that other dog again.”, in which he said the definite NP is the most salient in the domain of discourse, according to some contextually determined salience ranking.
    • Other sentences called recall sentences were also furnished that break the non-uniqueness of NPs that they can be understood to be indefinite instead: “Towards evening we came to the bank of the river.” (Christophersen), “Take the elevator to the sixth floor and turn left.” (Berner and Ward), “The boy scribbled on the living room wall.” (Du Bois). Abbott defended this by saying these sentences  can be explained in terms of location. I think these are situationally definite.
    • This also neglects plural and mass nouns, which Hawkins addressed by proposing inclusiveness – the  NPs are unique but only in reference to the whole set: “Bring the wickets in after the game of cricket.”,I must ask you to remove the sand from my gateway.” “In the case of singular NPs, their inclusiveness is restricted to the one member that constitutes the set.”
  2. Familiarity Theory – According to Christophersen, definiteness marking is associated with some kind of previous knowledge by the hearer. This familiarity with the NP can be on both the speaker and hearer, or can be introduced thru text as a previously introduced indefinite NP (explicit contextual): “I live next to a scientist. The scientist keeps to himself though.” or thru non-textual basis, (implicit contextual): “The book is so ridiculous – the author must be crazy.” or (situational) “For instance, upon mounting a bus, one can talk of the driver, the passengers, the seats and so on.
    • According to Heim, “definites must be used to refer back to a familiar discourse entity, where familiarity is satisfied when an entity has been either explicitly introduced into the discourse (strong familiarity) or implicitly introduced by the context (weak familiarity)”.
    • Its been  shown that familiarity is not a sufficient condition and can be used on unfamiliar referents: “What’s wrong with Bill? Oh, the woman he went out last night was nasty to him.”(Hawkins) or “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 and Ward). I think the definite NP here is unique.
    • In “The book is so ridiculous – the author must be crazy.”, Birner and Ward presses that since most books typically have one author, this is more in favour of uniqueness theory.
    • Birner and Ward also give an example where familiarity is insufficient: “Professors Smith and Jones are rivals in the English Department, and each of them has received a major grant for next year. The other members of the department are very excited about the grant.” Although the definite NP was mentioned as an indefinite NP beforehand, it did not resolve the confusion as to which grant is being referred to in the definite NP.
    • Familiarity is also problematic for definite NPs that are non-referential (pick out a referent) but are predicational (denote a quality or characteristic): “Chan is a scientist. Chan is the leader.” (Declerk), Familiarity can’t account for the definiteness (“the leader”) and indefiniteness(“a scientist”).
    • This was remedied by expanding familiarity to identifiability by Lyons:”They’ve just got in from New York. The plane was five hours late.”  “Using an expanded form of previous knowledge (linguistic or non-linguistic), one is able to identify the plane. It may necessitate going beyond a one-to-one association between a referent and its recognition (in the loose sense of the word).” This is said to be effective for contextual and situational definiteness.
    • Recall sentences are both problematic for familiarity and identifiability, so Du Bois proposed the curiosity principle: “a reference is counted as identifiable if it identifies an object close enough to satisfy the curiosity of the hearer”.
    • This becomes discourse familiarity to Heim and Kamp who anaphoricly linked a definite NP to an already introduced or ‘familiar’ discourse referent.
    • This is the origin of Löbner relational theory and  Lewis’ salience theory.
  3. Mixed theories
    • Hawkins – definiteness is the (a) ability of the referent (or referents) to be located in some shared set of objects between the speaker and hearer, and (b) being the totality of the objects or mass within this set which satisfy the referring expression. This looks like a combination of inclusiveness and familiarity. This is also called the Location Theory. 
    • Abbott – definite NPs are firstly unique, but needs to be enriched/refined by the pragmatic context, in the sense of P-sets à la Hawkins (1991). “the 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”.  I think her explanations for non-unique definite NPs are forced, especially for “The contestant gave the wrong answer and had to be disqualified.”
    • Lyons -  definiteness has to do with whether or not a referent is familiar or already established in the discourse – thus identifiability rather than inclusiveness. “(the definite) by itself does not identify, but “invites the hearer to exploit clues in the … context to establish the identity of the referent”. Lyons proposes that definiteness is a grammatical category (of identifiability) and not a semantic/pragmatic category, which explains its variability.
  4. Relational Theory – According to Löbner, “the definite article has no lexical meaning, but just indicates the way the reference is established, namely that the expression refers non-ambiguously.” He merges anaphoric and situational use as pragmatic definite and relational use as semantic definite: “Semantic definites refer unambiguously due to general constraints; Pragmatic definites depend on the particular situation for unambiguous reference. An NP is semantic definite if it represents a functional concept, independently of the particular situation referred to. An expression is inherently functional if it needs a further argument to refer to an object.” The definiteness is considered as a local property of the link between the head and its argument. “He was the son of a poor farmer.”
  5. Salience Theory – According to Lewis, “consider the sentence ‘The door is open’. This does not mean that the one and only door that now exists is open; nor does it mean that the one and only door near the place of utterance, or pointed at, or mentioned in previous discourse, is open. Rather it means that the one and only door among the objects that are somehow prominent on the occasion is open. An object may be prominent because it is nearby, or pointed at, or mentioned; but none of these is a necessary condition of contextual prominence. So perhaps we need a prominent-objects coordinate, a new contextual coordinate independent of the other. It will be determined, on a given occasion of utterance of a sentence, by mental factors such as the speaker’s expectation regarding the things he is likely to bring to the attention of his audience.” “It is not true that a definite description ‘the F’ denotes x if and only if x is the one and only F in existence. Neither is it true that ‘the F’ denotes x if and only if x is the one and only F in some contextually determined domain of discourse. The proper treatment of description must be more like this: ‘the F’ denotes x if and only if x is the most salient F in the domain of discourse, according to some contextually determined salience ranking.” Sample sentence: “The pig is grunting, but the pig with floppy ears is not grunting.” Two individuals with the same property are introduced into the discourse. However, the definite NP should unambiguously refer to one object even if no functional concept plays a role, since pig and dog are sortal concepts (except one would claim a functional concept from situations into objects of the mentioned kind).
  6. In other words, a definite NP refers to the most salient object in the discourse that fits the descriptive content, and such salience ranking “depends on the context, i.e. it is not global in the sense that each expression gets its referent for global constraints nor it is local in the sense of Löbner, since once established it can keep its ranking during the whole discourse if there is no other salience changing expression.” Heusinger added two other ideas into this:

  1. The Prague school’s (Sgall et al. 1973, 70) dynamic view of the information expressed in a sentence. In this approach, the “stock of shared knowledge” or repertoire [of objects, relations etc., K.v.H.] common between the speaker and the hearer is the set of potential referents for definite expressions, which is divided into background and foreground information or relative activation (in the sense of being immediately ‘given’, i.e. easily accessible in memory). Wherever its position within the salience hierarchy depends on encyclopedic knowledge, context information and thematic structure of the sentence. Different ways of shifts in a discourse model (“hearer’s image of the world”) shift in different ways, like mere mentioning of an element in that “stock of shared knowledge” brings it into the foreground of the stock, thus the last mentioned element is more in the foreground than the elements mentioned before, its foregrounding recedes if it is not supported by some specific recent moments due to the given situation. “This view differs from Lewis’ concept in that salience is regarded as a property of the cognitive discourse model, rather than as a property of the discourse such. Furthermore, it concentrates on the use of pronominals rather than on the analysis of definite NPs.”
  2. The AI approach of Grosz & Sidner (1985, 3), where the general discourse model consists of three components: “a linguistic structure, an intentional structure, and an attentional state….The third component of discourse structure, the attentional state, is an abstraction of the participants’ focus of attention as their discourse unfolds. The attentional state is a property of discourse, not of discourse participants. It is inherently dynamic, recording the objects, properties, and relations that are salient at each point in the discourse.” “In contrast to the Praguian approach, this structure does not depend on the hearer or speaker, but it is a property of the context (like in Lewis’ view). Webber (1983, 335) distinguishes between the act of reference by the speaker, and the referential behavior of expression in a certain discourse: That is, “referring” is what people do with language. Evoking and accessing discourse entities are what texts/discourses do. A discourse entity inhabits a speaker’s discourse model and represents something the speaker has referred to. A speaker refers to something by utterances that either evoke (if first reference) or access (if subsequent reference) its corresponding discourse entity.”
  3. According to Heusinger, the situational use is central to definite NPs by incorporating contextual information using a salience hierarchy into the representation of definite expression, where “each context can be associated with an ordering among the elements of subsets of the domain of discourse. The definite NP the F denotes the most salient F according to the situation i… the context crucially contributes to the interpretation of the definite NP by forming a salience hierarchy among the potential referents. It is assumed that each context can be associated with an ordering among the elements of subsets of the domain of discourse. The definite NP the F denotes the most salient F according to the situation i . This representation completes the ideas of discourse representation theories by producing a more comprehensive picture: a definite NP is not only linked to an already introduced discourse referent, it is rather linked to the most salient discourse referent of the same kind so far.”
  4. Robert’s Retrievability and Incomplete Descriptions states that “In previous work (Roberts 2003) I argued for a revision of the classical Russellian treatment of definite descriptions, proposing instead that they conventionally trigger two presuppositions, one of weak familiarity (a form of anaphoricity) and a second I called informational uniqueness. These are the informational counterparts of Russellian existence and uniqueness, respectively. In other work, I argued that these same presuppositions are central to the meaning of pronouns (Roberts 2004) and demonstratives (Roberts 2002). Now I show that the general Gricean view of discourse sketched here permits a simplification of that theory: The uniqueness effect observed in certain contexts follows from Retrievability, with no need to stipulate even informational uniqueness.” He describes it as “In order for an utterance to be rationally cooperative in a discourse interaction D, it must be reasonable for the speaker to expect that the addressee can grasp the speaker’s intended meaning in so-uttering in D….When we understand the interpretive effects of Retrievability in conjunction with an anaphoric theory of definites, there is no need to stipulate uniqueness for any of these kinds of NPs. The general requirement of Retrievability of an aphoric antecedents will suffice to account for uniqueness effects, when those arise…In interpreting a definite, an addressee must determine exactly which antecedent the speaker intends, out of all those familiar to the interlocutor. The NP’s descriptive content is a both a constraint on and a clue to the intended antecedent (which must also satisfy that content). Antecedents are not NPs per se, but discourse referents — as that notion is spelled out in the Heim/Kamp/van der Sandt theories.  What is important for salience is not just that something be in the immediate visual field of the addressee, perhaps as directed by deixis, but that s/he be
    attending to it, hence that it be Relevant to her immediate goals and associated intentions. So long as the descriptive content of a definite NP, along with what is predicated of it, is sufficiently rich to uniquely determine one element in the interlocutors’ QUD – limited attentional field, in accordance with Attentional Masking and the Descriptive Content Condition, there is no sense that the NP’s
    descriptive content is incomplete.
  1. Salience is a partial order of the elements of DR (the set of Discourse Referents), determined by the degree to which those entities would be immediately in the attentional field of anyone cooperatively paying attention to that context.
  2. Factors in a salience ranking in discourse include the following, themselves ranked in descending order of importance: (1) High perceptual salience in the situation of utterance. (2) RELEVANCE to the evident current purposes of the interlocutors, especially the QUD (cf. Grosz & Sider 1986) (3) Coherence, reflected in felicitous rhetorical relations in a relevant strategy of inquiry, with consequent relations between thematic roles in the two utterances (Kehler 2009) (4) Relative recency (Terken & Hirschberg 1994).
  3. Attentional Masking Hypothesis: The search for an anaphoric antecedent among the accessible discourse referents proceeds as follows: Look first to the most salient entities, then to all those that are less salient but still Relevant, and finally to all elements of DR, the domain reflecting all familiar entities in the Common Ground. The antecedent is the first discourse referent you encounter which is informationally unique among the discourse referents ranked at its level of salience in satisfying the NP’s descriptive content (while being plausible in view of what is predicated of the NP).
  4. Descriptive content condition: To guarantee Retrievability in using a definite NP, a speaker should choose one whose descriptive content is just sufficiently rich to uniquely identify the intended discourse referent among all those which are at least as salient. ”
  • Other examples:
    1. Jane entered the cafe and looked around. She sat down. The table was slightly wobbly.
    2. The cat is in the carton. The cat will never meet our other cat, because our other cat lives in New Zealand. Our New Zealand cat lives with the Cresswells. And there he’ll stay, because Miriam would be sad if the cat went away.
    3. In the cafe, an angry toddler threw around his spaghetti near where he was sitting. After he left, the waitress came and wiped the tables.
  • A study concluded that definiteness is not primarily based on salience. The same study concludes that uniqueness and previous mention effects are not driven by general salience-based processes that would also be instantiated by visual salience, but operate independently. The study noted that “Although the cases Lewis (1973:114ff; 1979) discussed are cases where the salience of a referent arises from the utterance situation, rather than from the linguistic structure of discourse, the notions of salience that were developed with some success in subsequent work (Ariel 1985, Gundel et al. 1993, Grosz et al. 1995, von Heusinger 1995, Roberts 2003, and many others) have remained limited to linguistic discourse parameters… If a general notion of salience could be developed that covers such cases of visual salience and could also substitute for anaphora and uniqueness, we would
    be pretty close to a general notion of definite reference.” But the study did mention a caveat: “But with no theory of such a mechanism in place the general salience hypothesis is hard to test. What is feasible, however, is an experimental comparison of the contributions that uniqueness and anaphora make towards the identification of DRE referents and the contribution that purely visual salience in the utterance situation makes…. The experiment will perhaps not yet permit any conclusions about salience in general , but it will be informative at least with regard to the interaction of visual salience with anaphora, and uniqueness….Our results thus seem to suggest that salience is considered only after anaphora and uniqueness have failed to identify a suitable referent.” This experiment failed because salience is a property of the discourse in situ. The discourses in the test pertaining to salience failed to provide the most salient object in the text or answer the question “which one?”  among the other similar objects, thus textually ambiguous or vague. Uniqueness is a form of salience. 
  • A similar study by Ahern and Stevens has a different conclusion, that uniqueness is salience by proving that uniqueness (maximally unique object or unique under the greatest number of descriptions) is the primary factor when interpreting ambiguous definite NPs: “We have provided a direct comparison of definite and indefinite descriptions. By allowing a period of temporary ambiguity we were able to isolate the contribution of definiteness to interpretation. Eye movements during this period of ambiguity suggest that the online interpretation of definite descriptions is guided by uniqueness. When processing definites, but not indefinites, subjects look reliably more toward the candidate referent that is unique under the greatest number of descriptions. These results suggest a role of uniqueness not only in theoretical models, but also in processing behaviors. However, it remains unclear whether uniqueness is exactly the right notion to capture the full range of semantic and psycholinguistic generalizations. Rather, one could posit based on our results that salience, and not uniqueness, plays a special role in interpreting definite descriptions. After all, what we have dubbed the “maximally unique” referent is also the most salient possible referent within its category in that it stands out or “suggests itself”, to echo Schelling (1960). Perhaps interpretation of the definite article triggers an online search for the most salient appropriate referent. ..Uniqueness typically confers a particular kind of salience on a potential referent, and maximal uniqueness a privileged sort of salience. Future research may be brought to bear on whether uniqueness and salience should be distinguished, and on what role these notions play in both psycholinguistic and theoretical analyses of definiteness.”
  • Ward, Ahern and Heyden demonstrated that "The felicity of both the definite and indefinite embedded NP suggests that neither (weak) familiarity nor uniqueness per se accounts for article choice in the case of attributive-possession NPs(APNPs)…What is relevant for the (in)definiteness of an APNP is whether its referent is interpreted as a typical or atypical member of its class….When uniqueness is not satisfied, participants rely significantly on the atypicality of the referent, the more atypical the referent (as judged by the participants themselves), the more likely it is to be realized with a definite APNP. We propose that atypical APNPs are being interpreted more as object-denoting, while typical APNPs are being interpreted more as property-denoting (Partee ’87).
  • I think the Salience Theory has more explanatory power than the Uniqueness Theory, especially as outlined by Roberts. To summarize:

    1. Selection by Differentiation Theory– Definite marking is the selection of a limited set of objects among many similar or identical objects, and this is can be achieved by being differentiable from all possible similar or identical objects (individually for singular and collectively for generic referents) so that the hearer is able to figure out the intended referent. The definite marked NP is distinguished from the indefinite by selecting and restricting its members.
      • Indefinite marking indicates the genericity and commonality of all referents, and may be further marked individually (singular) or in totality (plural). The speaker shows the scope of possible referents. Definite marking indicates the selectability and differentiability of a few referents, and the speaker has already chosen or done the selection from among the many.
      • Selection or restriction is done in a number of ways alone or in combination:
        1. Numerical Sufficiency: limiting the NP meaning numerically : singular count noun for a unique referent, plural count or non-count nouns for the exhaustive totality of referents.
        2. Contextual Saliency: the first to satisfy the descriptive content from the saliency hierarchy.
          1. Body parts (situational): “Mary banged herself on the forehead.” (the one that got banged, defaults to Mary’s head, otherwise will have restrictive clause.)
          2. Immediate surroundings (situational): “The roses are very beautiful” (those in the garden they’re at)
          3. general knowledge (situational): “the Prime Minister” (the one currently in the applicable country)
          4. referents presented as if “familiar, though they have had no previous introduction (textual/situational):  “All this happened more or less. The war parts anyway, are pretty much true” (those that the storyteller has chosen to talk about)
          5. anaphoric reference-direct (textual): “John bought a TV and a video recorder, but he
            returned the video recorder.
            ” (the one he bought)
          6. anaphoric reference-indirect (textual): “John bought a bicycle, but when he rode it one of the wheels came off.”  (those of the bicycle.)
        3. Restrictive Clauses – mixes contextual saliency and numerical sufficiency through additional words to enhance retrievability.
          1. logical use: “When is the first flight to Chicago tomorrow?” (the one that’s unique)
          2. cataphoric reference: “The girls sitting over there are my cousins.” (situational)
      • Selection may refer to unique individual or to the whole class. Some languages may not use definite marking here.
        1. Uniques.
        2. Generic – identifies “the class as represented by its typical specimen”. Using indefinites will (a) focus too much on the lack of specificity if single referent, (b) focus too much on many referents if the sense requires a single referent, (c) there is no plural indefinite for generics, or (d) the singular is preferred for its ease of understanding. I think this is language specific, at least in English.
          1. sporadic reference:  “My sister goes to the theatre every month.
          2. A great deal of illness originates in the mind.” , ”the monkey is a curious animal”, “Some people sit for hours in front of the television.
          3. adjectives denoting the whole class. These does not have plural generics: ‘the rich and the poor’ ,  ‘the Atlantic’ , ‘the Chinese’  (denoting nationality)
          4. In many idioms: ‘kick the bucket’, ‘grab the bull by its horns

    2 Responses to “What is Definiteness?”

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