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- This is an abbreviated version of a similarly titled piece retrievable from http://www.arts.monash.edu.au/ling/lexicon_quantity.pdf.
The Lexicon and Quantity Implicatures
Keith Allan Monash University [email protected]
1. Introduction
The present paper is about the conversational implicatures (hereafter referred to simply as ‘implicatures’) that result from the two maxims of quantity identified by Grice 1975 and subsequently discussed by (amongst others) Atlas and Levinson 1981, Horn 1984, and Levinson 1995. The question I seek to resolve is whether Q[uantity] implicatures should be entered in the lexicon or whether they constitute encyclopedic information. Allan 1995, fc argues for a division of labour between the lexicon and the encyclopedia. The lexicon contains formal, morphosyntactic, and semantic specifications of listemes and the encyclopedia contains other kinds of information about listemes, e.g. their etymology, and information about their denotata.
Conversational implicatures are pragmatic (Grice 1975, Gazdar 1979, Levinson 1983): they arise from the use of language in particular contexts. They differ from entailments in being defeasible. In other work (Allan 1999), Q1 implicatures, deriving from the first maxim of quantity, are included in lexical entries capture the default meaning (this is exemplified in §3). I shall argue here that what Jackendoff 1983, 1985, 1990 refers to as ‘preference conditions’ on lexical items are implicatures deriving from the second maxim of quantity augmented with the Atlas and Levinson principle of informativeness, a combination here referred to as Q2 — a quantity 2 implicature. Jackendoff incorporates preference conditions within his lexical entries. For instance, the lexical meaning of bird includes both an indefeasible part identifying the class of creatures (expressed in the lexicon as a truth statement), and a defeasible part “capable of flight” that identifies what is probably the case (in the absence of contrary evidence). Surveying as many examples of quantity implicature as space permits, I find that all Q implicatures based on a single lexical item are noted in the lexicon entry. Nonlexical implicatures arise from collocations of lexical items and can perhaps be located within the encyclopedia of which the lexicon is a part.
2. Cooperation, common ground, and implicature
Like other social activities, language interchange requires participants to mutually recognize certain conventions (in the sense of Lewis 1969). Among them, are the conventions that Grice described as maxims of the cooperative principle (Grice 1975:45). Grice identified four categories of maxims: quantity, quality, relation, and manner and we are concerned only with the first of them.
The category of QUANTITY relates to the quantity of information to be provided, and under it fall the following maxims:
- Make your contribution as informative as is required (for the current purposes of the exchange).
- Do not make your contribution more informative than is required. (Grice 1975:45)
The maxims are not laws to be obeyed, but reference points for language interchange — much as the points of the compass are conventional reference points for identifying locations on the surface of the earth. Conversational implicatures arise from both observing and from flouting the maxims. Conversational implicature is the pragmatic counterpart to the semantic relations of entailment and conventional implicature (cf. Lyons 1995:276, Allan fc). s In the formula 0 ¯ 4 , 4 is a conversational implicature of 0 , which is a part (or perhaps the whole) of Speaker’s utterance U made in context C under conventional cooperative conditions. 4 is a pragmatic inference calculated from the meaning of U considered in the light of: (i) the cooperative principle, (ii) the context C, and (iii) encyclopedic knowledge. A conversational implicature is defeasible (can be canceled) without contradicting the utterance which implicates it. It is defeasibility that distinguishes conversational implicature from entailment and conventional implicature.
Conversational implicature depends upon common ground (Stalnaker 1973, 1974, Clark 1996). S[peaker] and H[earer] are mutually aware that, normally, their interlocutor is an intelligent being. S does not need to spell out those things which are (a) obvious to the sensory receptors of H, or (b) which H can very easily reason out on the basis of (i) knowing the language and the conventions for its use, and (ii) using the knowledge that each of us develops from birth as we experience the world around us.
The Grice quantity implicatures can be usefully augmented with Atlas and Levinson’s (1981:40-50) informativeness principle, paraphrased in Levinson 1983:146f, ‘read as much into the utterance as is consistent with what you know about the world’. For the purpose of this paper, the augmented Grice implicatures are revamped as follows:
(2) a. It’s a bird ¯ It’s capable of flight (if it’s alive)
b. Sally climbed and climbed ¯ Sally used her legs and feet and went upwards c. Kim was able to win that race ¯ Kim won that race (cf.(1d)) d. Sam broke an arm ¯ Sam broke his own arm (cf. (1c)) e. The driver stopped the car ¯ by applying the footbrake
What I am here calling Q2 implicatures, Jackendoff 1983 Chs 7-8, 1985, 1990:35ff refers to as ‘preference conditions’. For example:
(3) T ERM PREFERENCE CONDITION
bird something which can fly [cf. (2a)] climb climb upward and use feet [cf. (2b)] go, drive, walk go, drive, walk forward
Consider them in more detail, starting with
(4) I’m looking at a bird.
Especially when unaided by a natural context, (4) denotes a bipedal creature with beak and feathers that can fly. Even though some chicks are naked when they come out of the egg, and penguins and emus don’t fly, these are all members of the category Bird. Jackendoff 1983:144 represents the condition that a typical bird can fly as (5).
TYPE (5) BIRD P(CAN FLY)
Preference conditions are common to reasoning in many areas of cognitive processing: scripts and frames (cf. Schank and Abelson 1977, Schank 1982, 1984, 1986, Fillmore 1982, Fillmore and Atkins 1992, Barsalou 1992, Lehrer and Kittay (eds) 1992) are examples; they operate in the perceived groupings of notes and chords in musical scores (Jackendoff 1983:131f, Lerdahl and Jackendoff 1982 Ch.3); and in visual perception. As common sense surely predicts, semantics is not autonomous from other aspects of cognition.
Preference conditions arise from reasonable expectations about the way the world is. They are implicated whenever the common ground (including what S says) gives no indication to the contrary. Like all conversational implicatures, preference
- If A and B are sentences of the object language and their respective semantic descriptions are respectively a and b , then A ENTAILS B, A.B, iff a b in all possible worlds. If A and B are sentences of the object language and their respective semantic descriptions are respectively a and b , then A IS SYNONYMOUS WITH B, A 0. B, iff a b in all possible worlds.
conditions are open to cancelation; for instance, preference condition (6) permits (7) without contradiction.
(6) ~x[ bird 11 (x) ¯ can 11 (x,[ fly 11 (x)])] (7) ~x[ emu 11 (x) bird 11 (x) Y ¬[ can 11 (x,[ fly 11 (x)])]]
Now take the verb climb (with grossly simplified semantics):
(8) ~x[ climb 11 (x) go_upward 11 (x) Z move_in_a_vertical_axis_using_feet 11 (x)] ~x[ climb 11 (x) ¯ go_upward 11 (x) Y move_in_a_vertical_axis_using_feet 11 (x)]
Hence (where A. B symbolizes “A entails B”, A B “A does not entail B”, A 0. B “A is synonymous with B”, A B “A is not synonymous with B”):
(9) Bill climbed the mountain^0.^ Bill climbed up the mountain
Bill climbed the mountain on his knees.
(10) Bill climbed down the mountain Bill climbed the mountain
Together with the necessary semantic properties, preference conditions identify the typical attributes of the denotatum. Preference conditions enable a rational explanation to be given for the application of a single lexeme to denotata with diverse characteristics such as birds that fly and others that don’t. It is a lesson in capturing the flexibility of natural language in a principled manner. The question that arises is whether all Q2 implicatures can be accommodated in the lexicon or whether some should be located in the associated encyclopedia.
3. Lexical entries for Q implicatures
The Q1 implicatures in (1) can be straightforwardly incorporated into the lexicon. In Allan 1999, fc the semantics for (1a), repeated below, is (11). is a measure function on ; it gives the quantity (not necessarily cardinality) of .
(1) a. three ¯ no more than three
(11) [ three y: yI[ PLQ x: cat 11 (x)]]( grey 11 (y)) cg 3
[ three y: yI[ PLQ x: cat 11 (x)]]( grey 11 (y)) ¯ cg =
- ‘[h/x] 0 ’ means replace every variable x in formula 0 by h. ‘[h=Harry]’ illustrates the device that introduces proper names to the calculus for quantification.
- Diagrams are imprecise illustrations. For instance, neither the formula in (15) nor the English it represents are specific about whether fGg (as in Fig.2) or f=g. Incidentally, there is nothing significant about the shape of ensemble boundaries in Figs 1-2.
The case of (1c) is more complicated. Contrast it with (13).
(1) c. I ran over a dog at the weekend ¯ The dog was not mine or yours (13) I ran over the dog at the weekend.
In Allan 1999, fc the indefinite and definite are contrastively defined as follows: s The INDEFINITE requires H to create an ensemble x from an ensemble y such that xGy. s The DEFINITE picks out the ensemble x for H by equating it with ensemble y such that x=y (which is what universals do), or naming it, for example [h/x] 0 where [h=Harry] and x is a variable in formula 0 . Thus the definite is used whenever S presupposes that the reference is identifiable to H. The conditions on identifiability are complex and I will not try to describe them here (see Allan opp.cit., Du Bois 1980, Hawkins 1978, Lewis 1979, Givón 1984, Lambrecht 1994, among others). Like other quantifiers, the definite article can be
formalized as a restrictive quantifier: [ the x: Fx] is semantically }!x[xIf x=f] to be
read “there is exactly one ensemble x and if it is a subensemble of f, then x is identical with f” which can be paraphrased by “there is exactly one ensemble f at the relevant world and time spoken of”. In a clause, the simplified formulation is (14):
(14) the x: Fx }!x[xIfg x=f]
(14), sketched in Fig.1, says the f is g is true in the world spoken of only if there is exactly one ensemble f identical with the ensemble of f which is g.
Figure 1. Sketch of (14)
The conditions on the indefinite are described above. The semantics of indefinite a(n) is identical with that for one ; but the implicature is not, because being an article, a(n) is in contrast with the (its Saussurean ‘valeur’). The semantics of one is given in (15), that for a(n) in (16).
(15) one y: yI[LQ x: Fx] fg 1
one y: yI[LQ x: Fx] ¯ fg =
(16) a(n) y: yI[LQ x: Fx] fg 1
a(n) y: yI[LQ x: Fx] ¯ fg =1 Y ¬}!y[yIf y=f]
Because (15-16) are indefinite, for both: ~y}z[yIf Y zGf Y zgy], cf. Fig.2.
Figure 2. Sketches of indefinites
The second conjunct of the implicature in (16), ¬}!y[yIf y=f], says that it is not
the case that there is exactly one ensemble y which, if it is a subensemble of f, is identical with f. This contrasts with a definite — as graphically demonstrated by comparing Fig.1 with Fig.2. Whenever possible, a definite is preferred to an indefinite, so the indefinite implicates that the definite is not applicable, and the relevant inferences are drawn. When applied to the particular context, it is this second conjunct of the implicature in (16) that gives rise to the implicatures in (1c). This condition applies with very different effects in respect of sentences like (2d), Sam broke an arm — by implication, his own. Such cases are discussed later. The
implicature given in (1c) is just one of several possible lexicalizations of ¬}!y[yIf
y=f] in the context of the implicating sentence.
Finally, consider the Q1 implicature in
(1) d. Kim had the ability to win that race ¯ S doesn’t know that Kim did
win that race
The negative implicature is not valid for a non-past: neither sentence in (17-18) implicates that Kim will not win that race; but they do entail that s/he hasn’t yet done so.
(17) Kim has the ability to win this race. Kim has not yet won this race. (18) Kim will have the ability to win that race. Kim has not yet won that race.
Win is a telic achievement verb in the sense that something effects winning (i.e. superceding competitors) as its conclusion. The winner may play an active part as in (19a) or not as in (19b) (x is the winner and L is a dummy argument that can be lexicalized something ).
(19) a. do 11 (x,[ effect 11 (x,[ win 11 (x, a_race )])])
- Sincerity condition on statements, if you will. See Allan 1994.
- There is idiolectal and perhaps dialectal variation with respect to these relations. For instance, some people find contradictory I had the ability to win but I wasn’t able to win. Others, like myself, do not.
(24) N [c[ N [ be_able 11 ( Kim ,[ do 11 ( Kim ,[ effect 11 ( Kim ,[ win 11 ( Kim , this_race )])])])]]] ¯ There are reasonable grounds for the belief that Kim has the ability to win this race
A reasonable ground might be Kim’s performance in comparable races. The implicature arises from the precondition^ for felicitous utterance. It is clear that the different implicatures of (1d) and (17-18) are a function of the tense operator that scopes over have the ability to. The question arises: Is this the kind of information to be noted in a lexicon?
I shall answer affirmatively, but before doing so, let’s turn our attention to (2c), Kim was able to win that race. The precondition for felicitous utterance of nonpast Kim is able to win this race gives rise to the same implicature as in (24). The grounds for such a belief in a race already run only justify the statement about Kim’s capability if s/he did win; hence, the Q2 implicature that Kim did win.
(25) P [ be_able 11 ( Kim ,[ do 11 ( Kim ,[ effect 11 ( Kim ,[ win 11 ( Kim , that_race )])])])] ¯ P [ do 11 ( Kim ,[ effect 11 ( Kim ,[ win 11 ( Kim , that_race )])])]
Looking back to (20-21), we can identify the following relations.
Kim won that race. Kim was able to win that race. Kim had the ability to win that race
outcome of ability exercise of ability potential ability
The exercise of ability is, by default, expected to lead to a successful outcome, hence the Q2 implicature in (2c) and (25). Potential ability, however, has unknown outcome; hence the Q1 implicature in (1d) and (23). The implicatures can be included in the lexicon as shown in (26) and (27), where T is a variable over tenses.
(26) be able to T [ be_able 11 (x,[ do 11 (x, ...)])] IF T = P THEN P [ be_able 11 (x,[ do 11 (x, ... )])] ¯ P [ do 11 (x, ...)]]
(27) is the basis for (2c) with its Q2 implicature.
(27) have the ability to Ti [c[ Tj [ be_able 11 (x, ...)]]] IF Tj = P THEN Ti [c[ P [ be_able 11 (x,[ do 11 (x, ...)])]]] ¯ Ti [c[ P [¬[ do 11 (x, ...)]]]]
(26) is the basis for (1d) with its Q1 implicature.
- I ignore the unlikely possibility of arm being used for “armament” rather than a body part. It behooves me to explain why the use of the indefinite in (2d) has, loosely speaking, the opposite effect from its use in (1c). An indefinite can only be used when the body-part NP refers to a proper subset of the relevant body parts. A possessive definite can be used, e.g. Sam broke his arm , even though Sam has more than one arm. A detailed explanation is outside the scope of this paper, but briefly it is explicable in terms of the newsworthiness of the event and distinguishing which of Sam’s arms it was is at best a secondary matter (see Allan 1986, fc).
The reason that (2c).(1d), i.e. Kim was able to win that race. Kim had the ability to win that race , despite their different implicatures is that implicature is in part a function of the choice of words in an utterance: choosing the former indicates that the implicature of the latter does not apply. The same rule applies when three is used instead of two : three logically implies two and two implicates “no more than two”, which is certainly not the implicature of three. The rule applies just as well to emu and bird : the Q2 implicature “can fly”, does not apply to emu despite the fact that x is an emu. x is a bird. It is therefore a regular effect of lexical choice that Kim was able to win that race does not implicate “S does not know that Kim did win that race”.
(26) gives the semantics for (2c) and, like (2a-b), it includes a Q2 implicature in the lexicon; so let’s consider the other examples of Q2 implicature in (2).
(28a-b) clearly contrast with (1c).
(28) a. Sam dropped^ an arm ¯ The arm is his own
waved $
b. Sam broke^ an arm ¯ The arm is his own
lost $
Examples like (28a) are restricted to movement of a proper subset of body parts when change in its location is in focus (consider the possible ambiguity of Sam shook a hand : shook his own hand about; performed a greeting by shaking the hand of another). At best (28a) would be a context sensitive rule such as:
(29) x moves y Y y is a body part do 11 (x,[ a(n) y: body_part 11 (y)]([ move 11 (x,y)]) Y }z[ have 11 (x,[ body_part 11 (z)]) Y yGz])] ¯ y is x’s body part
This would have to be located in a lexicon under a large number of either movement verbs or body part nouns; but neither seems appropriate. (29) characterizes knowledge about a combination of listemes, not a single listeme.
There is a similar problem with (28b). Injury to or loss of a proper subset of a set of body parts gives rise to the implicature as shown; but representing this in the lexicon is at least as problematic as for (28a). The default interpretation is unaccusative: “something happens such that x suffers damage or loss to a body part”. H must determine this from the combination of verb and body-part NP. In
(33) The driver stopped the car at time ti
. The car was in motion at ti-1 Y the person controlling the car did something at ti-1 to cause the car to stop . The car did not stop because it crashed, or ran out of petrol, or the battery died
Is it the semantic frame of car or its encyclopedia entry that carries the information that a car has a foot brake and a handbrake which serve different primary functions? The semantic specification of car in the lexicon will be a refined and expanded version of (34).
(34) car car 11 (x) y vehicle 11 (y) Y more_than_two_wheeled 11 (y) Y }z[ seat_for_the_driver 11 (z) Y face_front 11 (z) Y¬}w[ seat 11 (w) Y in_front_of 11 (w,z)] Y accommodate 11 (y,z)] ¯ x has a motor and up to about six passenger seats; it has two wheels at each side for forward and backward movement.
(34) says nothing about any means of stopping or starting a car. The encyclopedia entry linked to car will contain information of the following kind: s (a) An account of the semantic links between car, cart, carriage and carry and of the growing salience of the “automobile” sense of car during the 20th century. (b) The principal function of a car is to transport people. A car is controlled by one of them, the driver. (c) Description of the components of a typical car and of their functions. E.g. (i) The wheels of a car are rimmed by tyres that are typically pneumatic. The front wheels turn to direct the car as it moves. This turning is effected by the driver who changes direction by rotating the steering wheel inside the car. (ii) A car is typically propelled (and otherwise powered) by a motor, usually an internal combustion engine. The motor is started by an ignition switch, activated on most cars by a key. (iii) When running, the engine causes the wheels to move when the gears within the transmission are engaged. The speed of the running engine is controlled by an accelerator pedal operated by the driver. (iv) That the car’s motion is stopped by applying brakes to the wheels. These brakes are controlled by the driver applying a foot brake. A handbrake holds the car from moving when it is parked. (v) Most cars have two rows of seats facing forward, the driver occupying a seat in the front row. ... (d) Some car marques are: BMW, Ford, Holden, Lamborghini, ... ... Despite the fact that a motor car’s brakes are contingently inalienable, the weight of evidence suggests that their function within a car does not arise directly from
- ELSE conditions have not appeared in this paper. See Allan 2000 for their use.
lexical or semantic properties of the word car. Instead, it is something we know about the objects denoted by car. The Q2 implicature of (2e) must, therefore, derive from encyclopedic information about cars and the default means of stopping them.
In the preceding section I defined Q1 and Q2 implicatures and endorsed their pragmatic status. In this section I have defended the claim that the Q1 and Q implicatures of listemes should be included among their ‘semantic’ specification in the lexicon. An implicature identifies the default interpretations, i.e. the PROBABLE meaning in the absence of constraints imposed by a particular context. IF, THEN, ELSE conditions sequence probabilities among implicatures in the lexicon.^ The standard implicatures must be learned by the language user along with the NECESSARY sense(s) of the listeme. A strong argument for this innovation to the lexicon is a quantifier like two. Two necessarily means “at least two”; but if you ask a lay population, they interpret it as meaning “exactly two”, its most probable meaning. This is a fact ignored only by an incompetent lexicographer. The vast majority of the lay population of English speakers assumes that bull denotes a male bovine. This is the standard implicature; there are bull elephants, bull hippos, bull whales, bull alligators, etc. each of which can be referred to simply as a bull when common ground makes use of the term unambiguous and cancels the implicature. To my mind, there is no doubt that Q1 and Q2 implicatures must be entered into the lexicon; and I have shown how this might be done for a variety of listemes. The implicatures that attach to collocations of listemes, however, are not located in the lexicon; like the meanings of the collocations themselves, them must be computed.
4. Key points
A premise for this paper was that semantic specification in the lexicon should incorporate defeasible default (probable) meaning of a lexicon item together with the logically necessary components of lexical meaning. The defeasible default meaning is a conversational implicature; and, because such implicature is pragmatic and often based on encyclopedic knowledge, it seemed reasonable to suppose that implicature might be at the interface of lexicon and encyclopedia. Despite the fact that conversational implicatures are pragmatic entities, generalized quantity implicatures (the only implicatures examined) are readily included in a lexicon entry. All the Q implicatures associated directly with a single lexicon item were readily and usefully incorporated into the lexical entry for the item, and there is no reason to expect that exceptions will be uncovered. Where the implicature arises from a combination of listemes, it cannot be included in the lexicon, but must be generated by the semantic component of the grammar.
— 1984. Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. Meaning, Form, and Use in Context: Linguistic Applications (Georgetown University Round Table on Languages and Linguistics) ed. by Deborah Schriffin, pp. 11-42. Washington DC: Georgetown University Press. — 1989. A Natural History of Negation. Chicago: University of Chicago Press. Jackendoff, Ray. 1983. Semantics and Cognition. Cambridge MA: MIT Press. — 1985. Multiple subcategorization and the -criterion: the case of climb. Natural Language and Linguistic Theory 3:271-95. — 1990. Semantic Structures. Cambridge MA: MIT Press. Lambrecht, Knud. 1994. Information Structure and Sentence Form: Topic, Focus, and the Mental Representations of Discourse Referents. Cambridge: Cambridge University Press. Lehrer, Adrienne and Eva F. Kittay (eds). 1992. Frames, Fields, and Contrasts. Hillsdale: Lawrence Erlbaum. Lerdahl, Fred and Ray Jackendoff. 1982. A Generative Theory of Tonal Music. Cambridge MA: MIT Press. Levinson, Stephen. 1983. Pragmatics. Cambridge: Cambridge University Press. — Three levels of meaning. Grammar and Meaning: Essays in Honour of Sir John Lyons , ed. by Frank R. Palmer, pp.90-115. Cambridge: Cambridge University Press. Lewis, David. 1969. Convention. Cambridge MA: Harvard University Press. — 1979. Scorekeeping in a language game. Journal of Philosophical Logic 8:339-59. Lyons, John. 1995. Linguistic Semantics an Introduction. Cambridge: Cambridge University Press. Schank, Roger C. 1982. Dynamic Memory: a Theory of Reminding and Learning in Computers and People. Cambridge: Cambridge University Press. — 1984. The Cognitive Computer. Reading MA: Addison-Wesley. — 1986. Explanation Patterns. Hillsdale NJ: Lawrence Erlbaum. — and Robert C. Abelson. 1977. Scripts, Plans, Goals and Understanding: An Inquiry into Human Knowledge Structures. Hillsdale, NJ: Lawrence Erlbaum. Stalnaker, Robert C. 1973. Presupposition. Journal of Philosophical Logic 2:77-96. — 1974. Pragmatic presupposition. Semantics and Philosophy , ed. by M.K. Munitz and P.K. Unger. New York: New York University Press.
