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date: 21 March 2019


Abstract and Keywords

Implicature for speakers is meaning one thing by saying something else. Semantic implicatures are part of sentence meaning, whereas conversational implicatures depend on the utterance context. Conventional forms of conversational implicature include figures and modes of speech like irony and relevance implicature. A sentence has an implicature when speakers conventionally use sentences of that form with the corresponding implicature. Speakers implicate things for many reasons. Some apply to saying (communication, self-expression, record creation), others do not (verbal efficiency, misleading without lying, veiling, good social relations, style, and entertainment). A sentence has an implicature today because that use became self-perpetuating. The dependence of implicature on intention and convention, and the variety of conflicting goals implicature serves, show that implicatures cannot be derived from conversational principles. Interpreting implicatures is largely the automatic exercise of a competence acquired with one’s native language rather than calculation.

Keywords: Implicature, meaning, intention, convention, communication, comprehension, tropes, pragmatics

1. Speaker Implicature

Implicature denotes a type of meaning or implying. Which type? Contrast the following sentences, all of which, let us assume, are true. The same contrasts are evident with implies.

  1. (1) The fact that John has a temperature means that he is sick. (Evidential Meaning)

  2. (2) John has a temperature means that John’s temperature is above normal. (Sentence Meaning)

  3. (3) By (saying) John has a temperature, Steve meant that John has a thermometer. (Speaker Meaning, Cognitive)

Sentence (1) entails that John’s having a temperature is sufficient evidence for us to infer that he is sick. Evidential meaning typically exists because of correlations and causal connections. It can be purely natural, as in the paradigm case of black clouds meaning rain, or it can depend on human action and convention, as in the case of human utterances meaning anger or other mental states.1 Indicates is a near synonym only when means has its evidential sense, and is weaker. An indication that John is sick may not be enough evidence for us to conclude that he is. Sentences or speakers themselves, independent of their utterances, do not indicate anything and have no evidential meaning.

Sentence meaning is a property of expressions rather than of speakers. It depends on conventional usage and the syntax and semantics of the language, not on any particular speaker or utterance. Consequently (3) may be true even though (2) is: Steve may have used temperature either by mistake or purposely with an unconventional meaning.

Whether Steve meant that John has an above normal temperature or a thermometer depends on what Steve intended. Which intentions determine speaker meaning is a matter of debate. On Grice’s (1957) influential view, to mean that p by e is to utter e with the intention of producing the belief that p in one’s audience in a certain way. Thus whether Steve means that John has a high temperature or a thermometer depends on which belief he is trying to produce in his audience. Grice’s condition holds in the most typical cases, but far from all. People talking to foreigners or animals, for example, or answering a teacher’s question, need not be trying to produce belief. Speakers can mean things without intending to communicate with or inform anyone. On my view, to mean that p is to thereby express the belief that p, which is to do something that indicates (evidentially) that one has that belief in a certain way. The fact that natural signs and indications can exist even when they are not recognized by anyone avoids Grice’s difficulty with foreigners and animals. That indications need not be completely reliable allows people to express beliefs they do not have, and thereby lie.2

Speaker and sentence meaning may diverge even when the speaker makes no mistake and is using words with their conventional meanings. Imagine the following dialogue.

  1. (4) Sue: Can John play?

    Steve: John has a temperature.

If this was a typical exchange, Steve meant that John cannot play. But the sentence he uttered means something very different. Hence Steve did not say that John cannot play, he implied it. Speaker implication involves meaning that one thing is the case by meaning that something else is. Grice (1975: 24) introduced the technical term implicate for a closely related speech act: meaning or implying one thing by saying another.3 Thus Steve implicated that John cannot play. Implying and implicating are what Searle (1975: 265–266) called indirect speech acts. Someone who says Can you close the window? commonly makes a request indirectly—by asking a question. This differs from implicature in that the speaker did not say or mean that anything is the case. But otherwise the acts are similar.

In the definition of implicature, saying means not the mere utterance of words, but saying that something is the case, an illocutionary speech act like stating and affirming but more general. What Steve said is that John has a temperature, something he could have said by uttering different words, perhaps in French. Say is to be interpreted strictly in the definition of implicature, requiring that what a speaker says be something that the sentence uttered conventionally means (modulo indexicals and ellipsis).4 Stating something entails both saying and meaning it.

Dialogue (4) shows that we cannot fully understand a speaker without knowing what the speaker has implicated. If we know only what Steve has said, we would not realize that he had answered Sue’s question. If we do not know whether Steve answered directly or indirectly, we may not know how to evaluate him. For example, if Steve insincerely said John could not play, he lied. If he insincerely implicated the same thing, he misled Sue without lying.

What someone has implicated is not given to us directly. We have to infer it from evidence. We would typically recognize that Steve meant John could not play in (4) on the basis of what he said, what Sue asked, and our assumption that Steve was responding to Sue’s question. Alternatively, we may have asked him whether he meant John could not play, and inferred that he did from his answer “Yes.” Because implicatures have to be inferred, they can be characterized as inferences. But implicating is not itself inferring. Hearers infer what speakers implicate. Furthermore, while the evidence will differ from case to case, all speech acts have to be inferred from contextual evidence, including what was said and even what sentence was uttered. If Steve produces [plān], for example, we need to infer whether he was uttering an English or a German word; if English, whether he uttered the word plain or plane; and if plane, whether it meant “airplane” or “wood plane” on this occasion. Our recognition of what is meant is commonly automatic, though, whether it is said or implicated. Whether there is any significant difference in the kind of inference required to recognize an implicature is a matter of some debate (see, for example, Recanati 2002, and section 6 of this essay).

2. Semantic versus Conversational Implicature

Steve’s implicature is conversational. It is not part of the meaning of the sentence uttered, but depends on features of the conversational context. Had Sue asked, “Is John well?,” Steve could have implicated something completely different (that he is not well) by saying the same thing. A semantic implicature is part of the meaning of the sentence used.5

  1. (5)

    1. (a) Washington, a Virginian, was the first president.

    2. (b) Washington was a Virginian.

Speakers implicate (5)(b) when they use (5)(a) literally. They mean, but do not say, that Washington was a Virginian. Hence the literal use of (5)(a) while disbelieving (5)(b) would be misleading, but not lying. Steve’s sentence in (4) can be used literally with its conventional meaning without his implicature. Thus Steve could coherently have added but he is well enough to play. In contrast, (5)(a) cannot be used literally with its conventional meaning without implicating (5)(b); but Washington was not a Virginian cannot be added.

3. General Forms of Conversational Implicature

Many forms of conversational implicature occur widely and frequently in everyday speech and literature, with a wide variety of sentences and languages. They are common ways of both using and understanding language. The forms are differentiated by the relationship between what is said (S) and what is implicated (I), and in some cases by how or why I is implicated by saying S. I will only gesture at the latter here.

3.1 Figures of Speech (Tropes)

The most widely recognized forms of implicature have been known at least since Aristotle.

Irony: Implicating a contrary of S to make light of, belittle, or mock it.

When The weather is lovely is uttered ironically in a blizzard, the speaker implicates that the weather is awful, for he means that by saying the weather is lovely. He does so to make light of the awful weather.

Overstatement (hyperbole): Implicating a proposition describing things as being less in a certain respect than as described by S to emphasize how great it is in that respect.

Steve would have engaged in hyperbole if he meant that John’s temperature is quite high (high though not extremely high) by saying John is burning up and did so to express concern about how high his temperature is. This is not irony because Steve is highlighting rather than making light of John’s temperature.

Understatement: Implicating a proposition describing things as being greater in a certain respect than as described by S’s affirmation (meiosis) or by S’s denial (litotes), to deemphasize how great it is in that respect.

Steve used meiosis if he said John has a slight temperature and meant that John’s temperature is way above normal. He used litotes if he meant that by saying John’s temperature is not normal.

Metonymy and metaphor differ in lacking purposive differentia, and in not being marked intonationally when spoken.

Metonymy: Implicating that something has a property ascribed to a related object by S without meaning S.

The paradigm is the waitress who says The ham sandwich wants more coffee, meaning that the customer who ordered a ham sandwich wants more coffee. Synecdoche is a form of metonymy in which the related object is a part of the subject, as in The beard wants more coffee.

Metaphor: Implicating that something has certain attributes A by using a noncomparative sentence S without meaning S, where the speaker assumes either (i) that having A would make it similar in some respects to how it typically would be if it were as described in S, or (ii) that being as in S would make it similar in some respects to how it typically would be if it had A.

Steve might respond to Sue in (4) by saying John is in the penalty box. If this is either a truthful statement or a lie, Steve means what he said and thereby implies that John cannot play; no figure of speech is involved. Steve is assuming that being in the penalty box implies that John cannot play. If this is a metaphor, Steve also implicates that John cannot play but without meaning that he is in the penalty box. Steve is assuming that being unable to play would make John similar to the way he would be if he were in the penalty box. Steve is likening John to, and thinking of him as, someone in a penalty box. By saying John has a temperature, Steve might mean metaphorically that John is angry. Then Steve is likening John to, and thinking of him as, someone with a temperature. But his assumption is reversed: that being angry would make John similar to the way he typically would be if he had a temperature.6

Simile is the same as metaphor except that it is conveyed by using a comparative sentence, one containing like or as. The world is like a stage (simile) has the same implicature as The world is a stage (metaphor) and is only slightly less figurative. The speaker does not mean that the world is similar to a stage (which is a claim about overall similarity), only that the world has certain attributes (which, it is assumed, are respects in which it is similar to a stage). Simile resembles hyperbole in that to be alike, the things compared have to have much more in common than just the implicated respects of similarity. But being alike and being alike in certain respects do not themselves differ in degree.

The formulations above characterize simple figures. There are also complex figures. Ironic metaphor involves implicating that something has the contrary of A, to make light of or mock it, where the speaker assumes A to be related to S as in simple metaphor. If Steve says thus of someone totally unattractive, Bertha is the sun, he does not mean that Bertha is not that star, although he expresses that thought. What he means is that Bertha lacks the properties Romeo ascribed to Juliet in Shakespeare’s metaphor. Other complex figures, like meiotic metonymy, can be characterized similarly.

One figure of speech has been identified only recently, principally through the work of Horn (1985; 1989).7

Irregular Negation: Implicating that what is described by S is not good (or bad) by saying without meaning –S.

The exemplar is The glass isn’t half full, it’s half empty, but this has become an idiom applied not just to glasses. A live example is The performance was not somewhat flawed, it was nearly flawless. In a typical use, this is obviously false taken literally. But what the speaker is trying to convey is that the negative evaluation generally implicated by saying It is somewhat flawed rather than It is nearly flawless is mistaken. Irregular negations resemble irony in being marked intonationally. There are many other forms of irregular negation, but I believe they too have become idioms (Davis 2010; 2011; 2013).

In figurative speech, speakers generally do not mean (cognitively) what they said, and expect their audience to recognize that. (The exception is litotes.) Indeed, a typical clue that speech is figurative is the obvious falsity of what is said. When what is said is not meant, what is implicated is not implied. If Lovely weather is ironic, we are implicating but not implying that the weather is awful.

3.2 Modes of Speech

I use the term modes of speech for general forms of implicature that have become widely recognized only since Grice (1975). Like irregular negations, they are not taught in school as elements of style, and names for most are not in the lexicon of typical speakers. Nevertheless, they are as frequent and natural as figurative speech. They are not marked intonationally, and the speech is literal. Speakers do not intend what they say to be obviously false and, with one exception, do mean (cognitively) what they say.

Relevance Implicature: Implicating an answer to an expressed or implied question by stating something related to the answer by implication or explanation.

Example (4) is a relevance implicature. What Steve implicated (John cannot play) is information Sue requested, and is explained and possibly implied by what Steve said (John has a temperature). In Grice’s (1975: 32) petrol example, A said I am out of petrol, and B replied There is a garage around the corner. What B implicated (You can get petrol at the garage around the corner) implies what B said (There is a garage around the corner), and answers the question B implied (Where can I get petrol?). As with metaphor, the precise characterization of relevance implicature is unsettled, but clear examples are easy to recognize.

The petrol example is also a strengthening implicature.

Strengthening Implicature: Implicating a stronger proposition S+ when not litotes.

If Jack and Mary recently got married, and I tell you that they went to Hawaii, I would most naturally implicate that they went together. This would not be a relevance implicature unless I were answering the question, “Did they do anything together?” Litotes also involves implicating a stronger proposition, but is distinguished by form (negation), purpose (to deemphasize the magnitude of something), and its figurative character.

Limiting implicatures involve implicating the denial of a stronger proposition.8

Limiting Implicature: Implicating the denial of S+.

Suppose a teacher is asked whether everyone got an A. She might naturally implicate Not everyone got an A (–S+) by saying Some did (S). This is an implicature because the teacher did not say that not everyone got an A, and so could consistently have added Indeed, everyone did. This limiting implicature would be most natural if it were evident that the teacher had graded all the exams already. If that is not evident, the teacher might have implicated I do not know whether everyone got an A.

Ignorance Implicature: Implicating that one does not know whether S+ is true.

The ignorance implicature is not a relevance implicature because it neither implies nor is implied by either answer to the question Did everyone get an A? A proposition entailed by the ignorance implicature is a limiting implicature: I do not know that everyone got an A. But the ignorance implicature is not itself a limiting implicature. The proposition implicated is a denial, but what it denies (I know whether everyone got an A) does not entail the proposition asserted (Some got an A).

A form of implicature similar to relevance and limiting implicatures would be typical if A asks Did you get Hillary Clinton’s autograph? and B answers I got Bill’s. Then B implicated that he did not get Hillary’s autograph. This response would be natural in a context where getting Bill Clinton’s autograph is considered close to getting Hillary’s because of their personal relationship and public offices.

Close-But Implicature: Implicating a negative answer to a question by affirming something close to a positive answer in contextually salient respects.

Unlike a limiting implicature, the close-but implicature is not the denial of a proposition S+ entailing what is said. And unlike a relevance implicature, what is said is not related by implication or explanation to the answer implicated.

One mode of implicature with a common name is:

Damning with Faint Praise: Implicating that more laudatory claims are not true by affirming something not very laudatory, when not meiosis.

A famous example is Grice’s (1975: 33) letter of recommendation, containing little more than Mr. X’s English is excellent. If the recommendation was for a position in philosophy, the writer would be implying that Mr. X is not suitable. Damning with faint praise differs from limiting implicature in that what is implicated is not the denial of a proposition entailing what is said. It is like a relevance implicature in that the implicature is that nothing close to a positive answer to the question under consideration is true. It differs from meiosis in purpose.

A mode of speech similar in some respects to overstatement is loose use.

Loose use: Implicating that S is close enough to being true for current purposes without meaning (exactly) S or –S.

When I utter The train arrived at 3:00, I rarely if ever mean exactly what I said, which entails that the train did not arrive before or after 3:00. I am not lying if I know the train arrived a millisecond later. What I typically mean is that the arrival time was approximately 3:00—close enough to 3:00 for current purposes. What is close enough will vary depending on whether we want to know whether a passenger arrived in time for a 4:00 meeting or whether a report that it arrived at 3:02 was accurate to within a minute. Loose use seems similar to hyperbole because what is said is stronger than what is implicated. But approximation is not exaggeration. The proposition implicated in loose use does not ascribe a lesser quantity and is fully compatible with what is said. Hyperbole is typically conveyed in a special tone of voice and is used for effect. Neither is true of loose use. Loose use differs from figurative speech generally in that the speaker will typically not believe S to be strictly speaking false, or intend it to be obviously false.

There are also complex modes of speech. Jack and Mary arrived at 3:00 might be used to mean that they arrived together at approximately 3:00. Then what is implicated is that a proposition stronger than S is close enough to being true—loose use applied to a strengthening. A proud mother might say Johnny got some of the problems right to mean that he got all of them right—meiosis applied to a limiting implicature—to deemphasize how well he did.

Modes of speech differ from figures in not being used to make speech or writing lively. They appear in the driest reports.

3.3 Conventionality

Like lexical and syntactic conventions, the figures and modes of speech are customary ways of both using and understanding language. Given how pervasive they are in both conversation and literature, knowledge of them is an essential component of our linguistic competence. Without that knowledge, we cannot fully understand speech or the speakers who produce it. We cannot be fully fluent and natural speakers. Speakers who did not use any of the figures or modes of speech would be alien and robotic. Knowledge of the general forms of implicature and other forms of indirect speech is acquired along with knowledge of the semantics and syntax of our native language, including the vocabulary of speech acts (say, assert, warn, ask, order, etc.). Speakers learning English must learn not only that NP is VP differs in meaning from NP is not VP, but also that it can be used to mean what NP is not VP means. They must learn that Some S is P does not mean Not all S is P but can be used to mean what Not all S is P does. Studies have shown comprehension and production as early as age three for metaphor, four for limiting implicature, and six for irony.9

Speakers pick up figures and modes of speech from other speakers, as they learn vocabulary and grammar. Many speakers are taught figures of speech in school, just as they are taught vocabulary and elements of grammar, but not modes of speech. Knowledge of both figures and modes is as tacit as our knowledge of syntax and semantics. It is not knowledge of facts that define a language, but of how a language is used and understood. Since the figures and modes are not dependent on any particular language, they can be used with all languages. Whether they are true linguistic universals is an open question. Another is whether the speakers of any languages have customary forms of implicature that English speakers lack.

It is evident that the figures and modes of speech are common, socially useful practices that are self-perpetuating. They perpetuate themselves through precedent following, social acceptance, individual habit and association, and traditional transmission from one generation of speakers to another. Precedent operates when hearers call on their knowledge of the forms speakers commonly use to interpret speakers in new contexts, and when speakers rely on that knowledge when they use the forms and expect to be understood. The forms are less arbitrary than lexical or semantic conventions, but there are alternatives. No one has to implicate rather than say things, or use the implicatures we have identified rather than others. Alternative forms of implicature are possible and could well have become common. For example, Some S are P could have been used to implicate I know whether all S are P (“knowledge implicature”) or God is to be praised that some S are P (“Praise implicature”). So the general forms of implicature are conventions10—pragmatic conventions that complement the semantic and syntactic conventions defining particular languages. Since the forms are ways a sentence can be used to mean things it is not commonly used to mean, they are conventional ways of being unconventional.

4. Sentence Implicature

We distinguished sentence meaning from speaker meaning in section 1. Imply and implicate also have senses in which they apply to sentences. All semantic implicatures are sentence implicatures. Washington, a Virginian, was the first president implicates that Washington was a Virginian. The implicature is carried by the appositive construction. The implicature of p but q is carried by the meaning of but. As a first approximation, a sentence has an implicature when speakers conventionally use sentences of that form with the corresponding implicature.11

Most of the conversational implicatures we have examined are not sentence implicatures. John has a temperature does not itself imply or implicate that John’s temperature is below normal (irony), or that John cannot play (relevance implicature). It is conventional to use sentences in general with all of the figures and modes of speech. But sentences with the particular form N has a temperature are not customarily used ironically, nor to implicate that N cannot play. Neither the particular words in the sentence, nor the way they are composed, carries the implicatures.

Our illustrative limiting implicature is markedly different. It is what Grice (1975: 37–38) called a generalized conversational implicature. The use of sentences of the form Some S are P to implicate that not all S are P is common in a wide range of contexts. The implicature is carried by some and the form of the sentence. As a result, Some students got an A itself implicates Not all students got an A. In particular contexts, sentences of this form can be used with other implicatures. Some students got an A can be used to mean that none did (irony), that all did (litotes), or that some students studied hard (relevance implicature). But those implicatures are not associated with a feature of the sentence and are not generally conveyed when the form is used.

This relation between some and all is special. Contrast several. Several S are P is stronger than Some S are P. Consequently speakers could use Some students got an A to implicate that it is not the case that several did. (Imagine the sentence uttered in response to, “Did several students get an A?”) But Some students got an A does not itself implicate that several did not. Sentences of that form are not commonly used to implicate the denial of Several S are P.

4.1 Limiting Implicatures

Many generalized limiting implicatures have been identified. Here is a sample, accompanied by similar examples in which sentences lack such implicatures. I use p ⊐ q to mean that p implicates the proposition expressed by q, and p Implicature q for its negation. In some cases Not abbreviates It is not the case that.

  1. (6) Some S are P ⊐ Not all S are P

    Some S are PNot many S are P

    Not all S are PSome (not no) S are P

    A believes pA does not know p

    A entered a houseA didn’t enter his house

    x is a rectanglex is not equilateral

    x is warmx is not hot

    x may VPNot x must VP

    p or qI do not know whether p or q

  2. (7) Some S are P Implicature Not several S are P

    Some S are P Implicature Not half the S are P

    Not all S are P Implicature Not many S are not P

    A believes p Implicature A does not regret p

    A lost a book Implicature A did not lose his book

    x is a triangle Implicature x is not equilateral

    x is warm Implicature x is not lukewarm

    x may VP Implicature x will not V

    p or q Implicature I do not know that p or q

The first two examples illustrate a property of sentence implicatures that speaker implicatures lack: differences in strength. Some implicates not all more strongly than not many, presumably because some is used more commonly with the former than the latter. Other things equal, stronger implicatures can be inferred with greater probability. The relationships can be represented conveniently by the Horn (1989) scale 〈all, many, some〉, wherein the terms are ranked by entailment, with the strongest first. The higher in the scale, the more strongly the negation is implicated.

4.2 Strengthening Implicatures

A sample is presented in (8), along with contrasting cases in (9).

  1. (8) N took off his clothes and went to bed ⊐ N took off his clothes and then went to bed

    N turned the key and the car startedN turned the key and as a result the car started

    N studied and listened to musicN studied while listening to music

    N will obey or sufferN will obey or else suffer

    N went to Myanmar or BurmaN went to Myanmar or equivalently Burma

    N will swim if it is warm ⊐ N will swim if and only if it is warm

    N and M pushed the carN and M pushed the car together

    N entered a houseN entered someone else’s house

    N lost a bookN lost his own book

    N was able to solve the problemN did solve the problem

    N stopped the carN stopped the car in the usual way

    N made the car stopN stopped the car in an unusual way

    War is warIt is the nature of war that bad things happen

  2. (9) N saw Mary and Jane Implicature N saw Mary and then Jane

    N will turn left or right Implicature N will turn left or equivalently right

    N and M pushed the car Implicature N and M pushed the car separately

    N entered a house Implicature N entered his own house

    N could have solved the problem Implicature N did solve the problem

    N stopped the car Implicature N stopped the car in an unusual way

    Every war is a war Implicature It is the nature of war that bad things happen.

Strengthening implicatures are more content dependent than limiting implicatures. Each case in (8) represents a large and open class of examples. But the implicature may be blocked by different content. For example, N took off his clothes and got into bed does not implicate “N took off his clothes and as a result got into bed,” or “while getting into bed.” The general form p and q does not implicate p and as a result q, but the more specific form N turned the key and the car started does. A generalized implicature is blocked if background knowledge makes it something speakers are generally unlikely to implicate. When background knowledge permits, a sentence may have more than one strengthening implicature. Thus N will visit France or Germany implicates “N will visit France or else Germany” and “I do not know whether N will visit France or Germany” with equal strength.

4.3 Ignorance Implicatures

Many sentences with limiting implicatures have a second implicature that is never intended on the same occasion.

  1. (10) Some S are P ⊐ The speaker does not know whether all S are P

    At least n S are PThe speaker does not know whether more than n S are P.

    It is likely that pThe speaker doesn’t know whether it is certain/true that p

  2. (11) x is warm Implicature The speaker does not know whether x is hot

    x is equilateral Implicature The speaker does not know whether x is square

    x may VP Implicature The speaker does not know whether x must VP

4.4 Common Metaphors

Another category of sentence implicature is more ephemeral. Metaphors have a typical evolution: beginning as something a speaker means on a particular occasion; being picked up by others; catching on, which means becoming self-perpetuating and spreading through the population; and, finally, dying and becoming a new lexical meaning or idiom. When dead, what used to be indirectly expressed is directly expressed. The term virus as applied to computers went through this evolution in the last thirty years. The deadest of metaphors are used with no recognition of the meaning from which they arose. Most English speakers are unaware that cut and run began as a nautical term for cutting the anchor cable in order to run from danger as quickly as possible. At the stage when metaphors are widespread and self-perpetuating, they generate generalized conversational implicatures. One metaphor still at this stage, I believe, is ground zero.

  1. (12) The Lehman collapse was ground zero in the 2008 recessionIt was the initial point from which much damage spread.

The synonyms surface zero and hypocenter have no such use.

4.5 Common Litotes

Litotes is a form of understatement in which the speaker implies that something has a property by denying that it has a contrary property, and does so in order to emphasize how great it is in that respect. Thus when sampling some of the soup, Bill might say, “It is not cold,” when what he means is that it is hot. While litotes is a conventional form of implicature, most examples are not sentence implicatures, as this one illustrates. The use of x is not cold to mean x is hot is not a convention. But some litotes have become conventional. Thus a guest might praise the host’s cooking by saying That’s not bad, and a doctor might express concern about a symptom by saying That’s not good. The use of x is not bad to mean x is good, and the use of x is not good to mean x is bad, are conventions. So these forms generate sentence implicatures. There are a number of common litotes.

4.6 Embedded Implicatures

When a sentence with a limiting, strengthening, or metaphorical implicature I is embedded in a compound sentence, the compound often implicates a proposition with I as a component.

  1. (13) If they had a child and got married (α), the Church would disapprove (β) ⊐ If they had a child and then got married (αʹ), the Church would disapprove (β).

  2. (14) If some of the stolen art has been found already, the rest will be found ⊐ If some but not all of the stolen art has been found already, the rest will be found.

  3. (15) If Mickey ate some of his dinner, he cannot have dessert Implicature If Mickey did not eat all his dinner, he cannot have dessert.

  4. (16) If rain is likely, the ceremony will be indoors Implicature If the speaker does not know whether rain is certain, the ceremony will be indoors.

In (13), the conditional If α, β implicates If αʹ, β because the antecedent α implicates αʹ. The implicature of the antecedent is not an implicature of the whole conditional, so it is not projected in the manner of presuppositions. Sentence implicatures can embed in other compounds too. Consider They had a baby and got married, and the Church disapproved, and recall the irregular negation in section 3. As (16) illustrates, ignorance implicatures do not seem to embed. And (15) illustrates that not all strengthening or limiting implicatures embed.

Embedded implicatures have led some to think that the strengthening implicature of and must be more than an implicature (Carston 2004: 646–647) and others to postulate “pragmatic intrusion” into what is said (Levinson 2000: 213–217). But α is true as long as they both had a baby and got married, regardless of order. So while the speaker uttering “If α, β” means something true, what the speaker says (in the strict sense in which it is opposed to implicature) is too strong.

4.7 Conventionality

Semantic implicatures are part of the primary semantic and syntactic conventions, while generalized conversational implicatures are secondary conventions layered on top of them. The positive and negative examples discussed earlier show that generalized conversational implicatures display the arbitrariness characteristic of linguistic conventions. There is no particular reason for some to implicate not all and not many, but not not half or not several. Nothing about the form of ground zero favored it over surface zero to implicate the initial point from which damage spread. There are cross-linguistic differences too. While Horn’s (1989) research indicates that the some implicatures can be found in all languages, Brown & Levinson (1978) and Wierzbicka (1987) show that tautology implicatures are highly variable. In French, C’est la guerre rather than La guerre est la guerre implicates what War is war does in English. In Polish, Co N to N (“What is N is N”) implicates that there is something uniquely good about N, while in Tamil, Amerikka Amerikkataan (“America is exactly America”) implicates disapproval of things American. Sentence implicatures differ from lexical and syntactic conventions in not being completely arbitrary. In the case of common metaphors, there is a perceived similarity between the implicature and the meaning. In the other cases, what a sentence implicates bears a simple logical relationship to what the sentence means, such as being a stronger statement in the case of strengthening implicatures.

While figures and modes of speech are ways of using any sentence to implicate, sentence implicatures are facts about particular sentences or sentence forms. English differs from Polish, French, and Tamil in its tautology implicatures. English today has different metaphorical implicatures than it had just a few years ago. A complete description of a language must include its sentence implicatures.

Knowledge of generalized conversational implicatures is also a critical component of the linguistic competence of speakers and hearers. Speakers who are unaware of them are likely to mislead their audience. Imagine the possibilities if an oblivious speaker said Your husband saw a woman to the subject’s wife. Speakers who have not mastered sentence implicatures may either fail to communicate or be viewed as ignorant. Imagine an immigrant who says Every child is a child instead of Children will be children. Unknowing speakers may feel compelled to say what could safely go unsaid, making their speech long-winded. Hearers (and natural language processors) without such knowledge are likely to either misinterpret or fail to fully understand the speaker. Sentence implicatures, both semantic and conversational, resemble idioms and the customary forms of speaker implicature in being picked up by native speakers from other speakers in the course of learning the language. Sentence implicatures thus perpetuate themselves from one generation to the next. Recent metaphors are special in being picked up by adults and are liable to become idioms if they pass on to new generations.

Levinson (2000: Ch. 1) proposed that generalized conversational implicatures are default inferences or interpretations in the following sense: if I is an implicature of σ, then from the fact that a speaker used σ literally, we can infer that the speaker implicated I in the absence of evidence to the contrary; the inference is defeasible but probable. This characterization is plausible for many sentence implicatures. But not generalized metaphors: a literal interpretation would be the default if any were. Nor for sentences with multiple implicatures (Bezuidenhout 2002: 269–270). Some members are juniors has at least three implicatures (Not all members are juniors, Not many members are juniors, and It is unknown whether all members are juniors); none of them is a default interpretation. We have to have information about the specific context of utterance to infer what the speaker meant. Ambiguity similarly prevents defining word meanings as default speaker meanings.

5 Explaining Implicature

One of the fundamental goals of human inquiry is to explain why things occur. There are a number of questions to answer about implicature.

5.1 Why Do Speakers Implicate Things?

The primary reasons speakers implicate things are the primary reasons they say things, including communication, self-expression, and record creation. Speakers seek to communicate for a variety of reasons, from working with colleagues to achieve joint ends in situations of cooperation, to working against adversaries in situations of opposition, including competition and conflict. Whether speakers express beliefs directly or indirectly, others often recognize what they mean, resulting in communication. Implicature can thus assist in helping others (by conveying information or misinformation beneficial to them) or in opposing others (by conveying information or misinformation detrimental to them).

People sometimes speak simply to express themselves, however, with no interest in communication. And much writing is motivated by the desire to create a record, both for others to learn from and for insurance against memory failure. People can express their beliefs and record them via either saying or implicating.

5.2 Why Do Speakers Implicate Rather Than Say Things?

In many cases, the answer to even this question reveals nothing special about implicature. For like human action and speech in general, much implicature is done out of habit, and a lot is spontaneous. Most speakers develop a habit of using a particular name to refer to their friends when other names or descriptions are available—Jack as opposed to John or Prof. Smith, for example. They may do so on occasion purely out of habit, when another name would have been more appropriate. Sometimes a speaker will use another name spontaneously, for no particular reason. In a similar way, a writer’s style is in large part a distinctive pattern of using figures and modes of speech by habit or spontaneously. Some speakers tend to hyperbole, others to understatement. Some overuse irony, others metaphor. Some are more given to answering obliquely than others. Other elements of style are similarly matters of habit and spontaneity, such as the use of passive or active constructions, emphasis and exclamation, and words with Latin rather than Anglo-Saxon roots.

5.3 What Goals Are Served by Speakers’ Implicating Rather Than Saying Things?

This question finally gets at what is distinctive about implicature. The answers are remarkably various.

5.3.1 Verbal Efficiency

Levinson (2000: 28–31) argued that the relatively slow rate at which syllables can be produced in speech or writing creates a bottleneck in the communication process given that thought and comprehension are much faster. One way to overcome this is to convey more thoughts by uttering a sentence than the sentence itself expresses—which is precisely what we do when we engage in implicature. When Steve said John has a temperature and implicated He can’t play, he expressed the same thoughts as if he said John has a temperature and so cannot play. But the direct mode of expression takes twice the words and time. The hearer can make two inferences in the time it takes the speaker to utter just one clause.

5.3.2 Misleading without Lying

People often wish others to believe things that are false. This is often true in conflict and competition, but also occasionally in a cooperative setting. Most people, furthermore, believe it is better to mislead others than to lie. That belief provides a common and often powerful motive to implicate rather than say falsehoods.

Deniability is another motivation. If others accept the beliefs we express, and act on them to their detriment, it is often easier for us to deny responsibility for the harm if we have implicated rather than said what is false. For example, if a man we wish to harm asks whether a bridge is safe to cross, and we think the last person to cross fatally weakened the structure, we might truthfully tell him I’m not sure, but people have been crossing all day. If the man is misled into crossing, and the bridge collapses, we may escape blame by convincing people that we did not intend to convey what he unfortunately inferred.

5.3.3 Veiling

When their interests may be opposed, speakers are often willing to issue bribes or threats to motivate officials to act the way they want. But bribing or threatening officials is illegal and subject to serious consequences. This provides a motive to implicate rather than say that one will pay if the official does what you want, or punish if the official does not. For it may be harder to prove that one meant something if one did not say it. Pinker (2007) applies game theory to the driver pulled over for speeding who says I would very much like to take care of this now if I could, implying that he is willing to pay the officer to let him go without a ticket. The driver may hope that an honest police officer will do nothing because the remark could be innocent and bribery would be hard to prove, and that a dishonest police officer will take up the implied offer to their mutual gain.

Implicature can be used to veil anything we prefer not to acknowledge overtly, even when it is not plausibly deniable. Pinker analyzes You could come up for a drink if you like. The speaker prefers to imply that he wants sex rather than to state it baldly. If the date is uninterested, she can politely decline.

5.3.4 Good Social Relations

Brown & Levinson (1978), Leech (1983: Ch. 4), and Pinker (2007) note many ways implicature (and indirect speech generally) helps us to maintain expected or desired social relationships by being polite, tactful, respectful, modest, sympathetic, and deferential. An undefeated athlete might modestly say I have won some matches when asked how good he is. The date can minimize embarrassment by saying I have to get up early and implicating I do not want to. These speakers need not be attempting to mislead. The date may perform a face-saving act even if she expects the man to infer she is uninterested. The parties are cooperating, but the dominant interest is good relations rather than information.

5.3.5 Style and Entertainment

Stating the facts literally and precisely can be dry, tedious, pedantic, and boring. A good figure of speech can liven things up, and loose use loosen things up, resulting in more accessible and entertaining prose. Metaphors are engaging when the hearer has to think creatively to figure out what attributes the speaker meant to convey. It can also be amusing and illuminating to think of something as something it is not (Lepore & Stone 2010). Consider Heinlein’s Butterflies are self-propelled flowers. Figurative speech is a form of word play. It is also literary color, used for aesthetic purposes.

5.4 Why Are Certain Figures and Modes of Speech Common and Not Others?

Section 3 identified conventional forms of conversational implicature, from irony to loose use. Other forms are possible, but uncommon. Why isn’t Some S are P used to implicate I know whether all S are P rather than its negation? A “knowledge implicature” would also serve the purposes of communication, verbal efficiency, and so on.

Word meanings pose the same question. Plane is commonly used by English speakers to mean airplane and wood plane, but not hydrofoil. Why? Because they know plane means airplane and wood plane in English but not hydrofoil. Why is that? The obvious answer is that English speakers commonly use plane with the first two meanings but not the third. The same answer can be given for implicature: people use the limiting and ignorance implicatures because they know people commonly use them. Hence speakers have some reason to expect others will understand them. Speakers do not use the knowledge implicature because they know it is not commonly used and so is unlikely to be understood, unless of course something in a particular context signals it.

These explanations may seem circular. But in both cases the circularity is merely apparent because the common practices are conventions. Individual English speakers today use plane to mean airplane and wood plane because of the way conventions perpetuate themselves, spreading from speaker to speaker diachronically. Competent speakers today learned that the word is used with these meanings from speakers who were already competent. The knowledge that others have used the words with these meanings provides a reason to use them the same way. Individual usage and interpretation becomes habitual in time. Using plane to mean hydrofoil would be penalized by incomprehension, disapproval, or derision. To answer the further question of how it became conventional to use plane in certain ways and not others, we follow the chain of usage and transmission back to the first uses of plane by individuals to mean airplane and wood plane, uses that were necessarily unconventional at the time. Explaining how the figures and modes of speech became conventional would similarly require tracing their uses back through history. But in this case, the chain goes back to the beginning of written language, before which evidence of usage does not exist. So we may never be able to answer the diachronic question as we can for word meanings.

We will review alternative explanations of why certain implicatures are found and not others in section 6.

5.5 Why Do Sentences Have Implicatures?

Synchronically, a sentence implicates something in virtue of a convention to use a sentence with that form to implicate it (section 4). Diachronically, the convention exists today because the use was picked up by today’s speakers from previous speakers. Sentences could be used to implicate other things, but either no one has done so or the usage never caught on. Sentence implicatures die and become new lexical meanings or idioms when speakers begin meaning directly what speakers used to mean indirectly.

We identified four kinds of simple sentence implicature: limiting implicatures, strengthening implicatures, ignorance implicatures, and common metaphors. These correspond to modes and figures of speech identified in section 3. Presumably, the generalized limiting, strengthening, and ignorance implicatures originated the way common metaphors do: as particularized implicatures that caught on and spread. Sentence forms lacking these forms of implicature either were never so used or the usage never caught on. The same story is plausible for embedded implicatures.

5.6 Why Are There No Other Kinds of Sentence Implicatures?

Why have only five of the more than twelve forms of speech identified in section 3 generated sentence implicatures? There appear to be two types of answers.

5.6.1 Generality

Any sentence can be used ironically. Consequently the ironic use of The weather is lovely to mean that the weather is awful does not depend on any of its distinctive features. Speakers do not use sentences with the specific form x is lovely to mean x is awful because others have specifically used sentences of that form with that implicature or because they have a habit of doing so. They do it because it is conventional to use a sentence ironically to implicate a contrary of what it expresses. So the use of x is lovely to mean x is awful is not itself a convention. It does not perpetuate itself the way conventions do. A similar explanation seems to work for loose use.

5.6.2 Contextual Variability

A very different reason seems to account for why there are no generalized close-but implicatures: they depend on closeness scales that vary from context to context. Similar explanations seem to work for relevance implicature and damning with faint praise.

That there are common litotes and metaphors suggests that generality and contextual variability are just contributing factors and leads to the hunch that there may be some conventional forms of meiosis, overstatement, and metonymy.

6. Traditional Pragmatic Principle Theories

6.1 Grice’s Theory

In addition to defining and classifying implicatures, Grice (1975) developed an influential theory. The central tenet is that conversational implicatures can be derived from general conversational principles grounded in practical rationality.

Cooperative Principle (CP): Contribute what is required by the accepted purpose of the conversation.

Quality Maxim: Make your contribution true.

Quantity Maxim: Be as informative as required.

Relation Maxim: Be relevant.

Manner Maxim: Be perspicuous.

Grice held that any conversational implicature could be derived from the assumption that the speaker was observing CP (and the maxims) together with what the speaker said, features of the utterance context, and background knowledge shared by participants. Limiting implicatures are thought to be derivable from Quantity. Here is a typical derivation:

The speaker has said Someone got an A; if S was in a position to make the stronger statement Everyone got an A but did not, then he would be in breach of the maxim of Quantity. Since I the addressee assume that S is cooperating, and therefore will not violate the maxim of Quantity without warning, I take it that S wishes to convey that he is not in a position to make the stronger statement, and indeed knows that it does not hold.

(Adapted from Levinson 1983: 134–135)

Gricean derivations are unsound, therefore, when speakers are not observing the maxims because they are in situations of opposition rather than cooperation, or when they are more interested in being polite. Speakers are frequently motivated to lie and mislead their audience, or to withhold vital information. Speakers also fail to completely observe Quality and Manner when speaking figuratively.

Gricean derivations are also invalid. They can be used to predict the same implicatures where we do not observe them. If Levinson’s derivation were valid, then Some S are P should never be used with an ignorance rather than a limiting implicature, with an ironic or other figurative implicature, or with no implicature at all. His derivation assumes without warrant that the speaker knows whether or not Everyone got an A is true, and that the accepted purpose of the conversation requires the speaker to state rather than implicate what he knows. The invalidity of the derivation becomes stark when it is applied mutatis mutandis to cases in which the speaker implicates that he does not know whether all students got an A, or to the petrol example.

The speaker has said There is a garage around the corner; if S was in a position to make the stronger statement You can get petrol at the station around the corner but did not then he would be in breach of the maxim of Quantity. Since I the addressee assume that S is cooperating, and therefore will not violate the maxim of Quantity without warning, I take it that S wishes to convey that he is not in a position to make the stronger statement, and indeed, knows that it does not hold.

The conclusion of this derivation is that S implicated the opposite of his actual relevance implicature. Since there is no more basis for the derivation in one case than the other, it is just invalid. For the same reason, nothing in the Gricean principles enables us to explain why S believes p is generally used to implicate S does not know p but not S does not regret p, or why N stopped the car has the strengthening implicature N stopped the car in the usual way rather than the limiting implicature N did not stop the car in the usual way. If conversational implicatures could be derived from what is said and rationality, sentence implicatures could not be arbitrary to the extent they are.

Grice viewed figurative speech as conforming to CP despite “flouting” Quality. Here is his “gloss” for irony.

X, with whom A has been on close terms until now, has betrayed a secret of A’s to a business rival. A and his audience both know this. A says X is a fine friend. (Gloss: It is perfectly obvious to A and his audience that what A has said or has made as if to say is something he does not believe, and the audience knows that A knows that is obvious to the audience. So, unless A’s utterance is entirely pointless, A must be trying to get across some other proposition than the one he purports to be putting forward. This must be some obviously related proposition; the most obviously related proposition is the contradictory of the one he purports to be putting forward.)

(Grice 1975: 34)

One problem is that irony is possible even when A believes X is a fine but imperfect friend, and is conveying displeasure about one imperfection. Alternatively, A could just be lying. (Think of all the battered women who insist that their husbands never hit them.) And assuming A is trying to implicate something true, there are many other options, including X is not a perfect friend (limiting implicature), X must have had a powerful reason for what he did (relevance implicature), and X is a fine friend with a weakness (strengthening implicature). Finally, if A is being ironic, he is violating Manner. It is not perspicuous to mean the opposite of what you say—or to implicate anything rather than saying it.

Since Gricean derivations take what the speaker said as given, they are incapable of explaining why the speaker implicated the required information rather than just saying it. None of the principles reviewed in this section sheds light on this question.

6.2 Neo-Gricean Theory

Horn (1989: 194; 2004: 13) replaces Quantity, Relevance, and Manner with two principles.12

Q: Say as much as you can (given both Quality and R).

R: Say no more than you must (given Q).

Horn believes that strengthening implications like (17)(a) are derivable from R. The idea is that A did not need to say that he lost his own book because that is typical. Implicature (18)(b) is similarly attributed to Q. The idea is that since B did not say he entered his own house, he must not have been in a position to say that, and therefore meant that he did not.

  1. (17) A: He lost a book.

    1. (a) He lost a book of his own.

    2. (b) ✗He did not lose a book of his own.

  2. (18) B: He entered a house.

    1. (a) ✗He entered his own house.

    2. (b) He did not enter his own house.

These explanations are also spurious. We could just as well reason that since A did not say more, he must have meant (17)(b), and that B must have meant (18)(a) since that is the typical situation.

Levinson (2000: 156–157) sought to eliminate such conflicting predictions by postulating that the Q-principle takes priority over other principles. But then there should be no strengthening implicatures. Horn (2004: 14–16) intended the parenthetical cross-references on his principles to eliminate clashes. He says that each principle “constrains” the other. This seems to mean that A was not required to say that he lost a book of his own because of R, and that B had to say more than that he entered a house because of Q. But in fact the parenthetical cross-references prevent any predictions. You cannot tell what Q predicts before knowing what R predicts, and vice versa. From both R and Q, it is impossible to predict what A or B implicated. Without the parenthetical clauses, on the other hand, Horn’s principles cannot both be satisfied. B did not say as much as he can because he could have said He entered a house other than his own rather than implicating it. If B had said that, then he said more than he needed to. For he could have implicated it.

Horn’s (2004: 15) discussion of “The role of relevance and clarity in constraining the informative strength of the Q principle” makes more sense. The idea here is that we are not required to say things that are irrelevant or unclear. But while these are implications of Grice’s maxims, they are not implications of Horn’s R. Replacing given both Quality and R in Horn’s Q with given Quality, Relation, and Manner will not eliminate the clash either. (17)(b) is no less relevant or clear than (17)(a), and the same goes for (18)(a) compared to (18)(b).

Another way Horn (1989: 343–345) attempted to address the “mystery” of why similar or synonymous forms may have very different implicatures was by labeling them “short circuited implicatures,” which “are in principle calculable (as are all conversational implicatures by definition) but are not in fact calculated by speakers operating with the relevant usage conventions.” However, because the implicatures are conventional, they are not calculable, even in principle. What connects sentence implicatures to sentences are the conventions.

6.3 Relevance Theory

Sperber & Wilson (1986) replace Grice’s maxims with a single principle. There are a number of variations, but we will take the following to be representative.

Principle of Maximal Relevance (Communicative Efficiency): Contribute that which has the maximum ratio of contextual effects to processing cost.13

A “contextual effect” is roughly an addition to the representation of the world already given in the context. A significant problem is that we have no way of measuring either term of this ratio, so few predictions can be rigorously derived about what is implicated. If we rely on intuitive cost/benefit analysis, the propositions that are implicated in (17) and (18) seem no better than those that are not. The principle also provides no reason to think that You can get gas at the station around the corner is implicated rather than its negation, and conflicts with other goals of speech.

6.4 Teleological or Functional Explanations

The pragmatic principles just reviewed are imperatives. This is a natural way to state norms we should obey or goals we seek to achieve. It is not the way scientific generalizations that explain or predict behavior are formulated. Consequently, Gricean derivations use not CP itself, but the premise that the speaker was observing CP. Grice was attempting a Hempelian (1965: Part IV) nomological explanation of implicatures, in which the covering law is that Speakers are cooperative, contributing what is required by the conversation, making their contribution true, and so on. This generalization is not a law, and what speakers implicate cannot be inferred from it.

The imperatives can play a role in explaining implicature, however, if they are viewed instead as goals—as ends speakers desire and intend to achieve. Speakers do most of the time intend to be cooperative, truthful, informative, relevant, and perspicuous. These desires motivate much of what we say and implicate. Implicature practices are sustained by the fact that the goals are shared interests. In the same way, the collective interest in avoiding collisions sustains the convention of driving on the right (or left), and the desire to communicate sustains the various lexical conventions defining a language. Horn (2004: 14) spoke of Q and R as “antinomic forces,” with the prevailing force determining what is implicated. This language does not apply to scientific generalizations, but does fit human desires. The desire to say as much as possible often conflicts with the desire to say no more than necessary, and which desire prevails determines whether we say or implicate something. The same goes for the desire to be perspicuous versus the desire to be stylish, polite, or brief. So while the pragmatic principles do not explain implicatures the way Gricean, Neo-Gricean, and Relevance theorists intended, they can play a role in teleological or functional explanations of implicatures. A nomological explanation would require discovering and applying a law that predicts what a speaker will do given a description of all her occurrent beliefs and desires.14

6.5 Comprehension

Traditional theories assume that pragmatic principles explain not only the existence of implicatures, but how we understand them.

How is it possible for the speaker to say metaphorically “S is P” and mean “S is R”, when P plainly does not mean R? Furthermore, How is it possible for the hearer who hears the utterance “S is P” to know that the speaker means “S is R”? The short and uninformative answer is that the utterance of P calls to mind the meaning … in the special ways that metaphorical utterances have of calling other things to mind. But that answer is uninformative until we know what are the principles according to which the utterance calls the metaphorical meaning to mind.

(Searle 1979: 103ff)

I believe that … the hearer must go through at least three sets of steps. First, he must have some strategy for determining whether or not he has to seek a metaphorical interpretation of the utterance in the first place. Second, when he has decided to look for a metaphorical interpretation, he must have some set of strategies, or principles, for computing possible values of R, and third, he must have a set of strategies, or principles, for restricting the range of Rs—for deciding which Rs are likely to be the ones the speaker is asserting of S.

(Searle 1979: 104–105)

The faulty assumption to highlight here is that hearers must compute interpretations from principles. We have seen that implicatures are not derivable from conversational principles. Cognitive scientists have found that few cognitive processes are tractably computable from rules governing propositional representations (Horgan & Tienson 1998; Richardson 1998). To see that what Searle assumed “must” be the case need not be, let us ask instead how hearers know what a speaker says. Suppose we hear (19) spoken.

(19) Ford’s slow red rabbit finished the right bank.

Most of us come up with an interpretation instantly and automatically. We do need to infer that it is what the speaker said from what we know of the speaker and the context, and may need to find a more plausible alternative. But we do not rely on a strategy for determining whether English is being used rather than a code, or represent all the possible English interpretations (there are millions15), or select the intended interpretation using rules, even though conversational principles are as applicable to saying as implicating. Given the influence of priming, recency, and frequency, the process that activates interpretations seems associational. But little is known, except that it is a normal result of having learned English (Bock and Garnsey 1998). Searle’s short answer is not as uninformative as he thought: as a result of learning how language is used metaphorically from an early age, sentences used metaphorically call to mind interpretations related to what the sentences mean in the way metaphorical interpretations generally are. The process is normally automatic but may require effort when the metaphor is either inapt or especially creative. We have similar competencies for all the figures and modes of speech.16


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(1.) Grice’s (1957) choice of natural for this sense of meaning was unfortunate because Hobbes (1981 [1655]) and before him Augustine (1952 [397]) distinguished natural from conventional signs, both of which have “natural” meaning in Grice’s sense. Hobbes cited black clouds to illustrate natural signs, human vocal sounds for conventional signs.

(2.) Another kind of speaker meaning, “cogitative,” requires providing an indication that one is thinking a thought but not that one believes it. If Steve is engaging in irony, he means “John has an abnormally high temperature” by the sentence he utters, but does not mean that John has an abnormally high temperature by uttering it. See Schiffer 1972; Davis 2003: section 2.2.

(3.) See also Harnish 1976: 328–329; Levinson 1983: 97; Leech 1983: 9; Neale 1992: 519, 528; Horn 2004: 4; Camp 2006; Huang 2007: 27; Davis 2007. Contrast Sperber & Wilson (1981: 552) and Bach (1994: 126; 2006: 27–28), who give implicature narrower definitions, and Saul (2001: 632–633; 2002), who proposes a more normative definition.

(4.) See Grice 1975: 87ff; Harnish 1976: 332ff; Bach 1994; Levinson 2000: 170ff. Saying also requires meaning cogitatively what the sentence means (see note 1).

(5.) Grice 1975: 25; Levinson 1983: 127; Leech 1983: 11; Neale 1992: 523–529; 2004: 4; Potts 2005; 2007; Huang 2007: section 2.3. Grice’s term conventional is apt but confusing given that conversational implicatures can be conventional in different ways. Bach (2006: section 10) argues that semantic implicature is a myth on the grounds that a speaker using (a) says that Washington, a Virginian, was the first president, which involves more than saying that Washington was the first president. That is true, however, precisely because it also involves meaning without saying (hence implicating) that Washington was a Virginian.

(6.) Note that Steve is unlikely to believe that John would typically be angry if he had a temperature, and that Steve is unlikely to believe that John would typically be in the penalty box if he cannot play. The inequivalence of (i) and (ii) thus accounts for the irreversibility of some metaphors and similes: Blood is money versus Money is blood (Hills 2012: 25). And as Searle (1979: 90–91) observed, Steve may be right about John when he says metaphorically that he has a temperature even if Steve’s assumption about anger is wrong.

(7.) See also Burton-Roberts 1989; Van der Sandt 1991; 2003; Carston 1996; Geurts 1998.

(8.) Limiting implicatures are commonly called “quantity,” “scalar,” or “Q” implicatures, and strengthening implicatures are “R,” “I,” or “M” implicatures. These terms are theoretically loaded (section 6).

(9.) See Gardner et al. 1978; Eson & Shapiro 1982; Becker 1986; Winner 1988; Nippold 1988; Pearson 1990; Pouscoulous et al. 2007; Kennison 2014: 170. Recognition of indirect requests has been found in two year olds (Bates 1976: Ch. VIII).

(10.) See Lewis 1969; Davis 2003: Ch. 9; and Lepore & Stone 2015 for analysis of the applicable sense.

(11.) More explicitly: σ implicates I in language L iff there is a distinctive declarative form F and function f such that it is a convention for speakers of L to use a sentence “p” with form F to mean or imply f(“p”) by saying that p, where σ is an interpreted sentence of L with form F expressing proposition s(“p”) ≠ f(σ).

(12.) See also Horn 1985: 194–197; 1989: 196, 387–392; Meibauer 2006: 563; Huang 2006; 2007: 37–39. Levinson (2000) formulates similar principles but divides R into I (where what is implicated is the normal situation) and M (where what is implicated is abnormal). Bidirectional Optimality Theory (Blutner 2000; Dekker & van Rooy 2000) combines Q, R, and I into a single principle.

(13.) See Sperber & Wilson 1986: 46–51, 118–171; Wilson & Sperber 2004: 609. For other common formulations, see Sperber & Wilson 1995: 260ff; Carston 2002: 45, 379; Wilson & Sperber 2004: 612.

(14.) I explain the limitations of principle theories more fully in Davis 1998. See also Lepore & Stone (2015).

(15.) Using Webster’s Encyclopedic Unabridged Dictionary, I counted at least 6 interpretations for Ford, 14 for slow, 4 for red, 4 for rabbit, 4 for finished, 17 for right, and 14 for bank, which have 2,239,104 combinations.

(16.) I thank Paisley Livingston and Sandy Goldberg for helpful comments.