“Implicature” denotes either (i) the act of meaning orimplying one thing by saying something else, or (ii) the object ofthat act. Implicatures can be determined by sentence meaning or byconversational context, and can be conventional (in different senses)or unconventional. Figures of speech such as metaphor and ironyprovide familiar examples, as do loose use and damning with faintpraise. Implicature serves a variety of goals: communication,maintaining good social relations, misleading without lying, style,and verbal efficiency. Knowledge of common forms of implicature isacquired along with one’s native language.

Conversational implicatures have become one of the principal subjectsof pragmatics. An important conceptual and methodological issue insemantics is how to distinguish senses and entailments fromgeneralized conversational implicatures. A related issue is the degreeto which sentence meaning determines what is said. Historicallinguistics traces the evolution of conversational implicatures intoidioms.

H. P. Grice developed an influential theory to explain and predictconversational implicatures, and describe how they arise and areunderstood. The Cooperative Principle and associated maxims play acentral role. Neo-Gricean theories modify Grice’s principles tosome extent, and Relevance theories replace them with a principle ofcommunicative efficiency. Problems for such principle-based theoriesinclude overgeneration, lack of determinacy, clashes, and the factthat speakers often have other goals. An alternative approachemphasizes that implicatures can be explained and predicted in all theways intentional actions and conventions can be.

• 1. Speaker Implicature
• 2. Conversational and Conventional Implicature
• 3. Sentence Implicature
• 4. Common Forms of Conversational Implicature
• 5. Pragmatics and Semantics
• 6. Gricean Theory
• 7. Theoretical Difficulties
• 8. Overgeneration
• 9. Failures of Determinacy
• 10. Conflicting Principles
• 11. Neo-Gricean Pragmatics
• 12. Relevance Theory
• 13. Explicature and Impliciture
• 14. Speaker Implicature and Intention
• 15. Sentence Implicature and Convention
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Speaker Implicature

H. P. Grice (1913–1988) was the first to systematically studycases in which what aspeaker means differs from what thesentence used by the speaker means. Consider (1).

(1)

Alan: Are you going to Paul’s party?
Barb: I have to work.

If this was a typical exchange, Barbmeant that she is notgoing to Paul’s party bysaying that she has to work.She did not say that she is not going to Paul’s party, and thesentence she uttered does not mean that. Grice introduced thetechnical termsimplicate andimplicature for thecase in which what the speaker said is distinct from what the speakerthereby meant or implied.^[1] Thus Barb implicated that she is not going; that she is not going washer implicature.

In (2), Carla is a dispatcher in Denver, where it is sunny and dry.Don is a truck driver trying to get over the continental divide duringa blizzard.

(2)

Carla: How’s the weather over there?
Don: The weather’s lovely.

Don is using irony. He said that the weather is lovely, but he therebymeant that the weather is terrible. So he implicated that the weatheris terrible. Implicating is anillocutionary speech act,something done in or by saying something (Austin 1962: 98–103).Since it involves meaning one thingby saying something else,it is anindirect speech act, albeit not one that Searle(1975: 265–6) analyzed.^[2]

By “saying”, Grice meant not the mere utterance of words,but sayingthat something is the case, which Austin (1962:94) called alocutionary act. Barb could have said thesame thing by uttering different words. As Grice realized,“say” is used more or less strictly.^[3] Thus if Ed says “The largest planet is a gas giant”, wewill sometimes count him as saying that Jupiter is a gas giant. Wewill follow Grice in using “say” more narrowly, requiringthat what a speaker says be something that the sentence uttered meansor expresses in the context of use. So we will take Ed to haveimplicated that Jupiter is a gas giant by saying that the largestplanet is.Stating orasserting thatpentails both saying and meaning thatp.^[4] When Yogi Berra, famous for his malapropisms, said “Texas has alot of electrical votes”, he said that Texas has a lot ofelectrical votes; but since that was not something he meant, it wasnot something he asserted. Don did not mean what he said for adifferent reason. So he too said but did not assert that the weatheris lovely.

It is not possible to fully understand speakers without knowing whatthey have implicated as well as what they have said. Unless we knowwhat Barb meant by saying that she has to work, we will not know thatshe has answered Alan’s question. Unless Carla knows what Donmeant by saying that the weather is lovely, she might mistakenly inferthat he will arrive on time. The difference between saying andimplicating also affects how we evaluate speakers. If Barb knew shedid not have to work, then she was lying in dialogue(1). If she knew she was going to Paul’s party, she might be guiltyof misleading Alan, but not of lying or making a false statement.^[5] In court, witnesses are typically required to answer questionsdirectly. They cannot avoid perjury by implicating a falsehood ratherthan saying it.

What someone implicates is not given to us directly. We have toinfer it from evidence. We would typically infer in(1) that Barb meant she is not going from what she said, what Alan asked,our assumption that Barb was responding to Alan’s question, andsome background knowledge (e.g., that going to Paul’s partyis not work). An implicature can be characterized as an inference(“something inferred”), but implicating is not itselfinferring. To implicate something is to express a belief in aparticular way. To infer something is to acquire or possess a beliefin a particular way. Hearers have to infer what speakers implicate.But implicatures do notresult from inferences. Furthermore, the fact that implicatures are inferred is not what makesimplicating an indirect speech act. Implicature is indirect because toimplicate something is to mean itby sayingsomethingelse.

Even though it requires an inference, our recognition of what is meantis commonly automatic and effortless, whether it is said orimplicated. In(1), for example, competent speakers will grasp immediately that Barbmeant both that she has to work and that she is not going toPaul’s party.All speech acts have to be inferred fromcontextual evidence, including what was said and what words wereuttered. Whether there is any significant difference in the kind ofinference required to recognize an implicature is a matter of somedebate, and may depend on the type of implicature.^[6] While it is not our focus here, how competent hearers recognize---andlanguage learners acquire the ability to recognize---what a speakerimplicates is the subject of intensive experimentation and theorizingin the field of pragmatics.^[7]

Grice used his technical term “implicature” for a way ofexpressing a proposition by saying that something is the case. It is also common to express propositions by asking questions orissuing imperatives (Geurts 2010: 32–3), to express attitudes andother things that are not propositions by saying something (Braun2011; Sullivan 2023: §V), and to express things by not sayingsomething (Swanson 2017). While these acts do not count asimplicature as Grice defined his technical term, and are not the focusof his theory (or this entry), they are similar in many importantways.

2. Conversational and Conventional Implicature

The implicatures in(1) and(2) areconversational. Theydepend on features of theconversational context, and are not determined by the conventionalmeaning of the sentences uttered. A key feature in (1) wasAlan’s question. Had he asked “What are you going to dotoday?”, Barb could have implicated something completelydifferent (that she is going to work) by saying the same thing (thatshe has to work). Grice (1975: 25) contrasted a conversationalimplicature with aconventional implicature, by which hemeantone that is determined by the meaning of the sentence used.^[8] Here’s a variant of Grice’s example.

(3)

a.

The queen is English and therefore brave.

b.

The queen is English and brave.

c.

Being brave follows from being English.

We will use parentheses to refer to the sentences in an example like(3), and brackets to refer to what the sentences express. So (3c) isthe sentence “Being brave follows from being English” and[3c] is the proposition that being brave follows from being English.By using (3a) to say and mean [3a], speakers implicate [3c]. That is,by using (3a) to say and mean that the queen is English and thereforebrave, speakers implicate that being brave follows from being English.Theyimply rather thansay that being brave followsfrom being English. In contrast, (3b) would rarely if ever be used toimplicate [3c]. The meaning of “therefore” generates theimplicature of (3a). Other words “triggering” conventionalimplicatures arebut, even, too, still, yet, already, again, stop,start, know, andregret.^[9]

While Grice’s examples were triggered lexically, otherconventional implicatures are triggered syntactically. Speakers whoassertRavel, a Spaniard, wrote Spanish-style music implicatethat Ravel was a Spaniard—they imply but do not say that Ravelwas a Spaniard. Hence their utterance is misleading but not a lie ifthey know Ravel was French. The implicature is conventional in that itis determined by the meaning of the sentence via the appositiveconstruction. Other constructions that generate conventionalimplicatures are as-parentheticals (as a Spaniard) andparenthetical relative clauses (who was Spanish).

As(1) illustrates, when a conversational implicature is false, thespeaker’s statement is misleading. Barb’s utterance wouldnonetheless be linguistically flawless. Because [3c] is false, on theother hand, the use of(3a) to make a statement isinfelicitous andimproper aswell as misleading. The truth of [3c] is a precondition of properlyusing(3a) to assert what it says. Conventional implicatures like [3c] arepresuppositions in the non-technical sense in which thequestion “Have you cheated again?” presupposes that youcheated before. The question is inappropriate, and cannot be given astraight “Yes” or “No” answer, unless you didcheat before. For the same reason, the questionIs the queenEnglish and therefore brave? is improper; answering either“Yes” or “No” implies a connection betweenbeing English and brave.^[10]

Not all conventional implicatures are presuppositions in the same way.For example,Jack knows that 51 is prime entails andimplicates that 51 is prime. So it is false and possibly a lie because51 is not prime. Nevertheless, it is linguistically proper andfelicitous. That 51 is prime is an implicature because speakerswho useJack knows that 51 is prime imply rather than say orassert that 51 is prime; they imply it by saying that Jack knows 51 isprime. In both cases, ifand that’s a good (orbad) thing is added,that will refer to what is said butnot what is implicated (cf. Geurts 2010: 6).^[11]

Potts (2005: 35–6) claimed thata sentence cannot beused with its conventional meaning without implicating itsconventional implicatures.^[12] While this is a natural way to interpret Grice’s claim thatconventional implicatures are determined by sentence meaning, exampleslike (4) show that it is too strong.^[13]

(4)

a.

If the queen is English, and being brave follows from beingEnglish, then the queen is English and therefore brave.

b.

Trump, the stable genius, started a trade war (said ironically).

(3a) is used with its conventional meaning in (4a) as the consequent of aconditional. But because(3c) is a conjunct of the antecedent of that conditional, (4a) itself doesnot imply in any way that being brave follows from being English. Aspeaker asserting [4a] does not say [3a] and does not mean [3c]. Sothe speaker does not implicate that being brave follows from beingEnglish. The antecedent of [4a] prevents the conversationalimplicature of its consequent from “projecting”. Theimplicature triggered by the appositive in (4b) is not implicated fora completely different reason. When this sentence is used ironically,the speaker uses it with its conventional meaning and says that Trump,the stable genius, started a trade war. But because it is used to mockTrump’s claim that he is a stable genius, the speaker does notimplicate that Trump is a stable genius. Indeed, he implicates thevery opposite. The meaning of a sentence determines its conventionalimplicatures, but whether a speaker implicates them depends on how thesentence is used. What does entail implicating a sentence’sconventional implicatures is using itto assert what the sentencemeans or expresses. Doing that does not necessitate anyconversational implicatures.

While Grice used “conventional” to denote an implicaturedetermined by linguistic meaning, W. Davis (1998: Chs. 5–6) andLepore & Stone (2015: Pt. II) argue that even conversationalimplicatures can be conventional in the non-technical sense in whichit is conventional for women to wear a sari in India but not Mongolia,and for German speakers to userot to mean “red”but not English speakers.^[14] Conventions in this sense are common practices that serve a socialinterest, perpetuate themselves in certain ways, and are arbitrary inthat other practices could have served the same purposes andperpetuated themselves. New speakers pick up conventions from priorspeakers, often with no instruction. Consider (5):

(5)

a.

Some athletes smoke.

b.

Not all athletes smoke.

It would be unconventional (unusual, idiosyncratic, evenunprecedented) for people who say “Some athletes smoke” toconversationally implicate that some physically fit people willdevelop bladder cancer, but conventional (customary, normal, standardpractice) for them to implicate that not all athletes smoke. Thecustomary implicature is not conventional in Grice’s sense,though. For “Not all athletes smoke” is not determined bythe meaning of “Some athletes smoke”. Speakers can andoften do say and assert (5a)^[15]while implicating something other than [5b], as(6) will illustrate. The practice of using sentences of the form“SomeNPVP” to mean “Not allNP VP” is not a semantic or syntactic convention. It isapragmatic convention. To avoid confusion, I will describeimplicatures that are conventional in Grice’s sense assemantic. When not modified by “in Grice’ssense”, “conventional” will have the broader senseofcustomary.^[16]

Grice (1975: 37ff) called implicatures like [5b]generalized conversational implicatures(“GCIs”). The term is appropriate because (5a) can be used to implicate [5b] in a wide variety of contexts. Grice characterized generalizedimplicatures as those that “would normally (in the absence ofspecial circumstances)” be carried by “the use of acertain form of words”. Levinson (2000: 11–12,16–22, 42–46) characterized GCIs similarly as“default inferences”—implicatures we normally andautomatically infer in the absence of evidence to the contrary.^[17] These characterizations are too strong in one respect. There isnothing abnormal about the use of (5a) in (6), where Gina would normally implicate [6a] rather than [5b].

(6)

Fred: Do you know whether all athletes smoke?
Gina: Some athletes smoke.

a.

I do not know whether all athletes smoke.

The fact that “Some athletes smoke” can be used toimplicate [5b] in some contexts and [6a] in others shows that neither is the default, especially given thatfigurative use with a variety of implicatures is alsoa possibility (§4). The same fact also shows thatneither is a conventional implicature in Grice’s sense. Havingmore than one GCI is compatible with them all being conventional inthe broad sense, though. The wordbank has several meaningsin English, including “row”, as inbank ofswitches. So it is conventional to usebank to mean“row”, even though this cannot be described as its normalor default use.

Following Grice (1975: 39), it is widely accepted that generalizedconversational implicatures differ from semantic implicatures in beingcancelable, either explicitly or implicitly (contextually).^[18]Whereas (3a) cannot be asserted without implicating [3c], (5a) can be asserted without implicating [5b]. The speaker may do this explicitly by adding “Indeed, alldo” after uttering “Some athletes smoke”.Alternatively, the implicature may be cancelled implicitly by theutterance context, as when it is obvious that the speaker is eitherengaging in understatement or ignorant of further facts. Anactual implicature is cancelable if it could have been canceled. In example (1), Barb would not have implicated that she is not goingto Paul’s party if she had added “But I might be able toleave early.”

Whereas semantic implicatures are generally entailed by what is said,many believe that conversational implicatures cannot be.^[19] As(1),(2),(5), and(6) illustrate, conversational implicatures aretypically not entailments. But exceptions have been noted.^[20] When a speaker responds to “Is Tom 65 or blind?” by asserting “Tom is 65,” the speaker may well have answered the question by implicating that Tom is 65 or blind. That is, the speaker may have meant that disjunction by saying that Tom is 65. Neale (1992: 529) believes the cancelability of conversational implicatures prevents them from being entailments. But while an entailed implicature cannot be explicitly canceled if the result would be incoherent (“Tom is 65, but is not 65 or blind”), it can at least be implicitly canceled. This can happen if the speaker answers the simple question “How old is Tom?” in a context in which no one is thinking about blindness. Even explicit cancellation is possible in some cases. A mathematician could implicate that Tom’s age is a prime number by saying that it is 67. One form of explicit cancellation (“Tom’s age is 67, but not prime”) would be necessarily false, and indicate that the speaker is not a math whiz, but it is not incoherent. Another form (“Tom’s age is 67, but I don’t know if that is prime”) only indicates ignorance.

Grice observed that conversational implicatures are typicallyconnected to what is said rather than the way it is said, so that“it is not possible to find another way of saying the samething, which simply lacks the implicature in question” (1975:39). The implicature of(1) is thus said to benondetachable. Grice allowed exceptions,though, “where some special feature of the substituted versionis itself relevant to the determination of an implicature” (seeGrice’s “maxim of Manner” in§6). Metalinguistic implicatures—those that refer to the particularwords the speaker used^[21]—are also detachable.

(7)

Harry: What is thisspecies of bird called in English?
Irene: This is a widgeon.

In example (7), Irene used “This is a widgeon” toimplicate that the English word for the species is“widgeon”. Had Irene used a German sentence with the samemeaning (Dies ist eine Pfeife) she would have said the samething while implicating something different (that it is called“Pfeife”). Semantic implicatures, in contrast, arenondetachable because they are determined by what the sentencemeans.

3. Sentence Implicature

As we observed in§1, Grice defined implicating as a form of speaker meaning. But Grice andothers nevertheless began applying “implicate” tosentences, analogous to the way “imply”,“presuppose”, and “mean” apply to sentences aswell as people.^[22] If an implicature is conventional in either sense (that is, eithersemantic or generalized), we may say that thesentenceimplicates it, or has the implicature.^[23] Even though Barb implicates that she is not going to Paul’sparty, “I have to work” does not itself implicate this.But “Some athletes smoke” implicates that not all do eventhough speakers can use the sentence without implicating this.(Analogy:plane means “airplane” even thoughspeakers can useplane without meaning“airplane”.) Similarly,(4b) implies that Trump is a stable genius even though speakers can use itwithout implying that.

Whereas knowledge of what speakers implicate is essential to fullyunderstand speakers, knowledge of what sentences implicate is acritical component of our knowledge of a language. This is obvious forsentences with semantic implicatures like(3a). But speakers are not fully competent with “some” unlessthey know that it is related to “all” in a way it is notrelated to “several” or “two”. A man using (5a) may mislead others if he does not realize that it implicates [5b], and fail to communicate if he thinks it implicates “It is notthe case that several athletes smoke”.

4. Common Forms of Conversational Implicature

Many forms of conversational implicature occur frequently in everydayspeech and literature, with a wide variety of sentences and in allknown languages. They are common ways of both using and understandinglanguage. The forms are differentiated in part by the relationshipbetween what is said and what is implicated. Knowledge of them is animportant component of our linguistic competence, and is acquired atan early age.^[24]

The most widely recognized forms of implicature arefiguresof speech (tropes). Irony, overstatement (hyperbole),understatement (meiosis and litotes), and metaphor have been known atleast since Aristotle. They are taught in school as elements of style.When Don said in(2)The weather is lovely, he engaged in irony andimplicated that the weather is awful. Don did so in part to make lightof the awful weather. Don could have implicated the same thing bysayingThe weather is not good (litotes) orThe weatheris the worst in history (hyperbole).

Figurative speech isnon-literal: users generally do not meanwhat they say, and expect their audience to recognize that. (Litotesis an exception.) Don did not mean that the weather is lovely. The obvious falsity of what is said is a typical clue that speech isfigurative. Some figures also tend to be marked intonationally,including irony and hyperbole. Others are not, including metaphor andunderstatement. They are all used to make speech lively, interesting,and stylish (§10).

Many forms of implicature are not figures of speech, and have becomewidely recognized only since Grice (1975).(1) illustratesrelevance implicature: the speaker implicates ananswer to an expressed or implied question by stating somethingrelated to it by implication or explanation. [5b] is aquantity (orscalar) implicature: the speakerimplicates the denial of a proposition stronger than the one said.(6) illustratesignorance implicature: the speaker implicatesthat something stronger than what was said is unknown.(7) illustratesmetalinguistic implicature: the speakerimplicates that something has a certain name by using that name todescribe it. These “modes of speech” (non-figurative forms ofimplicature) are not taught in school, and names for them are not ingeneral use. Nevertheless, they are as frequent and natural asfigurative speech, and are learned at the same time. Modes of speechare not marked intonationally, and the speech is literal. They are notused to make speech or writing lively. Speakers do not intend whatthey say to be obviously false, and generally do mean what theysay.

Two modes of speech do have common names. One isdamning withfaint praise. Grice’s example has become classic:

A is writing a testimonial about a pupil who is a candidate for aphilosophy job, and his letter reads as follows: “Dear Sir, Mr.X’s command of English is excellent, and his attendance attutorials has been regular. Yours, etc”. (Grice 1975: 33)

By saying so little, A implicated that Mr. X is a poor candidate forthe job. The other named mode isloose use, orspeakingloosely, illustrated by (8):

(8)

Linda: When willdinner be served?
Mike: At six o’clock.

If Mike’s response is typical, what he meant is only that dinnerwill be servedclose enough to six o’clock for currentpurposes. That would be typically be true if dinner will beserved at 6:01. What Mike said, though, is that dinner will be servedat 6:00, which would be false if dinner is served at 6:01.^[25] If Mike gave the same response to a question about when a swimmertouched the wall in the final lap of an Olympic event, 6:01 may not beclose enough.

The figures and modes of speech are common, socially useful practices.They perpetuate themselves through precedent following, socialacceptance, individual habit and association, and traditionaltransmission from one generation of speakers to another. Precedentoperates when hearers call on their knowledge of the forms speakerscommonly use to either interpret speakers in new contexts, or topredict what hearers will understand. The forms are less arbitrarythan lexical or syntactic conventions, but no one has to implicaterather than say things, or use one form of implicature rather thanothers.

Since these conventions do not attach implicatures to particularsentence forms, they do not give rise to sentence implicatures.

5. Pragmatics and Semantics

As our examples make clear,semantics, conceived as the studyof the meaning of words and sentences, does not exhaust the study ofmeaning. The study of speaker meaning and implicature is included inpragmatics, which covers the broad range of speech actsperformed by using words and sentences.Applied pragmaticsarose from the recognition that second language learners cannot becomefully proficient without mastering more than grammar and literalmeaning (Kasper 2003; Zufferey et al 2019: Ch. 9).Forensicpragmatics studies the use of pragmatics in law enforcementand the courts (Solan & Tiersma 2005; Zufferey et al.2019: §4.4).Clinical pragmatics studiescommunication disorders that arise from failure to master pragmaticrules (Cummings 2009, 2014; Graci 2023).Formal pragmaticsuses formal models of utterances, contexts, and discourse to stateprecise rules specifying the interpretation of an utterance in acontext, including what is both said and implicated (Roberts 2006;Rothschild 2013).

The phenomenon of Gricean conventional implicature (§2) shows further that standard truth-conditional semantics does notexhaust semantics (Barker 2003). For example,Ravel, a Spaniard,wrote Spanish-style music andRavel was a Spaniard and wroteSpanish-style music have the same entailments. Yet they differ inmeaning in such a way that the former but not the latter isinfelicitous and improper because Ravel was French.“False” clearly applies to the latter but not clearly tothe former.

Implicature is important even in truth-conditional semantics. Forexample, logicians customarily take sentences of the form“p orq” to be true provided“p” or “q”or bothare true. Thus “It is not the case that cats meow or purr”would be counted as false. But there are also cases in which speakersuse “p orq” to mean that“p” or “q” is truebutnot both. This would be the natural way to interpret someone whosaid “John is going to invite Mary or Jane to the prom”.Some maintain that “or” isambiguous in English,with an inclusive and an exclusive sense. But another possibility isthat the exclusive interpretation is a generalized conversationalimplicature. One piece of evidence supporting the implicaturehypothesis is that the exclusive interpretation seems cancelable. Thus“Jane will visit France or Germany this summer; indeed, she willdrive through both on her way to Poland” has no contradictoryinterpretation. Some evidence against the implicature hypothesis isthat after “p or q,”or both does not seem any moreredundant thanbut not both. A methodological issue isto describe the evidence necessary to decide whether a particularinterpretation is a sense or a generalized conversational implicature.A foundational issue to is describe exactly what the differenceconsists in.

Implicature continues to be invoked in this way to defendcontroversial semantic claims:

• Knowledge. The standard of justification necessary toclaim knowledge varies from context to context depending on what is atstake and salient. On contextualist theories, sentences of the form“S knowsp” are indexical, withdifferent truth conditions in different contexts (S. Cohen 1986, Lewis1996, DeRose 2009). An alternative theory is that “Sknowsp” has a strict invariant semantics, but is usedloosely to implicate thatS is close enough to knowing forthe purposes of the context (W. Davis 2007b). Another is that“S knowsp” has a weak invariantsemantics but its negation is used to implicate that contextuallyrelevant alternatives cannot be ruled out (Rysiew 2001; Brown 2006;Hazlett 2007). Others argue that implicatures cannot account forthe data (Blome-Tillman 2013b; Dinges 2018; 2021).^[26]
• Names. The Millian theory that the meaning of a name isits referent entails that coreferential names are synonymous, and thatnames without a referent are meaningless. This seems untenable inlight of names like “Superman” and “ClarkKent”. Millians have proposed that the source of theselinguistic intuitions is a difference in implicature (Salmon 1986;Soames 1989). One hypothesis invokes metalinguistic implicature,noting that “Clark Kent can fly” implicates that a mancalled “Clark Kent” can fly (McKay 1981; Berg 1988, 2012).One problem is its implication that the Chinese translation of“Lois Lane believes Superman can fly” should seem as falseas “Lois Lane believes Clark Kent can fly”.
• Negation. On the regular interpretation of (9) below,“some” is equivalent to “any”, and the wholesentence is contradictory:

(9)

The boydid not eat some of the cookies, he ate all the cookies.

• But there is another interpretation, marked by intonation^[27] and other features, on which the negation in (9) denies the“not all” implicature of “The boy ate some of thecookies”, and is thus consistent. The question is how to accountfor the two different interpretations of negations given that the word“not” seems unambiguous (Geurts 1998). Horn (1989:362–4; 370–5) and Burton-Roberts (1989) propose that themarked interpretation of (9) is an implicature. W. Davis (2016: Ch. 6)argues that it is an idiom that plausibly evolved from a generalizedconversational implicature. Soria-Ruiz (2023) proposes aneo-Stalnakerian account.

Implicature plays a well-attested diachronic role ingrammaticalization and the origin of new meanings and idioms.^[28] For example, metaphors have a typical life cycle: beginning assomething a speaker means on a particular occasion; being picked up byothers; catching on, which means becoming self-perpetuating andspreading through the population; and finally, dying and becoming anew lexical meaning or idiom. When dead, what used to be indirectlyexpressed is directly expressed. The termvirus as applied tocomputers went through this evolution in the last few decades,originally denoting a biological organism that spreads from host tohost, now having another meaning on which it denotes computer programsthat spread from computer to computer in a similar fashion. When adead metaphor has syntactic structure likego viral, it is anidiom. When metaphors become widespread andself-perpetuating, but are not yet idioms, they generate generalizedconversational implicatures.^[29]

6. Gricean Theory

In addition to identifying the phenomenon of implicature, andclassifying its types, Grice developed a theory designed to explainand predict conversational implicatures and to describe how they areunderstood. Grice (1975: 26–30) postulated a generalCooperative Principle and fourmaxims specifying howto be cooperative. It is common knowledge, he asserted, that peoplegenerally follow these rules for efficient communication.

Grice viewed these not as arbitrary conventions, but as instances ofgeneral rules governing rational, cooperative behavior. For example,if Jane is helping Kelly build a house, she will hand Kelly a hammerrather than a tennis racket (relevance), more than one nail whenseveral are needed (quantity), and straight nails rather than bentones (quality); she will do all this quickly and efficiently(manner).

Relevance implicatures like(1) are thought to arise from the maxim of Relation. Barb would haveinfringed this maxim unless her contribution were relevant to thepurpose of the conversation. If Barb was being cooperative, then shewas trying to answer Alan’s question. Given that working isincompatible with partying, it is inferred that Barb must haveintended to communicate that she is not going to the party. Grice(1975: 34) thought other implicatures arise byfloutingmaxims. This happens when what a cooperative speaker says so patentlyviolates a maxim that the hearer must infer that the speaker meanssomething different. Irony is thought to arise from flouting the maximof Quality (§9).

Generalizing from such examples, Grice provided a theoretical accountof conversational implicature that has been widely adopted.^[31] A representative formulation goes as follows, withS thespeaker andH the hearer.

This says that an implicature is conversational provided conditions(i)–(iii) are satisfied, where (ii) is the condition thatS’sbelievingp is required forS to be in conformity with the Cooperative Principle. TheTheoretical Definition does not entail thatS implicated p isinferable from (i)–(iii). Calculability does that.

Grice’s calculability principle says more than that hearers aregenerally able to infer what speakers implicate on the basis of thelinguistic meaning of what they utter. That would not be distinctiveof implicature given that the same is true of what people say.^[33] Towork out an implicature is to infer it in a specific wayfrom the Cooperative Principle using particular facts about themeaning of the sentence uttered and the context of utterance.

To work out that a particular conversational implicature is present,the hearer will rely on the following data: (1) the conventionalmeaning of the words used, together with the identity of anyreferences that may be involved; (2) the Cooperative Principle and itsmaxims; (3) the context, linguistic or otherwise, of the utterance;(4) other items of background knowledge; and (5) the fact (or supposedfact) that all relevant items falling under the previous headings areavailable to both participants and both participants know or assumethis to be the case. A general pattern for the working-out of aconversational implicature might be given as follows:He has saidthat q; there is no reason to suppose that he is not observing themaxims, or at least the Cooperative Principle [CooperativePresumption]; he could not be doing this unless he thought thatp [Determinacy]; he knows (and knows that I know that heknows) that I can see that the supposition that he thinks thatp is required [Mutual Knowledge]; he has done nothing to stopme thinking thatp; he intends me to think, or is at leastwilling to allow me to think, thatp; and so he hasimplicated thatp. (Grice 1975: 31; my emphasisand insertions)

Key steps of the working out schema have been named in brackets,corresponding to (i)–(iii) in the Theoretical Definition.^[34]

In addition to postulating that the conversationality of animplicature depends on the Cooperative Presumption, Determinacy, andMutual Knowledge conditions, and that the implicature can be inferredin part from their satisfaction, Grice claimed that the conditionsgive riseto orgenerate the implicatures.The implicaturesexistbecause conditions(i)–(iii) are satisfied.^[35] From his assumption that conversational implicatures can be explainedand predicted on the basis of the Cooperative Principle, Grice drew amethodological conclusion:

The pithy formulation is “Senses are not to be multiplied beyondnecessity”, alluding to Ockham. If a phenomenon can be explainedand predicted in terms of psycho-social principles, then it istheoretically more economical to do so than to posit senses and thelike, which cannot be so explained. Grice’s Razor is ofteninvoked to support classifying the exclusive interpretation of“p orq” as an implicature rather thanas a second sense (§5).

Following Grice, “conversational implicature” was definedin§2 to meanan implicature that depends on features of theconversational context and is not determined by the conventionalmeaning of the sentence uttered. On this definition,Grice’s Theoretical Definition and Calculability are empiricalhypotheses that may turn out to be false. Indeed, we will reviewevidence against these hypotheses below. Many linguists andphilosophers, however, take Calculability to be true by definition.They take “conversational implicature” to meananimplicature that can be worked out from what is said and theCooperative Principle or its maxims.^[37] If this definition is adopted, then what the evidence would show isthat the implicatures illustrated in §§1–4 are not conversational, even those that are not conventional inGrice’s sense (cf. Lepore & Stone 2015: 6, 83, 148).

7. Theoretical Difficulties

While Grice viewed his ideas as tentative and exploratory, followershave taken the theory to be well established. Indeed, it has served asa paradigm for research in pragmatics. Serious difficulties haveemerged, though.

According to Grice’s Theoretical Definition (§6), conversational implicatures depend on a presumption that the speakeris observing the Cooperative Principle. W. Davis (1998: §2.5)notes, however, that speakers can engage in implicature when there isno conversation. All the figures and modes of speech can appear inprivate journals or in manuscripts that have little hope of beingread.^[38]

The Cooperative Principle further assumes that the participants inevery conversation strive only to achieve common goals. From theperspective of social psychology, evolutionary biology, and gametheory, Pinker (2007) and Asher & Lascarides (2013)observe that pure cooperation is generally an unrealisticidealization or naive assumption. Conversations are often amongadversaries, whose goals beyond communication are opposed. It would befoolhardy and possibly dangerous for an interrogator to presume that aprisoner of war or terrorism suspect is being cooperative. Even whenparticipants are friends or relatives, they often have some divergentgoals, and may give priority to other principles (§10). To the extent that they diverge, the speaker’s goals may bepromoted and the hearer’s goals thwarted by withholdinginformation, providing misinformation, going off on a tangent, orbeing obscure. Even when it is correctly presumed that a speaker isnot being cooperative, the speaker may use all the figures and modesof speech. If the prosecuting attorney asks the defendant whether hewas in the bank on the day of the robbery, the defendant might answer“I took my mother to the hospital that day”, therebyimplicating that he was not at the bank. He may do this in the hope ofmisleading the jury as well as the prosecutor. The official purpose ofthe conversation is to get at the truth, the whole truth, and nothingbut the truth. But the defendant’s purpose is to hide it.

Many conversations have goals other than the exchange of information.One is amusement, which speakers often pursue by making jokes (Lepore& Stone 2015: §11.3). Because the goal is not to provideinformation, the maxims of Quality, Quantity, and Relation do notapply. If for any of these reasons the Cooperative Principle does notapply, reasoning based on it will beunsound.

8. Overgeneration

Many have observed that for every implicature that appears to becorrectly predicted by Gricean theory, others appear to be falsely predicted.^[39] The schema used to “work out” observed implicatures canusually be used just as well to work out nonexistent implicatures. Sothe schema as formulated isinvalid—an unreliablemethod of inferring implicatures. By a simple application ofMill’s Methods, it follows that the observed implicatures do notexistbecause of the Gricean factors.

We will illustrate using the case that has been most extensivelystudied, and is generally considered a paradigm application of Griceantheory: the derivation of quantity implicatures from the maxim ofQuantity. Adapted to(5), here is Huang’s (2014: 34) formulation.

Since the speaker has used a semantically weaker expression (i.e.,some) where a semantically stronger one (e.g.,all)is available, he would contradict Grice’s Quantity Maxim if thesemantically stronger sentence held. Consequently, he believes thatthe semantically stronger statement does not hold. Furthermore, he hasnot done anything to stop the addressee thinking that he so thinks,therefore he conversationally implicates that not all athletes smoke.^[40]

In the typical case represented by(5),S says “Some athletes smoke” and implicates“Not all athletes smoke”. The stronger statementS does not make is “All athletes smoke”. Thereare countless relevant statements more informative than what S said,however, whose negations were not implicated, includingSeveralathletes smoke, Some athletes smoke regularly, I know some athletessmoke, and13% of all athletes smoke. The Griceanreasoning could be repeated using any of these stronger statements,with fallacious results. For example:

S said “Some athletes smoke”. IfS werein a position to assert the stronger statement “Several athletessmoke” but did not,S would be in a breach of the maximof Quantity unlessS wished to convey that it does not hold.SoS implicated that it is not the case that several athletessmoke.

But speakers who utter sentences of the form “SomeSareP” rarely if ever implicate the denial of“SeveralS areP”.^[41] Among the infinity of statements stronger than “Some athletessmoke”, “All athletes smoke” is highly unusual inthat people commonly implicate its denial. Since the derivations havethe same form whether or not their conclusions are observed to betrue, Lepore & Stone (2015: 143ff) call this the“symmetry” problem.^[42] The Gricean derivation seems plausible only because we knewantecedently that the conclusion is true.

An irony underscoring theex post facto character of theGricean calculation is that Grice himself derived anignorance implicature from the maxim of Quantity.

A is planning with B an itinerary for a holiday in France. Both knowthat A wants to see his friend C, if to do so would not involve toogreat a prolongation of his journey:

A: Where does C live?
B: Somewhere in the South of France.

(Gloss: There is no reason to suppose that B is opting out; his answeris, as he well knows, less informative than is required to meetA’s needs. This infringement of the first maxim of Quantity canbe explained only by the supposition that B is aware that to be moreinformative would be to say something that infringed the second maximof Quality. “Don’t say what you lack adequate evidencefor”, so B implicates that he does not know in which town Clives.) (Grice 1975: 32–33; example number deleted)^[43]

It is plausible that B would have implicated this. But ifGrice’s reasoning is valid, why shouldn’t Huang concludethat speakers uttering “Some athletes smoke” implicatethey do not know whether all athletes smoke (an ignoranceimplicature)? If Huang’s reasoning is valid, whyshouldn’t Grice conclude that B implicatedC does not livein the southernmost part of France (a scalar implicature)?

Accounting for the differences in implicature described in thissection is an outstanding problem for pragmatic theory.

9. Failures of Determinacy

Grice’s Determinacy condition states thatSconversationally implicatesp only ifS has tobelieve (and implicate)p ifS’s utterance isto be consistent with the Cooperative Principle. Determinacy is a keypremise in the working-out schema, so Calculability depends on it. As§8 illustrated, however, there are normally many alternative ways to becooperative, and contribute what is required by the conversation, evenwhen the meanings and referents of the words used are taken asgiven.

Grice believed irony involves flouting Quality. Here is Grice’soft-repeated “gloss” applied to(2), in which Don said “The weather’s lovely” during ablizzard.

It is perfectly obvious to Don and his audience (Carla) that what Donhas said is something he does not believe, and the audience knows thatDon knows that is obvious to the audience. So … Don must betrying to get across some other proposition than the one he purportsto be putting forward. This must be some obviously relatedproposition; the most obviously related proposition is thecontradictory of the one he purports to be putting forward. (AfterGrice 1975: 34).^[44]

While irony often involves saying something obviously false, it neednot have been obvious to Carla in(2) that Don believed the weather was unlovely. She may have had noindependent source of information about his weather. Don would alsohave made a suitable contribution to the conversation if he had meantand believed that the weather is lovely. So Determinacy is unsatisfiedin irony when the speaker could have been speaking literally,believing what was said (W. Davis 1998: §3.3; see even Grice1978: 53).

Many have observed that the obvious falsity of what speakers say maysignal that they mean something else, but it does not tell us whatelse they mean (e.g., Levinson 1983: 157–8; Lepore & Stone2015: 38–9). Indeed, metaphor is another case in which Grice(1975: 34) takes the speaker to be flouting Quality (Huang 2014:35–6). So the flouting of Quality does not tell us whichfigure of speech Don is using. He would have made a suitablecontribution to the conversation if he had been engaging in metaphorinstead of irony, meaning and believing that relations between he andhis partner (the “weather” in the cabin) are fine.

Metaphors are often difficult to interpret. Suppose a commentator says“Iraq was Bush’s Vietnam”, referring to George W.Bush and the second Gulf War. Did she mean that the U.S. lost in Iraqthe way it lost in Vietnam? That the reasons for going to war in Iraqwere as misguided as those that got the U.S. into Vietnam? Or did sheperhaps mean that even though the U.S. did not secure all itsobjectives, the Iraq war was still worth fighting? She could mean andbelieve any of these things and still be making a useful contribution.Lepore & Stone (2015: Ch. 10) describe such metaphors as invitinghearers to imagine all the things the speaker might have meant. Grice(1975: 39–40) himself acknowledged such cases when he saidthat

there may be many possible specific explanations … ; and if thelist of these is open, the implicatum will have just the kind ofindeterminacy that many implicata do in fact have.^[45]

But to say this is to deny Determinacy and Calculability.^[46]

Saul (2001, 2002, 2010) and M. S. Green (2002) suggested that“implicature” be definednormatively, asproperly implicating something. W. Davis (2007a) replied thatwhile determinacy is more plausible as a norm, similar considerationsshow that it is not required even for properly meaning one thing bysaying something else. For example, a speaker who says “I atesome of the cookies” could properly be meaning either “Iate them all” (engaging in understatement), or “I did noteat them all” (quantity implicature), or “I do not knowwhether I ate them all” (ignorance implicature). None of thesecontributions is required given that all would be appropriate.

Rysiew (2000: 577–8) suggested weakening the determinacycondition by replacing “has to believe (and implicate)p” with “is likely to believe (andimplicate)p”. As he notes, hearers commonly useabduction to figure out what speakers have implicated (cf. Hobbs etal. 1993; Geurts 2010: 34–5). Abduction is a specific form ofinductive or non-demonstrative reasoning in which a hypothesis isinferred to be true from the fact that it provides the bestexplanation of the data. By their nature, non-demonstrative methodsare not guaranteed to succeed. This fact of life is no reason to shuninduction when seeking to discover implicatures. W. Davis (1998:66–8) had observed, though, that an implicature can exist and beconversational even though the available evidence does not make thatimplicature (or belief) more likely than others. The problems ofindeterminacy and overgeneration show, in particular, that the Griceanhypotheses provide neither the only nor the best explanations of thedata, making the inferences fallacious instances of abductivereasoning.

10. Conflicting Principles

Grice (1975: 30) recognized that his maxims may “clash”.When they do, there is no way to determine what is required forconformity to the Cooperative Principle. In the case of irony, forexample, Manner clashes with Quality. When Don said “Theweather’s lovely”, we cannot interpret him as meaning whathe said because on that interpretation he would be violating Quality.But we cannot interpret him as meaning the opposite because then hewould be violating Manner (Wilson & Sperber 2012: 18–9). Itis more perspicuous to explicitly state something than to implicateit.

We use irony and other figures in part because we have conversationalgoals other than the efficient communication of information (Lakoff1977; Sainsbury 1984: 427–9). We observe not only theCooperative Principle, but also the Principle of Style.

Clear and simple prose—“just the facts,please”—can be boring, tedious and dull. We liven up ourwriting with figures of speech. Metaphor in particular makes speechmore interesting and insightful by engaging our imagination (Lepore& Stone 2015: Ch. 10). In the process, we sacrifice perspicuity(violating Manner). We sometimes “embellish” a narrationto make it more interesting (violating Quality) and delete boring orugly details even when they are important (violating Quantity).

The Gricean maxims often clash with the Principle of Politeness,emphasized by Leech (1983).^[47]

Speakers frequently withhold information that would be offensive ordisappointing to the hearer, violating Quantity. Speakers oftenexaggerate in order to please or flatter, and utter “whitelies” in order to spare the hearer’s feelings, violatingQuality. People pick “safe topics” (e.g., the weather) tostress agreement and communicate an interest in maintaining goodrelations, violating Relation. Euphemisms avoid mentioning theunmentionable, but in the process violate Manner.

One common motive for implicating something is that it is oftenperceived to be more polite than asserting it (Pinker 2007; Huang2014: 142; Haugh 2015: 2). In case(1), Barb may have answered Alan’s question indirectly because shethinks it is less likely to hurt his feelings, even if she realizes hewill assume that is what she is doing.

Blome-Tillmann (2013a: 177) has suggested that problems such asovergeneration and conflicting principles can be avoided byunderstanding calculability not as a way of predicting and explainingimplicatures, but merely as providing a criterion for them. Butif a criterion always gives false positives (overgeneration) or falsenegatives (indeterminacy), or cannot be applied (due to clashes), thenit is not a useful criterion.

11. Neo-Gricean Pragmatics

Prominent linguists have sought to improve on Grice’sformulation of the conversational principles, and provide a solutionto the problem of clashes. Horn (2004: §4) replaces Quantity,Relevance, and Manner with two interrelated principles.^[48]

Levinson (2000: 76, 114, 137) adopts similar principles, which hecalls “Q” and “I” (for “Informativeness”).^[49] Since Horn believes that interpretations like [10a] are derivablefrom the R-principle, he calls them “R-basedimplicatures”. The assumption is that there is no reason to makea stronger statement (say more) if the extra information can becontributed by implicature. Implicature [11b] is similarly describedas “Q-based”. The assumption is that if the speaker didnot make a stronger statement (say more), its denial wasimplicated.

(10)

He broke a finger.

a.

He broke a finger of his own. (“R-based implicature”)

b.

✗He did not break a finger of his own.

(11)

He entered a house.

a.

✗ He entered his own house.

b.

He did not enter his own house. (“Q-based implicature”)

Horn has clearly identified two distinct and very general patterns ofmeaning and interpretation. Critics maintain, however, thatHorn’s two principles provide no reason to expect the twoindicated interpretations rather than those we do not observe (Lepore& Stone 2015: §3.1; W. Davis 2016: §4.7). They ask how Qcan predict [11b] without predicting [10b], and how [10a] can bederivable from R if [11a] is not. What in R predicts [10a] rather thanother strengthenings, such as “He broke someone else’sfinger”?^[50]

Horn goes on to formulate what he calls theDivision ofPragmatic Labor:

Given two expressions covering the same semantic ground, a relativelyunmarked form—briefer and/or more lexicalized—tends to beR-associated with a particular unmarked, stereotypical meaning, use,or situation, while the use of the periphrastic or less lexicalizedexpression, typically more complex or prolix, tends to be Q-restrictedto those situations outside the stereotype, for which the unmarkedexpression could not have been used appropriately. (Horn 2004: 16)

Horn illustrates this division with the contrast between (12) and(13).

(12)

She stopped the machine.

a.

She stopped themachine in the usual way. (“R-based implicature”)

b.

✗She didnot stop the machine in the usual way.

(13)

She got the machine to stop

a.

✗ She stopped the machine in the usual way.

b.

She did not stop the machine in the usual way. (“Q-based implicature”)

Horn appears to be assuming, plausibly, that “stopped” and“got to stop” have the same meaning. If so, then it isdifficult to see how either implicature could be derived from Q or R,which refer towhat is said, nothow it is said.(Recall Grice’s nondetachability criterion.) Levinson (2000:136–7) therefore reinstated a version of Manner.^[51]

Levinson describes “got to stop” as “marked”because it is more complex and less lexicalized than“stopped”. W. Davis (2016: 160) notes, though, that whenwe look at clear cases in which a single word is synonymous with aless lexicalized phrase, we often find no difference in implicature(e.g.,mare versusadult female horse). And the wordoften connotes an unusually good example of the kind (e.g.,stallion in common parlance connotes an especially fast ordominantuncastrated adult male horse).

Horn sometimes describes Q and R as “antinomic forces”(e.g., Horn 2004: 14), which would be appropriate if the bracketedconditions were omitted. Without the conditions, Horn’sprinciples would clash as often as Grice’s.^[52] Without independent means of determining antecedently which forcewill “prevail” in a given case, Horn’s principleswould lack predictive or explanatory value. Lepore & Stone (2015:§3.1) suggest treating Horn’s principles as“simultaneous equations”, constraining but not determiningthe conversational implicatures. But this assumes the equations have asolution. Not all simultaneous equations do.

Levinson (2000: 157–64) sought to avoid clashes by stating anorder of precedence: Q > M > R. Huang (2014: 49) reverses theordering, saying that

the R-principle generally takes precedence until the use of acontrastive linguistic form induces a Q-implicature to thenon-applicability of the pertinent R-implicature….

Such orderings make sense only if the bracketed clauses in Q and R areomitted. W. Davis (2016: 159) responds that Levinson’s orderingmakes it is hard to see why(10) or(12) should have an R implicature rather than a Q implicature, whileHuang’s ordering makes it hard to explain why(11) and(13) have Q implicatures.^[53]

12. Relevance Theory

The most influential alternative to Gricean and neo-Gricean theory,called “Relevance theory”, was developed by Sperber and Wilson.^[54]

We have proposed a definition of relevance and suggested what factorsmight be involved in assessments of degrees of relevance. We have alsoargued that all Grice’s maxims can be replaced by a singleprinciple of relevance—that the speaker tries to be as relevantas possible in the circumstances—which, when suitablyelaborated, can handle the full range of data that Grice’smaxims were designed to explain. (Wilson & Sperber 1986: 381)

“Relevance” is given a highly technical sense, in whichthe relevance of a proposition in a context is directly related to howmany positive cognitive effects it has and inversely related to howmuch effort is required to process it (Wilson & Sperber 2012: 6,62–3, 219).^[55] “Positive cognitive effects” are “improvements inknowledge”, including “true contextual implications, orwarranted strengthenings or weakenings of existing assumptions”.Contextual implications are propositions logically implied by theproposition and the cognitive context together but from neither alone.Propositions or assumptions are objects of belief orknowledge—cognitive representations. Wilson and Sperberillustrate their concept by imagining a doctor whose choice of truestatements is confined to the alternatives in (14).

(14)

a.

You are ill.

b.

You have the flu.

c.

You have the flu or 29 is the square root of 843.

They conclude that [14b] would be maximally relevant on the groundsthat it entails everything [14a] does and more, while being as easy toprocess; [14c] has the same cognitive effects as [14b],^[56] but is harder to process.

Example (14) is a special case in that either the effects or theeffort are equal between alternative contributions. To know what ismaximally relevant in other cases, a particular function of effectsand effort must be specified (Hinkelman 1987). Sperber and Wilsonspecify one when describing the theory of cognition on which theyground their theory of communication. “Our claim is that allhuman beings automatically aim at the most efficient informationprocessing possible” (Sperber & Wilson 1986a: 49).“Efficiency in cognition … involves processing inputsthat offer the best possible cost/benefit ratio at thetime”(Wilson & Sperber 2012: 62).^[57] Selecting this function and formulating a principle in the style ofGrice’s yields:

We will see that Relevance theorists qualify this idea, but manyimportant points can be made with the simpler principle.

While Grice’s maxims enjoin the speaker to contribute therequired information and do so perspicuously and briefly, they do notrequire the speaker to maximize information, perspicuity, or brevitywhen other things are equal. For example, Grice’s maxims do notpredict that Barb implicatedI am not going anywhere in(1) even though it is more informative thanI am not going toPeter’s party, and may have a greater effects/cost ratio.Or suppose that in a discussion of a new prescription drug benefit,someone comments “It will take some money to fund thatprogram”. The speaker would normally be engaging inunderstatement, implicating “The program will be veryexpensive”. Relevance theorists account for this by saying thatbecause the proposition explicitly conveyed is trivial, and thus hasfew positive cognitive effects, the hearer will “recover”the more informative proposition.^[59] Critics respond that countless propositions are more informative thanthe one implicated, such as “The program will costtrillions”, and seem as easy to process.^[60]

Conversely, Maximal Relevance does not imply or subsume Grice’sprinciples. For instance, nothing guarantees that the contributionwith the most positive cognitive effects per unit processing cost isgermane to the topic of the conversation or as informative as required(less informative contributions might have more positive cognitiveeffects per unit processing cost). As a result, Maximal Relevance doesnot predict what Barb implicated in example(1). The propositionI am not going to Peter’s party willhave different effects thanI am not going to Paul’sparty, but seems as easy to process and could well have as manypositive cognitive effects.^[61] Only the proposition about Paul is relevant in the ordinary sense towhat Alan asked, but this does not entail that it is maximallyrelevant in the technical sense of Relevance theory.^[62]

Sperber and Wilson observe that Gricean theory provides no explanationfor why Don would say in(2) that the weather is lovely if he wanted to express the opposite belief.^[63] Maximal Relevance has the same problem: Don’s simply sayingwhat he means would seem easier to process and thus more efficient.Wilson & Sperber (2004: 621) think saying something in order tomean the opposite would be “patently irrational”. Adler(1987: 710) observed, however, that it need not be irrational givenhow readily hearers recognize when speakers do so. Moreover, speakersengaging in irony are doing more than meaning the opposite of whatthey said. As Grice (1978: 53–4) later recognized, they are alsopretending to mean and assert what they said,^[64] and are expressing more than disbelief of what is said. Sperber andWilson call it a “dissociative attitude—wry, skeptical,bitter, or mocking”.^[65] Hearers readily recognize and commonly enjoy the performance of thiscomplex speech act. The observation that irony involves expressing adissociative attitude does not lessen the theoretical problem,however. There is no reason to think, for example, that “Theweather is terrible and anyone who thinks it lovely is foolish”has the maximum effects/cost ratio. Processing just what Don actuallysaid (that the weather is lovely) would seem to require even lesseffort; so that proposition could conceivably have a greatereffect/cost ratio. And there is no reason to think an ironicinterpretation has a greater effect/cost ratio than a hyperbolic ormeiotic interpretation. If expressing a dissociative attitude involvessomething other than expressing a proposition, as seems plausible (cf.M. S. Green 2018: §5), it would not be a positive cognitiveeffect as defined, and thus would not affect the relevance ratio. Forreasons such as these, Levinson (1989: 463–4) charged that theaccounts offered by Relevance theorists are asex post factoas Gricean accounts.

The explanations of loose use offered by Relevance theorists areproblematic in another way. In(8), where Mike said “Dinner will be at six”, they explain whyMike did not say something true like “Dinner will be at six orshortly after” by saying that the strictly false statement hasthe same positive cognitive effects but is easier to process and somore relevant.^[66] But that would erroneously imply that Mike did notmean andimplicate that dinner will be at six or shortly after.Another reason the explanation is unsatisfactory is that there areother things Mike did not say with the same positive contextualeffects that seem as easy to process as “Dinner will beat six”. including “Dinner will bearound six”. This proposition has some true cognitiveeffects that “Dinner will be at six” lacks, including“Dinner may not be exactly at six”.

The recital example in§10 illustrates one reason why Relevance theories adopt Optimal ratherthan Maximal Relevance (Wilson & Sperber 2012: 64–5):

the communicator is manifestly limited by her own abilities (toprovide appropriate information, and to present it in the mostefficient way). Nor can she be expected to go against her ownpreferences (e.g., against the goal she wants to achieve incommunicating, or the rules of etiquette she wishes to follow).

However:

Since it is also manifest that the audience will tend to payappropriate attention only to an utterance that seems relevant enough,it is manifest that the communicator wants her audience to assume thatthe utterance is indeed relevant enough. There is thus a minimal levelof relevance that the audience is encouraged to expect: the utteranceshould be relevant enough to be worth the effort needed forcomprehension.

Relevance theorists thus propose that every utterance conveys apresumption of its own optimal relevance, defined by (a) and (b):

Presumption of Optimal Relevance:

a.

The utterance is relevant enough to be worth processing.

b.

It is the most relevant one compatible with thecommunicator’s abilities and preferences.^[67]

Because of its preference provision, Optimal Relevance does not clashwith Politeness and Style the way Maximal Relevance does. The parentsmay say “Your performance wasn’t perfect” ratherthan “It was horrendous” because they strongly prefer notto hurt their daughter’s feelings.^[68] This means, however, that Optimal Relevance would not predict thatBarb meantI am not going to Paul’s party in(1) even if it is relevant enough to process and more relevant than theother alternatives. For Barb might have preferred to dodgeAlan’s question. In(2), Don may have preferred an ironic utterance to ones with higher E/Cratios (Millikan 1987: 725).

We are focusing on Relevance theory as an alternative attempt topredict and explain what speakers implicate. The main focus ofRelevance theorists, however, is the process by which hearersinterpret utterances. The hearer’s aim, on their view,is “to find an interpretation of the speaker’s meaningthat satisfies the presumption of optimal relevance”. They inferthat the hearer “should follow a path of least effort, and stopat the first overall interpretation that satisfies his expectations ofrelevance” (Wilson & Sperber 2012: 7). It is unclear how toreconcile this with requirement that the optimally relevant utterancebe the most relevant one compatible with the communicator’sabilities and preferences.

The ratio of positive cognitive effects to processing cost is zerowhen there are no positive cognitive effects at all. Given thedefinition of contextual implication, any proposition that is part ofthe cognitive context has no contextual implications. So both Maximaland Optimal Relevance seem to imply that speakers cannot mean orimplicate anything already known, and must mean something else. Gerrig(1987: 718) and McCawley (1987: 724) find this implausible. If A and Bare walking in torrential rain, A might well say “It is rainingreally hard”, stating the obvious, and B might respond“There is indeed some rain coming down”, engaging inunderstatement and implicating exactly what A said.

Many critics have observed, and Sperber and Wilson have acknowledged,that relevance as defined is not measurable.^[69] Positive cognitive effects are non-denumerable. Anything a speakermight say or implicate will have infinitely many true contextualimplications if it has any.^[70] We do not know whether processing cost is measured by time, mentaleffort, electro-chemical energy, inferential steps, or some functionof them all. We have no unit of measurement for mental effort, and donot yet know how to measure the energy consumed in processing anutterance. If relevance is not well defined and knowable, it cannot beused to account for specific implicatures.

13. Explicature and Impliciture

As observed in§1, Grice (1975: 24) introduced the technical term“implicature” to denote either (i) the act of meaning orimplying one thing by saying something else, or (ii) what the speakermeant or implied. Grice (1975: 87ff) used “say” quitestrictly, requiring what a speaker says to be closely related to whatthe sentence uttered means on that occasion. Indexicals provide casesin which what a speaker says is not what the sentence used means. WhenBarb uttered “I have to work” in(1), she said that she, Barb, has to work; but the sentence she used doesnot mean “She, Barb, has to work” even on that occasion.Ellipsis allows people to say things without even uttering sentences.If John asks “Where did Mary go?” and Sue answers“To the gym”, then Sue said that Mary went to the gym. Theinfinitive phrase she uttered was elliptical for a sentence meaning“Mary went to the gym” but does not itself mean that.

Sperber and Wilson (1986a: 182–3) introduced the parallel termexplicature to mean what is “explicitlycommunicated”. Carston (1988: 33) initially identified this with“what is said, in Grice’s terms”.^[71] On this definition, Barb’s explicature in(1) was that she has to work, and her implicature was that she is notgoing to Paul’s party. Carston’s (1988: 40)paradigm case is less clear.

(15)

Alice ran to the edge of the cliff.

a.

Alice jumped.

b.

Alice jumped off the cliff.

After saying or observing that Alice ran to the edge of the cliff, aspeaker would typically use (15a) “Alice jumped” to meanthat Alice jumpedoff the cliff [15b]. Carston counts this anexplicature. It does resemble ellipsis, but a speaker who used (15a)to mean that Alice jumped up to the rescue helicoptersaid thesame thing while meaning something different. And if the speakerknew that Alice jumped up to safety, the speaker might be accused ofmisleading the hearer but not of lying.

Carston’s (1988: 45; 2004a: 646–8) most influentialargument is based on what are commonly called “embeddedimplicatures”. She would claim that if “Alice jumped offthe cliff” were an implicature of “Alice jumped”,then we should not understand (16a) and (16b) as having the same truthconditions. Yet we do, Carston believes. The alleged implicature seemsto fall within the scope of the logical operator. Yet it cannot giventhe definition of implicature (§1).^[72]

(16)

a.

If Alice ran to the edge of the cliff and jumped, she is probably dead.

b.

If Alice ran to the edge of the cliff and jumped off, she is probably dead.

W. Davis (2016: §5.3) replies as follows. A speaker who used(15a) to mean[15b] would just as naturally use (16a) to mean [16b], and hearers wouldunderstand the speaker accordingly. But what the speakersaidis not entailed by [16b]. What the speaker of (16a) said would befalse in circumstances in which Alice was unlikely to jump off thecliff if she jumped. Hearers would focus on what the speaker meant,though, which would be true even in those circumstances. Since thespeaker meant one thing [16b] by saying something else [16a], thespeaker implicates [16b]. The speaker cannot implicate anything byuttering the antecedent of (16a) because the speaker does not sayanything by uttering the antecedent, only by uttering the wholeconditional. So there is really no embedding of implicatures when(16a) is uttered.

The relationship between(15) and (16) is special. In many other cases in which a sentence“p” conversationally implicates“q”, the conditional “Ifp thenr” does not implicate “Ifp andq thenr”. For example,If Bill got someproblems wrong, he might have gotten them all wrong does notimplicate “If Bill got some but not all problems wrong, he mighthave gotten them all wrong”.

A lively debate between Relevance theorists and neo-Griceans concernsnumerical claims.

(17)

Peter has one child.

a.

Peter has at least one child.

b.

Peter has exactly one child.

All parties agree that a speaker can use (17) to mean either [17a] or[17b]. Horn (1972) and Levinson (2000: 87–90) further agree withCarston that (17) itself is unambiguous. But whereas the neo-Griceanshold that (17) means [17a] rather than [17b], Carston (1988:46–7) maintains that (17) means neither but can be used to sayboth. So the neo-Griceans hold that (17) always says [17a] whilesometimes implicating [17b]. Carston holds that (17) is sometimes usedto explicate [17a] and sometimes [17b]; neither is an implicature. Thethesis that sentence meaning leaves open what is said to this extentis calledsemantic underdetermination.

While still doubting that Carston’s view can fully account forcardinals, Horn (1989: 250–1; 2010: 314–5) now concludesthat they do not behave like quantifiers. For example, if you knowthat everyone passed, you must answer “Did some studentspass?” with “Yes”. But if you know that Peter hastwo children, you cannot answer “Does Peter have onechild?” without knowing whether the speaker meant “atleast” or “exactly”. Indeed, a case can be made that(17) is ambiguous, so that Neo-Gricean and Relevance accounts are bothwrong (W. Davis 2016: §7.3).

Following Sperber & Wilson (1986a: 182), Carston (2004b: 635)later defines an explicature as a development of a logical formencoded by the sentence uttered, and an implicature as any propositioncommunicated by an utterance that is not an explicature.^[73] The technical terms “development” and “logicalform” are understood in such a way that [15b] is a developmentof [15a]. Thus understood, “explicature” covers much morethan what is said, and “implicature” covers much less thanwhat is implicated as defined in§1.

Bach (1994: 160) uses “say” even more strictly than Grice,meaning “strictly, literally,and explicitlysay”. Since the speaker of(15a) did notexplicitly say[15b], Bach counts “The speaker said that Alice jumped off thecliff” as false. Bach (1994: 125–6, 140–1; 2006:28–9) agrees with Carston, though, in withholding the term“implicature” when what the speaker means is an“expansion” or “completion” of what is said.Bach introduces the termimpliciture (with “i”rather than “a” after soft “c”) to cover suchcases. Bach restricts “implicature” to cases in which whatis meant is “completely separate” from what is said.

A thesis attributed to Grice is that whatS says isdetermined by “decoding”, while whatSconversationally implicates is determined by whatS saystogether with an inferential, pragmatic mechanism (see, e.g., Sperber& Wilson 1986a: 182). An alleged problem, called“Grice’s Circle” (Levinson 2000: 173–4,186–7), is that many of the processes involved in figuring outwhat is said, such as reference identification and ambiguityresolution, “involve exactly those inferential mechanisms thatcharacterize Gricean pragmatics”.^[74] Grice never talked about decoding however, and observed himself thatconversational principles are involved in determining what is said(Grice 1957: 222). For example, if an ambiguous term is used, wenaturally assume—in the absence of specificcounterevidence—that the intended meaning is the one relevant tothe conversation. In a discussion of snow, “There is a largebank on Main Street” is naturally interpreted as referring to asnow bank.

There is no circle on Grice’s view because what is said is theconclusion of one pragmatic inference, and is one of the premises in afurther pragmatic inference to what is implicated.^[75] The process is serial rather than parallel, although laterconclusions may always lead to adjustment of earlier conclusions.

14. Speaker Implicature and Intention

W. Davis (2016: Ch. 2) describes ways of explaining and inferringconversational implicatures that do not rely on conversationalprinciples. The methods he proposes for speaker implicature aredescribed in this section and for sentence implicature in thenext.

For a speaker to implicate something is for the speaker to meansomething by saying something else (§1). It is generally agreed that what a speaker means is determined by thespeaker’sintentions. When Steve utters “Kathrynis a Russian teacher”, whether Steve means that Kathryn is ateacher of Russian nationality or a teacher of the Russian language,and whether he is speaking literally or ironically, depends entirelyon what Steve intends to convey. What “convey” meansprecisely is controversial, but is an independent issue.^[76]

We most commonly explain why people doA with the intentionof doingB by explaining why they believe they will doB by doingA, or why they want to doB. Wecan explain why speakers intend to convey a thought by uttering asentence that says something else in the same ways. Why do speakersbelieve they can convey thoughts by means of the various figures andmodes of speech identified in§4? One reason is that they have seen others doing so. Knowledge of thecommon forms of implicature is acquired along with knowledge of thesemantics and syntax of our native language. Speakers pick up figuresand modes of speech from other speakers, as they learn vocabulary andgrammar. After speakers have become proficient, their own past successin using figures and modes of speech is a reason for them to believethey will succeed again. Knowledge of both figures and modes is astacit as our knowledge of syntax and semantics. It is not knowledge offacts that define a language, but of how a language is used andunderstood. Since the figures and modes do not depend on a particularlanguage, they can be used with any language.

Why do speakers want to engage in implicature? The main reasons arethe reasons speakers make statements: to communicate, expressthemselves, and record their thoughts. These goals may serve tocooperate with others, or to oppose them. What goals are served byimplicating rather than saying something? One is verbal efficiency(Levinson 2000: 28–31; Camp 2006: 3; Wilson & Sperber 2012:62): through implicature we express two or more thoughts by utteringjust one sentence. Another is to mislead without lying (Horn 2010:§4; 2017; Zufferey et al. 2019: 77–84). People often wish othersto believe things that are false, and not only in situations ofconflict and competition. And they nearly always prefer misleading to lying.^[77] The greater deniability of implicature, and the fact that it enablesus to veil our intentions, are often motivating factors (Brown &Levinson 1978: 137; Pinker 2007; Camp 2022). We observed in§10 how implicature promotes the goals of style and politeness.

It should also be recognized that people perform many even highlyskilled actions automatically, spontaneously, or habitually. Suchactions are done without deliberation or conscious planning. Whatspeakers implicate as well as what they say commonly falls in thiscategory.

Given that speaker meaning is a matter of speaker intention, itfollows that speaker implicatures can be recognized or predicted bythe methods we use to infer intentions from behavior, includingabduction, analogy, and testimony. In example(2), Carla may suspect that Don means the weather is bad because irony isa common linguistic device (§4), and Don has been ironic in similar situations before. Don’sintonation may be a clue. On the other hand, if Don rarely speaksfiguratively when reporting in, Carla may infer that he meant what he said.^[78]

Conversational principles can play the same indirect role inimplicature recognition that known tendencies or goals play ininductive inference generally. Since speakers commonly observe theCooperative Principle, and hearers know this in a vague and tacit sortof way, hearers tend to assume that particular speakers arecooperating, in the absence of evidence to the contrary. If thehypothesis that Barb means she is not going to Paul’s party inexample (1) fits better with the assumption that she is being cooperative thanthe hypothesis that she is not answering the question, Alan may byabduction infer she is implicating that. Further support for thehypothesis may be provided by the recollection that other speakershave implicated similar things in similar circumstances before. Thefact that relevance implicature is a common practice thus providesanalogical evidence (§4). Recognition of an unconventional form of implicature is moredifficult, but no harder than recognizing when a speaker is using asentence with an unconventional meaning. As Sterelny (1982:192–3) observed, knowledge of the particular speaker isultimately more important than knowledge of non-universalgeneralizations.

WhenS is being uncooperative, we have to use othergeneralizations or analogies. We are familiar with the ways defendantsmanipulate language in an effort to avoid self-incrimination.

15. Sentence Implicature and Convention

Whereas what a speaker implicates depends on the particularspeaker’s intentions, what a sentence implicates onDavis’s theory depends on the conventions of the community ofspeakers who use the language. To know or explain sentenceimplicatures is to know or explain the relevant conventions. This isas true of generalized conversational implicatures as it is ofimplicatures that are conventional in Grice’s sense(§2).

When Grice talked about conventional implicatures he was referring tosemantic implicatures, like [3c]. These exist because ofconventions that give individual words or syntactic structures theirmeanings.The queen is English and therefore brave implicates“Being brave follows from being English” because it isconventional for English speakers to use “therefore” witha certain meaning, which determines the implicature. Aconversational sentence implicature is not determined by themeaning of the sentence used, even when sentences with the same formare conventionally used with that implicature. It is a second-orderconvention: a convention to use a sentence of a given form with animplicature that is not part of its meaning. The common modes andfigures of speech are also second-order conventions, but notrestricted to sentences with a particular form. A language is definedby first-order lexical and syntactic conventions, not by second-orderimplicature conventions. In this respect conversational implicatureconventions are like naming conventions, word formation rules,intonation rules, speech act rituals (e.g., saying “This isN” when answering a telephone), and indirect speech actconventions (e.g., asking “Can I get anN?” torequest anN).^[79] Second-order conventions are not as arbitrary, though, because thereis always some antecedent relation between what the sentence means andthe implicature that makes it natural to use one to convey the other.Implicature conventions promote style, politeness, and efficiency aswell as communication.

Like other second-order linguistic conventions, conversationalimplicature conventions differ in their cross-linguistic spread.Whereas the quantity implicature of “some” has been foundin all observed languages (Horn 1989), common metaphors differ as muchfrom language to language as the idioms that evolve from them do. Thefact that regularities in implicature obtain cross-linguistically iscompatible with their being arbitrary and conventional. Witness thepractice of using “?” and rising intonation to markquestions. Why some implicatures are common to more languages thanothers is an open question on any view. To the extent thatimplicatures are conventional, it is a question for historicallinguistics.

Knowledge of sentence implicatures is a crucial component oflinguistic competence.^[80] Speakers unaware of them are likely to mislead their audience.Imagine the possibilities if an oblivious speaker saidYourhusband saw a woman to the subject’s wife. Hearers withoutsuch knowledge are likely to either misinterpret or fail to fullyunderstand the speaker. Sentence implicatures, both semantic andconversational, resemble idioms and figures of speech in being pickedup by native speakers from other speakers in the course of learningthe language. Sentence implicatures thus perpetuate themselves fromone generation to the next as sentence meanings do. Recent metaphorsare special in being picked up by adults, and are liable to becomeidioms if they pass on to new generations.

An impressive body of research has attempted to discern generalregularities in the multitude of conversational implicatureconventions associated with a language. Wierzbicka (2003) has studiedhow implicature conventions reflect broader “culturalscripts”. Others study how the implicatures of a sentence arerelated to the implicatures of compound sentences in which thesentence is embedded (Gazdar 1979; Levinson 2000: §2.5.1;Sauerland & Stateva 2007)—the question raised by example(16).

The most influential work on conversational implicature conventionsdescribes “Horn scales”.^[81] Horn (1972, 1989) observed that the quantifiersall, most, many,some form a scale with the following properties. Instances of“___S areP” with one term entailinstances with any term to the right, but not to the left; the termsare thus ordered by logical strength. Moreover, the result ofsubstituting one term implicates the denial of the result ofsubstituting any term to the left, but not to the right. In thenegative context “It is not the case that ___S areP”, the logical and pragmatic relations are reversed.Other Horn scales are ⟨necessarily, actually,possibly⟩, ⟨certainly, probably,possibly⟩, and ⟨must, should, may⟩. Horn(1989: §4.5) correlates the existence of scales with the absenceof certain lexical items, such as a quantifier meaning “not all”.^[82] Levinson (2000: 156) looked for a generalization that would coverthese cases but not scales like ⟨Over90%, over 10%,some⟩ which have the same logical relations as Horn scalesbut not the pragmatic relations. One generalization is that the itemson a Horn scale are widely and frequently used monolexemes. Acompanion problem is to explain why some common monolexemes withsimilar logical relations lack the pragmatic relations, asseveral illustrates. Given the conventional nature ofgeneralized conversational implicatures, there may be no systematic(“synchronic”) explanation. All languages are“irregular” to some extent. For example, the regularpattern for adjectives in English is that oftall, taller,tallest. But there are exceptions, such asgood, better,best. No one expects that anything other than a historical(“diachronic”) explanation exists for these facts.

The literature on implicature is enormous and still growing. Thisentry, regrettably, had to ignore many valuable contributions.

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