## 1. Speaker Implicature



H. P. Grice (1913-1988) was the first to systematically study
cases in which what a *speaker* means differs from what the
*sentence* 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, Barb *meant* that she is not
going to Paul's party by *saying* that she has to work.
She did not say that she is not going to Paul's party, and the
sentence she uttered does not mean that. Grice introduced the
technical terms *implicate* and *implicature* for the
case in which what the speaker said is distinct from what the speaker
thereby meant or
 implied.[1]
 Thus Barb implicated that she is not going; that she is not going was
her 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 during
a 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 thereby
meant that the weather is terrible. So he implicated that the weather
is terrible. Implicating is an *illocutionary* speech act,
something done in or by saying something (Austin 1962: 98-103).
Since it involves meaning one thing *by* saying something else,
it is an *indirect speech act*, albeit not one that Searle
(1975: 265-6)
 analyzed.[2]



By "saying", Grice meant not the mere utterance of words,
but saying *that* something is the case, which Austin (1962:
94) called a *locutionary* act. Barb could have said the
same 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", we
will sometimes count him as saying that Jupiter is a gas giant. We
will follow Grice in using "say" more narrowly, requiring
that what a speaker says be something that the sentence uttered means
or expresses in the context of use. So we will take Ed to have
implicated that Jupiter is a gas giant by saying that the largest
planet is. *Stating* or *asserting* that *p*
entails both saying and meaning that
 *p*.[4]
 When Yogi Berra, famous for his malapropisms, said "Texas has a
lot of electrical votes", he said that Texas has a lot of
electrical votes; but since that was not something he meant, it was
not something he asserted. Don did not mean what he said for a
different reason. So he too said but did not assert that the weather
is lovely.



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



What someone implicates is not given to us directly. We have to
*infer* 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, and
some background knowledge (e.g., that going to Paul's party
is not work). An implicature can be characterized as an inference
("something inferred"), but implicating is not itself
inferring. To implicate something is to express a belief in a
particular way. To infer something is to acquire or possess a belief
in a particular way. Hearers have to infer what speakers implicate.
But implicatures do not *result from* inferences. 
Furthermore, the fact that implicatures are inferred is not what makes
implicating an indirect speech act. Implicature is indirect because to
implicate something is to mean it *by saying* *something
else*.



Even though it requires an inference, our recognition of what is meant
is commonly automatic and effortless, whether it is said or
implicated. In
 (1),
 for example, competent speakers will grasp immediately that Barb
meant both that she has to work and that she is not going to
Paul's party. *All* speech acts have to be inferred from
contextual evidence, including what was said and what words were
uttered. Whether there is any significant difference in the kind of
inference required to recognize an implicature is a matter of some
debate, and may depend on the type of
 implicature.[6]
 While it is not our focus here, how competent hearers recognize---and
language learners acquire the ability to recognize---what a speaker
implicates is the subject of intensive experimentation and theorizing
in the field of
 pragmatics.[7]



Grice used his technical term "implicature" for a way of
expressing a proposition by saying that something is the case. 
It is also common to express propositions by asking questions or
issuing imperatives (Geurts 2010: 32-3), to express attitudes and
other things that are not propositions by saying something (Braun
2011; Sullivan 2023: SSV), and to express things by not saying
something (Swanson 2017). While these acts do not count as
implicature as Grice defined his technical term, and are not the focus
of his theory (or this entry), they are similar in many important
ways.


## 2. Conversational and Conventional Implicature



The implicatures in
 (1)
 and
 (2)
 are *conversational*. They *depend on features of the
conversational context, and are not determined by the conventional
meaning of the sentences uttered*. A key feature in (1) was
Alan's question. Had he asked "What are you going to do
today?", Barb could have implicated something completely
different (that she is going to work) by saying the same thing (that
she has to work). Grice (1975: 25) contrasted a conversational
implicature with a *conventional* implicature, by which he
meant *one 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) is
the 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 therefore
brave, speakers implicate that being brave follows from being English.
They *imply* rather than *say* that being brave follows
from being English. In contrast, (3b) would rarely if ever be used to
implicate [3c]. The meaning of "therefore" generates the
implicature of (3a). Other words "triggering" conventional
implicatures are *but, even, too, still, yet, already, again, stop,
start, know,* and
 *regret*.[9]



While Grice's examples were triggered lexically, other
conventional implicatures are triggered syntactically. Speakers who
assert *Ravel, a Spaniard, wrote Spanish-style music* implicate
that Ravel was a Spaniard--they imply but do not say that Ravel
was a Spaniard. Hence their utterance is misleading but not a lie if
they know Ravel was French. The implicature is conventional in that it
is determined by the meaning of the sentence via the appositive
construction. Other constructions that generate conventional
implicatures are as-parentheticals (*as a Spaniard*) and
parenthetical relative clauses (*who was Spanish*).



As
 (1)
 illustrates, when a conversational implicature is false, the
speaker's statement is misleading. Barb's utterance would
nonetheless be linguistically flawless. Because [3c] is false, on the
other hand, the use of
 (3a)
 to make a statement is *infelicitous* and *improper* as
well as misleading. The truth of [3c] is a precondition of properly
using
 (3a)
 to assert what it says. Conventional implicatures like [3c] are
*presuppositions* in the non-technical sense in which the
question "Have you cheated again?" presupposes that you
cheated before. The question is inappropriate, and cannot be given a
straight "Yes" or "No" answer, unless you did
cheat before. For the same reason, the question *Is the queen
English and therefore brave?* is improper; answering either
"Yes" or "No" implies a connection between
being English and
 brave.[10]



Not all conventional implicatures are presuppositions in the same way.
For example, *Jack knows that 51 is prime* entails and
implicates that 51 is prime. So it is false and possibly a lie because
51 is not prime. Nevertheless, it is linguistically proper and
felicitous. That 51 is prime is an implicature because speakers
who use *Jack knows that 51 is prime* imply rather than say or
assert that 51 is prime; they imply it by saying that Jack knows 51 is
prime. In both cases, if *and that's a good (or
bad) thing* is added, *that* will refer to what is said but
not what is implicated (cf. Geurts 2010:
 6).[11]



Potts (2005: 35-6) claimed that *a sentence cannot be
used with its conventional meaning without implicating its
conventional
 implicatures.*[12] 
 While this is a natural way to interpret Grice's claim that
conventional implicatures are determined by sentence meaning, examples
like (4) show that it is too
 strong.[13]



(4)


a.
If the queen is English, and being brave follows from being
English, 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 a
conditional. But because
 (3c)
 is a conjunct of the antecedent of that conditional, (4a) itself does
not imply in any way that being brave follows from being English. A
speaker asserting [4a] does not say [3a] and does not mean [3c]. So
the speaker does not implicate that being brave follows from being
English. The antecedent of [4a] prevents the conversational
implicature of its consequent from "projecting". The
implicature triggered by the appositive in (4b) is not implicated for
a 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 mock
Trump's claim that he is a stable genius, the speaker does not
implicate that Trump is a stable genius. Indeed, he implicates the
very opposite. The meaning of a sentence determines its conventional
implicatures, but whether a speaker implicates them depends on how the
sentence is used. What does entail implicating a sentence's
conventional implicatures is using it *to assert what the sentence
means or expresses*. Doing that does not necessitate any
conversational implicatures. 



While Grice used "conventional" to denote an implicature
determined by linguistic meaning, W. Davis (1998: Chs. 5-6) and
Lepore & Stone (2015: Pt. II) argue that even conversational
implicatures can be conventional in the non-technical sense in which
it is conventional for women to wear a sari in India but not Mongolia,
and for German speakers to use *rot* to mean "red"
but not English
 speakers.[14]
 Conventions in this sense are common practices that serve a social
interest, perpetuate themselves in certain ways, and are arbitrary in
that other practices could have served the same purposes and
perpetuated themselves. New speakers pick up conventions from prior
speakers, often with no instruction. Consider (5):



(5)


a.
Some athletes smoke.
b.
Not all athletes smoke.



It would be unconventional (unusual, idiosyncratic, even
unprecedented) for people who say "Some athletes smoke" to
conversationally implicate that some physically fit people will
develop bladder cancer, but conventional (customary, normal, standard
practice) for them to implicate that not all athletes smoke. The
customary implicature is not conventional in Grice's sense,
though. For "Not all athletes smoke" is not determined by
the meaning of "Some athletes smoke". Speakers can and
often do say and assert
 (5a)[15]
while implicating something other than
 [5b],
 as
 (6)
 will illustrate. The practice of using sentences of the form
"Some *NP* *VP*" to mean "Not all
*NP VP*" is not a semantic or syntactic convention. It is
a *pragmatic* convention. To avoid confusion, I will describe
implicatures that are conventional in Grice's sense as
*semantic*. When not modified by "in Grice's
sense", "conventional" will have the broader sense
of
 *customary*.[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 generalized
implicatures as those that "would normally (in the absence of
special circumstances)" be carried by "the use of a
certain form of words". Levinson (2000: 11-12,
16-22, 42-46) characterized GCIs similarly as
"default inferences"--implicatures we normally and
automatically infer in the absence of evidence to the
 contrary.[17]
 These characterizations are too strong in one respect. There is
nothing 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 to
implicate
 [5b]
 in some contexts and
 [6a]
 in others shows that neither is the default, especially given that
figurative use with a variety of implicatures is also
a possibility (SS4). The same fact also shows that
neither is a conventional implicature in Grice's sense. Having
more than one GCI is compatible with them all being conventional in
the broad sense, though. The word *bank* has several meanings
in English, including "row", as in *bank of
switches*. So it is conventional to use *bank* to mean
"row", even though this cannot be described as its normal
or default use.



Following Grice (1975: 39), it is widely accepted that generalized
conversational implicatures differ from semantic implicatures in being
*cancelable,* 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, all
do" after uttering "Some athletes smoke".
Alternatively, the implicature may be cancelled implicitly by the
utterance context, as when it is obvious that the speaker is either
engaging in understatement or ignorant of further facts. An
actual implicature is cancelable if it could have been canceled. 
In example (1), Barb would not have implicated that she is not going
to Paul's party if she had added "But I might be able to
leave 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
 are *typically* 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 typically
connected to what is said rather than the way it is said, so that
"it is not possible to find another way of saying the same
thing, which simply lacks the implicature in question" (1975:
39). The implicature of
 (1)
 is thus said to be *nondetachable*. Grice allowed exceptions,
though, "where some special feature of the substituted version
is itself relevant to the determination of an implicature" (see
Grice's "maxim of Manner" in
 SS6).
 Metalinguistic implicatures--those that refer to the particular
words the speaker
 used[21]--are
 also detachable.



 (7) 
Harry: What is this
species of bird called in English?
  

Irene: This is a widgeon.


In example (7), Irene used "This is a widgeon" to
implicate that the English word for the species is
"widgeon". Had Irene used a German sentence with the same
meaning (*Dies ist eine Pfeife*) she would have said the same
thing while implicating something different (that it is called
"Pfeife"). Semantic implicatures, in contrast, are
nondetachable because they are determined by what the sentence
means.


## 3. Sentence Implicature



As we observed in
 SS1,
 Grice defined implicating as a form of speaker meaning. But Grice and
others nevertheless began applying "implicate" to
sentences, analogous to the way "imply",
"presuppose", and "mean" apply to sentences as
well as
 people.[22]
 If an implicature is conventional in either sense (that is, either
semantic or generalized), we may say that the *sentence*
implicates it, or has the
 implicature.[23]
 Even though Barb implicates that she is not going to Paul's
party, "I have to work" does not itself implicate this.
But "Some athletes smoke" implicates that not all do even
though speakers can use the sentence without implicating this.
(Analogy: *plane* means "airplane" even though
speakers can use *plane* without meaning
"airplane".) Similarly,
 (4b)
 implies that Trump is a stable genius even though speakers can use it
without implying that.



Whereas knowledge of what speakers implicate is essential to fully
understand speakers, knowledge of what sentences implicate is a
critical component of our knowledge of a language. This is obvious for
sentences with semantic implicatures like
 (3a).
 But speakers are not fully competent with "some" unless
they know that it is related to "all" in a way it is not
related 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 not
the case that several athletes smoke".


## 4. Common Forms of Conversational Implicature



Many forms of conversational implicature occur frequently in everyday
speech and literature, with a wide variety of sentences and in all
known languages. They are common ways of both using and understanding
language. The forms are differentiated in part by the relationship
between what is said and what is implicated. Knowledge of them is an
important component of our linguistic competence, and is acquired at
an early
 age.[24]



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



Figurative speech is *non-literal*: users generally do not mean
what they say, and expect their audience to recognize that. (Litotes
is an exception.) Don did not mean that the weather is lovely. 
The obvious falsity of what is said is a typical clue that speech is
figurative. Some figures also tend to be marked intonationally,
including irony and hyperbole. Others are not, including metaphor and
understatement. They are all used to make speech lively, interesting,
and stylish
 (SS10).



Many forms of implicature are not figures of speech, and have become
widely recognized only since Grice (1975).
 (1)
 illustrates *relevance implicature*: the speaker implicates an
answer to an expressed or implied question by stating something
related to it by implication or explanation.
 [5b]
 is a *quantity* (or *scalar*) implicature: the speaker
implicates the denial of a proposition stronger than the one said.
 (6)
 illustrates *ignorance implicature*: the speaker implicates
that something stronger than what was said is unknown.
 (7)
 illustrates *metalinguistic implicature*: the speaker
implicates that something has a certain name by using that name to
describe it. These "modes of speech" (non-figurative forms of
implicature) are not taught in school, and names for them are not in
general use. Nevertheless, they are as frequent and natural as
figurative speech, and are learned at the same time. Modes of speech
are not marked intonationally, and the speech is literal. They are not
used to make speech or writing lively. Speakers do not intend what
they say to be obviously false, and generally do mean what they
say.



Two modes of speech do have common names. One is *damning with
faint praise*. Grice's example has become classic:



> 
> 
> A is writing a testimonial about a pupil who is a candidate for a
> philosophy job, and his letter reads as follows: "Dear Sir, Mr.
> X's command of English is excellent, and his attendance at
> tutorials has been regular. Yours, etc". (Grice 1975: 33)
> 
> 
> 



By saying so little, A implicated that Mr. X is a poor candidate for
the job. The other named mode is *loose use*, or *speaking
loosely*, illustrated by (8):



 (8) 
Linda: When will
dinner be served?
  

Mike: At six o'clock.


If Mike's response is typical, what he meant is only that dinner
will be served *close enough to six o'clock for current
purposes*. That would be typically be true if dinner will be
served at 6:01. What Mike said, though, is that dinner will be served
at 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 swimmer
touched the wall in the final lap of an Olympic event, 6:01 may not be
close enough.



The figures and modes of speech are common, socially useful practices.
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 either interpret speakers in new contexts, or to
predict what hearers will understand. The forms are less arbitrary
than lexical or syntactic conventions, but no one has to implicate
rather than say things, or use one form of implicature rather than
others.



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


## 5. Pragmatics and Semantics



As our examples make clear, *semantics*, conceived as the study
of the meaning of words and sentences, does not exhaust the study of
meaning. The study of speaker meaning and implicature is included in
*pragmatics*, which covers the broad range of speech acts
performed by using words and sentences. *Applied pragmatics*
arose from the recognition that second language learners cannot become
fully proficient without mastering more than grammar and literal
meaning (Kasper 2003; Zufferey et al 2019: Ch. 9). *Forensic
pragmatics* studies the use of pragmatics in law enforcement
and the courts (Solan & Tiersma 2005; Zufferey et al.
2019: SS4.4). *Clinical pragmatics* studies
communication disorders that arise from failure to master pragmatic
rules (Cummings 2009, 2014; Graci 2023). *Formal pragmatics*
uses formal models of utterances, contexts, and discourse to state
precise rules specifying the interpretation of an utterance in a
context, including what is both said and implicated (Roberts 2006;
Rothschild 2013).



The phenomenon of Gricean conventional implicature
 (SS2)
 shows further that standard truth-conditional semantics does not
exhaust semantics (Barker 2003). For example, *Ravel, a Spaniard,
wrote Spanish-style music* and *Ravel was a Spaniard and wrote
Spanish-style music* have the same entailments. Yet they differ in
meaning in such a way that the former but not the latter is
infelicitous and improper because Ravel was French.
"False" clearly applies to the latter but not clearly to
the former.



Implicature is important even in truth-conditional semantics. For
example, logicians customarily take sentences of the form
"*p* or *q*" to be true provided
"*p*" or "*q*" *or both*
are true. Thus "It is not the case that cats meow or purr"
would be counted as false. But there are also cases in which speakers
use "*p* or *q*" to mean that
"*p*" or "*q*" is true *but
not both.* This would be the natural way to interpret someone who
said "John is going to invite Mary or Jane to the prom".
Some maintain that "or" is *ambiguous* in English,
with an inclusive and an exclusive sense. But another possibility is
that the exclusive interpretation is a generalized conversational
implicature. One piece of evidence supporting the implicature
hypothesis is that the exclusive interpretation seems cancelable. Thus
"Jane will visit France or Germany this summer; indeed, she will
drive through both on her way to Poland" has no contradictory
interpretation. Some evidence against the implicature hypothesis is
that after "p or q," *or both* does not seem any more
redundant than *but not both*. A methodological issue is
to describe the evidence necessary to decide whether a particular
interpretation is a sense or a generalized conversational implicature.
A foundational issue to is describe exactly what the difference
consists in.



Implicature continues to be invoked in this way to defend
controversial semantic claims:


* *Knowledge*. The standard of justification necessary to
claim knowledge varies from context to context depending on what is at
stake and salient. On contextualist theories, sentences of the form
"*S* knows *p*" are indexical, with
different truth conditions in different contexts (S. Cohen 1986, Lewis
1996, DeRose 2009). An alternative theory is that "*S*
knows *p*" has a strict invariant semantics, but is used
loosely to implicate that *S* is close enough to knowing for
the purposes of the context (W. Davis 2007b). Another is that
"*S* knows *p*" has a weak invariant
semantics but its negation is used to implicate that contextually
relevant alternatives cannot be ruled out (Rysiew 2001; Brown 2006;
Hazlett 2007). Others argue that implicatures cannot account for
the data (Blome-Tillman 2013b; Dinges 2018;
 2021).[26]
* *Names*. The Millian theory that the meaning of a name is
its referent entails that coreferential names are synonymous, and that
names without a referent are meaningless. This seems untenable in
light of names like "Superman" and "Clark
Kent". Millians have proposed that the source of these
linguistic intuitions is a difference in implicature (Salmon 1986;
Soames 1989). One hypothesis invokes metalinguistic implicature,
noting that "Clark Kent can fly" implicates that a man
called "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 false
as "Lois Lane believes Clark Kent can fly".
* *Negation*. On the regular interpretation of (9) below,
"some" is equivalent to "any", and the whole
sentence is contradictory:



(9)  The boy
did 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 the
cookies", and is thus consistent. The question is how to account
for 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 the
marked interpretation of (9) is an implicature. W. Davis (2016: Ch. 6)
argues that it is an idiom that plausibly evolved from a generalized
conversational implicature. Soria-Ruiz (2023) proposes a
neo-Stalnakerian account.



Implicature plays a well-attested diachronic role in
grammaticalization and the origin of new meanings and
 idioms.[28]
 For example, metaphors have a typical life cycle: 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 few decades,
originally denoting a biological organism that spreads from host to
host, now having another meaning on which it denotes computer programs
that spread from computer to computer in a similar fashion. When a
dead metaphor has syntactic structure like *go viral*, it is an
*idiom*. When metaphors become widespread and
self-perpetuating, but are not yet idioms, they generate generalized
conversational
 implicatures.[29]


## 6. Gricean Theory



In addition to identifying the phenomenon of implicature, and
classifying its types, Grice developed a theory designed to explain
and predict conversational implicatures and to describe how they are
understood. Grice (1975: 26-30) postulated a general
*Cooperative Principle* and four *maxims* specifying how
to be cooperative. It is common knowledge, he asserted, that people
generally follow these rules for efficient communication.



* **Cooperative Principle.** Contribute what is required by
the accepted purpose of the conversation.
* *Maxim of Quality.* Make your contribution true; so do not
convey what you believe false or
 unjustified.[30]
* *Maxim of Quantity.* Be as informative as required.
* *Maxim of Relation.* Be relevant.
* *Maxim of Manner.* Be perspicuous; so avoid obscurity and
ambiguity, and strive for brevity and order.




Grice viewed these not as arbitrary conventions, but as instances of
general rules governing rational, cooperative behavior. For example,
if Jane is helping Kelly build a house, she will hand Kelly a hammer
rather than a tennis racket (relevance), more than one nail when
several are needed (quantity), and straight nails rather than bent
ones (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 have
infringed this maxim unless her contribution were relevant to the
purpose of the conversation. If Barb was being cooperative, then she
was trying to answer Alan's question. Given that working is
incompatible with partying, it is inferred that Barb must have
intended to communicate that she is not going to the party. Grice
(1975: 34) thought other implicatures arise by *flouting*
maxims. This happens when what a cooperative speaker says so patently
violates a maxim that the hearer must infer that the speaker means
something different. Irony is thought to arise from flouting the maxim
of Quality
 (SS9).



Generalizing from such examples, Grice provided a theoretical account
of conversational implicature that has been widely
 adopted.[31]
 A representative formulation goes as follows, with *S* the
speaker and *H* the hearer.




**Theoretical Definition:** *S* conversationally
implicates *p* iff *S* implicates *p* when:


1. *S* is presumed to be observing the Cooperative Principle
(*Cooperative Presumption*);
2. The supposition that *S* believes *p* is required to
make *S*'s utterance consistent with the Cooperative
Principle (*Determinacy*); and
3. *S* believes (or knows), and expects *H* to believe
that *S* believes, that *H* is able to determine that
(ii) is true (*Mutual Knowledge*).




This says that an implicature is conversational provided conditions
(i)-(iii) are satisfied, where (ii) is the condition that
*S*'s *believing* *p* is required for
*S* to be in conformity with the Cooperative Principle. The
Theoretical Definition does not entail that *S implicated p* is
inferable from (i)-(iii). Calculability does that.




**Calculability**: Conversational implicatures must be
capable of being worked
 out.[32]




Grice's calculability principle says more than that hearers are
generally able to infer what speakers implicate on the basis of the
linguistic meaning of what they utter. That would not be distinctive
of implicature given that the same is true of what people
 say.[33]
 To *work out* an implicature is to infer it in a specific way
from the Cooperative Principle using particular facts about the
meaning 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 conventional
> meaning of the words used, together with the identity of any
> references that may be involved; (2) the Cooperative Principle and its
> maxims; (3) the context, linguistic or otherwise, of the utterance;
> (4) other items of background knowledge; and (5) the fact (or supposed
> fact) that all relevant items falling under the previous headings are
> available to both participants and both participants know or assume
> this to be the case. A general pattern for the working-out of a
> conversational implicature might be given as follows: *He has said
> that q; there is no reason to suppose that he is not observing the
> maxims, or at least the Cooperative Principle [Cooperative
> Presumption]; he could not be doing this unless he thought that
> *p* [Determinacy]; he knows (and knows that I know that he
> knows) that I can see that the supposition that he thinks that
> *p* is required [Mutual Knowledge]; he has done nothing to stop
> me thinking that *p*; he intends me to think, or is at least
> willing to allow me to think, that *p*; and so he has
> implicated that *p**. (Grice 1975: 31; my emphasis
> and 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 an
implicature depends on the Cooperative Presumption, Determinacy, and
Mutual Knowledge conditions, and that the implicature can be inferred
in part from their satisfaction, Grice claimed that the conditions
*give rise* *to* or *generate* the implicatures.
The implicatures *exist* *because* conditions
(i)-(iii) are
 satisfied.[35]
 From his assumption that conversational implicatures can be explained
and predicted on the basis of the Cooperative Principle, Grice drew a
methodological conclusion:




**Grice's Razor**: Other things equal, it is
preferable to postulate conversational implicatures rather than
senses, semantic implicatures, or semantic presuppositions because
conversational implicatures can be derived from independently
motivated psycho-social
 principles.[36]




The pithy formulation is "Senses are not to be multiplied beyond
necessity", alluding to Ockham. If a phenomenon can be explained
and predicted in terms of psycho-social principles, then it is
theoretically more economical to do so than to posit senses and the
like, which cannot be so explained. Grice's Razor is often
invoked to support classifying the exclusive interpretation of
"*p* or *q*" as an implicature rather than
as a second sense
 (SS5).



Following Grice, "conversational implicature" was defined
in
 SS2
 to mean *an implicature that depends on features of the
conversational context and is not determined by the conventional
meaning of the sentence uttered*. On this definition,
Grice's Theoretical Definition and Calculability are empirical
hypotheses that may turn out to be false. Indeed, we will review
evidence against these hypotheses below. Many linguists and
philosophers, however, take Calculability to be true by definition.
They take "conversational implicature" to mean *an
implicature that can be worked out from what is said and the
Cooperative Principle or its
 maxims*.[37]
 If this definition is adopted, then what the evidence would show is
that the implicatures illustrated in
 SSSS1-4
 are not conversational, even those that are not conventional in
Grice's sense (cf. Lepore & Stone 2015: 6, 83, 148).


## 7. Theoretical Difficulties



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



According to Grice's Theoretical Definition
 (SS6),
 conversational implicatures depend on a presumption that the speaker
is observing the Cooperative Principle. W. Davis (1998: SS2.5)
notes, however, that speakers can engage in implicature when there is
no conversation. All the figures and modes of speech can appear in
private journals or in manuscripts that have little hope of being
read.
 [38]



The Cooperative Principle further assumes that the participants in
every conversation strive only to achieve common goals. From the
perspective of social psychology, evolutionary biology, and game
theory, Pinker (2007) and Asher & Lascarides (2013)
observe that pure cooperation is generally an unrealistic
idealization or naive assumption. Conversations are often among
adversaries, whose goals beyond communication are opposed. It would be
foolhardy and possibly dangerous for an interrogator to presume that a
prisoner of war or terrorism suspect is being cooperative. Even when
participants are friends or relatives, they often have some divergent
goals, and may give priority to other principles
 (SS10).
 To the extent that they diverge, the speaker's goals may be
promoted and the hearer's goals thwarted by withholding
information, providing misinformation, going off on a tangent, or
being obscure. Even when it is correctly presumed that a speaker is
not being cooperative, the speaker may use all the figures and modes
of speech. If the prosecuting attorney asks the defendant whether he
was in the bank on the day of the robbery, the defendant might answer
"I took my mother to the hospital that day", thereby
implicating that he was not at the bank. He may do this in the hope of
misleading the jury as well as the prosecutor. The official purpose of
the conversation is to get at the truth, the whole truth, and nothing
but 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: SS11.3). Because the goal is not to provide
information, the maxims of Quality, Quantity, and Relation do not
apply. If for any of these reasons the Cooperative Principle does not
apply, reasoning based on it will be *unsound*.


## 8. Overgeneration



Many have observed that for every implicature that appears to be
correctly predicted by Gricean theory, others appear to be falsely
 predicted.[39]
 The schema used to "work out" observed implicatures can
usually be used just as well to work out nonexistent implicatures. So
the schema as formulated is *invalid*--an unreliable
method of inferring implicatures. By a simple application of
Mill's Methods, it follows that the observed implicatures do not
exist *because of* the Gricean factors.



We will illustrate using the case that has been most extensively
studied, and is generally considered a paradigm application of Gricean
theory: the derivation of quantity implicatures from the maxim of
Quantity. 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 the
> semantically stronger sentence held. Consequently, he believes that
> the semantically stronger statement does not hold. Furthermore, he has
> not 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 statement
*S* does not make is "All athletes smoke". There
are countless relevant statements more informative than what S said,
however, whose negations were not implicated, including *Several
athletes smoke, Some athletes smoke regularly, I know some athletes
smoke,* and *13% of all athletes smoke*. The Gricean
reasoning could be repeated using any of these stronger statements,
with fallacious results. For example:



> 
> 
> *S* said "Some athletes smoke". If *S* were
> in a position to assert the stronger statement "Several athletes
> smoke" but did not, *S* would be in a breach of the maxim
> of Quantity unless *S* wished to convey that it does not hold.
> So *S* implicated that it is not the case that several athletes
> smoke.
> 
> 
> 



But speakers who utter sentences of the form "Some *S*
are *P*" rarely if ever implicate the denial of
"Several *S* are
 *P*".[41]
 Among the infinity of statements stronger than "Some athletes
smoke", "All athletes smoke" is highly unusual in
that people commonly implicate its denial. Since the derivations have
the same form whether or not their conclusions are observed to be
true, Lepore & Stone (2015: 143ff) call this the
"symmetry"
 problem.[42]
 The Gricean derivation seems plausible only because we knew
antecedently that the conclusion is true.



An irony underscoring the *ex post facto* character of the
Gricean calculation is that Grice himself derived an
*ignorance* implicature from the maxim of Quantity.



> 
> 
> A is planning with B an itinerary for a holiday in France. Both know
> that A wants to see his friend C, if to do so would not involve too
> great 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 answer
> is, as he well knows, less informative than is required to meet
> A's needs. This infringement of the first maxim of Quantity can
> be explained only by the supposition that B is aware that to be more
> informative would be to say something that infringed the second maxim
> of Quality. "Don't say what you lack adequate evidence
> for", so B implicates that he does not know in which town C
> lives.) (Grice 1975: 32-33; example number
>  deleted)[43]
> 
> 
> 



It is plausible that B would have implicated this. But if
Grice's reasoning is valid, why shouldn't Huang conclude
that speakers uttering "Some athletes smoke" implicate
*they do not know whether all athletes smoke* (an ignorance
implicature)? If Huang's reasoning is valid, why
shouldn't Grice conclude that B implicated *C does not live
in the southernmost part of France* (a scalar implicature)? 



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


## 9. Failures of Determinacy



Grice's Determinacy condition states that *S*
conversationally implicates *p* only if *S* has to
believe (and implicate) *p* if *S*'s utterance is
to be consistent with the Cooperative Principle. Determinacy is a key
premise in the working-out schema, so Calculability depends on it. As
 SS8
 illustrated, however, there are normally many alternative ways to be
cooperative, and contribute what is required by the conversation, even
when the meanings and referents of the words used are taken as
given.



Grice believed irony involves flouting Quality. Here is Grice's
oft-repeated "gloss" applied to
 (2),
 in which Don said "The weather's lovely" during a
blizzard.



> 
> 
> It is perfectly obvious to Don and his audience (Carla) that what Don
> has said is something he does not believe, and the audience knows that
> Don knows that is obvious to the audience. So ... Don 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. (After
> Grice 1975:
>  34).[44]
> 
> 
> 



While irony often involves saying something obviously false, it need
not have been obvious to Carla in
 (2)
 that Don believed the weather was unlovely. She may have had no
independent source of information about his weather. Don would also
have made a suitable contribution to the conversation if he had meant
and believed that the weather is lovely. So Determinacy is unsatisfied
in irony when the speaker could have been speaking literally,
believing what was said (W. Davis 1998: SS3.3; see even Grice
1978: 53).



Many have observed that the obvious falsity of what speakers say may
signal that they mean something else, but it does not tell us what
else they mean (e.g., Levinson 1983: 157-8; Lepore & Stone
2015: 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 which
figure of speech Don is using. He would have made a suitable
contribution to the conversation if he had been engaging in metaphor
instead of irony, meaning and believing that relations between he and
his 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 Iraq
the way it lost in Vietnam? That the reasons for going to war in Iraq
were as misguided as those that got the U.S. into Vietnam? Or did she
perhaps mean that even though the U.S. did not secure all its
objectives, the Iraq war was still worth fighting? She could mean and
believe any of these things and still be making a useful contribution.
Lepore & Stone (2015: Ch. 10) describe such metaphors as inviting
hearers to imagine all the things the speaker might have meant. Grice
(1975: 39-40) himself acknowledged such cases when he said
that



> 
> 
> there may be many possible specific explanations ... ; and if the
> list of these is open, the implicatum will have just the kind of
> indeterminacy 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 defined *normatively*, as
*properly* implicating something. W. Davis (2007a) replied that
while determinacy is more plausible as a norm, similar considerations
show that it is not required even for properly meaning one thing by
saying something else. For example, a speaker who says "I ate
some of the cookies" could properly be meaning either "I
ate them all" (engaging in understatement), or "I did not
eat them all" (quantity implicature), or "I do not know
whether I ate them all" (ignorance implicature). None of these
contributions is required given that all would be appropriate.



Rysiew (2000: 577-8) suggested weakening the determinacy
condition by replacing "*has* to believe (and implicate)
*p*" with "*is likely* to believe (and
implicate) *p*". As he notes, hearers commonly use
abduction to figure out what speakers have implicated (cf. Hobbs et
al. 1993; Geurts 2010: 34-5). Abduction is a specific form of
inductive or non-demonstrative reasoning in which a hypothesis is
inferred to be true from the fact that it provides the best
explanation of the data. By their nature, non-demonstrative methods
are not guaranteed to succeed. This fact of life is no reason to shun
induction when seeking to discover implicatures. W. Davis (1998:
66-8) had observed, though, that an implicature can exist and be
conversational even though the available evidence does not make that
implicature (or belief) more likely than others. The problems of
indeterminacy and overgeneration show, in particular, that the Gricean
hypotheses provide neither the only nor the best explanations of the
data, making the inferences fallacious instances of abductive
reasoning.


## 10. Conflicting Principles



Grice (1975: 30) recognized that his maxims may "clash".
When they do, there is no way to determine what is required for
conformity to the Cooperative Principle. In the case of irony, for
example, Manner clashes with Quality. When Don said "The
weather's lovely", we cannot interpret him as meaning what
he said because on that interpretation he would be violating Quality.
But we cannot interpret him as meaning the opposite because then he
would be violating Manner (Wilson & Sperber 2012: 18-9). It
is more perspicuous to explicitly state something than to implicate
it.



We use irony and other figures in part because we have conversational
goals other than the efficient communication of information (Lakoff
1977; Sainsbury 1984: 427-9). We observe not only the
Cooperative Principle, but also the Principle of Style.




**Principle of Style**: Be stylish, so be beautiful,
distinctive, entertaining, and interesting.




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



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




**Principle of Politeness**: Be polite, so be tactful,
respectful, generous, praising, modest, deferential, and
sympathetic.




Speakers frequently withhold information that would be offensive or
disappointing to the hearer, violating Quantity. Speakers often
exaggerate in order to please or flatter, and utter "white
lies" in order to spare the hearer's feelings, violating
Quality. People pick "safe topics" (e.g., the weather) to
stress agreement and communicate an interest in maintaining good
relations, violating Relation. Euphemisms avoid mentioning the
unmentionable, but in the process violate Manner.



One common motive for implicating something is that it is often
perceived to be more polite than asserting it (Pinker 2007; Huang
2014: 142; Haugh 2015: 2). In case
 (1),
 Barb may have answered Alan's question indirectly because she
thinks it is less likely to hurt his feelings, even if she realizes he
will assume that is what she is doing.



Blome-Tillmann (2013a: 177) has suggested that problems such as
overgeneration and conflicting principles can be avoided by
understanding calculability not as a way of predicting and explaining
implicatures, but merely as providing a criterion for them. But
if a criterion always gives false positives (overgeneration) or false
negatives (indeterminacy), or cannot be applied (due to clashes), then
it is not a useful criterion.


## 11. Neo-Gricean Pragmatics



Prominent linguists have sought to improve on Grice's
formulation of the conversational principles, and provide a solution
to the problem of clashes. Horn (2004: SS4) replaces Quantity,
Relevance, and Manner with two interrelated
 principles.[48]




**Q Principle**: Say as much as you can [given Quality
and R].



**R Principle**: Say no more than you must [given Q].




Levinson (2000: 76, 114, 137) adopts similar principles, which he
calls "Q" and "I" (for
 "Informativeness").[49]
 Since Horn believes that interpretations like [10a] are derivable
from the R-principle, he calls them "R-based
implicatures". The assumption is that there is no reason to make
a stronger statement (say more) if the extra information can be
contributed by implicature. Implicature [11b] is similarly described
as "Q-based". The assumption is that if the speaker did
not make a stronger statement (say more), its denial was
implicated.



(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 of
meaning and interpretation. Critics maintain, however, that
Horn's two principles provide no reason to expect the two
indicated interpretations rather than those we do not observe (Lepore
& Stone 2015: SS3.1; W. Davis 2016: SS4.7). They ask how Q
can predict [11b] without predicting [10b], and how [10a] can be
derivable from R if [11a] is not. What in R predicts [10a] rather than
other strengthenings, such as "He broke someone else's
finger"?
 [50]



Horn goes on to formulate what he calls the **Division of
Pragmatic Labor**:



> 
> 
> Given two expressions covering the same semantic ground, a relatively
> unmarked form--briefer and/or more lexicalized--tends to be
> R-associated with a particular unmarked, stereotypical meaning, use,
> or situation, while the use of the periphrastic or less lexicalized
> expression, typically more complex or prolix, tends to be Q-restricted
> to those situations outside the stereotype, for which the unmarked
> expression 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 the
machine in the usual way. ("R-based implicature")
 b.  She did
not 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 is
difficult to see how either implicature could be derived from Q or R,
which refer to *what* is said, not *how* it is said.
(Recall Grice's nondetachability criterion.) Levinson (2000:
136-7) therefore reinstated a version of
 Manner.[51]




**M Principle**: Indicate abnormal, nonstereotypical
situations by using marked expressions that contrast with those you
would use to describe the corresponding normal, stereotypical
situations.




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



Horn sometimes describes Q and R as "antinomic forces"
(e.g., Horn 2004: 14), which would be appropriate if the bracketed
conditions were omitted. Without the conditions, Horn's
principles would clash as often as
 Grice's.[52]
 Without independent means of determining antecedently which force
will "prevail" in a given case, Horn's principles
would lack predictive or explanatory value. Lepore & Stone (2015:
SS3.1) suggest treating Horn's principles as
"simultaneous equations", constraining but not determining
the conversational implicatures. But this assumes the equations have a
solution. Not all simultaneous equations do.



Levinson (2000: 157-64) sought to avoid clashes by stating an
order of precedence: Q > M > R. Huang (2014: 49) reverses the
ordering, saying that



> 
> 
> the R-principle generally takes precedence until the use of a
> contrastive linguistic form induces a Q-implicature to the
> non-applicability of the pertinent R-implicature....
> 
> 
> 



Such orderings make sense only if the bracketed clauses in Q and R are
omitted. W. Davis (2016: 159) responds that Levinson's ordering
makes it is hard to see why
 (10)
 or
 (12)
 should have an R implicature rather than a Q implicature, while
Huang'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 factors
> might be involved in assessments of degrees of relevance. We have also
> argued that all Grice's maxims can be replaced by a single
> principle of relevance--that the speaker tries to be as relevant
> as possible in the circumstances--which, when suitably
> elaborated, can handle the full range of data that Grice's
> maxims were designed to explain. (Wilson & Sperber 1986: 381)
> 
> 
> 



"Relevance" is given a highly technical sense, in which
the relevance of a proposition in a context is directly related to how
many positive cognitive effects it has and inversely related to how
much effort is required to process it (Wilson & Sperber 2012: 6,
62-3,
 219).[55]
 "Positive cognitive effects" are "improvements in
knowledge", including "true contextual implications, or
warranted strengthenings or weakenings of existing assumptions".
Contextual implications are propositions logically implied by the
proposition and the cognitive context together but from neither alone.
Propositions or assumptions are objects of belief or
knowledge--cognitive representations. Wilson and Sperber
illustrate their concept by imagining a doctor whose choice of true
statements 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 grounds
that it entails everything [14a] does and more, while being as easy to
process; [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 the
effort are equal between alternative contributions. To know what is
maximally relevant in other cases, a particular function of effects
and effort must be specified (Hinkelman 1987). Sperber and Wilson
specify one when describing the theory of cognition on which they
ground their theory of communication. "Our claim is that all
human beings automatically aim at the most efficient information
processing possible" (Sperber & Wilson 1986a: 49).
"Efficiency in cognition ... involves processing inputs
that offer the best possible cost/benefit ratio at the
time"(Wilson & Sperber 2012:
 62).[57]
 Selecting this function and formulating a principle in the style of
Grice's yields:




**Principle of Maximal Relevance (Cognitive
Efficiency)**: Contribute that which has the maximum ratio of
positive cognitive effects to processing
 cost.[58]




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



While Grice's maxims enjoin the speaker to contribute the
required information and do so perspicuously and briefly, they do not
require the speaker to maximize information, perspicuity, or brevity
when other things are equal. For example, Grice's maxims do not
predict that Barb implicated *I am not going anywhere* in
 (1)
 even though it is more informative than *I am not going to
Peter'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 that
program". The speaker would normally be engaging in
understatement, implicating "The program will be very
expensive". Relevance theorists account for this by saying that
because the proposition explicitly conveyed is trivial, and thus has
few positive cognitive effects, the hearer will "recover"
the more informative
 proposition.[59]
 Critics respond that countless propositions are more informative than
the one implicated, such as "The program will cost
trillions", and seem as easy to process.
 [60]



Conversely, Maximal Relevance does not imply or subsume Grice's
principles. For instance, nothing guarantees that the contribution
with the most positive cognitive effects per unit processing cost is
germane to the topic of the conversation or as informative as required
(less informative contributions might have more positive cognitive
effects per unit processing cost). As a result, Maximal Relevance does
not predict what Barb implicated in example
 (1).
 The proposition *I am not going to Peter's party* will
have different effects than *I am not going to Paul's
party*, but seems as easy to process and could well have as many
positive cognitive
 effects.[61]
 Only the proposition about Paul is relevant in the ordinary sense to
what Alan asked, but this does not entail that it is maximally
relevant in the technical sense of Relevance
 theory.[62]



Sperber and Wilson observe that Gricean theory provides no explanation
for 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 saying
what he means would seem easier to process and thus more efficient.
Wilson & Sperber (2004: 621) think saying something in order to
mean the opposite would be "patently irrational". Adler
(1987: 710) observed, however, that it need not be irrational given
how readily hearers recognize when speakers do so. Moreover, speakers
engaging in irony are doing more than meaning the opposite of what
they said. As Grice (1978: 53-4) later recognized, they are also
pretending to mean and assert what they
 said,[64]
 and are expressing more than disbelief of what is said. Sperber and
Wilson call it a "dissociative attitude--wry, skeptical,
bitter, or
 mocking".[65]
 Hearers readily recognize and commonly enjoy the performance of this
complex speech act. The observation that irony involves expressing a
dissociative attitude does not lessen the theoretical problem,
however. There is no reason to think, for example, that "The
weather is terrible and anyone who thinks it lovely is foolish"
has the maximum effects/cost ratio. Processing just what Don actually
said (that the weather is lovely) would seem to require even less
effort; so that proposition could conceivably have a greater
effect/cost ratio. And there is no reason to think an ironic
interpretation has a greater effect/cost ratio than a hyperbolic or
meiotic interpretation. If expressing a dissociative attitude involves
something other than expressing a proposition, as seems plausible (cf.
M. S. Green 2018: SS5), it would not be a positive cognitive
effect as defined, and thus would not affect the relevance ratio. For
reasons such as these, Levinson (1989: 463-4) charged that the
accounts offered by Relevance theorists are as *ex post facto*
as Gricean accounts.



The explanations of loose use offered by Relevance theorists are
problematic in another way. In
 (8),
 where Mike said "Dinner will be at six", they explain why
Mike did not say something true like "Dinner will be at six or
shortly after" by saying that the strictly false statement has
the same positive cognitive effects but is easier to process and so
more
 relevant.[66]
 But that would erroneously imply that Mike did not *mean* and
*implicate* that dinner will be at six or shortly after.
Another reason the explanation is unsatisfactory is that there are
other things Mike did not say with the same positive contextual
effects that seem as easy to process as "Dinner will be
*at* six". including "Dinner will be
*around* six". This proposition has some true cognitive
effects that "Dinner will be at six" lacks, including
"Dinner may not be exactly at six".



The recital example in
 SS10
 illustrates one reason why Relevance theories adopt Optimal rather
than Maximal Relevance (Wilson & Sperber 2012: 64-5):



> 
> 
> the communicator is manifestly limited by her own abilities (to
> provide appropriate information, and to present it in the most
> efficient way). Nor can she be expected to go against her own
> preferences (e.g., against the goal she wants to achieve in
> communicating, or the rules of etiquette she wishes to follow).
> 
> 
> 



However:



> 
> 
> Since it is also manifest that the audience will tend to pay
> appropriate attention only to an utterance that seems relevant enough,
> it is manifest that the communicator wants her audience to assume that
> the utterance is indeed relevant enough. There is thus a minimal level
> of relevance that the audience is encouraged to expect: the utterance
> should be relevant enough to be worth the effort needed for
> comprehension.
> 
> 
> 


Relevance theorists thus propose that every utterance conveys a
presumption 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 the
communicator's abilities and
 preferences.[67]
 


Because of its preference provision, Optimal Relevance does not clash
with Politeness and Style the way Maximal Relevance does. The parents
may say "Your performance wasn't perfect" rather
than "It was horrendous" because they strongly prefer not
to hurt their daughter's
 feelings.[68]
 This means, however, that Optimal Relevance would not predict that
Barb meant *I am not going to Paul's party* in
 (1)
 even if it is relevant enough to process and more relevant than the
other alternatives. For Barb might have preferred to dodge
Alan's question. In
 (2),
 Don may have preferred an ironic utterance to ones with higher E/C
ratios (Millikan 1987: 725).



We are focusing on Relevance theory as an alternative attempt to
predict and explain what speakers implicate. The main focus of
Relevance theorists, however, is the process by which hearers
*interpret* utterances. The hearer's aim, on their view,
is "to find an interpretation of the speaker's meaning
that satisfies the presumption of optimal relevance". They infer
that the hearer "should follow a path of least effort, and stop
at the first overall interpretation that satisfies his expectations of
relevance" (Wilson & Sperber 2012: 7). It is unclear how to
reconcile this with requirement that the optimally relevant utterance
be the most relevant one compatible with the communicator's
abilities and preferences.



The ratio of positive cognitive effects to processing cost is zero
when there are no positive cognitive effects at all. Given the
definition of contextual implication, any proposition that is part of
the cognitive context has no contextual implications. So both Maximal
and Optimal Relevance seem to imply that speakers cannot mean or
implicate anything already known, and must mean something else. Gerrig
(1987: 718) and McCawley (1987: 724) find this implausible. If A and B
are walking in torrential rain, A might well say "It is raining
really hard", stating the obvious, and B might respond
"There is indeed some rain coming down", engaging in
understatement 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 speaker
might say or implicate will have infinitely many true contextual
implications if it has
 any.[70]
 We do not know whether processing cost is measured by time, mental
effort, electro-chemical energy, inferential steps, or some function
of them all. We have no unit of measurement for mental effort, and do
not yet know how to measure the energy consumed in processing an
utterance. If relevance is not well defined and knowable, it cannot be
used to account for specific implicatures.


## 13. Explicature and Impliciture



As observed in
 SS1,
 Grice (1975: 24) introduced the technical term
"implicature" to denote either (i) the act of meaning or
implying one thing by saying something else, or (ii) what the speaker
meant or implied. Grice (1975: 87ff) used "say" quite
strictly, requiring what a speaker says to be closely related to what
the sentence uttered means on that occasion. Indexicals provide cases
in which what a speaker says is not what the sentence used means. When
Barb uttered "I have to work" in
 (1),
 she said that she, Barb, has to work; but the sentence she used does
not 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. The
infinitive 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 term
*explicature* to mean what is "explicitly
communicated". 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 not
going 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, a
speaker would typically use (15a) "Alice jumped" to mean
that Alice jumped *off the cliff* [15b]. Carston counts this an
explicature. It does resemble ellipsis, but a speaker who used (15a)
to mean that Alice jumped up to the rescue helicopter *said the
same thing* while meaning something different. And if the speaker
knew that Alice jumped up to safety, the speaker might be accused of
misleading the hearer but not of lying.



Carston's (1988: 45; 2004a: 646-8) most influential
argument is based on what are commonly called "embedded
implicatures". She would claim that if "Alice jumped off
the cliff" were an implicature of "Alice jumped",
then we should not understand (16a) and (16b) as having the same truth
conditions. Yet we do, Carston believes. The alleged implicature seems
to fall within the scope of the logical operator. Yet it cannot given
the definition of implicature
 (SS1).[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: SS5.3) replies as follows. A speaker who used
 (15a)
 to mean
 [15b]
 would just as naturally use (16a) to mean [16b], and hearers would
understand the speaker accordingly. But what the speaker *said*
is not entailed by [16b]. What the speaker of (16a) said would be
false in circumstances in which Alice was unlikely to jump off the
cliff if she jumped. Hearers would focus on what the speaker meant,
though, which would be true even in those circumstances. Since the
speaker meant one thing [16b] by saying something else [16a], the
speaker implicates [16b]. The speaker cannot implicate anything by
uttering the antecedent of (16a) because the speaker does not say
anything by uttering the antecedent, only by uttering the whole
conditional. 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 "If *p* then
*r*" does not implicate "If *p* and
*q* then *r*". For example, *If Bill got some
problems wrong, he might have gotten them all wrong* does not
implicate "If Bill got some but not all problems wrong, he might
have gotten them all wrong".



A lively debate between Relevance theorists and neo-Griceans concerns
numerical 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 with
Carston that (17) itself is unambiguous. But whereas the neo-Griceans
hold that (17) means [17a] rather than [17b], Carston (1988:
46-7) maintains that (17) means neither but can be used to say
both. So the neo-Griceans hold that (17) always says [17a] while
sometimes implicating [17b]. Carston holds that (17) is sometimes used
to explicate [17a] and sometimes [17b]; neither is an implicature. The
thesis that sentence meaning leaves open what is said to this extent
is called *semantic underdetermination*.



While still doubting that Carston's view can fully account for
cardinals, Horn (1989: 250-1; 2010: 314-5) now concludes
that they do not behave like quantifiers. For example, if you know
that everyone passed, you must answer "Did some students
pass?" with "Yes". But if you know that Peter has
two children, you cannot answer "Does Peter have one
child?" without knowing whether the speaker meant "at
least" or "exactly". Indeed, a case can be made that
(17) is ambiguous, so that Neo-Gricean and Relevance accounts are both
wrong (W. Davis 2016: SS7.3).



Following Sperber & Wilson (1986a: 182), Carston (2004b: 635)
later defines an explicature as a development of a logical form
encoded by the sentence uttered, and an implicature as any proposition
communicated by an utterance that is not an
 explicature.[73]
 The technical terms "development" and "logical
form" are understood in such a way that [15b] is a development
of [15a]. Thus understood, "explicature" covers much more
than what is said, and "implicature" covers much less than
what is implicated as defined in
 SS1.



Bach (1994: 160) uses "say" even more strictly than Grice,
meaning "strictly, literally, *and explicitly*
say". Since the speaker of
 (15a)
 did not *explicitly say*
[15b],
 Bach counts "The speaker said that Alice jumped off the
cliff" 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 term *impliciture* (with "i"
rather than "a" after soft "c") to cover such
cases. Bach restricts "implicature" to cases in which what
is meant is "completely separate" from what is said.



A thesis attributed to Grice is that what *S* says is
determined by "decoding", while what *S*
conversationally implicates is determined by what *S* says
together 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 out
what is said, such as reference identification and ambiguity
resolution, "involve exactly those inferential mechanisms that
characterize Gricean
 pragmatics".[74]
 Grice never talked about decoding however, and observed himself that
conversational principles are involved in determining what is said
(Grice 1957: 222). For example, if an ambiguous term is used, we
naturally assume--in the absence of specific
counterevidence--that the intended meaning is the one relevant to
the conversation. In a discussion of snow, "There is a large
bank on Main Street" is naturally interpreted as referring to a
snow bank.



There is no circle on Grice's view because what is said is the
conclusion of one pragmatic inference, and is one of the premises in a
further pragmatic inference to what is
 implicated.[75]
 The process is serial rather than parallel, although later
conclusions may always lead to adjustment of earlier conclusions.


## 14. Speaker Implicature and Intention



W. Davis (2016: Ch. 2) describes ways of explaining and inferring
conversational implicatures that do not rely on conversational
principles. The methods he proposes for speaker implicature are
described in this section and for sentence implicature in the
next.



For a speaker to implicate something is for the speaker to mean
something by saying something else
 (SS1).
 It is generally agreed that what a speaker means is determined by the
speaker's *intentions*. When Steve utters "Kathryn
is a Russian teacher", whether Steve means that Kathryn is a
teacher of Russian nationality or a teacher of the Russian language,
and whether he is speaking literally or ironically, depends entirely
on what Steve intends to convey. What "convey" means
precisely is controversial, but is an independent
 issue.[76]



We most commonly explain why people do *A* with the intention
of doing *B* by explaining why they believe they will do
*B* by doing *A*, or why they want to do *B*. We
can explain why speakers intend to convey a thought by uttering a
sentence that says something else in the same ways. Why do speakers
believe they can convey thoughts by means of the various figures and
modes of speech identified in
 SS4?
 One reason is that they have seen others doing so. Knowledge of the
common forms of implicature is acquired along with knowledge of the
semantics and syntax of our native language. Speakers pick up figures
and modes of speech from other speakers, as they learn vocabulary and
grammar. After speakers have become proficient, their own past success
in using figures and modes of speech is a reason for them to believe
they will succeed again. 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 do not depend on a particular
language, they can be used with any language.



Why do speakers want to engage in implicature? The main reasons are
the reasons speakers make statements: to communicate, express
themselves, and record their thoughts. These goals may serve to
cooperate with others, or to oppose them. What goals are served by
implicating 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 uttering
just one sentence. Another is to mislead without lying (Horn 2010:
SS4; 2017; Zufferey et al. 2019: 77-84). People often wish others
to believe things that are false, and not only in situations of
conflict and competition. And they nearly always prefer misleading to
 lying.[77]
 The greater deniability of implicature, and the fact that it enables
us to veil our intentions, are often motivating factors (Brown &
Levinson 1978: 137; Pinker 2007; Camp 2022). We observed in
 SS10
 how implicature promotes the goals of style and politeness.



It should also be recognized that people perform many even highly
skilled actions automatically, spontaneously, or habitually. Such
actions are done without deliberation or conscious planning. What
speakers implicate as well as what they say commonly falls in this
category.



Given that speaker meaning is a matter of speaker intention, it
follows that speaker implicatures can be recognized or predicted by
the methods we use to infer intentions from behavior, including
abduction, analogy, and testimony. In example
 (2),
 Carla may suspect that Don means the weather is bad because irony is
a common linguistic device
 (SS4),
 and Don has been ironic in similar situations before. Don's
intonation may be a clue. On the other hand, if Don rarely speaks
figuratively when reporting in, Carla may infer that he meant what he
 said.[78]



Conversational principles can play the same indirect role in
implicature recognition that known tendencies or goals play in
inductive inference generally. Since speakers commonly observe the
Cooperative Principle, and hearers know this in a vague and tacit sort
of way, hearers tend to assume that particular speakers are
cooperating, in the absence of evidence to the contrary. If the
hypothesis that Barb means she is not going to Paul's party in
 example (1)
 fits better with the assumption that she is being cooperative than
the hypothesis that she is not answering the question, Alan may by
abduction infer she is implicating that. Further support for the
hypothesis may be provided by the recollection that other speakers
have implicated similar things in similar circumstances before. The
fact that relevance implicature is a common practice thus provides
analogical evidence
 (SS4).
 Recognition of an unconventional form of implicature is more
difficult, but no harder than recognizing when a speaker is using a
sentence with an unconventional meaning. As Sterelny (1982:
192-3) observed, knowledge of the particular speaker is
ultimately more important than knowledge of non-universal
generalizations.



When *S* is being uncooperative, we have to use other
generalizations or analogies. We are familiar with the ways defendants
manipulate language in an effort to avoid self-incrimination.


## 15. Sentence Implicature and Convention



Whereas what a speaker implicates depends on the particular
speaker's intentions, what a sentence implicates on
Davis's theory depends on the conventions of the community of
speakers who use the language. To know or explain sentence
implicatures is to know or explain the relevant conventions. This is
as true of generalized conversational implicatures as it is of
implicatures that are conventional in Grice's sense
(SS2).



When Grice talked about conventional implicatures he was referring to
*semantic* implicatures, like [3c]. These exist because of
conventions that give individual words or syntactic structures their
meanings. *The queen is English and therefore brave* implicates
"Being brave follows from being English" because it is
conventional for English speakers to use "therefore" with
a certain meaning, which determines the implicature. A
*conversational* sentence implicature is not determined by the
meaning of the sentence used, even when sentences with the same form
are conventionally used with that implicature. It is a second-order
convention: a convention to use a sentence of a given form with an
implicature that is not part of its meaning. The common modes and
figures of speech are also second-order conventions, but not
restricted to sentences with a particular form. A language is defined
by first-order lexical and syntactic conventions, not by second-order
implicature conventions. In this respect conversational implicature
conventions are like naming conventions, word formation rules,
intonation rules, speech act rituals (e.g., saying "This is
*N*" when answering a telephone), and indirect speech act
conventions (e.g., asking "Can I get an *N*?" to
request an
 *N*).[79]
 Second-order conventions are not as arbitrary, though, because there
is always some antecedent relation between what the sentence means and
the implicature that makes it natural to use one to convey the other.
Implicature conventions promote style, politeness, and efficiency as
well as communication.



Like other second-order linguistic conventions, conversational
implicature conventions differ in their cross-linguistic spread.
Whereas the quantity implicature of "some" has been found
in all observed languages (Horn 1989), common metaphors differ as much
from language to language as the idioms that evolve from them do. The
fact that regularities in implicature obtain cross-linguistically is
compatible with their being arbitrary and conventional. Witness the
practice of using "?" and rising intonation to mark
questions. Why some implicatures are common to more languages than
others is an open question on any view. To the extent that
implicatures are conventional, it is a question for historical
linguistics.



Knowledge of sentence implicatures is a crucial component of
linguistic
 competence.[80]
 Speakers 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. Hearers without
such knowledge are likely to either misinterpret or fail to fully
understand the speaker. Sentence implicatures, both semantic and
conversational, resemble idioms and figures of speech 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 as sentence meanings do. Recent metaphors
are special in being picked up by adults, and are liable to become
idioms if they pass on to new generations.



An impressive body of research has attempted to discern general
regularities in the multitude of conversational implicature
conventions associated with a language. Wierzbicka (2003) has studied
how implicature conventions reflect broader "cultural
scripts". Others study how the implicatures of a sentence are
related to the implicatures of compound sentences in which the
sentence is embedded (Gazdar 1979; Levinson 2000: SS2.5.1;
Sauerland & Stateva 2007)--the question raised by example
 (16).



The most influential work on conversational implicature conventions
describes "Horn
 scales".[81]
 Horn (1972, 1989) observed that the quantifiers *all, most, many,
some* form a scale with the following properties. Instances of
"\_\_\_ *S* are *P*" with one term entail
instances with any term to the right, but not to the left; the terms
are thus ordered by logical strength. Moreover, the result of
substituting one term implicates the denial of the result of
substituting any term to the left, but not to the right. In the
negative context "It is not the case that \_\_\_ *S* are
*P*", the logical and pragmatic relations are reversed.
Other Horn scales are <*necessarily, actually,
possibly*> , <*certainly, probably,
possibly*> , and <*must, should, may*> . Horn
(1989: SS4.5) correlates the existence of scales with the absence
of certain lexical items, such as a quantifier meaning "not
 all".[82]
 Levinson (2000: 156) looked for a generalization that would cover
these cases but not scales like <Over *90%, over 10%,
some*>  which have the same logical relations as Horn scales
but not the pragmatic relations. One generalization is that the items
on a Horn scale are widely and frequently used monolexemes. A
companion problem is to explain why some common monolexemes with
similar logical relations lack the pragmatic relations, as
*several* illustrates. Given the conventional nature of
generalized conversational implicatures, there may be no systematic
("synchronic") explanation. All languages are
"irregular" to some extent. For example, the regular
pattern for adjectives in English is that of *tall, taller,
tallest*. But there are exceptions, such as *good, 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. This
entry, regrettably, had to ignore many valuable contributions.