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Conversational Implicature

Being an excursion into the philosophy of language, with particular emphasis on problems arising in the context of belief ascription

Executive summary

Implicature is an idea in the philosophy of language due to H.P. Grice (1975). Its purpose is to formalize a particular way of resolving certain seeming paradoxes which arise when one thinks carefully about verbal communication. In particular, philosophers who seek to answer questions such as "what is meaning?" must confront the reality that sometimes the information or message conveyed by an utterance differs from the meaning of the utterance. Grice's notion of conversational implicature is a framework for analyzing such situations based on the idea that participants in a conversation abide by a certain set of unwritten rules which govern the transmission of information via speech. Here we explain Grice's idea and how it can resolve certain puzzles about the communication of beliefs.

For more information on implicature in general, especially as it fits into linguistics, see Gritchka's excellent writeup there.

Introduction and Statement of the Problem

In the course of preparing for a picnic in the countryside, Jill asks Jack about the weather. Perhaps Jack has recently checked a forecast, or has looked outside the window a few minutes ago. In response to Jill's inquiry, Jack might reply with either of the following two sentences.

(1) I don't believe that the sun is shining.

(2) I believe that the sun is not shining.

Certainly, if Jack utters (2), then insofar as Jill trusts Jack's knowledge of the weather and the accuracy of his report concerning his belief, she will be dismayed about the prospects of enjoying their picnic. But what if Jack utters (1)? Strictly speaking, (1) and (2) seem to express different propositions, say π1 and &pi2. And yet intuition suggests that in appropriate circumstances Jack could use either sentence to communicate to Jill the same information concerning his knowledge of the weather. In particular, Jack's utterance of (1), in addition to simply expressing or meaning π1, somehow "conveys" π2 as well. Problem: How does it do so?

In the following, we will be concerned with analyzing the mechanism of such conveyance, as well as related examples. After clarifying the the problem they present, we'll see that a class of belief ascriptions like (2) can be derived as Gricean conversational implicatures from negated belief ascriptions like (1).

Preliminary Analysis of the Problem

In this section we take up some preliminary questions about the problem as stated above. First the distinction between the propositions π1 and π2 expressed by the example sentences will be clarified. Then we will consider which elements of the example are essential for the problem it raises.

Negation and belief ascriptions

As a first order of business, we should remind our readers that the propositions π1 and π2 expressed by (1) and (2) respectively are actually distinct. (Which is good, insofar as it keeps philosophers off welfare: otherwise our "problem" simply evaporates!) This requires only a careful consideration of how negation interacts with contexts that involve belief ascriptions. Sentences (1) and (2) are instances of sentence schemata (S1) and (S2) below, respectively, where x is some agent and q is some proposition:

(S1) x does not believe q.

(S2) x  believes ~q.

If B(x,q) is a two-place predicate representing the proposition that x believes q, then a sentence conforming to schema (S1) expresses the proposition π1 = ~B(x,q), while a sentence conforming to schema (S1) expresses the proposition π2 = B(x,~q). These propositions are neither formally identical nor tautologically equivalent to one another. Indeed, if x has no evidence of any sort for either q or ~q, then if x is reasonable, x should believe neither q nor ~q. Although quite possibly he should believe (q v ~q).... Hence in such a situation ~~B(x,q) ^ ~B(x,~q) is true, so neither π1 nor π2 logically entails the other.

Essential features of the example

Secure in the knowledge that there really is something to explain, we now briefly consider which features of the example (1)-(2) are essential to the problem that arises.

Philosophical alarm bells should go off whenever a sentence ascribing somebody a particular state of mind - such as a belief - occurs in the first person, because each speaker has privileged access to her own mental experience. So it would be comforting to know that the question of how Jack conveys the meaning of (2) by saying (1) does not hinge upon the fact that these sentences express his own beliefs (as opposed to someone else's). Fortunately, it probably doesn't. Consider two residents of Los Angeles, Hank and Harold, discussing the possibility of a terrorist strike on L.A. in the near future. Speaking of a mutual acquaintance Hannah, who works for the CIA and would be in a position to know about such things, Hank might say either of the following sentences.

(3) Hannah does not believe there will be a terrorist attack tomorrow.

(4) Hannah believes there will not be a terrorist attack tomorrow.

A moment's reflection should convince the reader that (3)-(4) raise much the same problem as (1)-(2). This suggests that the first-person verbs used by Jack are inessential features of the problem under consideration.

Note that the terrorist example also points out another inessential feature of the original weather example: namely, that the object propositions "the sun is shining" and "the sun is not shining" might not be construed as genuine negations of one another. (What if it's partly cloudy?) For "there will be a terrorist attack tomorrow" and "there will not be a terrorist attack tomorrow" certainly are the negations of one another, as evinced by the fact that conjoining the two yields obviously self-contradictory nonsense.

Finally, we can also identify the belief ascriptions in (1)-(2) and (3)-(4) as potentially essential features of the examples. For there are other two-place predicates F(x,p) such as "If G(x) then p" which do not seem to share the problematic nature of the belief predicate. This can be seen from the following pair of sentences.

(5) It is not the case that, if rain falls on our heads 
    then we will not have fun at our picnic.

(6) If rain falls on our heads then we will have fun at our picnic.

Here G(x) = "x falls on our heads", x = "rain", and p = "we will not have fun at our picnic". (The slightly awkward phrasing is just to make this example parallel B(x,p) for object x and proposition p, as above.) By construction, (5)-(6) are structurally analogous to (1)-(2) and (3)-(4), but lack belief ascriptions. In addition, it seems clear that an utterance of (5) in no way conveys the proposition expressed by (6). For even if it is possible that rain won't ruin the picnic, it is still possible that it will!

This discussion has highlighted a few features which a successful and general explanation of the problematic phenomena under consideration should take into account. It has also given us a few examples to test a potential theory.

Conversational Implicatures and How to Detect Them

We now describe Grice's framework for analyzing when certain sentences convey propositions other than their meanings. We also describe Grice's diagnostics for detecting whether his theory is applicable to the problem at hand.


Grice draws a distinction between what an utterance of a sentence S says and what it implicates. A speaker's utterance of S says a proposition π if and only if π is the proposition expressed by the utterance - what Grice calls the "conventional meaning" of S. We will take this notion for granted in our discussion, and refer to what an utterance says as its assertion. In contrast, an utterance of S implicates a proposition π' if and only if the utterance conveys π' without saying π'. That is, π' is not the utterance's assertion, but a listener would still conclude π' if the speaker says S. The sense of "S implicates π'" coincides with the manner in which we used "S conveys π'" in introducing the problematic example at the beginning of this paper. Thus, in precisely the problematic way we hope to explain, sentences (1) and (3) implicate the propositions expressed by sentences (2) and (4) respectively.

Grice identifies a number of ways an utterance of S can implicate π'. For instance, the gestures and tone of voice that accompany the utterance in question might indicate π'. If I utter the sentence, "That was a funny joke" while whipping my hand over my head, my assertion is that the joke is funny, but my implicatum is that in fact, I could not understand the joke at all (it was over my head). In other cases, it may be part of the meaning of S that the speaker commits himself to π' whenever he utters S. For example, the implicatum of the sentence may be a necessary condition for the use of S. In this case the implicatum would be "contained in" the meaning of S, in the sense of "meaning" as "general directions for use" (see the Strawson reference for an explanation of this sense). This sort of implicature is called conventional. However, Grice is primarily concerned with a special class of non-conventional implicatures which he calls conversational.

Conversational implicature

The notion of a conversational implicature is predicated upon the assumption that in many forms of discourse, speakers observe a fundamental law of conversation, the Cooperative Principle. This states (Grice, p. 45): Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged. Adhering to this principle, by Grice's lights, involves following four maxims:

  1. Quantity: Make your conversational contribution just as informative as is required.
  2. Quality: Do not say what you believe to be false, or lack adequate evidence for.
  3. Relation: Be relevant.
  4. Manner: Avoid obscurity and ambiguity; be brief and orderly.

In certain circumstances, a speaker x can conversationally implicate a proposition π' by an utterance of S that asserts &pi', if the listener y can infer &pi' from π plus the assumption that x is adhering to the maxims above. The additional requirements are (a) that y can figure out that π' is required to make x's utterance consistent with adherence to the maxims, and (b) that x thinks y can figure this out (consciously or intuitively).

A classic example of a conversational implicature is that when x utters "either p or q" he often implicates "not both p and q" -- in symbols, he asserts p v q but implicates ~(p ^ q). To work this out, the listener calculates as follows. Since x asserted p v q he is in a position to know p v q, by the maxim of Quality; granted this, x would very likely be in a position to know p ^ q if it were true. Moreover, if indeed p ^ q were true, then according the maxim of Quantity x should say "p and q" since it expresses a proposition which logically entails the proposition expressed by "either p or q", and is thus more informative. (This implicitly assumes that asserting "p and q" would not violate the maxim of Relation; i.e. that p ^ q would be relevant since p v q is.) Since x did not say "p and q" it must therefore be the case that p ^ q is false, so x has implicated ~(p ^ q). For a more detailed discussion of the Conversational Principle and the associated Maxims, the reader is referred to Grice's original article (1975). In particular, the question of when one or more maxim is violated must be considered.

Tests for conversational implicature

Conversational implicatures, Grice argues, have several essential properties, which can serve as diagnostics for detecting an implicature in a particular case. First, conversational implicatures must be cancelable, in the sense that whether by context or by an explicit clause, the speaker may opt out of the Cooperative Principle, and thereby invalidate any Gricean derivation of an implicature. (Provided the listener is aware that the speaker has opted out, there are no valid assumptions about adherence to the conversational maxims from which to derive the implicature!) Thus if Hannah the CIA agent says "Some reports about potential terrorist threats against L.A. have been falsified" it is arguable that she implicates "Not all reports have been falsified" - but if she adds "but I can say no more" then she cancels the implicature, opting out of her commitment to make her conversational contributions maximally informative.

A second test for conversational implicature is non-detachability, the property whereby the implicatum is linked to the meaning of the utterance, rather than to the sentence (sign) itself. That is, another sentence S' which expresses the same proposition π that S expresses, should produce the same conversational implicatures π' that S produces. In the Davis article in the references, it is noted that non-detachability is not an entirely untendentious feature of conversational implicatures, and even Grice himself seems to have recognized exceptions to this rule. We will disregard such issues here, however.

Next, as was discussed above, conversational implicatures are non-conventional, so that they are not contained in the meaning of the uttered sentence which creates the implicature. Roughly, it is the fact of saying the proposition π asserted by S - as opposed to some other proposition - which produces a conversational implicature π'; but π itself does not produce or entail π'. Accordingly "the truth of a conversational implicatum is not required by the truth of what is said" (Grice 1975, p. 58).

Finally, perhaps the most crucial test for a conversational implicature is that it must be calculable; the listener must be able to work it out. While we presumably do these calculations in some subconscious way, if there does not exist a derivation of the implicatum (such as the way in which ~(p ^ q) was derived from "p or q") then, according to Grice, the implicature is not conversational. That is, it is not a product of the Cooperative Principle and the associated conversational maxims.

Negation-Implicated Belief Ascriptions

In this section we subject the implicated propositions in our example (1)-(2) to Grice's tests, and then present a Gricean derivation of these propositions as conversational implicata. In this sense, it follows that Grice's theory solves the problem of describing the mechanism of implicature in the example: that mechanism is Jill's assumption as listener that the speaker Jack is adhering to the Cooperative Principle.

Grice's diagnostics

First, is the implicature of (2) by (1) cancelable? It seems arguable that it is. If Jack and Jill have just quarrelled, perhaps Jack does not want to go on the picnic at all, and stubbornly intends for his conversational contribution to be as unhelpful as possible. In this situation, he might utter \eqref{belnegsun} without \textit{any} knowledge of the weather, just to confuse Jill with his uninformative and ambiguous statement. As a bonus, provided that he does not, in fact, believe the sun to be shining, the sentence \eqref{belnegsun} is not even a lie! Jill should probably find a new life-partner, but in any case this scenario suggests that the implicature is cancelable.

As evidence for the non-detachibility of (2), consider that the sentence

(1') I don't believe the weather is fine.

is a distinct sign from (1), but is almost identical in meaning, and still seems to implicate the proposition expressed by (2), to wit "I believe the sun is not shining."

Lastly, it was discussed above that the proposition expressed by (2) is distinct from and logically independent of that expressed by (1). Moreover, it does not seem that the implicatum is a necessary condition for uttering (1), for it would be perfectly correct for Jack to utter (1) if asked to introspect about weather-beliefs he does not have and to report one of them. In other words, (1) means just that Jack does not believe the sun is shining, and uttering it does not entail the proposition expressed by (2). The implicature only arises from Jack's uttering (1) in the context of his and Jill's cooperative talk exchange in the course of their picnic preparations; in other words, not from (1) itself. That is, the implicature is non-conventional.

Derivation of the implicature

Without further ado, we now propose a Gricean derivation of (2) from (1); this will prove that the implicature is calculable, and thus provide strong evidence that it is indeed a conversational implicature, and therefore stems from the Cooperative Principle. The derivation is indirect: we will show that sentence (1) conversationally implicates a proposition π4, and that the conjunction of this implicatum and the proposition π1 expressed by (1) logically entails the proposition π2 expressed by (2). Recall from above that

(1) I don't believe the sun is shining.

(spoken by Jack to Jill) expresses the proposition π1 = ~B(j, p) where j = Jack, p = "the sun is shining", and B(x,q) is the two-place predicate "x believes q". The desired implicatum is π2 = B(j, ~p), expressed by sentence (2). The proposition π3 = ~B(j,p) ^ ~B(j, ~p) logically entails π1, and could be expressed by the sentence "I don't know whether the sun is shining," or equivalently, "I don't believe the sun is shining and I don't believe it is not shining." If Jack's lack of belief that p is relevant, presumably his lack of belief that ~p is also relevant. Therefore, by the maxim of Quantity, if π3 were true, Jack should have uttered a sentence that asserted it. In informal terms, which are reassuringly intuitive in this case, all we have said is that it is conversationally inappropriate for Jack to assert (1) if in fact he has no belief concerning whether or not the sun is shining. Since Jack did not assert π3, it must be false, and we may therefore conclude that Jack has implicated 3, which is logically equivalent to π4 = B(j,p) v B(j,~p). Finally, Jack asserted π4 = ~B(j, p), and the conjunction π1 ^ π4 logically entails π2. Hence Jack has conversationally implicated π2.

It seems clear that the above discussion extends to the terrorist attack example (3)-(4) immdiately. In fact, the derivation above is sufficiently general to apply to most instances in which propositions π expressed by instances of sentence schema (S2) are implicated by utterances of instances S of sentence schema (S1). It therefore seems appropriate to give these implicatures a name: let us call them negation-implicated belief ascriptions, since in each case the implicatum is a belief ascription, and the sentence which creates the implicature is the negation of a belief ascription.


We have seen that a certain class of implicatures, in which ascription of belief that p is conveyed by negated ascription of belief that ~p, can be derived as Gricean conversational implicatures. Not only does such a derivation exist, these implicatures seem to satisfy all of Grice's tests for conversational implicature. Thus, Grice's theory accounts for such implicatures as consequences of the assumption by the listener in a cooperative talk exchange that the speaker is adhering to the Cooperative Principle and the associated conversational maxims. As a final thought, it would be interesting to explore whether the Gricean framework also accounts for a broader class of implicata involving propositional attitudes. For instance, if Jack asserts that he does not desire p, does he implicate that he desires ~p? Can ascriptions of beliefs arise as implicata from contexts other than the negations of ascriptions of belief in their negations? We must defer these questions to another place and time.


Wayne Davis, "Implicature." The Stanford Encyclopedia of Philosophy (2005). Online at http://plato.stanford.edu/entries/implicature.

Richard P. Grandy and Richard Warner, "Paul Grice." The Stanford Encyclopedia of Philosophy (2006). Online at http://plato.stanford.edu/entries/grice/.

H.P. Grice, "Logic and Conversation." In Cole, Peter and Jerry Morgan, eds., Syntax and Semantics 3: Speech Acts. New York, Academic Press (1975): 41-58.

P. F. Strawson, "On Referring." Mind, New Series, Vol. 59, No. 235 (Jul., 1950), pp. 320-344. Accessed Online via JSTOR.

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