I begin by introducing two implicature-related Moorean phenomena. Consider the following cases of implicature (I use ‘⇝’ to mean ‘conversationally implicates’):

The phenomena in question involve the cancellation behavior of implicatures. It is well-known that implicatures can be cancelled by explicitly denying them. The implicatures in (1) and (2) can be cancelled as follows (I use ‘⇝̸’ to mean ‘does not conversationally implicate’):

What is less often noted is that implicatures can also be cancelled by denials of knowledge or belief:

In examples (5) through (8), denials of knowledge or belief cancel the implicature. For instance, in (6), Bob cannot be taken to mean that this particular wine is cheap when he explicitly denies knowledge of that implicature. The implicature is thus cancelled. But why would denials of knowledge and belief cancel implicatures? There is something analogous here to Moore’s paradox. Consider the difference between the following:

Asserting either one of (9) or (10) results in infelicity. It’s easy to explain why we find (9) infelicitous: it’s a contradiction. The infelicity of (10) is trickier to explain: it is consistent—both conjuncts could be true—but it sounds in some way inconsistent. This is Moore’s paradox. The KNA explanation of it goes as follows: Since there is a knowledge norm of assertion, in asserting the first conjunct of (10), one commits oneself to knowing that it’s raining, which is inconsistent with what one asserts with the second conjunct. So (10) involves an inconsistency as well. It’s not a logical or semantic inconsistency, but a pragmatic one: an inconsistency between what one is committed to and what one asserts.

There is a similar difference between the cancellations in (3) and (6), reproduced here:

The cancellation in (11) is easy to explain: there is a contradiction between the putative implicature of the first conjunct and the second conjunct. The cancellation in (12), on the other hand, is more similar to Moore’s paradox. The putative implicature and the asserted second conjunct are consistent—both could be true—but the implicature disappears as if it were inconsistent with the asserted content. This can be explained along the lines of the KNA explanation of Moore’s paradox: By implicating p, one commits oneself to knowing p, and if one asserts that one does not know p, that assertion is inconsistent with what one would be committed to if one were to implicate p. Since in the case of conflict between assertion and implicature the implicature is always cancelled (as standard cases of denial such as (11) show), any putative implicature is cancelled when knowledge of it is denied.

The key point here is that by implicating p one takes a commitment to knowing p. This commitment comes about because of a knowledge norm for implicature: An epistemically permissible implicature requires knowledge. Cancellation by denial of belief is explained by KNI in a similar way, on the assumption that knowledge entails belief.

The second phenomenon is that it is impossible to convey a Moorean implicature of the form “p and I don’t believe p” or “p and I don’t know p”. Consider the following two exchanges, where the context is that Ann is hosting a party in her apartment, to which Bob has just arrived:

Bob’s reply in (13) conveys a relevance implicature: it implies that Carlos is coming—that’s how his reply is relevant to Ann’s question. Bob’s reply in (14) conveys a quantity implicature: it implies that Bob doesn’t know whether Carlos is coming, for otherwise he would have given a more informative reply. Importantly, if Bob’s answer is instead a conjunction of his answers in (13) and (14), the conjunction of the implicatures of (13) and (14) is not conveyed:

More generally, if an utterance conveys the implicature that p, adding something like “and it might be that p”, which implicates ignorance of whether p, removes the p implicature. It seems, then, that the Moorean proposition “p and I don’t know if p” cannot be implicated. But why is that? The knowledge norm of assertion only explains why such a proposition is not assertible, not why it cannot be conveyed as an implicature. The knowledge norm of implicature, in contrast, can explain this. By implicating p, one commits oneself to knowing it. By implicating “I don’t know if p”, one implicates a contradiction of that commitment. Since contradictions at the level of implicature simply result in cancellation, one of the conjuncts is ultimately cancelled.¹³

Assertions can be challenged. If one asserts p, a typically appropriate reply is to ask “How do you know that?”. Such replies often constitute challenges, because if the speaker concedes that she doesn’t, after all, know that p, the original assertion will have thereby been retracted, or at least not accepted by the hearer.¹⁴ For instance:

Once Ann pleads ignorance, her assertion is no longer part of the conversational common ground. Otherwise, maintaining her assertion while denying knowledge of it would result in Moorean infelicity.

If implicature has a knowledge norm, we should expect to find a similar pattern. We should expect, that is, two things: (a) when one implicates p with some utterance, it is generally appropriate to reply: “How do you know p?”; (b) when the speaker admits to not knowing p, the implicature is thereby retracted.¹⁵

This is exactly what we find. Consider:

Ann’s replies to Bob seem appropriate. It would be odd if Bob responded to those questions with “What does that have to do with what I said?”. It is clear how Ann’s challenges are relevant: in each case Bob implicates a proposition that Ann may not immediately accept, and she wants to know whether she should accept it. Moreover, if Bob responds by admitting that he doesn’t possess knowledge of the implicated proposition, the implicature is thereby retracted:

Challenges to implicature are not limited to imaginary cases. Here are two real-world examples:¹⁶

It’s important to note that we shouldn’t expect it to be appropriate to reply “How do you know?” to an implicature in every case, for two reasons. First, in some cases it is clear how the speaker knows, so the question is not appropriate. The same applies to assertion: if a speaker asserts that she lives in New York, asking “How do you know that?” seems odd. Second, in many cases speakers implicate not p but something weaker, such as “probably p” or “maybe p”. For instance, if Ann asks Bob whether Carlos is coming to the party and Bob replies: “Well, he has a lot of work”, the implicature is most plausibly that Carlos is probably not coming. In that case, it’s inappropriate to reply “How do you know he’s not coming?”, just as it would be to so reply to an assertion that Carlos is probably not coming.

Some arguments for a knowledge norm of assertion appeal to intuitions about cases in which the speaker has a true belief that p that is strongly supported by the evidence, yet does not know p. In such cases, it seems impermissible for the speaker to flat out assert p. For instance, suppose Ann has a lottery ticket and the draw has been held, but neither Ann nor Bob knows the result. Bob then asserts to Ann:

Bob’s assertion in (23) seems impermissible if Bob doesn’t know it to be true. That’s so even if he believes it, it’s highly probable on his evidence, and it is in fact true. Perhaps he should assert instead that the ticket probably lost, or that it’s almost certain that it did, but the flat out assertion that it lost seems inappropriate. The intuitive badness of lottery assertions has been taken to support KNA.¹⁹

If (23) seems bad to assert, it also seems bad if merely implicated. Consider:

Here Bob does not assert, but clearly conveys the implicature that Ann’s ticket lost.²⁰ Bob’s utterance in (24) seems just as epistemically inappropriate as the assertion in (23). If Ann finds out that Bob was ignorant of the actual result, she may criticize him for what he said. In both (23) and (24) it would be appropriate for her to later reply “You shouldn’t have said that”. Again, it might be appropriate to imply that the ticket probably or even almost certainly lost—perhaps by saying “don’t get your hopes up”—but implicating that the ticket in fact lost when the speaker lacks that knowledge sounds inappropriate. If so, and given that the badness (23) is evidence for a knowledge norm of assertion, the badness of (24) is evidence for a knowledge norm of implicature.

There is a more general pattern here. Speakers who assert without knowledge may be criticized for making such assertions. This is part of what happens in the lottery case. But speakers who convey implicatures without knowledge are just as criticizable. Here is an example from the wild. During the first weeks of the COVID-19 pandemic, President Donald Trump tweeted: “[President Xi] will be successful, especially as the weather starts to warm & the virus hopefully becomes weaker, and then gone.” Trump was later criticized for implying that the virus was seasonal and could be affected by warm weather, while there was no scientific consensus that any such thing was true.²¹ The criticism seems appropriate if indeed Trump lacked such knowledge. But what is criticized is not an assertion but an implicature—and it is clear why it is criticized: such an implicature conveys information to the audience, and conveying information without knowledge is epistemically inappropriate.²² Similarly, if a speaker is criticizable for asserting that it’s raining, she would seem just as criticizable if she said “Better take an umbrella”, implicating rather than asserting that it’s raining. More generally, then, implicatures seem criticizable in the same way that assertions do.

Granted, since implicatures are not explicit, speakers may in some cases plausibly deny that they intended to convey them to avoid criticism. But this does not tell against a knowledge norm for implicature. What the speaker denies is irrelevant—there’s a fact as to whether there was an implicature, and if there was one that was made while lacking the relevant knowledge, the speaker has done something impermissible. Implicatures are harder to detect than assertions, and speakers can take advantage of that. But this only means that violating the epistemic norm of implicature may be easier to get away with—it does not mean that there is no such norm.

Before moving on, let us consider a number of objections to the thesis that epistemically permissible implicature requires knowledge.

The first is that some implicatures don’t have determinate propositional content, and so cannot be the objects of a propositional attitude such as knowing. Consider Grice’s famous example:

There is clearly something that B implicates, but there may not be any particular proposition that is implicated. What does KNI say here? If it renders the implicature epistemically impermissible because it does not convey knowable content, it seems to deliver the wrong verdict for a broad class of implicatures. If it does not apply to such implicatures, then it’s not clear to what it does apply, since we don’t have a principled distinction between determinate and indeterminate implicatures.²³

In reply, I do not deny that some implicatures may be indeterminate. But let me note a few points. First, this is a problem for any plausible view that allows for some epistemic norm for implicature, as such views will require some propositional attitude or property such as belief, truth, evidence, and so on. And there are grounds to think that implicature has at least some such norm, for there seems to be something improper about conveying false or disbelieved implicatures.²⁴ Second, as Buchanan (2010; 2013) argues, there are reasons to think that not all assertions have determinate contents either. One can assert “each dish is almost ready” such that there is nothing in the relevant context that is sufficient to fully determine a particular proposition that is being expressed. If Buchanan is right, accounts of the norm of assertion are susceptible to the same problem. But this should not deter us from theorizing about the normativity of assertion. Third, there are ways of dealing with the indeterminacy problem. For instance, Buchanan (2010; 2013) argues that an indeterminate assertion or implicature conveys a proposition-type, which is an open-ended set of propositions.²⁵ KNI can be modified to specify a requirement with respect to such contents. For instance, the speaker might be required to know at least one proposition of a given proposition-type.²⁶ Developing such an account in full will take us too far afield, but I hope this suffices to see that such an account is possible. Finally, even if we take KNI to apply only to contexts where a speaker determinately implicates a proposition, a main thesis of this paper—that the KK thesis is supported by the knowledge norms of assertion and implicature—still stands, because it relies only on claims about determinate implicatures: that speakers who assert p implicate that they know p, and that this implicature is subject to a knowledge norm.

A second worry is that we often seem not fully committed to our implicatures. Even if it is granted that some implicatures require knowledge, as I claim, others seem to require less. Suppose at a party Ann asks Bob, who’s just arrived, if their friend Carlos is also coming. Bob replies: “I just saw him in the parking lot”. Bob seems to implicate that Carlos is coming to the party, but he does not seem to be committed to knowing it. For all he knows, Carlos may be on his way home. He might even continue to clarify his answer: “I don’t know for a fact that he’s coming, but it does seem that he is”. By answering as he does, Bob seems to be providing relevant information to Ann’s question in a permissible way.²⁷

I grant that Bob’s answer is permissible even though he does not know that Carlos is coming. But we should be careful in identifying the right implicature here. Here are some candidates: Carlos is coming, Carlos is probably coming, Carlos might be coming. As noted above, sometimes implicatures are indeterminate, and there will be nothing to decide between the candidates. This is a plausible reading of the case. It’s also one that is compatible with KNI, because then Bob is only required to know that Carlos might be coming. This reading also explains the sense in which Bob’s continuation “I don’t know for a fact that he’s coming, but it does seem that he is” provides a clarification: it rules out some of the candidates for implicature—in this case, the strongest one. Even if the implicature is determinate, I see no reason to think that it’s that Carlos is coming and not that Carlos is probably coming. On the contrary, taking the latter to be the determinate implicature (or taking the implicature to be indeterminate as suggested above) provides an explanation for why here and in some cases more generally speakers don’t seem fully committed to their implicatures: it’s because they implicate only that something might be or probably is the case, rather than that something is in fact the case. This is of course compatible with the claim that the required epistemic position with respect to such contents is knowledge.²⁸

A third worry is that my argument in this section overgeneralizes. It seems that implicatures can be canceled by denials of certainty just as with denials of knowledge or belief, that it is not possible to implicate “p but it’s not certain that p”, and that one can challenge an implicature that p with “Are you certain that p?”. So an alternative explanation of the data may be that there is a certainty norm of implicature.

Two points in reply. First, such a norm is not necessarily in tension with KNI, for the latter only places one necessary condition on epistemically permissible implicature and does not entail that this is the only necessary condition. Second, parallel concerns arise for KNA, and these have already been addressed in the literature.²⁹ Instead of repeating these replies I offer this: my arguments in this section show at least that if there is a knowledge norm for assertion, then there is also a knowledge norm for implicature, because the same sort of considerations support both. Why should one care about this conditional thesis? Because, as I argue in the following sections, the conjunction of KNA and KNI supports the KK thesis, which means that two central tenets of knowledge-first epistemology—the knowledge norm of assertion and anti-luminosity—may be incompatible.

One way in which implicatures are generated, on a broadly Gricean view, is by openly observing (rather than flouting) the conversational maxims.³⁰ For each conversational maxim there is a kind of implicature associated with observing that maxim. For instance, for the maxim of Quantity (Be as informative as required), there are scalar implicatures:

Given the assumption that the speaker is observing Quantity, an assertion of (25) generates the implicature that the speaker didn’t eat all of the pizza, since if the speaker did and was as informative as required, she would have said ‘all’ and not ‘most’. The maxim of Relation (Be relevant) can generate relevance implicatures:

In (26), Bob’s answer conveys an implicature (perhaps among others) that Ann can get gas at the station. The implicature is generated by taking Bob to be saying something relevant to Ann’s question. The maxim of Manner (Be perspicuous) generates manner implicatures:

An assertion of (27), on the assumption that the speaker is observing Manner, conveys the implicature that the event described by the first conjunct happened before that described by the second.

Finally, the maxim of Quality (Do not say what you believe is false or that for which you lack adequate evidence) generates Quality implicatures:

In (28), the assumption that Bob is observing Quality gives rise to the implicature that Bob believes what he says.³¹ Quality implicatures, like scalar, relevance, and manner implicatures, are a species of observance implicatures—implicatures arising from the overt observance of a given conversational maxim.

Importantly, if assertion has a knowledge norm, then speakers are not only required to believe and have evidence for what they assert, as Quality demands, but they are also required to know it. If so, then Quality should really be understood in terms of knowledge: Do not say what you don’t know.³² Knowledge implicatures are then a species of Quality implicatures. But even if KNA should be understood as distinct from Quality, Knowledge implicatures arise in the same way that Quality implicatures do: the speaker is assumed to be observing the norm of assertion, which invites the inference that she knows her assertion.

At this point the reader might worry: Aren’t implicatures supposed to be cancellable? If they are, there can’t be any belief or knowledge implicatures since those are clearly not cancellable:

My reply is threefold: First, we should distinguish, as Grice did, between explicit and contextual cancellation. Second, there are good reasons to think that not all implicatures are explicitly cancellable. Third, Quality implicatures, and in particular belief and knowledge implicatures, are contextually cancellable. I turn now to developing this reply in more detail. The reader who is not worried by this objection may skip to §4.

Grice distinguished between explicit and contextual cancellation:

Many, including Grice, take cancellability to be a necessary feature of implicature: If p is a non-cancellable implication of an utterance, then p is not an implicature of that utterance. In light of the above distinction, the cancellability hypothesis can be interpreted in two ways:

It is unclear, in fact, whether Grice held the strong or the weak version of the hypothesis. He merely wrote: “[An implicature] may be explicitly canceled, … or it may be contextually canceled” (1989: 39), which seems to leave open both interpretations. Regardless of what Grice actually held, however, there are reasons to think that the strong hypothesis is too strong. Some implicatures appear not to be explicitly cancellable.³³ Consider:

In (31), Bob’s answer implicates that he does not agree with Ann’s statement. The implicature comes about by the well-known mechanism of flouting a conversational maxim. Since it’s common ground between Ann and Bob that Bob’s reply is false, and Bob is nevertheless cooperative, he must mean something else: that Ann’s statement is as implausible as his, or something of that sort. However, the implicature does not seem explicitly cancellable:

The cancellation attempt results in infelicity: there seems to be no way to interpret what Bob is saying if the implicature is removed. The implicature is, however, contextually cancellable. For instance, in a meeting of monarchs:

In (33) the implicature of disagreement does not arise, since the speaker’s utterance is not obviously false as it is in (31) and (32).

Here’s another example of an implicature that does not seem to be explicitly cancellable, adapted from Åkerman (2015):

In (34), Bob implicates that he is happy with his new job in some respects and unhappy with it in others. But this does not seem explicitly cancellable:³⁵

The attempt to cancel the implicature in (35) results in infelicity—without the implicature, we are left with a mere contradiction.³⁶

Given such cases, it seems that implicatures are not always explicitly cancellable. But they may still be contextually cancellable. Thus we may still hold the hypothesis that all implicatures are cancellable, but only in its weak form: they are either explicitly cancellable, or contextually cancellable, but not always both. Note that contextual cancellation is still useful for distinguishing implicatures from other kinds of implications, such as conventional implicatures, presuppositions, and logical entailments. Logical entailments, for instance, are neither explicitly nor contextually cancellable. Presuppositions and conventional implicatures are typically harder than conversational implicatures to cancel, and whether they arise from a given utterance may not depend on contextual factors. The weak cancellation hypothesis thus preserves some of the attractive features of the strong one.

Importantly for our purposes, Quality implicatures, and in particular belief and knowledge implicatures, are contextually cancellable. We have already seen such a case:

In (36), Bob’s utterance does not convey the implicature that he believes that he is the Queen of England, because it is clear from the context, given the common ground, that he does not. Similarly:

In (37), Bob’s overstatement does not convey the implicature that he believes that he had a million exams to grade (although it does convey a weaker one: that he believes that he had a lot to grade). Quality implicatures do not arise in contexts in which they are clearly false. Many cases of verbal irony and hyperbole, as in (36) and in (37), exploit this fact.

Quality implicatures are cancellable after all—they are contextually, rather than explicitly cancellable, in accordance with the weak cancellability hypothesis.