1 What’s Wrong with Fallibilism?

According to the sceptic’s so-called “Ignorance Argument”:

Ignorance Argument (IA)

P1. If I know that I have hands, I can know that I am not a brain in a vat.

P2. I cannot know that I am not a brain in a vat.

C. Therefore, I do not know that I have hands.

Many philosophers reply to this argument by denying that knowledge entails (epistemic) certainty (see Audi 2003: 225 sq). They embrace fallibilism:

Fallibilism: S can know that p even if there is an epistemic chance for S that not-p (or even if it is possible, for S, that not-p)Footnote 1

Fallibilism comes in two main forms. On the first one, it implies the denial of epistemic closure.Footnote 2 It contends that a subject S can be in a position to know that p without being in a position to know that q (where p entails q). Thus understood, fallibilism can reject P1. I can know that I have hands even if I cannot know that I am not a brain in a vat (see Dretske 1970; Nozick 1981).

On its second form, fallibilism is compatible with epistemic closure. It merely holds that knowing that p is compatible with the epistemic possibility that not-p. Thus understood, fallibilism can reject P2. I can be in a position to know that I am not a brain in a vat even if I cannot completely rule out the possibility that I am a brain in a vat, provided that this possibility is sufficiently unlikely (see, e.g., Rysiew 2001).

As popular as it may be, however, fallibilism encounters a very troubling problem. Lewis puts the problem this way:

[I]t seems as if knowledge must be by definition infallible. If you claim that S knows that P, and yet you grant that S cannot eliminate a certain possibility in which not-P, it certainly seems as if you have granted that S does not after all know that P. To speak of fallible knowledge, of knowledge despite uneliminated possibilities of error, just sounds contradictory (…) If you are a contented fallibilist, I implore you to be honest, be naive, hear it afresh. ‘He knows, yet he has not eliminated all possibilities of error.’ Even if you’ve numbed your ears, doesn’t this overt, explicit fallibilism still sound wrong? (Lewis 1996, p. 549-550)

This problem has led a certain number of philosophers toward contextualism (see Lewis 1996; DeRose 2009; Ichikawa 2017). Yet, contextualism is not the only option. Fallibilists have proposed alternative explanations of the apparent incoherence.Footnote 3

In this paper, I consider Gricean explanations and I explain why they ultimately fail.Footnote 4 I then consider the recent suggestion to explain the incoherence in terms of a certainty norm for assertion. I argue that this proposal is much more promising.

My plan is as follows. Section 2 presents three kinds of data embarrassing for fallibilists. Section 3 argues that Gricean approaches fail to explain them away. Section 4 shows that if fallibilists embrace the recent proposal according to which assertions are governed by a (context-sensitive) certainty norm of assertion, they can accommodate all these data.

2 Embarrassing Data for Fallibilists

Fallibilists have it that S can know that p even if there is a chance (for S) that not-p, that is, even if it is possible for S that not-p.

Embracing fallibilism amounts to denying Moore’s Principle:

Moore’s Principle (MP) Whenever a speaker S does or can truly assert, “It’s possible that P is false”, S does not know that P. (DeRose 1991, p. 596)

Denying MP looks problematic, though. For if one denies MP, a certain number of data remains mysterious.

First, the following claims, often called “concessive knowledge attributions” (CKAs) clearly sound incoherent:

(1) I know that p, but it might be that q (where q obviously entails not-p).

(2) I know that p, but there is a chance that q (where q obviously entails not-p).

(3) I know that p, but it is possible that q (where q obviously entails not-p).

For example, it sounds incoherent to say “I know that I have hands but it is possible that I am a brain in a vat”. Assertions like that sound like “abominable conjunctions” (DeRose 1995). If MP is true, CKAs sound abominable because they are semantically inconsistent. Yet, if fallibilism is true, these conjunctions can be true. Why then do they sound abominable?

Fallibilists suggest that the clash is pragmatic, rather than semantic.

Consider:

(4) It is raining but I do not know that it is raining

(4) is somewhat incoherent but it is clear that there is no inconsistency between the proposition that it is raining and the proposition that I do not know that it is raining.

However, how are we to decide whether the clash is semantic or pragmatic?

DeRose observes that

it seems crazy to infer that it is not raining from the fact that I don’t know that it is raining. If it is raining and I don’t know that it is raining were inconsistent, then each would entail the negation of the other: it is raining would entail I know that it is raining and I don’t know that it is raining would entail It is not raining. But, clearly, neither entailment holds. (DeRose 1991, p. 597)

This suggests a method for distinguishing pragmatic and semantic clashes:

If a sentence clashes, if it is not clearly implausible to suppose that the entailments hold, and if we can find no good deflationary explanation for the clash, then we have good-reason to suppose that the clash is being produced by a genuine inconsistency in the sentence (ibid.)

Now, as DeRose notes:

when we apply this method to “It is possible that not-P, but I know that P,” I think we find that the sentence does seem to clash or cancel itself, and that, unlike “It is possible that not-P, but P”, it seems reasonable to suppose that the clash one senses may be that of genuine inconsistency, because the required entailments (from It is possible that not-P to I don’t know that P and from I know that P to It is not possible that not-P) don’t seem crazy. (DeRose, 1991, p. 599)

Indeed, the following inference is reasonable:

Reasonable Inference

P. S sincerely asserts “It is possible that not-p”

C. S does not know that p (or at least does not believe that she knows that p)

If we deny MP, it can be true that it is possible (for S) that not-p and that S knows that p. It is then obscure why this inference is not crazy. This gives us a second kind of data embarrassing for the fallibilist.

Third, note that the following sentences also seem incoherent:

(5) p, but it is possible that q (where q obviously entails not-p).Footnote 5

(6) S knows that p, but it is possible that q (where q obviously entails not-p)

MP in combination with the plausible and very influential claim that knowledge is the norm of assertion (see Williamson 2000) provides us with an easy explanation for the incoherence of (5) and (6).

According to the knowledge norm of assertion:

KN: You (epistemically) ought to assert that p only if you know that p.

Consider (5). Given KN, by asserting that p, you represent yourself as knowing that p. Given MP, the assertion that it is possible that not-p semantically implicates that you do not know that p. Therefore, by asserting (5), you represent yourself as knowing that p and not knowing that p (DeRose 1991, p. 600).

Consider (6). Given KN and the factivity of knowledge, by asserting that S knows that p, you represent yourself as knowing that p. Given MP, the assertion that it is possible that not-p entails that you do not know that p. Therefore, by asserting (6), you represent yourself as knowing that p and not knowing that p.

If we reject MP and embrace fallibilism, how are we to explain these data? This gives us a third kind of embarrassing data for fallibilists.

3 The Gricean Explanations

Fallibilists have mainly focused on the problem of concessive knowledge attributions. Until very recently, they have approached this problem by appealing to Gricean implicatures. We can find three different explanations in the literature.Footnote 6

3.1 Rysiew (2001)

First, Rysiew writes that CKAs

are bound to sound odd (...) “I know that p” standardly functions to convey the speaker’s confidence as to p and (thus) to counter a doubt as to whether p. However, the concession clause, “but, maybe, however, etc...,” raises the then-mentioned possibility to salience. So while “I know” communicates that the speaker is confident that p and thus that he (believes he) can rule out the salient not-p possibilities, the concession clause communicates that there’s a salient not-p possibility which the speaker can’t rule out. (Rysiew 2001, p. 493)

Why think that a first-person knowledge ascription conveys the speaker’s confidence that p? According to Rysiew, an assertion that p already communicates that the speaker takes herself to have a justified belief in p. Therefore, an assertion “I know that p” must communicate something

over and above what’s communicated by “p”; otherwise, saying “I know that p” would mean violating the maxim of manner (be perspicuous, relevant, brief, orderly, etc.) and thus CP (Rysiew 2001, p. 493).

Rysiew concludes that a knowledge ascription must convey that the speaker takes herself to be in a position to rule out the salient doubts. Yet, in asserting that it is possible that not-p, the speaker communicates that she cannot rule out a salient possibility that not-p. Hence the incoherence.

There are several problems with this approach. Firstly, Rysiew does not explain why, given Grice’s cooperative principle, we should expect a first-person knowledge ascription to communicates that the speaker has a sufficient confidence, rather than an insufficient confidence, to rule out the salient possibilities of error (including those possibilities which are not knowledge-destroying). After all, given Grice’s maxim of quantity, you should assert the stronger. And given that the speaker does not assert that she is certain (or knows for sure) that p, it is far from clear why her assertion that she knows that p does not communicate that she merely knows that p, and hence, that she is not certain that p and not confident enough to rule out the salient but not knowledge-destroying possibilities of error (see Dimmock and Huevenes 2011). Of course, there is no denying that the subject does convey by such an assertion that she is sufficiently confident that p. The point is merely that Rysiew’s appeal to Grice’s Cooperative Principle does nothing to explain that.

To see this, compare with “I believe that p”. As we should expect given Grice’s maxim of quantity, this assertion does not typically communicate a sufficient confidence in p but rather something weaker, like “I’m not completely confident that p”.

Secondly, if we suppose that the communicated meaning that the speaker has a high confidence that p is pragmatically inferred from her knowledge ascription that p, this pragmatic implicature should be cancellable without inconsistency. More precisely, the subsequent assertion that it is possible that not-p should cancel the supposed implicature. Thus, it is rather unclear in this framework why we should expect CKAs to sound inconsistent (see Dodd 2010).

Thirdly, it is hard to see how this approach could be extended to explain Reasonable Inference. Indeed, the speaker’s assertion “It is possible that not-p” is supposed to convey that she is not in a position to eliminate a salient possibility of error. But it would be crazy, if one adopts this fallibilist framework, to infer from S’s claim that she cannot rule out a salient possibility of error that she doesn’t know that p (or does not believe that she knows that p). As is plain, a salient possibility of error need not be knowledge-destroying.

Finally, this approach cannot be used to explain the incoherence of (5) and (6). Assume that an assertion “I know that p” conveys a specific confidence that an assertion “p” does not convey. Obviously, this assumption does nothing to explain why asserting “p but it is possible that not-p” sounds incoherent. In such a case, the speaker asserts “p” and not “I know that p”.

Similarly, this approach cannot be used to explain why “S knows that p but it is possible that not-p” sounds incoherent. In contrast to an assertion “I know that p”, there is no reason to think that an assertion “S knows that p” should convey that the speaker has a particularly strong confidence regarding p.

3.2 Dougherty and Rysiew (2009)

A second proposal, anticipated by Rysiew (2001: 493) and developed by Dougherty and Rysiew (2009: 126) relies on Grice’s rule of quantity. The idea is that “It is possible that not-p” pragmatically implicates that the speaker does not know that p, given that one must assert the stronger. Even if knowledge is compatible with non-eliminated possibilities of error, it is more informative to say that these possibilities of error are unlikely and not knowledge-destroying, if this is the case. Yet, in the first half of a CKA, the subject asserts that she knows that p. Hence the incoherence.

This second approach is better in that, in addition to being applicable to concessive knowledge attributions, it also suggests a simple explanation of Reasonable Inference.

However, as the previous attempt and for a similar reason, one might doubt that this proposal can succeed. As Dodd writes:

even if an utterance of ‘p’ pragmatically implicates that not-q, this doesn’t mean that an utterance of ‘p and q’ is infelicitous. Thus showing that ‘p’ implicates not-q shouldn’t be taken to provide an explanation of the infelicity of ‘p and q’. So I think [Dougherty and Rysiew’s] proposal of how to explain pragmatically the infelicity of CKAs fails. (Dodd 2010)

Compare with “John and Mary married and had children, but they have had their children first”. This assertion does not sound incoherent, even if the first half of the assertion pragmatically conveys that they first married.

The same problem arises if one wants to explain in this way why “p, but it is possible that not-p” and “S knows that p, but it is possible that not-p” sound incoherent. Assume that by asserting “p”, the subject represents herself as knowing that p. Then, by asserting “not-p is possible”, she should not pragmatically convey that she does not know that p, as this implicature should be blocked by the first half of the assertion. If MP is false, “p, and it is possible that not-p” should look like a banal truth.

Compare with “I believe that p, but p”. Due to the rule of quantity, “I believe that p” conveys that the speaker does not know that p. Now, assume that knowledge is the norm of assertion. By asserting that p, the speaker conveys that she knows that p. Yet, “I believe that p but p” does not sound incoherent but, rather, redundant.

Likewise, by “S knows that p”, the subject represents herself as knowing that p and, if MP is false, it is unclear why we should expect her assertion “but it is possible that not-p” to convey that she does not know that p.

3.3 Dougherty and Rysiew (2009)

A third proposal is developed by Dougherty and Rysiew (2009). It is based on the supposition that it is obvious that, with respect to (almost) every p, not-p is possible for S. According to Dougherty and Rysiew, given this supposition and the rule of relevance, we should expect “It is possible that p” to convey the possibility that not-p is particularly significant. Otherwise, they note, why mention it? If so, “I know that p” represents the speaker as confident enough that p and “It is possible that not-p” conveys that the speaker takes the possibility that not-p seriously. Hence the incoherence.

In Dougherty and Rysiew’s words:

either the doubt or reservation which “it’s possible that not-p” is naturally understood as indicating is significant, or it is not. If it is, there’s a norm to hedge the assertion which comprises the first half of CKAs. This may be a generic consequence of the CP, or a consequence of the Maxim of Quality. If, however, the doubt is not significant, then the Maxim of Relation recommends that one not mention it. Either way, the explanation of the oddity of CKAs is pragmatic plainly (Dougherty and Rysiew, 2009, p. 128-129)

Although interesting, this third proposal is not fully satisfying either. First, it is still unclear how this can explain why CKAs are bond to sound incoherent. This proposal is based on the idea that it is obvious that, for (almost) any p, there is a possibility for S that not p. But asserting obvious truths is not automatically infelicitous (Hawthorne 2004, p. 25). If fallibilism is obviously true, why is it that CKAs do not express this obvious truth?

Second, let us grant that mentioning that there is a possibility that not-p conveys that this possibility is significant, or that it should be taken seriously. It is crucial to note that either one supposes that this possibility is epistemically significant—where this means that it may well be incompatible with knowledge—or one supposes that it is merely practically significant—where this means that it should be taken seriously in practical decision and action.

Now, it is clear that there is a pragmatic incoherence between “I know that p” and “It is possible that not-p” only if it is assumed that “It is possible that not-p” imparts that there is an epistemically significant possibility that not p. For, if one supposes that the possibility is only practically significant, it is supposedly compatible with knowledge.

Likewise, (granting KN) it can be suggested that “p, and it is possible that not-p” and “S knows that p, but it is possible that not-p” are bond to sound incoherent only if it is assumed that, in these expressions, “It is possible that not-p” imparts that the possibility in question is epistemically significant. What reason to do we have to think that?Footnote 7

On this score, Dougherty and Rysiew (2011) write:

But of course the hearer who wishes to understand the mention-worthiness of “possibly not-p” might very naturally rely on the fact that, in a CKA, the relevant kind of significance is most likely epistemic significance. (After all, the mentioned possibility immediately follows upon a claim that p is known.)

Let us suppose this proposal can succeed in explaining the apparent incoherence of CKAs and assertions like “S knows that p but it is possible that not-p”. It can still not be used to explain the apparent incoherence of “p but it is possible that not-p”. For, in such a case, there is no antecedent claim that p is known.

For the same reason, this proposal cannot be used to explain Reasonable Inference. In asserting “It is possible that p”, it is assumed, the speaker conveys that there is a significant doubt as to whether p. But in Reasonable Inference, there is no claim that p is known possibly suggesting that the doubt is epistemically significant. Therefore, given that the doubt may be merely practically significant, it would be crazy to infer that the subject does not know that p, or does not believe that she knows.

Even more problematically, far from reinforcing Dougherty and Rysiew’s proposal, the observation that the speaker mentions in the first half of her CKA that she knows that p should suggest to the hearer that the speaker does not take the significance of the possibility of error to be epistemic. Otherwise, why would have the speaker said that she knows? If one sees the speaker as cooperative, one should expect her assertion “I know that p” to prevent the supposed implicature that the possibility of error is epistemic, rather than to lead to this implicature.

These considerations also apply to “p, but it is possible that not-p” and “S knows that p but it is possible that not-p”. Given the knowledge norm of assertion, it is clear that “p” and “S knows that p” convey that the speakers know that p. If one sees the speaker as cooperative, these assertions should block the epistemic interpretation of the significance of “It is possible that not-p”.

A third difficulty for Dougherty and Rysiew’s proposal is that it relies on the supposition that it is obvious that, with respect to (almost) every p, not-p is possible for S. This supposition is based on the claim that epistemic possibilities for S are possibilities logically or metaphysically compatible with S’s evidence. However, this version of fallibilism is not particularly obvious or attractive.

Consider these cases, from Huemer (2007, p. 121–122):

LOST WALLET. Having lost my wallet, I ask myself: Where could it be? Could it be at the movie theater? No, I reason, I remember buying gas after that, and I had to have my wallet to do that. Hm, but it might be out in the car... I then go out to search the car.

PHONE AIRPORT. Mary is picking up Sam from the airport, but she’s a little late, so she calls Sam on his cell phone.

- Mary: Where are you?

- Sam: I’m on the ground; we’ve just landed.

- Mary: Is it possible that you’re still in the air?

- Sam: No, it isn’t. I can see out the window right now, and we’re on the ground. I know what the ground looks like! Sheesh

Intuitively, the subject can truly say “It is not possible that my wallet is on the theater” and “It is not possible that the plane is still in the air”. This intuition contradicts the claim that not-p is an epistemic possibility for S if S’s evidence does not (logically or metaphysically) entail not-p. For, as Huemer writes, if this last claim is true

the epistemic impossibility claims in Lost Wallet and [Phone] Airport are incorrect despite my apparent memory of having bought gas after leaving the theater (...) I should still say the wallet may be at the theater. Indeed, the wallet may be on the Sun. Similarly, in Airport, rather than observing peevishly that he knows what the ground looks like, Sam might have more appropriately responded to Mary’s question with, Well, of course it’s possible that I’m still in the air. Isn’t that obvious? After all, it should be obvious to both Mary and Sam that Sam lacks the sort of justication for the claim that he is no longer in the air that would be metaphysically incompatible with his being in the air; indeed, it is doubtful that anyone could ever have such justication. (Huemer, 2007, pp. 127–128)

Of course, Dougherty and Rysiew might try to explain away AIRPORT and LOST WALLET by saying that, in these cases, “It is not possible that I am still in the air” and “It is not possible that my wallet is at the movie theatre” are pragmatically appropriate. According to their line of thought, these claims are, strictly speaking, false. But they might suggest that these claims convey that the possibility in question is not significant and should not be taken seriously.

In these cases, however, the insignificance should be practical. If so, we are now in an very uncomfortable position. We have to grant (without explanation) that “It is possible that not-p” conveys that not-p is epistemically significant whereas “It is impossible that not-p” conveys that not-p is practically insignificant.

In addition, it is clear that, in such cases, “I might still be in the air although it is unlikely” and “My wallet might be on the Moon but that’s unlikely” do not seem obviously true.

4 Fallibilism and the Certainty Norm of Assertion

So far, I have argued that standard defences of fallibilism, which are based on Gricean implicatures, do not really succeed in dealing with the embarrassing data. In this section, I shall show that invoking the norm of assertion does a pretty good job in this respect.

Recently a certain number of theorists have defended the claim that assertions are governed by a certainty norm, where “certainty” is context sensitive (see Lewis 1979) and not entailed by knowledge (see Stanley 2008; Petersen 2019; Beddor 2020; Vollet 2020).

This norm can be formulated as follows:

CN: S (epistemically) ought to assert that p in context C only if S satisfies the epistemic standards of epistemic certainty which are operative in C.

As we can see, endorsing this norm allows the fallibilist to straightforwardly accommodate the first and third kinds of embarrassing data.

Consider again the following assertions:

(1) I know that p, but it might be that q (where q obviously entails not-p)

(2) I know that p, but there is a chance that q (where q obviously entails not-p)

(3) I know that p, but it is possible that q (where q obviously entails not-p)

(5) p, but it is possible that q (where q obviously entails not-p).

(6) S knows that p, but it is possible that q (where q obviously entails not-p)

In the first half of these assertions, the subject asserts that p, or that she knows that p, or that someone knows that p. Given CN and the factivity of knowledge, the subject represents p as epistemically certain for her. Yet, in the second half of her assertion, she asserts: that it might be that q (where q obviously entails not-p), that it is possible that not-p, that there is a chance that not-p. On any account of epistemic possibilities, if p is certain for S, then not-p is impossible for S, and it might not be that q (where q obviously entails not-p), and there is no chance that not-p. Hence the infelicity.

Although it provides an adequate explanation for the first and third kinds of data, this approach does not provide a straightforward explanation of Reasonable Inference. After all, that p is not certain for S supposedly does not entail that p is not known by S. Still, I will now show that fallibilists appealing to CN have the resources to explain Reasonable Inference.

To begin with, note that reasonable inferences that are not deductively valid are defeasible. Consider:

BANK – John: There is a small possibility that the bank will be closed.

– Mary: You mean you do not know that the bank will be open?

– John: No. Normally it will be open. But I prefer to check.

John’s answer is intelligible and coherent. It seems to defeat the inference from “It is possible for John that not-p” to the conclusion “John does not know that p (or believe that she does not know that p)”, thereby suggesting that MP is false

These considerations do not yet explain why Reasonable Inference is reasonable. But such an explanation can be provided if we observe, first, that the certainty norm directly explains why the following inference is reasonable:

Reasonable Inference (Certainty)

P1. S sincerely asserts “It is possible that not-p”

C. S does not know for sure that p (or at least does not believe that she knows for sure that p)

Indeed, that not-p is possible for S entails that S does not know for sure that p.

To this observation, we can add that, according to all the main proponents of the certainty norm for assertion, the standards for certainty and knowledge plausibly coincide in ordinary contexts. In other words, proponents of the certainty norm of assertion maintain that, uttered in ordinary contexts, “S is in a position to know that p if and only if p is certain for S” is true.

This gives us an explanation why Reasonable Inference is not crazy. It is natural to assume by default that, in Reasonable Inference, the conversational context in which S asserts “It is possible that not-p” is an ordinary context. In this context, the standards for certainty and knowledge are equivalent. Therefore, the epistemic standards of knowledge are satisfied only if the epistemic standards of certainty are satisfied.

To conclude, let me stress two further advantages of the approach based on the certainty norm over its Gricean rivals. As we have seen, a major problem for Gricean approaches is that they are vulnerable to the objection that the supposed implicature does not seem cancellable. This objection has no force against an approach appealing to the norm of assertion, for there is no denying that implicatures based on such a norm are not cancellable.

Second, the approach based on the certainty norm of assertion does not need to embrace the potentially problematic claim that, with respect to almost any p, not-p is possible for S. Given the supposed context-sensitivity of certainty, this view is compatible with the intuitive thought that assertions of the form “It is certain that p” or “It is impossible that not-p” can be true (at least in ordinary contexts).