The obvious explanation is that it’s a contradiction: according to standard epistemic modal logic, ‘might’, in its epistemic reading, is just the dual of ‘know’. But the fallibilist of this stripe has closed off that response. What’s he say instead? Dougherty and Rysiew propose a pragmatic line: “p might be false,” they say, implicates but does not entail that there is a significant chance of not-p. And while a chance of not-p is consistent with knowledge that p, a significant chance of not-p is not. Fantl and McGrath supplement the story by suggesting that the significance of various chances can be a stakes-sensitive matter; the same possibility, with the same likelihood, can be significant if the stakes are high, and insignificant if the stakes are low.

Now I get nervous when Gricean pragmatic stories are asked to do work like this. Too often, the data don’t generalize the right ways. Here’s one problem: the pragmatic effect doesn’t seem appropriately cancelable. Consider:

It’s possible that it will rain today, but I know it won’t rain today.

The badness of this sentence is explained, on the view in question, by suggesting that the first conjunct pragmatically implicates that there is a significant chance that it will rain today. It predicts, then, that if we cancel the implication, we’re left with felicity. But this prediction is not borne out; this is still bad:

It’s possible that it will rain today, but there’s no significant chance that it will rain today, so I know it won’t rain today.

Also, there’s a point that Derek Ball raised in Jason Stanley’s seminar last week, inspired by Seth Yalcin: the infelicity of concessive knowledge attributions persists in non-assertoric contexts. “Suppose that you know it will rain today and it might not rain today.” “If you know it will rain today and it might not rain today, then you know something that might not happen.” Etc. The Gricean story is peculiar to assertions, and therefore insufficiently general.

I think there’s a better view in the same spirit. (Well, maybe in the same spirit; I’m not quite sure what the intuitive motivation behind this project is. My suggestion won’t vindicate the coherence of concessive knowledge propositions. But like I said, I’m not sure I see why anyone would want to do that.) The line we’ve been considering is one in which “there is some possibility of p” pragmatically implicates that there is some significant possibility of p. But the existential quantifier is going to have a context-sensitive domain restriction anyway. We could suppose that in the relevant contexts, we’re only quantifying only significant possibilities. Then “there is some possibility of p” would, in the relevant context, entail that there is some significant possibility of p.

On this approach, you can still get a lot of the stuff that Fantl and McGrath want. On this view, whether there is a possibility of p will depend on the stakes, since all possibilities are significant possibilities, and whether a possibility is significant depends on stakes. So their ‘impurism’ would infect ‘possibility’ talk too. (This is not a result of the view they actually offer, which I’m criticizing: they have ‘pure’ possibilities, where talk of them implicates results about ‘impure’ significant possibilities.) But the concessive knowledge attributions will be genuine contradictions.

Bohghossian and Peacocke write:

A priori justification is not infallible justification. Just as one may be justified in believing an ordinary empirical proposition that is empirically revealed on empirical grounds to be false, so one may be justified (non-conclusively) in believing an a priori proposition that is subsequently revealed on a priori grounds to be false.

I find this passage puzzling, for at least two reasons. First, Boghossian and Peacocke characterize a priori propositions for Boghossian and Peacocke as those which can be known a priori; so the idea of an a priori proposition that turns out to be false looks to me to be incoherent.

Second, it’s not clear what the second sentence has to do with the first. The second sentence is about what may happen when you’re justified in believing something — that thing may turn out, either empirically or a priori, to be fase. The first sentence, however, isn’t a claim about all justification; it’s a claim about a priori justification. It can’t be that a priori justification is fallible merely because it’s possible to be justified in believing some a priori proposition that turns out false; if a priori justification is fallible, then there has to be a sense in which you can be wrong even if you’re a priori justified. And that just isn’t established or claimed in this passage. Is the idea supposed to be that any time you are justified in believing some a priori proposition, you’re justified a priori? That would fill out the enthymeme, but it has the disadvantage to being totally implausible.

So I don’t really know what Boghossian and Peacocke are up to here. Or, in general, what people who talk about a priori justification being fallible are up to.

Faced with a choice between skepticism and uncertain knowledge, we should indeed choose the latter. But we shouldn’t forget that it’s an intuitive cost. Given the choice to avoid both, we should consider it seriously.

Is this sounding familiar? It’s exactly the opening structure of Lewis’s “Elusive Knowledge,” but discussing certainty instead of fallibility. I think the argument goes through in just the same way. Contextualists about ‘knows’ are uniquely positioned to vindicate that knowledge is certain knowledge, and to do it without resulting in skepticism.

The basic structure of it is easy. Let ‘knows’ and ‘is certain that’ both be context-sensitive, and let it be that for any context c, the property picked out by the former in c entails that picked out by the latter in c. But a typical effect of asking or enquiring about ‘certainty’ is to induce a more skeptical context. So I might answer differently to the question “do you know that p” than I would to the question “are you certain that p”. But once I’ve answered ‘yes’ to the first, I face strong pressure not to say ‘no’ the second — or if I do, it will feel like a retraction.

So if you’re a contextualist about ‘knows,’ then you can, if you want, think that knowledge requires certainty. And it looks to me as if there’s every reason we should want that. “I’m not certain that p but I know that p” sounds crazy.

(N) Iff S knows p, then S is permitted to phi

Some candidates for phi: S believe p; S rely on p in practical reasoning; S assert p. What I want to do right now is just outline the options for the contextualist who wants to make something suitably in the spirit of (N) true. I see four choices:

(1) Make the normative language contextualist. Now (N) is true in all contexts; “S knows p” is true in all the same contexts in which “S is permitted to phi” is true; the normative language shifts along with the ‘knows’ language. In skeptical contexts, “S is permitted to phi” will be false, while in nonskeptical ones, it will be true. In his “Knowledge, Context, and the Agent’s Point of View,” Timothy Williamson assumes this interpretation, and plausibly argues that the resultant view is pretty unattractive. If somebody says “S should phi,” and somebody else says “S should not phi,” and they’re talking about the same S at the same time and using ‘phi’ to describe the same course of action, then we shouldn’t think they’re both right. (Jenkins and Nolan have a paper defending contextualist ‘ought’ discourse, though; I’ve been meaning to have a close look at it to see if it can help.)

(2) Limit the norm to the claim that (N) be true in any subject’s context, leaving the right-hand side with an invariantist interpretation. If “S knows p” is true in S’s context, then S is permitted to phi. This is DeRose’s view about assertion. (His 2002 paper is not at all clear about how to interpret his version of (N), but his new book is explicit here. See my NDPR review for discussion.) We don’t get the oddness that Williamson charges against (1), but there are reasons to be unhappy. For one thing, Jason suggested in seminar that this interpretation is ad hoc. I’m not sure about that. Maybe. Also, as Danielle pointed out in seminar, we do, at least apparently, get some truths that are in tension with what might be the spirit of the knowledge norms. If I’m not in S’s context, for example, I might truly say “S knows p but is not permitted to phi.” As I mentioned in seminar, DeRose has a defense that mitigates quite a lot against this objection — in many of the relevant cases, we should expect speakers to adopt contextual standards appropriate to the subject’s situation. I think this will work a lot, but not quite enough. (I’m worried about, for example, cases in which speakers are ignorant of the subject’s situations. Here is a related blog post.) I’m also worried that there often won’t be a determinate standard in place in a subject’s context who isn’t talking about knowledge (another blog post). I am working on idea about the assertion norm that is in this neighborhood, but, I think, gets around a lot of these objections; more on that soon.

(3) Make (N) true in some particular favored context. Suppose I’m a contextualist and I agree with Williamson when he writes that knowledge is the norm of assertion. One way to do that would be to say that the particular ‘knows’ relation picked out by Williamson’s particular conversational context as he wrote his book is the invariantist norm of assertion. To take this strategy is to embrace a particular disambiguation of (N): Iff S knows(x) p, then S is permitted to phi. Now I’m not sure how plausible this kind of strategy will be in these instances (it certainly runs into at least some of the objections against (2)-type strategies), but it at least represents a position in logical space. I think there are some at least minimally parallel situations where this kind of strategy is correct. (This came out of a discussion I had with Derek Ball and Danielle Sgaravatti over dinner.) Here is an example of a normative principle that contains an uncontroversially context-sensitive term:

(M) S shouldn’t murder anybody.

The quantifier “anybody” in English takes a context-sensitive domain, so in theory, we face the same kinds of questions about how to interpret this principle. Strategy (2) here is of course nuts; take some subject S who isn’t talking about Derek, such that in his context, ‘anybody’ does not quantify over Derek. If S were to ask, in his present context, “is anybody taller than 6-foot-2?”, the correct answer would be ‘no’. According to the (2)-interpretation, (M) carries no prohibition against murdering Derek (who is tall). So the (2)-interpretation of (M) is not the best one. I think the (3)-interpretation of (M) is pretty plausibly correct; an utterance of (M) will typically be one about some privileged domain of individuals. A contextualist could interpret knowledge norms this way if he wanted to. I’m not terribly inclined toward this view, but it looks like a legitimate one.

(4) This is the kind of strategy I’m most interested in at the moment. Like the defender of (1), I want to make (N) true in all contexts, but I don’t want to do it by exploiting context-sensitivity of normative language. Instead, I suggest that in at least some instances of the schema, the ‘phi’ bits will be context-sensitive. (Notice, by the way, that a contextualist needn’t adopt a uniform treatment for all instances of the schema. There’s nothing stopping him, for example, from employing strategy (4) for the norm of belief by arguing that ‘believes’ is context-sensitive, picking a favored context for the norm of assertion, and flatly denying the norm of practical reasoning. Norms must be considered one at a time.) Suppose I’m a contextualist about ‘believes’. Then I might think that in any context c, it is permissible that ‘S believes p’ be true in c iff ‘S knows p’ is true in c. Then we can have ‘knows p’ and ‘is permitted to believe p’ swinging together, without the troublesome implication that two people could give contradictory advice, while both being correct. (Two people could each offer sentences that appear contradictory, but the sentences inside their ‘oughts’ will express compossible propositions.) Maybe you’ll think this sounds totally ad hoc. I wouldn’t blame you a bit; so far I’ve just pointed out a bit of conceptual space. But I’m working on a paper that pursues this strategy in some detail, hopefully along with a plausible motivation, with respect to the knowledge norm of belief. Again, more sometime soon.

According to certain prominent rationalist views, what explains this difference is that my knowledge about squares, unlike my knowledge of snow, is based not on perception but on intuition. I have the intuition that p, and intuitions are a source of evidence, and so now I have justification for believing that p. It’s hard for me to see how, on a view like this, the relevant knowledge comes out independent of experience. For intuitions are experiences, every bit as much as perceptual experiences are. Indeed, some rationalists characterize intuitions phenomenologically: intuitions feel a certain way, and having that sort of feeling provides justification for intuitive beliefs.

On this sort of view, intuitions look to be just another kind of way of experiencing the world. One way that we experience the world is by seeing things; another is by intuiting things. You can call things learned that latter way a priori if you want to, but this just doesn’t look to me like belief independent from experience. On the contrary, on this sort of a view, it looks like the a priori beliefs are those that are based on a certain kind of experience: the intuitions.