Knowledge Entails Certainty

The idea that knowledge entails certainty is a very intuitive one. It's easy to forget this, because most of us have it drilled into us, early in our epistemological careers, that embracing a certainty requirement on knowledge leads to skepticism, and we're rightly convinced that skepticsm is crazy, so we start getting used to the idea that there can be uncertain knowledge. Someone can know that p without being certain that p. If we say it enough times, it will stop sounding like a contradiction. And most of us have now said it enough times, so that it has stopped sounding like a contradiction.

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.

Contextualist Knowledge Norms

What should a contextualist who likes normative principles involving 'knows' say? Signing up to the knowledge norms means embracing something typically expressed by sentences fitting something like this schema:

(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.

Intuition and experience

I know that there is snow outside; this knowledge is based in part on my visual experience. When I look out the window, I have experiences that partially constitute seeing snow. I also know that squares have four sides. Arguably, this knowledge is independent of experience, depending only on my conceptual competence, or rational capacities, or something like that. My knowledge that squares have four sides is not derived from experience, the way that my knowledge that there is snow outside is.

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.

Varieties of Enabling Conditions

A priori justification or knowledge is meant to be independent from experience in some sense. But it's a bit tricky to explain just what that sense is. It's usually allowed that there are some roles for experience that are merely enabling in a way that is consistent with apriority. For example, maybe you think particular perceptual experiences are necessary for possession of color concepts -- you have to have seen yellow in order to entertain thoughts about that color, and so your knowledge that yellow things aren't green requires having had a certain experience. If you think that, you can still think it's a priori that yellow things aren't green, because you think that the role for experience here is not warranting -- it's just part of what lets you entertain the thought in the first place. (Side note: also, if you think that, you should read my colleague Derek Ball's paper to see why you're probably wrong in thinking that you need particular experiences to have these concepts.)

There are other ways for experience to be relevant to the justification of a priori beliefs than by enabling the concepts that are part of their contents. It's also standardly allowed that certain experiences would defeat a priori justification -- the experience of lots of misleading but authoritative testimonial evidence, for example, could make it unreasonable to retain some particular a priori belief. If such obtained, then you wouldn't be justified; therefore, your justification depends on such experience not obtaining. Thus does, for example, Marcus Giaquinto distinguish between 'positive' and 'negative' roles for experience:

We could mark the distinction by saying that if a belief is rationally revisable in the light of future experience, its retention is negatively dependent on experience; and if a belief cannot have been justifiably acquired unless some experience was used as grounds in the process, its acquisition is positively dependent on experience.

But there is room for a kind of dependence on experience that is neither 'negative dependence' nor 'positive dependence' in Giaquinto's sense. And I think that it, too, is consistent with apriority. We can distinguish between the reasons in favor of some belief, on the one hand, and various conditions that are necessary for those reasons to count in favor of the belief, on the other. And in at least some cases, we should think that experiences can play that latter role in a way consistent with apriority. I'll close with an example, and continue with further thoughts and possible applications in another post.

Consider a moderately complicated proof. Suppose it requires a couple dozen lines, and involves fairly lengthy sentences. In fact, it is valid, and indeed, I have produced it correctly -- every step followed from the previous one in a way that I appreciated while writing it down on my blackboard. I've reached my conclusion, but I do not, at this moment, know it to be true. The reason this is so is that the proof is too complicated for me to know it sound straightaway; the chance of making a mistake is too great. Sometimes I apply rules incorrectly; sometimes I accidentally change variables. I don't do this very often -- no more than most philosophers -- but I do it often enough that it would be unreasonable to be confident in the soundness at this point. Instead, I should go back and check my work. I review each step, looking for mistakes, and find that I made none. Now I know the conclusion.

My experience of checking my proof played a significant role in my knowledge of its conclusion. Certainly, that latter knowledge at least counterfactually depends upon it. But these experiences, of course, weren't necessary for the possession of any concepts in the conclusion; I was perfectly capable of entertaining the thought before I began. And this is a positive dependence on experience; it's not just that I need to lack particular misleading experiences. Nevertheless, this looks like a merely enabling role for experience; my belief in the conclusion is not based on my experience of checking the proof; it is based only on the premises. If those are a priori, then my knowledge of the conclusion is too.

So there are ways for experience to play merely enabling roles beyond the ones articulated above.