What is proof beyond a reasonable doubt?

As I finish up a few long-standing projects on knowledge (check out my draft monograph!) I'm hoping to start exploring a few new-for-me areas. In recent years my philosophical discussions on this blog have been relatively esoteric, trying out a new objection to so-and-so's third paper on such-and-such; when I was in grad school I used it as an early thinking-out-loud forum about more basic stuff. If I can swallow my pride enough, I may return to that form over the next several months. One area I'm quite ignorant and naive—but also curious—about is law. In particular, I'm curious about how legal concepts like evidence and testimony interact with epistemological concepts like evidence and testimony. I'm a complete novice in this field, so if I'm overlooking things that seem totally obvious to any readers, I'd be grateful to have it pointed out, especially if it comes along with reading advice.

One of my entry-points into the literature here is my UBC colleague John Woods's book Is Legal Reasoning Rational: An Introduction to the Epistemology of Law. (I'm maybe 40% of the way through a first read of it now.) Here's one thing I've found interesting so far. Woods writes, on p. 103:

Spike cannot be convicted unless a jury unanimously finds that his guilt has been proved beyond a reasonable doubt. Certainty beyond a reasonable doubt is sometimes said to be moral certainty. Under either name, as Gifis writes, it is a conviction based on persuasive reasons and excluding doubts that a contrary conclusion can exist. This is much too strong a formulation. There is plenty of case law that allows for conviction even in the face of a perfectly reasonable case to the contrary, recognized as such by the jury. On an alternative formulation of the standard. A juror is said to be morally certain of a fact when he or she would act in reliance upon its truth in matters of greatest importance to himself or herself. Although better, this appears to omit the essential requirement of criminal proof that this readiness to act, this moral certainty, be grounded in the juror's belief that the burden of criminal proof has been met. In other words, it seems not to be sufficient for criminal conviction that a juror be in a state of moral certainty of the accused's guilt. It also matters how he came to be in that state. 

So we have these notions:

• Proof beyond a reasonable doubt
• Certainty beyond a reasonable doubt
• A juror's being in a state of moral certainty

Woods slides between the first two without comment. Maybe the thought is that there is this tight relationship: proofs establish certainty. (In logic or mathematics, this seems plausible—if I have a proof of something, then it is certain for me.) But as Woods points out, it's another matter whether my psychology reflects this certainty. I might have a proof but doubt anyway; or I might be irrationally certain, even absent a proof.

I wish Woods had explained further what he had in mind when he discusses appropriate conviction in the face of 'a perfectly reasonable case to the contrary'. (I am not sure who Gifis is—I don't see a citation.) Can there be 'perfectly reasonable' cases that have been proven not to be the case? If 'provability beyond a reasonable doubt' is closed under deduction, then it seems like there must be. (If it's been proven beyond a reasonable doubt that Jones committed the crime, then it's provable beyond a reasonable doubt that Jones wasn't framed.)

The alternative formulation mentioned seems to target the psychological state of being in a state of moral certainty. This feels at least analogous, maybe more, to the epistemological notion of belief or commitment. Some epistemologists, like Jennifer Nagel and Brian Weatherson, have emphasized that whether one is in this state depends (causally or constitutively, respectively) on the practical situation—when the stakes are high, one is less likely to believe. Maybe moral certainty is something like, being such that one would count as believing even in very high stakes cases. And although this state isn't, as Woods points out, sufficient for appropriate conviction, a normative connection seems plausible: one should only be in this state if one has a proof of corresponding strength. Don't be sure unless it's proven.

It's hard for me not to think in terms of knowledge. One contextualist way of mapping these thoughts would have it that, given a high standard for knowledge, all and only that which is proven beyond a reasonable doubt is 'known', and jurors should vote to convict if and only if they know the defendant guilty. I think this could make sense of these issues—although it'll probably be too simple in other respects, such as the restriction of admissible evidence. (Some things jurors know, they're not supposed to consider. (Or maybe a weird standard could count them as unknown? Something to think about.))

Anyway, I know I'm being really naive here, but I'd be interested in digging in a little bit, if anyone has ideas or reading suggestions.

The Certainty Norm of Assertion

In a well-known paper, Jason Stanley argues against the knowledge norm of assertion, in favour of a certainty norm of assertion. As Jason notices, knowledge-denying Moore-paradoxes like (1) aren't the only Moore-paradoxes in town; certainty-denying conjunctions like (2) seem similarly paradoxical:

1. Jason works at Yale but I don't know that Jason works at Yale
2. Jason works at Yale but it's not certain that Jason works at Yale

Jason thinks that knowledge doesn't entail certainty, and so a knowledge norm of assertion can't explain what's wrong with assertions of (2). Instead, he opts for a certainty norm of assertion, that's meant to explain both.

The argument I thought I remembered from the paper was that the certainty norm was strictly stronger than the knowledge norm. The certainty norm explains (2) in the obvious way (just like the knowledge norm explained (1)); and it explains (1) by invoking the entailment of knowledge by certainty. If I don't know that Jason works at Yale, it's not certain, so I can't assert the first conjunct. But today I read the paper again, and that's definitely not the argument. Certainty, in the sense Jason discusses, does not entail knowledge.

The relevant notion of certainty here is 'epistemic certainty', according to which 'one is certain of a proposition p if and only if one knows that p (or is in a position to know that p) on the basis of evidence that gives one the highest degree of justification for one's belief that p'. (p. 35) Since certainty does not entail knowledge, on Jason's view, it is not quite clear to me how a certainty norm explains the infelicity of (1). Of course one can't know both conjuncts in (1), but I don't see why why one couldn't have certainty in both conjuncts. Here is Jason's attempt to deal with the issue:

Consider the proposition that there are no large Jewish elephants in my bedroom. This may have been an epistemic certainty for me five minutes ago, even though I did not know that there were no large Jewish elephants in my bedroom. I did not know that there were no large Jewish elephants in my bedroom, because I did not believe it, and I did not believe it simply because it didn't occur to me ever to entertain that possibility. Nevertheless, in this case, if I had entertained the propsition that there are no large Jewish elephants in my bedroom, I would have known it. The reason this counterfactual is true is because it is an epistemic certainty for me that there are no large Jewish elephants in my bedroom. So the fact that a proposition is an epistemic certainty for a person does not entail that the person knows that proposition. If a proposition is an epistemic certainty for a person at a time, then it does follow that the person is in a *position to know* that proposition. Being in a position to know a proposition is to be disposed to acquire the knowledge that the proposition is true, when one entertains it on the right evidential basis. Since epistemic certainty entails possession of this dispositional property, utterances [like (1)] are odd. (p. 49)

The thought seems to be that if something is certain, then if one asserts it, one must know it. But it doesn't follow from his explanations of these notions that this must be so—couldn't something be asserted without being entertained on the right evidential basis? Suppose for instance that p is certain for me, but I don't know p because I am ignoring my overwhelming evidence for p, and basing my belief that p on some bad evidence. Couldn't it be, in this case, that it's also certain for me that I don't know p? I think it seems plausible that I might—my evidence, which, suppose, includes some sort of introspective access to the source of my belief—might overwhelmingly establish that I don't know that p. But if so, the certainty norm predicts that 'p but I don't know that p' should be assertable.

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.