Imagine that 100 prisoners are exercising in the prison yard, and suddenly 99 of them attack the guard, carrying out a plan that the 100th prisoner is no part of. Now one of these prisoners is in the dock. No further evidence is available. Guilt is 99 per cent likely, innocence 1 per cent. Should the court convict? Everyone’s first reaction is – certainly not. The court has no information that rules out the defendant being the one innocent prisoner. You can’t convict someone solely on statistical evidence.
But, he says, this is puzzling because we will convict on things like eyewitness testimony that is only 95% certain. Papineau then says the most plausible of the many controversial explanations of this, is Clayton Littlejohn's argument that the difference is knowledge. Then he concludes, "If the courts are aiming to convict the guilty and free the innocent, and to avoid the converse results, what’s the logic in preferring sources of evidence, such as eyewitnesses, that lead to more false convictions?"
Notice that there's no significant connection here. Papineau himself recognizes that the Littlejohn account is not the only account, and that this whole area is quite controversial, so the only thing connecting this problem to knowledge at all is Papineau's estimate that it's the most plausible account. That is weak, at best.* And it's the assumption on which most of the rest of Papineau's argument is based.
The primary argument, mostly gestured at, that does not seem to be based on this assumption is his rejection of the knowledge norm of assertion (one ought to assert something only if one knows it). I agree with the rejection; knowledge has never been a good candidate as 'the norm of assertion'. But his argument doesn't rule out that knowledge might be a norm of assertion; nor does it rule out the possibility that knowledge might just be the optimal case of something fitting whatever norm of assertion we might be assuming. Since Papineau doesn't seem to think that 'knowledge' is an incoherent concept or a meaningless term, surely he would not say that, given merely believing X reasonably and knowing X, that the latter would always be worse. He says, "All we really care about is whether their beliefs are likely to be true.". But is that really all we ever care about? If nothing else the widespread attraction of the idea of knowledge would seem to suggest this is unlikely.
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* If you're interested in my view of it, I think Clayton's proposal is extremely implausible, and I think Papineau and most people who discuss this matter are making an error, all too common among people of analytic stripe, that because something can be modeled by probabilities it is a matter of certainty and uncertainty. (This gets things backwards; probabilities are often handy in dealing with things like certainty and uncertainty, possibility of error, and the like, but that doesn't mean that they are good for nothing else.) In legal cases (and in many others), the certainty of evidence, while important, is a secondary issue; the primary issue is admissibility as evidence to begin with, which has nothing to do with the percentages. The difference between the prison yard example and an eyewitness example is causation, not knowledge; evidence is a causal notion. Eyewitness testimony is a causal chain purporting to link us to the actual event. (This is one of David Hume's truly important insights.) If you have an eyewitness testifying that this person did something bad, that is evidence, even if defeasible, that this person did something bad, because you have an effect, the testimony itself, that purports to be caused by this person doing something bad. But in the prison yard case we don't have any causal chain, even a purported one, to this person doing something bad.
It's particularly odd to be thinking about knowledge in a legal case, because knowledge, unlike (say) reasonableness, is at least arguably never important in legal cases. This is partly because in legal cases (1) not all legitimate evidence is admissible, for both ethical and practical reasons; and (2) issues of corruption, abuse of power, and the like raise worries that are often more important than accuracy of conclusion, and their safeguards affect the examination process (courts are not supposed to be strictly impartial investigators but to apply law with a bias toward public good). Every DA knows cases where it was so very certain that someone committed a crime, but the obstacles to getting the right evidence, of the right kind and quality, to get a conviction, were just insurmountable. Courts of law are deliberately set up to guarantee that this will happen in certain kinds of cases.
Bizarrely, Papineau comes close to recognizing the issue here, saying,
We hanker for some clear and direct-seeming causal path from the facts to our mind, akin to how nothing lies between the banana and the alpha monkey. Eyewitnesses and their testimony fit that model, but the statistical evidence doesn’t. It’s too indirect.
But knowledge doesn't play any role here; causation explicitly does. (Even the 'clear' doesn't bring in knowledge, because it can be purely a matter of Papineau's preferred concept of belief.)