This article deals with decision-making in legal contexts. I will discuss which epistemic standard must be satisfied by a fact-finder, whether the fact-finder is a member of a jury, a whole jury, or a judge, in order to establish something as a fact so that this fact can serve as a proper basis for convicting a defendant. I will argue that the concept of knowledge plays a central and ineliminable role in such legal decision-making.

I will develop my own proposal via critical discussion of a like-minded proposal by Sarah Moss, namely that “legal proof requires knowledge” (Moss, 2023: 176). The unifying thread throughout this article are reflections on the beyond reasonable doubt (BRD) standard of proof. In Sect. 1, I will introduce the details of Moss’s account and how she motivates it via the BRD standard. In Sect. 2, I will argue that there are important disanalogies between BRD and knowledge that undermine Moss’s argument. There is however another motivation for the knowledge account: combined with auxiliary claims, that is probabilistic knowledge and moral encroachment, it can provide a general solution to the puzzle of statistical evidence. Section 3 spells out the details. In Sect. 4, I suggest to combine the knowledge account with pragmatic encroachment, instead of moral encroachment, in order to stay clear of the thorny issues whether corporations have moral rights. In Sect. 5, I argue that the verdicts of Moss’s account in cases of false justified beliefs and non-luminous knowledge conflict with the BRD standard and thus call for abandoning the account. Based on various functions of legal proof and the BRD standard, I suggest a replacement for the knowledge account that is also just as potent as a general solution for the puzzle of statistical evidence. While I will grant that knowledge is neither always necessary nor always sufficient for convictions, I will argue that the concept of knowledge nonetheless plays a significant and ineliminable role in legal decision-making.

1 The knowledge account and the reasonable doubt standard

Starting point for Moss’s account is the famous puzzle about statistical evidence.

Prisoners

99 out of 100 prisoners exercising in the prison yard start a sudden attack on the prison guards. There is no evidence available as to which prisoner was not involved in the attack. The prosecutor picks a random inmate and charges him with participation in the attack. (Moss, 2023: 175), but also Nesson (1979), Redmayne (2008), Littlejohn (2020))

The standard reaction to cases like Prisoners is that the statistical evidence makes it overwhelmingly likely that the randomly picked inmate participated in the attack. But a conviction based on merely statistical evidence is inappropriate. This is puzzling because other types of evidence, for example eye witness testimony, would make a conviction appropriate, despite the fact that relying on the eye witness is no more likely to deliver a correct verdict than relying on statistical evidence.Footnote 1 However, in Prisoners, you simply don’t know that the randomly picked inmate participated in the attack. This lack of knowledge might explain the inappropriateness of a conviction.Footnote 2

Moss motivates the claim that conviction demands knowledge, or in short “the knowledge account” with yet a different strategy. Her starting point is the standard of proof in criminal cases, beyond reasonable doubt, or in short BRD. She writes that “…the knowledge account not only explains why most attempts to describe reasonable doubt fail, but also why certain attempts are more likely to succeed.” (Moss, 2023: 182).Footnote 3 This is a novel motivation of the knowledge account that is independent of the puzzle of statistical evidence. Thus, a closer look at how Moss arrives at this conclusion is called for.

Moss (2023: 178) begins with the observation that even among practitioners, attempts to define the BRD standard in independent and helpful terms to make it clearer have failed. For the sake of brevity, I will not review the details Moss provides here.Footnote 4 Moss points out that definition attempts by judges via jury instructions have also resulted in overturned verdicts because providing such instructions is a ground for appeal in some jurisdictions. Moss (2023: 179) thus writes that “[t]here seems to be something elusive about the standard itself,”Footnote 5 which naturally leads her to the question why this standard is so hard to define and why to some, no further elaboration is more appropriate than any elaboration at all.

This brings Moss to David Lewis and his famous claim that knowledge is in a certain sense elusive. This elusiveness of knowledge is the result of Lewis’s brand of infallibilism.Footnote 6 Lewis suggests that “…S knows that p iff S’s evidence eliminates every possibility in which not-p – Psst – except for those possibilities that we are properly ignorning” (Lewis, 1996: 554). This saves our knowledge in everyday contexts, as there we are properly ignoring many uneliminated error possibilities. However, as soon as we attend to an error possibility, for example, when we do epistemology, we are no longer properly ignoring it. Therefore, our everyday knowledge vanishes as soon as we acknowledge uneliminated error possibilities, rendering our knowledge elusive.

Moss intends to connect this sense of the elusiveness of knowledge with the mentioned elusiveness of the BRD standard of legal proof as an argument for the knowledge account of legal proof (see Moss (2023: 180). Lewis assumes that we ordinarily know that our car is parked in the drive way via memory. But such ordinary knowledge seems to vanish as soon as we entertain the thought that it might just have been stolen a minute ago by a cunning car thief—that possibility is simply not ruled out by our evidence. Moss argues that the difficulty of giving a strict definition that distinguishes reasonable and unreasonable doubts is due to a similar issue. She asks us to imagine the following jury instruction:

It does sometimes happen that a defendant is framed as part of a government conspiracy. But you should ignore this possibility, along with any other possibility it would be unreasonable for you to consider. Now if you can truly say that you know that the defendant is guilty, you should return a guilty verdict.

(Moss, 2023: 181)

Moss contends that a simple reminder about the beyond reasonable doubt standard would remind jurors to not consider unreasonable possibilities. But by providing an actual example of an unreasonable possibility, one risks taking jury members out of the very context one wants them to be in, as one has them consider an unreasonable doubt that they should not be considering (Moss, 2023: 182). This leads Moss to the conclusion that the elusiveness of knowledge can explain the elusiveness of the BRD standard.

2 Reasonable doubt about Moss on reasonable doubt

In this section, I will argue that there are significant differences between the elusiveness of knowledge and the elusiveness of BRD so that the former will not be fitting to explain the latter. As mentioned above, for Lewis, the elusiveness of knowledge results from his infallibilism which requires the elimination of all error possibilities. For Lewis, the following concessive knowledge attribution sounds odd and is false.

(1) I know that the defendant is guilty, though my evidence does not rule out the unreasonable doubt that the defendant was framed by the government.

But even if you agree with Lewis, it is non-obvious that you should therefore find a fault with the following utterance.

(2) The evidence proves beyond reasonable doubt that the defendant is guilty, though it does not rule out unreasonable doubts such as that the defendant was framed by the government.

I hope that to you, an utterance of (2) sounds fine, or at least that it does not feature the oddness or simple falsity of a concessive knowledge attribution like (1). If you agree, then I have given you reason to assume that the elusiveness of knowledge must be different from the elusiveness of BRD, which in turn makes it reasonable to doubt that the former can explain the latter.

But we can go further to support this point. There is a structural reason that speaks against Moss’s claim. According to Lewis, you do not know as soon as you admit that there is an error possibility that is uneliminated by your evidence. Lewis’s claim about knowledge is contested by many fallibilists. But no matter where you stand on this dispute about knowledge, it seems that there cannot be the same dispute about BRD. If BRD would simply mean that all doubts have been eliminated, then the BRD standard would not be hard to define—we would have given a definition of it (though it would be impossibly hard to meet the standard so defined).

Moreover, everybody seems to agree that BRD does not mean beyond all doubt. If that were what it meant, then there could be no relevant distinction between reasonable and unreasonable doubts. The elusiveness that Lewis claims for knowledge is a byproduct of infallibilism. But while infallibilism is a respectable position when it comes to knowledge, it seems to be a non-starter for BRD. Therefore, one cannot explain the elusiveness of the BRD standard via the elusiveness of knowledge, because the latter is sourced in a feature of knowledge, infallibilism, that BRD simply does not have.

Moss might say that the relevant point of similarity is the relevance of error possibilities. According to Lewis (1996: 559), an error possibility attended to is an error possibility that is no longer properly ignored. In a similar fashion, Moss might claim that a doubt, which just is an error possibility, can no longer properly be ignored once it is attended to, and thus becomes a reasonable doubt. But again, it seems doubtful that BRD features a rule of attention analogous to the rule of attention that Lewis claims for knowledge. According to the suggestion under consideration, it would be true that by merely mentioning a doubt, that doubt would thereby automatically become a reasonable doubt. But if that was true, we could not ever give examples of unreasonable doubts, as by mentioning something as an unreasonable doubt, we turn it into a reasonable doubt. But that seems simply false, and it seems that Moss would agree. For otherwise, the instruction she envisioned, quoted in the last section, could simply not be given, at least not without the instructor speaking falsely. They explicitly mention the unreasonable doubt as an unreasonable doubt. But to me, the instruction has no inherent ring of falseness to it. And since Moss does not mention it, I would assume that she would agree.

What she does say, as I have pointed out in the last section, is that by mentioning the unreasonable doubt one risks that somebody will actually take the doubt seriously. But we can agree on this without agreeing that merely mentioning a doubt turns it into a reasonable doubt. Suppose my daughter is learning how to ride a bike on the side-walk, but there is an electricity pole. True, by instructing her “Do not look at the pole or you will crash into it,” I might increase the risk that she will look at the pole, and as a result crash into it. But in uttering the instruction not to look at the pole, I am not thereby automatically instructing her to look at the pole. Mutatis mutandis for unreasonable doubt. Surely, the instructor, asking me not to consider an unreasonable doubt, runs the risk that I will consider this doubt. But it seems a stretch that their instruction, by merely uttering it, actually instructs me to do the opposite of what is intended.

To sum up, we have considered whether the elusiveness of the BRD standard can be explained via the same feature that arguably plays a role for the elusiveness of knowledge, the rule of attention. But it seems that there is simply no proper analog when it comes to BRD. Thus, it is doubtful that the elusiveness of knowledge can explain the elusiveness of the BRD standard.

Here is one possible rejoinder for Moss. She does quote an actual jury instruction given by a district attorney and granted by the court in a burglary trail in Mississippi. Here is the instruction as it was quoted in the opinion of the appeal of the original trail, Nobles v. State (1970). The appeal was granted because the appeal court condemns such instructions.

The Court instructs the Jury for the State of Mississippi that you do not have to actually know that the defendant is guilty before you can convict him; but that it is only necessary that you should believe from the evidence in this case beyond a reasonable doubt that he is guilty; and if you do believe from all the evidence in this case, beyond a reasonable doubt, that the defendant is guilty, it is your sworn duty to find him guilty as charged. Nobles v State (1970).

Moss’s concern with this instruction is that it suggests that “knowledge requires eliminating all doubts, whereas conviction merely requires eliminating all reasonable doubts - and hence conviction cannot require knowledge” (Moss, 2023: 184). This concern is close to my point above that BRD does not have a natural infallibilist reading, as knowledge does. Thus, it merits considering what Moss writes about these jury instructions.

…as long as jurors are being reasonable, there will not be any difference from their perspective between eliminating all doubts and eliminating reasonable ones….[the instruction, A.M.] is problematic because by considering it, one calls attention to this difference, and implicitly grants the existence of the very possibilities that the reasonable doubt standard calls jurors to set aside. That is what is wrong with issuing the above jury instruction, and why it was right for the Mississippi Supreme Court to reject it. (Moss, 2023: 185).

Since the instructions were condemned, there must have been something faulty about them. According to Moss, what is faulty about them is that they presuppose a false contrast between knowledge and BRD. The Moss quote seems to suggest that the Mississippi Supreme Court rejected this instruction because it made it too hard for the jury to convict, as the instruction, according to Moss, brings into play the kind of doubts they need not consider. Notably, the Mississippi Supreme Court finds actually the opposite fault with this instruction.

We have condemned the use of this instruction for some time. We had hoped that the district attorneys would cease to use an instruction that is palpably unfair and misleading. It is obviously an effort to placate the natural caution on the part of the jury to require satisfactory evidence of guilt. Nobles v. State (1970).

Clearly then, in this particular case, the Mississippi Supreme Court was not concerned that the instruction might make it too hard to convict, but rather too easy. Moreover, while the Mississippi Supreme Court is concerned that the given instruction might unduly influence a jury, in a different case, they suggest that they do not disagree with the content of the instruction.

While the instruction contains a correct statement of an abstract principle of law, we think that it falls within that class of instructions which it would be better not to give. Carrol v State (1968).

By granting that the instructions are correct in stating an abstract principle of law, that is the BRD standard, the Mississippi Supreme Court position themselves as opponents to the knowledge account of legal proof. Needless to say that their judicial expertise might not necessarily position them to be the ultimate judges of the knowledge account, but it certainly must have some weight on this issue. Altogether then, the rejections of certain jury instructions by courts are hardly a point in favor of the knowledge account of legal proof.Footnote 7

In sum then, it is questionable whether the elusiveness of the BRD standard can be explained via the elusiveness of knowledge. That is bad news for the knowledge account of legal proof. But Moss gives two further considerations in favor of it.

First, Moss does concede that the BRD standard can be explained further, namely via the suggestion that a claim is BRD if one would act on this claim even in regard to one’s own most important affairs. Moss quickly points out that many take knowledge to be sufficient to rely on even in one’s own most important affairs. So there is another potential analogy that would suggest that the BRD standard can be spelled out in terms of knowledge. However, whether this practical explication of the BRD standard succeeds depends on the controversial matter whether knowledge is always sufficient to act on. For arguments to the contrary see Brown (2008), Lackey (2010), Gao (2017), and Schulz (2017). Since this is a controversial issue, I believe it is very much up for debate whether this practical explication of the BRD standard really supports the knowledge account.

The second consideration Moss mentions is that the BRD standard cannot be spelled out in terms of probabilities. Even an unlikely possibility can sometimes require consideration. The case Prisoners provides one example. While the randomly picked inmate was very likely involved in the attack, the evidence available does not seem to establish this BRD (Moss, 2023: 186). Since the knowledge account of legal proof comes to the same verdict, and a lack of knowledge is not always due to an error possibility being likely, the knowledge account of legal proof seems to explain some peculiarities of the BRD standard, which is a point in favor of the knowledge account of legal proof.

I think this is the argument that makes the best case for the knowledge account of legal proof yet. As I will explain in the next section, Moss’s version of the knowledge account can also offer a general solution to the puzzle of statistical evidence, and this capability certainly is a proper motivation of the knowledge account of legal proof.

3 Knowledge as an answer to the puzzle of statistical evidence?

We already introduced the relevant case, Prisoners at the outset. While it is highly likely that a randomly picked inmate participated in the attack on the guard, a conviction seems questionable. Now the knowledge account can easily account for this. All the jury has to go on is statistical evidence, but beliefs based on merely statistical evidence cannot amount to knowledge. Therefore, the knowledge account can easily explain why it is not proper to convict based on merely statistical evidence.

So far, so good. But one must worry that the knowledge account will be of no help in sufficiently similar cases. Here is another case commonly found in the debate, based on Cohen and Jonathan (1977):

Gatecrashers

499 tickets were sold for a concert. But all seats at the venue were filled, which means that 1000 people attended. Therefore, 501 persons of the people in attendance did not pay for their ticket.

If the venue owner would seek for damages from a randomly picked attendee, he would nonetheless fail, despite it being the case that there is a 50.1% chance that the randomly picked attendee gate crashed. But this is puzzling because in civil procedures, the relevant standard is “preponderance of evidence”: it has to be merely more likely than not that the attendee gate crashed. While it may be that the standard of proof in criminal cases, BRD, can be cashed out in terms of knowledge, it is anything but clear that the preponderance of evidence standard can be cashed out in terms of knowledge. And while the knowledge account does generate the right prediction in Gatecrashers, it does so at the expense of coming to the right verdict for the wrong reason. A lack of knowledge should never be the issue whenever the preponderance of evidence standard is in play, as then, asking for knowledge is simply asking for too much. And still, in the Gatecrasher case, a conviction seems improper, although it is more likely than not, that the randomly picked attendee did gate crash.

Moss’s solution to capture standards of proof other than BRD is to appeal to probabilistic knowledge and moral encroachment. According to Moss, credences can constitute knowledge, in the sense that your probabilistic beliefs can constitute knowledge. For example, your belief that it is more likely than not that you have strep virus can amount to knowledge, given that it is not influenced by knowledge undermining factors such as epistemic luck or that it is not merely based on hunches. The detailed case for probabilistic knowledge is given in Moss, (2013, 2018a), I will not review the details here, I accept that there can be probabilistic knowledge. To capture other standards of proof, for example preponderance of evidence, Moss’s idea is that conviction requires probabilistic beliefs that amount to knowledge. For example, in order to meet the preponderance of evidence standard, one has to know that it is more likely than not that the defendant did what they are accused of.

However, to capture why one lacks probabilistic knowledge in a case like Gatecrashers, Moss also appeals to moral encroachment. Moss does not explicitly use the term here. Though in the relevant passages, she does refer the reader back to her previous work on moral encroachment (Moss, 2018b) and the view expressed here seems to be identical. About a case just like the Gatecrasher case, Moss writes:

…your justified credence does not constitute knowledge. You do not know that this particular defendant is liable, because you can’t rule out a relevant possibility that is inconsistent with this content – namely that the defendant is an individual whose character makes him far less likely to trespass than just some arbitrary person (Moss, 2023: 200).

Later on, Moss explains why this is a relevant possibility.

…it is often held that whether a possibility is relevant depends partly on what is at stake – for instance, the cost of having a false belief if the possibility were to obtain. Falsely profiling an individual person as having a negative character trait might be morally different from other instances of false profiling, such as inanimate objects or corporate defendants (Moss, 2023: 202).

While the term moral encroachment is not used here, it would certainly seem fitting. An alternative can become relevant and thus knowledge undermining if a false belief is costly, in the sense that one falsely beliefs that an individual is guilty when this belief is based on their membership of some group, without taking into account that they might be quite unlike the group they happen to be a member of. Our randomly picked attendee might be quite unlikely to gate crash, though they happen to be part of a group that mostly gatecrashed. Similarly, our randomly picked inmate in the case Prisoners might be absolutely unlikely to commit violence, though they happen to be a part of a group that mostly committed violence. Since the statistical evidence does not rule out such possibilities, but these possibilities are relevant, one does not know that is it more likely than not that the randomly picked attendee gatecrashed, or that the randomly picked inmate attacked the guard. Hence, in both cases, the merely statistical evidence is insufficient for conviction.

Finally, Moss explains that the knowledge account can even capture cases in which, perhaps surprisingly, statistical evidence can suffice for conviction.Footnote 8 In Kramer v. Weedhopper, Kramer filed a complaint alleging strict product liability against Weedhopper, as well as against Lawrence, who supplied 90% of a specific bolt to Weedhopper, which was defective and thus a proximate cause of Kramer’s accident. The Appelate Court of Illinois decided that “under circumstances which show that a defendant supplied 90% of the parts used, this evidence is sufficient to withstand a motion for summary judgment” (Kramer v. Weedhopper of Utah, Inc, 1986). On Moss’s account, causation would be proved as long as the “factfinder knows that causation is more than .5 likely” (Moss, 2023: 202). For this to be the case, all relevant possibilities in which it is not the case that causation is more than 0.5 likely need to be ruled out.

Of course, there can be disagreement about this whether this is truly the case here, which Moss acknowledges, and which the dissenting opinion in Kramer v. Weedhopper clearly voices. However, the relevant point is that statistical evidence can at least sometimes give rise to probabilistic knowledge. A less controversial example may be a case in which I have statistical evidence that 90% of all cars of a specific manufacturer have engine failures within a year. If I possess a car of said manufacturer, it would seem that I know that it is more likely than not that my car will have an engine failure within the next year. Since statistical evidence can sometimes give rise to probabilistic knowledge, the knowledge account is in principle compatible with cases in which merely statistical evidence suffices for a conviction.

Therefore, it seems as if the knowledge account does after all generalize. It cannot only capture cases like Prisoners, but also cases like Gatecrashers, in which the relevant standard of proof is not BRD, but the preponderance of evidence. The knowledge account does thus seem to offer a general solution to the puzzle of statistical evidence, which would certainly be a point in favor of the knowledge account of legal proof.Footnote 9

4 From moral to pragmatic encroachment

Clearly, the general solution to the puzzle of statistical evidence that Moss offers comes with some controversial commitments, one of them being moral encroachment.Footnote 10 While I am not opposed to accepting moral encroachment, I worry that one can only offer a general solution to the puzzle of statistical evidence if one accepts that corporations have moral rights. As quoted above, Moss assumes that falsely profiling individual persons is morally costly, but falsely profiling inanimate objects or corporations is not or at least not necessarily so. However, one of the standard cases discussed in regard to the puzzle of statistical evidence does not involve persons, but corporations. Here is one such case based on Thomson (1986):

Cab Company

A vehicle damaged Jess’s car and then fled the scene. Jess could tell that the vehicle was a cab, as it had a taxi sign on the roof, but she has no further information that could identify which particular cab it was, or by which company it was operated. However, the police investigation quickly reveals that in this town, 60% of all cabs are owned by the Green Cab Company, and the other 40% by the Red Cab Company, and the proportion of cabs on the street at the time of the accident also reflects this. Jess sues the Green Cab Company for damages. There is no further evidence besides the statistical evidence just mentioned.

Intuitively, Jess should not be successful in her legal pursuit, although it would seem that the statistical evidence makes it more likely than not that a cab of the Green Cab Company damaged her car. But it is not clear that the knowledge account can capture this. The Green Cab Company is not a person. You do not need to have a bumper sticker on your car that says “I believe that corporations are people when Texas executes one” in order to doubt that corporations have the same moral rights or moral significance that actual persons like you and me have.

But if it is doubtful that corporations have the same moral significance as ordinary persons do, then it is doubtful that Moss can succeed in capturing Cab Company in the same way as she intends to capture Gatecrashers. While it would seem that we must consider that the randomly picked attendee is quite unlike the group of gatecrashers of which he happens to be a part of, it is not clear whether the Green Cab Company has the same moral standing as the randomly picked attendee that would make certain alternatives relevant that would undermine having the relevant probabilistic knowledge. Thus, it is not clear whether the knowledge account of legal proof does deliver a fully general solution to the puzzle of statistical evidence.

How pressing the issue I raise here is crucially depends on whether corporations have moral rights. Clearly, what gives human persons moral significance is a hotly contested matter. Are we morally significant beings because we have (sophisticated) cognitive capacities? Is it because we are all members of the same biological species? I defer the reader to Jaworska and Tannenbaum (2021) for an overview and discussion of these and other options. Just note that on all the options in the running, corporations clearly do not have moral significance. They do not have cognitive capacities and they are certainly not a member of the same biological species as us, either.

One might suggest that corporations have moral rights in virtue of their shareholders, or employees, having moral rights.Footnote 11 While I see the appeal of this view, one must wonder how this works. One might say that a corporation is constituted by the sum of its employees. But it is not generally the case that a whole has a property in virtue of its constituent parts having that property. A whole pizza does not have the geometrical shape of a circle sector, though all of its constituent pizza slices have the geometrical shape of a circle sector. This is by no means a knock-out argument against the proposed view, but it demonstrates the need for an explanation as to why a corporation should have a specific property just because its constituent parts clearly have that property. The ownership relation in which the shareholders stand to the corporation faces a similar issue. I stand in the ownership relation to a car, but it is clearly absurd that my car has moral rights because I, the owner, has moral rights. Therefore, as intuitively appealing as the idea that corporations have moral rights in virtue of their employees or shareholders may be, it stands on shaky grounds because it is unclear how and why the transfer of moral rights from owners or shareholders to a corporation would come about.

The good news is we need not settle whether corporations have moral rights, as I can offer a fix to capture cases involving corporations: switch from moral encroachment to pragmatic encroachment. Surely, pragmatic encroachment is itself a controversial theoryFootnote 12, but surely not anymore controversial than moral encroachment. What then is the difference?

Moral encroachment, as the name suggests, is rooted in the moral features, for example the moral rights of persons. Pragmatic encroachment is a broader view; it awards epistemic significance to practical considerations more generally. For example, in the famous high-stake bank cases (see for example Stanley (2005), being wrong about the hours of the bank could have significant practical consequences—loss of one’s house due to failing to make a deposit in time because one got the hours of the bank wrong. While the loss of one’s house is a significant practical costs, it is not a significant moral costs (assuming that this affects just yourself, and not others who have moral rights against you, for example, your children and their right to shelter). According to pragmatic encroachment, these practical costs can make it that you fail to know the hours of the bank, though you would know, if less was at stake, as these practical costs can make certain alternative possibilities relevant that would otherwise be irrelevant.

But surely, as soon as one is engaged in legal decision-making, one is in a high-stake situation not entirely unlike the one in the high-stake bank case. If you are a conscientious jury member, it will be of considerable practical significance to you to get the case right, as you value a justice system that does not convict an innocent defendant. This practical concern might sometimes align with moral concerns if the defendant is a person and thus has certain moral rights. But this practical concern does not require that the defendant is a person. For the conscientious jury member, it will still be of the utmost importance to get the case right and to not convict the innocent even if the defendant is not a person, but a corporation.

This gives us all we need for a slight modification of Moss’s account that provides a fully general solution to the puzzle of statistical evidence. We maintain that there is probabilistic knowledge and that the preponderance of evidence standard is met if one knows that it is more likely than not that the defendant is guilty of what they are accused of. So in Cab Company, a jury member should convict only if they know that it is more likely than not that the accident was caused by a cab from the Green Cab Company.

But for the conscientious juror, there is a lot at stake in getting things right. Thus, they ought to consider certain possibilities. For example, they might wonder: Do I really know that it is more likely than not that a cab of the Green Cab Company caused the damage based on the statistical fact that they own 60% of all cabs in the city? What if the Green Cab company is extremely cautious in their hiring process so that they are extremely unlikely to hire a driver capable of an act of moral turpitude such as fleeing from the scene of an accident? What if their competitor, the Red Cab Company has a practice of hiring only former race car drivers, which would make it unsurprising if they caused more accidents? Too far-fetched? Perhaps the Red Cab Company drivers have longer shifts, which might make it more likely for them to cause accidents? In light of these open questions, do I really know that it is more likely than not that the accident was caused by a Green Cab Company cab? Given that the statistical facts do not rule out the mentioned possibilities, one lacks the relevant probabilistic knowledge.

We can also bring this out with a contrasting low-stake case in which the mentioned possibilities do not seem relevant. For example, a police officer is tasked with investigating the accident, and they are aware of the statistical fact about the proportion of the cabs owned by each company that operates in the city. Here, it would seem perfectly fine for them to claim: “Hey, we know that it is more likely than not that the cab which caused the accident is owned by the Green Cab Company. Let’s go investigate them first so that we can close the case for good as soon as possible.” Here, in a given sense, not much is at stake if the officer is wrong and it is not more likely than not that the accident was caused by a Green Company cab. The only consequence is that their intended investigative strategy would not be the quickest way possible to close the case for good. But, assuming that nothing hangs on closing the case as soon as possible, that is not a dramatic consequence, at least compared to the consequence of punishing an innocent defendant. That is why the mentioned possibilities that the conscientious juror considers need not be considered by the police officer, and that is why the latter can claim to know, and why the former cannot.Footnote 13

The revised knowledge account can also be applied to cover cases like Gatecrashers or Prisoners. Here, for the conscientious juror, it will also be of the utmost importance to get things right. And that is why the possibility that the particular defendant is entirely unlike the group they happen to be a part of is relevant, and thus knowledge undermining. Therefore, the revised knowledge account can still provide a generalized solution to the puzzle of statistical evidence. While I am willing to grant that one may doubt that the revised account is necessary, as one may hold that corporations can have moral rights, I hope that such skeptics about the necessity of the revision can accept that the revised account has all the same qualities as Moss’s original account, and thus is as attractive as Moss’s original account.Footnote 14

5 From knowledge to justification to believe that one knows

And still, all is not well for the knowledge account of legal proof. Further reflections on the BRD doubt standard demonstrate that the knowledge account is problematic, due to two features of knowledge, that is factivity and potential anti-luminosity. However, these reflections on the reasonable doubt standard suggest a novel positive alternative account, which I call the JBK account. The JBK account can also resolve the puzzle of statistical evidence as efficiently as the knowledge account, and hence would thus seem to be a preferable alternative to it. That is the preview, the details will emerge over the course of the section.

The knowledge account of legal proof, since knowledge requires factivity, rules out that one can satisfy the BRD standard and convict an innocent person. But it seems that a tragic outcome, conviction of an innocent person, is at least a possible scenario, even when one satisfies the BRD standard (see Gardiner (2019a) or Blome-Tillmann (2017). Thus, the knowledge account must be rejected because it fails to allow for the genuinely possible tragic case of the conviction of an innocent person.

Moss (2023: 204) answers that in a case in which there is very convincing, but ultimately misleading evidence, a conviction is in one sense called for, but not in another. The knowledge standard can account for both of these judgments. To do this, Moss uses a distinction between primary objective norms and derived secondary subjective norms. Moss first points to ordinary norms like “water the garden iff it does not rain.” This is what she considers to be a primary objective norm, which determines the objectively right thing to do. Yet, there can be cases in which one has a very well justified but false belief that it did not rain today, and then one will end up watering the garden though it has rained. But every primary objective norm gives rise to secondary subjective norms, and your behavior, as long as it satisfies the secondary subjective norm, as it does in the justified false belief case, is blameless or perhaps even praiseworthy.

Now Moss assumes that the knowledge account delivers the primary objective norm for conviction: convict the defendant iff you know that the defendant is guilty (Moss, 2023: 205). She sees this supported by the fact that there is something unjust about convicting an innocent person, which is ruled out by the knowledge account. In the tragic case, one is following the derived secondary subjective norm, as from one’s perspective it would seem like one is following the primary norm, though one is indeed not. It is in this sense that a conviction is called for, as one meets the secondary subjective norm, although one violates the primary objective norm, which is the sense a conviction is not called for. The distinction between primary and secondary norms thus helps to capture the intuition that there can be tragic cases in which a conviction is called for, in a certain sense, while holding on to the knowledge account of legal proof.

The problem here is that Moss helps herself to a specific, but questionable primary objective norm. The only primary objective norm the law states clearly is: convict the defendant iff it is BRD that the defendant is guilty. It is non-obvious whether the BRD norm is co-extensive with a knowledge norm, in particular in light of the issue that the BRD norms seems to allow for false convictions, while the knowledge account would not. But Moss did rightly point out that there is something unjust about false convictions. Is there reason to assume that the BRD is meant to rule out such an injustice? According to the US Supreme Court, the BRD standard is meant to minimize the risk of false convictions, but it need not eliminate it entirely.

The requirement of proof beyond a reasonable doubt in a criminal case is ‘bottomed on a fundamental value determination of our society that it is far worse to convict an innocent man than to let a guilty man go free.’ Winship, 397 U.S. at 397 U. S. 372 (Harlan, J., concurring). The social cost of placing the burden on the prosecution to prove guilt beyond a reasonable doubt is thus an increased risk that the guilty will go free. While it is clear that our society has willingly chosen to bear a substantial burden in order to protect the innocent, it is equally clear that the risk it must bear is not without limits….[d]ue process does not require that every conceivable step be taken, at whatever cost, to eliminate the possibility of convicting an innocent person. (Patterson v. New York, 1977).

The BRD standard does not require eliminating all doubts, it only has the function to minimize the risk of false convictions (see also Ross (2021) and thus leaves room for tragic cases.Footnote 15 But then it cannot be that Moss’s suggested primary objective norm is simply co-extensive with the BRD norm, as Moss’s norm does rule out convicting the innocent. I think the law can legitimately claim authority over its own subject matter; thus, we can reject Moss’s suggested primary norm. The only objective primary norm the law accepts clearly is convict the defendant iff it is BRD that the defendant is guilty. Therefore, the fact that the knowledge account does not leave room for tragic cases is a decisive strike against the knowledge account. Moss’s defense is not convincing because she assumes that the primary objective standard norm for conviction must protect against the possibility of wrongful conviction by eliminating the possibility entirely. But the law sets a lower standard and finds conviction permissible as long as the risk of a wrongful conviction is minimized.

There is another reason to be skeptical about the knowledge account. Some have argued that one can know that p without it being reasonable to believe that p (see Lasonen-Aarnio (2010). Others have argued that one can know that p despite it being extremely improbable that one knows p (see Williamson (2014). Could it be proper to convict a defendant if one had such unreasonable or improbable knowledge? To me, the answer is no, but I will not press the issue here, as whether there is unreasonable knowledge or improbable knowledge seems somewhat debatable to me.

But at least nowadays, it is widely accepted that knowledge is not a luminous notion—there can be cases in which we know, but in which we are not in a position to know that we know. For example, we might have a lot of diverse evidence which is hard to evaluate, but that evidence ultimately puts us over the evidential threshold required for knowing, so that we do know. But for us, since the evidence is hard to evaluate, it will not be clear that we know. For all we know, we might just as well not know. This is a case of non-luminous knowledge.Footnote 16

Now, non-luminous knowledge is knowledge nonetheless. But can it be proper to convict in a case in which one’s knowledge that the defendant is guilty is non-luminous?Footnote 17 I contend that it is not. In a case of non-luminous knowledge, for all one knows, one does not know. But then it would seem that if one has to decide whether to convict or not that it must be a matter of luck that one’s decision is in accordance with the demand for proper conviction, even if it meets the demand. But it is widely acknowledged in the philosophical debate that a proper legal conviction cannot be compatible with merely being lucky in getting things right (see Thomson (1986: 214), which is also acknowledged in Moss (2023: 197), or Pardo (2005). In other words, legal proof has the function of providing a non-accidentality condition. But therefore, non-luminous knowledge is a serious problem for the knowledge account of legal proof. Non-luminous knowledge suggests that knowledge is sometimes not sufficient for a proper conviction, as non-luminous knowledge won’t serve the non-accidentality function of legal proof. That is because at least from the perspective of the fact-finder relying on non-luminous knowledge, it would seem to be a lucky accident that they did not end up convicting an innocent person.Footnote 18

I do think that there is a relatively simply fix to both, the false conviction issue and the non-luminosity issue. But it comes with a, at least at first sight, drastic departure from a knowledge-centric vision. Here is my fix. In order to convict, we should be able to provide a justification for our decision. Footnote 19 While not phrased in this term, the following passage about the BRD standard from the US Supreme Court suggests as much.

Moreover, use of the reasonable doubt standard is indispensable to command the respect and confidence of the community in applications of the criminal law. It is critical that the moral force of the criminal law not be diluted by a standard of proof that leaves people in doubt whether innocent men are being condemned (In re Winship, 1970).

This passage highlights that the BRD standard has a social function as well, which we can call the accountability function. I believe that in order to meet that social function, a juror needs to be able to provide a justification for their decision to their fellow citizens. For illustration, just consider a case of non-luminous knowledge again. Suppose a juror was asked why they decided to convict the defendant in such a case and that the juror admits that the evidence was complicated, that they are not sure whether they know that the defendant is guilty, that they actually might not know that the defendant is guilty. If that were to happen, that would surely make it doubtful whether a guilty person was convicted.

This then brings me to my positive proposal. Legal proof serves various functions that we have outlined above: minimizing the risk of false convictions, providing a non-accidentality condition, and generating accountability. The knowledge account is appealing because it captures two such functions of legal proof quite well. Knowledge does minimize the risk of false convictions, and it does entail getting rights not just accidentally (a point forcefully articulated in Pardo (2005), (2010), (2011). Knowledge entails getting things right not merely accidentally, but lesser epistemic states like justification do not. Therefore, a new proposal should continue to feature knowledge in some manner because it is a promising route to capturing a non-accidentality condition on legal proof, even if the issue of non-luminous knowledge demonstrates that knowledge does not capture it perfectly.

Moreover, we need to add something to knowledge in order to accommodate the accountability function of legal proof, which, again due to non-luminous knowledge, the knowledge account does not capture perfectly. Above, I suggested that an ability to provide a justification can satisfy the accountability function. Therefore, the three functions of legal proof, minimizing the risk of false convictions, providing a non-accidentality condition, and generating accountability, serve as an argument to put the separate pieces, knowledge, and ability to justify together. The resulting condition for legal proof is an ability to justify that one knows that the defendant is guilty—the JBK account. The mentioned functions of legal proof serve as an independent argument for the JBK account, as the components of the account make it suitable to serve these functions.Footnote 20 I demonstrate that below, where I will also say more about the ability to justify. First, though, here is how the JBK account can capture two standards of proof.

JBK-Conviction Norms

In a case in which the standard of proof is beyond reasonable doubt, convict the defendant iff you can provide a justification to believe that you know that the defendant is guilty.

In a case in which the standard of proof is preponderance of evidence, convict the defendant iff you can provide a justification to believe that you know that it is more likely than not that the defendant is guilty.

By “justification” I mean epistemic justification. I understand “providing a justification” quite literally, in the sense that you could either offer a verbal or written justification. I do not mean having merely propositional justification to believe, as it might not always be clear that one can take advantage of the propositional justification that one has and thus also not be able to provide it for others. The modal operator “can” is meant to have a strong reading; if asked for, you can provide a justification in the actual world, not just in another possible world. The relevant modal base is the evidence given in the case.Footnote 22 This evidence must enable you to provide a justification. The justification to believe that one knows will usually be the result of one’s reflection on one’s first-order evidence. If such reflection on one’s evidence does not support the claim that one knows, then even if one knows, for example in a case of non-luminous knowledge, then it is not proper to convict. Thus, the suggested JBK-Conviction Norms avoid the problem of non-luminous knowledge. Consequently, they are more suitable to accommodate the non-accidentality and accountability function of legal proof, as we have seen that non-luminous knowledge is a hurdle for the knowledge account when it comes to serving these functions.

The JBK-Conviction Norms also allow for false convictions. On most accounts of epistemic justification, epistemic justification is compatible with the falsehood of the proposition for which one has justification. Thus, one can also falsely but justifiably believe that one knows. That must not always mean that the relevant proposition is false, as a lack of knowledge can be caused by various considerations. But it does make room for cases in which the lack of knowledge is due to the falsehood of the relevant proposition. And hence, the JBK-Conviction Norms do not rule out that there can be false convictions of innocent persons.Footnote 23 At the same time, the JBK-Norms can arguably still serve the function of minimizing the risk of false convictions.

Then, there is the title of this paper which offers a slogan form of one aspect of the JBK-Norms. In order to deal with tragic cases of false convictions, we need to loosen the tie between knowledge and legal proof. According to my suggestion, knowledge that the defendant is guilty is not required for legal proof. However, knowledge plays a significant part in how the JBK-Norms are stated. We cannot simply replace the term “knowledge” with “justification” without losing something significant. We would immediately loose the capability to deal with the puzzle of statistical evidence. Statistical evidence may justify beliefs (see Lewis, 1996: 551). But we cannot know based on merely statistical evidence, and reflection on such evidence would also show that we lack such knowledge, hence we cannot provide a justification to believe that we know in cases of merely statistical evidence.

Furthermore, knowledge entails getting things right, and not only getting things right by accident, and that is at least what the law aspires too as well. It seems that we do not have any other epistemic concept that could serve this role. Justification certainly cannot, as justification is compatible with falsehood. Thus, we can conclude that while the JBK-Conviction Norms do not require you to know, but the notion of knowledge is nonetheless a significant and ineliminable feature of them, as it captures something that is of significance to the law and to which other knowledge-centric accounts appeal to (again, see in particular Pardo (2005, (2010), (2011) for the non-accidentality requirement on proper conviction).Footnote 24

Finally, the JBK-Norms have all the resources to solve the puzzle of statistical evidence just like the knowledge account did. The JBK-Norms easily account for Prisoners, as here, the evidence does not even support that one is justified in believing that one knows that the defendant is guilty. In order to capture Gatecrashers, one can appeal to probabilistic knowledge and pragmatic encroachment. Given what is at stake, the evidence in Gatecrashers does not justify one in believing that one knows that it is more likely than not that the defendant gatecrashed. The very same holds for civil cases in which the defendant is not a person, but a corporation, as in Cab Company. And just like the knowledge account, the JBK-Norms are compatible with convictions based on merely statistical evidence in cases like Kramer v Weedhopper. Here, reflection on the evidence can justify one in believing that one knows that it is more likely than not that the defendant caused the harm.

Therefore, the JBK-Norms can provide a general solution to the puzzle of statistical evidence. While the knowledge account can too, the knowledge account cannot allow for tragic cases of false convictions, which conflicts with the BRD standard, while it does allow for convictions in cases of non-luminous knowledge, which also conflicts with the BRD standard. Since the JBK-Norms do not have this shortcoming, they are a preferable alternative to the knowledge account.

6 Conclusion

We started with a critical evaluation of Moss’s motivation of the knowledge account via the BRD standard. I have argued that there are significant disanalogies between knowledge and BRD and also provided textual evidence that suggests that the knowledge account is unfitting to elucidate the BRD standard. Nonetheless, Moss’s knowledge account, combined with the auxiliary elements of probabilistic knowledge and moral encroachment, offers an ingenious solution to the puzzle of statistical evidence, which certainly is a sufficient motivation of the account. However, there is one significant caveat: it would seem that switching from moral encroachment to pragmatic encroachment can avoid controversial claims on which the resolution of the puzzle of statistical evidence hangs. Nonetheless, we must reject the knowledge account. On the one hand, it cannot account for tragic cases of false convictions, on the other, it allows for questionable convictions based on non-luminous knowledge. Both points also mark a conflict with the BRD standard. As a replacement, motivated by various functions of legal proof and the BRD standard, I have introduced the JBK-Conviction Norms. These norms avoid the two shortcomings of the knowledge account and yet, if supplemented with probabilistic knowledge and pragmatic encroachment, also offer a general solution to the puzzle of statistical evidence.

I want to close with a thought regarding general decision-making. I believe that the norms I have introduced here cannot directly support an account of decision-making in terms of knowledge. Such accounts aim at accounting for rational decision-making. But legal decision-making, or the law in general, does not necessarily aim to be rational, but to be just.Footnote 25 To arrive at just legal decisions, one may have to take steps that rationality does not demand. Rationality does not demand to discard any evidence in one’s decision-making, but the law may under specific circumstances, for example, if the evidence was obtained in an unlawful manner. Similarly, above, I have motivated the JBK-Conviction Norms via the demand that the law may not loose its moral force due to doubt about whether it convicts innocent people. But there is no obvious analog demand for rational decision-making one could use to argue for a norm akin to the JBK-Conviction Norm. This does not render my proposal insignificant, but I also want to stress that I see its significance limited to legal decision-making.