Uncertainty and Statistics – Lecture 12

Table of Contents

• Pappino’s paradox: prisoners versus witnesses
• A halakhic parallel: eyewitness testimony versus circumstantial evidence
• The dispute between Maimonides and Tosafot about conviction based on circumstantial evidence
• Probabilistic reasoning versus legal reasoning: reliability, admissibility, and intuition
• “A person cannot render himself wicked,” the Miranda ruling, and the Ritva on the structure of a religious court
• Formulating the difference between prisoners and witnesses, and the parallel to migo and presumption
• Majority that is before us and majority that is not before us: generalizing from a sample versus ignorance and symmetry
• Majority in monetary law: Rav and Shmuel, Tosafot, and Nachmanides and Rabbi Shimon Shkop

Summary

General Overview

The text presents Pappino’s paradox of statistical evidence in law: in a case of one hundred prisoners, of whom ninety-nine participated in an assault and one did not, no conviction is reached even though each defendant is apparently 99% likely to be guilty, whereas with eyewitness testimony from two witnesses assessed as 95% accurate, a conviction is reached. The author points to a parallel phenomenon in Jewish law between eyewitness testimony and very strong circumstantial evidence, brings Maimonides’ view that in capital cases one does not convict without eyewitness testimony even when there is very high circumstantial certainty, and notes that Tosafot disagrees and is willing to convict when the certainty of the circumstantial evidence reaches the level of two witnesses. The text then proposes a distinction between probabilistic-factual reasoning and legal-admissibility reasoning, through examples such as the disqualification of relatives, a litigant’s admission, and the rule that “a person cannot render himself wicked,” and develops the claim that sometimes legal intuition is decisive even without statistical justification. Finally, it offers an initial explanation through the distinction between a majority that is before us and a majority that is not before us, and the claim that there are situations in which “probability” reflects ignorance rather than information about the case itself, and it opens a Talmudic discussion of following the majority in monetary law through the dispute between Rav and Shmuel in the case of someone who sells an ox and it turns out to be goring, along with the explanations of Tosafot and Rabbi Shimon Shkop.

Pappino’s paradox: prisoners versus witnesses

Pappino describes one hundred prisoners, ninety-nine of whom attack the guard and one who does not, and yet no legal system would convict an individual defendant on the basis of the 99% statistical likelihood. Pappino contrasts this with a case of two witnesses testifying that a person committed an act, and even though we know witnesses can make mistakes, and for the sake of discussion assume 95% accuracy, conviction is based on their testimony. The text notes that the first case is defined as “statistical evidence” and the second as “evidence by force of testimony,” even though in both cases there is a probabilistic background assumption regarding reliability or frequency.

A halakhic parallel: eyewitness testimony versus circumstantial evidence

The text argues that a similar phenomenon exists in Jewish law, in that circumstantial evidence stands opposite evidence by force of witnesses. The author brings an example from the Talmud about a pursuer who entered a ruin with a knife, and after him a witness entered and found the pursued person dead and the pursuer holding a blood-dripping knife, with no other possible entrance or exit, and the conclusion appears “completely clear.” Maimonides writes that in such a case one does not convict as a matter of principle in capital law, whereas in monetary law the judge acts according to what appears correct to him. The text emphasizes that “statistical evidence” is not necessarily weak in terms of percentage of certainty, because circumstantial evidence may yield higher certainty than eyewitness testimony, and yet according to Maimonides it is rejected in criminal law.

The dispute between Maimonides and Tosafot about conviction based on circumstantial evidence

The text notes that Tosafot disagrees with Maimonides and argues that if the certainty in the circumstantial evidence is as high as the level one has with two witnesses, then one does convict. Maimonides’ position is presented as rejecting conviction in capital cases without eyewitness testimony even when the circumstantial evidence reaches a very high level of certainty.

Probabilistic reasoning versus legal reasoning: reliability, admissibility, and intuition

The text distinguishes between probabilistic-statistical reasoning, which grounds disqualification or acceptance on concern about lying or error, and legal reasoning, which grounds disqualification or acceptance on a principle of admissibility even without claiming that the information is false. In the example of testimony from relatives or an interested party, one possible explanation offered is probabilistic, namely a significant concern about lying; opposite that is the possibility of a legal explanation based on a principle or intuition according to which “it’s not right to convict in such a case,” even without claiming that the witness is less reliable. The text suggests that even if one can sometimes justify the intuition through social considerations such as undermining family relationships, there are also cases where a normative feeling remains without a full formulation of the justification. The author raises the question whether an intuition that has not been well formulated should be abandoned, or whether the failure of formulation should be seen as a limitation of the formulator rather than of the intuition.

“A person cannot render himself wicked,” the Miranda ruling, and the Ritva on the structure of a religious court

The text brings the principle that “a person cannot render himself wicked” and explains that even though confession is “the queen of evidence,” self-incrimination is not accepted. It notes that Israeli jurists are familiar with this Talmudic passage through the Miranda ruling in the United States, in which a judge quotes the Talmud and Maimonides. Maimonides is cited as offering a probabilistic-factual explanation, such as concern that the confessor has “gone mad” or was tortured and therefore confessed, but the text argues that in the Talmud and for most medieval authorities (Rishonim) the problem is not reliability but admissibility. In a responsum of the Ritva, a reason is brought according to which “it does not have the status of testimony” when a person testifies about himself, and a distinction is required between litigants and witnesses by force of the exposition on the verse, “And the two men who have the dispute shall stand,” connecting this to a similar line of thought that appears regarding the rule that “a witness cannot become a judge.” The text concludes that the Ritva defines a structure of three roles in the religious court—judge, litigant, and witness—which must remain distinct, and presents this as a legal explanation that defines a principle of admissibility even if there is no probabilistic explanation of reliability.

Formulating the difference between prisoners and witnesses, and the parallel to migo and presumption

The text proposes one possible formulation of the difference: in the prisoners example, the uncertainty concerns the defendant himself, whereas in testimony the uncertainty concerns the reliability of the witnesses and not the matter itself; but it argues that formulation is not the same thing as justification. The author parallels this to the distinction between migo and presumption: migo is evidence “about the person himself” that supports the claim that he is not lying, whereas presumption is evidence “about the matter itself” that supports a fact in reality, and a practical difference is presented in a case of mistaken impression, where migo does not solve concern about error that is not deception. The text returns to the claim that such distinctions may formulate a principle but do not necessarily provide a justification, and suggests that the gap between prisoners and testimony is a legal distinction rather than a probabilistic one, because the statistical calculations apparently point in the opposite direction.

Majority that is before us and majority that is not before us: generalizing from a sample versus ignorance and symmetry

The text brings the distinction between a majority that is before us, such as nine kosher stores and one non-kosher store, and a majority that is not before us, such as “most women give birth at nine months,” and defines the latter as a generalization from a sample about the nature of the world. It argues that a majority that is before us is not built on observation and generalization but on ignorance and an assumption of symmetry, similar to assuming a 50-50 chance when tossing a coin if one has no information whether it is fair. The text notes that statisticians may argue that without a defined distribution there is no probability, but a person who is forced to bet will choose a symmetrical division due to lack of information, and the difference between “half” based on knowledge and “half” based on ignorance is a substantive difference. On that basis it is argued that the case of the hundred prisoners resembles a majority that is before us in the sense that it relies on contextual information and not on a direct indication about the individual defendant, whereas eyewitness testimony relies on a natural generality of sensory reliability that resembles a majority that is not before us. In a discussion with a questioner, a difficulty is raised as to whether in the prisoners case this is really ignorance or full probability, and the author acknowledges that one can formulate it as a probability of random selection from a mixture, but continues to argue that the character of the probability there is connected to lack of information about the individual.

Majority in monetary law: Rav and Shmuel, Tosafot, and Nachmanides and Rabbi Shimon Shkop

The text brings the dispute between Rav and Shmuel in Bava Batra 92b regarding someone who sold an ox and it turned out to be a goring ox: Rav rules that it is a mistaken transaction because “most people buy for plowing,” while Shmuel rules, “He can say to him: I sold it to you for slaughter,” and determines that “in monetary matters we do not follow the majority; rather, the burden of proof is on the one who seeks to extract money from another,” and the Jewish law follows Shmuel. Tosafot asks how it can be that in monetary matters we do not follow the majority, if in a religious court we do follow the majority of judges, and suggests that the majority of people who buy for plowing “is not considered like those other majorities,” and therefore one does not rely on it in monetary law. Rabbi Shimon Shkop brings Nachmanides in Milchamot on “most women first marry and only afterward engage in intercourse,” and explains that a majority based on custom and human choice is weaker than a majority of “obligation and nature,” because many times a person behaves like the minority custom. The text illustrates that belonging to the minority can be normative and reasonable, and therefore is not “implausible,” and concludes by presenting a continuation for future discussion about parameters such as human decision, credibility, and interest in the claims of the litigants, stopping before the explanation is fully developed.

Last time I ran into a question that comes up in an article by someone named Pappino, who deals with statistical evidence in the legal world, and he compares two situations. One situation—the example he gives there—is a hundred prisoners in a prison yard. Ninety-nine of them attack the guard, and one does not. Then they bring them to trial one after another. Seemingly, there is a ninety-nine percent chance regarding each of them that he participated in this act, and therefore you could convict him. Ninety-nine percent is certainly a pretty good level of certainty. On the other hand—actually, before the “on the other hand”—Pappino says you do not convict in such a situation. Meaning, the claim is that in practice no legal system would really convict in such a case, even though we are apparently dealing with a ninety-nine percent likelihood. As against that, there is another case: two witnesses come and testify about some person that he attacked the guard, or did something else, whatever it may be, and we know that witnesses can miss things. They do not always see accurately or describe accurately what they saw, and let’s say for the sake of discussion that there is a ninety-five percent chance that they are right. In that situation we would convict the person. Now this comes out very strangely, because in the first case, where there was ninety-nine percent, we do not convict, and in the second case, where there is ninety-five percent, we do convict. So what exactly is the difference between these two situations? The first situation is defined as statistical evidence. The second is evidence by virtue of testimony; it is not statistical evidence, but underlying the testimony there sits some statistical assumption that witnesses are reliable, and that has ninety-five percent behind it. So in fact there too some statistic is sitting underneath; there is some degree of doubt that can be quantified in one way or another. And the question is why, in the various legal systems—apparently all of them, if I understand correctly from what I am reading—in the first case they would not convict, and in the second case they would. I devoted some time last time to showing that a similar phenomenon exists in Jewish law as well. We saw there that circumstantial evidence—circumstantial evidence is more or less basically a synonym for statistical evidence—is contrasted with evidence by witnesses. If there are two witnesses who saw so-and-so murder someone else, then that person is executed as a murderer. But if there is circumstantial evidence, even very strong circumstantial evidence, against him—for example, we brought the Talmudic text about someone who entered a ruin with a knife and was chasing someone else, and I go in after him, I find the victim dead, bleeding, and the pursuer standing there with a blood-dripping knife in his hand, and there is nobody else there, no way in or out—the conclusion is completely obvious. In such a situation Maimonides writes that as a matter of basic law you do not convict, unlike monetary law, where we saw that there the judge should act according to what he sees fit. That is in monetary cases. But in capital cases, or criminal law generally, one does not punish or convict unless there is eyewitness testimony. Circumstantial evidence—statistical evidence, if you like—is not accepted. And notice: exactly like in the example I gave before, statistical evidence does not mean that we have a significant doubt. In the example of the prisoners I call it statistical evidence, but it is ninety-nine percent, as against eyewitness testimony where I only have ninety-five percent. So “statistical evidence” sounds like something dubious, like evidence we have reason to doubt, but that is not so. With every kind of evidence we have some doubt. Every piece of evidence is statistical in that sense. When people speak about statistical evidence, they mean that it is not direct evidence but circumstantial evidence. But there is statistics behind both kinds of evidence. Therefore, in the halakhic context as well, at least according to Maimonides, statistical evidence is not accepted in criminal law, while direct evidence such as eyewitness testimony is accepted, even though in terms of level of certainty there can certainly be situations where the circumstantial evidence gives us a higher degree of certainty than the direct evidence of sight. I mentioned that Tosafot disagrees with Maimonides and claims that if there is high certainty in circumstantial evidence, at the level we have with two witnesses, then you do convict. And Maimonides’ position is that you do not. So that is just an analogy to Pappino’s distinction—we see it in Jewish law too. I said, and I mentioned that we would come back to this, that in the legal world and also in halakhic law there are two kinds of reasoning one can offer. One is what we may call probabilistic reasoning, statistical reasoning, evidentiary reasoning if you like. And the second is legal reasoning: a statistical argument and a legal argument. Meaning, for example, if a person testifies about a relative of his, or testifies in a matter in which he has a personal stake—yes, he is a litigant himself, or personally involved, or something like that—you can offer a statistical explanation for why that testimony is invalid. There is a significant concern that such a person will lie. A considerable number of people in that kind of situation will lie. It need not be a majority, of course; even if ten percent lie in such a situation, that means there is not enough certainty to convict, okay? That would be enough not to accept such testimony. But there could be another explanation, or another kind of grounding, a legal grounding. Meaning, I have some line of reasoning that says I do not convict on the basis of testimony by relatives. Why? I am not claiming that a relative is less reliable, or that someone with a personal stake is less reliable. Rather, there is some legal principle or legal intuition—sometimes I do not even know how to conceptualize it and formulate it, but there is some intuition, some feeling—that says it is not right to convict in such a case. We will come back to the question of intuition because it comes up in a very interesting way in these discussions, but for now I will leave it at that. And that intuition, sometimes I can also justify it—that is, formulate it, define it. For example, if I accept testimony of relatives, that may undermine family relationships in many families—not just that particular family, because everyone will start being afraid of family members when he does various things—and we want family life to proceed peacefully. I am just proposing an absurd suggestion, okay? That is an explanation unrelated to the reliability of the testimony. Meaning, it could be that the relative’s testimony is amazingly reliable, but I have good reasons not to accept his testimony, not because of the factual statistical consideration I called earlier a problem of reliability—that I think the testimony is incorrect—but because of some other side issue, legal or otherwise, something else. I have additional considerations for why I will not accept this testimony. Sometimes—here I may even have managed to formulate it a bit—and sometimes there is even a logic here that I can understand, even though it is not the probabilistic or factual logic, but it is a logic I can understand. I can understand why a halakhic system or legal system would take such a kind of consideration into account. Another example: in a responsum of the Ritva he writes that testimony by relatives is not accepted because just as a person’s testimony about himself is not accepted, we are not willing to incriminate someone on the basis of what we might call internal testimony. What does that mean? Or actually, he formulates it a bit differently: he says there has to be some kind of distinction—no, sorry, he is not talking about relatives, he is talking about a person’s testimony about himself. That is, why is a litigant disqualified as a witness? After all, a confession is the queen of proofs, so seemingly if a person confesses that he committed a crime, why is that confession not accepted? “A person cannot make himself wicked”—we do not accept that confession. By the way, here too there is an interesting example: where do Israeli jurists know this Talmudic statement, “a person cannot make himself wicked,” from? Through the Miranda ruling in the United States. Miranda is basically the Fifth Amendment, I think—the right to remain silent, the right to legal counsel, and all kinds of things of that sort, being warned that everything he says may be used against him. All of that is Miranda warnings. And in fact the non-Jewish judge in that case quoted the Talmudic statement that a person cannot make himself wicked, and Maimonides. Maimonides also has some explanation there; he even suggests one explanation that perhaps he is one of the insane people, so why in the world would a person convict himself? Apparently he has gone crazy, and therefore we have to cast doubt on this self-conviction, this self-incrimination. Others suggested, or there are other explanations that were suggested, that perhaps he was tortured by the police—otherwise why would he confess? A person does not confess and convict himself; apparently he was tortured, and they extracted the confession from him, and therefore you cannot rely on that confession. All of these are explanations of the first type I mentioned, factual statistical explanations—that is, explanations showing that in fact it is not right to rely on this testimony or this confession. But when you look at the Talmudic text, you see that in the Talmud that is not the issue. Meaning, in the Talmud there is no concern that the person went crazy, even though Maimonides writes that as one of the explanations. But even in Maimonides there is a contradiction on this point. And in the Talmud itself, simply speaking, that is not the case, and almost all the medieval authorities (Rishonim), of course, write that this is not the issue. Rather, it is not a problem of reliability but of admissibility. That is, a person’s testimony about himself has no problem of reliability; it has a problem of admissibility. I am not willing to accept such a thing. That is exactly what I described before as a legal explanation, as distinct from a factual statistical explanation. Now, how do we formulate this thing? Meaning, why did they impose a problem of admissibility? So the Ritva’s responsum writes that it is because—let’s see where I quoted it, I think… yes, here: “For everything a person testifies regarding himself, whether to his benefit or to his detriment, does not have any testimony upon it, does not have the status of testimony, but only of the litigant himself arguing and acquitting or obligating himself.” Right, so this is a person obligating himself or acquitting himself, and that cannot be accepted. Why not? So he says: “For witnesses are separate entities in themselves, apart from the litigants, as it is written: ‘And the two men who have the dispute shall stand.’ And we say: ‘the two men’—these are the witnesses; ‘who have the dispute’—these are the litigants.” Okay? He is obviously inventing that exposition; there is no such exposition in the words of the sages. “And the two men who have the dispute shall stand before the Lord”—this is brought in two contexts. In the context of women being disqualified from testimony: “the two men,” and not women, and from there the Talmud in tractate Shevuot derives the disqualification of women from testimony. And there is a discussion in Bava Batra and elsewhere—actually I think this appears only in the medieval authorities, not in the Talmud itself—regarding the rule that a witness cannot become a judge. There is such a rule, a dispute, but the practical halakhic ruling is that a witness cannot become a judge. A witness cannot turn into a judge in a case in which he served as a witness. And on that, I think the Rashbam brings this, that it is because it says: “And the two men who have the dispute shall stand before the Lord.” For “the men” are of course the witnesses, once again as the Talmud expounds, even though in the plain sense of the verse the two men are the litigants. But the Talmud expounds it regarding the witnesses, and they stand before the Lord; “the Lord,” “the judges,” means the judges. So we see that there must be a standing in which the witnesses stand opposite the judges. And therefore, says the Rashbam, this describes a courtroom situation that requires a distinction between these two functions. Witnesses and judges are supposed to stand opposite one another. Once a witness becomes a judge, there is no standing of two functions opposite each other. You are combining two functions that were meant to be separate from each other. And there is some value in keeping the functions in the court separate. Therefore, the Ritva continues in the same line of thought: just as we are careful to separate the witnesses from the judges, we are also careful to separate the litigants from the witnesses. And therefore a litigant cannot testify about himself, because if he is a litigant he cannot function as a witness, just as a witness cannot be a judge. Meaning, in court there are three roles: judge, litigant, and witness. And each such role is supposed to be distinct from the other two; none of them may be turned into something else. So a litigant cannot be a judge—that is obvious. The witnesses cannot be judges, and the litigant cannot be a witness. None of the combinations are possible. And again, notice: the explanation the Ritva offers here is not a probabilistic factual explanation. He is not claiming there is a problem with the reliability of a person’s testimony about himself. On the contrary—a confession is the queen of proofs. Rather, he is claiming there is a problem of admissibility. And how to explain this problem of admissibility? There is not really an explanation here; he is only defining it. He says the different functions in court are supposed to maintain distinctness, not get mixed up with each other. Why not? Why not? You defined that they should not be mixed, but you did not offer an explanation. Meaning, what is the problem with my mixing them? If you tell me the problem is reliability, then forget all the verses and all these explanations—just say there is a reliability problem. No, he says explicitly: no, this is not a reliability problem, it is an admissibility problem. And what sort of admissibility problem? Why? I think there is behind this some kind of feeling that legally there needs to be a distinction among these three functions. Meaning, when you convict a person, it is supposed to come from some external factor that imposes that conviction on him. A person convicting himself is something problematic. Why am I laughing? Because suddenly I see how much I wave my hands, and I remember my study partner who once told me, “The moment you started moving your hands too much…” He told me, “No hands. Put your hands aside and explain it to me only with your mouth, without your hands.” The moment you start waving your hands around, it means you cannot find a way to explain it logically. So there is something to that. But on the other hand, just because I cannot explain it logically does not mean there is no such feeling. Meaning, there is an intuition that says this is right. Therefore I bring this in contrast to the previous kind of legal explanation, that of relatives, where I proposed an explanation one can also understand—we do not want to create conflicts within the family. So that is not a probabilistic statistical explanation; it is a legal explanation, but it is a legal explanation that is understandable, you can make sense of it. Here I am claiming something more far-reaching: there is some kind of intuition that this is not an appropriate way to act, not an appropriate way to proceed. I do not really have a good explanation why not, but I feel that this is the right or wrong way to behave. Can such a thing also ground a legal principle or some rule? It seems that it can, and later on I will show you more examples of this. But already here—and I return to our problem—I think many of us feel intuitively that there is a difference between the prisoner case and eyewitness testimony, even though statistically the numbers seem to favor the eyewitness testimony less—in other words, they seem to favor the prisoner case. And still there is some intuitive feeling that in the prisoner case you cannot convict, while in the eyewitness case you can convict. Now suppose I did not find, did not manage, to rationalize that intuition, that feeling. Does that mean I should abandon it? Throw it out? Say, well, it is just a feeling, I need to get over it? In the end, if there is no logical explanation, then why behave that way? Or not? Or do I say: look, I have some such feeling, and I trust my intuition. The fact that I could not explain it, conceptualize it, formulate what lies behind it, does not mean it is not correct. It only means I cast doubt not on my intuition but on my ability to formulate. After all, there is a tension here between intuition and ability to formulate. In my ability to formulate, I cannot formulate it, but my intuition says this is not the right way to act. I can say then that the intuition is incorrect, because the proof is that I could not formulate it. And I can say no: probably my ability to formulate is not good enough, or my conceptualization is not good enough, but my intuition is something I do trust. But Rabbi, maybe it can be explained as follows: in the matter of the prisoners, the statistic bears on the defendant, on the person who is now the litigant. There is a ninety-nine percent chance that he is liable and a one percent chance that he is exempt, so the doubt is about the defendant himself. But in the case of the witnesses, the doubt is not about the defendant; it is only about the witnesses. If the witnesses are testifying truthfully, then there is no doubt about the defendant. There is only an issue of unreliability or not; the doubt concerns the reliability of the witnesses, but it does not touch the defendant himself. One hundred percent—even if I accept that—still, so what? What difference does it make? Maybe that does formulate… maybe that is one way to formulate the difference between them. To formulate the difference, yes. That is like the Ritva—he too formulates it. He says you need to separate the functions in the court: witnesses, judges, litigants. But he did not explain. So the question is, the fact that I know how to formulate it may be progress, but it still does not constitute an explanation. I still need to understand why not. Why should I care whether the doubt is in the witnesses or the doubt is in the person? Bottom line, if you ask me whether he is guilty or not guilty, there are certain percentages that he is guilty and other percentages that he is not guilty. Let us go with the percentages. Why should I care how those percentages were generated—whether through the witnesses or through the person? I once made such a distinction in the booklet on migo, and also in classes in previous years. I talked about the difference between evidence from a presumption and evidence from migo. The evidence of migo—that is, “why would I lie?” migo in its regular sense—is evidence that does not speak about the case at all. It does not give you evidence that so-and-so owes money. Rather, it gives you evidence that the witness or litigant is not lying. Consequently, if he says that so-and-so owes money, then he owes money. But the evidence is about the person, not about the matter itself. By contrast, a presumption—for example, the presumption that a person does not pay a debt before it is due—that is evidence that he did not pay. So that is evidence that deals with the legal issue itself. Migo comes to support someone who is speaking, and it does not prove to me that what he said is true; it only proves that the speaker is not a liar. Consequently, if he is not a liar, then what he said is also true, but it is evidence about the person himself. For example, the practical difference is in what the Talmud calls “he imagines it,” right? What is that? If I am concerned that the person is not lying but imagining things, or thinks that way but is mistaken—for example, in permitting an agunah, he identifies a man by the shape of the nose. But maybe he did not identify him correctly. Not that he is lying; he is simply mistaken. Migo will not help in such a case, right? Because migo only proves that the person is not lying. And if my concern is not that the person is lying but that he is mistaken—“he imagines it,” right?—then migo will not help. If I have evidence about the matter itself, then that solves even the problem of “he imagines it,” because I prove that this woman’s husband died. So right now I do not care what my concern was about the testimony—whether it was a concern about the person or about the issue itself. I brought evidence about the issue and solved the problem. This is somewhat like the distinction Yoav suggested here: migo is evidence about the person, and presumption is evidence about the matter itself. But still, as I said before, there is no explanation here. It formulates some principle, but we still need to think about what the justification for that principle is. The fact that we formulated something does not mean that we have given an explanation. So already here I am putting on the table the possibility—and we will return to it—that the distinction between the two situations, the hundred prisoners and the two witnesses, is essentially a legal distinction, not a probabilistic one, not a factual one. On the contrary, probabilistically the case of the hundred prisoners may be better than the case of eyewitness testimony. But as I tried to illustrate here, sometimes there is a legal line of reasoning that says, on the legal level, this is the proper way to behave or not the proper way to behave. Sometimes I can justify it, sometimes I cannot justify it, but there are situations in which legal intuition has some weight, even though on the factual level there is no justification for it, on the statistical and factual level. And then it would be natural to look for explanations of that type here, because statistically this really looks like a lost case. There is no way to justify it statistically. The statistical calculations point explicitly in the opposite direction. So it is natural to look for a legal explanation, not a probabilistic one. So with that tension between a probabilistic explanation and a legal explanation, we are now going to move forward step by step. And we will discover that the difference between a probabilistic explanation and a legal explanation—yes, a legal explanation—is not as sharp as it seems at first glance. And let us begin. I will start with the first explanation I want to offer for this. We did discuss the distinction between a majority that is before us and a majority that is not before us. So that same distinction—and now you want to unify them? What? You distinguished them, and now you want to unify them? No, no. I am distinguishing between a majority that is before us and a majority that is not before us. No, no—between legal reasoning and statistical reasoning. I am saying—we will return to this later—that the distinction I made between statistical reasoning and legal reasoning… okay, let us try to formulate an explanation that will justify the difference between eyewitness testimony and the judgment of those prisoners. So here I will use the distinction we made between a majority that is before us and a majority that is not before us. Okay? A majority that is before us is the case of nine stores. I found a piece of meat in the street. There are nine kosher stores and one non-kosher store in the city; we follow the majority. That is a majority that is before us. A majority that is not before us is “most women give birth at nine months,” or “most women are not barren,” or all sorts of things like that. We discussed that a majority not before us is a majority that deals with the nature of the world. It is, in a sense, a law of nature. And a majority before us has nothing to do with the nature of the world; it is simply an accidental constellation. Here, in this particular city, there happen to be nine kosher stores and one non-kosher store. There are cities where the distribution is completely different. In this case I have specific information; it is not a law of nature, not general information about the world, but specific information about a particular situation in which I know that the distribution is nine to one. Okay? What is the difference between these two things? Fine, as I said now, you made a distinction, but can you justify the distinction between these two things? This is ninety percent and this is ninety percent. Why should I care whether it is a majority in the nature of the world or a majority resulting from information about the specific constellation I am facing? What difference does it make? Is that a legal distinction or a probabilistic distinction? So my claim was that there is some difference here that in a certain sense one can say is probabilistic, even though it sounds very strange. Why? Because “most women give birth at nine months,” for example—the majority that is not before us—is a majority created by generalizing from a sample. Right? Meaning, I see a sample of cases, I see that the distribution is, say, nine to one, and I assume the sample is representative. Then from that I generalize to all cases in the world and say that apparently nine out of ten cases in the world will proceed this way. That is a majority not before us, and that is a generalization from a sample. A generalization from a sample means that the cases I know, the sample, are particular cases, but the conclusion I draw is about a case not included among them, another case. But I claim that it is also correct to apply to that case the same statistic I found in the representative sample, and therefore I generalize to all cases. By contrast, a majority that is before us—in that case there is no generalization from a sample at all; I have the full information. I know there are nine kosher stores and one non-kosher store. I am not assuming anything about all stores in the world or all meat in the world. This piece that I found in the street came from those very stores about which I have information. It is not some new piece; after all, it came from one of those stores, and I know that among those pieces ninety percent are kosher. So I say: fine, then probably this piece too has a ninety percent chance of belonging to the kosher group. Do you see? There is no generalization here, no generalization from a sample. That is the basic difference between a majority before us and a majority not before us. The question that troubled us was what to do with majority in court, which the Talmud in tractate Chullin brings as the source for a majority that is before us. Majority in court is supposedly a majority before us because the three judges are before us. Two of them say liable and one acquits, and so we follow the majority, and all three are before us, right? It is like the stores; it is not some majority in the nature of the world. But we already saw that this is not correct, because Sefer HaChinukh explains that the reason we follow the majority is that in most cases where there is a dispute between a majority and a minority, the majority is right. That is his claim. So Rabbi Shimon Shkop asks: if so, then in fact such a majority is a majority not before us, not a majority before us. Because you are speaking about all the cases in the world. You just, say, know a number of cases, and from them you assume some general law that if there is a distribution of opinions in a court, usually the majority will be right—say, in eighty percent of cases the majority will be right, okay? Then you apply that to the case being judged here and say that here too, if two judges say one thing and one says another, the majority is probably right. That is exactly the mechanism of a majority not before us, because you are speaking about the nature of the world, about all cases in the world, where the case before us is another case beyond the sample you know. That is Rabbi Shimon Shkop’s question. So I explained it and said that this is not right. Why is it not right? Because here what matters is the generalization from a sample. In the judges’ case, my conclusion that in most cases the majority is right is not the result of a generalization from a sample. Why not? Because I have no way of making observations on any sample whatsoever. I have no way of knowing in any case whether the majority was right or not. How would I test a case? Say I want to take a sample of one hundred rulings where there was a dispute between a majority and a minority, and I want to examine in each one whether the majority was right or the minority, and then do statistics. Say, I do not know, in eighty percent of the cases the majority was right, and then I can apply that here. So let us begin checking our sample now. I go over the protocols of one hundred trials in which there was a dispute between majority and minority. Now in each of those cases I want to check whether the majority was really right and build the statistic. Right? The sample is not the result of statistics; the sample is the result of observation. Statistics enter only after I have made observations on the sample. Then I do the statistics and say there is ninety percent here, and I generalize. Fine? Now I am speaking about the stage of observation of the sample, the pre-statistical stage. That stage cannot be done with judges. I cannot check in any case whether the majority was right or not, right? We discussed that. Therefore it is an illusion to think that the majority here is a majority not before us. How did I arrive at the conclusion that the majority is generally right? It is an a priori reasoning. It is simply reasoning. If my judge is a skilled judge, meaning he gets it right in a significant percentage of cases, then on the basis of that assumption one can make some statistical calculation that is entirely a priori—no observation, no generalization, simply nothing, just a calculation. And how do you know he is skilled in the first place? What? How do you know he is skilled in the first place? I test him on Talmudic passages, I do not know. No, I can test his halakhic knowledge. No, his skill at sorting things out, his grasp of reality—that is very hard to test. Maybe one can think of some way, but it is very hard. In any event, the point is—I assume the judge is… I get the impression that he has common sense, and therefore I say the percentage of cases in which he will hit the truth is p. We discussed this in conditional probability, where you have to reverse it: is it, given that the person is guilty, the judge will rule him guilty, or given that the judge rules him guilty, what is the chance the person really is guilty? Remember? We discussed this when we spoke about conditional probability. In any case, I am saying that in this stage too there is an a priori assumption that he is skilled. Completely. It is a kind of impression. I get the impression this person is smart, perceptive, understands reality, so I assume he has some probability p of hitting the truth. Now I ask, okay, I have three judges whose probability is p. That too assumes they all have roughly the same probability, because we saw that Sefer HaChinukh says that if there is one wise judge, he outweighs two fools, and therefore the assumption is that our panel is all more or less on the same level. So they all have probability p of being right, okay? And now, if you do the math, you will see that if two judges go against one, chances are that the two are right, assuming p is greater than a half, right? Meaning, they are skilled judges. So this case, this case, contains no element of observation, no element of generalization from a sample, nothing. It is simply a collection of assumptions that arise from, basically, a kind of impression—or if you like, from ignorance regarding facts. I do not know any facts; I am ignorant. So I have to use some of my a priori assumptions, impressions. Meaning, basically it starts from ignorance, okay? And because of that, I argued that majority among judges is a majority that is before us and not a majority that is not before us. Why? Because in the stores too, basically, we are dealing with a majority of ignorance. Think about the stores. I really have no way of making a generalization from a sample to test whether the chance that this piece is kosher really is ninety percent. What am I supposed to do? Look at all the pieces found in this city over the past ten years? But for each such piece I have no idea from which store it came. So I have no way to perform the sample statistics and then make the generalization. So what do I do? I have an a priori assumption, just like the calculation with the judges—remember? It is exactly the same thing. I am basically assuming that the probability that this piece separated from each of the stores is equal. I have no other information. Meaning, the assumption is ignorance. I know nothing. If I know nothing, then I assume all possibilities are equal, and if all possibilities are equal, then it comes out that there is a ninety percent chance this piece is kosher. But this whole business is just a collection of assumptions of mine with no observational basis whatsoever. Nothing. Right? It is all my assumption, and based on the assumption I can do a calculation. No, but you… it is more complicated. In the case of the stores the calculation is simple. No, but you know that each store sells the same amount of meat. True, and I do not know what the chance is that a piece of meat will be lost from each store. Is that the same chance? I do not know. My assumption is yes—why not? But that “why not” is exactly the point. It is always a matter of ignorance. Since I do not have… you know, it is like, say, there are two possibilities and I have no information about them, okay? Suppose a coin is put before you and you toss it, and I ask you what is the probability it will land heads. What is the answer? Half. Maybe the coin is unfair. Yes, assuming it is fair. Assuming. And if it is not fair? But I am asking the person questioned. You do not know; you have no information. What do you do? So I toss it a few times. No, you cannot do the experiment. There is one toss. It is still half because the coin might be unfair in either direction and that cancels out. Exactly. But that half has a different character from the half I get when I know the coin is fair. If I know the coin is fair, then it is a positive half. If I do not know anything about the coin, I will still assume half if I have to bet, on symmetry grounds. But that is merely the result of ignorance. I cannot really claim that I have any information about the coin, right? Still, the result will be half. But do you understand that there is a difference between these two situations, and it is also a probabilistic difference? It is not only a legal difference. Because the half in the second case is really a statement about me, not about the coin at all. About the coin I know nothing. It may be that the coin is in fact unfair, and in ninety-nine percent of cases it will land tails. I have no idea; I have no information. But because I have no information, because of my ignorance, I assign equal probability to all possibilities, right? That is what we usually do, on symmetry grounds. What else should we assume? We have nothing else to assume. But do you understand that this reasoning of “why not?” or “I have no basis for assuming otherwise,” is not reasoning that says something about reality. It is reasoning that says something about me—only about me. It is not a claim about reality; it is a claim about me. So in your opinion, is the difference between these two answers of “half” probabilistic or legal? The situation where I know the coin is fair, and the situation where I do not know anything about the nature of this coin? Ask statisticians—statisticians are not willing to say at all that the probability is half in the second case, because no distribution is defined here. Once no distribution is defined, you cannot do probability calculations. But an ordinary person who has to—someone points a gun at your head and you must bet—you will bet half, right? Even though it is not defined as a probability problem. But you will bet half. So you see there is a difference here that is not just a legal matter. It is a probabilistic difference. There is a difference in the answer even on the factual level. Here I tell you the chance is half, and that is a claim about reality. And there I tell you the chance is half because I have no idea what reality is. It may be that in reality itself I am just an idiot; in reality itself it is ninety-nine percent. But I have no information, so I assume half, just because I know nothing. This is a statement that is the result of ignorance. Do you see the analogy between this and a majority that is before us and a majority that is not before us? In a majority not before us, I have information about reality—or at least about a representative sample of it. In a majority before us, I have nothing. I have probabilistic calculations that are the result of my assumptions, that is all. So my claim is that the difference between a majority before us and a majority not before us—Pinchas Kuperstock writes something similar, though his analogy comes out very strange. Maybe he means this, but I do not think so. He claims that a majority before us is not an intellectual majority. I do not know whether he means what I mean. I claim it is not a probabilistic majority. The intellect does indeed say to follow this majority, but it is not a probabilistic majority. Meaning, you cannot say that the chance regarding this piece of meat really is ninety percent. That is simply not true. Just as you cannot say that the probability that the majority of judges are right is, I do not know, seventy percent. No, that too is not true. I am totally ignorant; I have no clue. So the assumption that emerges because of my ignorance and the symmetry among the possibilities is the assumption that the majority of judges are right in seventy percent of cases, or that this piece of meat is kosher with ninety percent probability. But that is not a statement about the world—I know nothing about the world. By contrast, if I have a majority not before us, I do have information about the world. I checked how many women—at least in the representative sample—give birth at nine months or at seven months. And once again, of course there is also an assumption there. The assumption is that the sample is representative and that women in the world behave similarly. Still, there is at least something there that contains some information about the world. Probability always involves assumptions, and therefore I assume assumptions—always. Probability always assumes something. Always. And still there is a difference between these two things. We trust scientific statistics as a result of generalization from a sample. But confidence that there is a ninety percent chance this piece is kosher is merely the result of ignorance; there is nothing to hold on to there. Therefore, once again, although I would bet on it, if I were asked to bet on it I would bet nine to one. But that is not… it is only because the logic of symmetry tells me so. It is not because of any facts I know about this piece. Therefore my claim—and now I return to Pappino—is this: the majority of the prisoners, is that a majority before us or not before us? Before us. Before us, right. It is really a majority before us. I have a hundred prisoners; it is like the ten stores. One of the prisoners… I really have two stores—or you know what, a hundred stores, and in each store there is one prisoner. Ninety-nine prisoners are criminals, and one prisoner is innocent. That innocent one—not innocent regarding what landed him in prison, but regarding the attack on the guard. Okay? Now a prisoner comes before me. I ask: which store did he come from? One of the ninety-nine non-kosher stores—or rather, the one kosher store. This is really parallel to the case of the stores, as you can see. Not quite, because here there is no assumption. What? Not quite. It is not so similar, because here there is no assumption of the mind. There is no a priori assumption. You are saying this prisoner came out of one of a hundred stores. There are ninety-nine non-kosher stores and one kosher store. Now I ask which store he came from. I say, assuming he can come from any of the stores equally, I assume he came from a non-kosher store. No, no—but in the meat case there is an assumption that the meat could come from each of the stores in equal distribution, because there is… there is a lot of meat, and the possibility of losing a piece, and all kinds of, what do you call it, x and y, all kinds of unknowns. Fine, so assumptions are made about them. But with the prisoner, either he comes out of that store or he does not. He necessarily comes from there. Those hundred prisoners necessarily come from those stores. So there are ninety-nine prisoners who come from store A and one who comes from store B. If I judge an individual prisoner, just one… yes, just one. Then there is a one percent chance he came from that one store? They necessarily come from those stores. That is not true of the meat. I do not see—I do not see an assumption in the prisoner case. You are actually right. I think you are right, and yet there is some feeling that this is still parallel to a majority… before us. I am trying to think of the formulation. Before us. You are right that here there is not that element of assumption that I make out of ignorance. Meaning, I will put it this way: you are right that it is not completely similar to the stores, but it is also not similar to a majority not before us. Okay? There is no informational basis here from which I generalize and then draw some conclusion about an additional case. It does not work that way. This is really built on specific information I have about this reality, not on something about the nature of the world. Okay? So in that sense, I think in the next formulations it will come out clearer. You are right that in this formulation it really sits in the middle; it is not quite like the stores. But later I think it will become sharper, because the three explanations I will offer are pretty similar; they are somehow different facets of a similar principle. So the claim for now is basically this: when I say that this prisoner is guilty—say, if I were to rule that he is guilty because there is ninety-nine percent—that does not really stem from information I have about this prisoner. I have no information about this prisoner. It stems from my ignorance. Since I have no idea who the one innocent person is and who the guilty ones are, the probability is ninety-nine percent that he belongs to the guilty group. That statement is a statement about me, not about him. By contrast, when two eyewitnesses come before me and testify that Reuven murdered Shimon, then I have a majority not before us, right? There is a general rule that most people see well. Some do not, but in most cases people do see well. That is a majority not before us; it is something about the nature of the world. The nature of the world is that our eyes function reasonably well. Okay? It is not some specific assumption about a particular constellation before me; it is something about the nature of the world. So that means I really do have information about these witnesses and, as a result, also about the event they testify to. And that information says that these witnesses saw correctly. I have information about the world. It is not the result of ignorance. I know that witnesses generally see well—true, only at ninety-five percent, but I know that. I know that witnesses generally see well. Okay? And on the basis of that, one can rule. Why? After all, one does not need one hundred percent certainty, because otherwise you could never convict anyone. There is never one hundred percent certainty. You need certainty beyond a reasonable doubt. But the uncertainty, the part with respect to which you are uncertain, stems from some uncertainty in reality, while the odds are that reality is such-and-such. By contrast, in the case of the prisoners, the certainty or uncertainty does not relate at all to the prisoner standing before me. I have no indication about him whether he belongs here or there. I simply say: I am ignorant, I have no idea who belongs where. I only know there are a hundred prisoners, of whom ninety-nine are guilty and one innocent. So from my ignorance I make the statistical calculation that there is a one percent chance he is innocent and ninety-nine percent that he is guilty. Do you understand that this distribution is a statement about me, not about the prisoner? And what difference does it make? What difference does it make where the ignorance lies? If you have one statistic of ninety-nine and another statistic of ninety-five, then go with the statistics. No. I am claiming that the ninety-nine statistic is not a statistic at all. A majority before us is not statistics. People call it that, but your decision to use those percentages to judge the person before you—that is your decision. It is not the result of information you have. I know that all objects with mass fall toward the earth. Now an object with mass comes before me; I assume it will fall toward the earth. Why? Because I have information about the world. My information about the world tells me that masses fall. Okay? Here this is simply a situation where I know there are a hundred people, ninety-nine of whom are guilty and one not. I have no idea who belongs to whom, and I have no concrete information about any of them. So I cannot say he is a criminal even though I have… no, I cannot say anything about him. I can say that for me it makes sense to assume he attacked rather than did not attack only because of my ignorance. So in the final analysis it is a statement about me. It is not really correct to use the term probability here. There is no probability here. Now regarding your earlier comment, I am indeed a little uncertain, because that is a good point. There would be room to say that there is probability here. Why? Let us look at the hundred prisoners as some kind of mixture. Now I choose one of them at random. Now I ask myself: what is the probability that I selected an attacker, yes, a guilty person? Ninety-nine. Here we really do have probability. That is clear, right? There is a ninety-nine percent probability of drawing a guilty person. So in fact one can even define this as probability. It is true that the root of this probability is my ignorance, not something in reality itself. But yes, following your remark, I do think one can speak here of probability. I am going to come to the second explanations, and they may also shed some light on this formulation. So let us leave it for the moment in this formulation, and I will offer you more. Yes, but according to what I said, there is not even ignorance in this case of yours. First of all there is no ignorance, and second it is not a statement about you; it is a statement about the case, because the prisoners necessarily come from the… No, no, there is ignorance. There is ignorance. Again, when two witnesses come and testify that Reuven murdered, I have information about Reuven. True, that information is not certain—maybe they did not see correctly. Here I have no information about the prisoner at all. Nothing. There is no reason to assume he is not the one innocent prisoner. Yes, there are ninety-nine reasons to assume he is guilty. Because those reasons are in me, not in him. No, in this case no. In the stores case the statistics are in you, but in this prisoner case… No, no, that I do not accept. I accept that it is not similar to the stores, but I do not accept that it is not like the stores on this plane of whether it is a statement about me or a statement about him. You understand? There is a difference between saying, I know something about you—true, my knowledge is uncertain, but I know something about you—and saying, I know nothing about you, but from the context it seems reasonable to assume with ninety-nine percent that you are such-and-such because, I do not know, there are ninety-nine people here as against one of another kind. That is not the same. You do not know anything about the defendant before you, nothing. You have nothing direct pointing to him. It is circumstantial; it is something that, from the circumstances, sounds reasonable to assume about him. It is not like the witnesses. The witnesses saw him murder. You can say, fine, but maybe they did not see him. Fine, maybe—but the basic information, before you cast doubt on it, is information about the event. It is not your own decision out of ignorance. In that sense, I do think this differs from a majority not before us and resembles the stores. You are right that this is real probability. That much is true. There is not here the same element of “what is the probability it came from each store,” where I simply assume and do not know. That element is absent here. Okay, so let us move on to the next formulations, and I think they may help us a bit. So this explanation I offered here—it is an interesting question whether it is a legal explanation or a probabilistic explanation. Before Eliav’s remark, I was inclined to think that it is a probabilistic explanation, not a legal one. Like with the fair and unfair coin—there I asked you, what is the difference between my having no information about the coin at all and my having information that this coin is fair? In both cases I bet half that it will land tails. Is the difference between these two cases probabilistic or—I do not know what to call it—legal? I think probabilistic, because in truth you do not have a probability of half for tails in the second case. That is simply not true. You need to assume it. You have no information about the coin from which you derive the conclusion that there is a half chance of tails—no information about the coin. On the contrary, the ignorance, the lack of information, is what leads you to assume the probability is half. When you know the coin is fair, you have information about the coin, you have a positive reason that leads you to assume the probability is half. If one can put it this way, the weight is completely different. In the first case I stand behind the half. It arises from positive information I have about the situation. It is half because the coin is fair. In the second case you say, listen, I cannot tell you anything; I simply know nothing. Fine, so let us assume half-half. Meaning, it is not just half-half because I do not know what will come out—I do not even know that it is half-half. Even that I do not know. But since I am assuming everything, that too is an assumption—that it is half-half. In the first case, that it is half-half is clear. The assumption I am speaking about there is that it will land tails, given that it is half-half. Here I do not even know that it is half-half. But because of symmetry I have nothing better to assume, so I assume it. You understand that there is a difference here in reality itself. The distinction between this case and that one—say I had to convict a coin, right?—if its probability is half of this kind or half of that kind, you understand that the difference is not only legal. There is a real logic here. How could you convict when you have no information? Suppose half were enough to convict, okay? Suppose it were enough. You know that in civil law, in fact, fifty-one percent is enough to prevail—not in criminal law, okay? Fifty-one percent. Now there is a coin for which you assume fifty-one percent, okay? And there is a coin for which you assume fifty-one percent because you have no information, so you say, fine, let us assume fifty-one. You understand that you cannot convict on the basis of the second but on the basis of the first you can, even though in both I am speaking about the same number. In my opinion this difference is a probabilistic difference, not a legal one, even though the probabilistic number is the same. That is what I really wanted to claim about the case of the prisoners versus the eyewitnesses. In terms of the numbers, eyewitnesses are only ninety-five percent, the prisoners are ninety-nine percent. But if with the prisoners that ninety-nine percent is a statement about me and not about the prisoner, then it is not the number that determines things, but whether I can really stand behind that number. Now I accept Eliav’s point that in the prisoners’ case I can also stand behind that number. Therefore I retreat—I retreat from the formulation I gave before. I remain with something that will become clear later. I still claim it is a statement about me, not about the prisoner. And that is indeed a real difference. When you have the information about the coin, is that a statement about the coin or about you? About it. So I am saying that here, in the prisoner case, you have information about the prisoner too, because you know he necessarily comes from those hundred. Yes, but you have no information about him. There is one innocent one. You have no information about him as to whether he is the one innocent or one of the ninety-nine guilty. You only assume that it is equally probable—that each person who comes before you has equal probability. That is not information. With the coin I know it is half-half. He is necessarily equally probable. What? He is necessarily equally probable. It cannot be otherwise. It cannot be otherwise, but it is still an assumption about you. Again, I am not retracting what… I retract what I said before and accept your point that there is probability here. But the character of the probability here is still a probability that is the result of ignorance. I know nothing at all about the particular prisoner before me. About the coin I do know. Or about the testimony, about the witnesses—I know something about him: there are witnesses who saw him murder. But Rabbi, the coin includes both heads and tails. Correct. So I am saying, you are comparing the coin and the prisoner. No—you need to compare the coin to the bag of prisoners, all the prisoners taken together. No, I am talking about the particular prisoner before me. About this particular prisoner whom I am judging, I cannot judge—I know nothing. But you need to judge where this prisoner comes from. The coin has heads and tails. I know where he comes from, just as I judge from which store the piece of meat comes. No, like you judge where the heads come from. Rabbi, where do heads and tails come from? From the coin. I am asking what the coin will land on, not where heads and tails come from. And I know something about the coin. I have information about the coin, that it lands half on heads and half on tails. By contrast, here I have no information about the thing I am judging. I have only circumstantial information, information about its surroundings. You are right—it is full-fledged probability. But still, the probability here describes the possibilities before me. It does not describe any concrete information about the defendant. No—the coin has two sides, heads and tails, and the group of prisoners has a hundred sides. This bag of prisoners has a hundred sides. Correct, but I am not adjudicating the bag of prisoners. I am adjudicating one particular prisoner right now. If I had to judge all hundred prisoners, you would be right—I would kill them all. But each prisoner comes before me separately for judgment, and I now have to decide about him. About him I have no information. In a moment—I already said—in the next formulations it will become sharper, because here it is somewhat confusing because the probability is indeed probability. But in a moment you will see that it still has significance in the next formulations. So let us begin with another explanation that at first glance looks legal, and I will also hesitate about that one. I will introduce it through an example of a Talmudic principle, namely the question whether one follows the majority in monetary law. There is a dispute between Rav and Shmuel; look at the Talmudic text in Bava Batra 92b: “It was stated: one who sells an ox to his fellow and it is found to be a goring ox. Rav said: this is a mistaken transaction. Shmuel said: he can say to him, ‘I sold it to you for slaughter.’” Meaning, someone sold me an ox, and the ox turns out to be a goring ox. So I complain to the seller: I did not want a goring ox—what am I supposed to do with it now? I have to watch it all the time. He says to him: what? I sold it to you for slaughter. Slaughter it and be done with it. Why should you care that it is a goring ox? Yes, but I bought it for plowing, not for slaughter. I want to keep the ox and work with it. I cannot watch it all the time. Who is right? What do we do? Rav said: this is a mistaken transaction. Go after the majority, and the majority of people buy oxen for plowing. And Shmuel said: he can say to him, ‘I sold it to you for slaughter,’ and we do not follow the majority. For we follow the majority in matters of prohibition, but in monetary matters we do not follow the majority. Rather, the burden of proof is on the one seeking to extract money from his fellow.” There is no dispute between Rav and Shmuel about the facts. The fact is that most people buy oxen for plowing, not for slaughter. Those are the facts. Rav claims that if so, then the person who says he bought the ox for plowing is right, because most people buy for plowing—we follow the majority. Shmuel says no; the other party can claim: I sold it to you for slaughter. Usually people buy oxen for plowing? We do not follow the majority in monetary matters; the burden of proof is on the claimant. And in practical halakhic ruling, since this is a dispute in monetary law, we rule like Shmuel against Rav, because the rule is that the law follows Rav in ritual prohibitions and Shmuel in monetary law. So we rule like Shmuel that in monetary law we do not follow the majority. But there are places where we see that we do follow the majority in monetary law. For example, in court. In court three judges sit and adjudicate monetary cases. Two judges say Reuven is liable; one judge says Reuven is exempt. The law follows the two judges—we follow the majority. But that is not a majority about the case; it is a majority among judges. Wait, we will see in a moment. We follow the majority, and by the way both of these majorities are derived from “incline after the majority.” And we follow the majority in court. A number of medieval authorities ask, for example Tosafot in Sanhedrin 3 and in Bava Kamma 27, about the contradiction between these two principles. If we do not follow the majority in monetary matters, then in monetary cases too we should not follow the majority in court. “And one may wonder, for in the first chapter of ‘One Who Sells Produce’”—that is the Talmudic passage we just saw—“Shmuel says we do not follow the majority in monetary matters. Why do we not derive by an a fortiori argument from capital law, as is said here?” There is an a fortiori argument from capital to monetary law; the details do not matter to us right now. “And one cannot say that in capital cases too we do not follow a majority…” There is no distinction there between a majority before us and a majority not before us. “And one must say that the majority that buy for plowing is not considered like those other majorities; therefore we do not rely on that majority in monetary law.” The answers to this contradiction raised by Tosafot fall into two kinds. One kind says that the general rule is really that we do follow the majority in monetary law, and the case of buying for plowing is a special case in which we do not; only there we do not follow the majority. Another direction says no: generally in monetary law we do not follow the majority, and the majority in court is a special case where we do. Okay, those are the two directions. Tosafot here goes in the first direction. Tosafot is basically claiming that the “majority buy for plowing” case is a special kind of majority, and in principle we do follow the majority in monetary law as well, and the dispute between Rav and Shmuel is only about this particular case of “majority buy for plowing.” But Tosafot does not explain how it differs from every other case—why is this case exceptional, this case of “majority buy for plowing”? So Rabbi Shimon Shkop in Shaarei Yosher, gate 3, chapter 3, says as follows: “One may say that the reason for this is according to the words of Nachmanides in Milchamot in chapter 2 of Kiddushin, and it is brought in Shev Shma’tata, where he wrote regarding the majority who send gifts and only afterward betroth. For it is difficult: why are we concerned for the gifts and do we not follow the majority?” Yes, this refers to a man who sends gifts to his intended, and the question is whether the woman had already been betrothed to him. It depends on whether gifts are usually sent after betrothal or before betrothal. If someone had relations with a woman and we do not know whether he had betrothed her or not, but we do know that her partner sent her gifts—now, if the assumption is that gifts are usually sent by someone who has already betrothed his fiancée, and only then sends the gifts, then once we saw the gifts the assumption is that she was already betrothed, she was a married woman. But if gifts come before betrothal, then we have no proof she was betrothed. The fact that there were gifts does not mean she was betrothed, and therefore she is exempt. So Nachmanides says, and this is his language: “But the reason for this question is that this majority is not like the dispute of Rabbi Meir and the sages, for there the majority is one of obligation and nature, and it cannot be otherwise. But here it is only custom, and many times a person behaves according to the custom of the minority. Therefore, in a case of a married woman’s prohibition, they were stringent.” What is he saying? He is basically saying that in the case of gifts, suppose that in that place most people send the gifts after betrothal. Okay? But a person can come and say: I decided to send the gifts before betrothal. I felt like it. Nachmanides says that since this is not a majority in the nature of the world but merely a matter—not one of obligation and nature but of custom, not the nature of the world but custom—this is a weaker majority. A majority that depends not on nature but on custom is weaker. What is the idea behind this? So he says: “It is clear from his words that by Torah law such a majority is effective even regarding the prohibition of a married woman; only the sages were stringent. And according to what we have written, the matter is that such a majority is a Torah majority and not an intellectual majority, and it is effective by Torah law, only the sages were stringent. And therefore also the majority that buy for plowing is not an intellectual majority, for if this person needed it for slaughter, this does not at all depart from the laws of nature and common behavior. Rather, it is a Torah majority and therefore it is not effective in monetary law and in capital law for the reason we wrote, that in monetary matters we certainly require an intellectual majority, as we wrote, because it is a matter of reasoning…” What is he claiming? He is basically saying this: suppose a person says, “I bought it for slaughter.” No dispute for the moment. Someone says, “I bought it for slaughter.” Would we say to him, “That is implausible—it is very strange, because most people buy for plowing”? Would we say that? No, no. Obviously not, right? There are people who decide to buy for slaughter. Clearly there are such people. True, most people, because the need for plowing is greater than the need for slaughter, buy for plowing. But there is also a need for slaughter; clearly there are people who buy for slaughter. So if someone comes and says, “I bought it for slaughter,” would we say, “What you are saying is implausible”? If a woman comes and says, “I gave birth at seven months,” would we say, “That is implausible; most women give birth at nine”? That is a majority in nature. But if it is a majority that depends on a person’s choice, then the person can always say, “I decided to act this way rather than that way, so what if a minority of people act this way?” But after all it depends on my decision; it is not something that happens naturally, in which case you ask what usually happens in the world, what is the nature of the world. That is when the thing happens naturally. But if this is a human decision and the person tells you, “Listen, I decided to behave like the minority”—what is the problem? What force does that majority have? After all, there are such people, and they are completely normal and reasonable. It is not that the person is saying, “I am some pathological creature.” No. Ten percent buy for slaughter, and I bought this ox for slaughter. There were nine others who bought for plowing. What is the problem? That is not a weak argument. Suppose I call someone on the phone and say, “You know, my height is one meter ninety-five.” Will he say, “Impossible—what percentage of the population is one meter ninety-five? I do not know, ten percent, five percent, I do not know how many, very few, therefore clearly you are lying”? Does that sound reasonable to you? Of course not. I tell him: I belong to the minority. Belonging to the minority is normal, it is reasonable, there is nothing strange about it. Okay? So the same thing—what about a woman? What? The same thing with a woman who gives birth at seven? No. If a woman belongs to the minority, then believe her. In a place where there is a dispute, maybe yes. Where there is a dispute—our discussion about the woman is one where there is a dispute, because the woman wants to make a certain claim in order to avoid, I do not know, illegitimacy or things like that. You cannot simply accept what she says. You ask what happened here, so I look at the nature of the world. What happened was either seven months or nine months; most likely it was nine. But here we have a case where the person tells you, “I bought it for slaughter.” What is the problem? There is nothing strange about that claim at all. In such a situation, he says, generally we do follow the majority, even in such a majority. But in monetary law, or in a very severe matter, and things like that, such a majority is not enough for me; it is a weaker majority. That is his claim. In other words, a person can always say, “I behave like the minority,” so long as that behavior is reasonable; he is not saying he did something unreasonable. So if he says, “I chose to behave like the minority,” that is perfectly fine. It is fine. There is no significance to the fact that the majority behaves otherwise. Do you understand? The majority has no force here. You are saying that this is the same thing with the one-meter-ninety-five example, even though there is no decision involved there? Correct, correct. The one-meter-ninety-five example is indeed a case without decision, but I still think the idea is there. Suppose a child is about to be born and I ask what the probability is that he will be one meter ninety-five. The answer is five percent. There I will indeed go with the majority. But if a child already exists with a given height and he tells you, “My height is one meter ninety-five,” I will not say, “What you are saying is implausible,” right? What is the problem? There are people like that. And with the woman, why would we say it? What? With the woman… if the woman came and said it to me herself, then likewise, yes. But where I am making a claim against her and she has an interest in saying that, then maybe she is lying because she wants to prevail in court. But in the case of the ox there is also a plaintiff and a defendant, so why is he believed? I did not understand. In the case of the ox too there is a plaintiff and defendant, and this ox case is a dispute, so why is he believed? Yes, but there it is truly a matter of the person’s decision. If the person decided to buy for slaughter—incidentally, one would have to discuss the different opinions there—it may be that the person is not even saying that the seller did not sell it to him for plowing, sorry, for slaughter. Rather, I, when I intended to buy it, intended it for plowing. Then we do not even have a contradiction. You cannot tell me that I did not intend to buy it for slaughter, because that is a reasonable purchase. Let us assume that for the sake of simplicity, okay? Therefore he says: in a case where the claim that you belong to the minority is a reasonable claim, the majority is a weak argument. So I can decide that I belong to the minority, and then I belong to the minority. That is a perfectly good claim; there is no problem with it. You cannot force a person to be like the majority. So it comes out, Rabbi, that there are two parameters: one is decision and the other is credibility, and one of them is enough to create a weak majority. Meaning, if there is concern that you are lying, then the fact that it is a matter of decision is not an argument. Just think: suppose one person says he sold it for slaughter, and the other says he bought it for plowing. So true, he has an interest in claiming he sold it for slaughter because he does not want to return the money, okay? But on the other hand, selling for slaughter is a reasonable sale. You cannot say that is not a good argument. On the other side he says, fine, but I bought it for plowing. That too is a reasonable claim. And assuming they are not contradicting each other—say I believe you that you sold it for slaughter, but know that I intended to buy it for plowing. And vice versa. Then there is nothing to do in such a case. Certainly it does not make sense to apply the majority here. Right? So what does the majority matter? After all, a person can decide why he is buying. Yes. Which is not the case with the woman. With the woman it is different; there it does make sense to apply the majority. Yes, because it does not depend on her decision. Yes. And she has an interest. Again, if she had no interest, then fine, then no. Okay? Good, I will stop here because we have gone over time. I will continue next time. All right? Comments or questions or…? Okay, have a peaceful Sabbath. Peaceful Sabbath. Peaceful Sabbath. Goodbye.