Probability and Statistics – Lesson 15

This transcript was generated automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.

🔗 Link to the original lecture

🔗 Link to the transcript on Sofer.AI

[Rabbi Michael Abraham] This is where I finished last time. It’s exactly the next sentence I was about to say: in the end, after David Enoch defined the concept of knowledge that way, he said, fine, but for heaven’s sake, why should that matter to me? In other words, what matters to me in the end is the probability that this is true. Why should I care whether you can call it knowledge or you can’t call it knowledge? Therefore, he says, that cannot be a legitimate explanation for the illegitimacy of statistical evidence. That is basically where we finished last time, and I’ll just remind you of the framework of the discussion, because it is very, very important here. If you remember, I talked about how there can be three kinds of explanations for principles of this sort, for example, the non-use of statistical evidence. There can be an explanation that is a statistical explanation, meaning the evidence is not good enough, and therefore I cannot use it. There are problems with the evidence. That is a factual, statistical explanation: an explanation based on the reliability of the evidence. The second type of explanation is a practical explanation. Meaning, you can explain that it is not advisable to use such evidence because it will lead to one problematic result or another, and that is usually an explanation specific to the legal world. In the legal world, rules—even rules in the law of evidence—are not always fed only by the reliability of the evidence. The legal system has broader considerations. I gave the example of the fruit of the poisonous tree, which at least in the United States is apparently a clear and absolute doctrine, if I understand correctly, that you do not use evidence obtained illegally. And again, the evidence is good evidence; there is no problem with its reliability. But a legal system makes considerations beyond questions of reliability. It says: if we accept this evidence, problematic outcomes will follow; people will break the law in order to obtain evidence; and therefore this kind of evidence is made inadmissible, meaning it is not accepted. So that explanation—we can call it a legal explanation, a practical explanation, a utilitarian explanation, whatever you want to call it. And I argued that there is also a third explanation, which people usually ignore, and that is the explanation of legal-moral intuition, whatever you want to call it, a legal intuition that says this is not an appropriate way to act, or this is an appropriate way to act. I have no way to show that there is a problem with the reliability of the evidence; so it is not the first kind of explanation. I have no way to show what the problematic outcomes would be if I used this evidence; so it is not the second kind of explanation either. And still, the feeling is that this is not how one acts—that is, one simply does not do it. So this type of explanation—yes, for example, migo by force of argument is a good example of reasoning of this type. I don’t remember whether I mentioned it. Migo by force of argument: when I say—someone sues me on the basis of a loan document, and I say to him that it has already been paid. Now the claim “it was paid” is not a good claim against a written loan document, because if I had paid, I would be expected to take the document back from you and tear it up, not leave you holding the document, which is evidence that you can always bring against me and collect from me again. It makes no sense that I would repay the loan and leave the document with you. The moment I repay the loan, you return the document to me and I burn it, I don’t know, whatever I do with it, hide it. Now if the document is still in the lender’s possession, that is evidence that I did not pay. Therefore, the claim “it was paid” against a document is ineffective. What I’m saying now is very rough; it’s not so simple, but that is the simple picture. But once I say “it was paid,” after all I could have made a different claim: I could have claimed it was forged. You forged that document; this document is not—let’s say it is a document that has not been validated, there are no witnesses here authenticating the signatures, and in fact maybe you forged it altogether. And if so, then even if you are holding the document, that is not evidence. So if I had claimed against the document that it was forged, I would have won—at least rabbinically, where documents require validation; I’m not getting into the details now, but in principle I would have won. I can claim the document is forged. But I did not claim it was forged; I agree that the document is valid, the document is reliable, authentic, but I claim that I paid. Yet the claim that I paid is problematic, because if I paid, then why is your document still in your hand? What is the document doing in the lender’s possession? But once I had the option of claiming that the document was forged, then even if I do not make use of that and instead say the document was paid and do not claim it was forged, I have a migo. I could have claimed the document was forged, and that migo is evidence in my favor. Now at the base of migo as evidence there is a simple explanation. Everyone understands the logic behind migo as evidence. After all, if I wanted to lie, I would say it was forged and I would win the case. What kind of idiot liar chooses a weaker claim if in any case he is lying? If you want to tell the truth, then you tell the truth—you don’t have a choice. But if you want to lie, then obviously you would choose the best possible claim with which to lie. And if you make not the best claim, apparently you are not lying. If you were lying, you would choose the stronger claim. That is what is called “why should I lie?”—that is the ordinary migo reasoning. Classic. But the later authorities point out that there is another mechanism in migo, not only the “why should I lie?” that I just explained. There are cases where you see that migo works in a different way. They call it force of credibility or force of argument or something like that. What does that actually mean? It means that once I could have claimed the document was forged and won the case, then even if I claim it was paid, I am believed. Not because there is evidence that I am not lying. Not because of the evidence. Because there are situations where that evidence doesn’t exist—it doesn’t matter now. For example, if I already know that there is this principle of migo, then you understand that once I know this, that undercuts the evidence. Because I choose the weaker claim simply because I know it will create a migo for me. So there is no question why I chose the weaker claim. It is not necessarily because that is the true claim, but because I knew that if I chose the weaker claim they would believe me on the basis of migo. Yes, that is the question of the prodigy from Meitshet: how can they believe him on the basis of migo? After all, once he knows that there is this type of evidence called migo in court, then he will choose the weaker claim in order to be believed by virtue of migo. And again, that undercuts the evidence. In other words, the very admissibility of such evidence undermines it. No matter—there are all kinds of cases; there are situations of migo de-ha’aza. What is migo de-ha’aza? Let’s say that to say this document is forged is not a comfortable claim. All in all, the person lent me money; he did me a favor. And I say to his face, “You forged a document; you didn’t lend me anything; you’re a liar.” To say such a thing to the face of someone who did you a favor is a very uncomfortable position for normal human beings. Maybe for psychopaths it’s different, but for a normal person it is hard to make such a claim. So that is what is called migo de-ha’aza. So if I say “it was paid,” and I want you to believe me—why? Because if I wanted to lie, obviously I would choose the claim that it was forged, because it is a better claim. So they say to me: not true. You did not choose the claim that it was forged because it was unpleasant for you to lie with such a direct falsehood. Therefore you preferred a lie that may be weaker but is also less blunt, less ungrateful toward someone who did you a favor. And if so, that undercuts the migo. Because the whole migo is based on the fact that I could have chosen the claim that it was forged—why didn’t I choose it? Apparently I am telling the truth. No, there is an alternative explanation for why you didn’t choose it. You didn’t choose it because it is unpleasant to make the claim that it was forged; you were uncomfortable saying it. Yes, in partial admission, like Rabbi Chiyya’s first teaching there in Bava Metzia page 5, there are all kinds of considerations of that sort: he wants to stall the person, so he admits half, otherwise he could have denied everything, all kinds of things of that kind. So what happens in such a situation? In such a situation I have a migo, because I claim “it was paid” and I could have claimed “it was forged,” but I do not have the evidentiary dimension of migo. I do not have that consideration that says: if I wanted to lie, I would have chosen that other claim because it is better. That does not exist. And still, even migo de-ha’aza can, for example, exempt from an oath, at least according to some of the medieval authorities (Rishonim). Meaning, even migo de-ha’aza carries weight. And the later authorities ask: why? Once you no longer have the logical consideration behind migo, what remains? If in truth that argument—that I could have lied more effectively—supports the idea that I am now telling the truth, then if that argument no longer exists, if it falls away, what good is it that I have a migo? Why does the migo help? So they say there is such a thing as force of argument or force of credibility. What does that mean? At the end of the day, I had the power to win if I had said “forged.” True, it is unpleasant, everything is fine. But if I had said “forged,” I would have won. Once I could have won, and I chose to claim “paid” rather than “forged,” they give me the same force that would have been given to me under that other claim. A kind of—yes, what Rabbi Breisch, Chelkat Yaakov—he was in Switzerland, yes—writes about this is that it is like electricity. That is, they give a person the force in claim A and transfer it to him for claim B, like some electric circuit transferring current from here to there. What is the meaning of this? Why does the force I have in the claim “forged” come to me when I claim “paid,” when the claim “paid” in itself does not really have that force of credibility? Where does it come from? So what if I could have claimed “forged”? If there is the logical consideration I mentioned before, fine—that appears in the Talmud. But to say that migo contains force of argument is an invention of the later authorities with no basis. That is basically what he claims. Because in the Talmud, migo is “why should I lie?” That’s it, there is nothing else. And then, how are we to understand what those later authorities are saying? The feeling is—and I think, at least for me—there is some feeling that such a migo nevertheless has some weight. The fact that I could have won in a different way does affect the legal standing even if I am now making the claim “paid” and not the claim “forged.” Not the claim “forged.” Now it is hard to explain this. I cannot show it consequentially; I cannot—actually I can, there is some explanation in Maimonides, but let’s leave that for now. So if I cannot show it consequentially, and it is also not in the—meaning there is no probabilistic weight here, let’s put it that way, no evidentiary weight—then why should that migo give me some sort of legal advantage? So I say: there is an intuition that this is how one ought to act. Or disqualification of relatives—I talked about that. Or yes, the lack of credibility of a litigant himself, or that a party to the case cannot be a witness. All principles of that sort are what I called legal intuition. There is some kind of feeling, an intuition, that it is not right to act this way, and that is enough. I do not know how to conceptualize it, to show why it is not reasonable as evidence, or to show what problematic outcomes there would be, as with the fruit of the poisonous tree, but there is still some intuition that this is not the right way to act. I claim that such a thing too can constitute a sufficient explanation. By the way, in the context of migo—migo by force of argument—in Kehillot Yaakov, I think this is the explanation, or something approaching a conceptualization of that legal intuition. The claim is this: after all, we know that someone in possession has an advantage. Right? If neither side has evidence, then the money stays with the one in possession. Now here, in this case, since I could have claimed “forged”—it’s unpleasant, everything is fine, but I had that option—and if I had claimed “forged” I would have won the case. That means I have the option of winning the case by claim alone. Right? Maybe it is an unpleasant option, not comfortable for me, but I have that option. That means I have the option of winning the case without bringing evidence. That makes me the one in possession—so claims Kehillot Yaakov. Because what is possession? Someone in possession is someone who holds the money. And what is his advantage? That even if he brings no evidence, he can win the case without evidence; he can win the case simply by asserting his position, unless the other side brings proof. But if there is no evidence, I can win without proof because the money is simply with me. That’s all. So the claim is that your ability to say “forged” actually turns you into the one in possession. Because yes, he has a document, but on the other hand, if I had claimed “forged,” I could have sent him flying down the stairs and stayed with the money—that is, everything depends on me. My control over the money is full control. And therefore it is as if I am holding the money; I am the one in possession. So that, for example, is one possible explanation for why migo by force of argument is accepted. But think for a moment about the nature of that explanation—what kind of explanation is it? This explanation does not say that I am right. It is not evidence showing why this evidence is good evidence, or that it raises the probability that I am right. It does not raise the probability; we already saw that in migo de-ha’aza. Now, it is also not the type of explanation that says let us see what the consequences would be if I acted in this way—the kind of explanation I earlier called the practical legal explanation. In other words, like the fruit of the poisonous tree—yes, I do not know how to present that here either. What is the problem if I do not accept such a migo? There will be no problem. And still, there is a feeling that someone who has control over the matter has an advantage, and the other side must bring proof in order to get the money. That feeling too is a type of explanation. And for me, a legal intuition that says this is how it is appropriate or inappropriate to act—that too is an explanation. Even though I do not know how to map it onto one of the first two kinds of explanations. Now this option is an option that everyone discussing these areas ignores. And I can understand why, because it really does sound irrational. What do you mean, you have a feeling? It has no evidentiary weight. There is no problem if we do not accept this evidence—yes, no problem will arise. So why accept it? One can understand the position that says: wait, what do you mean that you have some kind of inner psychological structure that feels, I don’t know, a deep affinity for migo by force of argument, and now because of that I am supposed to accept it as evidence? Take a pill and get over it. What is the meaning of this? But if I see it as a legal intuition telling me—it is like a moral intuition—I manage to discern a legal principle that says this is not an appropriate way to act. Then for me that legal principle is a kind of explanation. And so I do not know how to persuade people with this sort of explanation except by showing them that there are certain places where I think they themselves would also say this. But most people, once you put it in front of their eyes, ignore it. They will look for an explanation of one of the first two kinds. Sometimes they will offer a forced explanation, but they will force that principle into one of the first two kinds of explanation because they are unwilling to accept the third kind of explanation. And I’m trying to put… in this lecture, the claim is that they are unwilling to accept the third kind of explanation, and therefore they force the principle into one of the first two kinds. That was basically the framework of the discussion last time, and now we are standing exactly at that junction in Enoch. Notice what happens. He is basically saying this: I have found a distinction between situations about which I can say I have knowledge, and situations about which I can say I have a conjecture. Now that distinction does not fit the first kind of explanation, because there is no difference in probability. So from an evidentiary perspective there is no explanation; this evidence is no worse than that evidence. From the standpoint of legal considerations, there does not seem to be a problem if I accept this type of evidence. So it must be something else. He does not accept the third possibility, and therefore he rejects it. He says: no, that cannot be, so apparently this is not a correct principle. For the moment—we’ll move on in a second. In other words, I’m trying to show you that this exactly reflects the framework I described earlier. We have three options, of which the third for most people is simply out of bounds, and therefore every principle is examined through whether it fits one of the first two, one of the first two kinds of explanation. And once it doesn’t hold—there’s nothing statistical here, no problematic result—then it is simply wrong, so there is no explanation. But on the other hand, as I told you, Pappino also ends up with that conclusion, but he still remains with the principle that statistical evidence is not accepted. He just does not know how to explain to himself and to us why. But he does not say, well then I disagree with the jurists, in my opinion they are making a mistake, we should accept such evidence. No, he does not say that. He says it requires further analysis. I don’t know; I can’t explain it. But it is clear from the tone that he too understands that this is what one ought to do; he just says: I cannot find an explanation. Now, what David Enoch does at this stage—and this is where we got to last time—is the expected and standard move: he simply shows us that there is a practical legal, consequential explanation. And in that way he rescues this principle that one does not use statistical evidence. Okay? So unlike Pappino, who remains with “this requires further analysis” but somehow does not give up the inadmissibility of statistical evidence, Enoch finds himself compelled—since there is no statistical difference between this evidence and eyewitness testimony—to find a practical explanation. Now look at the explanation he offers. He basically claims—what is called the practical explanation—that if we convict a person on the basis of statistical evidence, the punishment will not achieve its legal purpose. Let us try once again to recall the example he discusses. There are two bus companies in the city. The blue company has 90 percent of the buses, or 95 percent, and the red company has 5 percent. Okay? Now a person was run over by a bus, but I do not know whether it was from the blue company or the red company. Seemingly there is a 95 percent chance it was the blue company, and therefore we should hold the blue company liable to pay compensation to the injured person. But this is statistical evidence, and we do not use that kind of evidence. Now he offers the following explanation. He basically says: I have a legal, consequential explanation. If you were to convict the blue company in such a case, after all the point of the penalty is to deter the blue company so that it will drive carefully and not cause damage. But if you hold it liable without knowing that it did it at all, then the penalty will not achieve its purpose. Because the blue company knows that it will pay even if it did not do it. It will pay on the basis of a statistical calculation. And then it turns out that the penalty does not function as a trigger, or as an incentive, for more proper behavior by the drivers of the blue company. Therefore, he says, because of this legal consequence of that policy, one can find an explanation for it. And we do not convict—or think about the prisoner in jail. If you convict this prisoner of attacking the guard by virtue of the statistical consideration that 99 out of 100 prisoners attacked him and therefore you most likely attacked him, what does that mean? It means that in such a situation a prisoner has no incentive not to attack the guard, because he knows he will be convicted even if he does not attack him. So the punishment does not achieve its purpose; it does not deter. And therefore, says David Enoch, that is the explanation for why we do not use statistical evidence. Now here I want to make a comment. Basically here too, the claim is that the explanation for why one does not use statistical evidence is connected to counterfactual statements. What does that mean? Basically the explanation says: I must not convict the blue company in such a case, or the prisoner who attacked in such a case—why? Because if I were to convict them, that is a counterfactual statement, then they would have no incentive not to attack. Or alternatively, whether he did attack and whether he did not attack, I would convict him. In other words, this policy is not sensitive to the facts. Remember? This is the notion of sensitivity that I mentioned earlier. Since in effect I convict him in a way that is not sensitive to the facts, whether he attacked or not, because there is a 99 percent chance that he attacked, then it does not matter whether he attacked or not. So in effect I am convicting him in a way that is not sensitive to the facts. But unlike the previous proposal, which said that because this is not sensitive to the facts, you cannot call it knowledge that this person attacked, and therefore I cannot convict him because conviction is only on the basis of knowledge—that was the previous explanation, and he rejected that previous explanation. Why did he reject it? Because he says: why should I care whether it is called knowledge or not? What matters is the chance that he is guilty. And if the chance that he is guilty is high enough—95 percent, 99 percent—that is high enough. Why should I care whether this is called knowledge or not? Now notice: that same very consideration of sensitivity to the facts suddenly does become a good explanation. Why? Because we moved from the statistical explanation—how good the evidence is—to the practical, consequential legal explanation of deterrence. And even though the practical explanation also in fact rests on sensitivity to the facts—because a ruling that is not sensitive to the facts of how you actually behaved should not be imposed—that is basically the claim, meaning the ruling should be sensitive to the facts, but not because rulings are supposed to be based on knowledge, some legal notion of that sort that would explain why this is correct, but because if it is not sensitive to the facts, it simply will not achieve the deterrent purpose of the punishment. So here too the sensitivity of the ruling to the facts comes in, but the role played by that sensitivity is not the philosophical role of whether this is knowledge or not knowledge; rather, there is a practical explanation here. If it is not sensitive to the facts, why would the person change his behavior? So sensitivity to the facts still exists, but now it is already a legitimate explanation. Because earlier I said it was not a legitimate explanation, because there is no statistical difference, and as long as we had no difference in legal consequences, then why accept an explanation of the form this is called knowledge and that is not called knowledge—who cares, these are just words. But now he says: no, I have an explanation of the second kind, a legal consequential one such as deterrence, and therefore now I really can accept this explanation. I’ll just remind you—he himself writes this—that the claim he made earlier was that if the distinction between eyewitness testimony and statistical testimony appears outside the legal context, then apparently the explanation for it in the legal context is not specific to the legal sphere. Because otherwise, why would it also appear in the philosophical realm? Right? That was his consideration; I talked about that last lecture. And therefore he said—and that is why he began with it—with the lottery paradox. The lottery paradox does not deal with law; it has nothing to do with a legal question. The question is whether a person can say, “I know I did not win the lottery.” That is a philosophical question. And once we find that sensitivity to the facts creates this distinction for us also in the non-legal context, then that apparently means that the explanation for the inadmissibility of statistical evidence in the legal world need not be a legal explanation, because otherwise this distinction should not have appeared in another context. What changes now? What changes now is that it indeed appears in another context, but for different reasons. That is, in the philosophical context too there is a distinction that depends on sensitivity to the facts, and in the legal context too there is a distinction that depends on sensitivity to the facts. But the reason for this dependence on sensitivity to the facts is different. In the philosophical context, it is a question of whether this is called knowledge—whether one can say “I know” or not. A conceptual question. And that depends on sensitivity to the facts, assuming I accept his analysis. So if it is sensitive to the facts, it is knowledge; if it is not sensitive to the facts, it is not knowledge. Fine, that is one distinction in the philosophical context. In the legal context, it turns out that the question whether the punishment will achieve its purpose also somehow depends on sensitivity to the facts. Okay? So it turns out that sensitivity to the facts plays a role in both places, but that does not mean the explanation is not a legal explanation, contrary to what he said earlier. Here the explanation is indeed a legal explanation. The explanation is a legal explanation: the punishment will not achieve the required deterrence. That is a purely legal explanation. But by chance—or not by chance—the question whether the punishment achieves its purpose depends on sensitivity to the facts. And sensitivity to the facts also has a meaning in a philosophical sense unrelated to law—that is true—but a different meaning. And therefore the whole earlier consideration falls away, where he said this could not be a legal explanation. It can be a legal explanation, because the distinction we find in philosophy and the legal distinction both depend on sensitivity to the facts, but for different reasons. That is basically his claim, and it is a very elegant presentation of the move. But if we look for a moment at the explanation he itself offers, I have to say that I do not accept his explanation. The legal explanation is not satisfactory in this context. First of all, suppose we held the blue company liable on the basis of statistical evidence. Does that mean its drivers would have no motivation to be careful? Obviously they would. After all, if they are careful, there will be no accident. Maybe the red company will have an accident, but the chance of that is small—they have a hundred—and then true, if the red company causes an accident, they will still convict us. But the discussion here is not about a competition between a blue bus and a red bus over who will run over the person first, and then I say, the question is whether to let the red one run him over or to run him over myself. That is not the discussion. If that were the discussion, then you would be right: after all, they convict me anyway, so what do I care? I may as well speed up and run him over myself. Even if the red one runs him over, they will convict me. But that is not the discussion. I am now driving; I am a blue bus driver, and I am driving in the city, and I ask myself whether to be careful or not. Obviously I should be careful. Why? If I am careful, there will be no accident. If there is no accident, they will not sue me. It may be that if the red company has an accident, they will sue me even though I was careful—that is true. But if the red company does not have an accident and I am careful, then I will not have an accident either, and they will not sue me at all. So certainly I have motivation to drive carefully if they hold me liable. Wait—if I drive carelessly, because that is the counterfactual, if I do not drive carefully there may be eyewitnesses who see me, so I have to be careful in any case because there may be eyewitnesses. Therefore I do have motivation to drive carefully if they hold me liable. Another thing I do not like in this explanation is that it assumes a very specific theory of punishment. It assumes a theory of punishment whose purpose is the deterrence of offenders. But I have two comments on that. First, such a theory of punishment can deter other offenders even if not me. There are still people who understand, who see that when a person causes an accident he is punished, and that will deter them. There are not only the blue company and the red company on the road. Punishing the blue company is not just to deter the people of the blue company; it is to deter others. That is true even if I accept that punishment is meant for deterrence. But beyond that, there are completely different theories of punishment. There are theories of punishment that do not base punishment specifically on deterrence, or not only on deterrence. There is some kind of sanction, some kind of metaphysical desert perhaps, recompense, controlled revenge if you want to call it that, or something like that. There are all sorts of theories of punishment that do not speak specifically about deterrence. According to those theories of punishment, once again the explanation for why statistical evidence is not accepted falls into the trash. So there may also have been another—wow—and one more final point. Look how many problematic claims there are in his explanation. A final point: the sum that I impose on the blue company to pay the injured person is not a punishment at all. It is compensation. Compensation is not meant to deter. Criminal punishment is meant to deter offenders so that they will not act because they will be punished. But compensation—what is called civil law, not criminal law—is meant to compensate the injured party, not to deter the one who caused the injury. Now someone here was injured, and if there is a 95 percent chance that you did it, then compensate him. Why should the fact that this is not sensitive to the facts, why should the claim that such a policy is not sensitive to the facts exempt you from paying when that person was injured and deserves compensation? There is a 95 percent chance that you are the one who did it. So pay, under civil law, not criminal law. Therefore I think that precisely in the bus case, which is a civil case, this is really not logical. With the prisoners it is better, because with prisoners it really is criminal law, not civil law. I want to punish you for attacking the guard, not compensate the guard, but punish you because you did something that must not be done. So there it is indeed criminal law and maybe you can talk about sensitivity to the facts. But precisely the bus example, which is the example Enoch himself brings, is exactly the case where I do not accept his explanation at all, for all five reasons I have just listed. Now why am I saying this? Because look where people go in order to rationalize their intuition. After all, what is really driving him? Exactly what drove Pappino, and what drives me. We all have an intuition that it is not right to convict this way. It is not right to convict on the basis of statistical evidence. So what happens? I see before me three options. Option one: a statistical explanation. That falls; there is no statistical explanation here. Option two: a legal explanation. Enoch offered a legal explanation; in my opinion it does not hold water. So the conclusion that Enoch and Pappino seemingly ought to have reached—because they are unwilling to accept the third path, the third kind of explanation—is that apparently this principle is not correct. It is built into us as a tendency, but one must overcome it; it is not correct. One should also use statistical evidence. By contrast, I argue no: if I have a legal intuition telling me that this is how one ought to proceed—like the advantage of the one in possession in the law of evidence, or migo by force of argument, or things like that—then that too is a sufficient explanation. It is good enough not to use statistical evidence. And that is exactly—now in my opinion Pappino feels this, and that is why he does not insist on a practical explanation; perhaps he did not find one either. But he does not insist on a practical explanation; he simply remains with “this requires further analysis” as to what the explanation is, because he is not aware of the third option, or does not accept the third option. But on the other hand it exists within him, and he does not give up on not using statistical evidence. Therefore, implicitly, he probably does accept the third option; he is just not aware of it, because the fact is that he does not give up this principle and remains with “this requires further analysis.” Enoch seems really to go all the way with this and says no: if there is not one of the first two explanations, then this rule is not correct, and therefore he forces it into the second explanation, the practical one. But as I have shown here, that is quite forced; the practical explanation does not really hold water. And then what Enoch should have done, if he were being fully honest with himself, would be to give up this principle that statistical evidence is not used. But if, on the other hand, that strong feeling convinces us not to use statistical evidence, then that basically means that we probably do accept a third kind of explanation, and that type says: I have a good intuition that it is not right to use this kind of evidence. And therefore I will not use it, even though I do not have an explanation of one of the first two kinds. Now here—Rabbi, Rabbi. Yes. Rabbi, is it not possible perhaps to conceptualize this intuition as follows: when you convict someone solely on the basis of statistics, in other words, you are saying: I’m not looking at you; you personally do not interest me, and I don’t even want to see you; I am looking at the general pool and running some statistical calculation on a computer and convicting you. There is something anti-compassionate about that, something our intuition rebels against. When you bring witnesses—even if the statistics were statistics—you looked at him, examined him, the witnesses; that is what you can do, you always bring witnesses.

[Rabbi Michael Abraham] I accept what you are saying, I accept what you are saying, and it seems to me that what you did here was simply describe in words the intuition of the third type. I accept that, because in the end you did not present me with any explanation from one of the first two types. You did not show that this evidence is weaker, you did not show that some legal problem would arise if we used such evidence; you simply showed that it is not right, that one does not act this way. It is simply immoral?

[Speaker B] It is simply immoral, and I think that since the whole issue here is moral, it is immoral to treat human beings this way; it is immoral to treat human beings this way.

[Rabbi Michael Abraham] That is exactly the kind of explanation I’m talking about. If I make it more concrete, I’ll take you back to the three explanations—two, three—that in the end, as I said, are in any case three angles on probably the same explanation that I presented before we started this whole move of Enoch, if you remember. I spoke about following the majority in monetary matters: you can’t convict a person when there’s nothing that pertains to him specifically, only some sort of broad general view; you don’t convict a person that way. That’s basically like what I said about the difference between an established prohibition and a non-established prohibition, right? About probability based on information and probability based on ignorance, on lack of information—and we do not convict on the basis of ignorance. When I gave the example—say they bring me a die, and I have information: the die is fair, or at least I saw in previous rolls that it is distributed more or less with one-sixth probability, and I draw a conclusion—that’s a majority not before us; I conclude that the die is fair. And now that the die is fair, I ask myself: what is the chance it will land on five? The answer is one-sixth, because that is a positive answer; it is based on knowledge, on information, as we discussed earlier, sensitive to facts. But what happens if they bring me a die about which I have no information at all? I don’t know whether it’s fair, unfair, in what way it’s unfair—I know nothing about it. Now they tell me, okay, bet: what are the chances it lands on five? I will still bet on one-sixth, but here you can’t really say that the probability is one-sixth. That isn’t really probability; it’s out of ignorance. I have no information about any of the possibilities, so I assume they all have equal weight. I have no basis to assume that one possibility differs from another. And since that’s so, I still bet on a one-sixth chance that it lands on five, but this is a bet founded on lack of knowledge. And the claim is that even though the chance is one-sixth here and one-sixth there, there is still some difference—and in a certain sense it even touches probability itself—because in the first case it is a probability of one-sixth, and in the second case I assume one-sixth, but it’s not really probability; it’s some kind of a priori assumption, I don’t know what you want to call it, but it’s not probability. So ostensibly this is one-sixth and that is one-sixth, but how would we define the difference between them? After all, I said that in Jewish law there is a difference between a doubt involving an established prohibition and a non-established prohibition, regarding a provisional guilt offering, for example, and Jewish law views these two kinds of doubt differently. And my claim is that this difference is a legal reasoning; that is what I earlier called legal reasoning. And I’m claiming that convicting the bus, or convicting the person who didn’t pounce on the guard, or all these statistical convictions, are basically convictions on the basis of ignorance, and we do not convict people on the basis of ignorance. Now you’ll ask me: why not? If in the end that ignorance gives me a ninety-nine percent chance, why should I care whether you call it ignorance? We’re back to labels. The answer is—and I return to the explanation of conviction on the basis of knowledge, what everyone here is bringing up—and I want to return and argue that this is the correct explanation. And it’s true that it also appears in philosophical contexts, like the lottery paradox, and Enoch is right that if it appears in non-legal contexts then apparently the explanation is not a legal explanation. But it’s not a legal explanation in either of the first two senses; it is an explanation of the third kind. I have an intuition that says that in the legal world, one does not convict except on the basis of knowledge. I have such an intuition. It doesn’t create legal problems, it’s not an evidentiary deficiency, it’s not a defect in statistical evidence. But you don’t convict in that way. That’s all the explanations I gave in the classes before the previous one, right? I claim that all these explanations basically fall under the third category of legal intuition, and I don’t know how to map that onto one of the first two explanatory mechanisms or types of explanation. And still, for me, that is sufficient. Therefore I will not use statistical evidence, and I will not remain with “requires further analysis” like Pappino, and I won’t force it into a legal explanation which in my view does not hold water, like Enoch. And still I will not give up this principle, because this principle emerges from a perspective—call it meta-legal or philosophical—which says that one does not convict a person except on the basis of knowledge. A person has the right—let’s put it that way—the right to benefit from his innocence if the evidence against him is only circumstantial evidence. Do you remember where I started? Circumstantial evidence versus eyewitness testimony in Maimonides there with the ruin, right? Someone who entered a ruin and found a knife dripping blood. Here I want to argue that the defendant has a right—the criminal defendant and the civil defendant too, I mean—that conviction concerning him should stem from some information that pertains to him and not from some general claims about the world. Okay? That is basically the claim. Now this—here I am again waving my hands—I remind you once again about the hand-waving. The hand-waving always comes when I don’t know how to express the explanation in a sharp, convincing form. And still I think it is correct. There is no explanation of the first two kinds, and still it is correct. That is my claim. I think that here it is even a bit stronger, maybe, because there really is something here that touches on the defendant’s rights. It is like the presumption of innocence. We talked about the presumption of innocence: as long as no evidence has been brought that you are guilty, the assumption is that you are innocent. Is that a statistical assumption? Because most people are innocent? No. I explained why not. Because most people who stand trial are not necessarily innocent. Most people in the world are innocent, that’s true. But once an indictment has already been filed and this or that circumstantial evidence has been gathered and you have already reached court—I also have no way to do that statistic—but in this case you have no indication that most people are innocent. On the contrary, the conviction rates seem to be very, very high. Some people criticize that. And the conviction rates are very, very high, so in fact there is no presumption of innocence in the statistical sense. And still the legal rule says that every person standing trial is presumed innocent until proven otherwise. Unless of course it’s Bibi. So what does that mean? It basically means that there is a principle here that has no statistical explanation, but everyone understands that this is the right way to act. These are the defendant’s rights. It is the defendant’s right. Maybe here one can point somewhat to consequences—I’m not sure about that. But it seems to me that this goes beyond consequences; people feel that this is simply the right way to act. You cannot convict a person without evidence against him; the presumption of innocence stands in his favor. Therefore the claim is that there is a third type of explanation that should not be ignored, and it exists in all of us. It’s just that those who are sufficiently self-aware and clear-eyed and rational tend to reject it as though it were something irrational, because you don’t know how to conceptualize and present a real explanation here, so why act this way? It’s just irrational. And what I want to argue is: no, that’s not true; it is rational. Every other explanation is also based on assumptions, on first premises—the old philosophical-logical thesis of mine—and therefore in the very end we always begin with our intuitions. Formulated explanations too begin with certain intuitions that we have. Therefore one should not disparage the intuitions we have, and if we have such a strong intuition, that is perfectly fine. That is how we will act, and that is rational behavior. It’s fine. That is basically my claim: this move is an interesting move, but it’s there, Rabbi,

[Speaker B] Can one bring an example for this not from the legal field, and in a somewhat extreme form? For example, I’m in the medical field. We’ve heard that—you know—it’s hard to understand this, and it’s not necessarily right either, this issue of how people of Ethiopian descent are treated. A topic that came up now—that they vaccinate them for tuberculosis, and in the past they threw away the blood units they donated. If you look at it from a statistical point of view, you say: look, there is a certain risk here that rises above a certain threshold, and therefore it doesn’t make sense to endanger people over this. And nevertheless, from their point of view they are hurt and they see this as, what, you don’t count me just because I’m—

[Rabbi Michael Abraham] I agree with the analogy you’re making, but I do not agree with the conclusion. Meaning—but this really isn’t related to our discussion. I think it is justified to do that.

[Speaker B] I also think so, I also think so. I’m only saying it shows an example of just how far this kind of thing can go.

[Rabbi Michael Abraham] Agreed, agreed. I agree that this is an example of this mode of thinking. Specifically here I don’t agree with the claim—that is, why, if it hurts them, should we therefore take their blood units? That doesn’t seem reasonable to me. Again, it could be that if it were practical to take blood units from them too and test all the blood units—I don’t know, practical also in the economic sense—to test all the blood units and then disqualify the invalid ones and use what passes the screening, then maybe it would even be worth the financial investment in order not to hurt them. But if it’s not practical, then I don’t see the logic of harming potential recipients in order not to hurt Ethiopians whose blood donations are not being accepted. If that really is…

[Speaker B] Absolutely, absolutely. Okay,

[Rabbi Michael Abraham] In any case, that’s regarding explanations of the third kind, and here I’ll conclude this part about statistical evidence. What I do want is to place this in context. We spoke about vagueness, we spoke about doubts, we spoke about statistics, and I tried to show that the concept of statistics hides under it all sorts of categories: a majority before us and not before us, an established prohibition and a non-established prohibition, and so on. And it may be that although we are talking about the same numbers in the statistical sense, there will be certain contexts in which we treat them differently. Even though the number is ninety-five percent, if it comes from a consideration of ignorance we will not accept it in the legal world; if it comes from a consideration of knowledge we will accept it in the legal world. Therefore statistics is not always the right instrument for resolving doubts. That is the lesson that I want explained—the purpose of this block we have just finished. This block that we’ve just finished came to show that despite what I said until now, that statistics is a tool for making decisions under conditions of uncertainty and it basically resolves doubts in reality—statistics helps me conduct myself in such a way, or resolve doubts, helps me conduct myself—the claim I now want to make in light of what we have seen is that this is not always and not necessarily so. There are situations in which I am in uncertainty, in lack of knowledge, I have some kind of statistical calculation—though usually it’s not really a calculation, as I said, because it’s not genuine statistics—but I still won’t use it because I have some constraints, call them legal, moral, whatever. Therefore, although statistically if you asked me what I would bet on, I would bet that this person really did pounce, from the standpoint of legal conviction it’s different; there it works differently. And therefore statistics does not always work there. Not that it does not work in clarifying reality, but it does not work in the sense of giving me a sufficient basis for conviction. Okay? That is a limitation on the significance of statistics. It is not a comment on statistics; the statistical calculation is fine. But it is a comment on what one does with the result of the calculation, what the statistical calculation means. And with one qualification I did note something that also touches statistics itself: that in certain cases the statistical calculation is not really a statistical calculation. For example, with a piece of meat from shops, I said that even though there are, say, nine kosher shops and one non-kosher one, then ostensibly there is a ninety percent chance that the piece of meat I found is kosher—there my claim was also on the statistical plane. Although if I had to bet, I would bet nine to one, still it is not correct to say that there is a ninety percent probability that this piece is kosher. That is a bet out of ignorance, not a bet based on information, and therefore I am making a comment here that this is not really probability. Again, practically, if I had to bet I would probably bet nine against one, but one has to understand that it is not really probability. It is not only a legal consideration; it is not probability. It is some kind of a priori assumption that I am supposed to treat it as nine to one, but no probabilistic basis for this can be presented. And in that sense there is here some evidence not only regarding the meaning of the statistical calculation—whether I use it or not, whether it is admissible in court or not—but also regarding the statistical calculation itself: cases that look similar to us—this is ninety percent and that is ninety percent—one of them is the result of a statistical calculation, and the other is some kind of default arising from ignorance, from options, ten equal options to which I assign equal probability without knowing anything. So that is not the result of a probabilistic calculation, and in principle someone could come and say: I do not even accept the ninety percent figure. Who said it is ninety percent kosher? How do you know that the chance it came from shop A, B, C through J is the same chance? Maybe some pieces are packaged differently and therefore get lost more easily? We already talked about these possibilities, and therefore in such a situation I still speak of ninety percent as a number, but the comment is already deeper than a legal comment. It is already almost a probabilistic comment. My claim is that this ninety percent here is a borrowed use of the concept of percentage. I would bet nine against one, but it is not the result of a probabilistic calculation. Now, that brings me to our next discussion. Our next discussion deals with the concept of fixed in Jewish law. Usually we follow the majority—whatever separates is presumed to have separated from the majority—but in the case of fixed, a situation I’ll define in a moment, we do not follow the majority. And again we need to ask ourselves: what is the explanation for that? This is a topic very parallel to the question of probabilities in law, statistical evidence in law. Because there too somehow it seems—and here too, that is—somehow it seems, as there, that separation and fixed have the same probability, and nevertheless here we use it and there we do not use it. And the question is why. So naturally, shortly after I thought about the question of probabilistic evidence, I returned to use these tools to try to think about the law of fixed. Maybe I can analyze the law of fixed in a similar way too, because there too, as you understand, we have three options. Why in the law of fixed do we treat it as fifty-fifty, and in the law of whatever separates do we treat it as majority? You know what? Maybe first of all I’ll present the concept. The Talmud in tractate Ketubot—this is the main passage on the law of fixed, Ketubot 15a—I’ll share it for a moment. “Returning to the main point, Rabbi Zeira said: Anything fixed is regarded as half and half, both leniently and stringently. From where did Rabbi Zeira derive this?” Right? Cases called fixed—we’ll define them in a moment—we do not follow the majority, but for us this is an even doubt, fifty-fifty. “From where did Rabbi Zeira derive this?” Where does Rabbi Zeira know this from? “Shall we say from the case of nine shops, all of which sell slaughtered meat, and one sells carcass meat, and one took from one of them and does not know from which one he took: his doubt is prohibited; but if it was found, one follows the majority.” Perhaps that is Rabbi Zeira’s source there? In the law of shops there is a difference. Never mind for the moment where the Talmud finds it, but there is a difference. If I find a piece of meat thrown in the marketplace and there are nine kosher shops and one non-kosher one, then we say: whatever separated is presumed to have separated from the majority. This piece separated from one of the shops, because its origin is in one of the shops and it left there and somehow got to the street, so I say: whatever separated, separated from the majority, meaning from the majority of shops, and therefore it is kosher by strict law. But if I walk into the shop—what it says here is “he took from one of them and does not know from which one he took.” I didn’t find the piece of meat in the street. I entered one of the shops, bought myself a piece of meat, got home, and then remembered: oh, there is also a non-kosher shop in town, maybe I went into that one; I don’t remember which shop I entered. That is the second case. This is called fixed. Why? Because the doubt arises not when I found the piece, because I didn’t find it. When did the piece reach my hand? When I was in the shop and took it from the shelf. And therefore from the standpoint of Jewish law, the moment the doubt arises is the moment when I am in the shop choosing this piece. And at that moment the piece has not separated from the shop; it is in the shop, in its place, fixed in its place. And in such a case, says the Talmud, I do not follow the majority, even though there are nine kosher shops and one non-kosher one; rather, it is half and half. That is the law of fixed. The Talmud asks where Rabbi Zeira knows this from. So it says: perhaps from that distinction in the shops. Again, this is not where in the Torah, but where he finds it in the words of the Sages, in tannaitic sources. But the Talmud rejects that and says no, because there it is stringent. Right, you cannot derive proof from there, because perhaps there you treat it as non-kosher because you go stringently. Who says one also applies it leniently? But stringently, it is indeed a source. So for our purposes, let us summarize for a moment: what is a case of fixed? The case of separation is this: I have ten shops; one piece separated from one of the shops. I ask myself where it separated from. Since there are nine kosher shops and one non-kosher one, the assumption is that it separated from one of the kosher shops. Whatever separated is presumed to have separated from the majority. What separated, separated from the majority group, and therefore by strict law the piece is kosher. That is the law of separation. The law of fixed is when I approach one of the shops, choose a piece of meat, but I do not know whether that shop was the non-kosher shop or one of the nine kosher ones. Ostensibly the probability is the same probability; here too it is ninety percent that the piece is kosher. And there the Talmud says the rule is that for me this is an even doubt whether the piece is non-kosher or not. Fifty percent, not ten percent. And therefore one must be stringent: a Torah-level doubt is treated stringently. So the Talmud says that from there one cannot bring a source, because maybe they tell you that you need to be stringent. The law of fixed is like half and half stringently. But what happens if there are nine non-kosher shops in town and one kosher one? If I found a piece of meat in the market, then the law of whatever separates is presumed to have separated from the majority, and the piece is non-kosher. Right? There are nine non-kosher ones and one kosher one, so the piece is non-kosher. What happens if I took the piece from within the shop, but I don’t remember whether it was one of the non-kosher shops or that one kosher shop? In such a case, anything fixed is regarded as half and half. It is a doubt whether kosher or non-kosher, where the default here is to say it is non-kosher, not kosher. Meaning, here to say that anything fixed is like half and half is a leniency, not a stringency. Do not treat it as certainly non-kosher; it is only doubtfully non-kosher. One still has to be stringent because of the doubt, but it is a doubt and not a majority. For example, if there were another doubt, then this would already be a double doubt. Okay? So that is a lenient statement, not a stringent one. And the Talmud asks: from where does Rabbi Zeira know that in a fixed situation it is considered a doubt both leniently and stringently? In the case of shops it goes stringently, because the case of shops speaks of nine kosher and one non-kosher. But who says that in the opposite case—which we do not find in the Sages, in the Mishnah—but the opposite case of nine non-kosher and one kosher, there too fixed will be like half and half? Maybe not; maybe there we will follow the majority. It is half and half only when that leads to stringency, not when that leads to leniency. So the Talmud says: I have another source for this law, and again it is a case of fixed. “Rather, from the case of nine frogs and one creeping creature among them, and he touched one of them and does not know which one he touched: his doubt is impure.” Right, I basically have ten creatures in some box, okay? There are nine frogs and one creeping creature. Now I put my hand in and, with my eyes closed, touched one of them, and I do not know which one I touched. If I touched the creeping creature, I am impure; if I touched the frog, I am pure. So they tell me: it is a doubt, and because of the doubt you are impure. What do you mean, why are you impure? Because this is fixed, right? There are nine frogs here; most likely I touched something pure. Why do they obligate me to be impure? Because this is fixed. And once it is fixed in its place, I put my hand into the box—it is not that some creeping creature came out; rather, I put my hand into the box and ask myself which of them I touched. Just like with the piece of meat that I chose inside the shop. In such a case this is a case of fixed, and the law is like half and half: his doubt is impure. It is not ninety percent pure; it is fifty percent pure. So the Talmud says: there too it is stringent. This too is a source for stringency, because they tell you that you are doubtfully impure instead of ten percent impure. “Rather, from the case of nine creeping creatures and one frog among them, and he touched one of them and does not know which one he touched. In a private domain his doubt is impure; in a public domain his doubt is pure.” The rule in doubtful impurity is that it is not like ordinary laws of doubt, ordinary Torah-level doubt; rather, it depends where the doubt arose. If it is in the public domain, then in case of doubt you are not impure; if it is in the private domain, then even because of doubt you are impure as though it were certain. That is the rule in the laws of impurity; it doesn’t matter, they derive it from the suspected adulteress. So in other words, what the Talmud is saying is that if there are nine creeping creatures and one frog, and I touched one of them and I do not know which one, then there is a ninety percent chance that I am impure. And the Talmud says no: this is fixed, therefore it is only fifty percent. That is already a lenient statement, right? Like the case of the nine non-kosher shops and one kosher one. And if we still say that these are the laws of doubts, and we say that doubtful impurity in the private domain is impure and in the public domain doubtfully pure, that means they are telling me that the laws of doubt apply here. It is not ninety percent; it is fifty percent. Here is the source for the fact that the law of fixed functions leniently too and not only stringently. Okay? Meaning, it is not that they tell me: in the law of fixed, be stringent just in case. No. The law of fixed is understood as a different probabilistic question. The law of separation goes by the probability. In the law of fixed the probability is fifty-fifty, both leniently and stringently. Meaning, this is real. It is not that they tell me: be strict for safety’s sake. They say: no, no—even to be lenient. And I say positively that it is fifty-fifty, not that perhaps it might be fifty-fifty. Therefore even leniently I treat fixed as though it were a case of evenly balanced doubt. That is the law of fixed. Now, when we ask ourselves what the explanation is—ah, before that, you know what, maybe let’s just finish the passage. The Talmud says: “And from the Torah, from where do we know it?” What do you mean, from the Torah from where do we know it? Until now they were asking where Rabbi Zeira knew it from, from tannaitic statements, baraitot or Mishnahs or something like that. But the question is: where did the tannaim themselves know the distinction between fixed and separation from? Where did the tannaim invent it from? They must have had some source in the Torah, or I don’t know, or some logical reasoning, or something. The Talmud asks: “And from the Torah, from where do we know it?” “The verse says: ‘and lie in wait for him, and rise up against him’—until he intends him.” That is Rabbi Shimon’s view, as emerges there from the Talmud. It doesn’t matter. The verse—look, the verse appears below—“If a man hate his neighbor, and lie in wait for him, and rise up against him, and strike him mortally so that he dies, and he flees to one of these cities.” We are speaking of a murderer, and he is liable to the death penalty. Right? Going to the cities of refuge will not help a deliberate murderer; they kill him. “From My altar shall you take him to die.” Okay? So this is basically the law of a murderer. But in the verse there appears a condition: “If a man hate his neighbor, and lie in wait for him, and rise up against him, and strike him mortally.” Why this addition? It should have said: if a man hates his neighbor, and strikes him mortally so that he dies, they kill him as a murderer. What is this addition, “and lie in wait for him, and rise up against him”? About that the tannaim dispute. I return to the section in the Talmud. “And from the Torah, from where do we know it? The verse says: ‘and lie in wait for him, and rise up against him’—until he intends him.” Meaning that he must be an intentional murderer, he must intend. “And the Rabbis of the school of Rabbi Yannai say: this excludes one who throws a stone into a group.” He threw a stone into a pit or a room in which there are ten people. What are the circumstances? the Talmud asks. “Shall we say that there are nine Canaanites and one Israelite among them?” There are nine gentiles there. The assumption is, again, that for gentiles there is no death penalty. The prohibition on murdering a gentile is not derived from “You shall not murder” but from “Whoever sheds the blood of man, by man shall his blood be shed.” It is a Torah prohibition, but there is no death penalty. Murdering a Jew carries the death penalty. Let’s say there is a room with nine gentiles and one Jew. I threw a stone into it; I do not know whom it will hit. So the Talmud says: “Then let him be exempt because the majority are Canaanites.” Right? What are we talking about? If there were in the room nine Canaanites and one Israelite, then there is a majority of Canaanites, so what, did he kill the Jew? And you say the condition “and lie in wait for him, and rise up against him” is not fulfilled. Why? Because from the outset he did not specifically intend to kill the Jew. So one cannot execute him in such a case. So the Talmud says: “Then let him be exempt because the majority are Canaanites. Or alternatively, even if it were half and half”—and even if we treated the law of fixed as half and half—“in capital cases one is lenient.” After all, you cannot execute a person even if it is half and half. To impose the death penalty, he must be a certain murderer, not a doubtful murderer. So the Talmud says: “No, it is necessary for a case where there are nine Israelites and one Canaanite among them.” If in the law of fixed we followed the majority, then we would execute the murderer. Why? Because there are nine Jews here, and we follow the majority, so he intended to kill a Jew, and he in fact also killed a Jew; he is liable to death. And the verse says that in such a case we do not execute him. The condition of “and lie in wait for him, and rise up against him” is not fulfilled here. So why not? We see that anything fixed is like half and half. And here it is lenient, right? Here we see that anything fixed is half and half, and this is lenient, because we do not execute him since it is half, not ninety percent. So that is the source for the law of fixed. Okay. Now, I’m not going to go into the law of fixed further right now; I’ll just finish by setting the framework for the discussion ahead. As I said earlier, the question why in fixed we behave differently than in separation is a question that very much resembles the question of statistical evidence in law. Why? Because if I took the piece from inside the shop or the piece separated, ostensibly this is ninety percent and that is ninety percent. Or with the frogs: whether I touch them or don’t touch them—or say one person came out of the room and then I threw the stone at him and killed him—that would be separation. I would be liable to death. But if I threw the stone into the room, then it is fixed. Like the shops. Fixed is like half and half. Now in both cases the chance is ninety percent. So the question is why in one case we treat that ninety percent as though it were a majority and it resolves the doubt, while in the second case from my standpoint I am still in doubt, it is like fifty-fifty—not probabilistically, but halakhically, it is like fifty-fifty. Exactly like statistical evidence in law, where despite there being a majority, from my perspective there is no evidence; it is fifty-fifty. So the law of fixed very much resembles the case of statistical evidence in law. And therefore here too I return to all the—I won’t repeat everything, I’m just making the link. The same three types of explanation stand before us now. Either I will show that fixed is a lower probability and therefore we do not take the probability into account there, or I will show that there is some legal consequentialist consideration here, or I will show a legal intuition. Right? Those three possibilities. And again, everyone who tries to explain fixed—it depends whether they in principle accept the option of the third kind of explanation or not. And into this enter all the strained explanations of the law of fixed that we are going to encounter. Okay? So the analogy is clear, and I will want to do an analysis similar to what I did in the previous topic of legal evidence, statistical evidence in law, for the law of fixed. Okay. We’ll stop here. Any comments or questions? Okay then, goodbye, Sabbath peace.

[Speaker B] Thank you very much, Rabbi. Thank you very much.