Majority in Halacha and in General 2, Lesson 6

Table of Contents

• Majority in a religious court, a qualified majority, and veto power for the minority
• Rabbi Shimon Shkop’s question on Sefer HaChinukh: a majority that is before us and a majority that is not before us
• Probability, sampling, and the nature of the world: how a majority that is not before us can become a majority that is before us
• Rabbi Shimon Shkop’s claim: a majority that is before us as a majority of “sides,” not as a statistical clarification
• A concluding position: a majority that is before us as an a priori rationale that requires authorization from the Torah
• A probabilistic model of a single judge and its implications for a majority of judges
• Probabilistic evidence in law: prisoners, buses, and a stadium
• Jewish law: capital cases, eyewitness testimony, and circumstantial evidence in Maimonides
• Admissibility versus reliability: the fruit of the poisonous tree, related witnesses, and self-incrimination
• Attempts at distinction: certainty of error, an established prohibition, and the question of intuition without explanation

Summary

Overview

The text presents the justification for following the majority in a religious court according to Sefer HaChinukh as a general tendency of the majority to hit the truth more often, and sets against it a question from Rabbi Shimon Shkop based on the Talmudic topic of a majority that is before us and a majority that is not before us in tractate Hullin. It then develops a distinction between a majority based on an empirical sample and statistical generalization, and a majority based on an a priori rationale that cannot be directly tested, and proposes this as a way to reconcile both Sefer HaChinukh’s view and the Talmud’s classification. Finally, it raises the problem of “probabilistic evidence” in law: a strong intuition not to convict or impose liability on the basis of “pure” probability even when the percentage is extremely high, as opposed to the admissibility of other kinds of evidence such as two witnesses, and the discussion is tied to questions of admissibility versus reliability and to the gap between monetary law and capital law.

Majority in a religious court, a qualified majority, and veto power for the minority

Following the majority in a religious court is presented as a rule of thumb chosen because, in most cases, the majority is right, provided the judges are more or less on the same Torah level, even though that is no guarantee of truth. The requirement of an absolute majority is understood as ensuring that there really is a majority, but requiring a qualified majority is described as problematic in principle because it gives the minority veto power. The claim is that when a decision has to be made, you cannot “do nothing” without effectively going with the minority, and therefore it is better to go with the majority as the more reasonable chance.

Rabbi Shimon Shkop’s question on Sefer HaChinukh: a majority that is before us and a majority that is not before us

Sefer HaChinukh explains following the majority of judges by saying that “generally speaking” the majority is closer to the truth, and Rabbi Shimon Shkop objects that such a justification turns the majority in court into a majority that is not before us. The Talmud in tractate Hullin presents the majority in a religious court as an example of a majority that is before us, from which we derive “follow the majority,” and this creates an apparent contradiction between Sefer HaChinukh’s explanation and the Talmud’s classification. The distinction between a majority that is before us and one that is not before us is explained as the difference between a concrete group standing before us and a general feature of the world.

Probability, sampling, and the nature of the world: how a majority that is not before us can become a majority that is before us

A majority that is not before us is described as general information about the world, such as “most women give birth at nine months” or “a person does not repay a debt before its due date,” which is not based on a complete concrete group standing before us. It is argued that if it were possible to measure the entire population and know its full distribution, then even a claim about “the whole world” would become a majority that is before us, because it would rest on complete concrete information. When information about the world comes from a sample from which one infers to the population as a whole, this is described as the ordinary statistical mechanism of surveys and experiments, and in Jewish law the size of the sample does not affect the basic legal status of majority, even though it does affect the perceived risk of error.

Rabbi Shimon Shkop’s claim: a majority that is before us as a majority of “sides,” not as a statistical clarification

Rabbi Shimon Shkop is presented as arguing that a majority that is before us does not “clarify” and is not about probability, but is rather a formal rule of a “majority of sides.” In this model, each store casts a “side” regarding the piece of meat, and each judge casts a “side” regarding the ruling, and the decision is made according to the majority of sides. The comparison to a double doubt is brought through the Rashba, who explains leniency as counting possibilities at the end of the decision tree, as a majority of sides.

A concluding position: a majority that is before us as an a priori rationale that requires authorization from the Torah

The text rejects presenting a majority that is before us as an arbitrary scriptural decree, and argues that a reasonable person really would intuitively assume that a piece found in a city where most stores are kosher probably came from the majority, and that in a religious court a majority of sages of equal level is probably right. At the same time, it is argued that there is no direct empirical way to test these assumptions, neither in the case of stores and a found item nor in court rulings, because there is no feedback of “the truth” against the decisions, and so this remains an a priori rationale rather than a statistical fact. From this, a reconciliation is proposed: Sefer HaChinukh is right that we follow the majority because it is reasonable to think it is closer to the truth, and yet it still remains a majority that is before us, as in the Talmud, because it rests on rational intuition rather than an empirical sample; the Torah gives explicit authorization for this in “follow the majority.”

A probabilistic model of a single judge and its implications for a majority of judges

A proposal is presented to calculate statistically the advantage of the majority based on the assumption that each individual judge has a probability of \(P>0.5\) of being correct, in which case a majority of judges will be more reliable than a single judge. It is said that this calculation works, but the initial assumption about \(P\) itself cannot be directly empirically verified, because there is no way to know when the judge was right as against “the truth,” and therefore even this does not turn the issue into a majority that is not before us. The discussion is connected to Kahneman’s idea of “System 1” and to the fact that intuitions can be biased, and still that is what we have when no other information is available.

Probabilistic evidence in law: prisoners, buses, and a stadium

Scenarios are presented in which there is a very high probability of guilt, yet the legal system refuses to convict on the basis of probability alone, such as a hundred prisoners of whom ninety-nine participated in an assault and one did not, but it is unknown which one, or two bus companies, one of which owns 95% of the buses in the city, so that a given accident is statistically attributed to it. Set against this is a case in which two witnesses identify an act, even though testimony too is not one hundred percent certainty, and nevertheless it is accepted and a conviction or liability is imposed on its basis. The claim is that there is a problem here of “probabilistic evidence,” in which two pieces of evidence with similar probability are perceived very differently in terms of admissibility.

Jewish law: capital cases, eyewitness testimony, and circumstantial evidence in Maimonides

A distinction attributed to Maimonides is brought between monetary cases, where one can rely on persuasive circumstantial evidence, and capital cases, where eyewitness testimony from two witnesses is required. The baraita in tractate Shevuot 34 is cited in the name of Rabbi Shimon ben Shetah about someone chasing another into a ruin, a man standing there with a sword and blood dripping, and a victim writhing, followed by the declaration, “What can I do, for your blood is not given into my hands,” because “by the testimony of two witnesses or three witnesses shall the dead be put to death,” with the conclusion, “They did not leave there until a snake bit him and he died,” to show that the factual certainty was very high and yet there was still no conviction. The text presents Maimonides as understanding the problem as one of circumstantiality and not only as a matter of the number of witnesses, and emphasizes that Jewish law recognizes situations in which the admissibility of evidence is separate from its level of reliability.

Admissibility versus reliability: the fruit of the poisonous tree, related witnesses, and self-incrimination

The principle of “the fruit of the poisonous tree” is brought as an example of disqualifying evidence for reasons unrelated to its reliability, but rather because of the way it was obtained, as is the example of disqualifying related witnesses even on the assumption that they are trustworthy. “A person cannot render himself wicked” and “a person is considered related to himself” are brought as matters of admissibility, not as concerns about reliability, and it is said that in Miranda they quote Maimonides in a way that mixes up the justification. The claim is that even if there are sometimes legal justifications for excluding evidence, that still does not explain why purely statistical evidence is rejected when the purpose of the proceeding is to reach a sufficient degree of certainty.

Attempts at distinction: certainty of error, an established prohibition, and the question of intuition without explanation

A distinction is proposed according to which, in a case where if they convict all of them it will be clear that one innocent person will certainly be convicted, there is a legal reason not to use majority, but it is said that this distinction does not solve cases like the buses or a situation where only one prisoner is caught. An analogy is brought to the halakhic distinction between a doubt involving “one piece out of two pieces,” which obligates a provisional guilt offering, and a doubt involving a single piece, which does not obligate a provisional guilt offering, based on the idea that in the former case permission leads in practice to certainty of prohibition if he eats both. The text ends with a general methodological question: when there is a strong intuition to distinguish between kinds of evidence but no ability to find a formal justification, should one conclude that the intuition is mistaken, or rely on it out of trust that there is some hidden flaw in the mathematical argument? It is said that the continuation of the explanation will next time be connected to a majority that is before us and a majority that is not before us.

Last time, last time we talked about the majority in a religious court. And I said that the Sefer HaChinukh, in commandment 78, writes that following the majority in a religious court is because usually the majority is right. Meaning, most likely. And again, we’re talking about a case where the judges are more or less on the same Torah level, and in that situation there’s a reasonable chance that the majority is right. And again, there’s no guarantee of anything. It’s not certain that they’re right. But if I need to set some kind of rule of thumb—whether to follow the majority or the minority—I’ll follow the majority. Yes, it’s always this dilemma. Say, for example, in Basic Laws, there are places where for Basic Laws you need an absolute majority, sixty-one members of Knesset. There are places that require a special majority, seventy members of Knesset. Now that’s a very problematic thing. It’s very problematic because it means giving the minority veto power. Because basically, if you don’t follow the majority, then you’re following the minority. Why follow the minority? You can require an absolute majority, fine, because you want to make sure there really is a majority. But a special majority is something that is problematic in principle. You’re basically giving veto power to the minority. Meaning, whenever you don’t follow the majority, there’s another side, so you’re following the minority. So if I say: we either follow the majority or the minority, then I choose the lesser evil. I don’t have the option of saying, okay, I’ll remain in limbo, I won’t do anything. If I do nothing, I went with the minority. And following the minority is less reasonable than following the majority. So follow the majority. That’s connected to what we talked about last time. So the Sefer HaChinukh says that we follow the majority of judges because it’s more likely that the majority is closer to the truth, hits the truth more accurately. And about that Rabbi Shimon Shkop asked—we saw this last time—about that Rabbi Shimon Shkop asked: such a majority is a majority not physically before us. The Talmud in tractate Hullin says that the majority in a religious court is the example of a majority physically before us, and from there we learn “incline after the many,” since that was said about a majority of judges in a religious court, and the Talmud says that this is a majority physically before us. But a majority not physically before us—how do we know that? And then the whole discussion begins. Meaning, a majority in a religious court is considered a majority physically before us. Rabbi Shimon Shkop says: according to the Sefer HaChinukh, it comes out that the majority in a religious court is a majority not physically before us. That goes against the Talmud. Why? Because a majority physically before us—I explained there what the difference is between a majority physically before us and one not physically before us. A majority not physically before us is some kind of feature of the world. In the world there’s a certain pattern of conduct: most women give birth at nine months and not at seven; most women are not infertile in that halakhic sense; it doesn’t matter, all kinds of things; a person does not repay a debt before its due date. Even a presumption—I said there’s a difference between presumption and majority—and in principle that too is some kind of natural pattern of the world. A majority of stores, which is the example of a majority physically before us—nothing in the nature of the world says that most stores here need to be kosher. It just happens that in this place many Jews who observe commandments probably live, so most stores are kosher stores. Somewhere else it won’t be that way. There’s nothing here that stems from the nature of the world. It’s an accumulation of a random group. Okay? So a majority physically before us basically refers to a concrete group before us, like ten stores. I ask myself about some specific item that I clearly know belongs to those stores, and the question is which of the stores it belongs to: the kosher stores or the non-kosher store. In “most women are not infertile” or “most women give birth at nine months,” there is no concrete group of women in front of me about whom I have information, one of whom I’m asking something about. No. I know some general information about the world, and then a woman comes before me and I say, well, if the world usually works this way, then probably with this woman too it’s that way. But that’s not something about some concrete group. And I said there are arguments both ways regarding what is more appropriate to compare to probability. At first glance, specifically a majority physically before us is probability, because I have ten stores, I have a clear sample space. There are ten stores here, nine of them kosher and one non-kosher. I know there are nine possibilities as against one. So I have a ninety percent chance that this piece is kosher. That’s the probability of a complete group standing before me. I have all the information about the group. About the individual item itself, I don’t know, but about the group I have all the information, and I also know that the item belongs to the group. I know that too. So I say, then the assumption is that this item has the same distribution as the group. In contrast, a majority not physically before us is some kind of hypothesis about how the whole world behaves. That group is not before me, I can’t measure what happens in that group. It exists. What? It exists. It exists, but I haven’t measured it. Fine. If it existed and I knew all the information, that would turn it into a majority physically before us. Let me formulate it this way: suppose I could measure it—I would check all the women in the world and count each one, whether she gave birth at nine months or seven months. And suppose there are, I don’t know, five billion women, okay? And among them I would discover that four billion give birth at nine months and one billion at seven months. Now a woman would come before me who has already given birth—not a birth that hasn’t happened yet. If it’s a birth that—if it’s a birth that hasn’t happened yet, that’s a majority not physically before us. But if it’s one of the births that already happened, and I’m only asking whether it was at nine months or seven, that becomes a majority physically before us, even though it concerns the whole world. Why? Because I’m not building this on the character of the world that I know from laws of nature or something like that; I’m building it on concrete information about a group standing before me, and I’m asking about an element within that group, which part of the group it belongs to. That is a majority physically before us; that is a majority not physically before us. When we talk about the world’s pattern of behavior as being a majority not physically before us, that’s only because we don’t have full information about the world. We understand roughly, from a sample or something like that, we estimate what happens in the whole world, and when a woman comes before me I estimate about her in the same way, but I don’t have concrete information about the whole group—that’s a majority not physically before us. So on the one hand, at first glance, a majority physically before us is probability and a majority not physically before us is not. But all of statistics works like that. I have a sample, I want to produce some medicine, I do some trial, and it worked in ninety percent. That’s the other side of the coin. The other side of the coin says exactly the opposite: specifically a majority not physically before us is probability. Why? Because what do we do—how do we arrive at a majority not physically before us? All laws of nature are a majority not physically before us. How do we know that majority not physically before us—for example, that most women give birth at nine months or that most women are infertile? I check it on some sample, say a sample of people I know, I don’t know, I know a hundred women who gave birth, I look how many gave birth at nine months and how many at seven. I discover that eighty gave birth at nine months and twenty at seven. My assumption is that this sample is representative. That’s an assumption; it’s not always justified and you need to be careful with it, but in principle if I have no reason to think this is a special group, I assume it’s representative—a representative sample. And if so, then I assume that this is the distribution in the whole population too, right? That’s basically how they find these things out, like polls before elections. They check it on five hundred people and tell you what the election results will be. By the way, all of it is completely accurate—contrary to the image people have, it’s definitely accurate. Their achievements, the pollsters’, are very impressive in my opinion. Everyone likes to make fun of them for missing, but they miss because the situation is balanced. In a balanced situation they say the tendency is this way and it comes out the opposite, because two votes moved from here to there. But the forecasts are very impressive in my view. Statistics depends on sample size. Right. But in Jewish law, whether it’s five or five billion doesn’t matter. Right, and in statistics too it doesn’t matter in that sense—that if you can’t get a sample of five hundred and you have a sample of five, you’d still rely on it, right? The significance level, right, the significance level, of course, is more problematic, but if that’s the information I have, I would still go with it. If I know only five women—nothing, that’s a very small sample—and I know that three of them gave birth at nine months and two at seven, and I have no other sample, then in the absence of other information I rely even on that. What can I do? Of course I know that my chance of error is greater. So in Jewish law too it’s like that. But if you can, take a big sample, go with a big sample. But if not, this too is enough. Meaning, it’s the best you have, even though “most women” is because they really had a bigger sample, maybe a symbolic sample; it was really significant, not fifty-one percent versus forty-nine percent. It’s like the Sages wouldn’t have said “most women give birth”—actually they say this about boys, whether it’s a boy or a girl—if there had been some significance concerning boy or girl of fifty-one percent, then they would have said it. Of course. A majority of fifty-one percent is a majority; that’s explicit. But that’s not physically before us. It doesn’t matter whether physically before us or not physically before us—fifty-one percent is yes. If you make a representative sample and it comes out fifty-one versus forty-nine and you assume it’s representative, then yes, you have a majority in the world. Even with a technical deviation of two percent—that could be the voters. Yes. Okay, significance is a concept that I don’t think the Sages knew. Maybe what you mean is that the Sages did some sort of induction, but in the end you explain it in terms of laws of nature, so it’s not—you’re not relying on a sample; you understand the category and the law. How do you know that’s the law? What? How do you know that’s the law? You know it from the statistics you did, from the experiments. No, but you’re doing induction. I’m explaining it in terms of—you explain it, but you explain it only after you have the data, so you’re relying on the data. Yes, but after I have the explanation, I have the explanation and I understand it in light of the sample, but that explanation too could be wrong; maybe you’re mistaken in that explanation. True. The support for that explanation is the sample. You could have been Newton and been right for two hundred years. The explanation for that sample is still a sample in the end—you remain with the sample; explanations come afterward. Right, it’s based on the sample. So in any case, the point is that from this perspective specifically a majority not physically before us is a majority that relies on probability. I conduct a survey on a representative sample and infer some conclusion about the world. In contrast—and this is the beautiful point—what happens with a majority physically before us? With a majority physically before us, Rabbi Shimon Shkop said that a majority physically before us does not clarify. It isn’t probability at all. Why? Because any store from which you assume the piece of meat came—after all, there are nine other stores it might have come from. Even the kosher stores—still, it could have come from the other nine stores. Therefore, basically, you can infer nothing about any particular store, and statistically speaking it’s the same thing—that’s his claim. Okay. And now I’m saying: on the statistical level that’s a mistake. It’s not true. Because if the other nine include kosher stores, what difference does it make to me that it came from another store? This is a bit connected to the table we discussed with Simpson’s paradox, remember? Basically it’s connected to the discussion there. But that’s what he claims, and therefore what he proposes is: the Sefer HaChinukh is not right. According to the Sefer HaChinukh it comes out that the majority in a religious court is a majority not physically before us, but the Talmud says it is a majority physically before us. Therefore—yes, because the Sefer HaChinukh says that the majority in a religious court is because usually the majority is right. What is the group from which you classify your case? All panels in all periods and all places. In every place where there was a disagreement between the majority and the minority, in most places where there was such a disagreement the majority was right. So this case too. That is clearly a majority not physically before us. And it’s not a group standing before you with full information about it. You are making an assumption about the whole world. That is a majority not physically before us, and in that respect he is seemingly completely correct. This is a huge difficulty for the Sefer HaChinukh. And so he says it can’t be correct, and he offers another explanation. He wants to claim that for stores and in a religious court we follow the majority as a formal rule; it’s not statistics. Why? Because we—meaning, what does this mean? Not that it’s not statistics—that’s what he explained earlier—but then what is it? What is “inclining after the many”? So he says: it’s a majority of considerations. We spoke about this at the end of the previous session. It’s a majority of considerations. When you have stores, you have a piece of meat here. You have ten stores, nine kosher and one non-kosher. Every store casts a consideration onto the piece of meat. From the standpoint of this store, it appears kosher. From the standpoint of this store, it’s kosher. From the standpoint of that one, it’s non-kosher. So I have nine considerations for assuming the piece is kosher and one consideration for assuming it’s non-kosher. He says the same thing with judges. I ask what the law is. That judge says kosher. That judge says kosher. That judge says non-kosher. “Kosher” and “non-kosher” aren’t judges, that’s rabbis—but liable and exempt. This judge says liable. This judge says liable. And this one says exempt. So I say: this judge casts a consideration on the case toward liability. This judge casts a consideration on the case toward liability, and this judge casts a consideration on the case toward exemption. Again, I go after the majority of considerations. That is the claim. Because “incline after the many.” That is what is written in the Torah. That’s what he says. It’s not because it clarifies something. Now you’re laughing; I’m laughing too, because it sounds strange. What does “majority of considerations” mean in monetary law—so you’ll say two-thirds? And from that argument, say for two-thirds he should pay two-thirds in a case of dispute. No, but if it’s kosher or non-kosher, you can’t. No, no, the fact that you can doesn’t mean you would. You only can. It could still be that the law says no, I don’t compromise, rather I go after the majority, and the majority determines the truth. Because if that is the truth, then he owes one hundred, not sixty-six. If that is the truth, and most likely that is the truth. If it’s just a consideration, and in monetary cases where it’s possible, then split it. No, I don’t think that’s necessary. The claim is that once you conclude that this is the truth, then go with that truth. Okay. By the way, in monetary law we do not follow the majority in practice—in fact we don’t follow the majority at all there, not only do we not compromise. It’s a dispute between Rav and Shmuel, but we’ll discuss that later. So that is Rabbi Shimon’s claim. Therefore a majority physically before us is some kind of scriptural decree where you count considerations. I mentioned, I think, that the Rashba explains a double doubt similarly. In a double doubt too, basically, I have a doubt whether A or B, and on the side of A I have possibilities x or y. So I really have four possibilities at the end of the tree; one is like this and three are otherwise. So the Rashba says that the leniency in a double doubt stems from the fact that it is a majority of considerations. There are several possibilities. Now this, I think, I haven’t yet said, so I want to explain it. I think Rabbi Shimon Shkop is wrong. Maybe I did explain it, I don’t remember. I think Rabbi Shimon Shkop is wrong. Obviously it’s very sensible. You can’t just say it’s a scriptural decree and that’s it. Any human being, even without scriptural decrees, what would he assume in life? Meaning, when you find such a piece of meat, and say it matters to you whether it came from these stores or from that store—any person would assume it came from the majority stores. Not necessarily. Nothing is necessary. But the question is what a reasonable person would assume. Suppose I need to decide, I need to find a basis to permit. No, no, there’s no need to find anything here. I’m asking what you think. I think you should throw it away. Okay, so most people aren’t like that. Most people say it probably belongs to the majority stores. Even if probably, the question is whether I eat something in doubt or not. Again, I’m not talking about doubt. That’s a different question. I’m talking now about which of the two possibilities is the more reasonable one, the one I’m allowed to act upon. I don’t need to rely on the less reasonable one. Now I ask: which is more reasonable? I think the majority. The majority stores are the more reasonable possibility. So I don’t think one can speak of a scriptural decree in that sense. I do claim that there is something in his words. I don’t remember if I said this explicitly, so I’ll say it. There is something in his words. If you think about the case of stores and the case of judges, then you’ll see that even if we accept the Sefer HaChinukh’s rule, it is still a majority physically before us. That’s surprising, but it’s so. Because with stores—after all I explained why a majority not physically before us is really probability. Because I make a sample, I conduct a survey on a representative sample and research, and then I infer from it a conclusion about the whole group. Okay? How do you do something like that with stores, with a majority physically before us? There’s a piece of meat I found in the street. I want to know whether it belongs to the majority group. There are nine kosher stores and one non-kosher here, or six and four. Six kosher stores and four non-kosher. Now I want to know whether this is based—maybe not, maybe yes—let’s check. How do you check? By counting? There’s no way to check. Count the stores? How do you know that the number of stores also determines the number of probabilities for the piece of meat? So fine. Do an experiment. You can do an experiment, right? With women who are not infertile there’s no problem: take the woman and see whether she gives birth or not, or whether she gave birth at nine months or seven. You do an experiment on a sample and from the sample infer to the whole population. Let’s try to think of an experiment on a sample that would establish a majority physically before us. There is no such creature. No such thing. Meaning, what I’m claiming is that a majority not physically before us is probability, and not only is a majority not physically before us probability, but a majority physically before us really is not probability. And in this Rabbi Shimon Shkop is right. Why? You have no way whatsoever to anchor the claim that this piece of meat is ninety percent kosher. No way to do that—it’s speculation. Try to make a controlled experiment and test it—you won’t succeed, there is no such experiment. Of course you can. Yes, what? Send a person who can’t read to buy randomly in ten stores a thousand times. Okay. And tell the store owners to mark kosher/non-kosher. Then you’ll do it and you’ll see that you get exactly that probability. That proves nothing. There, by the way, it’s fixed when he buys. But it proves nothing because I’m talking about a person who loses something. Now I don’t know—maybe people who lose things have some kind of bias. The people who lose kosher pieces are more absentminded; they’re involved in Talmudic discussions, they don’t think about it, so they lose the meat. There, on the question of physically before us and not physically before us, that’s an even greater wonder. No, there the claim is that this woman maybe has a tendency toward gestational diabetes—no, you’re talking about a large group; I’m testing it. You can’t test everything; the number of parameters is so great. It’s impossible to test everything, and here you can’t test anything. You can’t intentionally lose pieces of meat. There’s no such thing. Someone who loses a piece of meat lost it—you don’t know where it came from. If you sent people to lose pieces of meat, that would be something else, but there’s no way to do it. Let’s look for a moment—look at judges now and you’ll see it more simply. With judges it can be seen more simply. How do I test the Sefer HaChinukh’s assumption that usually the majority gets closer to the truth? There is no way to test it. No way. Because in order to test it, I’d have to check all the rulings of all the panels that had a disagreement against the truth itself, and see in how many cases the majority was right and in how many the minority was right. But who determines the truth? But how do I know what the truth is in that case? All I know is the evidence that was before the judges. So I have no way to get feedback. I have no way to test the claim that usually the majority is right, since I have no way to test when they were right and when they weren’t. But you’re claiming that the issue of meat is specifically in a lost-object case. What if it wasn’t lost? Then maybe indeed it wouldn’t be a majority physically before us. Say, deliveries of meat to an address. I know how to send deliveries. I said: that would be fixed. We’ll still get to the law of something fixed in place. In the law of the fixed case, maybe that is the explanation. We’ll get to that not in a moment—after some time. Rabbi Shimon Shkop is right, basically, that it is some sort of scriptural decree? No—the point is that both are right. Both the Sefer HaChinukh and Rabbi Shimon Shkop are partly right. Partly. What do you mean? What I want to say is this: there is no way to know that a piece of meat lying in the street is really ninety percent kosher. By the way, even if it were possible to conduct such an experiment, first of all nobody did it. So let them do it. After they do it, that would be a majority not physically before us. But first of all they didn’t do it. So why do I assume it is ninety percent? An a priori assumption, an a priori reasoning. If ninety percent of the stores are kosher, I assume that ninety percent of the pieces I find will also be kosher, right? I just assume that, not from life experience. I didn’t do such an experiment. If they did such an experiment I’d be willing to accept it. But in fact most people, or almost all people, do think that way. Wait, wait, that already has meaning; I’m getting to it. When you assume that what you don’t know is the same among them, there’s no reason to assume—wait, wait, I’ll get to it, I’ll get to it. So the point is like this, basically. This thing is not based on statistical research, on a sample survey, so what is it based on? An a priori reasoning. Not “reasoning”—after all, if there are wise people on the same level and two say one thing… This thing is not based on statistical research, on a sample survey, but on what then? On a priori reasoning. Why reasoning? Because if there are wise people on the same level and two say he is liable and one says he is exempt, my logic tells me that most likely the majority is right. This is not, this is not the result of—one second—this is not the result of science. This is philosophy. We talked last time about science and philosophy. This thing is philosophy. It is an a priori claim. It is not science. And because of that—philosophy is a good thing, I have a lot of respect for philosophy—but to call this some solid fact on which I can rely, for that you need a verse. That does not mean it doesn’t clarify. That’s the point where I disagree with Rabbi Shimon Shkop. Since I trust my a priori reasoning. If that is my a priori reasoning, I really think it’s true. It’s not that I say: it’s a scriptural decree because it’s nonsense, but the Torah told us to do it. No. It has no empirical basis. Fine, there are things that even without an empirical basis I believe are true. The principle of causality too has no empirical basis, as David Hume said. So what? I still think it’s true, that everything has a cause. Therefore here too I say: I don’t agree with Rabbi Shimon Shkop; I agree with him partially. In what are you right? That this is not the result of a statistical sample. In that sense this is not a scientific conclusion. This is not a fact you can treat as something solid. But he is not right that if that’s so then it’s completely arbitrary and merely a scriptural decree that the Torah told us. No. It is our a priori insight, but any reasonable person understands that it is true. I too think it is true. I don’t have a direct statistical anchor. Therefore I agree only partially. I say the reasonable person really will think that it is true. He will think so, and justifiably, in my opinion, justifiably he will think so. To say that this is a fact? It is not a fact. A fact is a majority not physically before us. A majority not physically before us was at least tested on a sample. Okay? A majority physically before us was not tested at all. Rather, it just seems that way to us. We assume it. An assumption is a beautiful thing. The Torah itself says: better to go with your assumptions. Even though you have no empirical anchor, you may go with an assumption. That is what is written: “incline after the many.” And therefore the Torah says one can accept the Sefer HaChinukh’s claim that following the majority in a religious court is because usually the majority is right. And it is not difficult that the Talmud in Hullin says this is a majority physically before us, because it really is a majority physically before us. Because a majority not physically before us is something that is the result of statistics. And here this is a majority based on a priori reasoning, not on empirical findings, not on tests, but on what I think, what seems reasonable to me. Therefore this is a majority physically before us. That does not contradict the Talmud in Hullin. It also makes clear why this resembles stores, because with stores too it is not the result of statistical research but the result of an a priori assumption. And in that sense judges and stores really are the same thing, unlike “most women are not infertile,” which is the result of statistical research. I know women, I know whether they are infertile or not, and I generalize to all women in the world. There too, of course, nothing is compelled; there are assumptions that the sample is representative and that there is no bias, true. But I still have some empirical basis for what I am doing. On top of that I need to make another assumption. In the first context there is no empirical basis at all—none. I simply think it is true; it seems reasonable to me. And again I say: I am not an empiricist, we talked about this last time. I am definitely a rationalist in this sense; that is, I do believe my intuitions even when they have no direct empirical anchor. By the way, there are those who say they have an indirect empirical anchor—that at some point it does emerge from our life experience, from other contexts—but not directly in any case. Okay? Therefore I say: I am not claiming that this is arbitrary. I am claiming that it requires the Torah’s approval to rely on it, because it is not a fact. And now the question is: why in a majority not physically before us can we rely on it without a source? The Talmudic passage in Hullin—the conclusion of the passage. The answer is that reasonable human beings rely on science. You don’t need a source for that. What if the store and the piece—there are many more pieces here? Then that’s a dispute among the halakhic decisors; the Shakh and all of them debate this issue. If there are nine stores, right, but there you can say: if it’s a hundred times as much—one hundred stores, right, that’s the discussion, exactly as he said. That’s the discussion. It’s the discussion among the halakhic decisors, but even those who say we don’t pay attention to the size of the store—it could definitely be that it’s simply a legal issue, not a probabilistic one. Once there are nine stores, I can’t now start counting pieces of meat in every store. There are nine of this kind and one of that kind, that’s it. It’s even possible to explain that maybe although they have many pieces, it all comes from one direction, so it’s not proportional to the number of pieces of meat there are. There are also some sensible explanations, but one could also say this is some kind of “no distinctions are made,” that we don’t look at the quantity of kosher meat, the quantity of meat… That’s what he said. Yes. As for a majority not physically before us—you’re saying that in judges this is really a majority not physically before us? Physically before us. Physically before us. It is not a majority that emerges as the result of a statistical survey on a sample. And it doesn’t emerge by negation—but isn’t it also not physically before us? Ah, that’s what I… I want to claim that a majority physically before us is this. That is the definition of a majority physically before us. How do we know it by negation? A majority physically before us is a probabilistic principle that does not come from a sample. That is my claim. And now I’m completing what I said last time and earlier. I said at first people think a majority physically before us is probability and a majority not physically before us is only a generalization from a sample. Now I’m saying exactly the opposite. A majority not physically before us… I didn’t do anything. I assume a priori that it is so. It has nothing to do with probability. But supposedly I tracked everyone who went into the store and looked at how many of them get a receipt. I didn’t do that. Maybe I didn’t do that, but… So what am I saying? That’s what I answered him too. If you do that and reach conclusions, then it becomes a majority not physically before us. But the Sages made this determination without doing such tracking, and therefore it is a majority physically before us. But it comes from other samples, it’s… Where does it come from? That’s what I noted earlier. Our a priori reasonings, what is called intuition—usually people think that this is not just the end-product of visual impressions. It is the result of accumulated but indirect experience; we didn’t test it directly. For me that’s not important; I’m not entering that dispute. There is still no direct test here of this principle; therefore it is a majority physically before us. A majority physically before us is a majority for which I have no direct empirical test. What does my accumulated experience say? I have no control; maybe I missed something, maybe this, maybe that. You need something conscious in order to say: okay, I understand my consideration, I know where the problems are, and I decided that it is correct. Here this is Kahneman’s System 1, right? It’s not System… something that works without supervision. Yes. Maybe I can suggest a slight variation on what you just explained? It’s hard to see how a person has the intuition that the majority is right. But it’s easy for me to accept something… that reaches the same conclusion with a small difference. It’s easy for me to accept intuitively that the individual person is right most of the time, because he isn’t stupid. If I assume that the individual judge is right most of the time, then it follows statistically that the majority of judges are right. Yes, I mentioned something like that last time; I wrote a column on the site about that suggestion. I fully accept it. I even mentioned last time that Grosskopf, in a lecture I gave then, made that comment. That basically when you do the probabilistic calculation—suppose each individual judge has a probability P of being right. And P is greater than one-half, right? One-half is a judge who is blind, who knows nothing. Half the time he is right, half the time wrong. Zero—a judge who is right in zero of the cases—is an excellent judge; you should take what he says and do the opposite. Therefore the problematic judge is one who is right in half the cases. A judge who is right in half the cases is a lemon. That’s someone where you can’t know what he’s saying; fifty-fifty. Either he’s right or he isn’t. Okay, so P is greater than 0.5 for a skilled judge. The larger it is, the better the judge; if it’s 0.9 that’s a good judge, 0.95 even better, and so on. Okay? Now what is the probability, assuming I have three judges, each of whom has probability P of being right—because the Sefer HaChinukh says the assumption is that they are equal in their level of Torah competence, so you can make majority calculations. So the question is: what is the probability that when there are two against one, the two are right? I mentioned once that someone asked me why this is not P squared. After all, P squared only lowers P; meaning, if the chance of one judge is 0.7, then P squared is 0.49, which is less than 50%. So the chance that two are right is 1 minus… 1 minus 1 minus P squared… Yes, exactly. So proportionally that’s what it is, though not exactly, because it’s a Bayes formula. But in any case, the calculation really gives—under very simple assumptions—the chance that the two are right as against the chance that the two are wrong is like P over 1 minus P. That’s what comes out in the calculation under binary assumptions. So what comes out, basically, is that if you assume your judge is a skilled judge, you can make a statistical calculation and show that the majority is usually right. That is a result that… it’s basically what you said. I’m just saying: true, but the assumption that the individual judge is right at level P is itself a majority physically before us. Because it doesn’t come from experience, since you have no way of knowing whether he is right or not. So even if I accept—I fully accept—that calculation, it still doesn’t solve the problem. Meaning, you still can’t reach that result empirically, and therefore this is a majority physically before us and not a majority not physically before us. Another question. What about the number of kosher stores? Here too they come from a sample. I’m in the middle of Tel Aviv, something fell… how many are there? I take a sample. Does that become… Certainly. Certainly! A majority not physically before us. Every time your information is incomplete and instead is built on a sample, it is a majority not physically before us. Of course, yes. As I said the reverse: if you have all the people in the world and you went through all of them and checked everything, and now you ask what is the status of one of them—that is a majority physically before us even though it’s the whole world. Because once your information about the complete group is full, then it is a majority physically before us. If your information about the whole group is the result of a sample, of a survey sample, then it is a majority not physically before us. In a lost object too it’s not physically before us, because I don’t know how many people entered, and I don’t know whether the bags are more noticeable here or there; I’m missing a lot here too. So is it physically before us or not physically before us? What you said before: I assume, in the absence of information, that all other conditions are equal. So is that physically before us or not physically before us? No, physically before us. Why? A lot of things are missing to me—you said that when something is missing… No, the fact that something is missing proves nothing. What do you mean, missing? But with the sample, the principle is built on a representative sample. The representative sample includes the assumption that it is representative. That is exactly the assumption you’re talking about. I said: that’s obvious, it’s always true. But still, it is built on a representative sample, and under that assumption there is an empirical basis. With a majority physically before us there is no empirical basis whatsoever. This isn’t some assumption that the sample is representative—there is no sample. You didn’t make any sample. If you make a sample, then maybe it really turns into a majority not physically before us. So I think that is the explanation of why the majority in a religious court is a majority physically before us, and that is also the logic behind what the Sefer HaChinukh says—that usually the majority is right. That is true, and it does not contradict the fact that this is still a majority physically before us. As an aside—maybe I mentioned this too, I don’t remember—in the United States, after they began using genetics as legal evidence, there was a way to test this issue, and the results were pretty grim. I don’t remember the numbers, but the results were… I don’t know if the majority wasn’t right, but let’s say there were far more mistakes than we would have thought. I don’t know if it was a majority, okay? I’m not sure, I’d have to look there; I don’t think so. But there were many, many errors. And if—if you remember that in… if you remember what? There were people convicted, say, of murder, and DNA wasn’t used. Then suddenly DNA became available, and they rechecked all the cases. It turned out that many of the people who had been convicted were not guilty, and they let them go free. No, so I said I don’t think it was a majority. I don’t remember the numbers, but it was a lot—far beyond what people had thought. Understand that in criminal law, even if there is a majority, obviously that’s not enough; there needs to be a very high probability, and the probability apparently turned out not to be high enough. And that is a very serious threat to convictions in general, even if the majority were right. Meaning, it’s… Could one argue that in general a foolish person tends more to convict? Then there’s a problem with the side too—meaning, this majority among sages, the problem… No—the wiser you are, the more you understand all the sides… But sages are not an advantage… Okay, so it comes out that even regarding the gut feeling majority you mentioned, that too is a bit… No question that these intuitions can be biased and can be problematic. That’s what we have. In the absence of other information we work with that, and therefore for that you need permission from the Torah. And the Torah said: “incline after the many.” The Torah gives permission to do this. Building one kind of majority on another kind of majority—maybe that comes to contradict what I’m saying. Why? That not the same majority that convicts for this is the one that… you need a bigger majority, like you said earlier. Maybe because we’re not satisfied with just half plus… Yes, but that’s not correct. According to Jewish law, any majority is enough. In criminal law? Yes. In murder? No. In capital cases you need a majority of two. That’s something else. There you need a majority of two; I don’t think that… No, in any case there too everyone rules—it’s not… not everyone is equal there… not everyone is equal. In any case, in any case, I want now to continue for a moment. Look, there is a very interesting discussion among philosophers of law dealing with the question of probabilistic evidence. Probabilistic evidence in law. I’ll give you a common example that many articles bring. There are a hundred people, a hundred prisoners in prison. A hundred prisoners in prison attacked some guard and, I don’t know, killed him, injured him, whatever, did something to him. Now they want to try them. It turns out that ninety-nine of them participated in the act and one did not. We don’t know who that one is, but it is known that one stood off to the side. The camera sees one person off to the side but only from the back. They don’t know who it is. Okay? So ninety-nine participated and one did not. A prisoner comes before the court, and we want to try him. What’s the problem? Ninety-nine percent chance that he participated, because ninety-nine out of the hundred people participated in the incident. So you can convict him, right? According to the David Lewis effect that I mentioned one of the previous times, that basically means we would convict all one hundred in this way. Okay? Meaning, each of the hundred, when he comes before us, there’s a ninety-nine percent chance he participated in the act. So there there is general agreement among jurists: you cannot convict in such a situation. Okay? But the philosophers ask—and the jurists aren’t interested in what the philosophers ask, just as physicists aren’t interested in what philosophers of science ask. But philosophers sometimes ask good questions; you have to think about them. Not necessarily follow them—meaning, do what you think—but the question is interesting; one has to address it. So the claim is this: suppose we have two witnesses that Yankeleh, who is now standing trial here, participated in the act. Two witnesses come. Okay? But two witnesses can make mistakes. Sometimes they don’t see well, with all the commotion and chaos there—how do you know they identified him correctly? Okay? So suppose the chance that they are right is ninety-five percent. Fine? And then he is convicted. That’s obvious; everyone agrees you convict him. You don’t worry that the witnesses didn’t see well. You check as much as you can, but that’s what you have. And with ninety-nine percent you do not convict in the first case, while in the second case with ninety-five percent you do convict. Physically before us, physically before us—we’ll see in a moment, we’ll see in a moment. So how can that be? That is what they ask, okay? And that is the problem called the problem of probabilistic evidence. I’ll give another example. Suppose there are two bus companies in a city, and this too appears in the articles. Two bus companies in a city: a blue company and a red company. The blue company has ninety-five percent of the buses; that’s the big company. The red company has five percent of the buses. Now a bus hit some parked car, okay? Now they don’t know which bus did it, and the car owner wants compensation. So he sues the big company, the blue one. You say: ninety-five percent of the buses are yours, so it’s pretty clear it was your bus—pay me. Nobody rules against them on that basis; nobody obligates them on that basis. That is obvious. But if there are two witnesses who saw a blue bus, and they saw it from far away but they say it was blue, okay, and there’s a two- or three-percent chance maybe it wasn’t blue, right? Then they would obligate them. Again, the same issue, right? Then they would obligate them. Then they begin to discuss this. Even if it’s the same number of buses? What? Ninety-five. Even if it’s half blue and half…? Right, obviously. But I mean assuming that is the probability. The probabilities are ostensibly equal, but here we take the high probability into account and there we do not take the high probability into account. We do take account of the minority and we do not take account of the minority. Why? What’s the difference between the two cases? In the end, the probability that this is the case is the same probability. So why here do we use this evidence and there do we not use this evidence? So there are various explanations. Before I get to them, maybe one more comment. In Jewish law there is a difference—I think I mentioned this once—between monetary law and capital law. I think it’s not only capital law; it’s also every… it’s also every legal matter, Hoshen Mishpat, not Yoreh De’ah. But lashes too, not only capital law. I think this needs a bit of discussion. In monetary law Maimonides writes that fundamentally one may rely on circumstantial evidence, as long as it convinces you. In capital law you need evidence—eyewitness testimony. You need two witnesses who saw the murder or the Sabbath violation or the adultery or whatever it was. Circumstantial evidence is not accepted. The example brought in the Talmud from which Maimonides learns this is a passage in tractate Shevuot 34: “It was taught: Rabbi Shimon ben Shetach said: By the consolation, if I did not see one man running after another into a ruin, and I ran after him and found a sword in his hand, blood dripping, and the murdered man writhing.” Okay? Meaning, he entered the ruin with a sword, ran after someone else, he comes out all bloody, the sword is bloody, and the other man was stabbed to death in there, lying dead on the floor. “I said to him: Wicked one, who killed this one? Was it I or you?” Yes, who else could it be? Only the two of us are here. It’s either me or you, and we both know it isn’t me, so it’s you. “But what can I do, for your blood is not given into my hands? For the Torah has said: ‘By the testimony of two witnesses or three witnesses shall the dead be put to death.’ Rather, the Omnipresent will exact punishment from you.” They said: “They had not moved from there until a snake bit him and he died.” The ending is important, because the ending shows that it’s clear he really did murder. Meaning, the certainty that he murdered is complete, and still they couldn’t convict him. Why? Because of the number of witnesses, or because he didn’t see the act? That’s it, here there is room to hesitate. Maimonides takes this as the basis for his ruling, and he claims that it’s because there is no eyewitness testimony here, only circumstantial evidence. And we need to understand: circumstantial evidence can be very strong, just as strong as eyewitness testimony and perhaps even stronger, but it is circumstantial. We did not see the case; rather the circumstances show that this is what happened. So Maimonides says that was the problem here—circumstantial evidence, and circumstantial evidence is not enough to convict someone of murder. One could certainly have said it was because there was only one witness and not two, and therefore he could not convict. “For the Torah has said: by two witnesses”—you emphasized the “two”; I emphasize the “witnesses.” By two witnesses—eyewitnesses, not… otherwise the Talmud would have brought a case where he saw him stab but he was only one witness. Right. The reverse. Why… why if it saw him… if the Talmud had brought a case where he saw him stab and there was one witness, and there were two and not… Maimonides would have been right. If the Talmud had brought two circumstantial witnesses, the exact same question would remain. The exact same question. If that’s the story, if that’s the story that happened, then neither that question nor the other is a good question. Obviously that’s the… and that’s how the story happened. The Talmud didn’t bring a story to prove something; the Talmud brought the story because that’s what happened. So it’s not a difficulty why the Talmud didn’t bring another story. It didn’t bring another story because there wasn’t another story. But the question “Who killed him, I or you?” indicates that the doubt is… that hints that the problem is the circumstantial nature and not the fact that it’s one witness. I don’t think that… But leave it—this is how Maimonides learned it, okay? Now what does that mean? It means that here too we really find ourselves in a very similar dilemma to what I described earlier. In both forms we have a very high level of certainty, 98%, that the man murdered. Two witnesses saw him—witnesses can make mistakes, lie, I don’t know, all kinds of things can happen. So even with witnesses it’s not 100%, it’s 98%, okay? But it is admissible. Yet circumstantial evidence with the same level of certainty is not admissible. All twenty-three judges sit outside the ruin—not one, twenty-three judges sit outside the ruin, see the man enter with a knife, come out with blood dripping, and the stabbed man is lying dead inside, and nobody else is around, nobody else in the vicinity. Okay, still they can’t convict according to Maimonides. Why? The level of certainty is no less, and perhaps higher, than the level of certainty of two witnesses. It’s exactly the same principle. Meaning, you see that sometimes the level of certainty does not determine the admissibility of evidence. We know this from all kinds of examples. For example, the fruit of the poisonous tree. In Israel the status of this is not entirely clear, but in the United States, at least as I understand it, fruit of the poisonous tree is categorically inadmissible. Meaning, say evidence obtained through an illegal recording. Now the recording shows that so-and-so is going to murder so-and-so, conspiring to murder him. Explicitly. It’s clear that it’s his voice, everything is fine, except that it was obtained through an illegal recording. So the evidence is inadmissible. Now the reliability of the evidence is complete, just like a lawful recording. The difference is only legality, not reliability. We don’t reject this evidence because it isn’t reliable but because it isn’t admissible. It’s a problem of admissibility, not reliability. So we know such things. Sometimes evidence is not accepted because of considerations that have nothing to do with its reliability. Relatives as witnesses. Why do we not accept testimony from related witnesses? The assumption of the Talmud and the medieval authorities (Rishonim) is that relatives are trustworthy as witnesses. We have no problem with them. Moses and Aaron are the famous example. Why don’t we accept them? It is not admissible. Not that it is not reliable—it is not admissible. Two different things. I already mentioned once that “a person cannot render himself wicked,” for example, is also the same thing. We do not accept a person’s self-incrimination not because he is not reliable but because it is inadmissible. A person is related to himself—that’s “related” here. A person is related to himself, yes; I’m my own relative because, as we know, we have the same parents. We’re brothers. So a person is related to himself, and a person cannot render himself wicked. Therefore this testimony is inadmissible. That’s Miranda, right, the famous Miranda decision in the United States, the Fifth Amendment that establishes the right to remain silent, that a person need not incriminate himself. Except that there the concern is various concerns—maybe he’ll be tortured by the police or things of that sort—and therefore they do not accept a person’s self-incrimination. The judges here in Israel—and in Miranda they quote Maimonides on this matter of “a person cannot render himself wicked,” and the judges here of course don’t know Maimonides and do know Miranda, so they quote Miranda too, along with the American judge’s mistake in interpreting this Talmudic passage. The interpretation of that passage is not because of concern about torture but because it is inadmissible. “A person cannot render himself wicked” is a disqualification of a relative; it is not a problem of reliability. In Maimonides, in one place it is written that maybe he is one of the insane or something; there’s a contradiction in Maimonides on this issue. Yes, but it is a contradiction. In Maimonides himself the second thing is also written. So how… In any case, we see that the fact that the evidence has a very high reliability level, 98%, still doesn’t mean that—depending on other considerations. But this doesn’t solve our problems. It doesn’t solve our problems because here there does not seem to be a legal reason to distinguish between witness testimony with 98% certainty and the 98% that comes from statistics. All you want is to be sufficiently sure that the person is guilty. So what difference does it make whether you are sufficiently sure at 98% in one way or in another way? With self-incrimination I can understand concern about torture, who knows what, all kinds of other things. There are reasons not connected to the reliability of the evidence. But there are reasons… What? About the tenth one, for example. But about the tenth one—if I convict them all, then I know with certainty that one of them I’m convicting though he is innocent, and in that situation I’m forbidden to judge. One second, I’ll say it in a moment, one second. So apart from the condition of reliability—two witnesses against a hundred—then you already have the issue… No, but one could say that’s just a cutoff. Otherwise there’s no end to it. But if two witnesses and up is a sufficiently high level of certainty—there is no guardian for claims about witness reliability. Once there is reliability, then we… I do not look, I do not think about the witnesses themselves—maybe they are lying; there is reliability. What do you mean you don’t think? The fact is they still can be mistaken or lying. We do checks; afterward we do examination and interrogation, we do refutation, we do contradiction. We do that. In monetary law we don’t. So after they pass that stage we say now… we say—but it still isn’t true, it’s not 100%. And the question is: why do we say that? So let’s say there too we say. Let’s say there too, and if he does not tell it then he bears his sin. You say the question is what the basis is. So this distinction basically means there is here—meaning if there is some reason like fruit of the poisonous tree, then no problem, I can understand that. The reliability of the evidence is the same, but the legal consequences are such that I still don’t want this evidence admitted, in order to lock the door before future illegal acts. But where there is no apparent legal reason of that type, and the reliability level of the evidence is the same, why is this accepted and that not accepted? Here I’ll preface one more thing. Really, okay, this is connected to what was said—that in one case there is ninety-nine percent certainty and here there is still doubt despite… But that doesn’t solve the bus case, it doesn’t solve the bus case. No, also in this case, let’s suppose that of those hundred prisoners, ninety-nine escaped from prison. One was caught. Now do we convict him or not? That is the difficulty David Lewis spoke about. Since you’re already saying it, I’ll say it here. Meaning, the point is that there really is an intuition that in, say, the prisoners’ case, there is a legal reason—legal, not probabilistic—not to convict on such a basis. Why? Because you are certainly convicting one innocent person. Because if you convict every one of the prisoners who comes before you on that basis—that’s David Lewis—every one of the prisoners who comes before us, we will convict from that same reasoning. And because of that, you are certainly convicting one innocent person. Now true, only one out of the hundred, and you are not willing to take that risk. As Maimonides writes, it is better that several wicked people go free by the law than that several innocent people be convicted, and therefore we play it safe. Okay? So here too, basically the same. In a place where there is a minority about whom you will certainly err, you do not use the rule of majority. But of course that will not explain the case of the buses, for example. In the bus case there is no problem—not all the buses are on trial here. There was one case, and he wants to obligate the blue company. What’s the problem? Here there is no situation in which you will certainly have an error in the case. The second challenge, what Shmuel said before, is: what happens if ninety-nine prisoners escaped? I only have one left, and him I put on trial; the hundred others I’ll put on trial if and when I catch them. In that case, again, it’s not certain I’ll err. This one has a ninety-nine percent chance of having participated; the others in any case I won’t be trying. So yes, there’s no situation in which it’s guaranteed that one innocent person will be convicted. Therefore the intuition is like the difference between “a prohibition was fixed” and “a prohibition was not fixed.” You know there are two kinds of doubt in Jewish law. There is a doubt of one piece from two pieces: one kosher piece and one non-kosher piece lying before me, and I don’t know which is which. I take one of them; then it is forbidden for me, because a Torah-level doubt is treated stringently. So if I took it, I am liable for a provisional guilt-offering, okay? Until it becomes clear to me what happened there. For the doubt itself I bring a provisional guilt-offering. What happens if there is one piece and I don’t know what it is—whether kosher or non-kosher? Again it’s still fifty percent. But it’s one piece, not one of two pieces. If I took it, it was forbidden for me—a Torah-level doubt treated stringently—but we do not bring a provisional guilt-offering for that. But why is it fifty percent? Fifty percent—I don’t know, either kosher or not kosher. It could be stores in a city, fifty percent kosher and fifty percent non-kosher. Fine. So I say I don’t know, but it’s fifty-fifty, and therefore ostensibly—the prohibition is the same prohibition, but a provisional guilt-offering I do not bring. Meaning there is something else in this doubt, and I think it is something like this reasoning. Because with one piece out of two pieces, once I permit one to you, there is no reason to prohibit the second one to you as well. You can eat the first one and then eat the second one too, and then you certainly ate a forbidden item. When you permit one piece, you eat it; either you ate something forbidden or you didn’t, but it’s not that you are directly giving him permission to commit a prohibition. So it’s something like this reasoning. Okay, so one can say that, but as I said before, there are problems with that. With the prisoners who escaped, or with the buses, it doesn’t work, and things like that. Now yes, they bring another example too: someone sneaked into a stadium. This too is an example that appears a lot in the literature. Someone sneaked into a stadium, and it turns out that most people broke through the fences; most of the spectators snuck in and did not pay. They entered the stadium and didn’t pay. Now they take one person and put him on trial. Can you try him on the basis that ninety-nine percent of the people there broke in? There is one percent who paid even though it was possible to get in. Same question, of course. So there too you cannot convict him, but when two witnesses see him sneaking in, then maybe they didn’t see well, maybe they didn’t understand the situation—then yes, they do convict. There are many examples of this. So I’m saying this example too, of the difference between “a prohibition was fixed” and “a prohibition was not fixed,” is problematic. Maybe one more comment—I see we need to finish—so one more comment that will connect us to next time on this issue. There is an interesting methodological point here, and this is a question that comes up in many contexts. There is a very strong feeling—not only among jurists, among anyone looking at this—that really it is hard to convict on this basis. But when there are two witnesses who saw you, even though two witnesses too are not one hundred percent certainty, yes, they can convict you. Now suppose I don’t find an explanation. I don’t know; I can’t find an explanation. This is ninety-nine percent and that is ninety-nine percent. I can’t find an explanation. What should be done in such a situation? I didn’t find an explanation. There are those who would say: fine, you didn’t find an explanation, then you made a mistake. That’s the rationalists. You didn’t find an explanation, so you were mistaken; you have feelings—take a pill. You said you were mistaken. Here there is ninety-nine percent; you should relate in the same way to both types of evidence. Others would say: no, I have a very strong intuition. True, I don’t have an explanation for it, but I trust my intuition. If I were smarter, maybe I’d also find the explanation. Therefore I go with what I think, even though I didn’t find the justification for it. That is a very interesting question, how to do this. It’s a philosophical temperament of people, how you relate to such a situation. Many times we hear some argument, and it’s clear to us that it isn’t right, but we can’t find the mistake in it. Yet it’s clear to us that it isn’t right. Should we accept the conclusion of the argument? No. If there is a sufficiently smart person who knows how to present arguments well, he can abuse many people—present them with crushing arguments, and they won’t know where exactly the problem is, but somehow the feeling is that it can’t be. All the paradoxes—Zeno’s paradox with Achilles and the tortoise, the arrow, and all the paradoxes you can think of—are basically like that. I raise an argument for you that seems excellent; there’s no way to put your finger on where the mistake is, but its conclusion is clearly not true. If you didn’t find a mistake and there’s a logical argument here, then the conclusion is true—what do you mean it’s obvious to you? If it’s obvious to you, then apparently you were mistaken. No, I think there is some mistake there and I’m just not smart enough to find it. So here too, same thing. Jurists in this sense usually belong to the wing—I don’t know whether the first or the second—the wing that listens to its intuitions. Okay? And once they say no, you can’t convict on such a thing, then you can’t convict on such a thing. And this is a known rule: you cannot convict on the basis of statistical evidence. You cannot convict. Explanations—if you ask them, you won’t get any. Philosophers of law do try to offer explanations; in my opinion they’re usually not successful. I’ll bring one or two of them. I think the explanation, at least for me, that is more convincing is of course connected to the distinction between a majority physically before us and not physically before us, what you said earlier. But we’ll get to that next time.