Uncertainty and Probability—in Halakha, Thought, and in General—Lecture 28 – Rabbi Michael Abraham

[Rabbi Michael Abraham] Okay, let’s begin. First of all, sorry about yesterday. It really just completely slipped my mind with all the nonsense going on around me, so I apologize. I want now to focus on a point that has already come up for us in the past, and that is how I relate to human actions from a statistical point of view. And I’m going to do this in two parts. In the first part, I want to talk about why we do not follow the majority in monetary law. There’s a dispute in the Talmud between Rav and Shmuel whether we do follow the majority in monetary law or we do not follow the majority in monetary law, and the discussion there basically deals with two people who made a transaction. Reuven sold an ox to Shimon, and Shimon took it to plow a field and the ox died. It turned out that it had been weak, sick, something like that. So Shimon sues Reuven, saying he sold him a sick ox. So Reuven says: I sold you an ox for slaughter, and an ox for slaughter doesn’t need to be strong—you slaughter it and eat the meat. And Shimon says: but I intended to buy an ox for plowing. So there’s a dispute here, right? One says, I sold it for slaughter; the other says, I bought it for plowing. And if it was for plowing, then selling a weak ox is problematic—it’s a mistake, you could say—and if it was for slaughter, then there’s no problem. The Talmud says that most oxen are sold for plowing. That means most oxen are sold for working the field and not for eating. Therefore, in principle, the law should favor the claimant, since he says he bought it for plowing. So the Talmud says about this that we do not follow the majority in monetary law. And then the Talmud says that this is a dispute between Rav and Shmuel. In other words, according to Shmuel we do not follow the majority in monetary law, and according to Rav we do follow the majority in monetary law. And in monetary law, in disputes between Rav and Shmuel, we generally follow Shmuel. The rule is: the law follows Shmuel in monetary law and Rav in matters of prohibition. So this is a general dispute about whether we follow the majority in monetary law or not. Now, it turns out there are places where we do see that we follow the majority in monetary law. For example, there’s a Talmud in tractate Sanhedrin 3b. The Talmud there discusses the composition of a religious court. And it says that in monetary law the religious court is a court of three judges, and in the background there’s a discussion that the court has to be capable of inclining, meaning an odd number of judges, so that a decision can always be reached by majority. So about that the Talmud says: “You can even say it follows Rabbi Yoshiyah, who derives it by an a fortiori argument from capital law. And if in capital law, which is more severe, the Merciful One said, ‘Follow the majority,’ then in monetary law all the more so.” In other words, if in capital law we follow the majority of judges, then in monetary law certainly we follow the judges. Tosafot asks there: “In monetary law all the more so”—this is difficult, because at the beginning of “one who sells produce,” at the beginning of Bava Batra, Shmuel says that we do not follow the majority in monetary law. So why don’t we derive it by an a fortiori argument from capital law as is said here? In the severe area of capital law we follow the majority, so in monetary law, which is less severe, certainly we should follow the majority of judges. So Tosafot says: and you cannot say that in capital law itself we follow the majority only when the majority is present before us, but not when it is not present before us, because at the beginning of the chapter of the wayward and rebellious son it implies that everywhere in capital law we follow the majority, such as most women give birth after nine months, and most people make mistakes in calculating the month of pregnancy. Right, so he says you can’t distinguish between a majority that is present and a majority that is not present before us. So Tosafot says: “It must be that the majority that people buy for plowing is not considered like those other majorities; therefore we do not rely on that majority in monetary law.” This majority—that most buy for plowing, which is the majority in the dispute between Rav and Shmuel regarding the ox bought there for plowing or for slaughter—Tosafot says that this majority is not considered like the ordinary majorities we know, and therefore with regard to this majority Shmuel says we do not rely on it in monetary law. So he is not saying that in general we never follow the majority in monetary law. In general, we do follow the majority in monetary law. With a majority like the majority for plowing—there we do not follow the majority in monetary law. Why? It is a more problematic kind of majority in some respect. Okay? So from Tosafot’s perspective, the principle is actually that even according to Shmuel we do follow the majority in monetary law. It’s just that with the majority for plowing, or majorities of that type, which are problematic, there we don’t. I’ll explain later what is problematic about them, but that’s one side of the equation. The other side of the equation is a Talmud in Bava Kamma. It teaches there, yes, whether a jug is a barrel, and so on. In short, there is a discussion there whether people call a jug a barrel or not. The Talmud ultimately says: this teaches us that we do not follow the majority in monetary law. Even though most people call a jug a barrel, we do not follow the majority in monetary law. Tosafot comments there: “This teaches us that we do not follow the majority in monetary law.” And Tosafot says: this is difficult—what is the reason we do not follow it? Let us derive it by an a fortiori argument from capital law, as we say in the first chapter of Sanhedrin, and Rabbi Yoshiyah derives it by an a fortiori argument from capital law: if in capital law, which is more severe, the Merciful One said, “Follow the majority,” then in monetary law all the more so. And even with a majority not present before us, we follow the majority in capital law, as it says at the beginning of the chapter of the wayward and rebellious son. So seemingly this is a similar move to what we saw in Tosafot in Sanhedrin. But you have to notice the difference. Tosafot in Sanhedrin raises the difficulty on the Talmud there. The Talmud there makes an a fortiori argument from monetary law to capital law—that if in capital law we follow the majority, then all the more so in monetary law we follow the majority—so Tosafot asks: then why does Shmuel say that we do not follow the majority in monetary law? The question is on Shmuel. Here the question is on the a fortiori argument itself. Embedded in the question is that indeed we should follow the majority in monetary law by an a fortiori argument from capital law. In any case, for our purposes, we still need to answer what the difference is. So Tosafot says: “There, regarding judges, is different, because their minority is considered as if it does not exist. And one cannot say there, ‘Let the money remain in the possession of its owner,’ because the religious court takes it out of his possession. But regarding other monetary matters, where there is a minority and a presumption, we do not follow the majority.” What is Tosafot saying? We basically have a contradiction between two laws. On the one hand, in a religious court, in monetary cases, if there is a dispute, we follow the majority. So apparently we do follow the majority in monetary law. On the other hand, in the Talmud regarding the majority for plowing, we rule like Shmuel that we do not follow the majority in monetary law. So what is the answer? Tosafot in Sanhedrin said that the answer is that the majority for plowing is a questionable majority. That means the sweeping rule is the law in religious court, that we do follow the majority in monetary law. What Shmuel says—that we do not—is only because we are dealing with a particular majority, a very weak majority. The majority for plowing is an exception. But the general rule is that we do follow the majority in monetary law, as we see in religious court, where we follow the majority of judges. And we already saw that following the majority is learned from the majority in a religious court. Tosafot in Bava Kamma says the opposite. Tosafot in Bava Kamma says that the rule is that we do not follow the majority in monetary law. It’s not only in the case of the majority for plowing; it’s true for every kind of majority. In every kind of majority in monetary law, we do not follow the majority. So why in religious court, even in monetary law, do we follow the majority of judges? Because in a religious court their minority is considered as if it does not exist. And the minority in the court is considered as though it does not exist at all. Therefore, this is not called following the majority; rather, the entire religious court established this law unanimously. That is why even in monetary law we follow the majority in a religious court, because really this is not called following the majority. So notice that the disagreement between the two Tosafot is a disagreement from one extreme to the other. Tosafot in Bava Kamma basically says that the rule is that we do not follow the majority in monetary law in any kind of majority—majority for plowing, not majority for plowing, he sees no difference. We do not follow the majority in monetary law. The exception is the case of a religious court, where in religious court we follow the majority of judges even in monetary law because the minority is as if it does not exist. But the law in religious court is the exception. Shmuel’s rule is the broader rule, the sweeping rule, that we do not follow the majority in monetary law. Tosafot in Sanhedrin is exactly the opposite. The sweeping rule is what happens in religious court—that we do follow the majority in monetary law. What happens in Shmuel’s case of plowing is the exception, because it is a particular majority that is too weak. So in that particular majority Shmuel says we do not follow the majority in monetary law, but that is the exception. In general, usually, we do follow the majority in monetary law. And just as a side point, you should know that many times in later authorities there are discussions like this where we find in various places that people do follow the majority in monetary law, and everyone immediately jumps in: wait, but the law follows Shmuel that we do not follow the majority in monetary law. Now, that depends on these two Tosafot. Because according to Tosafot in Sanhedrin, the rule is that we do follow the majority in monetary law. The majority for plowing is special; it is a weak majority. But in principle the rule is that we do follow the majority in monetary law. Usually people assume what Tosafot in Bava Kamma says. Tosafot in Bava Kamma really understands Shmuel literally: in general, we do not follow the majority in monetary law. What happens in religious court is the exception, because the minority is as if it does not exist. So you need to know that this is basically a dispute among medieval authorities as to whether we follow the majority in monetary law or not. In the case of plowing we do not, but that case may be exceptional; generally we may indeed follow the majority in monetary law. So that’s the general picture. One first remark I want to make about this. When we say that in religious court the minority is as if it does not exist, we really need to understand why there the minority is as if it does not exist. How is that different from every other case? Why, in the majority for plowing for example, is the minority of those who sell for slaughter and not for plowing not also as if it does not exist? Why not say that there too? There is a majority against it, so the minority is as if it does not exist. Here I think this is connected to a question that Rabbi Shimon also asks, along with other later authorities. We saw in one of the previous lectures that from the verse “follow the majority” several kinds of majority-laws are learned. There is the law of following the majority, there is nullification by majority, and there is “most of it is like all of it.” Following the majority is, say, a piece of meat that we find, and we follow the majority of stores. Nullification by majority is when there is a mixture of majority and minority—say, a minority of prohibited food fell into a majority of permitted food, so the majority of permitted food nullifies the prohibited minority. And “most of it is like all of it” is, for example, if most of the people are impure on Passover, then it is as though all of them are impure and they bring the Passover offering in impurity at the first Passover. That’s not related to our issue at all. I’m speaking only about the first two. And the question several later authorities ask is: fair enough, following the majority we see in religious court, where we follow the majority, but how do we know nullification by majority from this verse? The Talmud, by the way, does not state it explicitly. The Talmud says that following the majority is learned from the verse “follow the majority.” The law of nullification by majority is something the medieval authorities write is also learned from that same verse. And the question is: how is that learned from there? What is the connection to nullification by majority? Some explain—and there is Rabbi Shimon and Rabbi Chaim and others, in somewhat different formulations—they say that, as we saw in the Talmud in Sanhedrin that we just looked at, the Talmud requires three judges in monetary law. Now if there is a dispute of two against one, then in the end the law is ruled by two judges, not three. But the Torah’s requirement is that it be ruled by three. Some understand that the requirement is only that three judges participate in the deliberation, but not that the final ruling emerge from three judges. But some later authorities want to say no, the requirement is that the ruling emerge from three. So why, when two are against one, do we follow the two? Because the two nullify the one, by the law of nullification by majority—not by the law of following the majority—and then that one becomes as though he agrees with them, and now I have three judges ruling the case. And in that way the Torah’s requirement is fulfilled, that monetary law be ruled by three judges. And even though one of the judges expressed an opposing opinion, since there is a law of nullification by majority. How do I know this? Because otherwise we could not follow the majority in religious court, since three judges are required and there are only two. We are forced to say that the third is also considered one who signs the ruling together with those two, and therefore it is a ruling by three. So what do we see from here? We see that there is not only the law of following the majority but also nullification by majority. That is, we see that the minority is as if it does not exist. It’s as though there is no judge here opposing at all; all the judges effectively issued this ruling unanimously.

[Speaker B] Rabbi, Rabbi, couldn’t you explain it by saying that the minority—when a judge participates in the panel and he is aware that he may end up in the minority and that he will anyway be signed on the final ruling—so he agreed to that in advance? Because otherwise he could have simply not participated in the discussion at all.

[Rabbi Michael Abraham] Well, obviously he agreed. So what exactly are you trying to solve here?

[Speaker B] No, I mean, he agreed in advance that if he would be in the minority then he would also sign the majority ruling.

[Rabbi Michael Abraham] Fine, yes, that’s what people say. More than that, after all, we know from “do not go about as a talebearer among your people”—the Talmud says that the judge who is in the minority cannot go outside and say, listen, I opposed this ruling, but what can I do, my colleagues outvoted me. He is forbidden to say that: “do not go about as a talebearer among your people.” In other words, you have to present some kind of unified front outwardly: the religious court issued such-and-such a ruling.

[Speaker B] Right, so that’s what I’m saying—therefore it’s not really a majority; in the end this is actually a unanimous ruling.

[Rabbi Michael Abraham] Right, that’s the claim, and therefore the minority is as if it does not exist. That’s what Tosafot says. In other words, what I wanted to say is that this fits very well with what the later and earlier authorities say, that we learn not only the law of following the majority from religious court, but also the law of nullification by majority. How? Following the majority means that we rule in accordance with the majority of the judges. But how do we know nullification by majority? Nullification by majority means that I can eat the whole mixture, both the prohibited and the permitted, because the prohibited part is nullified. The answer is: we learn it from here. Since the ruling emerges from three judges, not two, even though one of them opposed, in the end he too has to sign the ruling, so in practice it was a ruling of three. That means that at this point we really don’t have a minority opinion. Since we don’t have a minority opinion, the minority is as if it does not exist. Therefore here too we follow the majority even though this is monetary law. Because here there is no minority that opposes. What Shmuel says—that we do not follow the majority in monetary law—applies when there is a minority opposing the majority. Then a majority against a minority is not strong enough to decide a monetary case. But if there is no minority opposing, then of course one can follow the majority even in monetary law. So that closes the parenthesis—this is only a remark on Tosafot’s answer in Bava Kamma. What he answers is that what happens in religious court—why do we follow the majority there? Because the minority is as if it does not exist. Or in other words, in monetary law we do not follow the majority unless it is not really a majority but actually the whole. Meaning, when the minority is as if it does not exist, that is not following the majority; it is simply the whole. But at the basic level, the rule is that we do not follow the majority in monetary law. Okay? But Tosafot in Sanhedrin does not accept this. Tosafot in Sanhedrin says the opposite: what happens in religious court is the rule, that we do follow the majority in monetary law. It’s not because the minority is as if it does not exist. We follow the majority in monetary law even when the minority does exist. So why not in the case of buying for plowing? Because that majority is a weak majority, and there we do not follow it in monetary law. Okay? Now how do we understand this Tosafot? Here I want to look at a passage from Rabbi Shimon Shkop. This is Rabbi Shimon Shkop, Sha’arei Yosher, Gate 3, chapter 3. First he brings this Tosafot from tractate Sanhedrin—the Tosafot in tractate Sanhedrin that we cited, that’s not the main point. And then he says: we need to understand—if this majority is effective in matters of prohibition, why should it not be effective in capital law, and why not in monetary law as well? Then he says as follows, in section 47: “It may be said that the reason for this is based on the words of Nachmanides in Milchamot, chapter 2 of Kiddushin, and this is also brought in Shev Shema’teta, fourth section, chapter 6, who wrote concerning the majority that people send gifts and then betroth, that it is difficult why we are concerned for gifts and do not follow the majority.” What does that mean—what is the discussion there? There is a discussion in the Talmud about what happens when we see someone giving money to a woman. Now the question is whether this was money of betrothal. The man, let’s say, claims he betrothed her, and she claims she was not betrothed. Okay? So what was the money, they ask her. She says: it was gifts—he gave me a gift, not for the sake of betrothing me. Now this depends on what the custom in that place is. Is it the custom in that place first to send gifts and then to betroth, or first to betroth and then to send gifts? Because this was the first payment he gave; it was not the second payment, it was the first. The question is whether there is room to claim that the first money was money of betrothal. If in that place the first thing is always gifts, and before giving gifts one does not betroth, then you cannot say this was money of betrothal, because this was the first money. If in that place people first betroth and only afterward send gifts, then you can say the first money was money of betrothal and not gifts. So seemingly this depends on what is customary in that place—what do most people in that place do? Do they send gifts and then betroth, or not? So the Talmud asks: if there is a majority who first send gifts and then betroth, why are we concerned for gifts? Why don’t we follow the majority? Why is it possible to say this was not betrothal but gifts? So Rabbi Shimon Shkop says, and Nachmanides whom he cites says—and this is his wording: “But the reason for this question is that this majority is not like the dispute between Rabbi Meir and the sages. There, the majority is one of obligation and nature, and it cannot be otherwise. But here it is only custom. And very often a person behaves according to the custom of the minority. Therefore, in a case involving a married woman they were stringent.” End quote. What does that mean? Nachmanides’ claim here is—what does he mean that here it is custom? He means that whether to give gifts or betrothal money first is something each person decides for himself. True, most people in that place first send gifts and then betroth, fine. But that person can say: yes, but I decided to give betrothal money before the gifts, or even without gifts. The fact that most people in that place decide, or usually do, give gifts first and then betrothal means nothing, because it is his decision. If I decided to give betrothal first, then I give betrothal first. Why is it relevant that most people say otherwise? And Nachmanides’ claim is that a majority dealing with human custom—you cannot follow such a majority. Why? Because if, say, you find a piece of meat in the market, and you ask whether it came from the non-kosher stores or the kosher stores, I say: that is a natural, random process, not under control, not the result of a human decision. Since that is so, we follow the majority—there is statistics, some assumption that the sample is representative or whatever, it doesn’t matter—and we follow the majority. So there there is room for probabilistic considerations. But in human custom, what do probabilistic considerations have to do with anything? The fact that most people first give gifts and afterward betrothal—what exactly does that say? It’s my decision. I have free choice. I decided to give betrothal first. So what are you telling me—that most people don’t do that? Fine, most people don’t, but I do. You yourselves admit that there is a minority that does do that. I belong to that minority. It’s like saying it can’t be that your height is six foot five because the average height is under six feet. Fine, but I’m six foot five. What, I don’t understand? There is also a minority above six feet. And all the more so when we are talking about human custom—when you’re talking about an act done as a result of a human decision, you cannot handle it with statistical tools. Because a human decision—remember the example of the balls? We had the example of the balls. We have a barrel full of balls, a hundred balls, ninety-nine red and one black. Now a person puts his hand into the barrel, looks inside, chooses a ball—not randomly, he chooses whichever ball he wants—and takes it out. You ask: what is the probability that he has a red ball in his hand? People will say ninety-nine percent, because there are ninety-nine red balls and one black. But it’s obvious that this is not true. Because he is not choosing randomly; he is choosing whatever ball he likes or wants, whichever color he wants. Now if he likes red, he’ll take a red ball, and if he likes black, he’ll look for that one black ball and take it. So why do I care that there is only one such ball? As long as there is one such ball, if I like it then I’ll take it. So the statistics here can at most work on the level of what colors people like, but the statistics of the distribution of the balls in the barrel is completely irrelevant. Why? Because the act is not random; it is an intentional human decision. A person decides which color ball he wants. Because this act is an act of choice, not a lottery. So why on earth use probabilistic tools to analyze it? What you need to know is what color he likes. If the person says: look, I like black, then the fact that most people in the city like red, or that most balls in the container are red—so what? But I like black, so it is no wonder that I chose the one black ball in the barrel and took it out. The fact that there is only one ball out of a hundred—does that count as any argument at all here? What does it have to do with anything? Obviously I choose what I want. And if I want a black ball, and I tell you I like black balls—that’s my preference—what can you tell me, that I don’t like black balls because the barrel contains ninety-nine red ones? What does that have to do with my preferences or my taste? What determines the outcome here is my taste, my decision. And therefore, says Nachmanides, in a place where the action we are dealing with is a human action that comes from decision, it is impossible to apply probabilistic tools. Because probabilistic tools tell you what would happen if we were doing something random here, choosing one result out of a hundred at random. Then if there is a majority of one kind of result, that is probably the result that will occur. That’s probability. But where this is a human decision, this is not a random act—I decide what I want. So if I want the minority, because that is what I decided I want, or that is my preference, or that is what I believe in, whatever, then I am fully credible in saying that I performed the act that only a minority of people perform. Because this is a human decision, and a human decision is not a random event; therefore there is no point in dealing with it using probabilistic tools. That is basically what Nachmanides is saying. And therefore in that topic there, about gifts and betrothal, which comes first—after all, this is a human decision. Now true, most people in the city first send gifts before giving the money of betrothal. But I say: listen, my taste is different. I like black balls. I like giving betrothal first and only afterward gifts. That’s me—that’s what I am. You cannot tell me that because most people in the city aren’t like that, therefore neither am I. So therefore there is no point in applying probabilistic tools here. That is basically what Nachmanides claims regarding the topic of gifts. Now Rabbi Shimon Shkop says: “And it is also clear from his words that according to Torah law such a majority is effective, even with respect to the prohibition of a married woman, except that the sages were stringent. And according to what we have written, the point is that such a majority is a Torah-majority and not an intellectual majority. And it is effective by Torah law, except that the sages were stringent. And therefore also the majority that people buy for plowing is not an intellectual majority. For if this person needed it for slaughter, that does not at all go against the laws of nature and ordinary practice. Rather, it is a Torah-majority and it is not effective in monetary law and in capital law for the reasons we wrote. For regarding money, certainly we require an intellectual majority, as we wrote, because it is a matter of logic. And regarding capital law, because it is written, ‘and the congregation shall judge,’ as we wrote.” I’m not going into the other points right now. But what is he basically saying? He is following his own position—I’ll remind you—that a majority present before us is not a majority based on logic but a scriptural decree. It does not clarify the truth. I said that in principle he is right, but not one hundred percent. The reason he gave is not correct. But I think the principle itself is correct. That is, there really is a situation here where statistical laws cannot be applied. So he says that if so, then the majority for plowing is also not a statistical majority; it is a majority that by Torah law one must follow. And here, from the standpoint of logic, there is no majority. And in monetary law, such a majority is not effective. In monetary law we need a majority that is based on reason, one that shows that this is in fact the truth. But a majority that is only a Torah law—such a majority will not help in monetary law. That is what he claims. Now I actually think his formulation is too weak.

[Speaker B] What do you mean?

[Rabbi Michael Abraham] He basically wants to tie it to the question of whether this majority is truth-clarifying or not truth-clarifying. I’m saying that not only in capital law and in monetary law would this majority not help—it wouldn’t help anywhere.

[Speaker B] Think about the ball, right—

[Rabbi Michael Abraham] About the person choosing a black ball or a red ball from the container, where there are ninety-nine red balls and one black ball—there is simply no majority here in any sense. It’s not a scriptural decree and not a scriptural decree. There is no law of majority here at all. It’s not just that the law of majority won’t work here in monetary law. The law of majority simply does not operate in such a case. And therefore I think that in the case of the gifts too, the explanation he gives of Nachmanides is too weak. Nachmanides means something much stronger. Nachmanides wants to claim that a majority regarding gifts is not a majority at all. It is not a majority at all. It’s irrelevant, because this is a human decision. And in a human decision you cannot apply probability. Now he says—and this is the same situation with the majority for plowing. Why in the majority for plowing? Because there too it is not a truth-clarifying majority. No—that’s not the issue, whether the majority clarifies the truth or not. Even if a majority present before us is truth-clarifying, that is not the point. Here I have no majority at all. Not because it is a majority present before us, but because there is no majority. There is no majority here. Why is there no majority? Because the question is what this person’s preference was. After all, there are people whose preference is an ox for slaughter, and there are people whose preference is an ox for plowing. So if the person says: look, I belong to that minority that wants oxen for slaughter, not for plowing—fine, what do you want? Are you going to tell him: no, you’re not like that; you’re not six foot five, you’re six feet, because most people are six feet? What does that have to do with anything? I’m six foot five. I decided I want an ox for slaughter. But it can’t be—most people want one for plowing. Fine, but there are also people who buy for slaughter; I’m one of them. I’m from that group. I chose the black ball even though it’s one out of a hundred. But I chose it because that’s what I wanted. So it’s irrelevant that there are ninety-nine red balls and one black one. Because the action is not random; it is an act of decision. Therefore what he writes here, that this is human custom—I think the translation I would give to that is: this is human custom, and therefore it makes no sense to apply probabilistic tools here at all. You can hesitate a bit about this.

[Speaker B] But we do in fact apply probabilistic tools here. In elections too we do apply them in matters of human decision.

[Rabbi Michael Abraham] I’m getting to that, I’m getting to that in a moment. No, elections themselves are not the point. You mean election polls, not elections.

[Speaker B] Polls, election polls.

[Rabbi Michael Abraham] We’ll get there in a moment. So the claim, basically, is that even if a present majority is indeed a clarifying majority, still the majority in the case of an ox for plowing is also not a present majority—it’s not a majority at all. There is no majority here if this is just a majority based on human custom. That’s the claim. Now I’m saying there’s some room to challenge that statement. Take the balls example: a person chooses a ball from a container of balls, so it seems obvious that the probability—if I had to bet right now: there are ninety-nine red balls and one black ball in this container. I tell someone, choose a ball for yourself, pick a ball and take it out. And now we bet between ourselves whether it will be black or red. I would bet fifty-fifty: black and red, not ninety-nine to one. Because if he likes black, he’ll take black; if he likes red, he’ll take red. Now since I don’t know what he likes, then it’s fifty-fifty: fifty that he likes red, fifty that he likes black. But that’s fifty-fifty, not ninety-nine to one. Okay? Now what happens here is that the person who bought it for plowing is basically making claims about his own nature—or his needs, whatever. He says his need was an ox for slaughter, not an ox for plowing. Even though most people, when they buy an ox, buy it for plowing. But he says: but I needed an ox for slaughter—what do you want from me? That’s a legitimate need; it doesn’t run against the natural order of the world the way a true majority does. Rav Shimon Shkop. Meaning, a present majority is not a majority rooted in the nature of the world. An absent majority is a majority rooted in the nature of the world. Right, we saw that. So in that sense it resembles a present majority, because it’s not a majority rooted in the nature of the world but in human behavior. I want to argue not only that it’s in human behavior, but that there is no majority here at all. Not only is it not a majority rooted in the nature of the world—there’s no majority here at all; it’s not a majority. Because the statistics should be about what kinds of balls people like, or what this person’s preference is—does his preference run to gifts before betrothal or betrothal before gifts, and what did he decide? He could decide this way, he could decide that way. The probability here changes nothing. But here there is some room to hesitate. Why? Because there is a dispute here. Suppose the woman says he betrothed her and he says he did not betroth her, for the sake of discussion, okay? Now when the woman says he betrothed her, what she’s really saying is: you’re one of those who act according to the custom of most people. You did in fact betroth me. And you’re claiming about yourself, no, I belong to that minority who first betroth and only afterward send gifts. Right? I belong to the minority. Now then there’s… you’re claiming that you belong to the minority, but she claims that you’re lying. So there is indeed a dispute over the person’s character. And if there’s a dispute over the person’s character, then the fact that the person says, “my character is such that right now I gave betrothal,” maybe he’s lying? After all, that’s his dispute with the woman. The woman claims he belongs to a different group. Now if that other group is the majority, then there is room to say that we really believe the woman, that he belongs to the majority group, and we do not believe him that he belongs to the minority group. Where there is a dispute, then there is room to rely on majority and minority and probability. When I talk about the balls in the jar, then with balls in the jar it clearly depends on which balls he likes. If he likes black, black; if he likes red, red. I have no information what he likes, so it’s fifty-fifty; the majority of balls in the jar is irrelevant. But if, for example, in that setting I had statistics among people and I said that most people like red balls, and he claims, yes, but I like a black ball—and someone else claims, no, you don’t like a black ball, I know you, your taste is that you like red balls—then there is a dispute over what you’re claiming. Someone else is claiming you’re lying. Now here there’s room to rely on the majority, because you’re claiming that you belong to the minority that likes black balls. He claims that you belong to the majority that likes red balls. So most likely he’s right, because there’s a dispute over which group you belong to. You would belong to the majority group. And then there is room to see this as some kind of law of majority. Regarding taking a ball out of the jar—if I didn’t have statistics about people’s tendencies, about people’s tastes—then there would be no room at all for statistics; it would just be nonsense. But if I do have statistics about people’s tastes, then it’s not such nonsense to say that if there is a dispute, we decide that you belong to the majority group and not the minority group. Now also in betrothal and gifts, in betrothal and gifts, if there were no dispute at all—if it were just a question, we would ask him and he would say, “Listen, I belong to those who first betroth and only afterward send gifts,” yes, and only afterward send the gifts, even though most of the public there in that place follows a different custom. Fine—if there’s no opposing claim, nobody is claiming that he’s lying or mistaken or anything like that, then I would accept what he says. So what if he says he belongs to the minority? But there is such a minority, so why not believe him that he belongs to the minority? If someone claimed he was lying, then there would be room… there is a dispute here over which group you belong to. You claim you belong to the minority group; I claim you belong to the majority group. Since we have no way to accept your view because we have a dispute, we now do need to bet which group you belong to, and then I would bet that you belong to the majority group and not the minority group.

[Speaker C] Is there perhaps room to say, regarding betrothal, that if there’s a majority and a minority, then as long as he didn’t explicitly explain what he meant, I’d say that even if I don’t know what he intended, in this country, since most people intend betrothal, let’s say, then I say that that’s the meaning of the act when it’s done without explaining what is intended.

[Rabbi Michael Abraham] Because in any case you need some kind of…

[Speaker C] But here there’s a dispute.

[Rabbi Michael Abraham] On the question of what happened—that makes all this irrelevant. The man says: I gave her money for betrothal and said to her, “Behold, you are betrothed to me,” and she said she agreed. There’s a dispute over what happened. And she claims: none of that ever happened; it wasn’t given to me for betrothal at all. It’s not a case where he gave it silently and we’re asking what his intention was—no. There’s a dispute over the facts of what happened here. It’s just that now, since we don’t know—he says the facts were like this and she says the facts were like that—then I say, let’s see what happens according to the majority. If the majority gives money at this stage for gifts, then apparently she is right that it was not for betrothal; if it’s for betrothal, then he is right. But clearly it begins with a dispute over the facts of what happened. Yes, I understand. Okay, so basically the claim Rav Shimon Shkop explains in the view of Tosafot in tractate Sanhedrin is really a claim that says that when we are dealing with human decision-making, with people’s decisions, you can’t apply probabilistic rules. Like with the black ball and the red balls: a person decides to do something, so it doesn’t matter—even if he decided to behave in a way most people don’t behave, so what? It’s a conscious, deliberate decision he made, and that’s the decision he made. If it were an act he did randomly, without paying attention, then I’d say, fine, most likely he performed the common act. But if it’s an act he decides upon, there is no impediment at all to his choosing the black ball. He decides. Okay? And so this reminds me a bit of the Talmud in tractate Makkot 10a. The Talmud says there: what is an unintentional murderer? So it says: Reuven murdered intentionally, Shimon murdered unintentionally. The Holy One, blessed be He, brings them to the same inn. Reuven below and Shimon above. Shimon is on the roof or on the tree with the axe and Reuven is below. And then the iron slips from the handle, unintentionally, and kills Reuven who is below. So Reuven, who was the murderer, deserved death and received his death; and Shimon, who had been an unintentional murderer and deserved exile, now will go into exile because he killed unintentionally. So each one got what he deserved. Meaning, the Holy One, blessed be He, arranges reality in such a way that whatever happens is what ought to have happened. Okay, that’s basically the Talmud’s claim. On the other hand, there is Rabbeinu Chananel in Sanhedrin, in Chagigah 5a.

[Speaker B] How does that fit there with free choice?

[Rabbi Michael Abraham] Right, so the Talmud there says that there is one who is swept away without justice—that’s what the Talmud says. So Rabbeinu Chananel says: what is “one who is swept away without justice”? For example, a person who killed his fellow. What does that mean? If I decide to murder you, then it could be that you die even though you did not deserve to die. You are swept away without justice—not because the heavenly court decided that you should die, but only because I decided to kill you; I have free choice. Rabbeinu Chananel says yes, such a thing can happen: a person can die even though he doesn’t deserve to die, because I decided to kill him. That is “swept away without justice.” So you see that in fact when a person performs an action, that is placed in his hands; it is not in the hands of Heaven. If I decided to murder, then the consequences of the act depend on what I will do, not on what Heaven decided. On the other hand, the Talmud in Makkot seemingly contradicts this. It says there that what happens to people is directed from above. The Holy One, blessed be He, somehow arranges things so that what needs to happen will happen. So beyond the question, of course, of how the first unintentional killing happened—right? You’re telling me he deserved exile because he had previously killed unintentionally, and this one deserved death because he had previously killed intentionally; the Holy One, blessed be He, brings them to the same inn and each gets what he deserves. And that earlier unintentional killing that I committed and for which I was not punished with exile—how did that happen? There too were they brought to the same inn? Meaning, how did the first unintentional killing happen, and this whole chain? Clearly that’s an explanation that can’t really hold water for all of reality, but that’s just an anecdotal remark. There is no contradiction between Rabbeinu Chananel and the Talmud there. Why? Because Rabbeinu Chananel is talking about someone who kills his fellow intentionally. If I kill my fellow intentionally, then clearly everything is in the hands of Heaven except the fear of Heaven. Meaning, the Holy One, blessed be He, gave me the option, free choice, to do good or evil, and I can actually succeed in doing either good or evil. So if I decide to murder someone, then I can succeed in doing that even though he does not deserve to die, because I chose to kill him and a person has free choice. The Holy One, blessed be He, gave a person the power to do things even without God wanting them to happen, or against God’s will. We have the ability to act badly, not only to act well. But in the Talmud in Makkot we are talking about unintentional murder. No, but the… one second, Shmuel, let me finish. So in such a situation it is clear that it is directed from above by the Holy One, blessed be He, because it is not my decision. Things that are not human decisions are random things, probabilistic things, or decisions from above—it doesn’t matter, but it’s via the natural order, and probability rules there. In a place where it is a human decision, then the outcome is connected neither to probability nor to the decision of the Holy One, blessed be He, but to what the person decided to do—which is exactly the same distinction I made regarding probability. If a person makes decisions, then it is not a random event; you can’t discuss it with probabilistic tools. What he decided is what will happen. But if the act is one he does unintentionally, a natural act that happens randomly, there you can treat it with probabilistic tools. Yes.

[Speaker B] But even in the unintentional case, we’re still talking about negligence, and negligence is also the fruit of a person’s decision. He tells himself he didn’t decide—that it’s some sort of illusory feeling of will—but the truth is that he did decide to be negligent, and that’s why he is punished, and so that doesn’t solve the problem.

[Rabbi Michael Abraham] You already hinted at the answer yourself: that’s weakness of will, not a positive decision.

[Speaker B] What difference does that make? He also decides, after all, to have weakness of will.

[Rabbi Michael Abraham] Fine, that’s the dispute; that was discussed at length in the topic of weakness of will, yes. Now I claim that a decision involving weakness of will is not like a positive decision to do something. In any case, when I decided to be negligent, clearly I did not decide to kill Reuven. So even according to your view, there would be room to say, fine, I decided to be negligent, but clearly the Holy One, blessed be He, will not let that negligence kill Reuven if he does not deserve to die. Let the iron fall and let me be punished for the fact that I could have killed Reuven—but He will not let Reuven die if he does not deserve to die. But if I decide to kill Reuven—not decide to be negligent—then here, since I have free choice, the Holy One, blessed be He, allows me actually to kill Reuven, not merely to be negligent. So in any case there is a difference whether you accept my thesis about weakness of will or not. I think here we can agree that there is a difference between a decision to be negligent and a decision to kill, and they are not the same thing. You can say that here the Holy One, blessed be He, intervenes: in a decision to be negligent—okay, you were negligent, you will be held accountable for the negligence, but that does not mean I will let Reuven die. But if you decided to kill him—that was your decision—then the meaning of your having free choice is that if you decide to kill him, you can kill him.

[Speaker B] I don’t see a categorical difference between the two. What? I don’t see a categorical difference between the two.

[Rabbi Michael Abraham] There is a difference in any case, a smaller difference perhaps, but clearly there is a difference. Clearly there is no contradiction between Rabbeinu Chananel and the Talmud there in any case. You can say maybe you disagree with Rabbeinu Chananel, fine, you can say that, but there is no contradiction from Rabbeinu Chananel to the Talmud there. So I return to our issue: that is basically the claim, that when a person makes decisions, then this is not a random act. It is not an act you can discuss in statistical terms, in probabilistic terms. Probabilistic tools are tools that deal with random events, arbitrary events, chance events. Then you can say: if it happens randomly, then it will probably be distributed according to the probabilistic rules. But if I decide something, then the decision is something deterministic—not deterministic in the sense that it follows from prior causes, but in the sense that I determine what the outcome will be; I’m not drawing lots here. I determine what the outcome will be. If I want a black ball, I will take out a black ball, even if there are ninety-nine red ones here and one black one. Therefore I cannot apply probabilistic tools to human behavior. So the point I wanted to add: Tosafot in Bava Kamma apparently did not understand it this way. And that also is not the plain meaning of the Talmud, because the plain meaning of the Talmud is that the majority for plowing is indeed a majority, and therefore according to Rav we do follow the majority even in such a case; only according to Shmuel do we not follow the majority in this case. So it turns out that this is not something completely absurd like a black ball and ninety-nine red balls. There is something here—indeed there are views among the medieval authorities (Rishonim) and in the Talmud among the Amoraim, even in the Talmud itself, that even in the case of a majority for plowing we follow the majority. Why? After all, there really is no majority here at all—it’s like a black ball and red balls. So that’s what I said earlier: that’s not precise. Because in the end we are talking about a situation where there is a dispute whether you sold me the ox for slaughter or sold it to me for plowing. And the moment there is a dispute, then I can say: listen, you say you belong to the minority population, but you’re lying. Most people are not like that, and I also know that you are not like that. The fact that you claim you are like that—you’re lying. Now the religious court has to decide which of us is speaking the truth. So come—let’s treat this as though we know nothing. Nobody claimed anything. What would I say about a person who sold an ox: did he sell it for plowing or for slaughter? In the absence of any other information, I would say he sold it for plowing, because most people sell an ox for plowing. Therefore there is room here to apply probabilistic rules. And that is what Tosafot in Bava Kamma holds, and Rav too according to Tosafot in Sanhedrin—that is what he holds. But Rav Shimon says yes, but according to Shmuel and according to Tosafot in Sanhedrin—Shmuel according to Tosafot in Sanhedrin—he really holds: no, such a majority simply cannot work, at least not in monetary law and not in capital law either, as he says. This majority cannot work, because there is no majority here at all; it’s a human decision. Now here comes the point Shmuel raised earlier, and that’s where I want to get now.

[Speaker C] Just a question: when we’re talking about selling oxen, is the division by people? Meaning, is there one type of people who sell only for plowing and another type who sell only for slaughter? Or is it most oxen? Here the case is the majority in transactions.

[Rabbi Michael Abraham] It makes no difference whether it’s a majority among people or a majority among transactions—what difference does it make?

[Speaker C] If it’s a majority among transactions, then it doesn’t really fit here to say, “I know you, and you only sell for plowing,” or “I know you, and you only sell for slaughter.”

[Rabbi Michael Abraham] Here I don’t need to say I know you. I know that this transaction was for plowing because we talked about it.

[Speaker C] Because we talked about it—so basically there is a dispute here.

[Rabbi Michael Abraham] Again, the same thing—a dispute about reality. Since there is a dispute here, I can’t rely on what they say; that is, they are saying opposite things. So the religious court now treats this as though we know nothing. Then I look at the majority of transactions. Most transactions are for plowing, so in the absence of information I’ll assume this transaction too was for plowing. Okay, so the first point I want to make—or another point that wraps up this section for the moment: I remind you that at the end of the previous class I brought Oren’s explanation, yes, Oren Margalit, that this is also Uman’s explanation of the law of fixed status. Yes, we spoke about the laws of fixed status. So they say that the law of fixed status is basically a situation in which we’re talking about a human decision. Right, remember that I approach a store and take out a piece of meat. So the doubt arose when the piece of meat was in the store itself, not when it had separated and I found it lying on the street floor. Okay? Uman and Oren after him say that the moment the question is which store I entered—and that is a decision a person makes, which store to enter—you cannot apply the statistics that there are nine kosher stores and one non-kosher store. And that is the law of fixed status. Therefore one does not follow the majority. You understand that this is the same idea? And the idea of the law of fixed status according to this explanation is exactly the idea that one does not follow the majority in monetary law according to Tosafot in Sanhedrin. It basically says that decisions made by a person, conscious decisions made by a person, are not decisions that can be handled with probabilistic tools. These are not random events. It is exactly the same idea, and so it really continues what we saw in the last explanation we saw regarding the law of fixed status last time. Now I really want to address Shmuel’s remark from earlier. There is a Maimonides in the laws of… one second… the well-known Maimonides in chapter 5 of the laws of Repentance—there is the question there about foreknowledge and free choice: “Perhaps you will say: does not the Holy One, blessed be He, know everything that will be? And before it happens, did He know that this person would be righteous or wicked, or did He not know? If He knew that he would be righteous, it is impossible that he not be righteous. And if you say that He knew he would be righteous and yet it is possible that he be wicked, then He did not know the matter clearly.” Right—how can it be that the Holy One, blessed be He, knows everything in advance and yet human beings still have free choice? “Know that the answer to this question is longer than the measure of the earth and broader than the sea, and many great principles and lofty mountains depend on it. But you must know and understand this matter that I say”—namely, “that the Holy One, blessed be He, does not know with a knowledge that is outside Him, as human beings do, who and their knowledge are two things; rather He, exalted be His name, and His knowledge are one, and human knowledge cannot grasp this matter clearly,” and so on and so forth. Okay, so that is basically the claim. “Therefore we have no power to know how the Holy One, blessed be He, knows all creatures and actions. But we know without doubt that a person’s actions are in the person’s own hands, and the Holy One, blessed be He, does not pull him or decree upon him to do so. And this is known not only by acceptance of the faith, but by clear proofs from the words of wisdom.” Now the Ra’avad disagrees with him; he says, yes, “This author did not follow the way of the sages. If you ask a question and have no answer, it is better not to ask it.” Meaning, he understood that Maimonides did not answer the question but left it open. This is a big dispute among the commentators on Maimonides: whether Maimonides there answered the question, or whether Maimonides is saying, look, we have no power to know, and therefore I have no answer to this question. It is a big question, and we must still remain with our belief that man has free choice. And the Ra’avad says: if you have no good answer, don’t ask the question.

[Speaker B] Is that wise to say? What? Is it wise to say that if you have no answer, don’t ask a question? That’s my next sentence.

[Rabbi Michael Abraham] Meaning, that’s an interesting methodological question before the question whether Maimonides really answered or really left it unanswered. Is it really wrong to ask questions when you don’t have answers to them? The Ra’avad assumes so, but it is certainly possible that Maimonides thought otherwise, even if he did not answer. I think he did answer, but even if Maimonides did not answer—fine—then he thinks that if there is a good question, you should put it on the table and say that you have no answer. That’s intellectual honesty. These sacred contradictions—that’s a widespread approach, but not necessarily an agreed one. Fine, but that really doesn’t concern us. What I do want to look at is Maimonides in chapter 6 of the laws of Repentance. Maimonides in chapter 6 of the laws of Repentance says as follows: “But is it not written in the Torah, ‘And they shall enslave them and afflict them’—so He decreed upon the Egyptians to do evil? And it is written, ‘And this people shall rise up and go astray after the foreign gods of the land’—so He decreed upon Israel to worship stars and constellations? Why then did He exact punishment from them?” He says: it is written in the Torah, in the covenant between the pieces, “And they shall enslave them and afflict them for four hundred years.” So basically the Holy One, blessed be He, tells Abraham our forefather in advance, hundreds of years earlier, that the Egyptians will afflict and enslave Israel. So afterward, when the Egyptians do that—You punish them? You knew in advance they would do it. It wasn’t their choice. And likewise He decreed upon Israel to worship idolatry. It is written, “And this people shall rise up and go astray after the foreign gods of the land,” so we see that the people of Israel will worship idolatry. So why exact punishment from them? What does He want from them? It was already foretold in advance. Maimonides says: “Because He did not decree upon a specific known individual that he would be the one to go astray; rather every one of those who go astray after stars and constellations—if he had not wanted to worship, he would not have worshiped. And the Holy One, blessed be He, informed not the Creator’s decree upon a person, but the way of the world. To what is this comparable? To someone saying: among this people there will be righteous and wicked. Because of this, will the wicked person say that it has already been decreed upon him that he be wicked, because He informed Moses that there would be wicked people in Israel? As it says, ‘For the needy shall never cease from the land.’ Likewise the Egyptians: every single one of those Egyptians who harmed Israel—if he had not wanted to harm them, the choice was in his hand. For He did not decree upon a known individual, but only informed him that in the end his descendants would be enslaved in a land not theirs. And we have already said that man has no power to know how the Holy One, blessed be He, knows future things.” Now on this the Ra’avad comments—

[Speaker C] “Abraham said”—

[Rabbi Michael Abraham] “These are lengthy words that have no substance. And truly, I almost say they are childish words. Will the Creator say to those who went astray, ‘Why did you go astray?’ and I did not mention you by name, so that you should say that I decreed it about you?” That, after all, is what Maimonides says. Meaning, what does Maimonides say? There was a general decree that Israel would worship idolatry, but each individual has free choice. The Ra’avad says: meaning, if now they come with claims against a person who worshiped idolatry, then he’ll say, what? The Holy One, blessed be He, comes to him and says, why did you worship idolatry? He’ll say: because You said that they would worship idolatry. The Holy One, blessed be He, will say to him: what are you talking about? I didn’t say that you would worship; I said that in general the people of Israel would worship idolatry. So the idolaters will say to Him—and I continue reading from the Ra’avad—“And upon whom did Your decree fall? Upon those who did not go astray? Behold, then Your decree was not fulfilled.” What is he saying? On whom did You mean that he would worship idolatry? On the others who did not worship idolatry? Then Your decree was not fulfilled there. So what was it talking about? About me? Well then, if it was talking about me, then it wasn’t my choice, so what do You want from me? Why are You punishing me? In another formulation, I would put it this way: suppose there are a hundred Egyptians, and suppose ninety-nine chose not to enslave Israel, but one chose yes, to enslave Israel. Now the Holy One, blessed be He, comes with claims against him, so the man says to Him: what did You want—that I too should not enslave Israel? Then no Egyptian would enslave Israel. So about whom did You prophesy in advance? What—did You prophesy wrongly? Therefore it’s clear that the fact that I worshiped idolatry was forced upon me; fate overrides my choice—that’s the Ra’avad’s claim. And he adds one more point. He says afterward, besides that—wait—besides that, he doesn’t understand at all why Maimonides begins this whole discussion. Right, he says this: “We have already said that in this matter the Creator’s knowledge is not a decree, and all the more so here.” What does that mean? He says: after all, you yourself, Maimonides, already said in the previous chapter that the fact that the Holy One, blessed be He, knows in advance does not mean we have no free choice. So why are you suddenly jumping again to the same question? The Holy One, blessed be He, knows in advance that the Egyptians will enslave, and still they have free choice, and if they enslave then that is their choice and they deserve punishment; they should bear responsibility. You yourself in the previous chapter already said that, so why are you posing this again now and offering answers? Back there you answered nothing at all. If you have an answer, why didn’t you say it there? If you don’t have an answer, then here too leave it without an answer. Why isn’t this discussion just duplicating the one in the previous chapter? That is basically the Ra’avad’s point. Now this can be understood quite simply. What does it mean? If the Holy One, blessed be He, knows things about what is going to happen—that still doesn’t… let’s say Maimonides says that this still doesn’t mean we don’t have free choice. We have free choice even though the Holy One, blessed be He, knows in advance. Let’s say that’s what Maimonides says, because that’s how the Ra’avad understood him. But here the Holy One, blessed be He, says to Abraham our forefather, “Your offspring shall be strangers in a land not theirs, and they shall enslave them and afflict them four hundred years.” So here already there is a human being who knows in advance that this is what will happen. This is not just the knowledge of the Holy One, blessed be He. When a human being knows in advance, then you can’t say that His knowledge is unlike our knowledge and all these things. If a human being knows in advance, then that does seem to dictate the outcome and negate freedom, and therefore Maimonides reopens the discussion here, because it is not the same discussion. There he is talking about the knowledge of the Holy One, blessed be He, and says that this knowledge does not force a person to do something; he still has free choice. But in chapter 6 Maimonides is talking about a human being’s prior knowledge, and that is seemingly different, so here we need to find an answer. That’s just a side remark; it is less relevant to our issue. What is important for us is really what Maimonides would answer to the Ra’avad. And I think what Maimonides would answer to the Ra’avad is basically the law of large numbers. What does that mean? Suppose there are many Egyptians, a million Egyptians, okay? Now I say that the Egyptians will enslave Israel. When I say the Egyptians will enslave Israel, what that means is that there will be a group of Egyptians who will enslave Israel. In general, when I look at the totality of Egyptians, there will be within it a certain percentage—I don’t know, some group—that will enslave Israel. That is the prior decree. Now each individual person has free choice whether to enslave or not, free choice. He can enslave, he can refrain. And still, if we are talking about a large number, I can tell you in advance that there will be some who enslave Israel even though each one has free choice. And that is basically Maimonides’ claim. The decree was not upon a specific person; it was upon the collective in general. So that means every person has free choice. So you’ll ask: if every person has free choice, then maybe they could all suddenly choose not to enslave Israel? True, that could happen, but it won’t happen, because the law of large numbers says that on average there will be a group that enslaves Israel. It’s like when we speak, say, about rolling a die. With a die roll—we’ve discussed this more than once—every time I roll a die there is a one-sixth probability for each face, okay? The next roll again has a one-sixth probability; there is no dependence between the rolls. Same thing every time, one-sixth. But if I rolled, I don’t know, six billion times, then already now I can tell you there will be a billion ones, a billion twos, threes, fours, fives, and sixes. More or less with very small deviations. Meaning, the prediction that one-sixth of the rolls will fall on each result is a very secure prediction, even though each individual roll is completely free. Thus—it’s not despite, it’s because. Meaning, because each individual roll is completely free, only then does this law of large numbers hold, and I can tell you in advance that one-sixth of the rolls will fall on each face.

[Speaker B] A die doesn’t have free choice? I can’t hear. A die doesn’t have free choice?

[Rabbi Michael Abraham] No, but the result is a random result—just a moment, that’s where I’m heading. The result is random on every die roll, and there is no dependence between the rolls, and yet I can still give you the big picture in advance. Even though everything, ostensibly—after all, in principle all the rolls could have landed on six, right? There is some chance that would happen. How can I know in advance to say that one-sixth of the rolls will fall on each face in large numbers? That is the wonder of the law of large numbers. The wonder of the law of large numbers is that although each event individually is a completely random event, still—not although, I said because, but ostensibly it’s although, yes—still, if you do a large number of rolls, I can tell you in advance according to the law of large numbers what the outcome will be, the collective outcome—what the totality of the rolls will look like. I can’t tell you for any particular roll where it will land; I can tell you how the rolls will be distributed: one-sixth on one, one-sixth on two, one-sixth on three, and so on. Maimonides claims the same thing happens regarding the Egyptians. What does that mean? Every Egyptian has free choice. He could enslave, he could refrain. Once there are many Egyptians, then the Holy One, blessed be He, can tell you in advance: look, thirty percent of the Egyptians will enslave Israel. Why? Because the law of large numbers says that if there are enough Egyptians, there will always be thirty percent who enslave Israel. And this is despite—or as I said, because—every individual Egyptian has complete freedom to decide whether to enslave or not to enslave. Therefore, according to the law of large numbers, says Maimonides, you can give a prophecy about what the collective will do even though each individual has completely free choice. Exactly like the die, which behaves in a completely random way. Now, as Shmuel said—and I won’t do this here, maybe we’ll discuss it next time—but as Shmuel said, what I just said is not trivial. Because the choices of the Egyptians are choices, whereas the rolls of a die are random results. So for random events, we saw that probability works. Probability is made to deal with random events. But events that are the result of choice—whether to enslave or not to enslave—that’s like whether to take out a black ball or a red ball, or whether to send gifts first or betrothal first. That’s a human decision. In a human decision, why in the world should we say that probability works? After all, regarding human decisions we say that probability is not supposed to work. More than that, I’ll add: after all, we know that even in human behavior you can still do statistics. As Shmuel rightly remarked earlier, we conduct election polls, right? Polls predict very well what the election outcome will be. They got a bad name, but not justly. Polls predict the election results with astonishingly high quality. And therefore the question arises again: after all, the decision whom to vote for is an intelligent, deliberate, conscious decision that each person makes. And I’m saying that nevertheless, if there are very many people, I can take a representative sample and from it predict what will happen among people in general. Why? After all, maybe everyone suddenly decided to vote for Bibi. They have free choice. Why can I use probabilistic tools on actions that a person performs out of his own free decision? After all, earlier I argued that you can’t—that’s what Rav Shimon Shkop said about majority in monetary law and so on. And here we see that probabilistic tools can also deal with human behaviors or decisions.

[Speaker B] And the question is, first, why is that true? And second, how does that fit with what we saw earlier—

[Rabbi Michael Abraham] Earlier with the container of balls, where it really makes sense that when the person decides on black, he’ll take out black; the probabilities play no role there. So why here yes? Okay, so that is basically the question needed to complete this picture: why, or how, do we deal with human behavior using probabilistic tools? I’m not going to start that here because it’s already ten o’clock, but I’ll complete it next time. So I’ll stop here. If there are questions or comments.

[Speaker B] Thursday, the class as usual?

[Rabbi Michael Abraham] Yes. Okay then, goodbye, good night.