Doubt and Probability—in Halakha, Thought, and Beyond—Lesson 46 — Rabbi Michael Abraham

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[Rabbi Michael Abraham] It could be that she had relations even before she was betrothed to him, not while she was under him, or that she had relations after the betrothal. That’s one doubt. And if you say it was while she was under him, even then, if she had relations after the betrothal and therefore should become forbidden, there is still a doubt whether it was by coercion or willingly. If it was by coercion, she still does not become forbidden. A doubt whether willingly. So notice, let’s go down for a moment to the diagram. Never mind, not this specific case, but this is the diagram. Right, a doubt whether while under him or not while under him. If not while under him, then she is completely permitted. We’re talking here. A doubt whether while under him or not while under him. If it was not while under him, then it doesn’t matter whether it was by coercion or willingly—in both cases she is permitted, right? If it was while under him, then it depends. If by coercion, then she is permitted, and if willingly, then she is not permitted. Alright? So this structure of a tree with two branchings is basically the structure of a double doubt. Okay? The structure of a double doubt. Except what? Here, ignore for a moment the bottom rows—in an ordinary double doubt, she is basically permitted, permitted, permitted, and forbidden. Meaning, in one out of the four endpoints she is forbidden, and in three out of the four endpoints she is permitted. Okay? That is the diagram of a double doubt. I go back to the Talmud. Right, the Talmud asks: but this is a double doubt. Either she was under him or not under him—that’s one doubt. And even if she was under him, in which case she ought to become forbidden, there is another doubt whether it was by coercion or willingly. So this is a double doubt. What happens when there is a double doubt? If it was not under him, whether by coercion or willingly she is permitted. If it was under him, then if by coercion she is permitted, if willingly she is forbidden. So three out of four possibilities are that she is permitted, and one that she is forbidden. So when a person comes and says, “I found an open entrance,” even if we believe him that he found an open entrance, still three out of four possibilities are that she did not become forbidden to him. So why does Rabbi Elazar say that he is believed to forbid her to him? It’s a double doubt. The Talmud gives two answers. It is necessary only in the case of a priest’s wife.

[Speaker C] What happens

[Speaker A] with a priest’s wife?

[Rabbi Michael Abraham] A priest’s wife becomes forbidden even if it was by coercion. So there is a doubt whether it was under him or not under him, because if not under him she did not become forbidden, but if under him then she did become forbidden. And the doubt whether it was by coercion or willingly does not exist, because with a priest’s wife, whether by coercion or willingly, she is forbidden. Okay? Notice, this basically means that the diagram—I’m going back here—the diagram is this diagram, but with a priest’s wife what happens is this: if it was under him, then whether by coercion or willingly she becomes forbidden to him in both cases. If it was not under him, whether by coercion or willingly she does not become forbidden to him. So there are two possibilities in which she did not become forbidden and two possibilities in which she did become forbidden, which is a case of a single doubt, right? It’s not three out of four possibilities, but two out of four. It is basically one out of two. If it was under him, then she becomes forbidden; if not under him, then she does not become forbidden. There is no difference between coercion and willingness. Coercion and willingness are irrelevant. If you insist that it is still a tree with two branchings, I don’t care, but the endpoints of the tree are two against two and not one against three. So this is called one doubt and not a double doubt, and therefore he is believed to forbid her to him, because a Torah-level doubt is treated stringently. That is one answer of the Talmud. The second answer of the Talmud: and if you wish, say it is a Jewish wife, for example where her father accepted betrothal for her when she was less than three years and one day old. The second answer: we are talking about the wife of an ordinary Jew, not a priest, but her father accepted betrothal on her behalf when she was under three years old by a week, or whatever, under a day. Okay? What happens in such a case? There is a doubt whether it was by coercion or willingly. Okay? If by coercion then she is permitted, because this is the wife of an ordinary Jew. If willingly, then she is forbidden. But the doubt whether under him or not under him does not exist. Why does it not exist? Because if it were not under him, then she had relations when she was very young, under three, and under three her virginity returns. Meaning, it would already have healed, and when he came to her he would not discover an open entrance. Therefore it cannot be that this happened before the betrothal; it happened afterward. Okay, and therefore here too there is only one doubt. So these are two cases in which the situation is not a double doubt but a single doubt, so says the Talmud. Now Tosafot asks: “And if you say there is still a double doubt—perhaps by coercion, perhaps willingly; and if you say willingly, perhaps when she was a minor, and the seduction of a minor is coercion, as we say in ‘one who has relations with his yevama.’” What is Tosafot saying? You tell me we are dealing with the wife of an ordinary Jew whose father accepted betrothal for her when she was under three. So what? Then there is no doubt that it was not under him, or no doubt whether it was under him or not under him. So Tosafot says: yes, but there is a doubt—because even if it was under him, seduction of a minor is coercion. Therefore even if he seduced the minor supposedly willingly, the willingness of a minor is not willingness; it is coercion. So there is still a double doubt. There is a doubt whether under him or not under him, and even if under him, it could be that it happened when she was a minor, and the seduction of a minor is coercion. Tosafot says: “And one can say, there coercion is one thing,” and we’ll get to that later. Tosafot is basically saying in his answer: there, coercion is one thing. What does that mean? Seduction of a minor is coercion, but it is still coercion. There are two possibilities here: either it was coercion or it was willingly. The coercion—either he really forced her, or he acted with her consent but the seduction of a minor is also coercion. What difference does it make to me? This way it’s coercion and that way it’s coercion. There are many kinds of coercion, so it is still only one doubt: whether it was by coercion or willingly, that’s all. But we’ll get back to this answer later.

[Speaker J] And Tosafot says here, by the way, apropos of mistakes in facts: when the Talmud claims that before age three virginity returns, is that actually factually correct?

[Rabbi Michael Abraham] Fine, I wrote about that too—there is the well-known Shakh. Clearly it is not factually correct, in the sense of a sharp line at age three. Presumably, if I understand correctly—I didn’t ask, but I assume the intention is that it’s around age three.

[Speaker J] But is there such a thing as virginity returning?

[Rabbi Michael Abraham] Yes, that’s what the Talmud says. I haven’t checked that it doesn’t. Do you know otherwise?

[Speaker J] No, I don’t know, and I also don’t want to know. But again, theoretically, I’m saying the Talmud is now basing its entire argument on a fact that I don’t know is true at all, and I don’t know how they knew it was true.

[Speaker F] It really is a question how they knew. What, did they run an experiment?

[Rabbi Michael Abraham] I have no idea how they knew, but that was their claim. Tosafot continues and says: “And if you say—let us establish her in the presumption of being permitted to her husband?” Let’s place her under the presumption that she is permitted to her husband.

[Speaker E] Right, so even if it’s just one doubt

[Rabbi Michael Abraham] basically she should be permitted to her husband. So Tosafot says: “And one can say that coercion has publicity, as we say in the Jerusalem Talmud: coercion has a public rumor. And now that there is no rumor, willing relations are the majority and coercion is the minority, and majority plus presumption—the majority is stronger.” What is Tosafot saying? It’s somewhat similar to what we saw with two majorities. He says that when coercion happens, word gets out, and when a girl is assaulted, word gets out. Now here we did not hear any report circulating about this girl, so there is a majority. Meaning, the possibilities of coercion and willingness are not balanced. This is not an even doubt. It is unlikely that it was coercion, because if it were coercion, word would get out. And if we did not hear any report, then most likely it was willingly and not by coercion.

[Speaker J] What does it mean, word gets out?

[Rabbi Michael Abraham] Word gets out—the public knows she was assaulted. So Tosafot says that therefore this doubt of willingness versus coercion is not an even doubt. There is a majority in favor of willingness, and therefore she is forbidden.

[Speaker H] So because of that, now, that’s why we don’t establish her in the presumption of being permitted? I didn’t understand. That’s why we don’t establish her in the presumption of being permitted.

[Rabbi Michael Abraham] Yes, that’s why we don’t establish her in the presumption of being permitted, because there is a majority that it was willingly.

[Speaker H] So what is the significance of this coercion? Do you treat it as an ordinary doubt?

[Rabbi Michael Abraham] As what do you treat it? As one doubt, and one doubt is treated stringently. After all, Tosafot says we are talking about the wife of an ordinary Jew who is a minor, right? You’re talking about the wife of an ordinary Jew who is a minor. The wife of an ordinary Jew who is a minor leaves us with one doubt, right? Because there is no under him and not under him—it was certainly under him. Okay? Right. Just the doubt of coercion versus willingness. And therefore Rabbi Elazar was not accepted, alright? Tosafot asks: but establish her in the presumption of being permitted and also accept what he says, “I found an open entrance.” Tosafot says no, you cannot establish her in the presumption of being permitted with one doubt, because this is not just a doubt—there is a majority. “Join the minority to the presumption and it becomes half and half.” The minority joins… what?

[Speaker H] Meaning this is a weak doubt. It is a doubt, but not such a good one, basically.

[Rabbi Michael Abraham] A rabbinic doubt—Tosafot says that later—but right now it’s even a majority, alright? There is a majority in favor of willingness. So in any case we do not establish her retroactively in the presumption of being permitted, and this remains an even doubt, and in an even doubt Rabbi Elazar does not believe him regarding “I found an open entrance” to forbid her. Now the Shev Shema’teta comes and says as follows: “And I saw in the responsa of Rivash, section 352, and this is his language: I also saw what I wrote to our teacher Rabbi Nissim on the topic of ‘I found an open entrance,’ and what you asked on Tosafot—that on the contrary, we should say: join the minority of coercion to the half that was not under him, and then ‘under him willingly’ is a minority.” What does that mean? We have a doubt whether coercion or willingness, but the possibility of coercion is considered balanced, right? Meaning the possibility of coercion plus the presumption is considered balanced against willingness. Okay? That is one doubt. And join the minority of coercion to the half that was not under him. He is basically saying this: if it was under him—we are now talking about an adult woman, not a minor; we went back to a double doubt—so Tosafot says there is a doubt whether under him or not under him, right? A doubt whether under him or not under him, and on the side that it was under him, there is a doubt whether coercion or willingness. But coercion is a minority, right? So the minority of coercion together with the half that was not under him creates a majority, right? If it was not under him she is permitted, and if under him then although there is a majority that it was willingly, there is still a minority of coercion, right? The minority of coercion joins the half of not under him, and together they create a majority. “Under him willingly” becomes a minority. Is what I’m saying clear?

[Speaker H] Again, I’ll go back a side. Did the Rabbi just explain the double doubt here simply? What? This is the Talmud’s double doubt, basically?

[Rabbi Michael Abraham] He says that with a double doubt you can go leniently. What does that mean? He says like this: we have a doubt whether under him and a doubt whether not under him, okay? If not under him, then she is permitted, right? If under him—then it depends whether by coercion or willingly. Now coercion is a minority because coercion has publicity, right? So here basically there is a majority—this is not an even doubt, right? There is a majority that it was willingly and a minority that it was by coercion.

[Speaker H] Okay. Or toward prohibition, yes.

[Rabbi Michael Abraham] Exactly. So overall, what do I have? I have fifty percent that it was not under him, which means permitted. I have another ten percent here, which is a minority out of the remaining fifty percent—ten percent that is also permitted—and forty percent that is forbidden. So true, forty against ten is a majority, but that ten joins the fifty here, and overall there is sixty in favor of permission. So in such a case, even when there is a majority toward prohibition here, on the other side I have another doubt, so I do not need a double doubt in order to permit; a doubt plus a majority is enough. Do you understand what I’m saying? Usually we want a double doubt in order to permit, right? But here it’s stronger—double doubt is seventy-five percent, okay? Right? If not under him, she is permitted; if under him, then there is twenty-five percent permitted and twenty-five percent forbidden. Overall there is seventy-five percent that she is permitted—that is double doubt. Now what happens if the other side is not an even doubt but a majority? A doubt whether not under him, if so she is permitted—that is fifty percent. If under him, then it depends whether coercion or willingness. But coercion and willingness are not an even doubt, right? We saw in Tosafot that there is a majority in favor of willingness. Let’s say eighty percent in favor of willingness. Okay? Now that should seemingly make her forbidden, because double doubt permits, but a doubt plus a majority is not good enough; it’s weaker than double doubt, right? Tosafot says—Rivash, who objects to Tosafot, says—what are you talking about? That too should be permitted. You don’t need a double doubt. Even a doubt followed by a majority should be permitted. Why? Because in practice there is sixty percent in favor of permission.

[Speaker E] The minority of coercion joins

[Rabbi Michael Abraham] the fifty percent that was not under him, and in practice there is over fifty percent in favor of permission. So why do you need specifically a double doubt? It is enough to have a doubt followed even by a majority toward prohibition, and it should also be permitted.

[Speaker H] Meaning, a double doubt basically is not better than a majority. What? A double doubt is equivalent, not better than a majority.

[Rabbi Michael Abraham] What kind of reasoning is that? After all, a double doubt is no more than a majority. That is the assumption of the question here. A double doubt is just a majority. So even if the second doubt is not balanced, I still have a majority here in favor of permission. The second doubt need not also be balanced. The second doubt can involve a majority toward prohibition, because still in the bottom line I have a majority in favor of permission. So what is the problem? Alright? That is how Rivash asks on Tosafot. And he proves that this is said according to all the Tannaim—leave it, I’m not going into it now. So he says like this—and this is still the quotation of Rivash—“However, that is there, where half are males and half are females certainly and necessarily, for thus the King, King of the universe, established it.” I think in Bekhorot there it speaks about an animal that gave birth, and we want to know whether this is a firstborn donkey that goes to the priest or not. Now there is a known fact: this animal had milk before. And there is a rule saying that animals that have milk are animals that most likely have already given birth. An animal doesn’t have milk if it didn’t give birth, okay? Now if it has given birth, that basically means that the newborn now is not the firstborn donkey, because there was already one before it—it is not the firstborn, right?

[Speaker A] There is the same topic also with the cow of a gentile. Wait, wait, this is complicated enough.

[Rabbi Michael Abraham] Yes. So in short, if this animal had milk, then most likely it had already given birth, and this offspring is not the first offspring, right? But it could be that what she bore previously was a miscarriage, and it could be that what she bore was female and not male. So there are two possibilities here. So there too, basically, you have a case of doubt plus majority, and not double doubt but doubt plus majority. And about that he says: “However, that is there, where half are males and half are females certainly and necessarily, for thus the King, King of the universe, established it for the continuation of the species. The Holy One, blessed be He, established a rule in the world that the distribution of males and females is fifty-fifty. Therefore necessarily the males born from pregnancies are a minority—a minority, since miscarriages are a minority, and there is no way around this from any angle.” Right—if she gave birth to a male, what is the chance that she gave birth to a male before? There is a minority chance that she miscarried, right? Sorry, there is a minority that she miscarried, and among the possibilities that she did not miscarry there is a doubt whether male or female, right? So altogether he says they can be joined, and we do not worry about the minority of males. So Rivash says—sorry, not the Shev Shema’teta—that there indeed we say this. Why? Because the balanced doubt between males and females is a fifty-fifty doubt. And we know that; it is the nature of the world. And besides that there is also a minority of miscarriages. So there is basically a majority chance that this offspring is actually a first offspring. But here we do not say that women who have illicit relations are half under their husbands and half not under their husbands, such that we should say: join the minority to the half and permit her, for from where do we know that this is half and half? How do we know that among those who have relations, whether it was under him or not under him, it is fifty-fifty? We assume that it is a doubt. Who told you it is a balanced doubt? How do you know? So Rivash says: “Rather, we say the matter is in doubt, that this is possible just like that.” We have two possibilities—either under him or not under him. We have no information. We do not know, unlike the doubt of males and females where we have positive information—that it is fifty females and fifty males. Under him or not under him is a negative doubt—I’m already using my own terminology, right? We say that the matter is in doubt, that this is possible just like that. Alright? And now he continues: “And even if we say: join the minority of coercion to the possibility of not under him, still ‘under him willingly’ would not thereby certainly become a minority.” But we still say that one possibility is like the other. What is he saying? He is basically—the only one I have seen at least—making an explicit distinction between a positive doubt and a negative doubt. That is Rivash, and afterward the Shev Shema’teta develops it more. He is basically saying this: when my doubt is a positive doubt, then even if the doubt that follows it is a majority toward prohibition, I add the minority toward permission to the positive doubt and I have sixty percent permission. So I follow the majority. But if the doubt is a negative doubt—whether under him or not under him—and even if under him there is some chance that it was by coercion, a small chance, twenty percent. But still there is a chance it was by coercion. So let’s join those twenty percent out of the fifty, which is ten percent, to the fifty percent that it was not under him, and there is sixty percent that she is permitted. Rivash says no. Because here it is a negative doubt. In a negative doubt you do not really know that it is fifty-fifty whether it was under him or not, right? It could actually be eighty-twenty. Since you do not know, negatively you determine that we treat it as fifty-fifty. But that is merely a negative determination. You do not really know. Therefore if you ask me statistically—statistically—when, say, it is mostly under him, the doubt of under him or not under him—let’s say actually under him is twenty percent… oh sorry, twenty percent, okay? Can you show it on the diagram?

[Speaker E] Yes, one second.

[Rabbi Michael Abraham] Look, let’s say we are now talking about under him and not under him. Alright? That is one doubt. And even if under him, there is coercion twenty percent and willingness eighty percent. Alright? So seemingly in this fifty percent she is permitted, and out of this fifty percent another twenty percent—meaning ten percent—she is permitted, and forty percent she is forbidden. So she is permitted in ten plus fifty, meaning sixty percent against forty. So she ought to be permitted. Rivash says no. Why not? Because the doubt whether under him or not under him, the upper doubt, is a negative doubt. In principle it could be that only twenty percent is sitting here and eighty percent is there. The opposite could also be true—I don’t know. And think what happens if here it is twenty percent. Then I basically have twenty percent that she is permitted, plus… eighty percent that she is forbidden, of which twenty percent by coercion is sixteen percent—twenty percent out of eighty. Sixteen plus twenty is thirty-six percent that she is permitted, and sixty-four that she is forbidden. So you have no certainty that there is a majority for permission here, because the doubt is a negative doubt. If the doubt were a positive doubt, then no matter what the majority was, I would know for certain that there is a majority for permission here. Rivash says: with a positive doubt, if the second part is a majority, that is enough to permit, even if it is a majority—there is no need for it to be a balanced doubt. Even if it is a majority toward prohibition, yes? It will still be permitted. But with a negative doubt, I need the second doubt also to be a balanced doubt. Negative too—I don’t care—but balanced. But if it is a majority toward prohibition, I will not attach it to a negative doubt, because in the bottom line in terms of numbers it could come out as a majority toward prohibition. You do not have certainty here that you have a majority for permission.

[Speaker F] But why would a balanced doubt be enough?

[Rabbi Michael Abraham] Ah, so you can ask: even with a balanced doubt it could also be like that. So I say: that is exactly the same thing as the two-majority cases we saw in the previous lesson. Right, I have here a balanced doubt negatively, and maybe in truth it is eighty-twenty and not fifty-fifty. But there is no end to it, because almost all our doubts are like that. So what do we do? We create a formal rule that says: look, if you have a double doubt, and both doubts are balanced, then fine—even if they are negative doubts. Then you can assume it is seventy-five percent. Just as with one doubt you basically assume it is a doubt and you do not prohibit it with certainty, even though it could be eighty-twenty, because I assume that a negative doubt is fifty-fifty. A double doubt is a rule; double doubt is a rule that basically comes to bypass the need for calculation. Or in other words, if you have a calculation, if you have a calculation, there is no need to get to double doubt—do the calculation and see. If you have a majority for permission, permit it. All the rules of double doubt are rules stated only in negative cases. But there, if the situation is negative, then the second doubt must also be a doubt; it cannot be a majority, neither a negative majority nor a positive majority—it cannot be a majority toward prohibition. It needs to be at least a doubt, or a majority toward permission—then of course that is also fine.

[Speaker A] Meaning a negative double doubt is always toward prohibition?

[Rabbi Michael Abraham] No, no, exactly the opposite. A double doubt is always lenient, even if the doubt is negative. Where will this make a difference—wait, wait—where will this make a difference, that the doubt is negative? In a place where the first doubt is a negative doubt and after it comes a majority toward prohibition. In such a case, if the doubt were positive, then count the bottom rows: the bottom rows come out as a majority for permission. Right? Because there is fifty percent permission, and out of the fifty percent prohibition there are still some percentages for permission—just a few percent are enough to join the fifty and make permission.

[Speaker A] That’s what I asked—if in double doubt the first doubt has to be negative, then it works for us as double doubt even in the negative case, and if the first doubt is positive, then even if below it is negative, that also works as positive? No, no—

[Rabbi Michael Abraham] No, I was talking about the opposite, exactly. I’m talking about the first doubt. The first doubt is a balanced fifty-fifty doubt, and under the prohibiting branch there is a split that is a majority toward prohibition, okay? So if the upper doubt were a positive doubt—

[Speaker A] then

[Rabbi Michael Abraham] we simply do the probability calculation, so that’s fifty percent for permission and fifty percent for prohibition, from which there are another ten percent for permission, so in practice there is sixty percent for permission. Once there is a calculation there is no formalism—sixty percent for permission, you have a majority for permission, you are permitted. But if the first doubt is a negative doubt, then you have no calculations. That is where the formalism comes in. If the second doubt is a doubt, even if it is negative, then you are allowed to go leniently even though in truth you may be mistaken. But if both doubts are negative doubts and yet they are doubts, not majorities, then one may go leniently. But if the first doubt is negative and the second is a majority toward prohibition, then you do not join the minority for permission with the fifty percent permission over there, because there is no fifty percent permission there; it is fifty percent negative, not positive. In such a situation, we do not permit. That’s what I asked, Rabbi. I

[Speaker A] said that in the case

[Rabbi Michael Abraham] And if the first doubt—it doesn’t matter. If that’s what you meant, then we agree; no point making this more complicated.

[Speaker H] Fine, so it comes out in the conclusion too that basically a double doubt, when balanced, is basically like a majority, there is no difference.

[Rabbi Michael Abraham] A doubt—no, a positive double doubt is like a majority, that is the conclusion. The whole concept of double doubt does not deal with positive doubts. If they were positive doubts, I am not interested in double doubt or any structure at all—just give me the bottom line. If there is a majority for permission, go with permission; what do I care whether it is double doubt or not? Right? In the end, suppose there is a double doubt where both are positively balanced, okay? Then I have a calculation of seventy-five percent for permission and twenty-five percent for prohibition. So that is permitted not because of the law of double doubt, but because of the law of majority—there is seventy-five percent for permission. And therefore… therefore the claim is that even if it is fifty-fifty and afterward there is a majority toward prohibition—which from the standpoint of the law of double doubt does not help—but from the standpoint of majority law that is fine, because it gives me a majority for permission. And once the majority is positive, it operates by the laws of majority, not by the laws of double doubt. And under the laws of majority you can permit even if the second is a majority toward prohibition.

[Speaker H] I understand. Meaning, a majority of a majority is already another stage, as it were? Right, it is basically certainty.

[Rabbi Michael Abraham] A majority of a majority is what we discussed in previous lessons, and we already saw the same phenomenon there.

[Speaker H] And that is just greater certainty, as it were? It’s simply a higher probability? Right. But it is always on the same probability scale? Exactly. Regardless of the question of the “sides,” because many people talk about sides in double doubt.

[Rabbi Michael Abraham] Wait, wait, I’ll get to sides in a moment—no, soon, we’ll get there, I’m already getting to sides. So that is a very important point.

[Speaker E] And that is what the Shev Shema’teta basically

[Rabbi Michael Abraham] says, after he finishes quoting Rivash. Here: “Rivash has enlightened our eyes, that there is room to discuss this in terms of majority: for even if the sides are not balanced, the minority joins the half and becomes a majority. And this is specifically where it is known from the nature of the world that it is half and half; then even the minority can join to make a majority. But where it is not from the nature of the world, but merely that this is possible like that”—a negative doubt—“then we discuss it in terms of double doubt, and we require that both doubts be equal and balanced.” If the first doubt is a negative doubt, the next junction must also be a doubt and not a majority toward prohibition. A majority toward prohibition will not work. It needs to be a doubt, or of course a majority toward permission, then there is no problem. Because the calculation of the… You cannot make the probability calculation. And if you cannot make the probability calculation, then we have the formalism: doubt stringently, double doubt leniently. When we have probability calculations, when we are dealing with positive doubts, then we do the calculations; there are no laws. The laws are irrelevant. Suddenly doubt, double doubt—just give me the probability calculation, and that’s it. We follow the majority. So here I found maybe the clearest expression of this distinction between positive majority and negative majority, and it is a distinction that is at the root of all these topics. And so many people miss it, which is why I am dwelling on it, because it is very important to understand this. Now I want to discuss for a moment, with the time I have left, what the law of double doubt actually is. People ask: if a Torah-level doubt is treated stringently, why does a double doubt go leniently? Already among the later authorities, and already among the medieval authorities, they ask this. Now just from the question itself, notice. What is the question? I don’t understand. An ordinary doubt is fifty-fifty, so we go stringently. A double doubt is a majority for permission, so we go leniently. What is the question? The moment you ask the question, and look for an explanation why with a double doubt we go leniently, it is clear that you are talking about a negative doubt. Then you have no probability calculation. And then basically the question is: one doubt and a double doubt are both situations of doubt, and you do not know how to make the probability calculation. You have two sides—either it is forbidden or it is permitted—and you have two sides that are both possible, so you are supposed to treat them as fifty-fifty. So why, why do you go leniently with a double doubt? Do you understand that this whole question of the medieval and later authorities rests only on the assumption that the doubts are negative doubts? Because with a positive doubt there is no room for the question why one is lenient with double doubt. One is lenient with double doubt because it is by the law of majority. There is seventy-five percent for permission, and there is no need for the law of double doubt; there is the law of majority—“incline after the majority.”

[Speaker F] And what really is the answer to their question in a negative majority case?

[Rabbi Michael Abraham] Wait, we’ll get there, slowly. I’m saying the question itself shows that we are talking about a negative doubt. A positive doubt is not a law of double doubt at all; it is a law of majority. And many later authorities are mistaken in this, because they think double doubt operates by statistical majority. That is incorrect. Double doubt is in negative majority, and in negative majority there is no statistical majority, as the Shev Shema’teta and Rivash are saying now. So what is it, then? Why does it nevertheless work on a negative doubt? There are two main approaches among the medieval authorities. In Maimonides’ view, many explained—Rashba already explains it, I think—that Maimonides says a Torah-level doubt treated stringently is a rabbinic law. So if I have a double doubt, then I have a doubt whether to be stringent rabbinically; that is a rabbinic-level doubt, so we go leniently. Again, this is a formal rule. We have no probability calculation. If we had a probability calculation, the whole discussion would not begin. But if we do not have a probability calculation, then we are talking about formal rules. So with one negative doubt, the rule is that one goes stringently on the rabbinic level. If on top of that there is another doubt—right, whether under him or not under him—then rabbinically we go stringently. But even on the side that it was under him there is a doubt whether by coercion or willingly, so I have a doubt whether there is an obligation to be stringent rabbinically. That is a rabbinic doubt, so one may go leniently. That is Maimonides’ view. Rashba himself says—he holds that a Torah-level doubt is treated stringently by Torah law. So he cannot explain that double doubt is a rabbinic doubt. According to him it is a Torah-level doubt, not a rabbinic one. So why indeed do we go leniently with a double doubt? Rashba says: it is by the law of a majority of sides. Rashba says this in Bedek HaBayit. He says it is by the law of a majority of sides. There are three sides for permission and one side for prohibition, so there is a majority of sides here. Many people mistakenly think this means a statistical majority. It does not. A majority of sides is not a probabilistic majority; it is a majority of sides. There is a side—three sides for… say, whether under him or not under him, and if under him, whether by coercion or willingly. So let’s count sides. What are the sides for prohibition? If it was under him willingly, right? That is a side for prohibition. If it was under him by coercion, that is permission; not under him willingly, permission; not under him by coercion, also permission. Three sides for permission, one side for prohibition—we follow the majority of sides. This is not the law of majority; it is the law of double doubt. Many people ask Rashba: why do you need the law of double doubt? After all, we already have the law of majority. That is a mistake. Because the law of majority applies only to positive doubts. With negative doubts you do not have a majority here; you do not know how to do the calculation. The novelty of the law of double doubt is that even by counting sides you can follow the majority.

[Speaker F] Why?

[Rabbi Michael Abraham] It is a rule, a formal law, like the law that a Torah-level doubt is treated stringently. With a majority of sides one may go leniently.

[Speaker F] What is the logic of that?

[Rabbi Michael Abraham] The logic is that you see it as though there were a majority here, just as with negative sides you see it as though it were fifty-fifty. So here there are four negative sides, three against one, and you see it as though it were a majority. Same thing.

[Speaker A] It comes out that according to Rashba, there is no such thing as double doubt at all; there is only either majority or…

[Rabbi Michael Abraham] Double doubt is another kind of majority—it is a majority of sides.

[Speaker A] Right, so for him double doubt is…

[Rabbi Michael Abraham] But many people are mistaken because they say, “So wait, according to Rashba why do you need the law of double doubt? We already have the law of majority.” No, it is not the ordinary law of majority. The ordinary law of majority is when you have a majority and can tell me that it is more than fifty percent.

[Speaker A] Meaning in a double

[Rabbi Michael Abraham] doubt where both doubts are negative, you cannot tell me that it is over fifty percent. It is not at all certain, as Rivash said. It is a law of the Torah that we follow a majority of sides, and that too is considered a majority. That is the law of double doubt: that a majority of sides is also a majority.

[Speaker H] But can I look at it—can I apply the law of a majority of sides also in a case where I know it is a positive doubt? You can, but it is unnecessary, because it is already permitted to me by the law of majority, because

[Rabbi Michael Abraham] you already have a statistical majority, so by the law of majority you are lenient.

[Speaker H] But I saw that they discuss, for example, “we do not follow the majority in monetary law,” but maybe in double doubt we would?

[Rabbi Michael Abraham] It depends what kind of double doubt it is—negative, positive—we need to see the case.

[Speaker H] But if in monetary law you do not follow the majority, then there is no chance that with double doubt, in the best-case scenario, you only get to majority—you don’t go beyond it, even according to what the Rabbi is saying now.

[Rabbi Michael Abraham] Right, it could be that the law of

[Speaker H] double doubt was also innovated in monetary law. Why not?

[Rabbi Michael Abraham] No, what I’m saying is that if double doubt at most reaches the law of majority…

[Speaker H] No, what do you mean “at most reaches”?

[Rabbi Michael Abraham] It is like majority, but it is the law of double doubt.

[Speaker F] It is a different law from the laws of majority. He said that a majority of sides is like a majority, but it comes from the laws of double doubt, not from the laws of majority. It is a different law.

[Rabbi Michael Abraham] Whether it was said regarding money or

[Speaker F] no, that’s a separate discussion. Meaning, maybe we say “majority of sides,” but not because of the statistical claim, as it were—not because most likely that is the case. Right, rather this law of double doubt, that we follow a majority of sides, was said also in monetary law. Rabbi, but still, if it’s a formal rule and it’s not a law given to Moses at Sinai, these are human beings who sat and thought about it and said it was reasonable. Reasonable, just with Torah-level implications—fine, so what? So that means what determines things is not reality, but what we feel. We really feel that the majority is… you understand, it’s not a matter of statistical calculation.

[Rabbi Michael Abraham] I’ll translate what you call “we feel” into “intuition,” and we’ll come back again to the same side. Alright friends, we’ll stop here. If there are comments or questions, you can ask.

[Speaker A] By the way, apropos of the supposed mistake of the sages in the Talmud about the cow giving birth—in Bekhorot it says that the sages determined that a cow does not give birth until age three. There, in the case of a gentile’s cow, which is transferred for firstborn issues. So? Nowadays at thirteen or fourteen months it already gives birth freely.

[Rabbi Michael Abraham] Okay—either nature changed or the species changed.

[Speaker A] No, no, it depends on weight, the weight of the cow. Today it reaches three hundred and fifty kilos.

[Rabbi Michael Abraham] I think that this knowledge was reasonably available to them, because this is not some new knowledge—any cattle herder can tell you that. So I don’t know; either nature changed, or there was some such large majority, or I don’t know exactly. Fine, but it doesn’t concern us. Mistakes of the sages are not our topic. There were mistakes—obviously there were mistakes.

[Speaker H] Okay, anyone else? Yes, Rabbi, regarding what I asked at the beginning—this was with several stores, let’s say, where the distribution is such that one store puts out more pieces of meat. Suppose there are three stores, and one store is huge, so if you really sum the probabilities, it is like a majority against the sides. So is there a possibility that we would actually rule according to the sides even though it is against the majority? Or not?

[Rabbi Michael Abraham] So I’m saying, this is a dispute among later authorities. There are many later authorities who follow the larger store and not the number of stores, so they apparently understand that we follow the distribution. But I already explained that in the law of stores and in the law of an available majority, it is not really a statistical majority. The number of stores does not really determine the probability. The question is how it got lost, the thickness of the bags in each store, and all sorts of things like that, so it is by no means certain that it is connected to probability. I understand. Rabbi, I just wanted… But Rabbi Shimon Shkop, when he says that an available majority is not probability, there he speaks—and I’ll discuss this at the beginning of the next lesson—there he speaks about a majority of sides. He claims that with an available majority, what was innovated there is the idea of a majority of sides. Because basically each store casts a side onto the piece of meat. That is nine sides for permission and one side for prohibition—not because of probability but because I don’t know the source, which is negative, so I count sides and follow the majority of sides. And therefore I said that whoever said earlier—I think it was Shmuel—said earlier that double doubt or majority of sides we derive from logic and not from a verse, and I said I’m not sure. I’m willing to assume that, but not sure, because it could be that an available majority is the source, and for an available majority they bring a source from a verse from the court.

[Speaker H] Thank you very much.

[Speaker A] Wait Rabbi, I want to go back a bit to the double doubt of a gentile regarding wine: whether he touched it or did not touch it, and if there’s a doubt whether a gentile even opened the barrel. Is that positive or negative?

[Rabbi Michael Abraham] Completely negative, as you are describing it.

[Speaker A] No, that’s an example they bring as a standard double doubt. It depends on the circumstances.

[Rabbi Michael Abraham] If you know—if you have information about the quantities of people around here, that there are fifty percent gentiles and fifty percent Jews, then the doubt whether it was a gentile or a Jew is a positive doubt, and the doubt whether he touched it or did not touch it is a negative doubt.

[Speaker A] Right, so here you have one positive and one negative. Right, so because of that it will be permitted, because it joins with the positive, double doubt.

[Rabbi Michael Abraham] Even two negative doubts are a double doubt and are permitted, so certainly if one is positive and one is negative it will be permitted. The negative one only makes a practical difference if the other is a majority toward prohibition. Okay, fine.

[Speaker A] Okay, good.

[Rabbi Michael Abraham] Thank you very much.

[Speaker F] Rabbi, do you have the energy for a question from the fruit series, or is that a bit…

[Rabbi Michael Abraham] Of course, yes, please.

[Speaker F] I listened to the Rabbi’s lectures at Bar-Ilan over the past few weeks, so one thing the Rabbi talked about there, for example, was this paradox: whether God can make a stone that He can’t lift. So the Rabbi said that this is meaningless babbling. As if—you haven’t actually asked any question. Explain the question, and then I’ll answer. But for example, when the Rabbi talks about free will, the question of foreknowledge and choice, then the Rabbi said yes, God can limit Himself and not know what I’m going to choose. Meaning, if God wants and says, I don’t want to know…

[Rabbi Michael Abraham] I said exactly that I do not agree with that explanation. After all, my words are written in the series “The Perplexed” on foreknowledge and choice—I reject that completely. I brought the Or HaChayim on Genesis chapter 6, where he writes that the Holy One, blessed be He, denied Himself the possibility of knowing, and I said that this solves nothing. Okay.

[Speaker F] One more small question, Rabbi. When the Rabbi also spoke—he also talked about this in the weekly series… at Bar-Ilan from last Saturday night—about this issue of his debate with David Enoch, and then he added things in supplements and so on. So the Rabbi always told us that the prescriptivity of the moral or normative command is part of the whole point. That if a person says, yes, I know it says “Do not murder,” but why not murder? then you haven’t understood what “Do not murder” means. Right.

[Rabbi Michael Abraham] Yes, but here, in this week’s series, I know that it says to him “Do not murder,” and I ask myself why not murder—that’s not a problem at all, because he did not know that what is written is binding. But if I understand that there is a binding moral command not to murder, then there is no question of why not murder.

[Speaker F] So in order to know the “Do not murder,” that also means knowing the prescriptivity of the command, right? So why, when the Rabbi says that morality is—he presented it as logic, as something

[Rabbi Michael Abraham] That belongs to all logic?

[Speaker F] So if it exists and God

[Rabbi Michael Abraham] Let’s say were not obligatory—he already asked me this on the website and I answered him. I’ll tell you briefly. The claim is that a person who reaches the conclusion that there is a binding morality cannot ask himself, wait, but why obey it? But the fact that you reached the conclusion that there is a binding morality means that behind it sits a belief in God. Because without belief in God, you cannot hold the position that there is a binding morality. Why? Because without God there is no binding morality.

[Speaker F] That’s really something—after all, the Rabbi doesn’t know something about God that maybe—well, I don’t claim to—but I have the feeling that the Rabbi doesn’t know something about God that I don’t know, or that David Enoch doesn’t know. And yet David Enoch is committed to the moral command, and the Rabbi is also committed. So what is the Rabbi saying—no, because I know something about God?

[Rabbi Michael Abraham] No, the claim is that he is mistaken; he believes.

[Speaker F] But what does he know about God? After all, both of them, both the Rabbi and David Enoch, don’t know something about God that I also don’t know.

[Rabbi Michael Abraham] I know that He makes the moral command binding because I hold the view that the command is binding.

[Speaker F] But if we remove the moral issue from the matter, what do we know about God? That at most He created the universe. That’s the maximum we know about Him. And that doesn’t obligate me in anything; that’s completely the classic is-ought gap.

[Rabbi Michael Abraham] Why should I care whether you think that His being the Creator is enough to make Him binding or not? I think so; you can decide whatever you want.

[Speaker F] But that’s a fact—it’s completely a classic naturalistic fallacy. What does that have to do with anything? How does the fact that He created a world obligate me? The world is so hard and incomprehensible, and on the contrary, if the world by itself were anything, it would be a reason not to obey.

[Rabbi Michael Abraham] So what? Excuse me? Because I am obligated to the One from whom I came.

[Speaker F] And who said it was good for me that He created me?

[Rabbi Michael Abraham] I didn’t say it was good. It’s gratitude.

[Speaker F] On the contrary, in some sense He is to blame for bringing me into the world.

[Rabbi Michael Abraham] He is to blame for the fact that He

[Speaker F] brought me

[Rabbi Michael Abraham] into the world—and that doesn’t mean I don’t have to obey. Gratitude is a moral obligation. Not because He did me good. “It would have been preferable for a person not to have been created than to have been created”—they debated and concluded that. That’s it.

[Speaker F] No, so

[Rabbi Michael Abraham] I wrote in my article about philosophic gratitude. It is not based on gratitude in the usual ethical sense. It is metaphysical gratitude. If I came from His power, then what He wants obligates me. Why? I came from Him, and I am very upset that He created me. Because I am from Him. He—I, my whole being—is only because of Him.

[Speaker F] And it’s a shame I’m here.

[Rabbi Michael Abraham] Fine. If you do not accept that reasoning, then you do not accept that reasoning.

[Speaker F] Okay. No, I’m trying to understand it.

[Rabbi Michael Abraham] No, it is a basic reasoning. I do not know how to ground it in prior principles. It seems self-evident to me, but it is a basic reasoning. Okay, thank you very much. Sabbath peace, good night.

[Speaker C] Thank you very much.