Uncertainty and Probability—in Halakha, in Jewish Thought, and in General—Lesson 42 – Rabbi Michael Abraham

Table of Contents

• A model of decision nodes, double doubt, and majority
• Negative doubt and positive doubt
• Negative majority and positive majority, a majority present before us and a majority not present before us
• “Better to dwell as two,” social reality, and women’s surveys
• Permitting agunot: formal leniencies and practical stringencies
• One witness, certainty, and the judge’s conviction
• Water with an end and water with no end
• Two majorities: the source in Kehillat Yaakov and Rabbi Chaim of Volozhin
• Use of two majorities by Rabbi Ovadia Yosef
• Tosafot in Yevamot, a young Torah scholar, and the distinction of the Chazon Ish
• The dispute between the Chazon Ish and Rabbi Ovadia over the meaning of water with no end
• Rabbi Herzog and two majorities that are not multiplicative

Summary

General Overview

The text presents a model of “decision nodes” in order to understand the laws of doubt, double doubt, and majority, and it distinguishes between positive doubt, which arises from information, and negative doubt, which arises from lack of information. It then applies similar distinctions to positive majority and negative majority as well. In the context of permitting agunot, it argues for a fundamental distinction between formal obstacles in the laws of evidence, where the Sages were very lenient, and practical obstacles in clarifying the reality of whether the husband died, where they are stringent and require a high level of certainty because of the severity of the status of a married woman and the consequences of error. It then presents the method of “two majorities” as a mechanism for leniency in certain situations involving water with no end, brings examples of its use by various halakhic decisors, presents the Chazon Ish’s opposition to creating such a leniency without an explicit source in the Talmud, and lays out a fundamental dispute over whether the prohibition of water with no end should be seen as a local stringency that ought to be limited, or as a principled rule that one does not rely on majority to permit an agunah. In the end it presents a critique of imprecise use of “two majorities” when the majorities are not in a multiplying chain but are parallel and do not reduce the minority.

A model of decision nodes, double doubt, and majority

The text describes nodes in which each node can either be an even doubt, “fifty-fifty,” or a node of majority, where one possibility is more likely than the other. In a situation of double doubt, a double branching is created, so that probabilistically one gets “twenty-five percent toward prohibition and seventy-five percent toward permission,” and therefore one permits—while qualifying that the issue is “not so simple” and will return later. In a case of majority, different combinations can arise of majority toward prohibition or permission at different nodes, and this can create situations where the ruling is unclear, or precisely clear.

Negative doubt and positive doubt

The text distinguishes between positive doubt, where there is positive knowledge that the two possibilities are equal, such as a fair coin where it is known that the chance of heads and tails is equal. The text presents negative doubt as a case where there is no information at all, and even if in practice equal weight is assigned to both possibilities, that equality is set “out of ignorance, not out of knowledge,” and so it is a different kind of doubt. The text notes that this distinction will have implications later in the context of double doubt as well.

Negative majority and positive majority, a majority present before us and a majority not present before us

The text states that a majority in essence rests on some kind of knowledge, because if there is no knowledge the assumption is an even doubt and not a majority. But in many cases people do not know the exact size of the majority, and so this is a negative majority. The text argues that the Sages did not have “measuring tools” and statistics, and therefore a majority not present before us in their world is generally a negative majority based on general impression, such as “most women are not infertile,” without knowing the percentage. The text explains that a majority present before us, like “ten shops, nine kosher and one non-kosher,” is more like a positive majority because the ninety-ten distribution is known, though even there there are assumptions about separation that are not necessarily correct. The text notes that in our time it is possible to measure statistically, to check whether the majority the Sages established really exists or has changed, and even to turn a negative majority into a positive majority through data.

“Better to dwell as two,” social reality, and women’s surveys

The text gives as an example the use of the assumption “better to dwell as two” in contexts of annulment of betrothal, and argues that we all know this is factually untrue today, because many women reject matches and remain single even when options exist. The text proposes dealing with conservative conceptions about the eternal factual status of statements in the Talmud by means of an orderly survey that would examine “what a reasonable woman expects from her partner” and which defects nullify consent. The text includes a discussion with a questioner who struggles with the logic of “better to dwell as two” when there are other men in the world, and the text responds that it is a good question but not one that touches the core of the argument about the reality of our time. The text notes that the claim was ruled on by halakhic decisors, but defines it as “a factual claim, not a halakhic one,” and therefore says it must be checked against reality, rejecting the idea of “authority” with regard to facts.

Permitting agunot: formal leniencies and practical stringencies

The text describes an apparent contradiction in the laws of permitting agunot: on the one hand there are major leniencies, such as accepting one witness, the testimony of a woman and of a non-Jew, and leniency regarding disqualified witnesses; on the other hand there are stringencies such as “water with no end,” where they are concerned even when it seems clear that the husband died. The text explains that the key is the distinction between formal obstacles in the laws of evidence and practical obstacles in clarifying reality, and that the Sages “erased” formal obstacles only when there is factual certainty that the husband died. The text argues that the Sages are not uprooting the prohibition of a married woman through positive action, but rather permitting within the framework of the laws of evidence, so that when the husband truly died, the woman is not a married woman. The text emphasizes that the stringencies stem from concern about mamzerim and the possibility that “the supposedly dead man may come back on his own two feet,” while on the other side there is the heavy distress of an agunah, and therefore the solution is to require factual certainty together with formal leniencies.

One witness, certainty, and the judge’s conviction

The text argues that the difference between one witness and two witnesses is not necessarily the difference between uncertainty and certainty, but rather “a formal threshold” that the Torah sets at two, even though in practice full conviction can also arise from one witness. The text brings the example of “one witness is believed in matters of prohibition” and emphasizes that permission based on one witness for agunot is an option available to the judge, and if the judge is not convinced, he will not permit it even if formally the possibility exists. The text notes that even with two witnesses there can be a “fraudulent case,” and if there is no conviction, that will not help either.

Water with an end and water with no end

The text defines water with an end as a situation where one can see all the banks of the body of water, and therefore if they did not see the husband come out, “he probably drowned,” and they permit even without identification of a body, as circumstantial evidence that creates certainty. The text defines water with no end as a situation where one cannot see all the banks, and therefore there is concern that he came out in a place that was not visible, and so “in water with no end one does not permit the woman.” The text notes that the accepted rule is that this is “a rabbinic law,” and mentions the Talmud’s reasoning of “because of caverns,” while raising a difficulty in light of the approach according to which the main thing is the judge’s certainty and not formal rules. The text notes that many halakhic decisors add “supporting factors” in order to permit even in water with no end, and in particular it is argued that today “there is mail and there is a telephone,” so if he had come out, “we would have heard about it,” but it is still said that water with no end by itself is not enough. The text raises the suspicion that water with no end functions as “a red flag” so that people should not “go wild” in permitting agunot and should remember that “this is not ownerless territory,” along with a discussion with questioners about rabbinic decrees and safeguards such as poultry with milk.

Two majorities: the source in Kehillat Yaakov and Rabbi Chaim of Volozhin

The text presents the “leniency of two majorities” as a relatively late leniency with no source in the medieval authorities (Rishonim), and gives as its first source the responsa Kehillat Yaakov, section 9, in the name of Rabbi Chaim of Volozhin. The case described is of a man who fell from a high bridge onto ice and from there into water and disappeared, and Rabbi Chaim “inclined to permit on the basis of two majorities,” combining a “majority toward death” from a fall from a significant height together with the majority that those who drown in water with no end die. The text illustrates the logic by means of a probability tree in which, in order to be stringent, one has to combine two minorities, and therefore one gets a relatively small probability that he is alive. The text suggests the possibility that Rabbi Chaim also relied on the fact that water with no end is a rabbinic law, so that a “rabbinic doubt” is created with respect to the stringency, and therefore one can be lenient.

Use of two majorities by Rabbi Ovadia Yosef

The text brings a case of an air force pilot whose plane was struck by a missile and crashed into the sea; neither the plane nor the pilot were found, and another pilot tracked him and did not notice any ejection and searched the crash area. Rabbi Ovadia uses two majorities: a majority that the pilot was killed in the crash, and even if we assume he ejected without the second pilot noticing, then in falling into the sea this is water with no end, where “most who drown die.” The text notes that at first glance one could see here even three majorities, but says that later it will be argued that not so, and the leniency is presented as a common mechanism for adding a “supporting factor for leniency” in cases of water with no end.

Tosafot in Yevamot, a young Torah scholar, and the distinction of the Chazon Ish

The text brings the words of the Talmud in tractate Yevamot about water with no end, and the distinction stated there with respect to “a young Torah scholar,” that “if he came out, word would spread,” along with the Talmud’s rejection that initially one still does not permit. The text cites Tosafot, who emphasize that despite the addition of another majority of “if he came out, word would spread,” still “she should not marry ab initio,” and the Pitchei Teshuvah raises a difficulty from here against the leniency of two majorities. The Chazon Ish answers that the case in Tosafot is not two majorities toward death, but one majority toward death and a second majority that indicates belonging to the majority, and it is not “another cause that kills.” But the Chazon Ish concludes that one should not create a leniency that is not explicit in the Talmud, and that “there is no distinction between one majority and two majorities.” The text includes a discussion of the underlying factual question of “if he came out, word would spread” as dependent on one’s assessment of reality, and presents the position that there is no “authority” for a factual determination; rather, it is tested in reality.

The dispute between the Chazon Ish and Rabbi Ovadia over the meaning of water with no end

The text presents the Chazon Ish as understanding that water with no end teaches that the Sages said not to rely on majority in order to permit an agunah, and therefore even two majorities do not change things, because in the end it is still majority. The text presents Rabbi Ovadia as seeing the prohibition of water with no end as an “extra stringency” concerned with an “uncommon minority,” and therefore saying, “let us not add to it,” and in a case of two majorities, “they did not decree.” The text presents a probabilistic formulation according to which two eighty-twenty majorities create ninety-six percent toward death, and then argues in the name of the Chazon Ish that even ninety-six percent is still only a majority, which is insufficient in water with no end, whereas Rabbi Ovadia bases himself on limiting the rabbinic novelty rather than expanding it.

Rabbi Herzog and two majorities that are not multiplicative

The text brings a case from Rabbi Herzog in Heikhal Yitzchak about a Jewish pilot in a South African plane that crashed in World War II in 1944, and Rabbi Herzog writes that the breaking of the airplane and its fall is “a majority toward death,” and the fall into the sea adds “another majority,” and one should discuss it on the basis of two majorities. The text argues that in the simple understanding this is not a multiplying double majority but two parallel majorities: either he fell on land with a majority toward death, or he fell into the sea with a majority toward death. Therefore the minority possibility that he is alive remains of the same order of magnitude and is not reduced by multiplication. The text explains that two majorities in the sense of “the majority of a majority” requires a tree in which one majority reduces the minority within an additional track, and it does not apply when the upper node does not add relevant information but only divides the cases by location. The text ends by pausing for questions and announcing, “Shabbat shalom” and “Goodbye.”

Last time I spoke a bit about nodes—decision nodes, or combinations of decision nodes—where each such node can be a doubtful node, say fifty-fifty, and also a node of majority, where the two possibilities that come out of the node are not equal, one is more likely than the other, and so on. And we saw, we saw that in situations of double doubt, then we basically have a double split, and so probabilistically, if we see each such node as fifty-fifty, then probabilistically we have twenty-five percent for prohibition and seventy-five percent for permission, or one side toward prohibition and three sides toward permission, and therefore we are lenient. That is in double doubt. We’ll still get to double doubt, and it’s not so simple, but for now, in the case of a majority, we saw that there can be combinations that lead to different results. The question is whether it’s a majority toward prohibition versus permission in both nodes, or in one of them it’s a majority toward prohibition and in the second a majority toward permission, or the opposite, and that can create situations where the permission is unclear, the prohibition is unclear, or situations where it’s clearly toward permission or toward prohibition. In the case of majority, the story is more complicated. I mentioned the distinction we made in the laws of doubts, and afterward I expanded it also to the laws of majority, between a negative doubt and a positive doubt. I said that a positive doubt is a doubt in which I have positive information that the two possibilities are equal. For example, with a fair coin. A fair coin—I know that if I know it is fair, then I know that the chances of heads and tails are equal, fifty percent for each. That is a positive doubt. I still don’t know whether it will land on heads or tails, but the chance of heads and tails is fifty percent, and that determination comes out of knowledge—I simply know that the coin is balanced, fair. As opposed to a coin about which I have no information at all. I know nothing. It could be fair, it could be unfair toward heads, unfair toward tails, eighty percent, twenty percent—anything. In short, I know nothing. Still, on the probabilistic level I would assign equal weight to heads and tails because there is no reason to prefer one over the other. In that case too, I would still regard it as an even doubt, fifty-fifty, but it is clear that the fifty-fifty odds are odds determined out of ignorance, not out of knowledge. Therefore I call that a negative doubt. It’s a doubt because of lack of knowledge. If I have no knowledge at all, then I say the two possibilities are equal. It’s a different kind of doubt. We’ll see implications of that also in the context of double doubt later on. But right now I want to move on to majority, because that’s our topic now. And with majority too, I said that in principle a majority is, in its essence, a majority based on knowledge. Because if I have no knowledge, then the assumption is that this is not a majority but an even fifty-fifty. If I have two possibilities about which I have no knowledge at all, then basically the assumption, as I explained before, is that this is a negative doubt. I still treat it as fifty-fifty. The moment I treat it as a majority, that means I have knowledge. In other words, I know the possibilities are not equal, I know that one possibility is preferable to the other. And still, I said, true, I have some knowledge. That knowledge takes me out of the category of doubt, but it doesn’t mean I already know the distribution—whether it’s eighty-twenty, seventy-thirty, ninety-ten, what the distribution is. I don’t know whether it’s a small majority, a large majority, fifty-one percent, ninety-eight percent—I don’t know. Therefore one can speak of majority, and in the context of majority too one can speak of a negative majority and a positive majority, even though in the background of a majority there is always some level of information. If there were no information, it would be doubt, not majority. So there is some level of information: I know that option A is preferable to option B, but I don’t know by how much it is preferable, and therefore this is a negative majority. In most cases, yes, in most cases the majority we deal with is a negative majority. The Sages did not have measuring tools; there wasn’t even a culture of measurement at all—to measure what the probability is, how many aylonit women there are in the population. They didn’t do statistics and say there are seven percent of women who are aylonit. They only knew, from general impression, that most women are not aylonit. What does that mean, how much is that majority? Ninety-three percent? Fifty-one percent? Seventy? I don’t know. Now, I don’t know—even though in principle you could do the measurement—but the Sages didn’t do it. And since they didn’t do it, then for us, in practice, the simple assumption regarding almost any majority you can think of is that it’s a negative majority. I’m talking about a majority not before us. A majority before us is, in a certain sense, a positive majority, because if I have ten stores and I know that nine are kosher and one is non-kosher, then I have information that ninety percent is kosher and ten percent is not kosher, and therefore to a large extent this is basically a positive majority. But a majority not before us is a majority that is usually negative. In our own time, since the culture has changed and the tools are stronger, we have more tools for measurement, for doing quantitative research, so we know how to identify a representative sample, how to neutralize various influences, we have better statistical information. So there would be room—there is room—to try to measure the various majorities that the Sages established, and first, to see whether it is really a majority or not a majority at all, or whether it changed, or whether the Sages were mistaken—it doesn’t matter—for various reasons. Another possibility is to discover that the majority is eighty-twenty. In other words, to turn it from a negative majority into a positive majority. Yes, I don’t remember if I mentioned this, but there is—when I was involved in annulling marriages—I think I mentioned it—when I was involved in annulling marriages, I had contact with various women’s organizations that work on behalf of women denied a get and the like, and I told them that in my opinion one of the most basic and important projects in this matter is to conduct a proper survey of what a reasonable woman expects from her partner. What kind of partner she is willing to accept and what kind she is not. Because the assumption that often stands in the way when people come to annul marriages—because when we come to annul a marriage, we do it because it turned out there was something in the husband that the woman did not know about, or something appeared in him, or something like that, of which she was unaware, and therefore on that basis she did not consent. That is basically the main path for annulling a marriage. Now the problem with this is that usually they quote the Talmud in Bava Kamma on page 110, I think, where the Talmud says that it is better to dwell as two. What does that mean? A woman consents to any partner. She wants a relationship; she doesn’t care what kind of partner—whatever, however bad, doesn’t matter right now. And since that is so, once you want to annul the marriage and you say no, if she had known this was the partner she would not have consented, then they tell you: what are you talking about? The Talmud says that a woman consents to any partner. In other words, it is better to dwell as two. Now, we all know this is not true. In other words, what is written in the Talmud—with all due respect, it is written in the Talmud—but we know that factually it is not true. I mean, yes, ask women around you, and obviously they won’t tell you that they are willing to accept any relationship. In fact, many women remain unmarried until an older age, and maybe until the end of their lives, and not only because there was no one willing to marry them; very often they too reject potential partners. That shows us that women are selective, meaning they are not willing to accept—at least today—they are not willing to accept just any partner. And therefore the claim brought from the Talmud is really a claim based on an error. What do I mean by error? It could be that the Talmud was right for its time, I don’t know, I wasn’t there. But for our time it is obviously not correct. Now, in order to convince people who believe in the sanctity of the Talmud and that the Talmud never errs even in facts, and that the facts the Talmud determines are always eternal too, of course, and never change—in order to fight these strange perceptions, I think the easiest way is simply to conduct a survey. To do statistics among women and present data and see what percentage of women do not consent to a husband like this, to a husband like that, to a partner like this. Rabbi, apropos that claim—just, this is a chance for me to clarify it because it’s been bothering me. What does “better to dwell as two” and “better than widowhood” mean? Is that only in a situation where she has no other option, where this is the last man left in the world, everyone else flew off to another world, so then maybe you can say it applies. But if she has other options—what does “better to dwell as two” mean when she has options? He’s not the only man. There are others. How is that relevant? And also in the Torah, with Rebecca for example, when they said, “Let us call the young woman and ask her,” why ask her? What do you mean, ask her? She’ll take any man, obviously. I completely agree with the claim, but for our purposes it’s not important, because we—we’re talking about a specific partner. So for us, this is the partner there is. Yes, but who says she prefers to dwell as two specifically with him? There are a few billion other men in the world. What do you mean? You mean she would basically want to go back and— No, if she had known in advance, not if she knew in advance. If she had known in advance that he had these flaws, then she would not have consented and would have counted on there being another partner. Obviously, obviously. I understand. Where does this claim come from? The Talmud seems very strange to me here; I never understood it. Good question. I hadn’t thought of it. It really is a good question. Meaning, it doesn’t touch the essence of the argument, because I want to claim that even on the level where this is the last husband, many women would still not consent if he were a very, very unsuitable partner—each according to her own parameters. So that’s my claim as a fact; regarding today I think that’s a correct claim. You’re right as to the passage itself—I don’t know, I hadn’t thought about it, one really has to think about it. Why do they assume this applies to any partner and not only to the last available partner? I don’t know, it needs thought. It’s a very good question. Anyway, anyway, for our purposes what I want to say is that if such a survey were done and solid data were presented—with rabbinic guidance and so on, never mind, so there wouldn’t be problems; you also have to know exactly what questions to ask. These are indeed somewhat delicate points: whom to ask, married women, single women, at what stage, what to ask—it’s quite a delicate matter, it needs rabbinic guidance and statistical knowledge. But after doing something like that and presenting the data, I think that at least some of the conservatives who cling to the eternality of the facts that appear in the Talmud would be willing to accept that all the same, a change took place here. I don’t know if all of them, but at least some of them. And therefore, in my view, this is a very important tool. I’m bringing it up here only as an example of this difference—that today we also have both a culture and tools to measure these layers and turn them into a positive majority, but among the Sages almost all the majorities were a majority not before us, yes? They were negative majorities. Okay? Rabbi, regarding the majority not before us that you mentioned—if it’s nine stores, then you assume it’s a positive majority, meaning you’re also assuming the distribution is equal among all the stores. Yes, we spoke about that when I discussed the difference between a majority before us and a majority not before us. You’re right, I expected that question. Obviously we still have assumptions there about separation from the stores—whether the probability of separating from each store is equal. And that very often is not true, by the way. So of course even there it isn’t really solid knowledge. You can’t really determine that the probability is ninety percent; not all the stores are the same size either. Yes, but still, there is some information there in the background. More information, kind of. Yes, there is some information there in the background. True, it’s not complete. In that sense it resembles a majority not before us, where there is some information but it is not complete. Meaning, it’s not doubt, so there is some information here, but it’s not full information because I don’t know how much the majority is. In a majority before us it’s even fuller, but not completely either—that is, in a majority before us it’s even more, but not one hundred percent. Right, so in that sense the boundary is really thin between a majority before us and a majority not before us. Okay, we discussed that when I gave lessons on the difference between a majority before us and not before us, and I spoke about exactly this point. Rabbi? Yes. Did the Mishnah Berurah rule “better to dwell as two”? Orach Chayim—what can the Mishnah Berurah do with that? In Even HaEzer… No, I mean, maybe in the time of the Talmud they said that, and it doesn’t necessarily have to be ruled as practical Jewish law. It is ruled as practical Jewish law by all the halakhic decisors. What do you mean? Not the Mishnah Berurah, because the Mishnah Berurah is on Orach Chayim, but it is ruled as Jewish law by all the halakhic decisors. I’m only claiming that the fact that it is ruled as Jewish law is very nice, but it has to be checked against reality, because that is a factual determination, not a halakhic one. Ah, so facts are something where you don’t necessarily have to act that way, so to speak. No. By the way, this is not a halakhic ruling, it’s a claim. A factual claim and not a halakhic one. Huh? What I’m saying is that this is a factual claim and not a halakhic one. Yes, yes—no, simply, it’s not really ruled. By the way, Soloveitchik claims—Rabbi Soloveitchik claims—that this is an overarching statement. Yes, yes, that it came down from Sinai, yes, I know. Yes, it’s really like laws, so to speak. They strongly disagree with him. I allow myself to doubt whether he himself believed that nonsense. Anyway, anyway, for our purposes. Rabbi disagrees with all the halakhic decisors who hold that this still exists today? Yes, obviously. What do you mean, disagrees with all the halakhic decisors? You’re talking nonsense. The facts are that it’s not true. The fact that they also do not think it’s true—it’s simply a kind of conservatism. They are not willing to rule against the Talmud because, I don’t know, because it seems Reform to them. I have no idea—feminist, or I don’t know exactly what. What? Even if the Talmud was formal? What does it mean, formal? That they had to obey it, so to speak. I didn’t understand. I mean, even if the Talmud—if the Talmud made that claim, and people had to obey the Talmud in its own time, so to speak. I didn’t understand what it means that they had to obey the Talmud. He means formal authority, formal authority. The Talmud has formal authority—so what does that mean? Why is that relevant here? He means that if the Talmud had written that this applies for all times, even if human nature changes, we still—the Talmud wrote it. Meaning, if according to—if I’m living in the time of the Talmud itself? No, I don’t accept that. It’s a factual error, clearly. No, but there’s an error here in principle. Like with lice, yes, lice that do not reproduce sexually. It’s not a matter of authority. Authority is a halakhic matter. All the claims of the Talmud that are not connected to Jewish law are just statements of the Sages, not reality itself. No, it is connected to Jewish law, except that it is a factual claim and not a halakhic claim. Yes, but in a factual claim there is no authority. A factual claim is facts; you have to check the facts. What does that have to do with concepts of authority? There is no such thing as authority with respect to facts. I understand. Authority applies to halakhic determinations. I discussed this in other series; let’s not get into it here. Anyway, so for our purposes, these nodes or the integration of these nodes that I described can occur both when each node contains doubt and when each node contains a majority. We saw the various possibilities that are created when the nodes contain majorities, and we distinguished between a negative and positive majority and between a negative and positive doubt. After that I spoke—it took me a long time, this summary—after that I spoke, I began speaking a bit about the permission of agunot. And I said that in the permission of agunot there are all kinds of inherent contradictions in the laws of permitting agunot: on the one hand, you find extreme leniencies; on the other hand, you find extreme stringencies. Yes, water with no visible boundaries and all kinds of things like that, where it seems obvious that the husband died and still we are concerned and do not permit the woman to remarry. And on the other hand, they permit one witness, and a woman, and a gentile, and all sorts of things—there are no disqualifications of testimony at all in this context, and so on. And I explained—and I also asked—how do the Sages uproot something from the Torah by positive action, and moreover permit a married woman, the most severe matter there is? So I said that the foundation for understanding all these difficulties in the laws of permitting agunot is the distinction between formal obstacles and practical obstacles. Meaning, if I know with certainty that the husband is in fact dead, but the evidence I have has formal defects—I have one witness, and according to Jewish law, regarding matters of forbidden sexual relations, fewer than two are insufficient; you need two witnesses. But let’s say I became very clearly convinced that this witness saw the husband dead, he saw his face clearly and he knows that the husband is dead. Okay? So factually I know that the husband is dead, but I have a formal obstacle because from the halakhic perspective there is no testimony in matters of forbidden sexual relations with fewer than two, and here I have only one witness. So the Sages erased the formal obstacles. They say there is no problem of hearsay testimony, testimony of a woman, whatever you want, everything is fine in the laws of testimony. But all that is only when I have complete certainty that the husband really died, because even a small chance that the husband is alive and I permitted the woman—and then that husband returns, yes, “the killed man came back on his own feet”—and the children are mamzerim and she is forbidden to both this one and that one, it’s a disaster story. So of course we are not willing to take risks in permitting a married woman in that sense. Those are the stringencies. The stringencies are to make sure that factually the husband is dead. The leniencies are always with respect to formal obstacles. That is essentially the point. And that also explains why the Sages did not uproot something from the Torah by positive action here, because they did not permit a married woman. The woman is not a married woman. They relaxed the laws of evidence, but they did not permit a married woman to remarry. So this double meaning, or this double aspect, basically stems from two things: first, the severity of the prohibition against a married woman. To permit a married woman unjustly is a step that Jewish law recoils from very, very strongly; there has to be full certainty. You remember Ron Arad and of course many other different cases. And on the other hand, the distress of the woman who is an agunah and whose husband is gone and she cannot remarry—that is a very great distress. So there are two sides here, both of them extremely difficult, both of them very weighty. And the solution the Sages found is the following solution: every formal obstacle, we erase it, provided we have complete certainty that the husband is dead. In that sense we are very strict. In other words, we require complete certainty that the husband is dead; we do not follow the majority as one generally does in Jewish law. It is inconceivable that if there is a fifty-one percent chance the husband died, we would permit the woman to remarry and then the husband would show up here. Okay? Meaning, it is obvious that we are not going to follow the majority here. We need some level of certainty here. And therefore, if factually we have certainty, we are not troubled by formal obstacles, but factually there has to be certainty. What? But certainty exists only if there are two witnesses. That’s part of certainty. I can’t decide that based on one witness I have certainty. No, that’s exactly what I’m claiming is not so. The difference between one witness and two witnesses is not that with two witnesses there is certainty and with one there isn’t. With three witnesses there is more certainty than with two; with five, even more. The Torah stops at two because that is some formal threshold. My level of persuasion can be complete even with one witness. For example, one witness is believed regarding prohibitions. With prohibitions, based on one witness I’ll eat pork—if there is meat that there is concern about, that it might be pork, one witness comes and says no, the meat is kosher. No problem. Based on one witness I can do that. That means one witness definitely has weight, and in certain cases at least he is enough to convince me one hundred percent. Of course if the judge was not persuaded, because there is something dubious about the witness or something like that, then he really would not permit the woman. The fact that they permit the woman based on one witness is only an option that Jewish law opens before the judges. But the judges can decide not to use that option. If this witness did not convince them clearly, then they will not permit the woman. Also with two witnesses, if it didn’t convince them, that won’t help either. With two witnesses too, right, it’s like a fraudulent case. Right. But with one witness we opened an option to permit the woman based on one witness. There are always options that are according to the strict law, and also options that are beyond the strict law, but there is always the possibility that if the judge was not persuaded, then he will not rule that way. That’s true. That’s obvious. Anyway, that is basically, in brief, what I think is the skeleton of the laws of permitting agunot. Now I’ll say perhaps more than that—maybe it’s too strong a sentence, but I think there is a lot to it, and quite a few halakhic decisors, it seems to me, really do work this way. You have to understand that it is customary in the world to think that permitting agunot is a very complicated subject. Now one has to distinguish: it is a very weighty and difficult subject because both sides of it are weighty—the distress of the woman on one hand and permitting a married woman to the public market, so to speak, on the other hand—that definitely is a matter carrying great responsibility. But the discussion itself, in my view, is not complicated. This is not one of the complicated passages, in my opinion. And therefore I think people mix up the level of responsibility required with the type of considerations or the complexity of the passages and so on. I’ll say more than that: in practice, if the judge was subjectively convinced, convinced that the husband is dead to a full degree as far as he is concerned, he can permit the woman without any connection to halakhic definitions. Therefore you do not really need to get into all the passages and whether this meets the standards of this one or that one. On the principled level, if you reached sufficient certainty that the husband is dead, you can permit the woman. As far as I’m concerned, all the precedents and all the laws that lie in the background here are basically examples. In other words, they are examples of cases where you can see that the certainty is complete and therefore they permit, or where there is some concern and therefore the certainty is not complete so they do not permit, and so on. There are certain exceptions in which there is room for a bit of hesitation. The most prominent is water with no visible boundaries as opposed to water with visible boundaries; we mentioned that. The rule in the laws of agunot is that in water with no visible boundaries they do not permit the woman, if the husband drowned. In water with visible boundaries they do permit the woman. This is a Talmudic passage in Yevamot, at the end there where they deal with the laws of agunot. Water with visible boundaries means water where I can see the entire shore of the body of water before me. And the husband drowned there; I saw that he drowned; I did not see him come out. Since all the shores are accessible to me, I see them, then if I did not see him come out, he apparently drowned. And therefore, in water with visible boundaries, if they see that the husband drowned, one can permit the woman, even though his body is not before us and was not identified. Yes, there is some kind of leniency here, because we did not see his face clearly and we did not see him die. There is no—this is basically circumstantial evidence. But it is complete circumstantial evidence. In other words, it created absolute certainty that the husband died, and that is enough for me. Even though it is only circumstantial evidence and I have no two witnesses and nothing. As opposed to that, if I have water with no visible boundaries—water with no visible boundaries means water where I do not see all the shores. Maybe I see part of them, but there is some part I don’t see. In that situation, even though it is still more likely that if he falls in the middle of the ocean he drowned and was not saved, but how do you know? He may have come out somewhere I did not see, some ship may have picked him up, he may have come out on some distant shore that I did not see, and therefore there is some concern that the husband did not die, that he was saved, and therefore one cannot permit the woman. In water with no visible boundaries they do not permit the woman. The accepted rule is that this is a rabbinic law. In other words, by Torah law, in practice, even there the certainty is sufficient, but rabbinically they are concerned. Now in light of what I said before, that is a bit problematic. Because what I said before was basically that if there is certainty then there are no rules. The precedents are only examples. They are examples that tell you what level of persuasion is required. So if I, as a judge, saw, received testimony that the husband died—or drowned, sorry—in water with no visible boundaries, and I have no knowledge that he came out, then I’m pretty convinced he died; I’m convinced he died in practice. So why, why shouldn’t I permit? The Talmud says that one does not permit in such a case. But I claim that if the certainty is sufficient, then it is sufficient. There’s no formal issue here. There, one really can see in this matter some kind of formal limitation. Even in the laws of agunot there may be formal limitations, because this is a special decree of the Sages because—because of underwater caves, excuse me—there is some concern that there is a cave in the water and the husband is there. The Talmud in Yevamot says this. And therefore, there the Sages decreed, and therefore this is only a rabbinic law. But the Sages decreed that even though according to the strict law one could have permitted the woman, they do not permit her in water with no visible boundaries. Therefore there this may be an exception where I would hesitate to permit the woman on the basis of drowning in water with no visible boundaries. The halakhic decisors, by the way, usually just bring in additional branches, and in the end they do permit the woman, even with water with no visible boundaries. But they always need to find some additional branch, because water with no visible boundaries by itself is not enough to permit the woman. Okay? But by the way, I’m not completely sure this is correct. What? What is the meaning of a rabbinic prohibition? If according to the Torah one could permit her, and the Rabbis do not permit, then the result is that one does not permit, right? Yes. Isn’t there some absurdity here, that the Torah comes and says, as far as I’m concerned this woman is not an agunah, and now the Sages come and enact some crazy decree after the Torah did permit it? There are many things like that. The Torah permitted poultry with milk, and the Sages prohibited poultry with milk. Yes, but there at least we know it’s only so he won’t come to actual eating. Here it’s something else entirely. No, no, and here it’s because of caves or because of things like that. They always have some reason, and because of that they decree. No, but here there is serious harm. This is not—every rabbinic decree is a prohibition of something that is permitted according to the strict law. No, but here there is serious harm. That’s true, true, and that’s why I say it was probably important to them. My feeling is—first of all I’m not sure this too is not only an example, and one could still permit if I was convinced that he really died. And many things get added—for example, today there is mail and telephone. So if he had come out somewhere else, we would have heard about it. And there are many halakhic decisors who say that today, in water with no visible boundaries, one can permit the woman. Because if he had come out we would have heard about it, so he apparently did not come out, even though we did not see the shore. Okay? That’s the kind of example of an additional consideration that they bring in, and in the end they permit even in water with no visible boundaries. But—but the point is that perhaps—I don’t know, it’s a feeling I have—that water with no visible boundaries is some sort of flag that the Sages raised so that we wouldn’t get—wouldn’t run wild. So that we wouldn’t think the world is ownerless and you can permit anything based on anything, because they wanted to signal: friends, there is this feeling in the world that permitting agunot justifies everything. What, do this, they permitted everything. Not true. As I said before, absolutely not. There are very, very great stringencies in permitting agunot, and the permission is only when we are dealing with a formal stringency; then they permit it. And perhaps in order to mark this, the Sages left water with no visible boundaries as a sort of red flag. Remember: there is a very weighty issue here, and do not be trigger-happy when you come to permit. Here, this for example we will forbid you to permit. Maybe. But the rabbi is always against substantive determinations because of a slippery slope. Right, but every rabbinic decree— But then because of that slippery slope, because of that warning, we are going to go and determine the fate of this woman? Every rabbinic decree is a slippery slope. You mentioned poultry with milk earlier; poultry with milk is because of concern lest one come to eat meat with milk. That too is prohibited because of a slippery-slope consideration. Rabbi, poultry with milk is not prohibited rabbinically in the same full sense. The prohibition doesn’t extend to cooking, or selling to a gentile, no benefit, nothing. Meaning there is a certain specific detail there that they prohibited because of concern—not concern, sorry, a fence. A fence around the Torah. Here what is being asked is that there is a Torah-level permission, excuse me, and the Rabbis come and prohibit it in a categorical way that doesn’t exist in the other example. I see no difference at all. No, it’s a fence. It’s a fence lest people come to permit an agunah in situations where it is not correct to permit. What’s the difference? That too is a fence. I don’t know, your example doesn’t quite fit here, because this is permitted and that is permitted. Fine, in any case, okay. So I say this is a suspicion; I’m not sure, but I have some suspicion that water with no visible boundaries is some kind of flag the Sages left to remind us that the laws of permitting an agunah are not ownerless. But what about today? I wanted to say one more thing about water with no visible boundaries. After all, we are speaking about a world—we aren’t used to this—but we are speaking about a world in which human beings did not yet know all the continents and all the islands and in general the structure of the earth, the globe. So indeed water with no visible boundaries could ultimately mean that we don’t know the entire perimeter of this lake. If we do know the entire perimeter of this lake, then we can say it is water with visible boundaries. But if it may be that Cyprus is a hundred and twenty kilometers from here and we simply don’t know it, and he swam there and came out, then that really is a realistic concern. It’s a substantial doubt, not— No, but I didn’t understand. But if we do know, then what? They knew there was an end. What does “water with no visible boundaries” mean? You know that today there is no such thing as water with no visible boundaries. In the Mediterranean—what do you mean? In the Mediterranean it’s not twenty kilometers, it’s much more. What does it mean that there are no visible boundaries? No visible boundaries means no end. It has an end. Everything has an end. Water with no visible boundaries means that you don’t see it. Today there is no such thing as water with no visible boundaries by definition. There is no such thing as water with no visible boundaries. Why not? We are talking about seeing, seeing the end, not knowing there is an end. What does seeing the end mean? Who said that’s the interpretation? Maybe water with no visible boundaries just means something where we don’t know what’s on the other side. Not that you, standing in one spot, don’t see it. If you have a satellite seeing, or some sensor— What does that have to do with it? If you have a satellite, that’s something else, but the satellite has to see all the shores, and then it would be water with visible boundaries, fair enough. But that isn’t generally the situation. But today we have no water with no visible boundaries. Why not? Of course we do. Because all water has boundaries. Even an ocean has shores. Again, what does “end” mean? When we don’t see it, that’s called water with no visible boundaries. So I suggest another interpretation, that maybe it’s not a matter of sight—me standing at one point and not seeing. But that interpretation is wrong. Why? Water with no visible boundaries means water where you don’t see the shore. It is explicit in the Talmud. It’s not an interpretation. It is explicit in the Talmud. Also, besides that, we have lots of stories—this really happened—that a person’s body drifted and came out hundreds of kilometers away and he was alive—there are such stories. No, no, okay, certainly. In any case, the point is that I’m saying there really is some kind of exception here. Water with no visible boundaries really is some kind of exception; there is room to hesitate about it, but it is some kind of exception where indeed the halakhic decisors see it as something binding. Meaning, if someone drowned in water with no visible boundaries, where we do not see the shore, and you have no additional data, they will not permit his wife. Meaning, because it is a determination of the Talmud; these are clear statements. How substantial the concern is, I don’t know. There is room to hesitate, as I said before. But those are the givens. Now I want to tell you something further. So, the permission of two majorities is a permission that basically has existed for only, I don’t know, maybe two hundred years or so, and the halakhic decisors use it a lot. You’ll see—it’s very, very practical. But it has no source, no source in the early sources. So the first source is in the responsa Kehillat Yaakov, section 9, by the student of Rabbi Chaim of Volozhin. It also appears in Pitchei Teshuvah in Even HaEzer, and he says as follows: “And I also remember that in my youth, when I was in the honored house of my teacher and rabbi, the great gaon our teacher Rabbi Chaim of blessed memory”—Rabbi Chaim of Volozhin, may he rest in Eden of Volozhin—“a question of this sort was asked concerning one who fell from a bridge that was much higher than the ice, and from the ice into the water, and was lost and not found.” Now of course we are talking about water with no visible boundaries, because if it were water with visible boundaries then there is no problem permitting him; you also wouldn’t need the bridge. The moment he fell there and the water has visible boundaries, he is permitted, his wife is permitted. But the water there was a river that has no visible boundaries in the sense of length; yes, it has width where perhaps we see the shores on both sides, but we need to see all the shores for the water to count as water with visible boundaries. So there it was water with no visible boundaries. Someone fell from a bridge onto ice and afterward from the ice rolled into the water. “And he inclined to permit on the basis of two majorities,” Rabbi Chaim of Volozhin. “Namely, a fall from the height of two stories is mostly unto death, from the law of the place of stoning.” Yes, the place of stoning was two stories high, as the Talmud in Sanhedrin says, and if you fall from the place of stoning, you die. So therefore, there is one majority that one who falls from the height of two stories to the ground dies. That is the fall from the bridge to the ground. “And from the law of the fallen animal that is torn,” which is a law given to Moses at Sinai; there too we see that by falling, the being dies. “And together with the weakness of water with no visible boundaries”—yes, together with that, there is also water with no visible boundaries here, another consideration. “And he elaborated on this in the responsum, and as I recall, this woman was permitted with the agreement of all the sages of Vilna. And I know that one may also find in this grounds to be stringent from some responsa of the later authorities, and one should not be overly concerned in water with no visible boundaries, which is rabbinic; and one may rely on the opinions of the lenient in this matter in a case of agunah.” What is he saying? He is basically saying this: the man fell from the bridge onto the ice, and the height was more than two stories, so here there is a majority toward death. Afterward he fell from the ice into the water and drowned in the water. All right? Again there is a majority—you remember, because even with water with no visible boundaries there is a majority that the person died, it’s just not an absolute majority and therefore they prohibit, but there is a majority here. So Rabbi Chaim of Volozhin says: what we have here is two majorities. It’s not just the majority of water with no visible boundaries; it’s two majorities. And therefore, although in ordinary water with no visible boundaries we do not permit the woman, here there are two majorities, and therefore we do permit her. There is a majority that he died when he fell on the ice, and if he didn’t die on the ice there is a majority that he drowned in the water—and after all there is a majority even in water with no visible boundaries that the person drowned. Therefore in this situation—this is like the probability you worked out last time, right? Meaning, this is the probability you worked out in the previous lesson—you’re summing all the paths, so to speak. Right. Meaning, this is basically—if I return to the diagrams from above, you see? This is the tree. Okay? If he fell on the ice, he died. If he fell into the water, then there is one chance that he remained alive, because it is water with no visible boundaries and he came out and we didn’t see, and a second possibility that he died. Here too, the majority is that he died. Yes, that is also a majority. There are two nodes here, and both are majorities. So in order to assume that she is prohibited—I mean the woman is prohibited, sorry—I have to assume both B and then B1, meaning that he fell on the ice and did not die, then fell into the water and did not die—and that is B1. All right? Therefore, since it is two majorities and not just one majority—if this were just water with no visible boundaries, then there would be only one node, yes, only this node would exist: he fell into the water and either died or did not die. Right? In such a state we do not permit. But where this node is layered onto a prior node and there is here a probabilistic multiplication of majorities, in such a case we do permit. That is what Rabbi Chaim of Volozhin claims. By the way, he adds in his reasoning that water with no visible boundaries is basically rabbinic law, and he calls this two majorities. In that sense he is really speaking about a double majority. Seemingly, even if water with no visible boundaries had been a Torah law that the woman is prohibited—let’s say that in water with no visible boundaries the woman were prohibited by Torah law—but still, after all, there is a majority to permit her, right? It’s just that a majority is not enough to permit a married woman. Now I have another majority—ice and then water. Seemingly, even then he could have permitted. Why does he need the fact that water with no visible boundaries is only a rabbinic stringency? So one can say it’s just for extra support—meaning he says it’s even more permitted because it’s only rabbinic anyway—but I think what he really intends to say is some kind of rabbinic-level doubt. Because the stringency of water with no visible boundaries is itself only rabbinic law, and within that law itself we have doubt, because perhaps he died already on the ice, before he even fell into the water. So we have a doubt about the stringency of water with no visible boundaries, which is a rabbinic law, and with a rabbinic-level doubt one may be lenient. Then it’s a somewhat different permission than the permission of two majorities. It is basically a permission of rabbinic-level doubt. Fine, so one can say it this way or that way, but this is the basic source for this law of two majorities, and the halakhic decisors use this permission of Rabbi Chaim of Volozhin quite a bit. By the way, Rabbi Chaim of Volozhin is one of the central halakhic decisors in this whole matter of permitting agunot; he has many responsa on permitting agunot. Many years ago, one of our series dealt with reading responsa. We read responsa, and among other things I think we also read responsa of Rabbi Chaim of Volozhin about permitting agunot. In any case, so for example a case in which Rabbi Ovadia used this permission of two majorities was an Air Force pilot whose plane was hit by a missile and crashed. Neither the pilot nor the plane was found. Now the pilot had a fellow pilot—another pilot, meaning in another aircraft next to him, not a co-pilot. There was another pilot in a nearby aircraft who tried to check for ejection and looked for him in the crash area and did not find him. So Rabbi Ovadia discusses this matter, and he uses two majorities to permit the wife of that pilot, and he says as follows: “And here, since the two pilots cast themselves, each one, to track the actions of his fellow and report them to control”—in other words, this is an instruction that pilots receive: if one is hit, the other must immediately track to see whether he ejected and where he fell and what happened to him; yes, this is a standing instruction to pilots—“it is uncommon,” says Rabbi Ovadia, “that there should be an ejection by the pilot at the time of impact and the second pilot would not notice him.” And that is one doubt. “And even if we are concerned for the minority and say that perhaps nevertheless the pilot succeeded in ejecting from his plane, and the pilot who testified”—yes, the one who remained alive, the other one—“did not notice this, in any case, when he fell into the sea, and the plane that hastened to the place to bring him escape and help in his distress did not find him, and this is like one who fell into water with no visible boundaries, where most who drown die.” Yes, water with no visible boundaries is also a majority. True, rabbinically we don’t permit on that basis, but there is a majority there: most who drown die. “And it turns out that here there are two majorities toward death, for according to the majority he was killed when the plane crashed, and if you should say he fell into the sea, most who drown die. And with two majorities one may say that we find leniency, as the gaon Rabbi Chaim wrote”—Rabbi Chaim of Volozhin, of course—“the gaon Rabbi Yaakov, head of the religious court of Karlin, in his responsa, who brings in the name of Rabbi Chaim of Volozhin, in Responsa Chut HaMeshulash in the name of Rabbi Chaim of Volozhin.” So basically what do we have here? The plane was hit. It may be that the pilot died from the hit to the plane itself, died in the impact. There is a possibility he did not die and ejected. But if he ejected, I would expect the second pilot to see him. The second pilot did not see him. So he fell into the water, and the water was water with no visible boundaries. Okay, but most who drown die. So in fact I would say that there are even three majorities here, not just two. Later on I’ll argue that no, it’s only two. But on the face of it, on the face of it there are three majorities here. And Rabbi Ovadia says that according to the permission of Rabbi Chaim of Volozhin one can permit the pilot’s wife. You see, this is basically water with no visible boundaries, but we added another majority—the damage to the plane—beyond this majority that most drown unto death, and then one can permit even in water with no visible boundaries. This is a classic example. There are many more examples like this, where in water with no visible boundaries they permit by finding another branch toward leniency, and that is basically the mechanism of two majorities. Wait, how is it three majorities? What? How is it three majorities? You said it’s three. One majority is that when the plane itself was hit, the pilot probably died. If he did not die, then he may have ejected, but most likely he did not eject because the second pilot did not see him eject. And he was looking for the ejection because those are their instructions. And the third majority is that if he nevertheless— Wait, it could be that he was not hit in the plane. And it could be that he ejected without being seen. And fell into the water—there is still a majority that most who drown die. That is the third majority. As for the relation between the first two majorities, let’s leave that for a moment. I’ll comment on that in a minute. Okay. But this invention of two majorities—the bottom line is that they use a majority to permit an agunah. That means they use a majority. Okay? This is a little… Only with two majorities. Not with one. Even if there were—even if there will be three majorities, it will still remain permission based on a majority. No, no, obviously. Three majorities is even better. Yes, yes. And it’s a little interesting that they use water with no visible boundaries, where the law is that it is prohibited, but they use the side of it that there is a majority that does permit. This is the ordinary mechanism in Jewish law, for example with double doubt. A Torah-level doubt goes stringently, right? But a double doubt goes leniently. Why? The first doubt is stringent, so now you have one Torah-level law. Now you have a second doubt; that too is a Torah-level doubt and again goes stringently. Here there is a recurrence. But I don’t forget that the first stringency was a stringency based on doubt, not a certain stringency. Therefore the two doubts combine and create a double doubt. The same thing here. Water with no visible boundaries is not a consideration toward stringency. It is a consideration toward leniency, it’s just that it is a consideration toward leniency that is not enough. Meaning, if it were standing alone we would prohibit her. But obviously if he fell into water with no visible boundaries, that is a consideration toward leniency—most who drown die. It’s just that this isn’t enough because I’m concerned that maybe all the same he came out. If another majority joins it, then I remember that water with no visible boundaries is also a majority toward leniency. And then I permit. Rabbi, but isn’t the logic just that you are simply combining this into a very high probability, so to speak? Wait, wait, we’ll get there, we’ll get there. No, because I’m saying—for example, in the case of double doubt, there it’s simply the case, say—let’s take kosher meat or say glatt meat, for someone who only eats glatt. So either what’s being brought before me is glatt or not glatt—that’s one doubt. Even if it’s not glatt, who says one needs glatt? These are two different doubts. It’s not about the same story. So what? No, I’m saying here, in the case of falling into the water, either he died… In both cases, at the end of the day, the bottom line is that he died. The question is how he died. Did he die this way or that way? And in the end the question is whether the meat is kosher or not kosher. What’s the difference? On all these points too I’ll get there; I just want to do it step by step. The Chazon Ish, in Even HaEzer section 31, deals with the agunot of the Palmach men from the bridge usually called Gesher HaZiv—it’s actually Gesher A-Ziv, in Arabic—on the Night of the Bridges, yes. So regarding the agunot of the Palmach men there too the question arose: what about them? So the Chazon Ish writes as follows. “In Pitchei Teshuvah, subsection 133, he brought the words of Kehillat Yaakov, who discussed whether where there are two majorities she may marry ab initio.” And here it marks me and drives me crazy. “And in Pitchei Teshuvah he raised an objection from the words of Tosafot: after all, in the case of a Torah scholar there are two majorities. And one can distinguish, for the discussion of Kehillat Yaakov has two majorities toward death, whereas in the words of Tosafot one majority is toward death and one majority testifies to the death. However, we have no right to innovate in what was not mentioned in the Talmud, and there is no distinction between one majority and two majorities. And in Pitchei Teshuvah 138 he brought the words of the Chatam Sofer that nowadays, when the mail is established and it is possible to notify his household, this is preferable.” So the Chazon Ish disputes the permission of two majorities; he does not accept it. He mentions that Pitchei Teshuvah—as I said, Pitchei Teshuvah brings this permission—but Pitchei Teshuvah objected. Tosafot in Yevamot writes as follows. Yes, the Talmud says: Rav Ashi said, “That which the Rabbis said, in water with no visible boundaries his wife is prohibited, that applies only to an ordinary person, but not to a Torah scholar. If he is a Torah scholar, then no. Why? If he came out, there would be publicity.” Because if a Torah scholar were saved, then we would hear about it, since this Torah scholar is a known person, he’s a celebrity, okay? And if we didn’t hear, apparently he wasn’t saved. This is like the permission of the Chatam Sofer with mail—a similar permission, that if someone were saved today there is mail and telephone, and today it is likely we would hear. These are all kinds of additional branches that get added. So the Talmud says—so the Talmud basically says that water with no visible boundaries, where his wife is prohibited, applies only to an ordinary person and not to a Torah scholar. In the case of a Torah scholar, even in water with no visible boundaries we permit his wife. The Talmud rejects this and says: “But that is not so. There is no difference between an ordinary person and a Torah scholar; post facto yes, but ab initio no.” Post facto we permit, but ab initio we do not permit even for a Torah scholar. Tosafot says here below: “And even though, in most cases, if a Torah scholar came out there would be publicity”—there is an additional majority here, because if he is a Torah scholar then if he were saved we would hear about it. So there is one majority of water with no visible boundaries—that most who drown die—and there is another majority that if he is a Torah scholar and he was saved, then even if he was saved we would hear about it. So seemingly this is two majorities. Tosafot doesn’t call it that, because this is Tosafot, centuries earlier, but this is basically two majorities. Tosafot says: “Nevertheless we are not concerned for that majority, and she may not marry ab initio.” Pitchei Teshuvah says: from here there is proof that Rabbi Chaim of Volozhin is not right—that even with two majorities they prohibit the woman. The Chazon Ish says that this objection can be answered. Why? Because the two majorities of the ice, what we saw, or of the plane, consist of two reasons to assume he died. Two reasons that cause death. Falling on the ice is the first reason; the blow from the ice itself kills. And falling in the water—drowning can also kill. There are two causes, each of which in most cases kills the person. That is called two majorities. In our case, in the case of Tosafot, it is not two majorities. There is a majority that most who drown die—that’s one majority. What is the second majority? That if he is a Torah scholar, most likely we would hear about it if he was saved. The second majority only proves to me that he was not saved—in other words, that he belongs to the majority of those who drowned unto death. It is not an additional majority. It only strengthens that he really belongs to the majority and not to the minority. There aren’t two causes that kill him here. In the case of the fall from the plane or from the bridge there are two causes that could have killed him, and each of them kills in most cases. That is called two majorities, and one can be lenient. But Tosafot is not evidence against Rabbi Chaim of Volozhin, because what Tosafot is talking about is a case of one majority, not two majorities. It is one majority that most who drown die. We just have an extra indication that he probably drowned because otherwise we would have heard that he came out, if he is a Torah scholar. But that is not another cause that could kill him. It is just another indication that he should be assigned to the majority who drowned in the water and not to the minority. So why doesn’t the Chazon Ish agree with him? What? Why doesn’t the Chazon Ish agree with Rabbi Chaim of Volozhin? He claims there is no such thing in the Talmud as two majorities. He claims that regardless, there is no proof from Tosafot against him, but he does not accept what Rabbi Chaim of Volozhin says—not because of Tosafot, but because we do not make such distinctions on our own. There is water with no visible boundaries. It is written in the Talmud that we do not permit based on this, and that settles the matter. He rejects the very concept of two majorities? Yes, yes. He rejects the concept of two majorities. In the case of Tosafot he says this is not two majorities at all, so the proof from Tosafot is not a proof. But even a case that really is two majorities, like the bridge and the plane, he is also unwilling to accept. Where does the assumption about a Torah scholar come from? I didn’t hear. Where does the assumption about a Torah scholar come from? The Talmud says so. What do you mean? Yes, but where does the Talmud get it from? What do you mean? If Rabbi Chaim Kanievsky had drowned in the sea and been saved and came out in Africa, you understand that we would have heard he was saved. I’ll tell you something, Rabbi—we are speaking here in principle, on the scale of the whole world, yes? The Torah scholar could also be in Babylonia. He could be, but most likely we would hear about him. It’s a majority, not certainty. That’s a very, very unclear assumption. Okay. That is the assumption of the Talmud. Again I say: all this is subject to the assessment of the judge sitting in judgment. If the judge sitting now thinks that there is no such majority, then indeed he won’t permit the woman. But there the assessment was that such a majority existed. I’ll tell you: until we reached this discussion now, yes, in that same Talmudic passage, this question didn’t even occur to me. Now when we come back to it, yes, suddenly it strikes me. I don’t know—it’s a somewhat strange claim. No, I say, maybe. The judge will have to consider the matter. This is not a rule, it’s a factual determination. A factual determination is not under the Talmud’s authority. Facts can be checked. If you think that factually it is not true that in most cases one would hear about a Torah scholar, then it really isn’t two majorities. All right? Because the fact the Talmud describes is not present in our circumstances, and therefore it is not relevant. But where it is present, as the Talmud assessed the situation in its time and place, then seemingly there would have been two majorities. The Chazon Ish says no, this is not two majorities. This is one majority. But the Chazon Ish says even in a place where it really is two majorities, like the bridge and the plane, he is also against permitting on the basis of two majorities. Because the Torah—the Talmud—prohibited water with no visible boundaries, so you see that even if you have a majority, basically it is not enough to permit agunot, so also with two majorities we do not permit. But I understand the distinction, but is there a logic behind such a distinction? What do you mean, logic? Meaning, okay, no problem—here you have two causes of death, either the ice or the water, and here it’s only one cause. But why specifically do you need two causes and one cause isn’t enough, even if it’s strong enough? Is this some verse-based decree that you need two? I’ll come back to that point too in a moment. All right? I need one more thing. No problem. And another question regarding the Chazon Ish: does he accept the concept of two majorities at all, or only here specifically did he uproot the concept of two majorities, or does he not accept it at all? No, no, he does not accept the permission of two majorities. Also in places where there is no issue of water with no visible boundaries? Meaning, also in places… No. In places where there is no water with no visible boundaries, then the whole story doesn’t start, because the decree was about water with no visible boundaries. Meaning, in places… Okay, yes, fine. So Rabbi Ovadia brings this Chazon Ish and does not accept it as practical Jewish law. “And the gaon Chazon Ish, although he rejected the objection of Pitchei Teshuvah to the ruling of Rabbi Chaim of Volozhin from Tosafot in Yevamot, because there it is different, for that case of Tosafot is considered one majority toward death, since the second majority only testifies to and proves the first majority, that he indeed drowned and was not saved; nevertheless he concluded that we have no right to innovate leniently in what was not explicitly mentioned in the Talmud, and for us there is no difference between one majority and two majorities, see there. But his words are not compelling, because on the contrary, since the prohibition itself in water with no visible boundaries is an extra stringency, to be concerned for an uncommon minority, we say: let us not add to it; and with two majorities they did not decree.” So this is a very interesting halakhic dispute. Because Rabbi Ovadia is basically saying: the question is what the point of departure is. Rabbi Ovadia says, look, the point of departure is that the prohibition in water with no visible boundaries is a strange, puzzling prohibition. Because it’s obvious that he died. Fine, but what can you do—the Talmud prohibited it. The Talmud prohibited it, and we are bound by that. But we minimize it as much as possible. “You have only its novelty,” because it is a very great novelty. And Rabbi Ovadia’s point of departure is that in water with no visible boundaries the facts are known to us: the man is dead. All we have is only a formal limitation, because there is a rabbinic decree about water with no visible boundaries. Except that this rabbinic decree is indeed a formal decree, but it was said in the context of agunah. I cannot say that because it is formal, therefore I permit agunot, because with agunot formalism doesn’t interest me. No, because this formal decree was said specifically regarding the laws of agunot themselves. But still I remember that the problem here is a formal problem. And then what? Then I say: if I find another branch that takes me out of this formal definition, that is enough for me to permit. “Let us not add to it”—the Talmud prohibited in the case of one majority. I have two majorities. It didn’t speak about that. If the Talmud didn’t speak about it, from where should I prohibit? The point of departure is permission. To prohibit, you need proof. You have proof that with one majority they prohibit. From where is there proof that with two majorities they prohibit? From Ketubot. What? From Ketubot. What there? In Ketubot there, two majorities—it’s the story of Rabbi Yochanan who was raised, no, no, no, leave Ketubot, you’re talking about lineage. We’ll get to that, to two majorities there—not now, later. This is an invention of Rabbi Chaim of Volozhin; it’s not in the Talmud, this matter of two majorities in permitting agunot. And we’ll also see later that it’s not similar. Anyway, that is one option. The Chazon Ish assumes the opposite assumption: that in principle water with no visible boundaries is basically some sort of majority, and the Sages told us not to rely on a majority to permit agunot, so why should I care if it’s two majorities? Let me get ahead of myself and say this: after all, these two majorities are a negative majority, right? Let me formulate it differently. Let’s say that most people who fall from the bridge onto ice die—the majority is, say, eighty percent, okay? And most people who drown in the sea, in water with no visible boundaries, also die and do not come out, even though it is water with no visible boundaries, okay? So basically we have two majorities. What is the chance that the person still came out? Four percent. Twenty percent of twenty percent. A fifth of twenty percent—four percent. Okay? So basically we have a majority of ninety-six percent that he is dead. But a majority of ninety-six percent is still a majority, and on a majority we do not rely. Why should I care if you built this majority by multiplying two majorities? After all, if you had only one majority—say you have some especially stormy ocean and there the chance of drowning is not eighty percent but ninety-six percent—you still wouldn’t permit, right? Because it’s water with no visible boundaries. So says the Chazon Ish: what’s the difference? Here you have a multiplication of two majorities, but in the end you have some number, and that number is a majority, and the Sages told you that based on a majority one does not permit. So why should I care that it’s two majorities? Suddenly the Chazon Ish actually sounds very logical. Halakhically logical, again. Not factually. You have to understand, after all, even based on a majority we do not permit, so why should I care that this majority is the product of multiplying two majorities? Statistics is anything above fifty percent. Whether I reach that eighty percent in one shot or by multiplying ninety times eighty—I don’t know, ninety times ninety actually—ninety times ninety gives me eighty percent. Doesn’t that turn into eighty plus eighty, like one hundred sixty, meaning stronger? I didn’t understand. I’m saying, doesn’t it become a multiplication, like eighty plus eighty, which is stronger—one hundred sixty percent more? I didn’t understand how there can be one hundred sixty percent more. No, Rabbi, there’s a bit of mathematical confusion here. I understood his question. His eighty plus eighty accumulates to one hundred sixty in his mind, but that’s not our mathematics. We only have one hundred percent. There’s eighty plus twenty, and there eighty plus twenty also gets divided within the same hundred percent. No, look, I’ll present it—let’s go back for a moment to the diagram, because that’s exactly why I introduced the diagrams. It’s easiest to look at diagrams. You’ll see later that it really makes it easier also to think about these passages. Here is the diagram, you see? So let’s say either he dies on the ice—eighty percent—or he remains alive on the ice and then falls into the water. If he fell into the water, there is an eighty percent chance that he drowned and a twenty percent chance that he remained alive, right? Now I ask, what is the chance that he remained alive? We said the chance of getting here is basically the multiplication of the probabilities of the path. It’s twenty percent times twenty percent—0.2 times 0.2—so the chance of being here is 0.04, four percent. The chance of being here is twenty percent times eighty percent, which is sixteen percent. Sixteen plus four is twenty; the chance here is eighty percent. Eighty, sixteen, and four. Okay? Therefore there is a ninety-six percent chance that his wife is permitted and a four percent chance that his wife is prohibited. The Chazon Ish says, why should I care? Let’s imagine that this whole story doesn’t exist, this whole lower node—there is only the upper node, or only the lower one, say he fell into water with no visible boundaries and let’s say there is a ninety-six percent chance he drowned and a four percent chance he didn’t drown. Do we permit his wife? No. We don’t permit her? No. We do not permit. No, it has to be absolute. Right. Even though there is—even though there is a majority—in water with no visible boundaries we do not permit his wife. So then with ninety-six percent you also do not permit. So why should I care that it’s a multiplication of majorities? But you can’t ignore that there are two stories here. That it is the result of multiplication. Why does that matter? In the end it’s still ninety-six percent that the husband died. Is ninety-six percent enough for you to permit her? No. Not enough. The question is whether to look at it from outside or from inside—like, from within the story or from outside. Not from outside and not from inside and not anything else. I’m asking a question: is ninety-six percent that the woman is permitted enough to permit her? No. It isn’t enough. If it isn’t enough, then it isn’t enough. Why should I care that this ninety-six percent comes from the multiplication of two majorities? Okay. Fine, but like you said, it depends how you relate to the event of water with no visible boundaries. Whether it’s a matter of probability or whether it’s something else, like some sort of—I don’t know what. This two-majorities mechanism is seemingly a probabilistic look. You’re basically multiplying probabilities. No, but you also mentioned that perhaps it simply means that the Sages did not speak about this case; they only spoke about a very specific situation of water with no visible boundaries. So that is Rabbi Ovadia’s approach. That’s his other side, against the Chazon Ish, so to speak. That is Rabbi Ovadia’s approach, yes. And the Chazon Ish says: what do I care? In the end I have a majority, right? A bigger majority, but still a majority is not enough to permit a woman. What do most halakhic decisors claim? And what do they rule in practice? I think most of them permit with two majorities. Yes, because it’s subject to decision. As far as I know. It’s subject to decision. It’s not tied to what is written. What? There’s a halakhic discussion, but in the end it’s subject to the decision of those people. Fine, that’s what I’m saying. I think that most, most halakhic decisors do use two majorities to permit. Now, there was another case, with Rabbi Herzog, who also uses two majorities. There was a South African plane that crashed in an air battle in World War II, in 1944, and there was a Jewish pilot there. And a question arose regarding the wife of that pilot. And Rabbi Herzog discusses it in Heikhal Yitzchak, and he says as follows: “And now, regarding our present case, behold, since there is a compelling presumption that the airplane broke and fell, then even if it had fallen on land, this would already be a double majority toward death. And all the more so from a ship lost at sea, regarding which we say in Bava Batra that it is mostly toward death. And the Rivash and the Noda B’Yehuda and others already noted this. It follows,” I’m reading here, “it follows that the very fact that the airplane broke and fell from a great height is mostly toward death, and the fall into the sea adds another majority. And this can be discussed on the basis of two majorities.” Now notice what he says. He says, basically, the plane fell. I don’t know whether it fell on land or fell into the sea. If it fell on land, most likely the pilot crashed. If it fell into the sea, again most likely the pilot crashed. So this is two majorities. It’s a double majority. If it fell on land, he died, and even if you say it fell into the sea, most likely he died. What do you say? That’s not certainty. Meaning, “crashed” here means drowned in the water, and there “crashed”? Yes. Died or drowned in the water. Why isn’t that certainty? I claim that not only is this not certainty—it’s not even two majorities. Why does he need to get to water with no visible boundaries if the plane crashed from a great height? No, it could be that the pilot fell into the water. Yes, okay, so what? He fell from the sky, so he crashed, he died. Not necessarily. It fell—it either fell on land or it fell into the water. Yes, but the very fall will kill him. Who says? If he fell into the water, maybe he remained alive. The water breaks the fall. No, no, not from such a height. But on land too, even on land he may have ejected. Meaning, he does not treat the plane crash as certainty, even on land. Yes, I’ll show you—look at his wording again. He says: let’s say eighty-eighty, yes—“the very fact that the airplane broke and fell from a great height is mostly toward death, and the fall into the sea adds another majority.” Now look. In the straightforward understanding, Rabbi Herzog’s consideration is not similar to Rabbi Ovadia’s. Because Rabbi Herzog is basically saying: look, either he fell on land or he fell into the sea. If he fell on land, either he died or he didn’t die. If he fell into the sea, either he died or he didn’t die. When you count below the number of possibilities that the person died versus the number of possibilities that he lived, it’s two and two. Not one and three. That’s what I’m saying. If he fell on land, there is a majority he died and a minority he lived—say eighty-twenty. If he fell into the sea, again eighty-twenty, because most who drown die; that’s water with no visible boundaries. What is the chance that he died? Four percent like before? No. Twenty percent. Or even twenty-five—that he lived, not that he died, sorry. Twenty percent. Why? Because on the side of land it’s twenty percent, and on the side of sea it’s also twenty percent. So I don’t care whether he fell on land or into the sea; there is a twenty percent chance he lived. Okay, he ends up in a bind according to Rabbi Ovadia too—at the end it’s just two. The claim is that this is not a double majority because there is no multiplication. This isn’t even a double majority at all. What? It’s not a double majority at all. No, it is a majority. He claims it’s not. If he fell on land there is a majority that he died, and if he fell into the sea there is a majority that he died. That’s one side. On the other hand, if what we are doing is multiplying this and reaching ninety-six and that’s still not enough, then here where it’s twenty, obviously it’s not enough. I didn’t understand. Obviously not. So what is it here then? Here I’m claiming that even Rabbi Ovadia would not permit, not only the Chazon Ish. But why isn’t it multiplication here? Why? Because either he falls into the sea or he falls on land. Okay. Now if he fell on land, there is an eighty percent chance he died and a twenty percent chance he lived. If he fell into the sea, there is an eighty percent chance he died and a twenty percent chance he lived. Okay, so in the end it’s half times eighty plus half times eighty, right? Fifty times eighty plus fifty times eighty. Right. So that is multiplication, just multiplication that gives you a lower sum, but still multiplication. No, that’s not multiplication. So let’s see. What is the chance that he dies here? Let’s say half times eighty percent—that’s forty percent, right? Plus forty percent on the other side. Wait, what is the chance that he dies here? Also forty percent. Half times eighty percent. So in practice the chance that he dies is eighty percent. Right, but it’s still multiplication because in the end it’s two, like, two stories, two questions, two nodes. No, this is not multiplication at all. It’s not multiplication at all. Because the first multiplication is irrelevant; it changes nothing. Whether he fell into the sea or whether he fell on land. It’s like saying—I could tell you he may have fallen on the kilometer of land near the sea or on the second kilometer of land near the sea, and in each of them the chance of dying is eighty percent, so would that also be a double majority? Okay, I understand. You’re saying that the question whether he fell into the sea or onto land is not interesting with regard to the question whether he lived or died. In any case it’s eighty-twenty. Either way. It’s like asking which part of the sea he fell into or which part of the land he fell onto. It always remains one majority and that’s it, not a double majority. It’s one majority, not a double majority. Yes, because basically the chance of dying, whether he fell in the sea or on land, is identical, and therefore it’s not—okay. Even if it weren’t identical, it still would not be a double majority. It’s not a double majority because there is only one node here with one majority. Even though the majority may be different in the sea and on land, I don’t care. It is still one majority and not a double majority. Because in the upper node, the split is not a relevant split at all. It doesn’t multiply anything. I understand. And therefore I claim that according to his description—again, perhaps with some effort, I did not see the whole responsum inside—but with some effort I can think maybe he means to say that if he fell on land then he certainly died, and even if you say he fell into the sea, then he may have drowned and he may not have drowned. That would be a double majority. Because most likely he fell on land, and even if he fell into the sea, most likely he drowned. But from the way he presents it in his wording, that’s not what it says. On land there is a majority that he dies, and in the sea there is a majority that he dies. That is not a double majority. Call it two majorities if you want, but a double majority is the multiplication of one majority by another. There is no multiplication here. And therefore it is very, very useful to look at this in the tree form that I described above. The moment there is a tree here that gives me multiplications, that is a double majority. If there is no multiplication between the majorities, and instead there are just two parallel majorities, then this is not a double majority. It is one single majority. And therefore it is not correct to permit there. Even Rabbi Ovadia would not have permitted there. The Chazon Ish certainly would not—he does not permit. Again, unless he meant that on land he certainly dies, and even if you say he fell into the sea, most likely he dies—but his wording does not seem to say that. His wording seems to say that on land, most likely he dies, because maybe he ejected, and also in the sea, most likely he dies. So basically in a double-majority case you need one side of the tree to decide the issue, like here it ends the event, and then on the second side, that’s where the point is. The second side narrows the minority, the concern for the minority, even further. Fine. Okay? So here is an example of the use of a double majority, where if we carefully follow the definition with the trees, we see that it is incorrect. It seems similar at first glance, but it is not. In other words, we are constantly returning to one majority. In Rabbi Herzog’s case, yes. Yes, I understand. Okay? So we’ll stop here. Any questions or comments? Okay, have a peaceful Sabbath. Goodbye.