Doubt and Probability—in Halakha, Thought, and in General—Lesson 45—Rabbi Michael Abraham

This is an English translation (via GPT-5.4). Read the original Hebrew version.

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

🔗 Link to the original lesson

🔗 Link to the transcript on Sofer.AI

Introduction to two majorities in cases of agunot
Positive majority versus negative majority
Negative majority and the need for multiplication
Overwhelming majority and absolute majority in agunot
When two majorities are not enough
Critique of Rabbi Goren’s examples
The importance of phrasing questions in statistics
Test reliability and conditional probability
Legal testimony and risk assessment
Is permitting an agunah a probabilistic consideration?
Introduction: statistics with missing information
Using an overwhelming majority and multiplying negative majorities
The connection between intuition and facts in halakhic judgment
The connection between multiple majorities and the structure of the tree
A matter that will eventually become permitted: Jewish law and rabbinic law
The difference between a 51% majority and a 49% majority from the standpoint of Jewish law
Danger to life versus an object: a halakhic discussion
Reaching statistical certainty by means of two majorities
The case in Ketubot: two majorities in the city and in the caravan
The justification for two majorities: determining multiple fixed groups
The requirement of both a majority in the city and a majority in the caravan
Rabbi Chaim of Volozhin’s question about certainty
Ketubot versus statistics — what matters?
The possibility of an identifying sign instead of a majority of the city
The decree lest one rely on the city and caravan — explanation of the Talmud
Maimonides’ interpretation of the majority of the city and the caravan
Conclusion and break — questions and closing

Summary

General Overview

The speaker argues that permitting agunot depends on reaching factual certainty that the husband died, and therefore the issue is ultimately statistical rather than formalistic. He distinguishes between positive majorities and negative majorities, says that two majorities are meaningful only when dealing with negative majorities that cannot be directly quantified, and criticizes applications of two majorities that use majorities that are not overwhelming or that ask the wrong probabilistic question. He also explains that the case in Ketubot of two majorities is a different halakhic structure from the one relevant to agunot, because there the law is driven by halakhic form and by the rule of fixed status, whereas in agunot the goal is factual confidence.

Positive Majority and Negative Majority

A positive majority is a majority whose percentages are known, such as 80% or 90%, and in that situation there is no difference between one majority and two majorities. A negative majority is a majority learned from experience without the exact numerical proportions being known, such as the fact that most women give birth after nine months, and that is the context in which two majorities have significance.

Overwhelming Majority, Absolute Majority, and Two Majorities

The speaker says that one overwhelming majority can already suffice to permit an agunah according to the basic law, but rabbinic stringency requires a firmer basis. Two overwhelming negative majorities can serve as a way of approaching absolute certainty, because their combination gives a stronger factual indication than either one alone. If the majorities are not overwhelming, then even two of them do not create enough certainty to permit remarriage.

Mistakes in Applying Two Majorities

The speaker rejects applications of two majorities when each majority is only moderate, such as in cases he attributes to Rabbi Goren and in the example of Kfar Etzion. He says these cases fail because a 70% majority combined with another 70% majority still leaves too much risk, and therefore one cannot permit an agunah on that basis. He also says that in such cases the structure is often not really two majorities at all, but just a mistaken use of two questions that look similar.

The Direction of the Probability Question

The speaker emphasizes that in statistics and probability, the wording of the question is crucial. He gives examples from medical tests, criminal testimony, and judges, and says that the question “given the condition, what is the chance of the result?” is not identical to the question “given the result, what is the chance of the condition?” According to him, many mistakes, including the one he attributes to Rabbi Goren regarding Kfar Etzion, result from reversing these two questions.

Permitting an Agunah as a Probabilistic Matter

The speaker says that at first he thought permitting an agunah was a formal halakhic mechanism, but later concluded that it is purely statistical. The goal is to reach factual certainty that the husband died; the halakhic framework only removes formal obstacles once that certainty has been achieved. He says that the whole discussion of two majorities is a statistical tool intended to bring one to that factual conclusion when precise numbers are unavailable.

Majority versus Halakhic Formalism

The speaker sets up a contrast between the laws of agunah and ordinary majority rules in Jewish law, such as a piece of meat following the majority of stores. In ordinary Jewish law, majority functions as a formal rule derived from the verse “follow the majority,” but in the laws of agunah, that formalism is not what determines the outcome. According to him, the case of an agunah requires factual confidence, not just a legal presumption.

Ketubot and the Two Majorities of City and Caravan

The speaker turns to the topic in Ketubot about a young woman who was raped near a city and the question whether she remains fit to marry a kohen. He explains that the two majorities in the Talmud there refer to the city and to the wagon or caravan, but the city is regarded as fixed and therefore does not count as a real majority. The Talmud requires the caravan in addition to the city as a rabbinic safeguard, not because the combination changes the factual probability in a way relevant to agunah cases.

Majority upon Majority versus Two Majorities

The speaker says that the Ketubot case is not identical to the two-majority model discussed in agunah cases. In Ketubot, the city and the caravan function as a legal arrangement involving the rule of fixed status, and the final permission is a halakhic decision accompanied by a decree. In agunah cases, by contrast, the question is whether the accumulating evidence creates enough factual certainty that the husband died, and therefore only genuine statistical strengthening counts.

Maimonides and the Explanation of the Topic

The speaker notes that Maimonides interprets the Ketubot topic differently, saying that the city itself must contain a majority of fit people, while the caravan is also made up of people coming from that same city. According to him, even this still does not turn the case into a true case of majority upon majority, because the second group is not created independently so that the probabilities can be multiplied together. At the end he says that there may still be some advantage according to Maimonides’ reading, and refers listeners to his written discussion of that point.

Full Transcript

[Rabbi Michael Abraham] are dealing with the topics of two majorities in cases of agunot, and in general. I’ll remind you that this is a novel idea of Rabbi Chaim of Volozhin: that in order to permit a woman to remarry, an agunah, we require two majorities. One majority is not enough, as you see from the case of water with no end in sight. I suggested that the source for two majorities might be from the Talmudic case that in water with a visible end the woman is permitted, and in water with a visible end there really are two majorities: one, that he drowned, and even if he didn’t drown, we would have seen him if he had come out. In any case, that could be a source for the law of two majorities. I said that two majorities are really a novel idea; the Chazon Ish doesn’t accept it. And I explained that the Chazon Ish doesn’t accept it because what difference does it make whether it’s one majority or two majorities? It’s just a question of how we calculate the majority. If we arrive at, say, a 96% majority — is that a 96% majority directly, or is it two 80% majorities? Two 80% majorities also give 96%. So if I arrive at that 96% through multiplication or arrive at it directly, what difference does it make? In the end, the question is whether you’re prepared to permit a woman on the basis of 96% or not. What difference does it make whether it’s defined as a product or not as a product? And then I explained that I distinguished between two kinds of majority: a negative majority and a positive majority. The claim is that a positive majority is a majority where we know the percentages, we know the size of the majority: 80%, 70%, 90% — that’s a positive majority. Usually a majority that is before us is a positive majority. Say there are ten stores in the city, nine kosher and one non-kosher, so that’s a 90% majority; I have the number, so that’s a positive majority. A majority not before us, in most cases — in most majority-not-before-us cases — is a negative majority. Right? Most women give birth at nine months, not at seven months; that’s not a majority based on numbers we know, rather we know from experience that generally women give birth at nine months and not at seven. That’s what I called a negative majority. Now, in a place where we’re talking about a positive majority, there’s no significance at all to the difference between one majority and two majorities; there the Chazon Ish is right. Because if it’s a positive majority and we know both majorities, then I know that 80 times 80 gives me 96%. There’s no reason in the world there to require a multiplication of majorities rather than one majority; in that sense the Chazon Ish is right. But the point is that not all majorities are positive majorities — on the contrary, most of them are negative majorities. Now, with negative majorities I can no longer make the argument I made earlier. I can’t say, look, you have 80% and another 80%, so altogether that’s 96%; what do I care whether it’s defined as a product? No — I don’t have the numbers for either of the two majorities. So you can’t say, what difference does it make whether it’s one majority or two majorities, it’s just two ways of getting to the same number. We don’t have a number at all. So why do we permit? The answer is that we permit because really, according to the basic law, even one overwhelming majority permits, like in water with no end in sight. So an overwhelming majority permits the woman, but rabbinically they required an absolute majority. Now how do I know that the majority is absolute and not merely overwhelming? If I have numbers, I can say, okay, I don’t know, from 99% and up that’s called an absolute majority, or 99.9%, it doesn’t matter — put the threshold wherever you want. That’s called an absolute majority. But when we’re talking about a negative majority, we have no numerical way to verify that we’re dealing with an absolute majority. So what do we say? That if we have two majorities that are overwhelming — meaning, they’re very, very significant; I don’t have numbers for them, but they’re very, very significant — then their product can already be considered, for our purposes, absolute. Again, remember: according to the basic law, one overwhelming majority already permits. The entire requirement here is a rabbinic requirement. So what the rabbis are saying is: we want there to be a product of two majorities — maybe two overwhelming ones. I said I’m not even sure about that, but let’s say both of them are overwhelming. That’s the way to verify that even though we don’t have numbers attached to each of the majorities, because they are negative majorities, we still have some criterion that gives us an indication that this is an absolute majority. With the product of two overwhelming majorities, it really can already count as an absolute majority. I think that in the case of water with no end in sight, 90% is an optimistic estimate. That is, I think it’s more than that — 95%, or even more. And therefore the overwhelming majority being discussed is around 95%. And 95% times 95% already leaves me with less than half a percent error. And therefore, therefore, that’s the criterion chosen by Jewish law — for those who accept it, Rabbi Chaim of Volozhin — to give me an indication that I’m indeed in a state of absolute majority, if it is the product of two overwhelming majorities. Okay? So all this applies only to negative majorities. With positive majorities there’s nothing to discuss. With positive majorities I need to decide whether this is an absolute majority or not an absolute majority. It makes no difference whatsoever whether it was created by multiplying two majorities or whether it’s a single majority. I said that a person who identifies the deceased by facial recognition, by the nose together with the face, is believed. One witness is believed. There is still some chance that he made a mistake. Fine, but the chance is so small that for me it counts as an absolute majority. Ah, but don’t we need two majorities? No, we don’t need two majorities. Why? Because this is an absolute majority. An absolute majority doesn’t need two majorities. You need two majorities when the two majorities are overwhelming. And this is also true in the opposite direction. Just as with an absolute majority you don’t need two majorities, only with an overwhelming majority, so too with a majority that is not overwhelming, it won’t help that I have two majorities. Meaning: if I have two majorities that are not overwhelming — I don’t know, even 70%, okay? That’s a majority, a nice respectable majority, but not overwhelming. Okay? Obviously, on the basis of 70% we would not permit an agunah to remarry. A 30% chance that her husband will come back, and then all kinds of disaster follow — obviously we would not permit her to remarry. What happens when I multiply the majorities? 70% and 70% leaves me basically with 90%. More or less. Okay?

[Speaker B] So that leaves me with 91%, yes.

[Rabbi Michael Abraham] Right. So I’m saying, that leaves me roughly with 90%. And since 90% is still not an absolute majority — it may be an overwhelming majority, but not an absolute majority — therefore it won’t help even if it’s two majorities. If the majorities are not overwhelming, then it won’t help that it’s two majorities. And here I said, I pointed to mistakes — Rabbi Goren, and I also brought two examples there — where they take majorities that are not overwhelming and say, well, there are two majorities here, so we can permit the woman. For example in Kfar Etzion, where most of the people were single, and most of them also died. So that’s two majorities. So Rabbi Goren says, therefore you can permit the woman to remarry. In my view that’s nonsense. I mean, the majority of single men there was not an overwhelming majority. I don’t know how many there were, I didn’t check, but it wasn’t some overwhelming majority. It wasn’t like there was one married man there and ninety-nine single men. I assume it was, I don’t know, maybe 70-30, something like that if we’re being optimistic. Okay? So 70-30. Now if the majority of those who died there among the people was again 70, then in practice you’ve got 90%. Ninety percent means that for ten percent of the people, for ten percent of the women you permit, their husbands will come back. Are you prepared to take the risk of permitting women to remarry when in ten percent of the cases the husband will return and she’ll be forbidden to both men and the children will be mamzerim and there will be complete chaos? There is no justification for taking this idea of two majorities and applying it when the majority is not an overwhelming majority. This issue of two majorities is not a formal matter. It’s simply a criterion for making sure that at the factual level we are confident that the husband is dead. We don’t have two witnesses, so at the formal level that still isn’t enough, but factually we are calm, we know the husband died, and that is an absolute majority. That can exist only if I multiply two majorities that are overwhelming.

[Speaker C] Rabbi, can I ask a second question? Yes, yes. Just now, from this — not related to majority — does Jewish law ever take into account a woman’s age in these cases?

[Rabbi Michael Abraham] What do you mean?

[Speaker C] Because most of the problems, all the disastrous consequences involving women and so on, are very much connected with children and mamzerut and so on — not increasing mamzerim among the Jewish people.

[Rabbi Michael Abraham] And if—

[Speaker C] If a woman is very old and doesn’t want to be alone, the question is whether a religious court takes that into account. Just a small side question I was thinking about.

[Rabbi Michael Abraham] I don’t know of such discussions, and I also don’t think it’s possible to take such things into account. Because if there’s concern that the husband will return, then the result is severe even without children. Even without the mamzerut of children, the result is that she becomes forbidden to both men and all her relations are relations of promiscuity — that’s serious enough. I don’t think — I don’t know, in any case I’m not familiar with people who made a distinction between a case where there’s a question involving children and a case where there isn’t. So that was regarding an overwhelming majority and an absolute majority. And I ended with the examples, yes — for example the Kfar Etzion case. I brought two such examples where I said these are majorities that are not overwhelming, but it’s actually much worse than that. It’s not even majority upon majority. Not only are the majorities not overwhelming, the structure here is not a structure of majority upon majority. Why not? Because if I were asking a question, I would say: look, there is one person from Kfar Etzion who was taken captive, all the rest died, okay? And now I ask: what is the chance that this person is that woman’s husband? Then I say: most of the people were single, and most of the people died, so the chance that he is her husband is very small. But if I ask the question the way Rabbi Goren in fact asked it — a woman comes before me and I ask: is her husband alive? Here there are not two majorities. Because the doubt whether he was single or married doesn’t exist here. This woman’s husband is married. There is no doubt here whether he was single or married, or a majority in favor of his being single. I’m asking a question about a concrete person, and about that concrete person I know that he is married. I only have one majority, that most died — but that is one majority, not two majorities. This isn’t even a two-majority structure. And that brings us back — and here I just want to complete what I talked about last time — this brings us back to a point we’ve already run into more than once throughout this series: that in statistics and probability, it is very, very important to formulate the question precisely. The moment you formulate the question precisely, you’ve already done half the work. From there on it’s calculation, but it’s clear what has to be calculated. When the question is formulated well and precisely and correctly, then we know how to calculate it, generally speaking. The calculation is the easy part. Very often the mistakes and confusions in statistics come from our not distinguishing between two questions that look similar but are actually different, with different answers. In our case, with Rabbi Goren, you can ask: if someone survived, what is the probability that it’s her husband? That’s one question. The reverse question is: this is her husband — given that it’s her husband, what is the probability that he survived? Now since this can be presented as conditional probability — we’ve already talked several times about conditional probability — you understand that this is the reverse question. The first is P of A given B, and the second is P of B given A. Given that one person survived, what is the chance that it’s her husband? Given that it is her husband, what is the chance that he survived? That’s the reverse question, and therefore the answers are completely different. In our case, one answer will be two majorities, and the other answer will be a single majority, not two majorities. And we saw examples of this, if you remember, in Munchausen syndrome by proxy, with that woman whose two children died of crib death. Or I gave the example of very, very reliable tests that check for a rare disease. And I said that the reliability of the test is based on the question: given that the person is sick, what is the probability that the test will come back positive? Ninety-nine percent. Reliable test. But now I got a test result saying I’m sick. When I ask what is the chance that I’m really sick, the answer is not 99%. Because the question I’m asking is the reverse question. Given that the test said I’m sick, what is the chance that I’m really sick? The reliability of the test examines the reverse question: assuming I’m sick, what is the chance that the test will say I’m sick? Here I’m asking the reverse: assuming the test said I’m sick, what is the chance that I really am sick? The first is P of A given B; the second is P of B given A. Same thing we also discussed regarding judges. The quality of the judge is based on the question: assuming so-and-so murdered someone, what is the chance that the judge will find him guilty? Let’s say that’s 90%; that means the judge’s quality is 90%. But now I have a court that ruled that so-and-so murdered. And I ask: what is the chance that he really did murder — that they were right? That is not 90%. Because the question here is not: assuming he murdered, what is the chance they would rule that he murdered? Here the question is the reverse. Given that they ruled he murdered, what is the chance that he really murdered? And when the event is a very rare event — the prior is very small, as it’s called — then the difference between those two questions is dramatic. A very, very reliable 99% test can give me a result that isn’t worth even a tenth of a percent, if it came back saying I’m sick. A 99% reliable test says that I have some rare disease. Now I ask whether I need to start worrying. The answer is no. If the disease is rare, the chance that I’m sick is negligible. A 99% reliable test — and the chance that I’m sick is negligible. And therefore it’s very, very important to distinguish between the two directions of that question, and that is exactly Rabbi Goren’s mistake regarding the people of Kfar Etzion: instead of asking the question, this is her husband — what is the chance that he survived — he asked, if someone survived, what is the chance that it’s her husband?

[Speaker D] That’s really a first-year statistics mistake, it really is.

[Rabbi Michael Abraham] Fine, call it that, call it something else, I don’t know. But it’s a mistake many people make. Certainly people who aren’t skilled in statistics. I mentioned this once: I gave a lecture to medical students and asked them these questions, and they all fell for it. I said to them: you send a patient for a test, the test is 99% reliable, it’s for some rare disease, and the result says he’s sick. What is the chance that he’s sick? Almost all of them answered 99%. Afterwards, when we talked a bit more, it became clear to me — these were students at Tel Aviv University — that in fact they already do learn about these fallacies. In the past they didn’t learn them, and then there was no chance a doctor would understand this. Meaning, doctors didn’t understand it. But I think for quite a few years now they have been learning this, and doctors are supposed to understand — and still they fall for it. Many of them fall for it. It’s hard not to. If you think intuitively, you don’t always stop and make conceptual distinctions and formalizations and calculations with pen and paper. Intuitively you say: this test is very, very reliable, so apparently if the test said he’s sick, then apparently he’s sick.

[Speaker C] But all of medicine works on general rules. In an individual case, when they relate to a specific person, then you really need to ask the reverse question. But in their studies they learn it as a general rule. And generally it comes out the reverse, like we just learned.

[Rabbi Michael Abraham] When I’m talking about a patient who comes to a doctor, the doctor has to decide whether this particular patient is sick or not.

[Speaker C] Exactly, that’s what I’m saying. Since his practice is with an individual person, it has to be the reverse. But in the learning, when they study it, it goes as a general rule.

[Rabbi Michael Abraham] Okay, no, but they also need to learn how to examine patients. They learn that too, not just the theory. Medical theory is how you determine that a test is 99%. I understand. But by the same token, they also have to be prepared to receive patients and treat patients. They need to learn that in their studies too.

[Speaker C] They need to learn — not statistics, they need to learn to relate to the individual.

[Rabbi Michael Abraham] And that is called learning statistics — what do you mean? That is learning statistics. The difference between the individual and the non-individual is statistics; that’s a statistics lesson.

[Speaker D] Rabbi, are there halakhic decisors who object to Rabbi Goren for exactly this reason — that they simply point out that there’s—

[Rabbi Michael Abraham] I don’t know, I didn’t check, I’m not… And I also didn’t say — I didn’t actually see Rabbi Goren’s responsum itself. Rabbi Bass told me about the responsum and this line of reasoning. I didn’t see the responsum inside, and it’s certainly possible that he had all kinds of other considerations that joined in, and therefore it may be that the permission itself was more justified. But this particular reasoning of the two majorities is a mistake.

[Speaker C] But in principle, in those days people tried not to deal with this. Everybody ran away from these questions. Rabbi Goren basically stood alone facing this issue.

[Rabbi Michael Abraham] Fine, all credit to him, and still this argument is a mistaken argument. Maybe I’ll add one more comment. Yes, it’s the same thing as… you know that even at the legal level — I think we already talked about this a little, long ago — even at the legal level, two witnesses come and say that so-and-so murdered. We already discussed the fact that witnesses are not 100% proof. Let’s say it’s 99% proof, fine? They might have missed something. Ninety-nine percent. Now how many murderers are there in the population? What is the probability that a person in the population is a murderer? Ten million residents. Ten million residents means the probability is one in a hundred thousand, right? Murderers are a very rare phenomenon. The prior is one in a hundred thousand. Okay? Now, evidence with 99% reliability is worthless relative to a phenomenon that is one in a hundred thousand. In a simple statistical calculation, if witnesses come and say that I murdered, and there is a one percent chance they are wrong and a ninety-nine percent chance they are right, then the chance that I murdered is one in a thousand. Meaning, you can release me with a full heart. There’s no chance I’m the murderer. Two witnesses came and testified against me.

[Speaker E] But they didn’t just say it randomly about someone. Or—

[Rabbi Michael Abraham] Exactly — and that’s why I’m bringing it up. Exactly — and this is also true for a doctor. Exactly — but obviously, if we were talking about one person out of the whole State of Israel, then that really would be true. Meaning, the testimony of two witnesses would be worth nothing. But the point is, we have various indications that the person was in the area, say, or some other indications — obviously not enough to convict him, okay? But enough to reduce the prior substantially. What do I mean? Suppose there were only ten people in the area. Meaning, beyond that nobody else could have come to commit the murder because he wasn’t there. Suppose only… so altogether there are only ten suspects. If so, then the chance that I’m the murderer is one in ten, not one in ten million. One in ten. Relative to a probability of one in ten, eyewitness testimony is perfectly fine. But you do need some additional indications that by themselves are not worth much. One in ten is very weak in criminal law, yes? Ten percent certainty is nothing, fine? But that ten percent plays a decisive role here. And similarly on the legal plane, I mentioned that with a confession, the law requires some additional corroborating detail — some indication, some circumstantial evidence that joins the confession — and in my opinion it’s the same logic, even though the legislators didn’t understand that, but it’s the same logic. That additional detail, even though it isn’t significant in itself, plays a very, very significant role in reducing the prior. And the same applies with doctors. Let’s say I go to a doctor and I’m not feeling well. The doctor sees certain indications that I have disease X, which is very rare. But there are some indications; he doesn’t just send me for that test out of nowhere. There are some indications, and because of that — let’s say that means there is a 30% chance that I’m sick, not enough to determine it. He sends me to a 99% reliable test in order to be sure. And now when I come back, then it’s true that the disease is rare, say one in a million, but for me it’s not one in a million that I’m sick; there is a 30% chance that I’m sick. Relative to a 30% chance that I’m sick, a 99% reliable test is perfectly fine. Therefore it isn’t true that a doctor who sends me for a rare-disease test is operating in the dark — no. If he sent me for a reason, not blindly, but because there were certain indications, then the reliability of the test is highly significant. So that’s perfectly fine. But for example, when I mentioned mass testing people for COVID — say they tell everybody to get tested just to get some kind of sample — that has no meaning. It has no meaning, because they didn’t send me to be tested because there were any indications that I was sick. They sent me blindly. If they sent me blindly, then the test is worth nothing.

[Speaker D] But I mean, in Jewish law, if two witnesses testify that so-and-so murdered, then they also — maybe they’re misleading us — but they presumably testify that they saw him there. Meaning there isn’t some external testimony or certainty from another source that he was in that place. And classic testimony is always testimony that says he murdered, without getting too deep into whether we know for sure he was there, some special population. Right.

[Rabbi Michael Abraham] But if they saw him there, that’s already some kind of indication, because most of the world was not there.

[Speaker D] No, but that itself is the testimony. Meaning, based on testimony that’s what we accept.

[Rabbi Michael Abraham] Fine. They testify that he was there, and they testify that he murdered. Very good. Again, if they’re lying, that’s something else. But in the case of error, they would have to be mistaken about both of those things now. That’s already more complicated. So I’m saying, we don’t need to get into all the details too much. I’m just saying on the conceptual level: the direction of the question is critical, and therefore very often we make mistakes when we ask a question of P of A given B instead of P of B given A, and these mistakes can lead to absolutely dramatic errors. There’s simply no connection. Instead of ninety-nine… Therefore the direction of the question is very, very critical. And that brings me to the discussion I said I wanted to have, because basically what I’ve done now is probabilistic calculations, right? P of A given B, P of B given A — these are probability calculations. Are these considerations in permitting an agunah really probabilistic considerations? In other words, are the considerations we make here actually statistical considerations? Or are these halakhic rules and not necessarily probability calculations? At first glance, in that same conversation with Rabbi Bass, I told him that in my opinion this was a formal matter, not a probabilistic one. But after everything we’ve seen here, and after I wrote the columns and so on, I went back to him and said: I retract; this is a purely probabilistic matter. It’s only a probabilistic matter. The point is — maybe I’ll also explain why it has to be that way, and then I’ll explain how that fits with what we actually find. It has to be that way because of what I said at the beginning when I talked about permitting agunot. The discussion of permitting agunot really begins only at the point where, on the factual level, I am convinced that the husband died. Right? Only then do we begin discussing one majority, two majorities, water with a visible end, water with no visible end, things like that. If we are not convinced that the husband died, nothing will help. If we are convinced that the husband died, we still don’t have two witnesses, so at the formal level there are problems. But that formalism we bypass. Meaning, we don’t have a problem with the formalism. Maybe there’s a rabbinic enactment, but that’s what the rabbis enacted. Now what does that actually mean? That at the basis of permitting the agunah stands the factual statement that the husband is dead, not the halakhic one — the factual one. As opposed to, say, when I follow the majority among stores. A piece of meat was separated from the shops; nine shops are kosher and one non-kosher, fine. There the permission is based on Jewish law, not on facts. Think about it: if the number of stores were not nine against one, but ninety-nine — sorry, fifty-one against forty-nine — even then the piece would be permitted. Now you understand that you can’t say that I’m factually convinced that this piece is kosher. Obviously not. That is a formal permission, not a factual, reality-based one. You can’t say I’m factually convinced that the piece is kosher. And therefore indeed in permitting agunot, a majority that is not an absolute majority — according to Torah law even an overwhelming one, but rabbinically it has to be an absolute majority — will not help. Why? In the entire Torah, an ordinary majority is enough; 51% is a majority. Because in permitting agunot, as I explained, we want permission that is based on a factual determination, not on a halakhic determination. The ordinary majority says there is a halakhic determination here, but in the case of an agunah I want a factual determination that the husband is dead, not a halakhic one, not merely a halakhic one. And therefore it’s obvious that when we talk about principles for permitting an agunah, we must use principles whose purpose is to clarify facts, to reach the factual conclusion that the husband died. So you can’t say that we are ignoring statistics and engaging in halakhic formalism. On the contrary — exactly the opposite. Here halakhic formalism does not play the role. All that matters is being convinced that factually the husband died. So if that’s the case, the calculation is only statistical. What made me initially think otherwise? Why did I think there were formal issues here? Precisely because of this issue of two majorities and one majority. I asked, like the Chazon Ish: what’s the difference? This is a majority and that is a majority — what difference does it make whether it’s two majorities or one majority? So apparently it’s some sort of formal trick. But no, it’s not a formal trick. Truly, if it’s a positive majority, then there will be no difference between one majority and two majorities. I will need an absolute majority. Why? Because what determines the matter is the factual conviction I have, and with a positive majority I can take a position about the facts, a clear position about the facts. The whole issue of two majorities and all the devices we spoke about here arise only because the majorities we are dealing with are negative majorities. So what? So with negative majorities, apparently that’s not statistics? No — it is statistics. It is statistics that takes into account missing information. I know there is a majority; I don’t know how large the majority is. And I know there is a majority, or I know there is an overwhelming majority. So what do we do? We use statistical tools to increase the probabilities, the factual certainty. So we say: I want two majorities, because I want the product of two overwhelming majorities. But the multiplication of two overwhelming majorities is a statistical act. I am calculating the probability that the husband is alive; I’m just doing that calculation not on the basis of numbers, because I don’t have the numbers. So I use indirect maneuvers to make sure the numbers work out, but in the end what I want is for the numbers to work out. After all, I want to verify factually that the husband died. I’m not playing formal games here. I need to reach the factual conclusion that the husband really died. And therefore in the end it’s all statistics. The point is that Jewish law tells me that even if you don’t have numbers, I’m willing to treat it as an absolute majority as long as it is built from the product of two overwhelming majorities. And again, when I speak about multiplication, I’m already talking statistics. Everything here is statistics. What confuses people is that the whole story of two majorities, and everything we’ve discussed up to now, deals with negative majorities. So with negative majorities you don’t make the numerical calculation because you don’t have the numbers, but you still use statistical tools, you still use the fact that multiplying two majorities improves the result, and that is a statistical result. I don’t know by how much it improves the result because I don’t have the numbers, so I use statistical thinking where I don’t have exact data about the probabilities. I have a range, I know that this majority is an overwhelming majority. I don’t know whether it’s 90%, 95%, or 98%, but it is an overwhelming majority. And I say, fine, if it’s an overwhelming majority there’s some range there. Ninety percent is problematic, ninety-eight percent is already better; multiply it by another overwhelming majority and I’m more at ease. So the purpose of the multiplication is really to reach the factual conclusion. It is a statistical act, not a formal issue at all. Formal issues are not what matters in permitting agunot; the Sages set them aside.

[Speaker E] Rabbi, this concept of being factually convinced — what does that mean? For example, the rabbi is speaking about agunot. Suppose what was at stake was not that, but say the explosion of an atomic bomb that would kill millions of people. Then suddenly the conviction stops being so convincing. Even if you have two majorities, and it’s a majority that yesterday helped in some case of an agunah in an overwhelming or absolute way — but now, because what’s at stake is a much greater risk, suddenly our gut feeling is no longer so convinced. Wait, suddenly our factual conviction changes. What does that mean? It means that what we feel is terribly, terribly important — what we feel, not the data and not the numbers, but what we feel.

[Rabbi Michael Abraham] You always come back to this point, and I always go back and argue with you: that’s not true. It has nothing to do with what we feel. You are right that there is room to say that the level of certainty required depends on the question I am dealing with. The fact is that a majority that is not absolute and not even overwhelming helps with eating pork. Why? Because apparently eating pork, from a halakhic standpoint, is not such a dramatic matter as permitting an agunah. And you say to me, if it’s an atomic bomb over a country, that’s an even more dramatic matter, so maybe there I would indeed want an ultra-absolute majority, the product of five overwhelming majorities, I don’t know. Fine, no problem. But still, the scale is a scale of factual conviction.

[Speaker E] But yesterday the rabbi told me that in the very same case, with exactly the same percentages, yesterday the rabbi said that on the halakhic issue of agunot he was completely convinced, absolutely. Now—

[Rabbi Michael Abraham] The “absolute” here is a function of the question I’m asking.

[Speaker E] So that’s exactly what I’m saying… how can “absolute” change depending on the function? What does that have to do with it?

[Rabbi Michael Abraham] Because what is “absolute”? It’s paradoxical. Where do you stop with “absolute”? There is no 100%, right?

[Speaker E] There’s never 100%. There too, there too the answer is the same answer, there too—

[Rabbi Michael Abraham] The answer is that our consciousness matters here; it’s very important what we feel. Our consciousness determines where it is right to draw the line, but it doesn’t invent the line.

[Speaker E] I didn’t say it invents it, but it feels, in the phenomenological sense of the matter, its significance. We’ve already talked about this point many times.

[Rabbi Michael Abraham] Right, that’s correct, it’s just a classic example. In the formulation you’re giving, in the end you basically come out saying what I’m saying. I have no problem with the fact that I feel it, because I’m not measuring it, I don’t have numbers; I also say I don’t have numbers. The question in dispute here — that’s at least how it started; now it’s already ending differently — but the question in dispute here was whether that feeling contains an element of truth on the factual level, or whether it’s just my arbitrary invention, a feeling, that’s just how I feel.

[Speaker E] Right. So in phenomenology, that feeling has meaning, at least according to some of the…

[Rabbi Michael Abraham] No problem. If so, then we’re not arguing.

[Speaker E] Right, I think so too.

[Rabbi Michael Abraham] Fine.

[Speaker D] Rabbi, one more question. In one of the previous classes there you talked about a case where there are two doubts, but the tree, so to speak, doesn’t stop at the first vertex but continues — so basically we have four branches — and you said that’s not a case of two majorities.

[Rabbi Michael Abraham] No. There’s a case of four branches that is two majorities, and a case of four branches that is not two majorities. It’s not connected to the number of branches. No, sorry, it’s connected to the question of what sits at the endpoints. If there’s, say — think, let me put the diagram up here for a moment, then it’ll be easier to see. Let’s go back to the drawings that accompanied us earlier. Here. Okay. So here, leave aside Rabbi Herzog and the headings, just the drawing. Okay? Here there’s a drawing of two doubts — one, or majority and minority; here there’s majority and minority and here there’s majority and minority. Okay? Now, it depends what sits at the endpoints. If here it says kosher, non-kosher, kosher, and non-kosher — meaning two against two — then it’s not two majorities. If it’s three and one, that is two majorities. Meaning, if in the end the second majority improves the situation relative to the first majority, that’s two majorities. But there are situations, like Rabbi Herzog’s, where the second majority doesn’t improve the situation of the first majority. In such a case it’s not two majorities. Understood? Okay.

[Speaker D] Meaning whenever I have here two possibilities, like kosher, non-kosher, kosher, non-kosher, then it won’t improve the first situation, so it isn’t defined as two majorities. Yes.

[Rabbi Michael Abraham] We’ll see this in the topic of doubts. In our later classes we’ll deal with doubts, and there it’ll be much clearer, so when we get there we’ll see. Okay.

[Speaker D] And Rabbi, another question regarding what you said about, say, a piece of meat, 51 percent versus 49 percent, something like that, that it’s more formal — so does that basically mean that there’s no prohibition on it at all? There’s also seemingly no reason to be stringent?

[Rabbi Michael Abraham] Maybe there is reason to be stringent, but it’s permitted according to Jewish law.

[Speaker D] But why is it permitted according to Jewish law? I mean, is it not because of some consideration of the Sages, that okay, apparently it’s not prohibited, or apparently it really is…

[Rabbi Michael Abraham] No. Fifty-one versus forty-nine — what’s the difference between that and a 50-50 doubt, which is prohibited? It’s really not reasonable. Rather, they set some threshold, and that threshold is majority. Okay. Fine, but that threshold is on the formal level. Meaning, they derive it from the verse “follow the majority,” and so on. Okay? An overwhelming majority or an absolute majority of estimation is not learned from any verse. The Sages simply determine when, for our purposes, this counts as sufficient certainty, sufficient factual certainty. That doesn’t come from a verse. “Follow the majority” — going after the majority — comes from a verse, because following the majority is a formal rule.

[Speaker D] It’s not a rule — meaning it’s not reasoning.

[Rabbi Michael Abraham] Right. Again, there can be reasoning here, but that reasoning is not strong enough. Say if I had to bet, I’d bet on the 51 against 49, but if I need to permit on that basis, I would never in my life permit eating meat that has a 49 percent chance of being pork.

[Speaker D] But the stringency is apparently not connected to the prohibition or something like that, because maybe it’s only pork?

[Speaker E] You said it’s not connected to the severity of the prohibition either.

[Rabbi Michael Abraham] No. Any prohibition — at least any Torah-level prohibition — any prohibition I wouldn’t permit. You’re concerned that you may be violating a Torah-level prohibition — what do you mean?

[Speaker E] But Rabbi, that proves that the prohibition isn’t in the object itself; there’s not really any problem with pork meat — it’s perfectly fine, tasty, everything’s fine.

[Rabbi Michael Abraham] That’s a discussion that can be discussed separately; I don’t know if we’ll get into it. Maybe I’ll say it in one sentence. It depends on the question asked here earlier: whether there is still reason to be stringent. Now, if yes, then you can say the prohibition is a prohibition in the object itself, but the person is permitted to go after the percentage majority — but he is taking some risk that maybe this will defile his soul, I don’t know, all kinds of things like that — and therefore a conscientious person should be stringent. For example, I’ll give you an example: in tractate Beitzah, the Talmud says there’s a rule of “something that will later become permitted.” “Something that will later become permitted” means a prohibition — say a prohibition like muktzeh, okay, or an egg that was laid on a Jewish holiday. An egg laid on a Jewish holiday is prohibited, but the next day you can eat it on Sunday — meaning if it was laid on the Sabbath, never mind, then you can eat it on Sunday. Now what happens if I have a doubt about that egg? It got mixed up with another egg, and now I don’t know which egg is the one laid today and which is not. So I have a doubt about each egg, whether it was laid today or not. Now since this is a rabbinic prohibition, one could be lenient. The Talmud says no — this is something that will later become permitted. Don’t be lenient now; wait until tomorrow and eat it without… And the same is said about a Torah-level prohibition that was nullified by majority. Nullification by majority does not work for something that will later become permitted. Some explain this, for example, as the reason why leavened food on Passover — yes, that’s already timely — why with leavened food on Passover nullification doesn’t help on a Torah level—

[Speaker E] And on a rabbinic level? What? It doesn’t help on a Torah level or on a rabbinic level? What? A Torah-level doubt that will later become permitted?

[Rabbi Michael Abraham] “Something that will later become permitted” is a rabbinic rule. Except for what the Ran says in Chullin, but all the medieval authorities (Rishonim) agree that it’s a rabbinic rule.

[Speaker C] The well-known dispute of Maimonides with the Beit Yosef regarding leavened food.

[Rabbi Michael Abraham] Yes, exactly. So regarding leavened food, some explain that leavened food on Passover is not nullified even in the tiniest amount because it is something that will later become permitted. Instead of eating it now and relying on majority, wait until after Passover and then you won’t have to take any risk at all — you’ll eat it freely. Now, there’s the prohibition of leavened food that remained over Passover, which is a rabbinic prohibition; never mind, there are all kinds of penalties about that. Not everyone agrees that leavened food is something that will later become permitted. But no matter; there is such an approach. What does it mean that with something that will later become permitted we are stringent? It basically means that when I follow the majority and eat something that was nullified by majority, I’m not doing something neutral. If I were doing something neutral, then why should I care that this is something that will later become permitted, and why wait until tomorrow? After all, even now I’m eating something perfectly clean. Why do I need to wait until tomorrow? I wait until tomorrow because they tell me: look, now you’re indeed allowed to eat it, but you’re taking a risk, because there is some chance that it is still prohibited. So wait until tomorrow, just a moment — wait until tomorrow; tomorrow it’ll be one hundred percent perfectly clean. But if in truth already today, when it is nullified by majority, it’s perfectly clean, there’s no issue, nothing wrong with it, everything is fine — then there would be no reason at all to wait until tomorrow in a case of something that will later become permitted. Meaning, the law of something that will later become permitted teaches us that these permissions — that in a rabbinic doubt one may be lenient, and that nullification by majority works for Torah prohibitions — are permissions in which it is appropriate to be stringent.

[Speaker E] But not because of any problem in the object itself at all, absolutely not. It’s because in our consciousness.

[Rabbi Michael Abraham] No, that makes sense—

[Speaker E] If it, if it will defile — they’re telling a person: listen, you’re eating pork with a certain 49 percent risk, and it will defile your soul, it will roll down to your descendants, it will change your world, all your powers — how can you take that risk? Is that what Jewish law says? No way. That doesn’t make sense in any way. No doctor would tell any patient: listen, you can — it makes sense for you to eat this, you—

[Rabbi Michael Abraham] You know what? Because danger is treated more stringently than prohibition — Jewish law says that too.

[Speaker E] So then defiling my soul isn’t danger?

[Rabbi Michael Abraham] No, it’s danger, but not mortal danger; it’s danger to something else. There’s a difference between danger of discomfort and danger of dying, right? Also in medicine.

[Speaker E] But, but a risk to my soul, for eternity — something that doesn’t make sense, it wouldn’t even enter the mind.

[Rabbi Michael Abraham] Let’s see what kind of risk it does to the soul; I don’t know.

[Speaker E] But that means that “defiling the soul” is just empty, hollow statements.

[Rabbi Michael Abraham] Fine,

[Speaker C] But that doesn’t exist in Jewish law. Why are we arguing about something that isn’t written in Jewish law?

[Rabbi Michael Abraham] What? What?

[Speaker C] What isn’t

[Rabbi Michael Abraham] written in Jewish law?

[Speaker C] These stringencies in Torah-level cases and so on, and “danger is treated more stringently than prohibition” — these are two different layers; they don’t even, so to speak, pass by one another. I didn’t understand. Regarding pork, yes? Completely dry law: now I take this, it’s fifty-one against forty-nine, it is permitted for a person to eat, unequivocally. On the Torah level he can eat.

[Rabbi Michael Abraham] I claim that despite that, there is still no proof that there is no problem in the object itself. That’s my claim.

[Speaker C] That’s not what I’m talking about. That’s not what I’m talking about. On the other hand, you take something that is because of danger, yes? That’s some sort of occult matter.

[Rabbi Michael Abraham] No, but the Sages said no no — danger, physical health danger, not occult.

[Speaker C] No, but all the physical dangers they spoke about, yes? We don’t know — that’s not Jewish law, it’s a saying.

[Rabbi Michael Abraham] “Danger is treated more stringently than prohibition” refers to danger, not occult danger and nothing of the sort. It’s ordinary danger. The fact that the Sages also thought about occult dangers, which they also considered dangers — fine, I disagree, it doesn’t matter — but the principle that danger is treated more stringently than prohibition was said about any danger, not occult dangers.

[Speaker C] I was speaking now specifically about pork itself, specifically about it. No one knows what the cause is and what the dangers are and what it is. It’s dry law: it’s permitted to eat. Right. And when a person eats — again, I don’t know, but in my opinion he violates no prohibition. If people are stringent, that’s individual to each person.

[Speaker E] But the question is whether in the 49 percent case, when something happens, the eternal aspect of the letter is damaged and the eternal aspect of the soul is damaged as a result of that 49 percent — that’s the question.

[Speaker C] But again, you’re speaking emotionally; halakhically it’s not correct.

[Rabbi Michael Abraham] I’m asking. Forget the eternal aspect of the letter and the metaphysics. Is there some result in reality here — that’s the claim about the object itself. Is there some result in reality here — forget mystical danger for a moment, just a second — that this prohibition causes? Okay. Now I’m asking: even if I am allowed to be lenient at fifty-one percent, that still does not mean there is no factual problem here. There is — there could be — a factual problem here. And they tell you: listen, you can take the risk, but know that it is a risk. How does Maimonides, for example, say that in a Torah-level doubt one may be lenient? The meaning of a Torah-level doubt being lenient is that there’s a fifty percent chance that you are eating pork. Exactly, even better. And on the rabbinic level they were stringent with you.

[Speaker E] There — another proof, another proof.

[Rabbi Michael Abraham] No, that’s not another

[Speaker E] proof, it’s not a proof, it’s the opposite.

[Speaker C] It’s

[Rabbi Michael Abraham] proof that there is no problem with pork at all. There’s no problem with pork at all. But know that you are taking some kind of risk, and if you hit the pork, then you have defiled your soul. But you can’t say that you violated a prohibition — those are two different things. The question whether the soul was defiled and the question whether you violated a prohibition are two different things.

[Speaker E] But that sentence also requires explanation: what does it mean to violate a prohibition? It means that the Holy One, blessed be He, does not want you to do it. So does He want you to defile your soul? No. He doesn’t want you to defile your soul. It doesn’t make sense that He would want—

[Rabbi Michael Abraham] that you should defile your soul — that doesn’t make sense. He permits you; not that He wants it. He says: there is no prohibition on this.

[Speaker E] But it will defile your soul and harm the eternal aspect in hod and will harm—

[Rabbi Michael Abraham] everything that the Holy One, blessed be He, wants. Before Hanan Porat passed the law “do not stand idly by your neighbor’s blood,” okay? Do you think the legislator didn’t want people to save others who are drowning in a river? Everybody wanted that, right? So why wouldn’t the law obligate it? What are we arguing about? There are things that, even though they are problematic, we do not require a person to do them, right? Same thing with eating pork. True, eating pork is problematic, but from the halakhic point of view we do not require it of you — you’re not obligated; if you want, take the risk. Taking the risk in itself is not a prohibition. Okay? But know that if you hit the pork, it will have defiled your soul; make your own calculation. And a conscientious person should be stringent. I don’t see any problem with that. Okay, in any case let’s get back to our subject; that’s not our topic. So what I want to say — how did we get into all this?

[Speaker F] Rabbi, sorry, regarding the conclusion, the upshot of the matter — if you say that bottom line even majorities that are negative, where it’s a multiplication not of numbers, but the basic assumption is that this all runs on statistics, then there’s no more room to distinguish with two majorities even when they’re negative? If everything altogether stands on statistics.

[Rabbi Michael Abraham] Yes, but how do you want to get there? Suppose you want to reach 98% certainty that the husband is dead, okay? Yes. Now you have an overwhelming majority, but you don’t know how much that overwhelming majority is. So you ask yourself, have I reached 98%? I don’t know. So they tell you: look, if you multiply two overwhelming majorities, you may assume that you’ve reached 98%. That’s a statistical consideration.

[Speaker F] Right, and we reject a statistical consideration as grounds to permit.

[Rabbi Michael Abraham] No. It’s a statistical consideration to permit — that is the two majorities.

[Speaker F] But why, if they’re two positive majorities that also reach 99%, wouldn’t we accept it?

[Rabbi Michael Abraham] No, of course we would accept it. More than that: there we’d accept even one majority, not two majorities. If there is one majority of 99%, I would permit the woman. That’s exactly the point. I need to reach a level of certainty called absolute-majority certainty — say that level is 99%, okay? I can reach that in many ways. For example, I can reach it with one majority that is 99%. No problem, the woman is permitted. Someone who identifies a face, nose with nose, okay? I can also reach it by multiplying two smaller positive majorities, 90%, both of them; the product of the two gives me 99%, and again the woman is permitted. What happens when the majorities are negative? I don’t know how to get to 99%; I don’t have numbers. So they tell me: look, if you multiply two overwhelming majorities, you may assume that you’ve reached 99%. But the goal in the end is to reach a statistical number. It’s all statistical thinking. It’s just that statistics teaches us how to work even when we don’t have all the data. Okay? That’s exactly it. It’s a bit tricky, but I think it’s a very important point, because you’ve seen all along how many mistakes people make when they don’t understand this. The whole idea here in permitting agunot is basically to reach statistical certainty that the husband is dead — that’s the whole idea, and the rest go and learn. Meaning, everything else doesn’t matter. How do we reach that certainty? There are various ways to get there. There are no formal gimmicks here. Formal Jewish law is irrelevant in the context of permitting agunot. It’s not interesting. We need to reach factual certainty that the husband is dead. That’s it. One principle and no other in permitting agunot. Therefore, when we started learning it on the analytic level — meaning, it’s an easy topic. You need to reach complete factual certainty that the husband is dead. This is not a matter of halakhic understanding at all. The halakhic complexity does not exist here. You need to reach a factual conclusion. The one who should decide here is a statistician, not a rabbi. On the principled level. Of course, when you don’t have numbers, the statistician will say: look, I don’t know how to answer you. Fine. Then the rabbi says what Jewish law tells us to do when we don’t know the numbers. But on the principled level, the entire question is how to reach certainty. There’s no halakhic complexity here at all. Therefore the greatness of the halakhic decisors who deal with permitting agunot and all things of that kind — I never understood that whole business. You don’t need any great analytic or halakhic brilliance here and so on. You need very good statistical understanding. Because we saw that even important decisors and outstanding Torah scholars and all that sometimes fail because of poor statistical understanding. And that is the focus of permitting agunot. Not Talmudic analysis. Not halakhic understanding. Okay, so now I want to get to the topic of two majorities that appears in the Talmud itself. The Talmud in Ketubot — yes, Kortzky, I think you brought this up one of the previous times.

[Speaker C] I asked twice when we’d get to it.

[Rabbi Michael Abraham] Here, now we’re getting to it. And the topic in Ketubot — I won’t study it inside, because there are all kinds of complications there — I’ll describe orally what’s going on there. There’s a story there about a girl, a girl who was raped by someone. Now the nearest city — yes, like in the case of the heifer with the broken neck, you go to the nearest city; apparently the rapist came from the nearest city. Most of the people in that city are people fit for the priesthood. Why is that important? Because if she was raped by someone disqualified from marrying into the priesthood, then she herself is also disqualified from marrying into the priesthood. If she was raped by someone fit for the priesthood, then she herself remains fit for the priesthood. So it matters very much who that rapist was, okay? But we don’t know who he was. We do know that in the city most people are fit for the priesthood. Therefore, there is a majority to permit this woman, this girl, okay? So Rabbi Yochanan ben Nuri says that we follow the majority of the city. If most of them are fit to marry into the priesthood, then she too is fit for the priesthood. But the Talmud there says no. Rabbi Yochanan ben Nuri doesn’t mean to say that one majority is enough to decide the doubt regarding this girl, to permit this girl. There, the case was one of two majorities, and therefore they permitted the girl. What are these two majorities? The Talmud says that there were the wagons of Tzipori there. There was some caravan, a group of people that passed by and encamped there too in the area of the city, okay? And in that group too there is a majority of fit people. Fine? There is a majority of fit people in that group too. So basically there are two majorities here. There’s a majority of the city and a majority of the caravan, and once there is a majority of the city and of the caravan, that’s two majorities, so we permit. But on the basis of the city majority alone we do not permit. Meaning, only with two majorities do we permit this girl to marry into the priesthood.

[Speaker E] Now, these are two separate populations. What? These are two separate populations: the city and the caravan. So what are the two majorities here?

[Rabbi Michael Abraham] Ah, excellent question, the obvious question. In fact, when we think about this Talmudic passage—

[Speaker F] It reminds us of Rabbi Herzog, Rabbi Herzog’s tree.

[Rabbi Michael Abraham] Exactly. Wait, let me see how I get back to the screen where I can see you. Good. So Shmuel’s question is an excellent question, the obvious question. This simply is not two majorities. Why? Because there are two groups of people: the people in the city and the people in the caravan. In the city. You understand that this graph looks exactly like Rabbi Herzog’s graph above. What does that mean? The question is what are the “two majorities”? There’s a majority — meaning, the question is whether you are in the city or in the caravan, and even if you are in the caravan there is a majority of fit people, but even if you are in the city there is a majority of fit people. The question whether you belong to the caravan or belong to the city is irrelevant; it’s uninteresting. Practically speaking, look at the caravan and the city as one large group; within that group there is a majority of fit people. So that is one majority, not two majorities. So in fact this thing — in our jargon I called it — is not a “majority of a majority,” it is “two majorities.” It is two majorities, but it’s like one majority; that is, there is no real significance here. A “majority of a majority” is when one majority multiplies another majority. Here the majorities do not multiply each other. It’s just two majorities; this pair of majorities is uninteresting. Now of course we need to understand — so seemingly, let’s phrase it like this — seemingly what we see here is against what I said. I said that two majorities exists only when the majorities are multiplied, and therefore I said Rabbi Herzog was mistaken and there is no such thing. But here is the case of two majorities in the Talmud, which is apparently the inspiration for applying two majorities to agunot, and it too is apparently a case of two majorities and not of a majority of a majority. Now here — this is what you asked, Turetzky, right? Now I want to answer that. The Talmud discusses there the question why we really need two majorities. Why isn’t the majority of the city’s people enough? In Jewish law we follow the majority. Why do we need two majorities here? So the Talmud says: because the majority in the city is not a majority, it is fixed. The people living in the city are fixed in their place, unlike the caravan, whose people are mobile. Okay? Therefore, the majority in the city is considered half and half. It is not considered a majority. Right? Something fixed — we discussed fixed status — something fixed in its place, there we do not follow the majority; it is considered half and half. Therefore we need two majorities. So why not permit on the basis of the caravan majority? Say there is no city, only a caravan. Even then they do not permit; they require two majorities. Now this is even stranger. What do you mean, you need two majorities? The city only harms the majority. Say the caravan majority is 80%, and the city majority is also 80%, okay? For the sake of discussion. Now when you tell me that two majorities are required, you still understand that the bottom line is 80%, because whether he came from the city or from the caravan, there’s an 80% chance he is fit. That’s why this is not a majority of a majority but just two majorities. But even the two majorities here are highly problematic, because if the city is considered fixed, then the fact that there are 80% fit people in the city is halakhically irrelevant to me — halakhically it’s 50-50. Now look: I have two groups. In one group there are 80% fit people; in the second group there are 50% fit people. So what is the chance that the man who had relations with her was fit? Suppose there are the same number of people in both groups? Sixty-five percent, right? Between 50 and 80 — the middle. Say there are one hundred people in the city and one hundred people in the caravan. Eighty people in the caravan are fit. Fifty people in the city are fit, halakhically. In reality it’s 80% fit, but halakhically since it is fixed, it is considered 50% fit. So how many fit people are there altogether? 130 out of 200. 130 out of 200 is a majority of 65%. In short, our situation is worse than the caravan alone. So why do I need both city and caravan? So the Talmud says this is a decree. It is a decree, because if you permit based on the caravan majority, then people will come to permit based also on the city majority, and based on the city majority one cannot permit because that is fixed. Therefore they do not permit on the basis of caravan majority alone, but require two majorities. The city majority alone does not permit because there simply is no majority; it is half-half, halakhically half-half. Meaning, that’s fixed. Caravan majority alone also does not permit — why? Because of a decree lest one come to permit based on the city majority, where it is fixed and one cannot permit. Therefore they require that there be both city and caravan. That’s what the Talmud says. Now if that really is the situation, then we are not in the world of statistics at all. It’s completely irrelevant what the majority is here. Why? Because the whole need to also have the city is only to block permission based on caravan majority. In fact, based on the caravan majority alone she is permitted. And even if the majority were 51%, she would also be permitted. You don’t need an overwhelming majority or anything. This is not the law of agunot. Rather, there is a rabbinic decree requiring also the city majority, so that if we permit only on the basis of caravan majority, someone else will come to permit only on the basis of city majority. So it’s a decree; it doesn’t come to solve a statistical problem. It doesn’t come to improve the statistical percentages, because that isn’t needed. Because in the end, if I have 51%, everything is fine. Say there is a caravan majority of 51%, and in the city too it is 51%. Excellent, everything is fine. By contrast, a caravan majority alone of 99% is not fine. How can that be? Ninety-nine percent there, and there it’s 51; the 99 isn’t okay and the 51 is? The answer is: the 51 is not okay because of the decree. Statistically I would permit there, but there is a rabbinic decree lest people come to permit on the basis of city majority. Now if so, then this has nothing at all to do with Rabbi Chaim of Volozhin’s question of two majorities. Because Rabbi Chaim of Volozhin is speaking about a statistical question: how can I be sufficiently certain that the husband is dead? Only if I multiply two majorities. Only then can I reach absolute certainty. If I have not a majority of a majority but just two majorities, like Rabbi Herzog, it helps not at all, because it does not improve my situation on the factual level. But in the Talmud in Ketubot, on the halakhic-statistical level, 51% is enough for me. Majority is enough to permit, like everywhere else in Jewish law. Therefore the question that the Talmud in Ketubot is dealing with is not a statistical question at all and not a factual question. Statistically, 51% is permitted. I am only concerned that there is a decree lest one come to permit based on city majority. So I say, fine, let there be both city majority and caravan majority in order to permit. Just to prevent people’s mistake. It doesn’t come to improve our statistical situation by combining the city majority. Therefore there is no difficulty from the Talmud in Ketubot against what I said regarding permitting agunot. And the whole idea — and note this — everything follows from the understanding that has accompanied us all along, that the discussion in permitting agunot is a factual statistical discussion. We need to reach factual certainty; I’m not interested in the law. I need to reach factual certainty. The discussion in Ketubot is exactly the opposite. The statistics don’t interest me in Ketubot. Understand something: if in the city it’s 50-50, then whatever majority there is in the caravan, the combination of the two is still a majority, right? Maybe a smaller majority, but always a majority. It won’t fall below fifty percent. Therefore I have no problem; it is always a majority, and any majority is enough to permit. The whole reason you need the city is only, first, that it not ruin the majority, and second, because of the decree, so that they not permit based on the city alone.

[Speaker E] But is the decree specific to that story there, of a daughter of a priest, or maybe it’s a general decree for everything?

[Rabbi Michael Abraham] As far as I know, no one extends it; it’s a decree only there.

[Speaker D] Meaning, in principle she’s permitted because of the city majority; it’s just that I need the caravan majority to distinguish this from an ordinary majority. From an ordinary caravan majority? No, the opposite. You need the city majority, and caravan majority alone is not enough, in order—

[Rabbi Michael Abraham] to distinguish it from a case of an ordinary majority.

[Speaker D] Yes, and in the end she’s permitted because of the caravan majority, practically speaking. Right, exactly.

[Rabbi Michael Abraham] You just need the city majority only to sort of light a torch: pay attention, this is only a caravan, and don’t permit on the basis of fixed status. Understood. Basically, could there also have been some other distinguishing marker? What? Practically, there could also have been some other marker in principle. In principle, it is certainly possible that if they set up some very very clear marker, one could permit on the basis of caravan majority without city majority. I’d even say that perhaps as practical Jewish law. Yes, it’s only a marker; it doesn’t come… I’ll give you an example so the point becomes sharper. Say in the city there is a majority of disqualified people, not a majority of fit people. In the city there’s a majority of disqualified people, say 80%, and in the caravan there is a majority of fit people of 70%. So what is the chance that the man who had relations with her was fit?

[Speaker C] Forty. No, not forty, yes, but even that doesn’t come out because it’s the average between thirty and eighty.

[Rabbi Michael Abraham] The average between thirty and fifty.

[Speaker D] But aren’t you treating it as fixed 50?

[Rabbi Michael Abraham] Fifty-five, the average between thirty and eighty.

[Speaker C] But the city is fixed.

[Rabbi Michael Abraham] What? Ah, exactly. So on the statistical level there can be a situation where the city majority ruins things for me. Because with the caravan majority — say the caravan majority is 70%, and in the city there are ninety — ninety percent disqualified. Then I now have forty percent fit, forty percent chance that the intercourse was with someone fit, right? The average between ten and seventy. In the city there are ten percent fit, in the caravan seventy percent fit. So in the entire population, say there’s the same number in both groups, there’s a forty percent chance that the man was fit. Right? Now on the principled level, we still validate her here. Why? Because on the formal level the city is considered fixed, so it’s 50-50. Because with fixed status we go that way whether leniently or stringently — that’s the Talmud there in Ketubot. Whether leniently or stringently, it is considered fixed, like half and half. So it comes out that in the city it is fifty, and I have seventy percent in the caravan, so practically speaking halakhically it’s sixty percent, even though statistically it’s forty percent. And still we permit it. Why? Because the question is not a factual question; it is a halakhic question. In such a situation with an agunah, Heaven forbid to permit. So there’s some sort of formal problem here by the way — the issue of fixed status in an agunah will play no role at all, that’s my claim. I don’t know a source for that, but it’s clear to me. The issue of fixed status will play no role. What matters there is only the statistics.

[Speaker D] And here too you see that sometimes the halakhic consideration actually wrecks things, I mean goes against the real consideration.

[Rabbi Michael Abraham] Right, to that extent — that’s why I brought it. Meaning, to that extent reality doesn’t interest us here; we are dealing with the formal halakhic layer, such that sometimes in reality there is a majority of disqualified men and still we will permit because halakhically, formally, it is permitted. This is to sharpen the claim I made earlier, that the Talmud in Ketubot deals with Jewish law, whereas permitting agunot deals with reality.

[Speaker D] Does the Rabbi have an explanation for that? I mean, when do we, how do we just ignore reality like that?

[Rabbi Michael Abraham] That’s the law of majority — what do you mean? What is the law of fixed status? The law of fixed status says that we ignore reality.

[Speaker F] Rabbi, you once explained that when it’s intentional — I don’t remember exactly what — but that one doesn’t use majority and probability when it’s intentional. And here the person who left the city did so intentionally, and he knows, he himself knows.

[Rabbi Michael Abraham] No, I didn’t go into all the details there in the Talmud. There they discuss that the girl came from the city to him, not that he went out. Otherwise it wouldn’t be fixed; he would have separated from the fixed place. But even if he separates intentionally, it may remain fixed. The topics there are very complicated, so I didn’t get into them.

[Speaker E] The fixed status here is because she went out to him; now that also fits the Rabbi’s explanation.

[Rabbi Michael Abraham] Exactly. Although even if he leaves the city — I don’t even remember all the details at the moment — even if he leaves the city, since he leaves intentionally, it may still be considered fixed.

[Speaker C] The Talmud there on the spot says that the decree “because of the city” also applies with the caravan. Meaning, right, it doesn’t matter what happened — whether she went to him or he to her — the Talmud says that the conclusion there, Rashi there writes that it’s the city itself and a decree because of city-and-caravan. Meaning, they connect them to each other. Yes, I remember Ketubot very well. But there’s another question here. There’s another question here. In one place in the Talmud we learn two majorities, yes? We learn it here in Ketubot 15. And we started this whole discussion of doubt and probability here from two majorities. But it comes out that those very two majorities learned from the Talmud are not at all in the reality we’re dealing with here.

[Rabbi Michael Abraham] That is exactly my claim here. That the concept of two majorities is apparently drawn from the Talmud in Ketubot, and Rabbi Chaim of Volozhin merely wanted to say: we apply it also to the laws of permitting an agunah. And now I’ve shown you that this isn’t true. Because if one properly understands the two majorities in permitting agunot, one sees that it has nothing whatsoever to do with the two majorities of Ketubot. That is Rabbi Chaim of Volozhin’s innovation.

[Speaker C] But why call it two majorities? It should be called something else.

[Rabbi Michael Abraham] Because it is two majorities — I don’t know why. Fine, but it’s not — it really isn’t. Okay, so the claim — so this is another implication of how important it is to understand the idea behind the Talmudic or halakhic discussion. Are we looking for reality? Are we looking for Jewish law? How all the considerations are laid out in light of that principle. I just want to finish this topic as well; it took me more time than I planned.

[Speaker B] Just a question, Rabbi. I didn’t understand the calculation you did where you took the average. I mean, earlier when we spoke about, say, two 70 percents, then you did a calculation like a binomial distribution, meaning you calculated and got 91 percent, right? By multiplication.

[Rabbi Michael Abraham] Yes. And now why did you take an average?

[Speaker B] I didn’t understand.

[Rabbi Michael Abraham] Here it’s not multiplication. That’s exactly the point. It’s two majorities; it’s not a majority of a majority. Okay. In Maimonides, Maimonides explains the topic a bit differently, the topic in Ketubot. He says: “When are these words said? When the place where she had intercourse was a crossroads or the corners in the fields, where everyone passes, and most of the passersby there were fit, and the majority of the city from which those passersby came were fit; for the Sages made an extra safeguard in matters of lineage.” By the way, from Maimonides it sounds as though the city itself must have a majority of fit people. If there is a majority of disqualified people — true, halakhically it is considered fixed, but there still needs to be a majority of fit people there. Fine? And again, that is probably because of the logic of the decree; it’s not a regular halakhic consideration. So he says, “and the majority of the city from which those passersby separated were fit.” He explains that the caravan outside the city is not random passersby passing by the city, but a group that separated from among the city residents. There are city residents, some of them separate out, and in that separated part too there is a majority of fit people. And in the city too there is a majority of fit people. That now seems more like a majority of a majority. It’s not that there is a caravan and a city and each has a majority — that’s like Rabbi Herzog, just two majorities, not a majority of a majority. But Maimonides says that the second majority came out of the first. Meaning, there is a city majority, and from it some separated, and there too there is a majority of fit people. But of course that’s still not right. Why? Because think about the group that separated. In the city, say there are seventy percent fit people, and say there are one hundred people in the city and seventy percent are fit. Say fifty people separated from the city. And among those fifty too there is a majority of fit people. Why? Because the fifty who separated from the city residents — say this is a representative sample — then it is made up of thirty-five and fifteen, right? Assuming the separation happens more or less according to the composition of the city residents. And then what do we get? That we have two groups, fifty people here and fifty people there, and in each of the groups there are seventy percent fit people. Therefore this is still just two majorities and not a majority of a majority. It looks like a majority of a majority, but it would be a majority of a majority only if we knew that the group that separated from the city was a group, say, of disqualified people, and then suddenly a majority of them turned out to be fit. That could have been a majority of a majority. They’d basically be saying: there is a minority of disqualified people, and even from that minority only a minority remain disqualified. There you would already have multiplication of majorities. That would be a majority of a majority, and not just two majorities. But according to Maimonides it is not like that. The people who separated from the city are people whose distribution is like the distribution in the city. So what difference does it make? Think of it as two groups located in the city in two different parts of it, and everything is distributed seventy-thirty. Nothing changes. It is still just two majorities and not a majority of a majority. There is some gain in Maimonides’ picture, but okay, I won’t get into that here; whoever wants can look on my website, column 612. At the end of the column I explain that perhaps Maimonides still gains something with this interpretation. Okay. We’ll stop here. If there are comments or questions or…

[Speaker C] What about Passover?

[Rabbi Michael Abraham] We’re going on break until Thursday after Passover.

[Speaker C] Okay. And next semester, does it go back to regular studies at Bar-Ilan?

[Rabbi Michael Abraham] You’ll get updates. It depends on the war. Okay, good. Rabbi,

[Speaker C] Rabbi?

[Speaker E] Yes. Can we go back to the riddle you asked us at the beginning of the class? Next class? So does the Rabbi remember? With the woman and the two children and all that. In the previous class. In the previous class, I said — yes, yes — I said in the previous class that it bothered many people. I actually asked: if, assuming I understood correctly, the case was when the woman said that one of the children is a boy. If she had said that the firstborn is a boy, or that the second one wasn’t born at all, then here it would already be a split of fifty-fifty, am I right?

[Rabbi Michael Abraham] Yes. I sent the video explaining it, I think, on WhatsApp.

[Speaker C] In English, what was there with the percentages? Yes. More or less, yes, it works out.

[Rabbi Michael Abraham] Okay, friends, have a kosher and joyous holiday, and may we hear good news. Happy holiday, thank you very much, thank you very much, thank you very much, goodbye.

Doubt and Probability—in Halakha, Thought, and in General—Lesson 45—Rabbi Michael Abraham

Table of Contents

Summary

General Overview

Positive Majority and Negative Majority

Overwhelming Majority, Absolute Majority, and Two Majorities

Mistakes in Applying Two Majorities

The Direction of the Probability Question

Permitting an Agunah as a Probabilistic Matter

Majority versus Halakhic Formalism

Ketubot and the Two Majorities of City and Caravan

Majority upon Majority versus Two Majorities

Maimonides and the Explanation of the Topic

Full Transcript

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Table of Contents

Summary

General Overview

Positive Majority and Negative Majority

Overwhelming Majority, Absolute Majority, and Two Majorities

Mistakes in Applying Two Majorities

The Direction of the Probability Question

Permitting an Agunah as a Probabilistic Matter

Majority versus Halakhic Formalism

Ketubot and the Two Majorities of City and Caravan

Majority upon Majority versus Two Majorities

Maimonides and the Explanation of the Topic

Full Transcript

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