Doubt and Probability—in Halakha, in Thought, and in General—Lesson 48 – Rabbi Michael Avraham

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

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Review of what we learned: probabilistic products and double doubt as a product of doubts
The two central rules of double doubt — a single type of doubt and reversible double doubt
A single type of doubt — Tosafot on Ketubot 9a in the passage of “I found an open entrance”
Reversible double doubt — Old Tosafot on Ketubot 9b (doubt about the husband’s expertise in identifying an “open entrance”)
The example of the blemished slaughtering knife (the Shakh in the name of the Agur) in which both rules hold together
The dispute of Rabbi Akiva Eiger: are the two rules really one rule?
The Rabbi’s claim: the two rules are independent and unrelated principles
The distinction between the legal ground of the ruling and the concrete reality as the key to understanding a single type of doubt
The counterexample from Old Tosafot — non-reversibility without a single type of doubt
The explanation of a single type of doubt: counting sides in a negative doubt on the basis of the grounds for permission
Additional examples: doubt whether blood came from the upper chamber or from elsewhere in the laws of niddah, and the case of two majorities among stores
A first attempt to explain the requirement of reversibility — a formal overwhelming majority (75%)
Rejecting the first explanation: sides are not a real indication of probability
A second attempt (toward the next lecture): probabilistic dependence between events
The example of crib death in Britain and the problem of multiplying probabilities in dependent events
Non-reversibility as an expression of logical dependence between the doubts
A moral question: asking forgiveness when one only later discovers that one acted improperly

Summary

General Overview

This lecture continues the discussion of double doubt — a product of doubts, which we discussed in the previous lecture in the context of probabilistic multiplication. The Rabbi focuses the discussion on the two main formal rules of double doubt: a single type of doubt and reversible double doubt. He argues — against Rabbi Akiva Eiger and many others — that these two rules are independent principles and do not depend on one another, and he tries to explain why each one is separately required.

The Two Main Rules of Double Doubt

The first rule — a single type of doubt — appears in Tosafot on Ketubot 9a in the passage of “I found an open entrance,” in the case of the wife of an Israelite whose father accepted her betrothal when she was less than three years old. Even though there are in practice two doubts there (whether it was by coercion or consent, and whether she was a minor or already grown), Tosafot rule that this is “a single type of doubt” because the ground for permission in both branches is the same ground — coercion. The second rule — reversible double doubt — appears in Old Tosafot on Ketubot 9b, and requires that the two doubts be presentable in either order. The Shakh rules this as practical Jewish law, although some later authorities disagree.

The Example of the Blemished Slaughtering Knife

The Shakh cites in the name of the Agur the example of someone who slaughtered an animal and only afterward discovered that the knife was blemished. There is a double doubt: perhaps the knife became blemished only after the majority of the סימנים were slaughtered, and perhaps it became blemished only upon hitting the vertebrae. The Shakh rules that this is a double doubt that is not reversible, because the doubts cannot be presented in the opposite order. The Rabbi emphasizes that in this example both rules hold together: the type of doubt is also single (there is one ground of permission — that the slaughter was valid at the relevant time), and it is also non-reversible. That is why many identify the two rules with each other.

The Dispute with Rabbi Akiva Eiger

Rabbi Akiva Eiger holds that the two rules are really one and the same: when Tosafot on Ketubot 9a say “it is one type of coercion,” what they really mean is that the double doubt is not reversible. The Rabbi disagrees: in that passage the double doubt actually is reversible — one can doubt whether she was a minor or grown after first doubting whether it was coercion or consent, even if legally the seduction of a minor counts as coercion. The Rabbi emphasizes an important distinction: when we speak about a single type of doubt, we are speaking about the legal ground of the ruling, not about the detailed factual reality — the same ground (coercion) can arise from several different realities.

The Counterexample — Non-Reversibility Without a Single Type of Doubt

In contrast to the knife example, where both rules hold together, in the example of Old Tosafot (doubt about the husband’s expertise in identifying an open entrance plus doubt of coercion/consent), the double doubt is not reversible, but the type of doubt is not single: there are two different grounds for permission — one because there was no intercourse at all (if he is not expert), and one because there was intercourse but under coercion. This is the counterexample that proves the two rules are independent.

The Explanation of a Single Type of Doubt

The Rabbi explains that a single type of doubt is, quite simply, a sensible rule: when counting sides in a negative doubt (where the probabilities are not known), one must decide what counts as an independent side. The accepted criterion is the ground for permission — different sides that lead to the same ground count as one side. Otherwise, one could split every side into infinitely many sub-sides and permit anything. The Rabbi also discusses the example of doubt whether blood came from the upper chamber or from elsewhere in the laws of niddah, and the borrowed example of nine kosher stores מול one non-kosher store.

A First Attempt to Explain the Requirement of Reversibility — A Formal Overwhelming Majority

The first explanation the Rabbi suggests is this: when the doubt is reversible, there are three sides for permission out of four (75%); when it is not reversible, there are five out of eight (62.5%). This would be a formal requirement of an overwhelming majority, similar to the requirement of a double majority in permitting agunot — since in a negative doubt we do not know the real probabilities, we require a formally larger majority so there will be a good chance that there is also a real probabilistic majority. But the Rabbi himself rejects this explanation, because under different formulations of the doubt there are not really more or fewer sides — it is just a formulation that does not allow all the doubts to be expressed.

A Second Attempt (Toward the Next Lecture) — Probabilistic Dependence

The direction the Rabbi is heading in is that non-reversibility expresses logical dependence between the doubts. In probability, when two events depend on one another, you cannot multiply their probabilities. The Rabbi demonstrates this with the case of crib death in Britain: the argument that a chance of 1 in 8,000 twice equals 1 in 64 million is mistaken, because the events are dependent (there may be a shared genetic problem). So too with a non-reversible double doubt — there is logical dependence between the doubts, and therefore it should not be treated as the product of two independent doubts, but as a single doubt with a chance of one-half rather than one-quarter.

A Moral Question — Asking Forgiveness Based on Retrospective Discovery

At the end of the lecture a side question comes up: is there any significance to asking forgiveness when a person discovers only afterward that he acted improperly? The Rabbi presents a nuanced position: one should distinguish between the moral dimension and the psychological dimension. Morally, the knowledge that the act was wrong adds nothing to the injured party; the psychological dimension of sharing in the pain is a separate issue.

Full Transcript

[Rabbi Michael Abraham] In the topic of probabilistic multiplication, we talked about multiplying one majority by another majority, and now we moved into double doubt, which is really a product of doubts. And we saw that in this world of double doubt there are two common rules — not both of them are completely agreed upon, but they are both widely used, and the halakhic decisors at least use them as though they were clear rules. One is the rule of a single type of doubt, and the second is the rule of reversibility, that a double doubt has to be reversible. Now, the rule of a single type of doubt — let’s remind ourselves — suppose someone comes and says, “I found an open entrance,” to his wife. Then there is a doubt whether it happened before she was under him or while she was under him, and a doubt whether it was by coercion or by consent. The Talmud says, in the end, that this is set up as a case of the wife of an Israelite — one of the possibilities — whose father accepted her betrothal when she was less than three years old. Then really there is a doubt of coercion or consent; the doubt whether it was before she was under him can’t apply, because if it was before she was under him then her virginity would have returned — the virginity of a girl under three returns. So therefore there is only one doubt, and that is what Rabbi Elazar said: that someone who says “I found an open entrance” is believed to prohibit her to him. And Tosafot ask on that: there is still an additional doubt. There is the doubt of coercion or consent, and even if you say it was consent, it still may have been when she was a minor. And when she was a minor, the seduction of a minor counts as coercion. So in fact she still would not be prohibited to him. So really, even in this case that the Talmud presented as a case of a single doubt, in fact we are dealing with a double doubt. And Tosafot answer: it is one type of doubt. What does that mean, one type of doubt? If it was by coercion, then she is not prohibited to him — we are dealing with the wife of an Israelite, and if it was by coercion then she is not prohibited to him. If it was by consent but she was a minor, then she also is not prohibited to him. But why is she not prohibited to him? Because intercourse with a minor, even if it was by seduction and not by force, is considered coercion, as we know even today in Israeli law — there is no such thing as the consent of a minor, because she lacks legal capacity. So Tosafot say that this is not a double doubt, and it is not a double doubt because her permission to remain with her husband, whether because the intercourse was by coercion or because it was by consent but she was a minor, is the same permission, based on the same ground of permission, namely coercion. And therefore it is one type of doubt; basically the only doubt is whether this was coercion or not coercion. The doubt whether she was a minor or grown is just another kind of coercion. In exactly the same way, I could have said: maybe it was consent, or maybe coercion with a gun, or coercion with beatings, or coercion through the seduction of a minor. I have lots of options, or kinds of coercion, that I could insert here as additional possibilities. But that does not count as additional branches of doubt or additional options on the map of doubts, because from our point of view all of these are simply kinds of coercion. So the whole question is whether it was coercion or consent. What exact kind of coercion was involved here — what difference does it make whether it was the seduction of a minor, coercion with a gun, coercion by beatings, or coercion by hypnosis, I don’t know exactly what. It doesn’t matter: coercion or consent. And I explained that the whole idea here is that we are not talking about a positive doubt, a doubt where we know the chances are split fifty-fifty, because if that were the case then there is no game here at all in the realm of double doubt. Then it is simply irrelevant whether it is one doubt or a double doubt — check the probabilities, and if there is more than fifty percent then you have a majority and everything is fine. Therefore the whole idea of double doubt applies only to negative doubts. In a situation of negative doubts, you really have no way of knowing the distribution of probabilities. And on that the Talmud says — yes — if you have two doubts, a double doubt, you can assume these are two balanced doubts, and then in effect there is a majority in favor of one side. We talked about the fact that this is a majority of sides, not a probabilistic majority. Now once we speak about a majority of sides, that of course raises the question: what counts as a side? After all, we are not talking here about probabilities. If it were about probabilities, there would be no problem — do the calculation and that determines whether there is a majority or not, simply by percentage. If you have more than fifty percent, you have a majority. But when you count sides, you have to decide, because “sides” is not a probabilistic concept. “Sides” is a concept from everyday thinking, from the way we think. So what counts as sides? I can define the sides of a doubt in lots of ways. Understand that if I now have, say, a doubt of coercion — only a doubt of coercion — it is clear that it happened while she was under him, but there is a doubt of coercion or consent. So that is one doubt, right? We have to be stringent. Okay. But I could say: what are you talking about? On the side that it was coercion, maybe it was coercion with a gun, maybe coercion with beatings, maybe coercion because he hypnotized her, so in fact I have three kinds of coercion and only one kind of consent, of willing participation. So if that is the case, I have a majority of sides in favor of coercion even in a single doubt. I have a majority of sides in favor of coercion.

[Speaker B] So why do I decide that this is just one doubt and not a double doubt or a majority that would permit her? Rabbi, didn’t we say that when it’s the same reason for prohibition, we don’t count it as another side?

[Rabbi Michael Abraham] Right, that’s what we’re saying, and that’s why I’m now summarizing what we said. The claim is that when there are several sides and behind all of them there stands the same reason for prohibition, they count as one side. And again, that is only because the doubt is negative. Because in a negative doubt, every decision is a formal decision. I count sides, but I have to decide what counts as a side, and probability does not determine that because I do not know the probabilities, so all I’m doing is counting sides. Now here there is some element of arbitrariness, so what counts as a side? So the claim of a single type of doubt, the claim of Tosafot, is that where the halakhic ground of the ruling — in this case, the ground for her being permitted to her husband — is the same ground, in this case the ground of coercion, I don’t care that there are several factual possibilities that generate that ground of coercion. At the end of the day, the ground that brings about her permission to her husband is coercion, and therefore it is one side. That is the point. It could be weak coercion, strong coercion, this kind of coercion, that kind of coercion — I can raise one hundred thousand sides. We don’t get tangled up in that, because when we count sides we formally decide what counts as a side. And that is the meaning of “it is one type of doubt.” And I explained that of course in every double doubt you could say there are three sides for permission and one for prohibition, so there is one type of permission, and then every double doubt would become only a single doubt. But no, that’s not correct, because the sides we are counting — the “type” we are talking about is the type of the sides that lead to permission. It is not the type of the ruling itself. It is not “one type of permission,” but “one type of coercion.” “One type of coercion” — coercion is the ground for permission; it is not the permission itself. In other words, different sides that lead to the same ruling are different sides. But when there are different forms of the same side that lead to the ruling, that is one side. Okay, so that is the idea of a single type of doubt. Now after that we saw the second principle, namely reversible double doubt. So here, reversible double doubt is basically Old Tosafot one page later in Ketubot 9b. The first one was Tosafot on Ketubot 9a; this is Old Tosafot on Ketubot 9b. Tosafot basically say: we have a monetary question, say whether the woman married as a virgin or not as a virgin. And when the husband comes and says, “I found an open entrance,” he is basically claiming that the woman was not a virgin, so she deserves a ketubah of one hundred zuz and not two hundred. Even if it happened before she was under him, yes, that does not matter — in fact specifically if it happened before she was under him. So if it happened before she was under him, then in effect already at the time of marriage, at the betrothal, she was no longer a virgin, and the ketubah of a non-virgin is one hundred. Fine? So Tosafot ask: why should this be a case where we have to be stringent? After all, there is really a double doubt here. It could be that the husband is not expert in identifying an open entrance. It could be that the husband does not know how to tell whether the woman in fact had an open entrance, whether intercourse had already taken place or not. Remember, this is his first intercourse — he just got married. He is surely not a great expert in these matters. And since that is the case, I really have a doubt whether he correctly diagnosed the situation. In other words, even if she had had intercourse — that is, the question whether she was a virgin or not, meaning whether — wait, I have a doubt whether this happened while she was under him or not, but beyond that I have a doubt whether there was any open entrance there at all. Okay? Meaning, does the husband know how to identify such a thing at all? So Old Tosafot answer it like this: this is not considered a double doubt. Why? Because this double doubt is not reversible. What does that mean? We are really saying the following: there is a doubt whether the husband is expert in identifying an open entrance or not expert in identifying it, and then I have the doubt of coercion or consent. Okay? Now if it were the other way around, I would doubt whether it was coercion or consent, and if you conclude that it was consent, then the question would be whether the husband is expert in identifying an open entrance. That would be the reverse formulation of the doubt; now I’m arranging the doubts in the opposite order. But it can’t be arranged that way. After all, on the side that it was by consent, I am already assuming there was an open entrance, otherwise what does it mean to say it was by consent or by coercion? So there is no room to wonder whether the husband is expert in identifying an open entrance, meaning whether there was any opening there at all. You can only present the doubts in one order: first the question whether the husband is expert in identifying an open entrance or not, and if he is expert — meaning, there was an opening there — there still remains the question whether it was by coercion or by consent. But you can’t present it in reverse. You can’t say: I have a doubt whether it was by coercion or by consent, and even if you conclude that it was by consent, the question is whether the husband is expert in identifying an open entrance. If it was by consent or by coercion, in either case we are talking about a case where there was an open entrance, so there is no point now in doubting whether the husband is expert or not. In this formulation, we are assuming he is expert. And therefore this double doubt, says Old Tosafot, is not reversible. If we compare it to the basic doubt there in the Talmud, where the Talmud says: a doubt whether it happened while she was under him or before she was under him, and a doubt whether it was by coercion or consent — here you can present the doubts in either order. Was it by coercion or by consent, and even if you conclude consent, the question is whether it happened while she was under him or not. Or: did it happen while she was under him or not, and even if you conclude that it did, the question is whether it was by coercion or by consent. The order in which the doubts are presented makes no difference; I can present the two doubts in whichever order I choose. That is called reversible double doubt. I can present the doubt of coercion/consent first and then whether it was while she was under him or not, and I can decide that the second doubt will be first — whether it was while she was under him or not — and then present the doubt whether it was by coercion or by consent. That is called reversible. By contrast, the doubt whether he is expert in identifying an open entrance or not expert, together with the doubt of coercion or consent, is not reversible. Because if I first ask whether it was by coercion or by consent, I have already assumed there was an open entrance. I cannot then go back and ask: wait, but maybe there was no open entrance at all. I can only present it the other way around: first wonder whether there was an opening or not, and then, if there was, ask whether it was by coercion or by consent. That is a valid path, but only that path is possible. You cannot reverse the order in which the doubts are presented. That is called a double doubt that is not reversible. Old Tosafot say that a double doubt has to be reversible; if it is not reversible, then it is a single doubt and one must be stringent. That is how the Shakh rules in practical Jewish law. There are other later authorities who disagree, so this rule is not universally agreed upon, this rule that a double doubt must be reversible. But among contemporary halakhic decisors it is somehow accepted to think that a double doubt needs to be reversible. So for our purposes, let’s discuss it on the assumption that it does. Fine? So we basically have two rules, and we need to explain both of them.

[Speaker C] Now the rule of why it has to be reversible?

[Rabbi Michael Abraham] Why is it important that it be reversible? Now I’m coming to the explanation of the rules. Why is it important that it be reversible? Now I’m beginning to talk about the explanation of the rules. We have to explain why it needs to be reversible and why “it is one type of doubt.” Why is a single type of doubt not a double doubt? We need to explain both of these rules. So, first of all.

[Speaker D] Actually, Rabbi, I think it’s intuitive that it has to be reversible in order to count as a double doubt. No, it makes sense, because if it can’t be reversed then it’s really only one doubt; there aren’t two doubts here. Why? Because if the husband — if… there is a doubt whether the husband is expert or not, then the second doubt doesn’t even get off the ground.

[Rabbi Michael Abraham] Why? Of course it gets off the ground. If the husband is expert and there is an opening here, then now there is a doubt whether it was by coercion or by consent. What is the problem?

[Speaker D] So what does it mean, then, that it’s not reversible? What is the move?

[Rabbi Michael Abraham] In the reverse order you can’t say it. You can’t first doubt whether it was by coercion or by consent and then doubt whether the husband is expert. Because once you assumed that it was either coercion or consent, you already assumed there was an

[Speaker D] opening. Okay.

[Rabbi Michael Abraham] And the first side is indeed a side that can be formulated. There are four sides here, of which three lead to permission and one to prohibition. It’s just that it’s not reversible. There is another example of double doubt regarding a blemish in a slaughtering knife. The Shakh brings it in his rules of double doubt in the name of the Agur. He says that what the Talmud in Hullin says — that if someone slaughtered an animal and after the slaughter found that the knife was blemished, and with a blemished knife the slaughter is invalid — so if someone slaughtered an animal and afterward looks at the knife and sees that it is blemished, then the slaughter is invalid and the animal is considered a carcass. That is what the Talmud says in Hullin 10. So some medieval authorities asked why, nevertheless, we should not permit the animal on the basis of double doubt. There is a doubt whether the knife became blemished during the slaughter or after it. “After it” means after he passed through the two סימנים and reached the vertebrae, and only the vertebrae are what damaged the knife. So at the stage of slaughter the knife was fit, and therefore in that case the slaughter is valid. So I have a doubt whether the knife became blemished during the slaughter or only after the slaughter. And even if it became blemished during the slaughter, before meeting the vertebrae, it could still be that this happened only after most of the neck had already been cut. And if one slaughtered the majority of the two סימנים, the slaughter is valid. So this is really a double doubt. Maybe it became blemished only on the vertebrae, and even if you conclude that it was before the vertebrae, it could still have been after he had already slaughtered the majority of the two סימנים, and therefore the slaughter is still valid. So that is a double doubt. And about this the Shakh says that this is a double doubt that is not reversible. Why? Because if we begin the formulation with the second doubt — whether the knife became blemished before the slaughter of most of the neck or after it — then you cannot now decide whether, assuming the knife became blemished before the slaughter of most of the neck, maybe it became blemished after the slaughter. What? Wait. What? It’s impossible. I can’t. Did someone ask something? You cannot formulate these doubts in reverse order. I cannot say: there is a doubt whether the knife became blemished before the slaughter or after the slaughter, and even if it became blemished before the slaughter, maybe that happened when it met the vertebrae. Meeting the vertebrae happened much later than the slaughter. You can’t present it as: maybe it was before the slaughter, but even if it was before the slaughter, maybe it was when it met the vertebrae. No. If it was before the slaughter, it was not when it met the vertebrae. The order of presentation of the doubts is one order; the reverse order is not possible here. So the Shakh says that this doubt is a double doubt that is not reversible, because it can only be presented in one way. Namely: did it happen during the slaughter or after it? And even if it happened during the slaughter, which is the stringent side, it could still have happened after most of the סימנים had already been slaughtered, and therefore the slaughter is still valid. But if I ask whether it happened before most of the סימנים or after most of the סימנים, then on the stringent side — that it happened before most of the סימנים — I cannot raise the possibility “yes, but maybe it was when it met the vertebrae,” because meeting the vertebrae happened only afterward, after everything, and therefore it is not relevant.

[Speaker D] Rabbi, just as general information, aren’t you supposed to check the knife before every slaughter? You do check it.

[Rabbi Michael Abraham] Okay, let’s say that… let’s say he forgot to check, or he forgot what happened with the check, or he checked but afterward he suddenly found that it was blemished anyway. So what do we do now? The question is when it became blemished. Did it become blemished during the slaughter? After all, “during the slaughter” means after the check that he did, right? He checked at the beginning, looked at the knife, everything was fine. Then he went to start slaughtering. After he finished slaughtering, he takes out the knife and sees that it is blemished. Now I’m asking at what point in the process this happened. It could have happened after the initial check, obviously, because at that point the knife was fine. It could have happened before most of the סימנים were slaughtered, in which case the slaughter is invalid. It could have happened after most of the סימנים were slaughtered, in which case the slaughter is fine. And it could have happened only when it met the vertebrae, after the whole slaughter, in which case of course the slaughter is fine. Okay?

[Speaker D] Meaning that even if in principle you check the knife beforehand, even if you check beforehand it can still turn into an invalid slaughter.

[Rabbi Michael Abraham] Of course. It became blemished during the slaughter, and now the question is when during the slaughter. In any event, so the Shakh claims that this is a non-reversible double doubt. Now notice: in this example it is very easy to see that in fact we could also have said that this is a double doubt of one final type. The second principle is also relevant here. Why? Because the permission of the animal, whether the knife became blemished after the majority of the two סימנים or whether it became blemished when it met the vertebrae, is the same permission. What is the permission? That at the time of the slaughter it was valid for the first majority of the סימנים. Yes, it was valid. Whether that happened one second later or five seconds later, it is one type of permission. In other words, it just means that it was valid at the time of slaughter, and therefore the slaughter is valid. I could of course say that it happened one second after the majority of the סימנים, two seconds after, three seconds after, or when it met the vertebrae. Then it would become a triple, quadruple, quintuple doubt — of course you can go on forever. And precisely about such a case we say: it is one type of doubt. Once it became blemished after I had slaughtered the majority of the two סימנים, I don’t care when. Everything that happened in later stages does not invalidate the slaughter. So it is one type of permission, just like one type of coercion. It is exactly the same thing. And that in fact leads many students, and also many later authorities, to identify these two rules. They basically claim that the requirement that a double doubt be reversible is the same requirement as the demand that the type of doubt not be single. Because when the double doubt is not reversible, that basically means that its type of doubt is single, just as we saw regarding the knife. And they do not recognize these as two separate rules at all. That is the claim of several later authorities, and of students and contemporary writers as well, and so on. Now.

[Speaker D] Rabbi, but there is a fundamental difference between the case of the woman and the case of slaughter, because I don’t remember the exact formulation, but I think last week we said that when the woman is raped there is usually a rumor about it, people talk about it.

[Rabbi Michael Abraham] No, no, that’s a different argument. Let’s not get into the details of the passage in Ketubot now. We’re discussing the topic of double doubt now, not the topic of “I found an open entrance.”

[Speaker D] Fine, but what I’m trying to say is that in slaughter there is no way at all to know what really happened. You can’t know, because it happened inside, and there is no way whatsoever to know when it really happened.

[Rabbi Michael Abraham] And regarding the woman there is also no way to know, so what?

[Speaker D] No, so I’m saying that with the woman maybe there is a rumor, maybe there are witnesses, maybe there’s—

[Rabbi Michael Abraham] No, no, we have nothing. No rumor, no witnesses, nothing. Again, there are cases where it would be different. I’m talking about a case where it isn’t different. That is the case that interests us here. Rabbi Akiva Eiger, for example, argues that even Tosafot on Ketubot 9a, when they speak about one type of coercion, basically mean to say that this is a non-reversible double doubt. Yes — when they say that the seduction of a minor is coercion. So what are they really saying there? They are really saying: doubt of coercion or consent, and even if it was consent, it may be that she was a minor, which is really also coercion. So Tosafot there say: it is one type of coercion; this is not a double doubt. One type of coercion. Rabbi Akiva Eiger says that what Tosafot really mean is that the doubt is not reversible. Why? Because you say: if you begin with the doubt of coercion or consent, then even on the side of consent it may be that she was a minor. No — it cannot be that she was a minor, because if she was a minor then it was not consent, because the seduction of a minor is coercion. But you already took that into account in the first doubt. You have a doubt of coercion or consent, and now what do you want to say? Even if you conclude that it was consent, which is the stringent side, there is still a lenient side because maybe she was a minor. No — because once on the side of consent you already excluded the possibility of coercion, you can’t now doubt whether she was a minor. If she was a minor, that belongs to the side of coercion, not to the side of consent. So this is really a non-reversible double doubt. Because if you formulate first the doubt of consent or coercion, you can no longer doubt whether she was a minor or grown. Therefore Rabbi Akiva Eiger, for example, understands Tosafot there, when they speak about one type of coercion, as using that expression to say that this double doubt is not reversible. But it is the same idea. I don’t think he is right. These are two different things. In my view, the double doubt in Tosafot there is completely reversible. And that is why I said in advance that when we talk about one type of coercion, we are talking about the ground of the ruling, not about the ruling itself. Now, it is true that the seduction of a minor is coercion. But from the standpoint of “one type of doubt,” one type of coercion, then yes, the seduction of a minor is coercion and ordinary coercion is also coercion. But you cannot say that once you doubted whether it was coercion or consent, then even on the side of consent you cannot — I want to ask whether she was a minor. Rabbi Akiva Eiger says: no, you cannot ask whether she was a minor, because if she was a minor that is coercion. That is the law, that the seduction of a minor is coercion. But I am doubting the factual reality: was she a minor or was she grown? That is a doubt I can definitely formulate. A doubt whether it was coercion or consent, and even if you conclude that it was consent, the question is whether she was a minor or grown. And true, the consent of a minor has the legal status of coercion. So from the standpoint of one type of coercion, yes, it is a double doubt of one type of coercion. But from the standpoint of a non-reversible double doubt, I disagree — it is a reversible double doubt. I can certainly doubt whether she was a minor or grown even after I have asked whether it was coercion or consent. The law will converge. And the law that the seduction of a minor is coercion will converge with ordinary coercion.

[Speaker E] But how would that change the ground? What? How would that change my decision?

[Rabbi Michael Abraham] I would still remain within coercion. And therefore it is one type of coercion, because it does not change the ground. I’m trying to explain that yes, in this case it is indeed one type of coercion, but Rabbi Akiva Eiger is wrong to say that it is a non-reversible double doubt. I claim that it is reversible.

[Speaker E] But what difference would it make if he’s wrong? What difference would it make to the situation?

[Rabbi Michael Abraham] Suppose it is reversible. Rabbi Akiva Eiger wants to identify these two rules with each other, the rule of a single type of doubt and the rule that demands reversibility. And I’m claiming that there is no identity between these two rules. A single type of doubt is an independent rule, and the double doubt being discussed there is a double doubt that is reversible, and nevertheless we do not rule leniently because of the principle that it is one type of coercion. These are two independent principles. So in practice—

[Speaker E] So it doesn’t matter whether it’s reversible or not reversible.

[Rabbi Michael Abraham] No, it matters. It matters in places where I have a double doubt that is not reversible but the type of coercion is not single, and places where the type of coercion is single but the double doubt is not reversible. Okay? If I can show that both such situations exist, that means that these two principles are independent principles, right? Yes. Good. Now one case I’ve shown. The case of Tosafot. Well, “shown” — Rabbi Akiva Eiger disagrees, but I think from straightforward reasoning he is wrong. Especially in light of what I explained, that we are talking about the ground of the ruling and not the ruling, the ground of the ruling and not the ruling.

[Speaker F] Excuse me, Rabbi, doesn’t Rabbi Akiva Eiger just mean to say that it’s an incorrect use of language to propose those two options with respect to a minor, whether by coercion or by consent? As if there is no consent here. It’s just a misuse of language. Is that what he means to say?

[Rabbi Michael Abraham] That’s what he claims.

[Speaker F] Yes, yes,

[Rabbi Michael Abraham] and therefore the double doubt is not reversible.

[Speaker F] So I’m trying to say that in order to defend his position. But what you’re saying is that he is mistaken because for him the ground of the ruling and the ruling itself overlap. But he is simply eliminating one possibility. It just doesn’t exist; it doesn’t exist to say, to use the language—

[Rabbi Michael Abraham] Yes, but why doesn’t it exist? Because from his perspective the side of consent cannot tolerate the possibility that she was a minor, because if she was a minor then it wasn’t consent. Okay? But I claim that it can tolerate it; it just cannot tolerate it in the law. Meaning, legally the status of a minor’s consent is the same as coercion. But factually I can still doubt whether she was a minor or grown even on the side of consent. It’s just that legally the consent of a minor does not count as consent. And therefore I claim that since this deals with law, it is not correct to say that this double doubt is not reversible; it is reversible. It is correct to say that it is one type of doubt, because here the ground is the same ground, the ground is coercion. But—

[Speaker F] He means to say that there is no such factual reality as consent in the case of a minor. There is no such reality.

[Rabbi Michael Abraham] What do you mean? You understand that factually there are two situations even with a minor, right? There is a case where someone rapes a minor by force, and there is a case where someone seduces a minor. Halakhically, we relate to those two things in the same way.

[Speaker F] I meant to say that even factually we take it the same way as legally. Why? But not at all.

[Rabbi Michael Abraham] Factually — what do you mean? There are clearly two different situations here: if he does it to her by force, versus if he seduces her.

[Speaker F] From her perspective there’s no difference at all, for her there isn’t.

[Rabbi Michael Abraham] Halakhically that is a normative determination, not a factual determination.

[Speaker F] Yes, yes, I understand what you’re saying. I had understood that according to Rabbi Akiva Eiger, even factually one cannot take such a reality into account.

[Rabbi Michael Abraham] That is what he claims, I just don’t agree with him. Fine. Okay, okay.

[Speaker G] If I understand correctly what the Rabbi is saying, then these are really two things, two definitions, but it is the same reason — meaning the same foundation underlies both definitions.

[Rabbi Michael Abraham] That explains why it is one type of doubt. But I’m asking: why is it not reversible? If it is not reversible, what is the reason on the level of doubt itself? I’m asking what the

[Speaker G] foundation is?

[Rabbi Michael Abraham] The seduction of a minor is also coercion — that has practical relevance for one type of doubt, because in both cases you want to permit her because she was coerced, whether she was actually coerced as an adult or seduced as a minor. So as far as one type of doubt is concerned, that is correct. I am only claiming that it is not correct to define this as a non-reversible double doubt.

[Speaker G] I’m asking what the reason is that a reversible doubt is not a double doubt?

[Rabbi Michael Abraham] Wait, we haven’t gotten there yet. I’ll get there.

[Speaker G] Maybe it’s the same foundation, the same reason, and that’s—

[Rabbi Michael Abraham] That’s what Rabbi Akiva Eiger claims. Maybe yes and maybe no; we’ll see in a moment. We’ll see.

[Speaker B] Rabbi, but why does the Rabbi have to say that this is a doubt that is not reversible?

[Rabbi Michael Abraham] I don’t have to,

[Speaker B] that’s just how I think of it. So regardless, did Rabbi Akiva Eiger raise this as a difficulty and bring proof from Tosafot for his view, or was he simply commenting on Tosafot?

[Rabbi Michael Abraham] No, he didn’t bring anything. He just — yes, that’s how he understood Tosafot.

[Speaker B] I see, so the Rabbi is saying that—

[Rabbi Michael Abraham] I’m saying this is typical. Many people understand these two principles as two sides of the same coin. And I think not.

[Speaker E] But from the moment it is one type of doubt, in practice it makes no difference whether it is reversible or not reversible. Why do I need the distinction?

[Rabbi Michael Abraham] You need the distinction in a place where the type of doubt is not single.

[Speaker E] Agreed, but then the Rabbi is also arguing with Rabbi Akiva Eiger about the case where the type of doubt is single.

[Rabbi Michael Abraham] No, there I’m arguing about the characterization of the case. That will not make a practical legal difference. According both to my view and to Rabbi Akiva Eiger’s, this is not a double doubt. According to him, because it is not reversible; according to me, because it is one type of doubt. Here there will be no practical difference. The practical difference will arise in places where there is such a double doubt in which the type of doubt is not single but it is not reversible. Then according to Rabbi Akiva Eiger, if the type of doubt is not single, then it is a valid double doubt, because for him reversibility and a single type of doubt are the same thing. And I say no: there is an additional principle, that a double doubt must be reversible.

[Speaker E] And do you have an example where there would be a legal distinction? Coming up.

[Rabbi Michael Abraham] is arriving. So the example I gave earlier about the knife—in that case, the double doubt really does not reverse, and there too it’s a single category of doubt, right? If it was nicked after most of the two סימנים were cut, or at the neck joint, in both of those situations the slaughter is not rendered forbidden, because it was simply kosher at the time of slaughter. So there too both conditions hold: it doesn’t reverse, and it’s also a single-category doubt. Okay? For example, we saw a case where it was in fact a single-category doubt, but the double doubt does reverse. That’s what I argued with Rabbi Akiva Eiger about. Now I want to claim that in Tosafot Yeshanim in Ketubot—doubt whether it was coercion or consent, and doubt whether the husband knows how to identify an open entrance or not—I want to claim that there the doubt is not a single category. Right? There the doubt is not a single category. Agreed? Because if the husband does not know how to identify an open entrance, then she is permitted to him simply because she was not had relations with at all. But if he does know how to identify an open entrance, and she was coerced, then she is permitted to him because she was coerced, not because she wasn’t had relations with. Those are two different grounds. So here you can’t say it’s a single category of doubt, or a single category of coercion, or anything like that. But the double doubt still does not reverse. So there—you have the counterexample. Fine, here I think this example is more complex. Because here it’s pretty clear that you can’t say it’s a single category of doubt, even though the double doubt really does not reverse. Meaning, regarding the side where you were uncertain whether it was coercion or consent, you can’t then go back and ask whether the husband knows how to identify an open entrance, because whether it was coercion or consent, you already assumed that the entrance was open. So there’s no point now in going back and doubting: wait, maybe the husband doesn’t know how to identify an open entrance. Only the other direction works. The first direction is possible. So in that sense this is not a reversing double doubt; the double doubt does not reverse. But you still can’t say this is a single category of doubt. It is not a single category of doubt. The question is whether she wasn’t had relations with, or whether she was had relations with under coercion. Those are two different grounds for permitting her. Okay? So therefore there is no single category of doubt here. So that’s the second example; it shows us that these two principles, at least in my opinion, are independent principles. Why is that important? It matters because if I say it’s the very same principle—let’s put it this way—the explanation for why a single category of doubt is not considered a double doubt, that I explained. Why? Because I said the concept of “sides” is a non-probabilistic concept, right? A non-probabilistic concept. Since the concept is non-probabilistic, obviously we have to decide what counts as a side, because otherwise every double doubt basically won’t be a double doubt. I have three sides permitting and one forbidding. The three sides permitting are one side permitting, and there is one side forbidding. Clearly I need criteria that tell me what counts as an independent side, a separate side. And clearly those criteria are not probabilistic criteria. Okay? So therefore Tosafot says—and I think the Shakh says—that the criterion is how many grounds of permission there are. If you are coming by virtue of the same ground of permission, that is one side. If you have several different grounds of permission, that is several sides. Yes? As an example: if I say doubt whether coercion or consent, I said there could be coercion by force, coercion by hypnosis, coercion in all kinds of strange and different ways. If each of those counted as a separate side, I would always permit her. I can play with the doubts however I want. If it’s doubt whether pig or cow, I can say yes, but maybe it’s a warted pig, maybe it’s a pig from Indonesia, maybe it’s a pig from—I don’t know—Kamchatka. Fine? So what difference does it make? I’m in doubt whether it’s pig or not pig. Fine? Therefore it is obvious that a single category of doubt is a very reasonable rule. It doesn’t need an explanation. It’s obvious. You need to decide what your criterion is for treating a side as a separate side, a distinct side that gets counted independently. And therefore a single category of doubt is basically… you can argue in different places whether this counts as a single category of doubt or not. Fine. But the idea itself—that when it is a single category of doubt, it gets counted as one side and not as many sides—is an intuitively simple idea. Okay? The idea itself.

[Speaker G] Why is that actually not related to probability? What? Why is it not also related to probability?

[Rabbi Michael Abraham] Because this is a negative doubt. In a negative doubt there are no probabilities. If it were a positive doubt, the whole discussion would never get off the ground. You would simply see what percentage you have for each side. Think, for example, about the pig, right? Suppose I know the data about all the animals in the area that could possibly be relevant, and I have a doubt: cow or pig, and around here there’s an Indonesian pig and a Kamchatka pig. Both are in the area. Okay? So apparently there are two pig-sides here and one cow-side. So you should forbid it. I say no. Why not? Because it’s a single category of doubt. What does that mean, a single category of doubt? If I know the numbers, then let’s see how many Kamchatka pigs there are, how many Indonesian pigs there are. If in total that comes to 70%, then fine. But not because there are two sides; rather because there is a majority for pig. The whole idea of counting sides only applies where the doubt is a negative doubt. I don’t have data about percentages. So I count sides. But in order to count sides, I need to decide what counts as a side. But that’s all, all…

[Speaker G] I always found this difficult in that Talmudic passage in the laws of niddah, where they permit there in the case of a wound on the basis of double doubt: doubt whether from the upper chamber, doubt whether from elsewhere.

[Rabbi Michael Abraham] And what

[Speaker G] difference does it make to me whether it’s doubt whether from the upper chamber or doubt whether from elsewhere? There’s one question here: does it come from the womb or not? Call it elsewhere, call it the upper chamber, call it this nest, call it that cow.

[Rabbi Michael Abraham] Here’s the proof against Rabbi Akiva Eiger. I’m saying: I don’t care whether the seduction of a minor girl is also coercion, fine? The coercion of an adult woman and the coercion of a minor girl are two sides. Why? Because true, from the standpoint of the law it’s the same ground, but the causes are different causes. And when I count sides in a negative doubt—again, if it were a positive doubt then I’d count percentages, I wouldn’t care where the blood came from. If I know there’s a 20% chance that the blood came from the upper chamber and a 30% chance that the blood came from outside, that is still one doubt and not a double doubt.

[Speaker G] Yes, but the decisors there do treat it as a double doubt.

[Rabbi Michael Abraham] Why? Because we don’t know the percentages. Exactly. When we don’t know the percentages, then I don’t know what percentage each side has. So I count sides. Yes, but everything is included in “elsewhere.” Why?

[Speaker G] Everything is considered “elsewhere,” or it’s… either it comes from the womb or it comes from elsewhere. What difference does it make to me if it’s from the upper chamber?

[Rabbi Michael Abraham] You know more with sides; otherwise in every double doubt—for example, doubt whether under him or not under him, doubt whether under coercion or with consent—all the permissions stem from the fact that it was not under him with consent. Right? After all, only if it was under him with consent does she become forbidden to him. All the permissions stem from the fact that it was not under him with consent.

[Speaker G] Then there too it’s not a double doubt. Right, but the point is that even in defining the category we have to insist on defining what the category is. We can’t define whatever we want. After all, if the core point under discussion is whether it comes from the womb or from somewhere else, that is really the question. So “somewhere else”—what could that be? It could be the outside world, it could be the upper chamber. Why on earth split that up?

[Rabbi Michael Abraham] So I’m saying: because in a negative doubt those sides are different sides. The sides are different sides because this is blood from outside and this is blood from the upper chamber. True, both of them are not blood from the womb. So what? So I go back again and ask: then why should I care whether the woman was coerced, or whether it was not under him with consent? In any case, it was not under him with consent, and therefore she is permitted to him.

[Speaker G] Why is that considered two sides? Those are two different halakhic issues.

[Rabbi Michael Abraham] They are two different halakhic issues. No, they are not different halakhic issues. It doesn’t matter. As long as it was not under him with consent, she is permitted. Why should I care whether it was not under him with consent because it wasn’t with consent, or because it wasn’t under him? What difference does it make? You see that we do indeed go into the different grounds, even though the side of prohibition is one side. Everything that does not fit the definition of prohibition is permission. No, also…

[Speaker G] Right, but there those are two completely different grounds for permission. Here, in the subject of niddah, there is one essential question: does it come from the womb or from somewhere else? Somewhere else—why split “somewhere else” up? That’s what I’m asking.

[Rabbi Michael Abraham] But that’s not so. I have two possible ways to attribute it to… after all, there is blood here, right? Now you want to tell me that this blood did not come from the womb. Why not? I’ll show you: I have a double consideration why not. It could also have come from outside, and it also could have come from inside, from the upper chamber. Okay? So I have a double reason that explains to you why it is not blood from the womb. It’s like nine stores versus one store: you say nine stores are nine sides for assuming that this piece is a kosher piece, even though all those sides amount to no more than a piece that came from a kosher store.

[Speaker G] And there that’s because there it isn’t negative, there it’s probabilistic.

[Rabbi Michael Abraham] Right, obviously. I’m only bringing it as an illustrative example. Yes,

[Speaker H] but

[Speaker G] this example is very hard to understand. I can’t grasp what the point of distinction is. Because in the end the question is: somewhere else. Somewhere else—maybe say it’s this nest and this nest and this nest, so we have

[Rabbi Michael Abraham] three nests, so is that a double doubt? Yes, if there were three nests here, then yes indeed. If there were concrete reasons in front of me and I saw three nests, then that’s three reasons. No, the nests don’t need to be in front of us. The nests don’t need to be in front of us. Okay, so I say: in principle it could come from a nest, and in principle it could come from the upper chamber. So I have two sides to permit.

[Speaker G] And that’s not two sides.

[Speaker E] It’s not… I agree with you—with whoever… with the speaker. It’s not two sides; it’s two kinds of evidence for the same side. You simply have two kinds of evidence saying that this side is the correct one. One is evidence that maybe it could come from here, maybe it could come from the side… what?

[Rabbi Michael Abraham] It’s not evidence; they are possible attributions. Yes, fine. Reasons. And you attribute this blood—even though it is found there—to the fact that it did not come from the womb. If I have two alternative sources from which this blood could have come, and not from the womb, that is stronger than thinking it came from one source that is not the womb, from some origin that is not the womb. Fine?

[Speaker E] Yes, but again, that’s to… but again, that’s in order to prove that it’s from the womb. Not to prove.

[Rabbi Michael Abraham] In order to prove that it’s from the womb is not necessary.

[Speaker G] Yes, but I’m asking this, Rabbi. I’m asking this. In practice I can define it as one category. How? By defining the point of doubt this way: I say either it comes from the womb or it comes from somewhere else. You can define whatever you want.

[Rabbi Michael Abraham] Wait, wait, if I

[Speaker G] call it “somewhere else,” everything falls under “somewhere else.”

[Rabbi Michael Abraham] You can define whatever you want—that’s what you said earlier too. But I’m saying again: you can define whatever you want, sure, you can define everything. The whole question is what the reasoning says; this is not a mathematical issue. What does the reasoning say? Now of course there are places where you can argue about the reasoning, but here too I think there is logic in the reasoning. Why? Because I am showing you that it really does improve the possibility that it did not come from the womb. If I have two possibilities to which I can attribute this blood, such that it is not from the womb, that is better than if I had only one possibility to attribute it to as not being from the womb.

[Speaker E] So then tell me that in the knife case in slaughter too, I have two things to attribute the flaw in the knife to during the slaughter: one, that it happened before the neck joint bone, and two, that it happened after the neck joint. Those are two possibilities that strengthen it for me.

[Rabbi Michael Abraham] But the ground of permission—the ground of permission—is that the slaughter was valid. Agreed. That’s it, so therefore it’s one. And it also doesn’t reverse, and it’s also a single category of doubt. The slaughter was valid—what do you want?

[Speaker I] All this again proves that we’re not talking at all about the reality itself and what happened

[Rabbi Michael Abraham] C- come on, let me finish the sentence; I already know what you’re going to say.

[Speaker I] Exactly, it’s only what we

[Rabbi Michael Abraham] think—what we think. So let’s save time; you already know what I’m going to answer too. So fine, okay, fine. So in short, that is about… Now, why was it important to me to show the independence of these two principles? Because since the rule of a single category of doubt has a logical explanation, then if a non-reversing double doubt were not a double doubt because of a single category of doubt, I wouldn’t need to look for explanations for that rule. It would be the same rule—that is, the rule of a single category of doubt, a single category of coercion. Okay? But if I show that it’s not that—that these are two different principles, and there can be a case where the category of coercion is not single and yet the double doubt still does not reverse, and therefore I will not see it as a double doubt—if so, then the explanation of a single category of coercion is not enough to explain why reversal of the double doubt is required, right? I need an explanation why reversal of the double doubt is required as an independent explanation. Fine? Therefore it was important for me to show you that these are two independent principles, each of which can appear without the other. And if so, we are left with explaining why a double doubt has to reverse. Okay? Because a single category of doubt—we understand that. But why does it have to reverse? That is basically the puzzle left for us. Here I want to say the following. I thought of one explanation following the approach of the Rema of Fano that I brought in the previous lesson. You remember that the Rema of Fano explained that in a doubt that does not reverse, I really have two ways to present the doubt: either as a tree that branches, and here there are two more branchings, ending in four endpoints, yes? Or as a doubt that does not reverse, which is really only a single doubt because the second doubt cannot be presented. Okay? And since I have a doubt either way, a Torah-level doubt is ruled stringently. And we discussed whether that was logical or not logical, doesn’t matter. I maybe thought to suggest that since I really do have two possible ways to present this doubt, what is the difference between them? On one side I essentially have four—two branchings that at the endpoints… maybe I’ll do some sharing of the… no

[Speaker F] We want the branchings to depend on the narrative.

[Rabbi Michael Abraham] Wait just a second. Fine, I have two sides. Okay? That’s the possibility of presenting it as a regular double doubt, okay? And the second possibility is really that there’s only one doubt; the second one is irrelevant. To normalize it, I also put in two branchings here, but really it’s only the top doubt. This side is “she is permitted” and this side is “she is forbidden.” Fine? And I split it into two more just to make it look similar, but really it is only one doubt. Now here maybe—let’s count the sides. So let’s say all these sides here are sides that I can take into account. So now I have five sides here that say she is permitted, and three sides that say she is forbidden, out of eight. Right? You see that? Here three and one, and here there are two and two. So three plus two gives me five sides that say she is permitted, and one plus two gives me three sides that say she is forbidden. There is still a majority of sides that say she is permitted—five out of eight. But that is not three out of four; it is less, right? Three out of four is 75%; five out of eight is 67%. Right? Five out of eight, yes, that’s sixty—not sixty-two percent. Okay? So sixty-two.

[Speaker H] Sixty percent.

[Rabbi Michael Abraham] Sixty-two and a half, yes. In any event, perhaps we need to remember that we are dealing with negative doubts, right? Now, with negative doubts, we never have any guarantee that on the probabilistic level there is really a majority for permission, right? Because we are counting sides here, not probabilities. These are negative doubts. It could be—this was the first suggestion that occurred to me—that in order to rely on a double doubt in negative doubts, I want there to be three out of four sides for permission, so that the percentage of sides is 75%, as this sort of formal requirement. Just as I said that in a single doubt I am stringent, but in a double doubt I am lenient. Even in a double doubt there could be a majority for prohibition, right? Because these are negative doubts. It could be that probabilistically there is a majority for prohibition. Fine—but you can’t live that way. I assume that if there is a double doubt and both are negative, then as far as I’m concerned if there are three sides for permission, I assume that probabilistically too it is permitted. Okay? That is a halakhic assumption. Now maybe, for that assumption, I want a large majority of sides—75%, not 62%. Like we discussed regarding an overwhelming majority and an absolute majority in permitting agunot, remember? Whenever we try to build rules from a negative majority or from a negative doubt, the rules will be some sort of formal rules that set a limit. For example, usually an ordinary majority is enough for me; in permitting an agunah I want an overwhelming majority. Fine? Now in a case where I have the majority—the numbers—I don’t care whether it is two majorities or one majority. If the majority is 99%, then it is overwhelming; if not, not. But if the majority is negative, then I have no numbers. So one says: good, if there are two majorities—that is, a majority of a majority—I can assume that this is an absolute majority, or an overwhelming majority, or an absolute one, depending on whether it’s rabbinic. Okay? But that isn’t really so; it is only a halakhic assumption. On the probabilistic level I have no numbers here; I don’t know how to assign numbers here. Something like that, I thought, maybe we can say here too. True, there is a majority of sides for permission here, but it is a majority of sides in negative doubts. Meaning, probabilistically there could be prohibition here. So I set a limit: if I have 75% of the sides for permission, then fine. But if it is only 62%, then no, because I want a significant majority of sides in order to rely even on a majority of permitting sides, despite the fact that I do not know what the probabilistic majority is, if it exists. So that is one possible explanation I thought of for this idea that a double doubt must reverse.

[Speaker B] Sorry, does that basically mean that with sides I always need a 25–75 ratio, and that’s always what I need?

[Rabbi Michael Abraham] No.

[Speaker B] There will never in practice be a case of permission with sides of two against one? There won’t be such a thing?

[Rabbi Michael Abraham] Yes, that’s the claim.

[Speaker H] By the way, yes, but it comes out that in every direction of 75%, presumably if you find it, it will be possible to reverse it from every direction. Meaning each of these three sides, yes—for it to be a reversing double doubt, it has to be that no matter how I switch the routes, I still always arrive at permission.

[Rabbi Michael Abraham] I’m not reversing sides, I’m reversing doubts. Doubts, yes. One way to reverse, not from every direction. One way to reverse: either doubt one comes first and doubt two after it, or doubt two first and doubt one after it. That’s it. I’m not reversing sides, I’m reversing doubts. But in… yes, yes,

[Speaker H] I

[Rabbi Michael Abraham] say, this possibility—of explaining the requirement of reversibility—is very strange to me. It is strange because the number of sides here is not really an indication of the level of certainty I have. When with two majorities I said there is some formal standard—I want there to be two majorities—that really does improve my chances that probabilistically there will be an absolute majority. It doesn’t guarantee it, but it improves it. In our case that is not true. When the double doubt does not reverse, do you think there is less than 75% chance that she is permitted? Of course not. It’s only a way of presenting the calculation, that’s all. After all, I genuinely have a doubt whether he knows how to identify an open entrance or not, and a doubt whether it was coercion or consent. So there really is…

[Speaker H] What’s the reason the Shakh set it up this way in Yoreh De’ah there? What did he say? He said that a double doubt has to reverse.

[Rabbi Michael Abraham] We’re dealing with that right now. I’m trying to propose an explanation for why a double doubt has to reverse. That’s our topic now. And the first explanation is to say that maybe I count the sides of the two possibilities. But that’s strange because they are not really different sides. For example, look at this possibility. Wait, I was here. Yes, these are the two possibilities, right? Here I say that the regular way to present the doubts is simply three sides to permit and one side to forbid. Here it’s the reverse presentation. I have a doubt whether he knows how to identify an open entrance, doubt whether coercion or consent, and there is no question whether he knows how to identify an open entrance. What do you mean there’s no question? But of course there is a question! I just can’t present it after I’ve already asked whether it was coercion or consent. But clearly, if I ask myself: do I know whether the husband knows or does not know how to identify an open entrance? I don’t know. He may know and he may not know. Meaning, this doubt exists for me in any case. You cannot say there is any possibility that this doubt does not exist for me. It is just a formulation problem, right? Just a formulation problem. These are not really different sides. All the possible combinations here are as follows: either the husband does not know how to identify an open entrance and there is no opening at all; or the husband does know how to identify an open entrance and there is an opening and it was coercion; or there is an opening and it was consent. Those are the sides that exist. There are no more sides. Okay? Now I say: what difference does it make that in the reversed formulation I cannot phrase it? So what? My doubt really is between those possibilities. It’s not that the second presentation presents other sides. It does not present other sides; it’s just an unsuccessful formulation, that’s all. A formulation that does not allow me to present the doubt whether the husband knows or does not know how to identify an open entrance. That’s all. But I do have that doubt. The fact that this formulation is unsuccessful—so I won’t use it.

[Speaker B] What do you mean “unsuccessful”? It’s just different, this formulation. And in this formulation there is one side and one side.

[Rabbi Michael Abraham] No, that’s not correct. That’s exactly the point—not correct. Because when I am in doubt whether it was coercion or consent, implicitly behind that I have already assumed that there was an opening, right? Now ask me: tell me, are you sure there was an opening? Of course not; maybe the husband does not know how to identify an open entrance and there is no opening at all. I just have no way now to present this doubt that is nesting inside me, because once I opened with the question whether it was coercion or consent, I can no longer say, “and if you say it was consent, maybe the husband doesn’t know how to identify an open entrance.” Meaning, this mode of presentation does not allow me to express the doubts that are inside me. But they are there inside me! I really am in doubt whether the husband knows or does not know how to identify an open entrance.

[Speaker I] But the fact that you formulated it in a certain way determined what you feel about this reality.

[Rabbi Michael Abraham] You can’t say I also feel that way.

[Speaker I] If you felt that way, you would have formulated it differently.

[Rabbi Michael Abraham] No, it didn’t determine it; it includes it. It didn’t determine it; it includes it. So formulate it! Again, I really do have two doubts. There really are two doubts. The doubt whether the husband knows how to identify an open entrance or not—we are all uncertain; we really don’t know. And we also don’t know whether it was coercion or consent; that too we do not know. Now the way I opened the formulation—with the second doubt, whether it was coercion or consent—shuts my mouth, doesn’t allow me to express the fact that I am also uncertain whether there was any opening at all.

[Speaker I] But why did you formulate it that way?

[Rabbi Michael Abraham] Well, because you felt something in a certain way. No, it’s a formulation I’m trying…

[Speaker I] But the possibility of formulating it that way—there will be people who formulate it that way.

[Rabbi Michael Abraham] No, then I’ll explain to them: gentlemen, you are using an unsuccessful language; don’t formulate it that way. If you formulate it that way, it doesn’t let you express the full world of your doubts.

[Speaker I] But that is the real formulation. The doubt is not from reality; the doubt is something we feel. And if we express it in a certain way, that has weight.

[Rabbi Michael Abraham] Wait, wait—but that’s not what people feel. Do I have a doubt whether the husband knows how to identify an open entrance or not? Do I have such a doubt?

[Speaker I] What do you mean “do I have”? The doubt exists in reality.

[Rabbi Michael Abraham] Good—in reality, so

[Speaker I] isn’t that what I feel?

[Rabbi Michael Abraham] No, you feel it too. So why did I formulate it this way and not otherwise? You didn’t formulate it; it’s only one possible formulation.

[Speaker I] But there will be people who formulate it that way!

[Rabbi Michael Abraham] There won’t be people who formulate it that way! After they see this, they’ll abandon that formulation. No, it’s just a hypothetical possibility that one could have formulated it that way and then gotten stuck. Fine, then don’t formulate it that way and don’t get stuck.

[Speaker I] But Rabbi, in reality when we feel doubt—forget Jewish law for a moment—when we feel doubts in reality, it matters very much how we… it’s not reality itself that presents itself as a set of doubts.

[Rabbi Michael Abraham] That’s not how reality itself works. Wait, wait—there is no person who says this; you’re inventing him. We have—every human being in the universe will be uncertain about these two doubts: whether the husband knows how to identify an open entrance or not, and whether it was coercion or consent. Now there will be a person who formulates the double doubt by starting with “knows or doesn’t know,” and then moving to “coercion or consent,” and there will be someone who starts with “coercion or consent,” and then he suddenly gets stuck when he tries to formulate whether he knows how to identify an open entrance, and then he will realize he formulated it badly and abandon it.

[Speaker I] But that’s only if we define doubts in terms of the objective reality.

[Rabbi Michael Abraham] No, not reality. It’s our knowledge of reality.

[Speaker I] Not our knowledge—our relation to reality. And if we want to relate…

[Rabbi Michael Abraham] Those are just words. Our knowledge of reality—that’s just words. Our knowledge of reality.

[Speaker I] A person comes

[Rabbi Michael Abraham] and looks at the Holocaust: one person will say the Holocaust proved there is no God; one will say I have a doubt whether there is a God; one will say I am certain there is a God.

[Speaker I] Nothing in reality changed; there is no disagreement about reality.

[Rabbi Michael Abraham] Shmuel, Shmuel, don’t drag me into the Holocaust now, and not into God either. I’m talking about something simple now. I’m talking about a person—this person is called Tosafot. Ever heard of him? Tosafot Rabinovitch. Fine. This person is uncertain about two things. He told me he is uncertain. He is uncertain about whether the husband knows how to identify an open entrance or not. He has that doubt. And he is also uncertain whether it was coercion or consent. He solemnly informed me that he has these two doubts. Now I say to him: okay, formulate this for me in the structure of a double doubt. Fine, so now Tosafot Rabinovitch the father says to me: doubt whether he knows how to identify an open entrance, doubt whether not; and if he does know how to identify an open entrance, doubt whether coercion or consent. I say to him: excellent. Now Tosafot Rabinovitch the son says to me: no—junior, yes—Tosafot Rabinovitch junior says: no, doubt whether coercion or consent, and doubt… oops—and then he gets stuck. Wait. But he himself told me from the outset that he is uncertain about both things. He gets stuck; he can’t say it. Excellent. Since you chose an unsuccessful language, leave it, go back to your father’s language. That’s all. Because you too are uncertain about the same doubts he is uncertain about. You just don’t know how to express them.

[Speaker I] So the junior will tell me that since there will be people who choose to formulate specifically the second…

[Rabbi Michael Abraham] Don’t tell me “there will be people”—he!

[Speaker I] No, but in order to permit we have to permit for everyone. We can’t permit for one person and not permit for another according to what he feels.

[Rabbi Michael Abraham] In Tosafot, Tosafot himself is uncertain about these two doubts. It never enters his mind that there is someone who is not uncertain about the second doubt. These doubts are real, existing doubts. We have no answer to either one of them, and therefore both doubts exist. And nevertheless Tosafot says—Tosafot Yeshanim—that if it does not reverse, then it is not a double doubt. Right, because he wants to say…

[Speaker I] Right, but when the feeling is such that whenever you formulate it you arrive at two doubts, then you have a certain feeling of doubt. When there is one formulation that does not lead you to two doubts, then you already feel differently, even if you formulate both of them, because you know…

[Rabbi Michael Abraham] And what does “feel differently” mean? You have two questions you are uncertain about. If you feel differently, take a pill. You are uncertain about two questions. You are still uncertain about both of them. The fact that you don’t know how to express that means you chose an

[Speaker B] unsuccessful language.

[Rabbi Michael Abraham] What does that have to do with anything? I can say—you know—if the ox gored the cow. Now I say: look, I forgot the word “ox.” I don’t have it, I don’t have the word “ox” in the dictionary, it escaped me, and in my dictionary the word “ox” doesn’t appear. So I have no way to sue him, because I want to say to him, “your ox gored my cow.” So what, then he’ll be exempt? What is this? You are just using unsuccessful terminology or unsuccessful language, that’s all. You fail to express the ideas that you yourself feel.

[Speaker I] That’s assuming language expresses reality. If language expresses not reality but how I create reality, then it’s really very different.

[Rabbi Michael Abraham] In this language you create nothing at all. This language is a foolish language, and anyone who starts using it will say, okay, right, I’m throwing it out. It is simply unsuccessful language. But there will be someone who says it isn’t foolish because to him

[Speaker I] it seems very logical.

[Speaker F] Shmuel, let it go.

[Rabbi Michael Abraham] No—to him it won’t seem logical. There isn’t such a person! Everyone, if they start formulating it this way, will throw it out. There is no one who will say otherwise. That’s exactly the point. Fine, let’s continue. So in any case, we now need… so in short, that’s why I say this explanation is not plausible. This explanation. Let’s say: if that were the explanation, then I wouldn’t accept the rule that a double doubt has to reverse. After all, it’s not in the Talmud. It’s a dispute among the medieval and later authorities. If that were the explanation, then as far as I’m concerned a double doubt does not have to reverse. What nonsense. So I am still looking for something that will give it some kind of logic. You can still reject it, but

[Speaker F] something that will give it some kind of logic. And the claim I want to make is basically the following. There is… Rabbi, you get stuck on this problem because you refuse to say, as others do, that double doubt is really just another formulation of a single category of doubt. Right, obviously.

[Rabbi Michael Abraham] No, I don’t refuse; it’s just not true. What do you mean, I refuse? I showed that it isn’t true. With Rabbi Akiva Eiger one can argue, but the other side—I showed that there can be a case of a non-reversing double doubt where the category of doubt is not one. Now the question is why there too you call it not a double doubt. In any event it needs an explanation. So I say my claim is the following. Since it’s already taken me a long time, I’ll nevertheless try to explain and get to the bottom line. We have, I claim, in ordinary probability, fine? Let’s leave aside for the moment the kind of doubts we’re talking about here. In ordinary probability, when we arrange doubts one after another, what does it mean that there is a doubt built on top of a previous doubt? It means probabilistic multiplication, right? That was our topic in the last few lessons—probabilistic products, right? So if I now present such a form, this tree—do you see? I present this tree. Okay? What does that mean? I ask: what is the probability of being here? Here. It is a product, right? One-half from here multiplied by another half from here. Here it’s half and half, and here too it’s half and half. So I am really multiplying the probability of passing through this node to this side, to side A, times the probability of passing from A to A1. That comes out to one quarter—half times half. What is the probability of being here? Also one quarter, right? That’s half times half. The probability of being here is also one quarter. And likewise here, and likewise here. Meaning, when I create such a graph of doubts that come one after another, what I’m really doing is multiplying probabilities. Right? The probability in this doubt of being here is half, and then in this sub-probability again I have half-half, so altogether it’s half times half, which is a quarter. For each result, I essentially have to multiply the probabilities of the two nodes through which I passed. Okay? Now think for a moment what it means that when I multiply two probabilities in a different order, I do not get the same result.

[Speaker B] Dependent events. What? Dependence among the events.

[Rabbi Michael Abraham] Right! The events are dependent. There is dependence between the events. Right? We know in probability—we discussed this before, but I’ll mention it again—maybe I won’t manage today, but next time perhaps a bit more. My claim is that when the order of appearance of events matters, that means there is dependence between them. Think, if you remember, of the crib-death case in Britain, where a certain woman had two babies die of crib death in the home. Then they accused her and said she was a murderer, because the chance of crib death is 1 in 8,000, and the chance that two children would die of crib death is the product, 1 in 64 million. And that’s implausible; she probably murdered them, it didn’t happen on its own, for it to happen naturally is utterly implausible. Now there are many reasons that’s complete nonsense, but here I’ll bring not the main reason. One reason it’s nonsense—and not the main one—is: why are you multiplying the probabilities? You are assuming that the events are independent: that the first dies and that the second dies. But if the first one died because of some genetic problem in the family—therefore he died of crib death—then the fact that the second died is not an event independent of the first one’s death. They both died because of a common cause, some genetic problem in the family. Remember? We talked about generalizations; we talked there about murky blood, the Talmudic discussion there regarding a presumption after three times, yes, whether the spring causes it or destiny causes it, so that the woman’s bodily source causes all her husbands to die, and therefore I assume there is one cause for all their deaths. Those are not independent events. And here too, when you make this calculation, you are really multiplying probabilities. You say: what is the chance that the first will die naturally without her murdering him? 1 in 8,000. What is the chance that the second will also? 1 in 8,000. The product is 1 in 60 million. Not correct. The multiplication to 60 million is correct, but it is not correct to multiply here. Because when you multiply probabilities, you are essentially assuming that the events are independent. But if the events are dependent, when I now ask—suppose that the percentage of families that have a genetic defect leading to crib death is 1 in 8,000, okay? The number of families in which one child dies and the number in which two children die will be almost the same. Because in all families that have this genetic defect, all their children will die of crib death. If they had one child, then only one child died; if they had two children, both died. So it is not true that the probability that two children die is much smaller than the probability that one dies; it is the same probability. The assumption that it is much smaller comes from my seeing these death events as independent events. For each one I held a lottery: for the first, 1 in 8,000, it came out; I held a lottery for the second, again 1 in 8,000. What is the chance that both came out in the same house? 1 in 64 million? Yes—if I am holding independent lotteries, if the cause is random and unrelated in the two cases. But if the events are dependent, then I may not multiply probabilities. Now what happens in dependent events is that the order of appearance matters. We talked about conditional probability, P of A given B and P of B given A. Given that B happened, what is the chance that A happens? Or given that A happened, what is the chance that B happened? It is not the same probability. If the events are independent, then in both cases P of A given B is P of A, if it doesn’t depend on B. But if it does depend on B, then the appearance of A after B is not the same chance as the appearance of A itself. The order of the events matters, and therefore you cannot multiply probabilities. Now what I want to claim—and I won’t get to it today, but I at least want us to close the circle—is that a non-reversing double doubt basically means there is some kind of dependence between the events. You cannot formulate the second formulation before you formulate the first. If you formulate it before the first, you won’t be able to formulate the first; the first won’t occur. So that means there is dependence between them. If there is dependence between them, then these are not really two independent doubts, and I may not multiply the probabilities. So it won’t go down to a probability of a quarter; it stays at a probability of a half, like with crib death, yes? So the probability is 1 in 8,000, not 1 in 64 million. So it is not a double doubt; it is one doubt. Therefore, if the doubts are order-dependent, they do not reverse, then we see them as probabilities of events that depend on one another. And the probability of events that depend on one another is not the multiplication of probabilities. And since that is so, you cannot assume the chance here is small, because only because of the multiplication do you assume the chance is small. But here you cannot multiply. That is the claim. Now this claim needs a lot of explanation, and on its face it is not entirely correct, but that I’ll do next time.

[Speaker F] Yes, because the dependence is… when the dependence is in time, that doesn’t mean the dependence is in reality; those are two different things.

[Rabbi Michael Abraham] Here it isn’t even in time but in formulation, yes. But you’re right: it is logical dependence, not causal dependence. But we’ll talk about that. Yes, regarding…

[Speaker H] Regarding coercion and consent, maybe in that case they’re not dependent on each other at all. The fact that he isn’t expert in an open opening has nothing to do with dependence; there’s no dependence between the two.

[Rabbi Michael Abraham] That doesn’t change the odds of coercion or consent, his expertise in an open opening. If he isn’t expert in an open opening, then there simply is no opening, so I have nothing to deliberate about as to whether it was coercion or consent.

[Speaker H] That’s what I’m saying.

[Rabbi Michael Abraham] But it doesn’t change the probability, the distribution of probabilities between coercion and consent.

[Speaker H] But on the other hand, in the Shakh on slaughtering in Yoreh De’ah there, regarding the knife, there it actually is dependent.

[Rabbi Michael Abraham] Okay, so we’ll talk about that distinction too. But in any case, I just wanted you to see the closed circle. Next time I’ll just complete this point, I’ll complete the… I’ll go a little more into the explanation of why a double doubt that cannot be reversed is similar to events that are probabilistically dependent. And therefore we can’t multiply the probabilities or assume that it’s a more remote doubt than a single doubt. Then I’ll move on to dependence in general between events, and with that… with that we’ll finish the probabilistic products, and after that one more class and we’ll finish the series.

[Speaker B] But if we rule based on the sides, why do we even need to worry that you can’t multiply the probabilities? Why not just look at the sides themselves? Meaning, why should I care…

[Rabbi Michael Abraham] Because the doubts are negative doubts, so you have to require formal conditions that hopefully, indirectly, will make sure that the probability somehow also works out. If these were positive doubts, then we wouldn’t need all the whole discussion I’m talking about now.

[Speaker B] No, that’s true, I’m saying, but now we’re in the negative case, so we’re not… apparently we’ve abandoned the attempt to get to a fifty-percent chance…

[Rabbi Michael Abraham] No, no, we haven’t abandoned it, absolutely not. I’m just trying to maximize the possibility of reaching a high probability through formal requirements without actually knowing how to calculate the probabilities. Exactly as I explained regarding permitting agunot. In permitting agunot, my claim is that all the reasoning is in fact probabilistic reasoning. It’s just that because the majority is a negative majority, how can I make sure that the majority is overwhelming? I have no way to do that by calculation. So okay, let’s require that there be two overwhelming majorities; then the assumption is, hopefully, that if those two majorities are overwhelming enough, then their product will probably be conclusive. I don’t know that, but I’m trying to get as close to that as possible through formal requirements. I’m claiming the same thing here.

[Speaker B] Okay, so a majority of sides can never really be better, for our purposes, than a double doubt, say? Because there, if the double doubt were, say, positive, then I’d be talking with certainty about the numbers.

[Rabbi Michael Abraham] Positive, yes, but there’s no such thing as a positive double doubt. A positive double doubt is a majority.

[Speaker B] But if I have the numbers, then I don’t even need to… right.

[Rabbi Michael Abraham] A positive double doubt is a majority. It’s not a double doubt. You don’t need the law of double doubt for…

[Speaker B] No, so yes, but let’s say you remember I asked the Rabbi why some are uncertain whether we follow a double doubt in monetary law, even though with a majority we don’t follow it, so according to what we’re saying now, it’s completely obvious that we also wouldn’t follow it here. The opposite.

[Rabbi Michael Abraham] Usually we don’t follow a majority in monetary law.

[Speaker B] Right, but some are uncertain whether maybe with a double doubt we would follow it in monetary law, we would follow a double doubt. Okay. So I’m saying, according to what the Rabbi is saying right now, then it’s not… there’s no question at all. It’s obvious that…

[Rabbi Michael Abraham] No, I don’t know that there’s no question, but it’s a different principle. According to the way I’m explaining it now, there actually is a question, because my claim is that a double doubt is our way of generating a majority without really knowing that there is a majority. But it’s a formal way, an attempt to maximize the chance that there’s a majority here. But if in the end all we really get is a majority, then apparently you’re right. So if in monetary law we don’t follow a majority, then why should I care that I maximized the chance of getting a majority? Even an actual majority doesn’t really help me here.

[Speaker B] So in the end, a majority of sides isn’t some new principle; in the end it’s just a case of majority under conditions of certainty, something like that.

[Rabbi Michael Abraham] Right, exactly. Okay, fine. Good.

[Speaker G] I’m trying to understand: if it’s not a reversible doubt, then does it in practice become, instead of a quarter, a third or a half?

[Rabbi Michael Abraham] A half. Why not a third? Again, there’s an upper bound. It’s neither a third nor a half nor three-quarters. But the bound is: you can’t know that it’s less than a half.

[Speaker G] Could you define it by saying that there are three points here, three options, according to the Rabbi’s diagram for example, so you could define it as one on the first layer and two more on the layer below.

[Rabbi Michael Abraham] No, there’s no lower layer at all. If you were in doubt whether it was coercion or consent, then you can no longer be in doubt about whether he is expert or not expert.

[Speaker G] No, on one side there are two more. Meaning…

[Rabbi Michael Abraham] No, on no side are there. Whether it was coercion or consent, the question whether the husband is expert or not expert has no significance; in any case there is an opening.

[Speaker H] Exactly, we talked about this five minutes ago, that’s exactly the point: there’s no dependence between the things.

[Rabbi Michael Abraham] Okay?

[Speaker G] Once there is dependence, it even becomes a half, not a third.

[Rabbi Michael Abraham] Right, a half. That’s the claim. Fine, I’ll still qualify this next time because there are problems here, but that’s where I’m heading. Meaning, I think they require a double doubt to be reversible because reversibility expresses independence between the doubts. And when there is independence between the doubts, we rely on that because the majority created here—or what we hope to get close to—is a better majority. That’s it for today. Rabbi, Rabbi.

[Speaker I] Yes. Rabbi, this is connected to another series the Rabbi spoke about last week, but it’s also connected to today’s discussion. In another series at Bar-Ilan, the Rabbi brought the story he told us about asking forgiveness from someone who doesn’t feel anything, and afterward he simply discovered that he had… done something improper and asked forgiveness. The Rabbi says that this is the finest kind of apology, right? So I’m asking: what happens when he asks forgiveness in that situation? He says: I didn’t know that in that book, in that little סעיף, it says that what I did is forbidden. Suddenly I remembered, or someone opened my eyes that it says so; I checked, and it really is written there…

[Rabbi Michael Abraham] Fine, that’s about what’s written, but in morality it has nothing to do with what’s written.

[Speaker I] Wait, the injured person says to him: what does it help me that you know? I also knew before that it was forbidden, and you’re telling me that now you also know it’s written in some little clause in some ethics book that it’s forbidden. So what? Nothing changed. The fact that it’s written—I knew that before and I know it now. What did your apology give me? What are you talking about?

[Rabbi Michael Abraham] When you’re talking about harming another person, you’re talking about moral harm, not halakhic harm.

[Speaker I] Right, right, no, I wasn’t talking about Jewish law.

[Rabbi Michael Abraham] Wait, wait, wait—this is moral harm; it doesn’t begin from the fact that it’s written somewhere. So why did I do it? Either because my impulse overcame me, or because I didn’t notice that it was immoral, and now suddenly I do notice it and I’ve decided to overcome the impulse.

[Speaker I] But what does it mean that now the same person notices? He saw it because someone told him: look, it says so in the ethics book; after all, the ethics book is oral or written.

[Rabbi Michael Abraham] No, no, no, nothing is written, leave me alone with what’s written. Nothing is written.

[Speaker I] I understood that it was an act that was not…

[Rabbi Michael Abraham] Moral, that’s all.

[Speaker I] No, but I’m trying to decipher what this expression means when he says: I came to ask your forgiveness; I feel exactly the same, I have no emotional problem at all with what happened, I only discovered that it’s morally forbidden. The injured party says to him: I also knew it was morally forbidden; all you’re telling me is that now you know it too. Great joy for my young old age. How does that help me? Explain it to me. Am I supposed to educate you? I didn’t become the educator of the world.

[Rabbi Michael Abraham] And if your stomach hurts—great joy for my young old age—why should I forgive you?

[Speaker I] But what is asking forgiveness in that situation?

[Rabbi Michael Abraham] When you come and ask forgiveness in your situation…

[Speaker I] In my situation? Yes, there’s the opposite situation—in my situation, when I come and say I’ll be the opposite. No, no, I atone. What is that? When a person answers—we know that it matters. Now, the early pietists rolled in the snow, and there’s no joy in the fact that you suffer. Really? Doesn’t the Rabbi understand that when a person says: I am now sharing your pain—until now you suffered from my injury, now I am sharing it with you.

[Rabbi Michael Abraham] You deserve to suffer; I’m very glad that you suffer.

[Speaker I] And there’s no reason for me to forgive you. No, it’s not necessary, but you can understand the possibility of forgiving. And there’s no joy in it? No, absolutely not, no way. What do you mean? Until now I felt I was suffering alone; suddenly someone comes to visit me when I’m sick and suffers together with me. Does that carry no weight? The Rabbi doesn’t see any weight in that? When the Rabbi goes to comfort mourners or visit the sick and shares in their suffering and is empathetic with them, does that carry no weight, no importance? Of course it does.

[Rabbi Michael Abraham] And that’s in the psychological sense; different people are built in different psychological ways. No—that’s the whole sharp point. Morally it’s worth nothing.

[Speaker I] So what, when a person comes—when the Rabbi goes to visit the sick, he says to him: listen, it doesn’t matter what I feel; maybe I don’t even care that you’re sick, there’s just a סעיף in the Shulchan Arukh about visiting the sick, so I’m coming to visit you. Does that count as visiting the sick?

[Rabbi Michael Abraham] Why not? Of course.

[Speaker I] The Rabbi would really accept such a sick visit?

[Rabbi Michael Abraham] What a question. I would admire a person who does that.

[Speaker G] Bottom line, does the Rabbi place double doubt under the law of majority?

[Rabbi Michael Abraham] No, it’s not under the law of majority. It’s a formal rule, but the idea behind it is that we’re trying, through formal means, to get close to a high probability. A substantial majority. Whatever you want to call it.

[Speaker G] Seventy-five percent.

[Rabbi Michael Abraham] Let’s say, yes. And again, if it were really a majority, fifty-one percent would be enough. Since this is negative, I require more in order to ensure that there will be at least fifty-one percent here. That also doesn’t ensure it, but it’s enough to be lenient in Jewish law.

[Speaker H] Rabbi Michael. Yes. I want to ask a question totally unrelated to the whole series, just a random halakhic question. A person who wants to make a match between a dog and a wolf. Halakhically Maimonides writes that this is kilayim. Scientifically, as of today, is that also considered kilayim?

[Rabbi Michael Abraham] I have no idea.

[Speaker H] Okay. Fine.

[Rabbi Michael Abraham] Okay. Sabbath שלום, goodbye.

[Speaker H] Sabbath שלום

[Speaker I] Thank you very much.

Doubt and Probability—in Halakha, in Thought, and in General—Lesson 48 – Rabbi Michael Avraham

Table of Contents

Summary

General Overview

The Two Main Rules of Double Doubt

The Example of the Blemished Slaughtering Knife

The Dispute with Rabbi Akiva Eiger

The Counterexample — Non-Reversibility Without a Single Type of Doubt

The Explanation of a Single Type of Doubt

A First Attempt to Explain the Requirement of Reversibility — A Formal Overwhelming Majority

A Second Attempt (Toward the Next Lecture) — Probabilistic Dependence

A Moral Question — Asking Forgiveness Based on Retrospective Discovery

Full Transcript

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Table of Contents

Summary

General Overview

The Two Main Rules of Double Doubt

The Example of the Blemished Slaughtering Knife

The Dispute with Rabbi Akiva Eiger

The Counterexample — Non-Reversibility Without a Single Type of Doubt

The Explanation of a Single Type of Doubt

A First Attempt to Explain the Requirement of Reversibility — A Formal Overwhelming Majority

A Second Attempt (Toward the Next Lecture) — Probabilistic Dependence

A Moral Question — Asking Forgiveness Based on Retrospective Discovery

Full Transcript

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