Torah Study – Lesson 4
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- [0:00] Introduction: a sample conceptual inquiry and examining the basis for liability in damages
- [3:08] Occam and Zermelo’s theorem: choosing the simplest theory
- [7:36] The signs of the imbecile in the Talmud: three or more
- [11:02] The question of two signs: when it is enough to declare someone insane
- [27:08] The statistics of investments and the probability of profit
- [28:44] A presumption based on three times and its connection to the Talmud
- [31:12] Occam’s razor and drawing scientific conclusions
- [32:16] The common denominator in Scripture and legal rulings
- [48:32] The example of fire and pit in studying the common denominator
- [51:26] The law of one who spits on the Sabbath according to the Rema
- [54:08] Winnowing and throwing together – what happens?
Summary
General overview
The text presents the Brisker-yeshiva way of thinking as beginning with a dichotomy and then possibly moving to a synthesis, and demonstrates this through an inquiry into the basis of liability in damages and through what is called Rabbi Chaim’s “kind of chemistry,” which includes analysis and synthesis. It adopts a ranking of simplicity in the spirit of Occam’s razor and sharpens the distinction between “there is one factor and I don’t know what it is” and “the factor is either this or that.” It then moves to topics of presumption based on three cases, questions of statistical generalization, and criticism of incorrect use of probability in medicine and law, and finally to the study of “the common denominator” in Bava Kamma and its implications for constructing derivative categories and exemptions, while setting an analytical-general reading against a synthetic reading in the style of the Rosh.
An inquiry into the basis of liability in damages and the Brisker synthesis
The text lays out two possibilities for the basis of liability in monetary damages: either the very fact that my property caused damage, or negligence in guarding it, and suggests that it is hard to find a practical difference, though there may be some connection at least in one direction with the burden of proof. It cites the Pnei Yehoshua and the Chazon Ish as presenting the possibility that both sides are true together, and in that way the inquiry demonstrates a beginning with a dichotomy and a continuation to a synthesis in which, under different circumstances, a different aspect is emphasized in order to resolve contradictions. It asks why one assumes at the outset that only one of the two possibilities is true, and presents a ranking of simplicity: one simple cause, one compound cause made of both together, or a formulation in which “the cause is either this or that.”
Zermelo’s theorem and the distinction between a trivial “either-or” and a dictated result
The text brings Zermelo’s theorem in chess: “Either White wins, or Black wins, or it is a draw,” and explains that its force lies in the claim that there is a predetermined result in optimal play, even though we do not know which of the three it is. It distinguishes between the trivial statement that “there are three possible outcomes” and a statement about one result being forced in all games given optimal strategies. It uses this to distinguish between a model in which there is always one factor behind liability but our knowledge is lacking, and a model in which each time the liability may stem from one of two different factors.
Occam’s razor, the signs of the imbecile in Chagigah, and a presumption based on three
The text applies Occam’s razor to the Talmud’s discussion at the beginning of Chagigah regarding the signs of an imbecile: tearing one’s clothes, going out alone at night, and sleeping in a cemetery, and the dispute whether all three are needed or one is enough. It brings Rabbi Chaim’s question: why, when there are three, do we not attribute each sign to a separate reasonable explanation? It suggests that a preference for one explanation unifying all the signs is better than three different coincidences. It explains the question “what about two?” through the need for stronger evidence in order to remove a person from an established presumption, and connects this to the dispute in Yevamot between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel over whether a presumption is formed after two or after three cases, emphasizing that Jewish law tends toward three: “three knocks on the can.”
The forewarned ox, goring different species, and the Talmud’s comparison
The text emphasizes that the Talmud itself compares the three signs of the imbecile to an ox that gored an ox, a donkey, and a camel and thereby became forewarned for all of them. It describes the logic of presumption in cases of goring: every individual goring can receive a local explanation, but three gorings create an assumption of a general tendency to gore. It notes that if the gorings are only of one species, the ox is forewarned only for that species, and if of different species, it is forewarned for all species, adding: “There’s a dispute between Maimonides and the Raavad what exactly ‘all species’ means, but it doesn’t matter.”
Yevamot: circumcision, marriage, “the spring causes it” versus “fate causes it”
The text brings Yevamot 64 about the dispute between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel regarding circumcision when two children died following the circumcision, and the parallel case in marriage where a woman married and two husbands died. It explains the Talmud’s question why there should be room for a presumption in marriage if the husbands come from different families, and brings Rav Mordechai’s answer in the name of Avimi of Hagronia in the name of Rav Huna: “the spring causes it,” and Rav Ashi’s view: “fate causes it.” It defines “the spring causes it” as a possible physiological-medical explanation, and “fate causes it” as the assumption of a dark, unexplained factor that replaces chance when something rare happens three times.
A practical difference: “he betrothed her and died” and “he fell from a palm tree and died”
The text brings the Talmud’s question “What practical difference is there between them?” and presents a practical difference between “the spring causes it” and “fate causes it” when the husband dies after betrothal (“he betrothed her and died”) without marital relations, or when he dies for an external reason such as falling from a tree (“he fell from a palm tree and died”). It explains that these cases do not fit with “the spring causes it” but can fit with “fate causes it,” thereby sharpening how the same presumption can depend on the kind of explanatory mechanism involved.
Statistics, Munchausen syndrome by proxy, and mistakes in probabilistic inference
The text describes a case in which the British doctor Sir Roy Meadow used the probability of crib death to infer that if two children died it must be murder, and links this to “Munchausen syndrome by proxy” as an explanation of motive. It says the conclusion was utter nonsense, and presents two criticisms: first, there is no justification for assuming independent events, since there may be a familial factor; and second, even if the probability is very low, that alone does not decide the matter against another low probability, namely murder. It explains that proper inference requires taking account of base rates and additional indications, and without supporting indication, “99% evidence is worth a fever.”
Medical tests, base rates, and court cases as an application of the same principle
The text presents an example of a medical test “99% reliable” for a rare disease affecting one in ten thousand, and calculates that most “positives” will be false positives, so that the chance of actually being sick may be only one percent. It argues that doctors who are unaware of this may send people to chemotherapy, and parallels this to legal evidence, where even 99% evidence is not sufficient when the proportion of murderers in the population is low. It adds that a screening mechanism such as the decision to file an indictment raises the base rate in the group being examined and therefore changes the evidentiary value, though it notes that the screening itself also depends on a similar calculation.
Nassim Taleb, “The Black Swan,” and survivorship bias in long-term success
The text brings Nassim Taleb and “The Black Swan” to argue that long-term success in the stock market may look like genius even though it could be the product of chance within a large sample. It presents a scenario in which, out of a million investors, small percentages of winners remain after a few years, and in the end there will still be “champions” over fifty years even if no one has any special ability, simply because a huge sample produces rare winners. It sharpens the point that announcing the winner in advance changes the calculation, but identifying the winner after the fact is not proof of ability.
“The common denominator” in Bava Kamma: rule versus examples and methods of study
The text brings the first Mishnah of Bava Kamma: “There are four primary categories of damages… the common denominator among them is that their way is to cause damage, and the obligation to guard them is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of his land,” and also mentions the Rif’s version, “that they are your property, and their way is to cause damage, and the obligation to guard them is upon you.” It presents an expectation that the rule alone should suffice, but explains that the Talmud asks the opposite: “What does the common denominator come to include?” and establishes that the common denominator comes to include a derivative category learned from two primary categories together, such as “his stone, his knife, and his load, which he placed on top of the roof and they fell in a normal wind and caused damage,” learned from fire and pit. It describes the structure of learning through a common denominator as the combination “this is not like that, and that is not like this” until “the rule returns,” and then the presentation of a shared denominator, but raises the concern that the law in the source cases may stem from their different unique qualities rather than from the shared denominator, in which case there is no necessity to apply it to the learned case.
Occam versus “either this or that” in the common denominator, and the connection to the first inquiry
The text argues that the common denominator relies on preferring a simple explanation in which one shared cause generates liability, and not a model in which the liability arises “either from X or from Y,” and explicitly parallels this to the earlier inquiry about the basis of liability in damages. It notes that in nature one may need three cases to be convinced, but in the hermeneutical principles by which the Torah is interpreted, a common denominator already works from two examples, and explains this by saying that the Torah was written with the assumption that we would make such a generalization. It presents a claim that in the dispute between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel one cannot decide on the basis of the common denominator, because one can argue that the Torah itself “arranged” the examples in a way that justifies generalization, whereas in nature there is no such arranging factor.
Special exemptions in the four primary categories, the problem of generalization, and the words of the Rosh
The text details that every primary category of damages has special exemptions: tooth and foot are exempt in the public domain; fire is exempt for concealed items; pit is exempt for vessels, “ox but not a human, donkey but not vessels”; and an innocuous horn pays only half-damages. It raises a question about a derivative category learned from fire and pit: does it receive the exemptions of both, of neither, or of one of them? It brings the Rosh, who cites: “And some of the great authorities wrote that one is liable only for what both of them are liable for… and exempt for damage to vessels… and for concealed items as in fire.” It presents the Rosh’s rejection and his conclusion: “And it seems to me that all the laws of pit apply to them,” so that the derivative category receives the laws of pit, including the exemption for vessels, but not the exemption for concealed items of fire.
Two conceptions of the basis of exemptions and their implication for the common denominator
The text presents the well-known opening lecture in the name of the Rabbi of Brisk and formulates two conceptions: either the liability in a primary category is general and the exemptions are later novelties layered on top of it, or the category is liable only within a defined field from the outset, so there is no “liability for everything with an exemption,” but rather “liability only for part.” It states that if the exemptions are essential, then in a derivative category learned from two source cases one can obligate only in what both are liable for, and therefore the derivative category will receive the lenient side of both. But if the exemptions are merely exemptions from a general liability, then one can learn the liability from the two source cases but cannot learn the exemptions, and therefore the derivative category will be liable without unique exemptions.
Reading the Rosh as a synthetic model: a main source case and a source case that removes an obstacle
The text interprets the Rosh as reading the learning process in such a way that one source case is the basis and the other merely removes a side difficulty, so that in the case of his stone, his knife, and his load, the liability is “under the law of pit” because it lies in the public domain and causes people to stumble, while fire only teaches that “another force being involved” does not exempt. It distinguishes between a logic of elimination seeking a shared characteristic and a logic of synthesis in which one takes a component from one primary category and a component from another in order to build a third case. It argues that this difference explains why the common denominator can be seen not only as an abstract rule but also as a structure in which reasoning determines what remains “at the end,” and the second source case only corrects the problem.
Sabbath example: “one who spits on the Sabbath is liable” between winnowing and throwing
The text brings a law attributed to the Jerusalem Talmud that one who spits on the Sabbath is liable, and presents in the name of the Mishnah Berurah citing Rabbi Menashe of Ilya a correction and explanation that this is “because of throwing” and not “because of winnowing,” with the suggestion that both primary categories participate: the liability is like throwing four cubits in the public domain, and winnowing teaches that when the wind is involved in the labor this does not exempt. It emphasizes that on the Sabbath we generally do not find a derivative category made from two primary categories together, and presents the case as a hint to a mechanism similar to the Rosh’s, in which there is no shared characteristic but rather a combination of the wind element from winnowing and the throwing element from throwing to create a third liability. It concludes that the logic here is synthesis and not analysis, thus returning to Rabbi Chaim’s framework of “a kind of chemistry,” in which there is both breaking apart and putting together.
Full Transcript
[Rabbi Michael Abraham] Last time I finished the discussion of a sample inquiry, what in the yeshivot is called a chakirah, meaning an attempt to clarify what the basis is that creates liability for paying damages. If my property causes damage, then the question is why I’m obligated to pay. And we saw that basically the form of thinking here is to begin with two possibilities for understanding that basis: either the very fact that my property caused damage obligates me, or negligence in guarding it obligates me. After that I said that it’s hard to find some practical difference, but maybe there’s something at least in one direction having to do with the burden of proof. In the end we saw that there is also a possibility—and you can see this both in the Pnei Yehoshua and in the Chazon Ish—that really both sides are true together. And therefore this discussion demonstrates several foundation stones of Brisker, yeshiva-style thinking. When people say “yeshiva-style,” of course they mean the Lithuanian yeshivot and their present-day continuations, where we begin with some dichotomy, and at some stage sometimes we create a synthesis between the two possibilities, and that synthesis expresses itself in different ways. Under certain circumstances one aspect of the synthesis is emphasized; under other circumstances another aspect is emphasized; and that’s how we can explain various contradictions. I want to continue a bit with what some of the yeshiva people in Lithuania called something like chemistry—that’s what they called it. Rabbi Chaim’s method was to learn how to combine things, like making a chemical synthesis between materials, both analysis and synthesis. So I want to look at a few more things like that, this time in earlier sources. I’ll start maybe with what we ended on last time, when I asked why in fact we assume as an initial assumption that only one of the two possibilities is true. Meaning, either negligence in guarding creates the liability, or the very fact that my property caused damage creates the liability. Why not assume that both together create the liability? So I said there’s probably some ranking of simplicity here. Occam’s razor says that we choose the simplest theory. And we made some kind of ranking of simplicity. I said that the most problematic—or the simplest—thing is basically that one of them is the cause: either negligence in guarding, or that my property caused damage. A second possibility is to say that both together are the cause, which is still one cause, but one compound cause. And the third possibility is to say that either this or that is the cause. Not that this is the cause or that is the cause, but that the cause is either this or that. Those are two different things. I’m remembering now: there’s a theorem in game theory, Zermelo’s theorem, which I think was first formulated about chess, and it says that either White wins, or Black wins, or it’s a draw. That’s the theorem. A game like chess: either White wins, or Black wins, or it’s a draw. Nice theorem, right? In any case—
[Speaker B] Somebody wins.
[Rabbi Michael Abraham] Amazing theorem. Right? Powerful theorem. It’s not a trivial theorem.
[Speaker B] Tomorrow he’ll scribble some names and become a leader.
[Rabbi Michael Abraham] Right, but it’s not the same thing. Why isn’t it the same thing? It’s exactly the distinction I mentioned before. Zermelo’s theorem is basically saying that the game of chess has a predetermined outcome. We just don’t know which of the three it is. We don’t know how to prove which of the three is the predetermined result. But there is a predetermined result. That’s not the same as saying that in every game either Black will win, or White will win, or it’ll be a draw. Fine, that’s trivial. There are no other possibilities in this game. The claim is—
[Speaker C] In all games—
[Rabbi Michael Abraham] If you play optimally, with an optimal strategy, you’ll get the same result. We don’t know whether the result is that Black always wins, or White always wins, or that it’s always a draw, that a draw can always be forced. That’s really not trivial. Do you understand the difference? Right? Silence in the audience. Not clear. If I take one specific chess game, I say it has three possible outcomes: either White wins, or Black wins, or it’s a draw. Fine, that’s trivial. There’s no fourth possibility. But when I say that in all the chess games on earth that will ever be played, if you play optimally there is one outcome that can be forced and no other—that’s something else entirely. At the moment I don’t know which of the three outcomes is the one that can be forced. I don’t know whether Black always wins, or White always wins, or whether it’s always a draw. But it will always be the same result; I just don’t know which one of the three it is. That’s a very nontrivial theorem. In fact not all games satisfy that, only games of a certain kind, a certain family of games. Okay, when I first read this it took me some time to understand what they were trying to say there.
[Speaker D] What does the theorem mean? Why always?
[Speaker B] That’s what the theorem says.
[Speaker D] That’s why it took time, and we didn’t understand. The theorem says that if both players play optimally, then always—you don’t know which one—either White will win or Black… If both players play optimally, that’s the part that was missing at the beginning, that you didn’t say.
[Speaker E] For example, White always starts. If you play optimally, then maybe White will always win because he has the advantage of moving first. I said two people can’t both win. The question is why it’s the same result. If you play optimally, that’s what was missing.
[Rabbi Michael Abraham] For one game the statement is completely trivial, that’s no problem.
[Speaker F] I’m talking about the theorem for all games. Usually if there are two opinions, there are two opinions inside one game. No, yes, one. I didn’t mean two opinions. Let’s say you were talking about the issue of two opinions, right? That in the end maybe the two opinions are really one. That’s one possibility. Or really they’re playing the same game, no? That together the two opinions explain the same question, and you come to the conclusion that within this game both opinions can be true.
[Rabbi Michael Abraham] No, that’s what I’m saying.
[Speaker F] I gave the example of—
[Rabbi Michael Abraham] Zermelo’s theorem. Now I see it in English-English. I wanted to bring Zermelo’s theorem as an example to demonstrate the difference between the two possibilities I gave here. Meaning, what I said here is that either negligence in guarding is the factor that creates the payment, or the fact that my property caused damage is the factor that creates the payment. That’s one possibility. A second possibility is that there is one factor for the payment—either negligence in guarding or that my property caused damage. What’s the difference between those two possibilities? The difference is that according to the first possibility there is only one factor, I just don’t know which one it is. I’m simply missing knowledge, but it’s always one factor. According to the second possibility, no: every time either this or that can exist, and that will generate liability for payment. Those are two completely different things. Fine, that was just parenthetical. Anyway, Occam’s razor basically tells us to choose the simplest possibility. Where do you see the application of Occam’s razor in earlier literature? This is Rabbi Chaim. Rabbi Chaim is famous for the signs of an imbecile. The Talmud at the beginning of Chagigah says—these Talmud volumes here are too big to bring everything I would have needed—the Talmud says: who counts as an imbecile? There’s a dispute there; it brings three signs. There’s a dispute among the Amoraim whether you need all three or whether one is enough. Now according to the view that you need all three—I think that’s Rav Huna, I don’t remember anymore—according to the view that you need all three, the Talmud asks: why do you need all three? Either way, if he behaves in an insane way then one sign should be enough. And if not—if he does these things for sensible reasons—then even all three shouldn’t help. What are the sensible reasons? The Talmud says either he tears his clothes, or he goes out alone at night, or he sleeps in a cemetery. Those are the three signs. And the one who sleeps in the cemetery may want a spirit of impurity to rest upon him, so he’s a perfectly logical person; he’s doing it because he wants a spirit of impurity to rest on him, not because he’s insane. The person who tears his clothes may be lost in thought and simply not paying attention, distracted—like the Talmud in Shabbat where Rabbah was so immersed in learning that he made himself bleed without noticing. Then that heretic said to him, “A hasty people, who put your mouths before your ears”—you’re a rash people, you don’t pay attention to what you’re doing, you said “We will do and we will hear” before even asking what the merchandise was. So in short, each of those signs has a sensible explanation. Therefore, if there were only one of them, the Talmud says, he would not be an imbecile. But if he has all three signs, then he is an imbecile. What about two? No—the Talmud says specifically three.
[Speaker G] Over what period of time? Over what period? What does it mean that he did this?
[Rabbi Michael Abraham] The Talmud doesn’t get into the question of time period. I assume it doesn’t matter. Let’s say he did each of them once.
[Speaker G] If he did it once, then he’s an imbecile.
[Rabbi Michael Abraham] Once you saw that he was an imbecile. Unless you decide that he has periods of sanity and periods of insanity, as the Talmud calls it—a person who is sane only intermittently. In any case, what comes out of the Talmud, at least according to that Amoraic opinion, is that you need three signs. One by itself has an explanation; two can also have two separate explanations; but three—no. Rabbi Chaim’s question is: why? If you tell me that each of these signs by itself can have a sensible explanation, it doesn’t necessarily show that the person is an imbecile, then why not with three as well? With three too, it could be that he went out alone at night because… Meaning, Rabbi Chaim says, look: if you have three difficulties and you can answer each one with its own answer, that’s one possibility. A second possibility is that you have three difficulties and you answer all three with the same answer. Which is preferable? Obviously the second possibility is more reasonable—again, Occam’s razor. So if you have three signs and you explain all of them with the same principle—the person is insane.
[Speaker D] Wait, so that argument would work for two also, wouldn’t it?
[Rabbi Michael Abraham] What? Right, one second, one second. So then this person is an imbecile—that’s one explanation that explains all three signs. Whereas otherwise you would have to assume three separate coincidences: here he wanted a spirit of impurity, there he forgot, and here he wasn’t paying attention—those are three separate answers. Therefore we prefer the simpler explanation, and that is really the principle behind three: once there are three signs, we no longer attribute each one to its own explanation. Now Shmuel asks, quite rightly: what about two? With two, it’s the same thing. So here I think a quantitative question really comes in. By the way, there’s a dispute in the Talmud in Yevamot between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel about whether a presumption is created only after three cases, and that’s exactly the argument. In Jewish law we generally rule—at least in most cases; the Talmud distinguishes among different cases—that you need three cases. And I think the point is more quantitative. Meaning, with two cases, true, it’s less likely that he’s insane, but in order to declare someone insane you need more decisive evidence. So true, the single explanation is still more likely than two different explanations for the two signs, but the difference isn’t dramatic enough for you to declare him insane. To declare him insane means changing his established presumption; he has the standing presumption of being a normal person. To remove someone from a presumption, you need three knocks on the can, yes? You need three proofs for it to be clear. With two—who knows? Maybe, like you said before, he does it once a year. Maybe it’s some sort of tic. Maybe there’s just a sensible explanation. Once there are three things, we already assume not. And that’s basically the foundation. People always quote this in the name of Rabbi Chaim, but really these are explicit Talmudic passages. The Talmud itself connects it there in Chagigah; the Talmud says it’s like one that gored an ox, a donkey, and a camel and became forewarned for all of them. That’s what the Talmud says about the signs of the imbecile. Meaning, the Talmud itself compares it to a forewarned ox. A forewarned ox that gores three times—there too you can say, fine, maybe he woke up angry that morning, or that animal annoyed him. So maybe he’s not really an ox with a goring disposition by nature; it just happened. But if he does it three times, then apparently he’s a goring animal by nature, even though there could have been a local explanation for each goring. Similarly, if he gored three oxen, then he’s forewarned only for oxen—he gores oxen; he’s angry at oxen, not at donkeys. Fine. If he gored only donkeys, then it’s only donkeys. But if he gored one ox, one donkey, and one camel, then he’s forewarned for all species. There’s a dispute between Maimonides and the Raavad what exactly “all species” means, but that doesn’t matter—he’s forewarned for all species. Why? Because you don’t say it’s specifically oxen, or specifically donkeys, or specifically camels. Rather it’s something that is apparently general. And again, we prefer the simpler explanation. That’s exactly what the Talmud says. It’s not Rabbi Chaim; the Talmud says it.
[Rabbi Michael Abraham] Now in the Talmud in Yevamot—they bring here on page 64—the Talmud presents the dispute between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel regarding circumcision. What happens if a child was born, they circumcised him, and he died; then another child was born, they circumcised him too, and he also died—what do you do with the third one? Do you circumcise him too—so he’ll die on us as well? So Rabbi Yehuda HaNasi says you do not circumcise him; it’s a matter of saving life. And Rabban Shimon ben Gamliel says yes—only after three times, not after two; a presumption is formed after three times. You need a strong heart for Rabbi Yehuda HaNasi; the parents need a strong heart, in short. So their dispute is regarding circumcision. Then the Talmud says: if they disputed with respect to circumcision, do they also dispute with respect to marriage? Yes, they also dispute with respect to marriage. As it was taught: if she married the first and he died, then the second and he died, she should not marry the third—these are the words of Rabbi Yehuda HaNasi. Rabban Shimon ben Gamliel says: she may marry the third; she should not marry the fourth. So again the same dispute: a woman was married to one husband and he died; she married a second husband and he also died. Is it permitted to marry her?
[Speaker D] Is there any issue of age gaps, and how long he lived after the marriage? Does the Talmud—
[Rabbi Michael Abraham] The Talmud doesn’t bring that. In a moment there’s a little bit about it later—we’ll soon see—but not right now. In short, not whether it’s wise. Whether it’s wise, everyone can decide for himself. The question is whether it’s permitted. It’s danger to life; it’s forbidden to endanger life; it’s a halakhic prohibition. Okay? So the question is whether it’s permitted to marry her. So that’s the dispute between Rabbi Yehuda HaNasi and Rabban Shimon ben Gamliel: whether after two times it’s forbidden, or after three times it’s forbidden. So the Talmud says—it doesn’t understand why there’s a dispute between them. Granted, with circumcision there can be one family whose blood is loose and another family whose blood congeals well. Meaning, there are families that have some blood-related issue—I don’t know. But with circumcision, it could be that within the family there’s something in the blood because of which circumcision can kill him. It doesn’t necessarily mean literally something in the blood, but some illness, some weakness, whatever, because of which they can’t withstand circumcision and therefore they die. So there I can understand that if it happened to two or three, you have to be careful with the next one. But in marriage, what’s the reason? These are people from different families, from different places. They all died. So there’s no connection between them. Why assume that there is some phenomenon here that one has to be wary of? This is really a question of scientific generalization: how do you generalize on the basis of cases? There are places where the cases demonstrate a general law, and there are places where—who knows?—it’s just three cases, there’s no connection between them.
[Speaker H] Even though here you can apparently see that the Talmud doesn’t believe in the evil eye, mysticism, right?
[Rabbi Michael Abraham] You’ll see in a moment—don’t jump to that so fast. Wait, let’s read one more line. “But in marriage, what is the reason?” Why in marriage are we concerned? Rav Mordechai said to Rav Ashi: this is what Avimi of Hagronia said in the name of Rav Huna—that same Rav Huna we saw before, yes, it was Rav Huna—“the spring causes it.” The woman’s spring—when he has marital relations with her, her bodily fluids, I don’t know exactly what—there’s some problem there, and that’s what kills all the husbands. So there too there is an explanation. A kind of AIDS, yes, I don’t know, something like that. And Rav Ashi said: “fate causes it.” We’ve arrived. Rav Ashi said: fate causes it. What does “fate causes it” mean? Demons, spirits, I don’t know, stars, I don’t know exactly what. This woman is apparently a serial killer of husbands. Not a killer, of course. This reminds me of that trial not long ago of some friend of Finkelstein, about that man who murdered three of his wives and in the end he was convicted for two. So there too the evidence was basically only circumstantial. It’s really a question of presumption. Three of his wives died. And the question is whether he murdered them, or whether, I don’t know, there were three cases. This reminds me of something else, actually very interesting. There is—you know the psychological syndrome called Munchausen syndrome by proxy? Munchausen syndrome—better not know it, and I’m not even sure there is such a thing. Munchausen syndrome is someone who does provocative acts or problematic acts in order to attract attention, like Baron Munchausen from the stories. Now Munchausen syndrome by proxy—it was a British doctor named Sir Roy Meadow. He formulated that syndrome, or psychiatrist—I don’t remember exactly what he was. And he said what?
[Speaker D] A psychiatrist is also a doctor.
[Rabbi Michael Abraham] Yes, yes, something like that. In any case, he formulated it, and it came up because there was a woman whose two children died of crib death. Today we’re doing a little math. Two children died of crib death. So he said: look, the probability of crib death is one in eight thousand. One in eight thousand children dies of crib death. The probability that two children would die of crib death is one in sixty-four million. Meaning, they didn’t die of crib death—she murdered them. There’s no chance they died of crib death. And since that’s so, it’s obvious that she murdered them. You ask why?
[Speaker B] What would she gain by murdering them? So he formulated Munchausen syndrome by proxy. Meaning, she did provocative things, attention-grabbing things, in order to attract attention to herself. It broadens the regular Munchausen syndrome. Regular Munchausen syndrome is when I do the acts myself. Usually in hospitals, with children—you see people who do various things to their children so that afterward they’ll be taken to the hospital and they’ll get attention.
[Rabbi Michael Abraham] Right, so that’s the point—that’s Munchausen syndrome by proxy. What does “by proxy” mean? It means through someone else. I’m not doing it to myself; I—
[Speaker B] Do it to someone else. They spoke about the starving mother in that context, that this was Munchausen syndrome by proxy and things like that. In hospitals social workers check how many times—
[Rabbi Michael Abraham] Social workers don’t check whether there is such a phenomenon, but never mind. So that was basically the claim, okay? What does that really mean? Again: something improbable may have an explanation. But if it happens two or three times, then there’s a presumption. That means there is some mechanism behind it. Now here, of course, this is complete nonsense. That poor woman sat in prison—I don’t remember how long, but for a substantial amount of time—until some statistician came and explained to that idiot judge that this evidence was stupid. Stupid. You can present it in several ways; it all relates to our issue.
[Speaker D] Independent events.
[Rabbi Michael Abraham] Yes. First of all, who says these are independent events? Maybe there’s some family factor, you understand? If there’s some family factor, then that means there is dependence. In that family there is something that causes babies to die. So no, you can’t multiply the probabilities if they’re not independent. But beyond that, even if you say it really is one in sixty-four million and they are independent—so what? What is the probability that a woman would murder her child or children?
[Speaker E] Much smaller than that.
[Rabbi Michael Abraham] Very small, right. How many such women are there? Okay, so there’s a small probability that children like this would die, and there’s also a very small probability that a woman would do this. So now the question is which probability is smaller. I don’t know. How many women are there in Great Britain? I don’t know, some tens of millions? Okay, so among them let’s say there is a chance that one or two will do this, actually do it. Okay, now the question is whether this woman is the realization of that small probability, or whether by chance this was really the one-in-sixty-four-million case that happened by chance. This is one in many millions, and that is one in many millions. How can you decide? And there’s someone who has—this can be formulated a little differently. Let’s formulate it a little differently. Look, suppose you want to detect a rare phenomenon. If you want to catch small fish, you need a net with small holes, right? A net with big holes won’t catch small fish. And when you want to catch a rare phenomenon, you need an instrument with high resolution. Okay, for example: I go to a doctor and he suspects I have some rare disease. So he sends me for a test. The test is 99% reliable, okay? It’s 99% reliable, meaning it gives the correct answer 99% of the time, and let’s assume for now in both directions—that is, 99% of healthy people test healthy, and 99% of sick people test sick. There are tests whose error rates differ in the two directions. Okay, now I went for the test and I was found to be sick. What is the probability that I’m sick?
[Speaker D] The question is how rare the disease is.
[Rabbi Michael Abraham] Yes. What’s the probability that I’m sick? 99%? No.
[Speaker D] No.
[Rabbi Michael Abraham] It depends how rare the disease is. Exactly. Let’s say the disease is one in ten thousand, okay? For the sake of discussion. And a million people took the test, okay? So among them there are a hundred sick people, right? One in ten thousand, so a hundred sick people, and the rest of the million are healthy. Now all of them take the test. Among the healthy people—there are roughly a million healthy, a million minus a hundred, doesn’t matter, a million healthy, fine—among them there’s a one percent error. So ten thousand come out sick, right? Now there are a hundred sick people, and there’s a one percent error, so among them one comes out healthy. So out of the whole million, how many sick results do you get? Ten thousand—
[Speaker C] Ninety-nine.
[Rabbi Michael Abraham] Ten thousand and ninety-nine. Fine? How many actually sick people are there? A hundred. A hundred. Meaning, the test produced ten thousand positives, of whom only a hundred are genuinely sick. Meaning, if the test said I’m sick, the probability that I’m actually sick is one percent. I can go home cheerful and happy-hearted; no chance I’m sick. No need for the test. Doctors, by the way, today already study this at university—at least at the Hebrew University I know they already study it—because doctors who aren’t aware of this will send you to chemotherapy. This test is 99%—
[Speaker K] It’s—
[Rabbi Michael Abraham] A 99% test, an amazingly reliable test, okay? And that tells you nothing about whether I’m sick or not. It depends on the rarity. If you’re looking for a rare phenomenon, you need an instrument whose resolution is roughly on the order of the rarity of the disease, more or less. Okay? Even more than that—it should be better than that, because otherwise it’s only fifty percent. If it’s equal, it’s fifty-fifty. But for it to be effective, you have to match the size of the holes to the size of the fish.
[Speaker B] In short, you don’t take medication. What? You don’t take it.
[Rabbi Michael Abraham] Only if there’s some additional indication. Meaning, if there’s another indication besides this test, that changes the statistical calculation completely. Even a weak indication.
[Speaker E] Not three.
[Rabbi Michael Abraham] What? I didn’t understand. Ah, three. Okay. No, a weak indication—that’s exactly it. Three is a weak indication, but a weak indication changes the whole calculation. We were talking while he was writing that verdict, because there were exactly those kinds of statistical problems there; that’s what we discussed there. Because in legal evidence it’s the same thing. A judge comes and says: I have evidence at a 99% level that this person is a murderer. But how many murderers are there in the population? The chance that you’re a murderer is very small. Right? How many murderers are there in the general population? Thank God, not that many. Right? I don’t know how many—a tenth of a percent, a hundredth of a percent, I don’t know how many murderers there are in the population. Now you have evidence at the 99% level that this person is a murderer. What’s the chance that he really is a murderer? One percent. He’s not a murderer. It’s the same thing as in medicine. Now in law too they need to teach this; there, I think they still don’t teach it. They should teach it; it’s a problematic thing. Meaning, if you don’t have some supporting indication from the side—even a weak one—it changes everything. But if you have no side indication, evidence at ninety-nine percent is worth nothing. It’s worthless. So what can you rely on? If the person is already standing trial, then among those who are standing trial, the number of murderers is greater than in the population as a whole. So fine—if you trust the enforcement system, the police, or the prosecution, or if they decided to file an indictment, then that creates some kind of filtering, and that filtering is very important, very important. That’s the rationale behind—maybe, I don’t know what they were thinking—but that’s the real rationale behind this whole business of the decision to file an indictment. Because after you decide on an indictment, basically someone examined the matter and decided that you are a candidate to be a murderer, a reasonable candidate to be a murderer. So now, among those against whom an indictment was filed, the percentage of murderers is already much higher. Then evidence at ninety-nine percent is okay. Okay?
[Speaker D] After all, if you take it from the general population, unless—
[Rabbi Michael Abraham] Then the one who filed the indictment made the same calculation. Exactly. If he made the same calculation, it won’t help at all.
[Speaker E] That’s basically what you’re saying—that if he went to trial, say, three times, then the probability would already be much higher.
[Rabbi Michael Abraham] Could be, yes, right. And if I go back to Munchausen syndrome, that woman came from the general population of women in Britain. There was no indication that she murdered, other than the statistics themselves. If there had been supporting evidence, that would be something else, but there was nothing. She went to prison based on statistics. Now that’s ridiculous. Meaning, one in sixty-four million—let’s say the probability is one in sixty-four million, leave aside the dependence issue, okay? The probability is one in sixty-four million. That means there is one woman in Britain to whom this will happen, statistically, right? So this is that woman—what’s the problem? How do you know she’s a murderer? There’s a book by Nassim Taleb—we talked about it—The Black Swan. He’s this Lebanese guy who deals with stock-market investments. And he writes there that people think—not Trump, what’s the other one’s name? The investor, that famous American billionaire. Warren Buffett. Warren Buffett—people think he’s an economic genius. I don’t remember if he’s talking about Warren Buffett, but it doesn’t matter. He says: there’s no indication of that. Think about a million people entering the stock market. Fine? Now among them there will be some who profit, and more who lose, who will support those who profited. Now say that over time you profit for a month. Fine—there will already be fewer people who profit over time, right? Some will profit, all completely random, nobody has any economic ability. That’s the assumption. What will happen in practice? Say that nobody has such a thing as the ability to invest in the stock market, let’s suppose.
[Speaker D] In truth there’s no such thing.
[Rabbi Michael Abraham] Let’s say. Doesn’t matter. I’m not sure, but let’s say. So let’s assume that, and let’s see what happens. Over a month, say, I don’t know, ten percent of people will profit. Over a year, five percent of people will profit. Over ten years, one percent of people will profit. Over fifty years, one tenth of a percent of people will profit. Now a million people entered the stock market. One tenth of a percent of them means a thousand people will profit over fifty years. There really is a person who profits for fifty years and doesn’t lose continuously. You have no indication that he has economic ability. It could be pure chance—he just happens to be that one person, one in a thousand, who profits over fifty years. Someone like that has to exist even if it’s all random, even without ability. Statistics are very deceptive.
[Speaker B] Tell me, how do you make it so that it’ll be me?
[Rabbi Michael Abraham] That’s the million-dollar question. By the way, that’s the difference—if I tell you in advance that this person will profit for fifty years, then it changes the probability completely. But that can’t happen.
[Speaker B] But it’s interesting—do you read all these books? Where do you find the time to read that guy’s book?
[Rabbi Michael Abraham] I get up at six-thirty in the morning to come here for the class; after that I have plenty of time, I can read books to my heart’s content. Okay, anyway, I’m going back to the presumption of three times. Basically, the presumption of three times says that if something rare or unlikely happened three times, then that means there is some explanation behind it, right? That’s basically what it says. Now what does the Talmud tell us here? There’s a dispute between the Amoraim about what happens if a woman killed three husbands. Killed, in the sense that… yes, Munchausen syndrome—meaning, they died because they were married to her. So the Talmud says: either the source causes it, or fortune causes it. What’s the difference between those two views? “The source causes it” means there is a physiological reason, meaning there is a physiological, medical explanation for why the men died. “Fortune causes it” is a dark speculation, right? I have no explanation, but if it happened three times, then it’s probably not a coincidence, according to the logic of the Munchausen syndrome case, yes? It happened three times in a row, so it’s not a coincidence. So there is something behind it, even though I don’t know what. Now you have to understand: if I have medical knowledge, then there’s no need to get to presumptions. I have the medical knowledge; I know that such a thing causes the husbands to die. But here we’re talking about a situation where I don’t have knowledge, but I do have a possible suspicion. Meaning, “the source causes it” doesn’t mean that I know there is such a phenomenon that a woman’s source kills people, but it is something that, in light of my experience, could be taken into account. And the other one says you don’t even need that. If something happened three times, that’s it. Okay? Now the Talmud says: what practical difference is there? What’s between them? The difference between them is a case where he betrothed her and died. If he died after betrothal, not after marriage—there hadn’t been marital relations at all. So if it’s “the source causes it,” then here there’s no explanation at all. And if it’s fortune, fortune can always be relevant.
[Speaker D] What you’re saying is, if he died, then what’s the explanation regarding the ruling if three were born—if three died? Again: after all, both agree that she’s forbidden to marry after however many times the husband died. The one who holds “the source causes it”—if one of them was only betrothed to her, then does that not count? No? No?
[Rabbi Michael Abraham] You need three who died after marriage. And the practical difference is one after betrothal. Another practical difference: if he fell from a palm tree and died. He fell from a tree, committed suicide—saw whom he had married, climbed the tree, and killed himself. Meaning, he fell from the palm tree, where it’s obvious that this can’t be “the source” again, but rather apparently—it’s fortune. So if it’s fortune, it’s fortune. If it’s the source, then here there won’t be a presumption. And again, what do we see here? Basically, we see Occam’s razor here. We’re looking for the simplest explanation. In that sense it’s similar to what we saw before. We choose the simplest possible explanation and prefer it to a collection of all kinds of explanations. By the way, scientific thinking is also built this way. This is something we maybe talked about once. Scientific thinking basically says yes: if I saw a phenomenon happen three times—or not specifically three, however many times—or to several different objects, and if there’s variety that’s better, then apparently there’s a general phenomenon here and we make a generalization. Okay? I saw three black crows, so I assume that probably all crows are black. I may be wrong, but the assumption is that it’s probably not coincidence. Although it could be—if there are lots of crows in lots of colors, then maybe there happen to be three that are black—but if the sample is random, I didn’t choose specifically those three crows, then the assumption is that blackness is probably a property of crows and not something accidental. So basically, this is just a form of scientific thinking that’s being discussed here. Now I want to show this in another place too, and that is the common denominator, learning by the common denominator. Once we talked about—we talked once about rules, yes, about working with rules in Jewish law. I brought this Mishnah, the first Mishnah of Bava Kamma: “There are four primary categories of damages: the ox, the pit, the maveh, and the fire. The case of the ox is not like the case of the maveh, and the case of the maveh is not like the case of the ox,” and so on; each one is different. And in the end they conclude: “The common denominator among them is that they tend to cause damage, and their supervision is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of his land.” There’s also a version in the Rif that says: “that they are your property, and they tend to cause damage, and their supervision is upon you, and when they cause damage, the damager is liable.” So I talked about this even just now, actually, when I discussed the conceptual analysis there, in the analysis from the previous time. Now here the Mishnah ends with a rule: what is the common denominator? That they are your property, their supervision is upon you, and when they cause damage the damager is liable. So we would expect that basically all the mishnayot would be formulated this way. At last they give the rule—I know how to work. Why are you giving examples? The ox, the pit, the maveh? And what if it’s a dog? I don’t know. How can I derive? Give me the rule. Anything that is my property, tends to cause damage, and is under my supervision—if it causes damage, I have to pay. Wonderful, right? So from the Talmud I would have expected it to say: why do we need the examples? I now have the rule. You gave me the rule—why are you giving me ox, pit, maveh, what difference does it make? Give me the rule and that’s it. Right? What does the Talmud say? On “the common denominator among them,” the Talmud asks: what does that come to include? Who needs the common denominator, who needs the rule? There are examples—why do we need the rule? Or the opposite: why do we need the examples? There’s the rule. The Talmud asks: we have the examples, why do we need the rule? The rule is redundant.
[Speaker D] It doesn’t express all the behavior; it only describes the common side. That is, what’s called—fine—from each one there is a specification. But why does that matter?
[Rabbi Michael Abraham] But they’re all liable.
[Speaker D] Yes, but maybe that’s not enough. It’s necessary but not sufficient.
[Rabbi Michael Abraham] No—then the common denominator can’t work. “Common denominator” means that if the common denominator is present, that is sufficient. If it’s your property and under your supervision, you’re liable to pay. Anything. That’s the meaning of a common denominator. A common denominator means that once I distilled the common denominator out of the examples, everyone who satisfies that common denominator—the law applies to him.
[Speaker D] Or, anyone who doesn’t meet one of the conditions is exempt. But not necessarily that here it’s sufficient or not.
[Rabbi Michael Abraham] No, then that’s not a common denominator. I’m saying again: common denominator always means that you take what is shared by the examples, and you’re basically saying it doesn’t need to be like one of the examples. What you need is to fulfill the common denominator.
[Speaker B] What we talked about, about restrictive interpretations at the beginning—did we talk about that?
[Rabbi Michael Abraham] Yes, maybe. I don’t remember.
[Speaker B] I don’t remember. But I remember you brought that too.
[Rabbi Michael Abraham] Okay. Anyway, what do we see here? Good. So there are people here who are following. What do we actually see here? So the Talmud says, on “the common denominator” in the texts, it brings a derivation from two primary categories to a derivative category. For example: his stone, his knife, and his load, which he placed on top of a roof and they fell in a normal wind and caused damage. That is learned from fire and pit together. Okay? The common denominator comes to include that. Then the question is: how is such an inclusion structured? This is an example—common denominator appears in many places throughout the Talmud. So how is such an inclusion structured? We have two sources that teach, say in this case fire and pit. Each of them has a trait. Fire, for example, has an external force involved in it, because it moves with the wind. Pit: its very creation is for damage. Meaning, when you dug a pit, it was already poised to damage. Now his stone, knife, and load that he put on top of the roof and they fell in a normal wind and caused damage—caused damage after they fell—have characteristics that can be built out of fire and pit together. Okay? You need both fire and pit together to teach this. Fire is because an external force is involved in it; so fire shows that even if an external force is involved, you are liable. Pit teaches that when its creation is for damage, you are liable. And you’re basically making some synthesis. The general structure is like this: suppose we have two teachers, A and B, and we have a learned case, C. A and B have unique properties, and they also have a shared property. Let’s say A has property X, B has property Y, and both have property Z. Fine? This one has X and Z, that one has Y and Z, and the learned case C has only Z. It doesn’t have X or Y. Fine? Now I say this: I try to learn C from A. I say: it can’t be learned, because A has property X, a special trait. I can’t learn from it to C. Then I say: B will prove it. But B has property Y, which C also doesn’t have. So then I say: okay, then the law returns—it’s not like this one and not like that one. The common denominator among them is that both have Z, and in C, the learned case, there is also Z. So because of that, it can be learned from both of them. Now of course here too the question arises: who says so? Meaning, maybe in A the law applies because of property X, and in B the law applies because of property Y. If so, then in C, which has neither X nor Y, that law would not apply.
[Speaker D] It could be that in order to obligate, you need either X or Y.
[Rabbi Michael Abraham] Either X—
[Speaker D] Or Y.
[Rabbi Michael Abraham] Or X and Z, or Y and Z. Yes, but then you don’t need Z; Z is already redundant. Or X or Y, sorry.
[Speaker D] No, I said maybe you also need Z.
[Rabbi Michael Abraham] Maybe yes and maybe no. Not necessarily. But it’s enough for me to assume that you need X and Y in order to say that in C there won’t be liability. Okay? So that’s basically the question that comes up here. Every common denominator throughout the Talmud, we’re really supposed to ask ourselves what it’s based on. After all, I can always say that the law—for example the obligation to pay—comes either from the fact that you’re like fire, where an external force is involved, or something like that, that it tends to move and cause damage, because that’s the obligating factor. “External force involved” is an exempting factor, yes. So the fact that it tends to move and cause damage is the obligating factor. And in pit, where its creation is for damage—what creates liability is only either something whose creation is for damage, or something that tends to move and cause damage. But who says that something that has some other feature, that from your lack of guarding it went and caused damage, but doesn’t have those two features—who says that it too is liable? Maybe only something that has one of those two features. You see that this is exactly the same thing as the previous topic. Exactly the same thing. What are we basically saying? That the simpler explanation—Occam’s razor—says that instead of saying the reason is either X or Y, I prefer to assume that the reason is Z, that there is only one reason and not either X or Y. And if the reason is Z, then also in C, which has Z, there is liability.
[Speaker D] So usually the common denominator should be based on three examples and not two.
[Rabbi Michael Abraham] Right. Here, common denominator is one of the hermeneutic principles by which the Torah is expounded; for the common denominator, two examples are enough. Two are enough. Not three, yes. In things written in the Torah. Apparently, when the Torah is written, it is written under the assumption—the Holy One, blessed be He, when He wrote the Torah, basically assumes that we will generalize on the basis of two examples, and therefore He has to take that into account.
[Speaker I] Why is the dispute between Rabban Shimon ben Gamliel and Rabbi? Why didn’t they bring this example?
[Rabbi Michael Abraham] Good question. Rabbi could have brought the common denominator as proof for his view, but then Rabban Shimon ben Gamliel would have answered him what I answered you: that it could be the Torah is written under that assumption. The Torah was written. Nature is nature—what is, is. But the Torah was written by an agent who wrote it, the Holy One, blessed be He, and maybe when He wrote the Torah, He wrote it so that every two examples—if you see a common denominator between them—then the rule that comes out of them will be correct. That’s an assumption built into the writing. If so, then He gives me a hermeneutic principle that is passed down as a law given to Moses at Sinai, the interpretive principle of building a principle from two texts. It says that if you have two texts, you can—
[Speaker D] And then in nature, it happens that way.
[Rabbi Michael Abraham] It happens in Torah. In nature itself, you need to be convinced that it really is so; nobody organized nature so that you would make—
[Speaker J] That’s a bit—
[Rabbi Michael Abraham] The opposite of “if you grasp too much, you grasp nothing,” because this basically says: don’t draw conclusions beyond what you must.
[Speaker D] Right, take Occam’s razor, yes—the simplest thing.
[Rabbi Michael Abraham] In terms of Occam’s razor, yes. But there they’re actually telling me to narrow, not expand; here I’m expanding. Yes. Anyway, that’s the common denominator.
[Speaker D] Now in the case of the knife and the normal wind, after all that example also meets the criterion that it is your property and under your supervision. So why do I need the examples at all? Why couldn’t I infer it just from the common denominator?
[Rabbi Michael Abraham] That’s what the Talmud explains: when the Mishnah says “the common denominator,” it means to tell you: take the examples and make a common denominator out of them, as in this example, and when you do that, you’ll arrive at the rule that if it’s your property and under your supervision, you are liable to pay.
[Speaker D] But in this case I don’t need the examples.
[Rabbi Michael Abraham] What do you mean, you don’t need the examples?
[Speaker D] After all, if the Mishnah had taught only this without the examples, and had said: anything that is your property, under your supervision, and tends to cause damage—you are liable—
[Rabbi Michael Abraham] That would have been enough.
[Speaker D] Meaning that the examples brought here are for the sake of teaching you in other places.
[Rabbi Michael Abraham] No, and that’s what I’m saying: what troubled the Talmud was not why they brought the examples—that was obvious to the Talmud. What troubled it was why they brought the rule.
[Speaker D] And why did they really bring the examples?
[Rabbi Michael Abraham] Because the examples are obvious—that’s the Talmud’s assumption. We talked about this when we talked about rule-based thinking. So yes, I said that the example basically—the Talmud is casuistic, meaning the Talmud—
[Speaker D] But in this case, this knife, I know how to learn it also from the rule. I don’t need the examples.
[Rabbi Michael Abraham] Obviously. But I’m saying the opposite: they tell me the examples because that’s the basic thing. The Mishnah tells me: you can generalize the examples by means of rules of common denominator, and an example of that is this case of his stone, his knife, and his load; and then the Mishnah already sums up all the generalizations you made—but this is one of them, basically. Okay. The Rosh here—I don’t remember whether we talked about it—the Rosh here on this Talmudic passage brings several views, brings several views on how to relate. Maybe I need a little introduction. The four primary categories of damages—each one has special exemptions. Tooth and foot are exempt in the public domain. Fire is exempt for concealed items. Pit is exempt for utensils—“ox, not a person; donkey, not utensils.” What else do we have? Horn is liable only for half-damages in the case of a harmless horn, yes, with an innocuous ox. Okay, so each of them has certain special exemptions. And here it really becomes problematic, because if each of the primary categories is not just an example but an example with other laws too, then the generalization is already problematic. Because then, say, what happens now with his stone, knife, and load that fell from the roof and caused damage? We learn it from fire and pit, right? Will it be exempt for utensils? Pit is exempt for utensils, but fire isn’t. Will it be exempt for concealed things? Fire is exempt for concealed things, but pit isn’t. Will it receive the exemptions of both its two sources? Will it receive neither of their exemptions? Or will it receive one of them, and if so which one? Meaning, there is an open question here. Okay? So the Rosh here brings: “And some of the great ones wrote that it is only liable for what both of them are liable for, and exempt for damage to utensils and for causing the death of a person like pit, and for concealed things like fire, since they come by way of the common denominator, we give them the more lenient side of the two.” Fine?
[Speaker D] Basically it takes—
[Rabbi Michael Abraham] The two exemptions. That’s the simple logic. Right? Why? Because if you need both teachers in order to learn A and B—yes, in order to learn C—then all you can obligate in C is only what is obligated in both teachers, because you need both of them. What? You can’t obligate more than the common denominator of both of them, because you’re taking what they share. So that’s the logic. And therefore the Rosh doesn’t agree with this. And he says: “And there are those who were uncertain about the matter.” What does he mean, “there are those who were uncertain about the matter”?
[Speaker C] I don’t agree. What? I don’t agree with what?
[Rabbi Michael Abraham] Ah, no—“and there are those who were uncertain about the matter.” What does “uncertain” mean? He doesn’t spell it out. I would understand it to mean: should we give them the—should we give them no exemption at all, or should we give them both exemptions, or give—right? What’s the idea behind giving no exemption at all? I’ll tell you the idea. Basically I say this: it depends—this is Rabbi Chaim of Brisk, this is the opening lecture of Bava Kamma in the yeshivot. Those who don’t do the conceptual analysis I did last time bring this Rabbi Chaim of Brisk. You can choose which opening lecture you want in Bava Kamma. So Rabbi Chaim of Brisk basically says that the question is: what is the meaning of the common denominator, or what is the meaning, basically, of the four primary categories of damages? I can say this: every primary damaging category is liable to pay. Besides that, an innovation was made in it that it is exempt for concealed things—for example, fire is exempt for concealed things, or pit is exempt for utensils. Okay? Or you could say: no, fire was obligated only for something that is not concealed. Not that it is liable for everything and just has an exemption for concealed things; rather, it is not liable for concealed things at all—it is liable only for what is not concealed. Or tooth and foot are liable only in the damaged party’s courtyard and not in the public domain. Or you can say: no, it is completely liable, but it has a special exemption in the public domain. What’s the difference? If I understand that in each primary category the exemptions are essential, meaning it’s not an exemption but rather you were never liable for some of the things in the first place, then certainly the first opinion in the Rosh is correct. Meaning, you have no source to obligate in the case of something concealed. For something concealed, fire is not liable, and only pit is—but to obligate, after all, you need both. But if you understand: no, first of all they are all liable. After that, each has its own exemption. Okay? So now I say: that his stone, knife, and load that fell from the roof and caused damage is liable—certainly yes, because both are liable. Now I want to know whether it also has the exemption of concealed things. In order to learn the exemption of concealed things, the exemption would need to exist in both pit and fire. But it exists only in fire, so you can’t learn the exemptions. You can learn only the liabilities. Okay? Then it comes out that basically there won’t be any exemption at all. You will be liable whether the item was concealed or not concealed, whether in the public domain or in the damaged party’s courtyard. What? Wait, in a moment we’ll get to the middle position, but first I’m speaking about the first two possibilities. Either you receive the exemptions of both of them—that’s the first opinion in the Rosh—or you receive none of their exemptions. What’s the difference between these two conceptions? The difference is how you understand the common denominator here. Does the common denominator here teach the basic liability, and on top of the basic liability there are special exemptions for each primary category? Or do you say: no, what are you talking about? Each one is liable only in its own area, and the common denominator is a combination of the two liabilities. There is no such general liability that you learn; rather, whatever is liable here and also there, that you can learn by common denominator. But there’s no general rule like what you said before, that if it’s your property and under your supervision you’re always liable. No—that has to emerge from the combination of the two primary categories, and therefore they brought the examples. You asked why they brought the examples? According to this conception, they brought the examples because it’s not true that everything that is your property makes you liable to pay. Yes, exactly. Okay, so those are the first two possibilities. Then the Rosh says, but he’s not satisfied with that either. So he says: “And it seems to me that they have all the law of pit.” They have the law of pit, including pit’s exemptions for utensils. They will be exempt for utensils. For concealed things they will be liable; they won’t have the exemptions of fire, only the exemptions of pit. Now what was wrong for him with the previous methods? Why does he choose this method, and why specifically pit? Why not fire? Let it have the exemptions of fire and not of pit.
[Speaker D] What advantage does pit have over fire?
[Rabbi Michael Abraham] So let’s explain, because this is really another way to learn the common denominator. Look, let’s go back for a moment to the mechanism of the common denominator. I presented the common denominator before in terms of Occam’s razor, right? Occam’s razor basically means that I can propose an explanation of either X or Y, and I can propose an explanation that everything depends on Z. Now Z—the second explanation—is simpler, so I prefer the simple explanation. The Rosh didn’t learn the common denominator that way, at least not the one here. The Rosh says this: I learn his stone, knife, and load from fire, because in fact from the beginning their nature is to cause damage and an external force is involved in them, and so on, therefore it is liable. Ah yes—but what about his stone, knife, and load being unlike fire in some respect, I don’t know, that fire was produced by the person from his own property. But pit is not the person’s property; no matter, some objection in pit that you can’t know. So I say: then pit proves that the fact that it is not his property doesn’t matter. Fine? I am basically learning it—or really, according to the Rosh it works in reverse. I learn his stone, knife, and load that caused damage from pit. It resembles pit because it is lying in the public domain, someone stumbles on it and falls—it is literally a pit. But I have a side problem, because this pit was created by another force involved in it, unlike an ordinary pit that I dig with my own hands. Fine. I will prove that from fire. What do I prove from fire? I prove from fire that when another force is involved, that does not exempt. But the liability is the liability of pit. Basically, you are liable by the law of pit; it’s just a special kind of pit that has some characteristic of fire. I tell you that in fire itself they are liable, which means that this characteristic does not exempt. So fire only helps remove an obstacle, but fundamentally I learned it from pit.
[Speaker J] How do you know what is basic and what remains in the end?
[Rabbi Michael Abraham] Reasoning. Not what remains in the end—reasoning, what remains in the end.
[Speaker B] Yes, in the end there’s no fire; in the end it remains pit.
[Rabbi Michael Abraham] Right, fine, that’s why I say—it’s reasoning. The reasoning says that if in the end it caused damage because it was lying in the public domain, then it’s really pit.
[Speaker J] So the essence is what the Talmud says, that pit is the basis?
[Rabbi Michael Abraham] No, I don’t think that’s necessarily according to the wording of the Talmud, but according to logic. Meaning, in the end there is his stone, knife, and load lying in the public domain and someone stumbles on them—that’s literally pit. You had a problem here because it got there by means of the wind. Fine, fire shows that I don’t need to care—that this problem doesn’t bother me.
[Speaker B] Couldn’t there be an example where the pit becomes fire? What? Couldn’t there be an example where what remains in the end from the whole story is fire?
[Rabbi Michael Abraham] How would you know? It could be. Why? If I placed my stone, knife, and load in the public domain, okay? I dug a pit. And now they flew by means of the wind and caused damage? That would be fire.
[Speaker B] A pit rolling along by people’s feet?
[Rabbi Michael Abraham] A rolling pit—and later on, there is such a thing—
[Speaker B] But that isn’t learned from the common denominator.
[Rabbi Michael Abraham] Why not? It is learned.
[Speaker B] Yes, it’s one of the examples, an example of, as it were, half of this.
[Rabbi Michael Abraham] Yes, it’s one of the examples here. Anyway, for our purposes, what is the Rosh basically saying? Look, I’ll now give you maybe another example where you can see this idea better, although there it’s uncertain. Look, the Rema brings a law from the Jerusalem Talmud that one who spits on the Sabbath is liable. Someone who spits. So all the medieval and later authorities are astonished: where, why is he liable? What, is it forbidden to spit on the Sabbath? Liable by Torah law—liable by Torah law. Okay, what, is it forbidden to spit on the Sabbath? Fine, so the Mishnah Berurah brings in the name of Rav Menashe of Ilya, a student of the Vilna Gaon—a very interesting figure, by the way, Rav Menashe of Ilya; not important now. He brought from him that this is talking about the public domain, and the Jerusalem Talmud says more than that: one who spits is liable משום זורה—liable for winnowing. Winnowing—what is winnowing? In winnowing you throw the kernels and the chaff of the grain into the air, and the wind blows away the chaff and the kernels fall; it’s a kind of sorting. Okay? So one who spits is liable for winnowing. So Rav Menashe of Ilya emends the text; he says: one who spits is liable for throwing, not for winnowing. Meaning, it’s talking about the public domain, and in the public domain, one who throws four cubits is liable. And then he says this: really this isn’t an emendation from winnowing to throwing; rather, it’s both. It’s winnowing plus throwing. Because notice that here, for example, there are four primary categories of damages, right? And the Talmud brings derivative categories that are learned from two together; from the common denominator we learn derivatives. In the laws of Sabbath we don’t find a common denominator anywhere. There too there are thirty-nine primary categories. The derivatives are always derivatives of a single primary category. Never a derivative of two primary categories together. Very interesting, very strange. I once asked several very great Torah scholars; I didn’t get a good answer. Why is that? Why in the primary categories of damages do we learn a joint derivative from two primary categories, but in Sabbath every derivative is a derivative of a single primary category? There are no derivatives that derive from two primary categories together.
[Speaker D] Is there anything like that?
[Rabbi Michael Abraham] I don’t know. I’m not familiar with one. In the Sages you don’t find it. Okay. Now it could be that because the resolution is higher there, many more kinds entered there, so it covers all the possibilities, and therefore every derivative you find will be sufficiently similar to a single primary category. Maybe it’s just a technical issue.
[Speaker D] But according to the Rosh here? So it simply couldn’t happen on the Sabbath?
[Rabbi Michael Abraham] You’re saying: let’s explain Sabbath according to this Rosh. Meaning that even in damages we are really looking for only one. Yes, but you still need the second one; there is a common denominator there. The logic of the common denominator is that one is basic and the second only removes obstacles. Okay? Now I’m claiming that Rav Menashe of Ilya says that spitting is the example on the Sabbath. Spitting—you learn it from winnowing and throwing together. How does that work? You say like this: basically I spat in the public domain, right? And the wind took it, so it’s similar to—I’m liable for throwing, right? I threw something four cubits in the public domain. What’s the difference?
[Speaker D] That in throwing, my force carries the thing four cubits.
[Rabbi Michael Abraham] I spat and it went four—
[Speaker D] Cubits in the public domain?
[Rabbi Michael Abraham] It went four cubits in the public domain. Throwing. Throwing is a derivative of carrying out, of transfer.
[Speaker D] But you said by Torah law there’s no throwing?
[Rabbi Michael Abraham] Transfer is by Torah law. Carrying from a private domain to a public domain is one of the primary labors. So this person spitting is basically, fundamentally, throwing. Why? Because you threw something four cubits in the public domain. Not exactly. Because when I throw, my force carries the thing four cubits. From winnowing I learn that the fact that the wind is involved in it—exactly like “an external force is involved” in fire—it’s really the same thing. From winnowing I learn that if wind is involved in it, that doesn’t exempt. So now this is basically throwing according to the logic of the Rosh, where I’m really liable because of winnowing, with winnowing only solving a side problem. He says: even when the wind helps me, that doesn’t stop me from being liable. Right? Now notice what is there, basically. Look at it and you’ll see—there is nothing shared by winnowing and throwing. You won’t find a common denominator. Right? There is no common denominator. Try to formulate it in terms of X, Y, and Z, yes? So that winnowing has X and Z—exactly, right—and throwing has Y and Z, and then I want to learn from that. What is shared by throwing and winnowing? Nothing. Two distinct labors. Fine, but what is shared by them?
[Speaker B] No, also on the Sabbath the derivative has to be something you need. In sowing you need the seeds.
[Rabbi Michael Abraham] Fine, that’s a side condition; I don’t care. So let it not be a labor not needed for its own sake. But you still need it to be a labor learned from two primary categories. Now there is no Z here. So therefore, at first glance it looks like a common denominator. The logic resembles the logic of a common denominator, but it isn’t. The logic of common denominator is elimination. The logic of common denominator says: apparently what determines things is not X and Y, but Z. I am doing elimination. Right? Here I am doing synthesis. There it is analysis; here it is synthesis. I say: I take component X of winnowing, take component Y of throwing, X plus Y creates for me a third labor, and for that one there is liability. Under the logic of common denominator, you would be exempt for this labor, because it does not fully have the characteristics either of winnowing or of throwing. Right? Say according to the first conception in the Rosh, that you take only what is shared by the two teaching categories—there is nothing shared by the two teaching categories. Here you couldn’t do that. A new creation. Exactly. Here you take characteristics of source A, other characteristics of source B, combine them, and in a synthesis produce labor C, a third labor.
[Speaker K] If you go in the direction of the Rosh, that’s perfectly fine.
[Rabbi Michael Abraham] Exactly, that’s why I’m bringing it. Meaning, when the Rosh learns the common denominator, he apparently doesn’t learn it with Occam’s razor, yes? Not with Occam’s razor. Rather, he sees it as some kind of synthesis. What does that mean? I basically learn from pit, but I have some difficulty because wind is involved. No problem—I take from fire that when wind is involved, that’s okay. Then I have built a new damager in which the wind does something that I myself would have done with my own force, and it is still a damager for which there is liability.
[Speaker I] But there’s no rule for that, meaning there’s no reasoning?
[Rabbi Michael Abraham] Why? There is reasoning. Why not?
[Speaker I] No, because you’re taking two completely different things—
[Rabbi Michael Abraham] And there’s no—
[Speaker I] justification, at least not like the common denominator as we learned before.
[Rabbi Michael Abraham] Fine, that’s the disagreement. But there is logic to it. The logic is understandable. What’s the problem?
[Speaker I] I’m talking about a tree and I’m talking about a table. They’re both—
[Rabbi Michael Abraham] No, but here I’m showing you. I’m saying: winnowing—after all, I want to learn the spitter from throwing, right? I want to learn it from throwing; it’s similar. They just tell me: look, you can’t learn it from throwing, because in throwing your force does it, whereas in spitting the wind is involved. So he says: that I’ll prove to you from winnowing, that the fact that the wind is involved does not exempt.
[Speaker D] Fine?
[Rabbi Michael Abraham] So there is logic to it, just a different kind of logic. It is the logic of synthesis, not analysis. So I—that’s just another angle to show the chemical composition, so to speak, of concepts or of ideas or of principles, which basically it seems to me you can already see in the Talmud or in the medieval authorities, not only in the later ones. Maybe one more point I’ll do next time; we’ll complete the matter.