Learning from Experience – Lesson 8
This transcription 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
- [0:04] Introduction: induction, abduction, and Occam’s criterion
- [2:09] The presumption of three times: halakhic examples
- [3:58] The presumption regarding houses in the Talmud – opening
- [5:17] The three-year presumption regarding land
- [7:22] The comparison to an ox forewarned for goring
- [8:43] The need for a fourth goring for the law to apply
- [11:50] Three proofs – proving ownership
- [18:37] Circumcision and presumptions – competing theories
- [21:04] Theories: the spring is the cause versus fortune is the cause
- [28:26] Summary: induction, abduction, and halakhic application
- [32:01] The comparison to Warren Buffett and a successful investor
- [33:44] John Verdon’s envelope story
- [36:08] Induction versus theory in recurring cases
- [39:04] The view of Avimi of Hagronia about theory
- [42:42] Mekor Chayim and the presumption of three times in the Talmud
- [49:31] Summary: induction, abduction, and drawing conclusions
- [55:04] Occam and the importance of simplicity in science
Summary
General Overview
The text presents a halakhic application of the tension between induction and abduction through the “presumption of three times,” emphasizing that generalizing from cases to the future depends on an explanatory theory in the background and on choosing the simpler explanation according to Occam’s razor. It moves through the laws of presumptive ownership of land, an ox forewarned for goring, menstrual cycles, circumcision, and a “fatal woman,” and shows how the Talmud looks for “the thing that causes it” in order to justify a presumption, and how different theories produce different generalizations and practical consequences. Later, a conceptual interpretation is brought regarding the signs of a mentally incompetent person in Tractate Chagigah through that same mechanism of unifying phenomena under one simple explanation, and a distinction is presented between presumptions that serve as evidence and presumptions that are habituation, with the claim that the number three is mainly a formal halakhic threshold. The conclusion includes questions about the authority of the Talmud, collective obligation, the reliability of prophets, and the limits of using Occam’s razor when the probabilities of the parameters are not uniform.
Induction, Abduction, and Occam’s Razor in Midrashic Inference
The text continues from a previous demonstration using a fortiori reasoning and the common denominator, where one can both make a generalization and also examine the theory behind that generalization. It states that when several generalizations fit the facts, the choice of theory is made באמצעות Occam’s razor and a preference for simplicity, and in theoretical terms this means preferring a minimal number of parameters or “entities.” It formulates that the issue is not only “simple generalization” but the simplicity of the theory that generates the generalization.
The Presumption of Three Times in Jewish Law as a Mechanism of Generalization
The text presents the idea that the presumption of three times means that when something happens three times, the assumption is that it reflects a fixed law and not a chance occurrence, and it identifies this as a generalization similar to scientific generalization. It brings examples such as an ox forewarned for goring after it gored three times, women’s cycles that are established after three regular appearances, and brothers who died because of circumcision, in which case the fourth son is not circumcised. It sets out to read these passages “through the lenses” of induction and abduction and to examine the relationship between the generalization and the theory underlying it.
The Presumption of Ownership in Bava Batra and Learning from the Forewarned Ox
The text distinguishes between possession as an act of acquisition in land and a “presumption as evidence” regarding land, where three years of eating produce without protest allow one to claim ownership even without a deed. It quotes Rabbi Yochanan in the name of “those who came from Usha,” who derive the number of three years from the forewarned ox: just as goring three times removes it from the presumption of being non-forewarned and places it in the presumption of being forewarned, so too eating produce for three years removes the land from the seller’s possession and places it in the buyer’s possession. It presents the Talmud’s difficulty from the fact that with a forewarned ox the obligation to pay full damages begins only with the fourth goring, and its answer that the status of being forewarned is created after three gorings, and only the basis for liability arrives with the fourth.
The text argues that the analogy between three gorings and three years seems formal, and suggests that in practice both cases are understood as an accumulation of three pieces of evidence. It formulates that with land, each year of eating produce without protest is evidence, and three pieces of evidence join into sufficient force; and with the ox, each goring is evidence of a forewarned nature, and three pieces of evidence are decisive. It explains that even if there is relative logic to three years because of the crop cycle, there is still a line here that appears arbitrary in principle.
Yevamot 64–65: Rabbi and Rabban Shimon ben Gamliel on the Number of Times, and the Entry of Abduction
The text brings the Mishnah in Yevamot about a woman who did not give birth for ten years, and the inference that she is permitted to a second husband, implying not to a third, and identifies this as the view of Rabbi. It compares this to a baraita about circumcision: “He circumcised the first and he died, the second and he died, the third should not be circumcised,” according to Rabbi, versus Rabban Shimon ben Gamliel, who says: “The third should be circumcised; the fourth should not be circumcised.” It also brings that the same dispute exists regarding a fatal woman: “She married the first and he died, the second and he died, she should not marry a third,” according to Rabbi, while Rabban Shimon ben Gamliel permits a third and forbids a fourth. It formulates that at this stage we are dealing with induction “without theory”: from repetition one infers about the future.
The text states that the Talmud introduces abduction when it explains that in the case of circumcision there is “a family whose blood is loose” as opposed to “a family whose blood clots,” that is, a physiological theory that explains the cases. It presents the Talmud’s question regarding a fatal woman, “What is the reason in the case of marriage?” as an objection to generalization without explanation, and then brings two theories: “the spring causes it,” in the name of Rav Huna, and “fortune causes it,” of Rav Ashi. It emphasizes that the Talmud formulates a practical difference that distinguishes between the theories: “if he became betrothed to her and died,” or “if he fell from a palm tree and died,” and identifies here a logic of prediction and testing that resembles scientific elimination, even though in practice they avoid a dangerous experiment.
Abduction as Determining Induction, and an Alternative Proposal for Understanding “Fortune Causes It”
The text formulates that abduction sets up a theory from which a generalization is derived, and that when there are several theories, each produces a different induction, and therefore practical policy is determined according to the chosen theory. It proposes the possibility that Rav Ashi is not offering an alternative mystical theory but rather allowing induction even without an identified theory, on the assumption that there is some unknown causal factor. It situates the dispute as a matter of how much weight to give chance versus the assumption that there is a hidden cause, and adds that the implications in matters involving danger to life intensify the need for caution.
Nassim Taleb, Warren Buffett, and the “Choose a Number” Example as a Test of Randomness Without Theory
The text cites Nassim Taleb’s The Black Swan to show that prolonged success can be a statistical result without any special talent. It proposes a model in which, out of many people, only one succeeds for a long time, and therefore the existence of a “Warren Buffett” is not necessarily evidence of talent but could be the product of probabilistic filtering. It brings the plot device of “choose a number” from John Verdon, in which sending many letters creates the appearance of supernatural prediction, and concludes that the decision whether to generalize to the future depends on the existence of an explanatory theory and not only on repetition.
Mekor Chayim in the Laws of Passover: “There Is No Presumption for Coincidences” and Its Application to Presumptive Cases
The text quotes Mekor Chayim in the laws of Passover, which states: “We do not say there is a presumption of three times except where there is some causing factor that is plausible… but in something that happens by chance… there is no presumption for coincidences.” It brings proof from Yevamot in the case of a fatal woman, that according to the view that “the spring causes it,” there is no law of a fatal woman in the case of a betrothed woman, and concludes that where there is no plausible cause, there is no presumption. It adds proof from the dispute whether fixed menstrual cycles are Torah-level or rabbinic, and suggests that the ruling depends on the plausibility of the theory that the state of the moon is connected to seeing blood, though he himself questions the broader application of that to all types of cycles.
The Signs of a Mentally Incompetent Person in Chagigah and Rabbi Chaim of Brisk: Occam’s Razor as the Basis of the Presumption of Three
The text brings the baraita in Chagigah about the signs of a mentally incompetent person: “one who goes out alone at night,” “one who sleeps in a cemetery,” “one who tears his clothing,” and the dispute in which Rav Huna requires all of them together, whereas Rabbi Yochanan says that one is enough. It brings the Talmud’s reasoning that each sign can have some alternative explanation that is not madness, and therefore the three together are decisive, and quotes the comparison: “like one whose ox gored an ox, a donkey, and a camel, and it became forewarned for all.”
The text presents Rabbi Chaim’s difficulty: why are two not enough, and why even with three can each sign not still be attributed to a different cause? It answers that three events make us prefer one unifying explanation that accounts for them all rather than three independent causes. It interprets this as Occam’s razor: the simple explanation, “he is mentally incompetent,” is preferable to a coincidence of three different explanations. It also relates to this the dispute between Rabbi and Rabban Shimon ben Gamliel over whether a presumption is created after two or after three, and connects it to the principle of “removing from a prior presumption,” which requires a more significant preference.
Ox, Donkey, and Camel: Forewarned for All as a Preference for a Unifying Explanation
The text explains that with an ox that gored an ox, a donkey, and a camel, there are two possibilities: either each goring was accidental and there is no forewarned status toward any particular species, or it has a general goring nature and therefore it is “forewarned for all.” It quotes Rashi, who emphasizes that we do not require three gorings in each and every species, because the fact that it was forewarned through three species shows that it is not particular about one species. It uses this to strengthen the idea that preferring one unifying explanation over three coincidences is a basic mechanism in creating a presumption.
Presumption as Evidence Versus Presumption as Habituation, and the Claim About the Formality of the Number Three
The text presents a distinction between presumptions that are “evidence” of an existing reality and presumptions that are “formation or habituation” that produce a new nature. It shows how, in the case of the forewarned ox, one can understand it either as proof of a forewarned nature that already existed, or as a habituation that comes into being after three gorings, and connects this to the question whether one should have imposed liability retroactively. It notes that there are views that reconcile even the “evidence” understanding without retroactive liability because of a claim of duress on the owner’s part, since he did not know he had to guard it.
The text cites Kehillot Yaakov on Taharot, section 47, who asked the Chazon Ish, and the Chazon Ish answered, “there are presumptions of this kind and presumptions of that kind,” but it argues that the sweeping discussion among later authorities rests on a mistaken assumption. It states that the number three is a “formal number” and a halakhic threshold needed for the work of a judge, because in habituation and in probability there is no sharp jump but a continuum. It compares this to the example that “when a girl is three years old, her hymen returns,” and to the discussion of intercalating the month, and interprets that Jewish law establishes status and not biological reality, and therefore sets a uniform and practical threshold.
Closing Questions: The Authority of the Talmud, Collective Obligation, and Prophets
The text includes a question about the authority of the Talmud versus the possibility of disagreeing with medieval authorities (Rishonim) and later authorities (Acharonim), and an answer explaining that the obligation derives from the commitment of the public as a collective entity that does not die even though the individuals change, with an example from Tosafot in Me’ilah 9a about a communal offering, where the rule of “its owners died” does not apply. It compares this to general legal systems in which legislation binds later generations, and formulates that the individual is bound because of his belonging to the collective.
The text includes a question about the likelihood of the truth of the prophets compared with claims such as Jesus, and an answer that the practical significance is limited because prophets do not introduce new Jewish law for future generations, and that since the Torah itself commands us to listen to a prophet who has been tested, there is no reason to doubt the principle unless there was a failure in the testing or the person was a false prophet. It includes a question about Occam’s razor when one unifying parameter is less plausible than three separate parameters, and an answer that acknowledges that the probabilities of the parameters do matter and that this is not pure formalism, with the example of an a fortiori argument about a doorpost and ritual fringes that is rejected because there is no fitting intuitive parameter. It concludes with a question about death at the hands of Heaven in a prophet’s instruction and an answer that this mainly concerns words of tradition or a temporary directive, because “a prophet is not permitted from now on to introduce anything new.”
Full Transcript
[Speaker A] Okay, last time I tried—just one second.
[Rabbi Michael Abraham] Last time I tried to demonstrate the relationship between induction and abduction through midrashic inferences. I tried it through a fortiori reasoning and the common denominator, where in both cases you could make the generalization—that is, induction—and you could also look at the theory behind the generalization. And when you look at the theory behind the generalization, you discover that in fact there can be several possible generalizations for us. Each theory can lead to a different generalization, and we need to choose a theory in order to know which generalization we’re left with. Usually, what we do if we have several generalizations that all fit the facts is use Occam’s razor—that is, we choose the simplest theory. Because the generalizations usually are not—well, you can also talk at the level of the generalization itself, about the simplest generalization; yes, a straight line is simpler than some curved line. But in terms of theories, we’re talking, say, about a minimal number of parameters, a minimal number of entities. That was really the original formulation of Occam’s razor: preferring a theory with a minimal number of entities.
So today I want to move to some halakhic application that illustrates the relationship between these two, the tension between them if you like. And I want to deal a bit with presumptions of three times. In Jewish law we talk about presumptions of three times: if something happens three times, the assumption is that if it happened three times it’ll probably continue to happen in the future as well, meaning that this is some kind of fixed law. And that is really a kind of generalization, like the way we make a scientific generalization or something like that. We saw the phenomenon three times; the assumption is that it probably expresses a general law and isn’t accidental. Okay? That’s basically what this means.
Where do we encounter things like this? There’s an ox forewarned for goring that gored three times; our assumption is that if it gored three times, we’re probably dealing with an ox that is forewarned, not an innocuous ox. Women’s menstrual cycles—if there is some pattern or regularity in the appearance of the cycle, a monthly cycle, an interval cycle, whatever, there are different kinds of regularity—then if it happened three times we assume that this is the pattern that will continue. There’s the case of brothers who died because of circumcision: if a family circumcised three children that were born to them and all three children died, then the fourth child is no longer circumcised. The assumption is that a child from this family who is circumcised will die, and again this is a presumption of three times, and so on. There are quite a few more examples; we’ll meet some of them.
So the question is this: I now want to look at these halakhic passages about the presumption of three times through the lens I’ve been describing until now—that is, to talk about the induction, to talk about the abduction underlying it, and exactly how the relationship works between these two levels, between the generalization and the theory that underlies that generalization.
So I want to begin with a Talmudic passage at the beginning of the chapter Chazkat HaBatim, the third chapter of Bava Batra. Just a brief introduction there: the Talmud there—or really the Mishnah already—begins by discussing presumptive possession of land. What is presumptive possession of land? That phrase has two meanings. There is possession by which one acquires land: with money, with a deed, and with possession. In our terms you could call that taking possession of land. Taking possession means using the land, acting toward the land in the manner of an owner—locking, fencing, breaching. Yes? Once I express ownership over the land, that is one of the ways to acquire it, one of the ways land is acquired, just as movable property is acquired by pulling, so land is acquired by money, by possession, or by deed. So possession there means acting like an owner with respect to the land.
I’m not talking about that. I’m talking about presumptive possession of land in the sense at the beginning of Chazkat HaBatim. The kind of possession I just described appears later. At the beginning of Chazkat HaBatim, we’re dealing with possession as evidence regarding land. What does that mean? If someone has been in possession of land for three years, the assumption is that the land is his. There are various explanations—it’s not important right now exactly what is needed there—the original owner, the one known as the previous owner, the mara kama, must not protest. He needs to claim he had a deed and the deed was lost; not important right now. But the principle established by the Mishnah is that after three years the person can claim the land is his even without producing a deed.
[Speaker C] Does the presumption make him the owner? I can’t hear. Does the presumption make him the owner? No, the presumption doesn’t show that he really is the owner. The presumption itself makes him the owner.
[Rabbi Michael Abraham] No. Okay, so what’s the question?
[Speaker C] The question is that it’s not a generalization at all. It’s not a generalization. It’s as if he stood on the land for three years, and then he becomes the owner of the land.
[Rabbi Michael Abraham] No, he doesn’t become the owner. This is a matter of the laws of evidence. He bought the land with a deed—that’s his claim.
[Speaker C] So this presumption isn’t acquisition law, it’s evidentiary law?
[Rabbi Michael Abraham] Obviously. The first kind of possession belongs to acquisition law. When I take possession of the land, that’s one of the ways of acquiring it—either money, or deed, or possession. This kind of presumption belongs to evidentiary law. Meaning: I claim that I bought it from you. You were known as the owner in the past, what’s called the mara kama. And I claim that I bought it from you. How did I buy it? Not through possession. I bought it with a deed. I had a deed—or whatever, with money—but I had a deed, I performed an act of acquisition, and the land is mine. Only what? I don’t have the deed now. They tell me: show your deed. I don’t have it. Now, if I was on the land for three years and the other person didn’t protest, that’s evidence that he sold me the land. Because otherwise he would have thrown me out. He would have protested and thrown me out. So this presumption functions within the laws of evidence; it’s not a presumption of acquisition.
So that’s the presumption at the beginning of Chazkat HaBatim. There are some disputes about how to understand it, what exactly it means. I’m not going into all the details now, only the minimum I need for our discussion. So now let’s look for a moment at the Talmudic passage.
Rabbi Yochanan said: I heard from those who came from Usha that they would say: From where do we know that the presumption is three years? Where do we know that a presumption is created after three years? From the forewarned ox. Just as in the case of the forewarned ox, once it has gored three times it leaves the presumption of being innocuous and stands in the presumption of being forewarned, so too here, once he has consumed produce for three years it leaves the domain of the seller and stands in the domain of the buyer.
Meaning: just like with the forewarned ox, when it gores three times it leaves its presumption of innocuousness—after all, every ox begins with the presumption of being innocuous. After three times that it gores, it becomes forewarned. By the way, afterward it can revert to being innocuous if there are three times when something passes before it and it doesn’t gore. So it moves from—what? I can’t hear. It moves from the presumption of innocuousness to the presumption of being forewarned. So too with land: after three years that he possesses the land, harvesting the produce and so on, it leaves the seller’s domain, the seller’s presumption, and passes to the buyer’s presumption, yes, the one sitting on the land. So there is some comparison here between an ox being established as forewarned, its transformation from innocuous to forewarned, and presumptive evidence regarding land.
The Talmud asks: If so, just as in the case of a forewarned ox he is not liable until the fourth goring, so too here perhaps it should not stand in his possession until the fourth goring? With a forewarned ox, after three times it becomes forewarned, but only on the fourth goring does he begin to pay full damages instead of half damages. So in that case too, really, you need four gorings to be forewarned. So here too you should need four years, not three years.
The Talmud rejects this and says: How can you compare? There, once it gored three times it is forewarned; and if there isn’t another goring, what should he pay for? Here, once he has consumed produce for three years, it stands in his possession. Yes, it’s a simple answer. After three times that the ox gored, it becomes forewarned, but you need a fourth goring so that, as a forewarned ox, there is something on the basis of which to obligate him. It’s not that it becomes forewarned after four gorings; it becomes forewarned after three gorings. But in order to obligate him financially as a forewarned ox, you need the fourth goring because that is the cause of action against him. So the status of being forewarned is created after three gorings, not after four, and therefore with land too we’re talking about the transfer of presumptive possession after eating the produce of the land for three years.
[Speaker D] The comparison seems arbitrary. And also not at all. Why? The comparison between moving from three gorings to three years—what can you say? It could be three days, three months, three hours.
[Rabbi Michael Abraham] You’re asking: why years? So here there is some logic, because in a year, when you harvest one crop from the land—there are crops that come up once a year—basically you need to harvest the land’s crop three times. The basic unit is the crop. Now if you only picked one tomato on one day—that’s talking about harvesting the produce; that’s really the essence of the presumption. That’s not necessarily what the Jewish law requires, but at the foundation of the presumption was “once he ate,” right? That’s what the Talmud says: he ate for three years. Meaning you take the produce of the land three times. Now every year a crop grows. It may take you a month to harvest it, but still, you’re harvesting that year’s crop. For us that counts as one time. Okay? That’s the assumption there. We’ll see later that in any event there is some arbitrary cutoff here, but that will come later.
So the Talmud compares the establishment of an ox as forewarned to presumptive possession of land. From the Talmud’s formulation, it seems they are really making a one-to-one analogy here. After three gorings it leaves the presumption of innocuousness for the presumption of being forewarned; after three consumptions it leaves the seller’s presumption for the buyer’s presumption. But when you really think about the content, that’s not actually what it’s built on. Rather, why do you need three years? Three years are really three pieces of evidence in my favor that the land is mine, right? I took the crop one year and the other guy didn’t protest—that’s one piece of evidence that it’s mine. It happened another year—a second piece of evidence that it’s mine. It happened another year—a third piece of evidence that it’s mine. Three pieces of evidence join together to become sufficiently weighty evidence. So for us, after three pieces of evidence, we assume the land is his.
The same thing with the innocuous ox. If it gores once, we begin to suspect. It could be that really it isn’t innocuous but forewarned. A second time—that’s another piece of evidence. A third time—I have three pieces of evidence, and after I have three pieces of evidence I assume the ox is a forewarned ox. But it’s not that those three pieces of evidence mechanically transfer it from one presumption to another. Rather, the accumulation of three pieces of evidence simply constitutes good evidence. The analogy they make here, this movement from one presumption to another, seems a bit formal; not really the essence of it.
[Speaker C] Does that mean it was already in the category of a forewarned ox from the beginning?
[Rabbi Michael Abraham] That’s a question the later authorities ask, but I’ll comment on it later, okay? So therefore this analogy itself—okay—it apparently speaks about the accumulation of three pieces of evidence. In fact, those who came from Usha—Rabbi Yishmael, the Talmud explains there—derive the three-year presumption regarding land from the presumption of being forewarned after three gorings. And for them, apparently, the three-year presumption regarding land—not everyone agrees with this—is another example of a presumption of three times, where after three times a presumption is created. That’s the assumption there.
The source for this whole discussion of the presumption of three times is a passage in Yevamot, pages 64–65. Let’s look at that a bit. So there, the Mishnah was talking about someone married to a woman who had not given birth for ten years. There is a concern that she is infertile. Okay? So he divorces her. The Mishnah says she is permitted to marry another one. What does “permitted” mean? It means he does not thereby neglect the commandment of being fruitful and multiplying if he marries her, because maybe she is not infertile. It didn’t work once; with another husband maybe it will work. A second time also is permitted; a third time is permitted; a fourth time already not. Meaning, if for three times she did not give birth for ten years, then we already get to some age where I’m not even sure a woman can still give birth, but let’s say—then from that point on she is no longer married.
And this is what the Talmud says: “He divorced her, she is permitted,” etc. A second, yes; a third, no. Meaning, the Talmud infers that the second man may marry her, implying that the third already may not marry her. Meaning, if this happened to her twice, the third time we no longer check. After two times the assumption is already that she is infertile. The Talmud says: Whose view is the Mishnah? Rabbi’s. As it is taught in a baraita, this is Rabbi’s position. For it was taught in a baraita: He circumcised the first and he died, the second and he died; the third should not be circumcised—these are the words of Rabbi. It’s not talking about the woman circumcising; rather, children of a woman are circumcised. Let’s say the father circumcised the first, circumcised the second; if he circumcised the second and the first two that he circumcised died, died, then the third is not circumcised, according to Rabbi. Rabban Shimon ben Gamliel says: The third should be circumcised; the fourth should not be circumcised.
There is a dispute between Rabbi and Rabban Shimon ben Gamliel as to whether a presumption is created after two times or whether a presumption is created after three times. And if that’s so, then the Mishnah from which the Talmud infers that if a woman did not bear children for ten years once and then a second time, then she is not married a third time, apparently follows Rabbi’s view—because clearly two times were enough to establish a presumption.
Later on—I’m skipping a bit—the Talmud says there: perhaps they disagree only regarding circumcision; do they disagree regarding marriage? Rabbi and Rabban Shimon ben Gamliel disagree regarding circumcision, where the children were circumcised and died. But why do you think that should be applied to marriage? The Talmud says: yes, they also disagree regarding marriage. How do I know? For it was taught in a baraita—Rashi says here that “for it was taught” is not a difficulty but stated calmly—that it was taught in a baraita: She married the first and he died, the second and he died; she should not marry a third—these are the words of Rabbi. Rabban Shimon ben Gamliel says: She may marry a third; she should not marry a fourth.
What does that mean? If she marries a husband—yes, this is what the halakhic decisors call a fatal woman—and the husband dies, then she marries another one and he also dies, the third is already forbidden to marry her. Rabban Shimon ben Gamliel says: a third is permitted, a fourth is forbidden. Again according to their respective views: the question is whether a presumption is created after two times or after three times. So we see that the dispute between Rabbi and Rabban Shimon ben Gamliel is not only about circumcision but also about marriage. If so, then in our Mishnah too, where the case is a woman who did not give birth for ten years, when the Mishnah says that after two times a presumption is created, this is apparently Rabbi’s view against Rabban Shimon ben Gamliel, even though it is speaking about marriage.
Now, I’ll pause here for a second. Up to this point, notice that what we have done is really induction. Meaning, the assumption is that if three—let’s say according to Rabban Shimon ben Gamliel—if three husbands who married her died, the assumption is that husbands who marry her from now on will probably also die. So far we have no theory, right? Without a theory, it happened three times, and the assumption is that it will continue to happen. That’s pure induction. We have three examples—or two examples according to Rabbi—and we assume it will continue from now on. The same with children who died because of circumcision: if someone circumcised them and they died, same idea. Or the menstrual cycle, same thing. If the woman saw blood every time on the fifth of the month, then probably next month too she will see blood on the fifth of the month. Again, this is induction. We have no theory behind it; we’re simply assuming that what has been will be. So for now we are talking on the plane of induction, of generalization.
Now I go back to the Talmud, and you’ll see that now abduction enters. The Talmud now says as follows: Granted, regarding circumcision, there is a family whose blood is loose and there is a family whose blood clots. The Talmud says this: regarding circumcision, I can understand why you follow presumptions. Why? Because regarding circumcision there are families whose blood genetics apparently produce blood that is too loose—yes, thin or something like that—and therefore the bleeding following the circumcision kills him. And therefore it kills the infants, and if another baby is born to this child—well, to this family—then probably he too will die, because there is some theory behind why the children died. There is a theory. The theory is that this couple apparently has children with loose blood, okay? And there is a family whose blood clots. Meaning, it’s clear to us what theory could underlie the facts. So if it happened once, maybe that was chance. If it happened twice, according to Rabbi that’s already enough; according to Rabban Shimon ben Gamliel it could still be chance. But if it happened three times, then we assume that there is probably some feature in the blood of the infants being born, namely that it is loose blood, and therefore we no longer want the next infants they have to be circumcised.
You suddenly see that we’re moving into the theory behind the generalization: loose blood—that’s why the infants died. It’s not just that we say, well, if it happened… But in marriage, what is the reason? And there too you tell me that if she married the first and he died, the second and he died, she should not marry a third. Why? What, does she have some thing by which she kills her husband? How does that happen? It’s not—nothing in the woman’s physiology passes over to the husband. With the children it comes from the parents’ physiology, but with the husband I have no theory behind the generalization.
So what is the difficulty? The difficulty is: you don’t make a generalization unless there is some theoretical explanation to justify it. Right? That’s the Talmud’s difficulty. You don’t do induction unless there is abduction in the background. That is essentially what the Talmud is objecting.
Rav Mordechai said to Rav Ashi—I’m returning to the Talmud here—this is what Avimi of Hagronia said in the name of Rav Huna: the spring causes it. The woman’s spring—yes, in the woman’s sexual organs there is some feature there such that the husband who encounters it is killed by it. In intercourse the husband somehow encounters it, is affected by it, and it kills him. So we have a theory. The woman’s spring causes everyone who has intercourse with her to die because of that contact. That’s the first theoretical proposal. So in marriage too we have a theory, just like in circumcision.
Rav Ashi said: fortune causes it. What does “fortune causes it” mean? This woman has some kind of bad fortune. “Fortune” here is not in the sense we use the word today in its ordinary meaning, but rather there is some kind of—I don’t know—mystical something or whatever that accompanies the woman and causes her husbands to die. Meaning, fortune causes it. So we have two theories.
The Talmud says: What practical difference is there between them? This conclusion is beautiful. What practical difference is there between them? There is a difference between them in a case where he betrothed her and died, or alternatively where he fell from a palm tree and died. What does that mean? What is the practical difference between Rav Ashi’s theory and the theory of Avimi of Hagronia in the name of Rav Huna? Notice: this is really scientific elimination. They are giving a prediction. What do I mean? We have two theories; let’s see what test we would perform, what experiment we would do in order to see which theory is correct.
So for example, what happens if the woman was only betrothed to the three husbands who died? They weren’t even married yet. Already from the betrothal they died. If that happened, then obviously her spring did not cause it, because there had not yet been marital relations between them. Intercourse only comes after marriage. While they were only betrothed, there was no intercourse, and if they died, then according to the view that the spring causes it, there is no concern at all—she can become betrothed to a fourth man. But according to the theory that fortune causes it, then even if it happened from the stage of betrothal, her fortune is such that anyone who gets betrothed to her dies. So she is forbidden to marry a fourth man. Okay?
So if we’re talking about a situation where the three husbands who died were in fact only betrothed to her and not married to her, then according to the view that the spring causes it, she can continue and marry a fourth husband. According to the view that fortune causes it, she cannot.
What do we see here? Notice a very interesting point. The abduction—maybe I’ll explain the second case and then come back to this. Or alternatively where he fell from a palm tree and died. It could be that we’re talking about husbands who had already married her, but they died because they fell from a palm tree. Each of them fell from a tree—I don’t know, something else happened, okay? Then clearly here too it can’t be that the spring caused it, right? According to the view that fortune causes it, of course, here too: don’t marry another one, because he too will fall from a palm tree. But according to the view that the spring causes it, this has nothing to do with the spring; he fell from a palm tree, that’s why he died, so there’s no need to worry. Okay? So there are two practical differences.
[Speaker C] So that’s not elimination in the way you defined it; it’s only a practical difference between two theories. No, actually you can see it as both elimination and application.
[Rabbi Michael Abraham] What do you mean? If we had a Helsinki committee that would approve an experiment like this, that would be the experiment we could perform. Let her marry a fourth husband and let’s see—at the betrothal stage, and let him climb a tree. And now we’ll see whether he falls or not. If he doesn’t fall, apparently there is no issue of fortune. If he does fall, there is an issue of fortune. If he dies without the tree, then apparently fortune causes it without the tree. If only after the marriage he dies and not because he climbed a tree, then it means the spring causes it. So we have ways of conducting experiments that would check for us which of the theories is correct.
It’s true that here in the Talmud they’re not talking about future experiments—on the contrary. We’re trying to prevent the future situation that could verify the theory, because we don’t want another human being to die. So here they really are talking about the practical difference regarding what we’re supposed to do, not about what we’re supposed to expect, what result of a future experiment we’re supposed to expect—but it’s the same logic. Meaning, if we were supposed to do a scientific experiment to test which theory is correct, the Talmud here is giving us the algorithm. Take a person who is only betrothed to her and wait and see whether he dies or not. That’s the experiment that should be done. Of course, here the Talmud is not recommending conducting experiments with human lives. What they’re saying is: no—if the spring causes it, then if he is only betrothed there is no problem. If fortune causes it, then there is a problem, and so on. But it’s the same logic. It is really scientific logic. This is exactly Bacon’s inductive logic. That’s precisely how it is built. Meaning: we have two competing theories, we try to construct some prediction that will distinguish between the two theories, I do the experiment, and that experiment decides which of the two theories is correct. Okay? No—what?
[Speaker C] I didn’t understand it that way. I understood the Talmud to be saying that even if the first theory, for example, is correct—that is, specifically for this woman it’s not correct—but that doesn’t mean for all women.
[Rabbi Michael Abraham] Nobody said for all women. We’re talking about this woman. A theory about this woman.
[Speaker A] I don’t understand—in circumcision there is—
[Speaker C] According to Rav Ashi, Rav Ashi says that fortune causes it in all fatal women.
[Rabbi Michael Abraham] The fortune of this woman.
[Speaker C] And if he sees another woman whose husbands died—
[Rabbi Michael Abraham] Not all women in the world are fatal women. The fact that he sees another woman is irrelevant. What happened to her three times—she is a fatal woman.
[Speaker E] What is scientific about fortune?
[Rabbi Michael Abraham] If there are three women whose husbands died, the conclusion is not that all women in the world are fatal women.
[Speaker E] But what is scientific about fortune? In circumcision you can understand there is something physiological that you can—
[Rabbi Michael Abraham] It’s scientific in the sense of the methodology of drawing conclusions. The fact that modern science doesn’t like concepts like fortune doesn’t matter.
[Speaker E] Meaning, if I do an experiment and I do eliminations and I test it and it really works, then he would have to admit that there is such a thing called fortune.
[Rabbi Michael Abraham] No, but it is a certain concept that we are talking about, meaning we understand that there is something that exists which we call fortune. Right, and therefore it’s scientific.
[Speaker E] And from the standpoint of Jewish law, is that something that exists? Yes.
[Rabbi Michael Abraham] So that’s why I say this is exactly scientific methodology. The only thing is that the range of options we’re willing to take into account when we build our scientific theory is broader than contemporary science. Contemporary science won’t take astrology into account. But in principle, even contemporary science ought to recognize that if we’ve done the eliminations and checked things and it really works, then it would have to admit that there is such a thing as what we call fate. We talked about jaundice, right, the example of jaundice. Meaning, a rational person is supposed to accept that if there is good evidence and we’ve eliminated all the theories that we think are relevant and nothing worked out, then we need to recognize that apparently there’s something here we don’t know. Call it fate, it doesn’t matter. Therefore this is completely scientific. Or completely scientific logic, again. The logic here is really logic of elimination and scientific generalization. Now what we see here in the Talmudic text is basically two things, or three. First, they do induction. Second, induction is done only if in the background we have a theory we arrived at through abduction, which grounds the induction. Third, if there are several theories, each theory will give us a different induction, right, a different generalization. The theory that the source causes it will give us a law that this woman—whoever marries her, and actually enters marriage, not just gets engaged—will die. That’s the theory. In contrast, the theory that fate causes it says that whoever gets engaged to this woman may also die. So we see that the generalization changes if the underlying theory changes. In other words, the abduction determines the induction. A fourth point is that we shape our practical policy according to the scientific theory we arrived at, according to the abduction. Okay? All that we see here in the Talmudic text. In other words, in a nutshell, this is basically everything we’ve seen until now. Okay? And that’s really what’s here in the Talmudic text. Now look at a nice example of this. Maybe I’ll say—I’ll maybe add one more sentence. When I say “fate causes it,” there may be another way to understand that. That is, it could be that when Rav Ashi says “fate causes it,” he’s not proposing an alternative theory, but saying: forget it, I’m not looking for theories, I’m doing induction without abduction. If three husbands died, if three husbands died, then the fourth husband will also die even if I have no explanation whatsoever. And he doesn’t mean to say that there’s such a thing as fate, some mystical force that causes husbands to die. He doesn’t mean to propose a theory. On the contrary, he means to say: even if you don’t have a theory, go with the induction even without abduction. If three husbands died, assume that more will continue to die—not because there’s some theory at the base, or not because you know how to point to the theory. Presumably there is some theory for why they die, but you don’t need to have some plausible theory in order to make the induction. Even if you don’t have a plausible theory, yes, according to Rav Ami of Geronya—Rav Ami of Geronya—if you don’t have a plausible theory, you don’t make a generalization. If there is no source, you don’t make a generalization, right? If the woman didn’t marry but only got engaged, and three times her husbands died—only fiancés, without marriage—what would Rav Ami of Geronya say?
[Speaker A] That there had been intercourse before marriage?
[Rabbi Michael Abraham] No, no, the assumption is that there wasn’t. Yes, that’s also a possibility, but the assumption is that there wasn’t. He would say it’s coincidence, right? He says: if I have no plausible theory explaining the three cases, you can’t rule out that this is just a coincidence that happened three times. It can happen. By the way, this is exactly Nassim Taleb, right, Taleb’s black swan. Meaning, he basically says—and we’ll talk more about this later—but he says, look, think for example about someone like Warren Buffett, some investor in the stock market—or actually I don’t think he invests in the stock market, I think he invests in various businesses—and he succeeds over many years in an exceptional way. Very few people apparently—so they say, I haven’t checked, but that’s what they say—very few people really succeed consistently over so many years like Warren Buffett. Now Nassim Taleb says that this doesn’t at all mean he has special talent, not at all necessarily. It may be purely statistical. What does that mean? Say a thousand investors enter the market. Okay? Over the course of a week, nine hundred of them will succeed over a week. How many will succeed over a month? Seven hundred. How many over a year? Four hundred. How many over five years? One hundred.
[Speaker A] And how many over fifty years?
[Rabbi Michael Abraham] One. That one is Warren Buffett. Now notice, I’m talking about a thousand investors all with the same abilities—not that one is some genius economist, no. They all have the same level of ability. But statistically, this one wins, that one loses; the lottery works out so that with odds of one in a thousand, even an amateur investor will succeed over fifty years. So if a thousand investors enter, one of them survives fifty years and succeeds. So the fact that you have a Warren Buffett doesn’t prove that Warren Buffett is talented. There has to be one such person. It just happened to be Warren Buffett; it could have been anyone else. I brought here—or maybe I didn’t, I’ll bring it later—but the illustration is from a thriller by John Verdon called Think of a Number. He says: imagine a person gets an envelope, opens it, and sees inside a letter and another small envelope. He reads the letter, and it says this: Hello. Know that I have supernatural powers. That’s what the writer tells him: I have supernatural powers. In the enclosed envelope there is a number between one and a thousand. I want you to guess the number, guess a number between one and a thousand, and afterward open that envelope and you’ll see that inside it is exactly the number you guessed. So in short, the person guesses, say, I don’t know, 712, opens the small envelope—712. Unbelievable, exactly what he guessed. Later in the letter it says: listen, if I guessed correctly, then you understand that I have supernatural powers. Send me ten thousand dollars and I’ll make you a millionaire. Well, the guy of course sends ten thousand dollars; he has a supernatural power at his disposal, he’s guaranteed to become a millionaire. At the end of the book, the solution to the mystery is that the man sent a thousand such letters, or ten thousand such letters, and he put random numbers inside the small envelopes. And of course, if he sends ten thousand letters, then let’s say that when people guess numbers, assuming uniform distribution and each number has probability one in a thousand, then ten people will guess correctly. Okay? Those ten people who got such a letter, chose a number, and found that their guessed number was indeed inside the envelope—each of them will send him ten thousand dollars. Well, a hundred thousand dollars is not a bad deal when he has no ability to guess at all, of course. Nothing at all—it’s simply statistics. Understand, this is exactly the same as Warren Buffett, or as Nassim Taleb’s explanation of Warren Buffett. Not necessarily that he’s right, but it’s a very interesting perspective. Meaning, many times we’re sure we have wonderful evidence because the case, as they say, doesn’t stop repeating itself—something that keeps happening, so we make an induction that it will probably keep happening. Warren Buffett has been successful for fifty years—what, in the coming years he won’t succeed? The answer is no. There is no indication whatsoever from the first fifty years that it will continue. Because if those first fifty years indicate that he has special talent, then presumably he’ll keep succeeding, because he’s talented. But if those fifty years are coincidence, then there is no indication in those fifty years of success that he’ll also succeed in the next ten years. It’s coincidence. From here on, evolution or probability can choose another successful coincidence, or choose no one at all. What’s the difference between these two situations? The question is whether I have a theory behind the induction. If I have a theory, the theory is that Warren Buffett is talented. If that’s the theory, then it’s reasonable to think he’ll continue succeeding. But if I have no theory—something is happening here that no talent can explain. If someone wins the lottery fifty years in a row, no talent can cause that. So fine, either it’s fraud—but let’s say we checked it thoroughly and it isn’t fraud. I have no theory, so apparently it’s coincidence. So in the absence of a theory, I won’t say he’ll guess the lottery right in the next drawing as well, even though he guessed fifty drawings correctly. Because if I have no theory, then the assumption is that it’s coincidence. If it’s coincidence, then there is no indication that next time it will happen. You see that to do induction, to generalize from what I saw to what will happen next, depends on whether I have a theory. If I don’t have a theory, I don’t make any generalization.
[Speaker C] No, but I understand what you’re saying—Nassim Taleb isn’t claiming that when you have no theory, you should say it’s coincidence.
[Rabbi Michael Abraham] No, no, of course not.
[Speaker C] He also presents the possibility that it’s coincidence. What?
[Rabbi Michael Abraham] He says that you need to consider the possibility that it’s coincidence. If I could do a calculation to know the probability that by chance a person would succeed for fifty straight years in investments—if that probability came out very, very small, then maybe I would prefer the theory that Warren Buffett really is talented, or very, very small relative to the number of people in the market. Right—if there’s one out of, I don’t know, a thousand people in the market who keep going for fifty years in a row, because someone who doesn’t succeed also doesn’t continue for fifty years, right, you have to remember there are very interesting tricks here in statistical inference. But let’s say I have enough people who continue for fifty years, and Warren Buffett is one out of a thousand. But if the probability that this would happen is one in a million, then even if he’s one out of a thousand, who says it’s statistics? It could be his talent. Clearly what Nassim Taleb says is not conclusive. He’s only saying: pay attention, there’s also such an option—take it into account too. Okay? Now, if I go back to our example, what does Avimi of Geronya say? The same thing. He says: if you have some possible theory explaining why the husbands died—because the source causes it—then that’s perfectly fine, then that’s the theory. But if three husbands died from the engagement stage, not from marriage, I have no theory, because they never encountered the woman’s source, so apparently it was just coincidence and there’s no need to worry about next time. Okay? What does Rav Ashi say? Rav Ashi says: I have another theory—fate causes it. Earlier I presented this as an alternative theory; now I want to suggest a new explanation of Rav Ashi’s view. Maybe Rav Ashi is not claiming there is an alternative theory, but is saying: we make inductions even without a theory. If this happened three times, it will probably continue, even if I have no sensible theory. Now I want to say again: clearly Rav Ashi does not mean to claim that there is no theory at all, because if he wanted to claim that there is no theory at all and these three times were coincidence, then there would be absolutely no reason to be concerned about next time. There is no correlation at all between the cases that happened and the case that will happen. Rav Ashi only wants to claim that even if you didn’t find a theory, necessarily there is some theory in the background. You just didn’t figure it out; you’re not clever enough. Remember Semmelweis and Card, the examples I brought there with childbed fever and Napoleon’s victory? That’s exactly the case. You have nothing sensible that can explain the findings. So you go like a blind man in the dark, searching for some theory, firing shots in the dark, because you can’t find a theory. But it’s obvious to you that something has to be there. So Rav Ashi says yes, but if I didn’t find one, I found no explanation at all, am I going to be hospitalized in Semmelweis’s ward? Or she’s going to? Of course not. I have no sensible explanation why specifically in his ward people die—maybe it’s coincidence? Yes, but maybe not. Maybe there is an explanation there and I just haven’t figured it out, so if I value my life, I’m not going to be hospitalized with Semmelweis. That’s what Rav Ashi is saying. Rav Ashi is not claiming that fate is an alternative theory. Rav Ashi is claiming: I make induction even if I have no abduction. Even if I haven’t come up with a theory. But again, he’s not saying there is no theory—on the contrary, his assumption is that there is a theory. I just haven’t managed to think of anything sensible, like with jaundice.
[Speaker C] So what is the basis of the dispute? The weight of coincidence?
[Rabbi Michael Abraham] Yes, that is, yes, exactly. If something happened three times, you have two possibilities: either it’s coincidence—a small chance that something happened three times and it’s coincidence—but the second possibility is that there is a theory and I just didn’t hit on it. Now, a theory that doesn’t fit at all with the accumulated logic up to now—that too has a small chance of existing, right? Nothing I know so far explains it, can even explain it. I don’t even know what to check. Okay? A small chance. So now you have a dilemma: which option do you choose? Is it coincidence, or is there nevertheless some theory I haven’t found? Avimi of Geronya prefers the second possibility; Rav Ashi prefers the first.
[Speaker G] But maybe it’s only in a case where something serious could happen, then you…
[Rabbi Michael Abraham] Yes, obviously it’s also a function of the consequences. If the consequences involve life-and-death issues, then of course we will worry about the more severe possibility even if it is less likely. That’s obvious. I’m being very schematic here for the moment, but I’m trying to show you that all these ideas we’ve talked about until now are really here in the Talmudic text. Now look: there’s the Mekor Chaim on the laws of Passover, Orach Chaim, section 467. Mekor Chaim is by the Malbim, I think, or Chavot Yair—I already don’t remember. In any event, the Mekor Chaim on the laws of Passover discusses there a three-time presumption regarding leavened food. The first passage isn’t important right now. He says: “Therefore it seems to me that we do not say a three-time presumption except where there is some causing factor such that it makes sense it should be so, where rational analogy requires it to be so. But in something that occurs by chance, where there is no reasonably plausible causing factor, there is no presumption for coincidences.” What is he saying here? You don’t do induction unless you have abduction. If there is a causing factor that plausibly gives rise to the phenomena I encounter—I have a theory—then I say that this is probably a general law and I have to assume it will continue. But if not—if I have no plausible theory explaining it—then no, there are no presumptions. Even if it happened three times, the assumption is that it’s coincidence. I don’t take it into account; there is no presumption for coincidences. In short: you don’t do induction without abduction. That’s basically what he says in our language. And a clear proof of this, says the Mekor Chaim, is from tractate Yevamot regarding a lethal woman, where according to the one who says: if the source causes it, there is no law of a lethal woman in the case of engagement. Right? According to Avimi of Geronya’s view, if his theory is that the source causes it, then if three husbands died from engagement, he is not concerned about the fourth husband. Why? From the standpoint of induction, it happened three times, so be concerned about the fourth time. No—one does not make induction unless there is abduction in the background. If you have no sensible explanation, you don’t make induction. And similarly there is no status of killer in the man. It follows that wherever there is no plausible cause, there is no presumption. If there is no cause that is plausible—yes, a theory explaining what causes these phenomena—then there is no presumption, no three-time presumption. And another proof is from Niddah 16, where they dispute whether fixed cycles are Torah-level or rabbinic. Yes, if a woman sees blood, say, three times on the same date or in some pattern of three repetitions, there is a dispute whether one must be concerned the fourth time—must one be concerned on the fourth occurrence of that same date in the month or something like that. But the question is whether this is Torah-level or rabbinic. Jewish law rules that it’s rabbinic, but it’s a dispute in the Talmudic text. And what is this—a three-time presumption on a Torah level? How can one say that menstrual cycles are rabbinic? After all, here we have a three-time presumption. So how can one say that cycles are rabbinic? For we allow going out on the Sabbath into the public domain with an established amulet. What is that? An amulet that healed people three times; one may go out with it on the Sabbath. Because there is a presumption that it really is an effective amulet. It’s a good remedy. If it healed three times, that’s not coincidence; it indicates that the amulet is established. Yes, like an ox with established goring behavior. So it must be that this is what they disagree about: whether there is a plausible causing factor. The question is whether, when a woman sees blood on the same date in the month three times, is there some logic to the theory that the state of the moon—because the date in the Hebrew month is basically the state of the moon—whether there is a connection between the moon’s phase and the woman’s seeing blood. That’s the dispute. If we understand that this theory is a plausible theory, or at least more plausible than the possibility that it just happened three times by chance, then I assume that’s the correct theory, and if so then cycles are Torah-level. That is the view of the one who says cycles are Torah-level. The one who claims that this theory is not plausible—because what does the moon’s phase have to do with a woman seeing blood?—for him, it’s coincidence, and therefore the concern is only rabbinic, but in essence on the Torah level there is no real concern. By the way, I’m a bit doubtful about his conclusion, because according to that, it should have been—after all there are several kinds of cycles: a monthly cycle, an interval cycle, and an average cycle. Meaning, intervals, or always thirty days, or yes, whatever it may be. So the dispute whether cycles are Torah-level or rabbinic concerns all three kinds of cycles. Now if the dispute is about whether the date in the month is plausible or not plausible, why should those same authorities also dispute whether fixed intervals are plausibly fixed or not? That is an entirely different dispute. It might be worth arguing about that too, but why make this dispute depend on that dispute? When they speak about whether cycles are Torah-level or rabbinic, the dispute is about all types of cycles. So it’s a bit hard for me to accept what he says, but never mind—I only want to bring him as support for what I described earlier: that we don’t do induction unless there is abduction in the background. And the abduction in the background asks: is it plausible that there is a theory explaining this? If it is totally implausible, then it’s probably coincidence. Let’s return, for example, to the jaundice case. I saw someone healed of jaundice by putting pigeons on his navel, let’s say. Okay? Now I have no theory explaining this. It doesn’t sound sensible to me. So I try it again. And wow, it heals another person, and another one—three times it healed. Now I have to start weighing things, because to say this happened three times by chance is implausible. On the other hand I also have no plausible theory explaining it. So now I have to examine how implausible it is that there is some theory I haven’t discovered, versus how implausible it is that this was coincidence. Again, I don’t know how to make the calculation, of course, but that is essentially the consideration one has to weigh when forming a view about such a case. Okay? That’s basically what is written here. Now, these things actually bring us to a well-known insight of Rabbi Chaim of Brisk. He brings the Talmudic text at the beginning of Chagigah regarding the signs of an imbecile. “The Sages taught: who is an imbecile? One who goes out alone at night, and spends the night in a cemetery, and tears his clothing.” Yes, three signs of an imbecile: someone who goes out alone at night wandering around, someone who sleeps in a cemetery, and someone who tears his clothing—just tears his own clothes. It was stated there, a dispute of Amoraim. Rav Huna said: only when they are all present together. Meaning, in order to decide that someone is an imbecile, you need all three signs; one alone is not enough. Rabbi Yochanan said: even one of them. One sign is enough—this one or that one or the other one. Rav Huna says no, only if all three are present. What are the circumstances? If he does them in an imbecilic way—if it’s clear he’s doing this out of some kind of insanity—then even one sign is enough, even one alone. And if he does not do them in an imbecilic way—if he doesn’t look deranged, his body language doesn’t, there are no signs of some kind of madness—then even all of them would not suffice. So the Talmudic text says like this: really, he does do them in an imbecilic way; he is indeed doing this in a way that looks odd, looks unreasonable. And still, if he does them in an imbecilic way, we asked, then one sign should suffice. Why do we need three? It says no, we need three—why? It says as follows: if he sleeps in a cemetery, perhaps we can say he does it so that an impure spirit may rest upon him. Why does he sleep in a cemetery? He wants an impure spirit to rest upon him. So he’s not crazy; he just wants impure spirits to rest on him. Yes, the assumption of course is that there is such a thing as an impure spirit resting on him and so on; it’s not madness to think such a thing exists. And if he goes out alone at night, if that’s the only sign, perhaps some fit seized him. And if he tears his clothing, perhaps he is deep in thought—he was absorbed in thought and absentmindedly tore his clothing. Since he did all of them, he is like one who gored an ox, a donkey, and a camel, and thereby became established as dangerous toward all. Suddenly there’s an analogy to an ox with established goring behavior; we’ll soon see that analogy. But what is really written here? You need all three signs because each sign could have an explanation. Right? If he went out alone at night, maybe some fit seized him. If he slept in a cemetery, maybe he wanted an impure spirit to rest upon him. If he tears his clothing, maybe he is deep in thought. So each of these signs could also have some rational explanation; it needn’t be that he does it because he’s an imbecile. Therefore you need all three signs. Rabbi Chaim asks: why aren’t two enough? Two should suffice. Or alternatively, even if there were three, it could still be that he slept in the cemetery because he wanted an impure spirit, he went out alone at night because of the fit, and he tore his clothes because he was deep in thought. So who says he’s an imbecile even if all three signs are present? The answer is: if he had two signs, then indeed there is no presumption that he is an imbecile. Why? Because it could be, say, that he both went out alone at night and tore his clothing. Fine—it could be that he is deep in thought and therefore tore his clothing, and a fit seized him and therefore he went out alone. So in any case it’s not because he’s an imbecile. Therefore with two there is no presumption that he is an imbecile. Rabbi Chaim asks, fine, so why with three yes? Even with three you can still say that the third one too happened for its own third special reason. He says no: two things can happen by chance from two different causes. But three things—it’s clear there is some one cause threading through all three, namely that he is an imbecile. Basically what Rabbi Chaim says is this: suppose we have all three signs here. And by the way, this is exactly the common denominator from what we saw in the previous class. What does Rabbi Chaim say? He says: I see someone going out alone at night. Fine, so I say okay, he’s probably an imbecile. Why suddenly? It could be that some fit seized him. What can you infer from going out at night, since that can happen because of a fit? So I say: sleeping in a cemetery will prove otherwise. He also slept in a cemetery, so it can’t be because of the fit. No—sleeping in a cemetery could be because he wants an impure spirit. Right? So I say okay, then let the fact that he tears his clothing prove it. No—tearing his clothing could be because he is deep in thought, yes, absorbed in thought. So now I have three examples, and I have two possible explanations for the appearance of the three examples. One explanation is a single explanation threading through all three cases: he is an imbecile. Because he is an imbecile, he did all three things. The second alternative is that each of these symptoms has a different explanation: here it’s a fit, here he wanted an impure spirit, and here he was absorbed in thought. Two explanations—which is better?
[Speaker C] The first, obviously.
[Rabbi Michael Abraham] The first. Why?
[Speaker C] Occam’s razor.
[Rabbi Michael Abraham] Occam’s razor, right. It’s the simpler explanation. Why assume he did acts characteristic of an imbecile, but each time not because he was an imbecile, rather because of some particular reason that just happened to seize him? It is much more reasonable that these three cases actually happened because of the same factor itself, because of the common denominator among them. He’s probably an imbecile. Yes, if something is green on the outside and red on the inside and has watermelon seeds, then it’s probably a watermelon. If you see a green fruit, I don’t know what’s inside it. If you see that it’s also red inside and green outside, who knows, maybe it has different seeds. But if it’s green outside and red inside and has watermelon seeds, then it’s a watermelon. In other words, the point—and this is how science works. We talked last time about the common denominator. I let go of this phone and it falls to the earth. Then I let go of the pen and it also falls to the earth. Then I let go of the microphone and it too falls to the earth. Fine, maybe each one has its own reason why it falls. This one because it’s an electronic device, that one because it writes, and this one because I don’t know what, because it has a mesh with holes. Nonsense—it’s possible. But more plausibly, Occam’s razor prefers that all of them fall because they have mass. They have a shared property causing all three. That is exactly scientific generalization.
[Speaker C] So why, when he did only two things, don’t we say that there too?
[Rabbi Michael Abraham] Ah, that’s the dispute between Rabbi and Rabban Shimon ben Gamliel. Rabbi maintains that two things are enough. You don’t need three. And according to Rabbi, I think here too in Chagigah two signs of an imbecile would indeed suffice. In Jewish law, in most cases, we rule like Rabban Shimon ben Gamliel—the Talmudic text makes some distinctions, not important now—but in most cases we rule like Rabban Shimon ben Gamliel, and therefore a presumption is established after three times. But Rabbi really says that two are enough, and why? Because with one case, you have either one explanation—that he is absorbed in thought—or that he is an imbecile. Those are two explanations equally simple. But if two things happened, then there is already an advantage to the explanation that he is an imbecile, because for the two things there are already two different independent explanations causing them, as opposed to one explanation based on a single parameter—that he is an imbecile. That’s already preferable. Rabbi says, correct—but apparently that is Rabbi’s view. Therefore Rabbi says that even with two there is a presumption. Rabban Shimon ben Gamliel claims that in order to create a presumption—we are, after all, removing something from its prior status, and that’s why I remind you of the wayfarers of Usha. We move from one presumption and reveal another presumption. In order to remove something from its prior presumption, you need significant evidence. It isn’t enough that one explanation be just a little preferable. It has to be a significant preference. Three times is a significant preference. That’s what Rabban Shimon ben Gamliel says. But apparently Rabban Shimon ben Gamliel would say that only where this comes to dislodge an existing presumption. If in fact I have no prior presumption about him—there’s a mental institution nearby and I see a person walking in the street. In that city half the people are residents from the institution and half are not. Now I see a person: there’s a fifty percent chance he’s mentally ill and a fifty percent chance he isn’t. For such a person, two times doing things characteristic of an imbecile would suffice. You don’t need three. Because I’m not trying to remove him—I’m not acting against the normal presumption. When I see an ordinary person, the presumption is that he is normal. In order to remove him from the presumption of normality, you need three examples, because I need a much stronger preference for the explanation that he is an imbecile over the explanations that this happened coincidentally. But if I’m not trying to remove him from a prior presumption, then a slight preference between two possibilities is enough, and I’ll always take the one that is slightly preferable.
[Speaker C] And in inferences like an a fortiori inference and inference from a paradigm case and so on, is the preference significant or only slight? I didn’t understand. When one makes an a fortiori inference or an inference from a paradigm case, is the preference of one model over another weak or strong?
[Rabbi Michael Abraham] For example, with an a fortiori inference, the rule is that we do not impose punishments based on an inference. Because when you want to punish, that is already significant, and there you need a significant preference. If you’re only saying that something is forbidden—let’s be stringent and forbid it anyway—it may still be that there is a refutation of the a fortiori argument. But to forbid, you can still forbid on that basis. To punish is something else. Okay? So Rabbi Chaim’s claim in the end is that these three-time presumptions are basically just Occam’s razor applied to the different abductions. The question is: what is the theory underlying the phenomena we see? We perform all the possible abductions, choose the simplest among them, and then go with it; we make the induction that follows from the simplest abduction. Will every engaged husband die? Will every married husband die? Will he die if he climbs a tree? That is already the induction we make after deciding what the best, simplest theory is. Exactly as we saw in the previous class with a fortiori, common denominator, and all those things. We choose the simplest abduction, and then fill in the missing slot according to that abduction. And that is the generalization we make on the basis of that abduction. Okay? And the Talmudic text here really—as we just read—really compares it: “he is like one who gored an ox, a donkey, and a camel, and became established as dangerous toward all.” What does that mean? The Talmudic text is already comparing this to the presumption established by testimony about an ox, right? How does an ox become established as dangerous? If it gores three times, it becomes established. What happens if it gores once an ox, once a donkey, and once a camel? The Talmudic text says it becomes established as dangerous toward all. It is prone to gore anyone who passes before it. Okay? What does that really mean? Because if it gored an ox, a donkey, and a camel, again I have two ways to interpret it. One possibility is that each one was coincidence. One time it gored an ox—but only once; it didn’t gore three oxen, so I have no proof that it is dangerous to oxen. One time it gored a donkey—I have no proof that it is dangerous to donkeys. One time it gored a camel—I have no proof that it is dangerous to camels. It could be that each of these was coincidence. That is one possibility. The second possibility is no: it gored all of them because by its nature it is an ox with established goring behavior, and it is not dangerous only to a particular type of animal. It is dangerous to gore any animal it encounters. Because otherwise, if it were a specific type, that wouldn’t work—here it gored three different animals. So those are the two explanatory possibilities. The possibility that it is dangerous to all is simpler than the possibility that by chance it gored an ox once without being prone to that, by chance it gored a donkey once without being prone to that, and by chance it gored a camel once without being prone to that. Those are three coincidences. And if I have three coincidences as against one explanation that stitches together all three cases, I will obviously choose the second option. That is Occam’s razor. That is what Rashi writes there: “Like one who gored an ox, a donkey, and a camel,” in Bava Kamma 37, “for it becomes established as dangerous toward all, and we do not say that it must be established by three instances in each species.” We do not require it to gore three oxen, three donkeys, and three camels in order for it to be dangerous to donkeys, dangerous to oxen, and dangerous to camels. “Since its three gorings were attested in three species, it is not particular about one species.” It should probably say “one” there, not “another.” “So too here, these three things did not come upon him all at once, but all are due to imbecility.” Yes, if the alternative is that I have one explanation accounting for the three cases, or that we are dealing with three cases each of which is mere coincidence, with no explanation, which just happened for no reason—mere coincidence—then I will prefer the first option, because it is simpler. Okay? Exactly the same thing as with an ox, a donkey, and a camel.
[Speaker A] So basically the claim is—
[Rabbi Michael Abraham] The claim is that apparently—at least that’s the accepted view—we do not make inductions unless in the background we have some abduction that is plausible. Not that we are certain it is correct, but it offers us a plausible explanation. Once one plausible explanation is offered for the three cases, that is preferable to assuming that all three happened by chance, with no explanation. Okay? Now, how plausible does that explanation need to be? I don’t know. Some sort of explanation. Because “the source causes it” is not a super-plausible explanation. It only says that maybe there is something in the woman’s source, and that is enough to prefer it to the possibility that three coincidences occurred here. So one has to understand that the intuition with which we try to evaluate possible explanations has limited weight. There has to be some intuitive weight to the possible explanation, but one has to understand: it doesn’t need to be a very strong intuition that it’s true. It’s enough that it’s not absurd, that I have some way to attach it to a plausible explanation. Because the alternative—that these are three coincidences—is very implausible. Now, that is the first chapter of this topic. Now I want to move on to the second chapter, or at least begin it. When discussing these three-time presumptions, the later authorities discuss that there are really—one can divide them into two kinds. One kind is presumptions that serve as evidence, and a second kind is presumptions of formation or habituation. What do I mean? Look, for example, at an ox with established goring behavior. After it gores three times, it becomes established as dangerous. This can be understood in two ways. One possibility is that those three times testify that it has a naturally dangerous disposition, because otherwise each of these gorings happened by chance. That’s implausible. So apparently it has some dangerous disposition, and that’s why it committed the three gorings. That means the three gorings constitute evidence that it has a dangerous disposition. Another possibility is to say no: an ox that gores three times becomes dangerous—it gets used to goring. That turns it into one with established goring behavior. It’s not evidence that by nature it is dangerous; rather, it implants in it a dangerous nature. Now look—the apparently simple understanding is the first.
[Speaker C] No, or the opposite.
[Rabbi Michael Abraham] Right, yes. Eliav already understands why that isn’t correct, because that is exactly the question you asked earlier. What you asked earlier was basically this: if the first understanding were correct—if the three times the ox gored were an evidentiary presumption—then I would have to assume it was dangerous from the start. Before, I didn’t know it; after it gored three times, it becomes clear to me that this ox is probably dangerous by nature. And if that were so, then I should have to go back and pay the earlier victims full damages as well. I simply didn’t know it was dangerous; now I know. Now that I know, it turns out that it was always dangerous. Therefore, apparently, it makes more sense to say that the presumption of dangerousness is a presumption that creates dangerousness. It does not testify that it has a violent nature; it creates in it a violent nature. So what, after three times that it gored, now it already has a violent nature. The heart follows the actions, as they say.
[Speaker E] And the liability falls on the owner and on his negligence, and his negligence can arise only after three times—
[Rabbi Michael Abraham] Because in the first two times he didn’t know. Okay. Indeed we’ll see later that the later authorities and the medieval authorities discuss these presumptions of goring regarding an ox with established goring behavior: is this an evidentiary presumption or a presumption of habituation? And there are definitely views that say it is an evidentiary presumption, and in truth that is the simple reasoning. The question why it doesn’t apply retroactively can definitely be answered by saying that the owner, after all, did not know that his ox was dangerous, so you cannot come to him with claims about why he didn’t guard it. He was under compulsion. Ordinary oxen are presumed guarded. So because of that, you can’t obligate him, even though it’s true that the ox was dangerous from birth. But if the owner does not know, and you want the owner to pay, then it is not enough that the ox be dangerous; I also need a claim against the owner as to why he didn’t guard it. Okay? So there are explanations even for the view that says that the gorings of the ox are evidence and not habituation. In any case, I’m only using this in order to present to you two possibilities, or two kinds of presumptions. One kind is where I have three pieces of evidence that combine to prove something about reality: an ox that is dangerous, that I bought the land, that the woman has a fixed cycle, and so on. Or presumptions of habituation that say, for example, if the woman saw blood three times on the fifth of the month, it may be that her body has already gotten used to emitting blood whenever the moon is in exactly that phase corresponding to the fifth of the month. Then it’s actually habituation and not evidence. Or the ox—after three times that it gored, it got used to being violent. So it isn’t evidence; it’s habituation, and so on. So in many presumptions one can discuss whether it is an evidentiary presumption or a presumption of habituation. There are presumptions where it is clear that it is one of the two. There is a Kehillot Yaakov on tractate Taharot, section 47, where he discusses at great length three-time presumptions and the question whether they are habituation or evidence. He brings that he asked his brother-in-law, yes, the Chazon Ish, and the Chazon Ish answered him that there are presumptions of this kind and presumptions of that kind. Because the later authorities conduct here a sweeping discussion, a conceptual inquiry of the later authorities, asking whether every three-time presumption is an evidentiary presumption or whether all these presumptions are presumptions of habituation. And why do they conduct the discussion so sweepingly? Because the Talmudic text itself compares three-time presumptions from one case to another. For example, the wayfarers of Usha compare an ox with established goring behavior to the presumption regarding land. The Talmudic text in Chagigah that we saw compares an ox with established goring behavior to the signs of an imbecile. So you see that the Talmudic text itself understands that our position regarding three-time presumptions should be uniform across all the examples. But if some were habituation and some were evidence, then what proof is there from one to the other? It could be that evidence arises after three times and habituation after two, or vice versa, or maybe there is no habituation at all. Who says that if there is a presumption for evidence there is also a presumption for habituation, and vice versa? You can’t learn one from the other. And that is aside from the question of who says one can learn from habituation at all. So why, if Rabbi says it’s two times and Rabban Shimon ben Gamliel says it’s three times, does that have to apply in all the examples?
[Speaker C] No, that’s not because of that. It’s the definition of habituation. The definition of habituation starts from three times. It’s not because an ox starts with three times, so a woman—
[Rabbi Michael Abraham] What do you mean by definition? The question is whether it became habituated or did not become habituated.
[Speaker C] Yes, but what are we assuming?
[Rabbi Michael Abraham] Fine, but why assume the same thing in every case? How would you do that?
[Speaker C] If
[Rabbi Michael Abraham] Reality is different—think logically about what the reality is. It could be that in some cases reality would favor two times within a presumption, and in other cases it would be three. Here it’s habituation, here it’s observation. Even within habituations, maybe here people get used to something quickly and there they get used to it slowly. This itself—and I’m already hinting ahead—this itself says to me that all these discussions among the later authorities are incorrect. They’re based on a mistake, because it’s clear that the number three is a formal number. After all, there’s no end to the matter. Obviously you get somewhat used to something after two times, more after three, even more after four, five, six. At some point you have to draw the line. Where do I draw the line? It’s not really a question of whether I got used to it or didn’t get used to it; it’s not a question of one or zero. You draw the line somewhere that Jewish law determines, because you need some criterion. So Jewish law determines that three times is the criterion. If something needs to happen several times in order for us to assume that this is the general rule—whether for habituation or for observation—then I’ll assume three. After three times, that’s what I assume. It’s a formal halakhic rule, and therefore you can compare from one area to another, and even compare observations to habituations.
[Speaker C] But why make that kind of threshold?
[Rabbi Michael Abraham] No problem, no problem.
[Speaker C] Why set that kind of formal threshold for all customs?
[Rabbi Michael Abraham] Because you need a tool for the judge to work with.
[Speaker C] Right, so say that for a woman it’s X times, and for an ox—
[Rabbi Michael Abraham] The simpler thing is to set the same threshold. Right? Let’s see—this is like the case that at age three her virginity is restored. Right, the famous Jerusalem Talmud that the Shakh brings: at age three her virginity is restored. What happens if the religious court intercalated the month? Then she’s not yet three.
[Speaker C] Right, that too.
[Rabbi Michael Abraham] So he says no, then her virginity will not be restored, because the religious court determines nature; Jewish law determines nature. With all due respect, that’s nonsense. Clearly that’s not true. Rather, what’s going on is that halakhically we set a formal threshold that up to age three her virginity is restored. Obviously, factually, there are girls for whom it would be restored until age two years and ten months, and there are girls for whom it would be until age three and a half. We need to set a threshold for our halakhic assumptions, so we place the threshold at age three. And what they’re saying here is that age three is age three—I don’t care whether it comes from a court determination or not—because we need a formal threshold, that’s all. There is no reason whatsoever to interpret it as though the religious court determines reality. That’s just unnecessary mysticism; there’s no reason to assume it. Okay? So here too it’s the same thing.
[Speaker H] It doesn’t determine reality; it determines halakhic status.
[Rabbi Michael Abraham] What I’m saying is: it determines halakhic status, not reality.
[Speaker H] So if so, if he determined that her virginity is restored, then she’s considered like a woman injured by wood or some other similar status—it doesn’t totally change everything.
[Rabbi Michael Abraham] I assume her virginity is restored, and that’s it. Therefore, from my standpoint, halakhically her virginity is restored, because I’m not going to start checking each woman individually. The question is: what is the basic presumption, what is the presumption from which we proceed, what is the point of departure? The point of departure is that up to age three her virginity is restored. What does age three mean? Age three according to the calendar established for that year, because that’s the simplest thing. Now what does that mean? Does it mean there’s some kind of thing in nature here? No. After all, even age three without any court intervention—it never really happens exactly at age three. A little before, a little after. We set some formal threshold because we need to function halakhically, that’s all. So too, in presumptions of three times, in my opinion that’s how it works. Therefore all the pilpulim of the later authorities here, in my opinion, are simply incorrect. Okay, we’ll stop here and continue next time. Any comments or questions?
[Speaker C] Rabbi, I just wanted to remind you that a question came up here from Ezra, that your model is rather too formal. It’s too formal, and I don’t know if you remember—Ezra Brick, something like that.
[Rabbi Michael Abraham] Ezra Brick, yes.
[Speaker C] Brick. So he asked that the model doesn’t represent the data properly—it’s too formal, with one and zero. And which model? The model of a fortiori reasoning. Right, of a fortiori reasoning and the analogy-based derivations and so on.
[Rabbi Michael Abraham] He asked that you can’t—
[Speaker C] use one and zero for halakhic data.
[Rabbi Michael Abraham] And why not? What do you mean? Liable or not liable—that’s just the notation one or zero.
[Speaker C] I don’t know, I’m just reminding you of his question because you said you’d come back to it.
[Rabbi Michael Abraham] I didn’t understand the question. What, one is liable and zero is exempt—what’s the problem?
[Speaker C] I don’t remember anymore—
[Rabbi Michael Abraham] Exactly, but—
[Speaker I] Rabbi, may I ask a question? Yes. My question isn’t related to today’s class. By the way, thank you very much for the class, it was very enlightening. My question is about the authority of the Sages, and I’ll define it more specifically in terms of the authority of the Talmud—the Talmudic text. That is, if a person sees himself as understanding the topic or the Jewish law, then he can disagree, for example, with medieval authorities (Rishonim), with the Chazon Ish if he wants, with the Kuzari, with Maimonides—there’s no binding force there. But the Talmud has formal authority. Okay. I tried corresponding with the Rabbi about this several times; I wasn’t able to understand it, so I’d like to try to understand it now. I’m trying to understand why today, if I think otherwise, it still obligates me. Suppose I do understand that I have an obligation to God because He created me and I belong to Him. I don’t…
[Rabbi Michael Abraham] No—but why do you think… And suppose I think not?
[Speaker I] If I think not—what? That I’m not obligated to listen to God?
[Rabbi Michael Abraham] Yes. Then I really—
[Speaker I] What do you mean? Then I really don’t listen to Him.
[Rabbi Michael Abraham] That you won’t listen is obvious; that’s true by us as well. But the question is whether there is a claim against you. Yes.
[Speaker I] Why? I can’t explain it, I just find that understanding within myself.
[Rabbi Michael Abraham] Fine, but it’s the same understanding here. What do you mean? The point is: if the public undertook an obligation—if the public undertook an obligation—then the party that undertook it here is the public, not you personally. And therefore everyone who belongs to the public stands obligated. That’s why even those who were not at Mount Sinai are obligated by those commitments that we undertook at Mount Sinai, even though I wasn’t there. Like Israeli law, like any—
[Speaker I] Wait, wait, wait, let’s see. That really is a good question. Why am I obligated by what my forefathers accepted at Sinai? I didn’t accept anything, I didn’t sign anything.
[Rabbi Michael Abraham] I said that the answer is that the one who undertook the obligation here was the collective, not you. The collective is the entity that obligated itself. And once the collective—
[Speaker I] Wait, and if I choose—
[Rabbi Michael Abraham] If I choose to leave the collective? What?
[Speaker I] If I choose to leave the collective, why is there still a claim against me?
[Rabbi Michael Abraham] There is a claim against you because you cannot leave the collective; you are part of the collective. Why? If I choose—if I choose to be called Moshe and to be one meter eighty, what can I do? I’m one meter ninety-five, not one meter eighty.
[Speaker I] No, there’s an understanding that if I committed to something, I have to fulfill it. If I joined something, maybe I can’t leave it. But if my father made a decision… what?
[Rabbi Michael Abraham] Also assuming that I have to be a private individual—but no, I can also be a collective entity. Every legal system in the world assumes that.
[Speaker I] Fine, I can understand that, but that’s because several people made a decision together. I don’t understand how someone else made a decision and it obligates me.
[Rabbi Michael Abraham] You didn’t understand: every legal system in the world—when parliament made a decision, it obligates even five hundred years into the future, unless a new parliament repeals it. Now, I didn’t choose that parliament from five hundred years ago, and that law obligates me.
[Speaker I] Fine, I see myself… I see myself today as obligated… no, I don’t see myself. What?
[Rabbi Michael Abraham] I don’t see myself.
[Speaker I] Today I’m obligated to state law only because of the categorical imperative.
[Rabbi Michael Abraham] I’m asking: but if I don’t see myself that way, is there still a claim against me?
[Speaker I] No, but if you live here, you’re subject to the laws of the state.
[Rabbi Michael Abraham] Of course I’m subject—the law will put me in jail.
[Speaker I] Law and order.
[Rabbi Michael Abraham] What do you mean, law and order? The claim is that I am obligated. Law and order addresses you as obligated. Why? Why? Because you undertook it. Me?
[Speaker I] Who—
[Rabbi Michael Abraham] undertook it five hundred years ago? You, as part of the public, yes. A public is also an entity. A public can undertake obligations. That’s it, that’s the explanation. If—if—
[Speaker I] if that isn’t acceptable to you, then there’s no explanation. That’s the explanation I can give.
[Rabbi Michael Abraham] I understand that a public can undertake obligations; I don’t understand how that can carry over to their descendants. You didn’t understand: when a public undertakes an obligation, it means that everyone who belongs to that public is obligated. What Tosafot says: “One generation goes and another generation comes, but the earth stands forever,” Tosafot in Me’ilah 9a. What does that mean? There is no communal offering whose owners died. The entire public that brought the offering died. Now only their descendants are alive. That is not an offering whose owners died. Its owner still exists. Why? Because the people alive now are the same public that set aside the offering a hundred years ago. It’s the same public. A public does not die. The limbs that compose it are replaced—the private individuals—but the public remains.
[Speaker I] The idea—the idea that accompanies the public.
[Rabbi Michael Abraham] The public exists, and it remains obligated in what it obligated itself to. That’s it, that’s the explanation. If—if that isn’t acceptable to you, then there is no explanation. That’s the explanation I can give.
[Speaker I] So basically the Rabbi can make a claim against me if I decide that I don’t think what they accepted was a correct decision. No—I mean a negative attitude, seeing me as someone who isn’t doing the right thing.
[Rabbi Michael Abraham] Yes, but you know, if you believe this in—
[Speaker I] Okay, I—I need to think about it, I—
[Rabbi Michael Abraham] don’t—
[Speaker I] can’t manage to understand it.
[Rabbi Michael Abraham] If you believe this, if you believe this, then—
[Speaker I] I’ll assume you’re coerced, fine. But you’re coerced and still a transgressor. Yes. No, but I’m trying to understand; I can’t understand it.
[Rabbi Michael Abraham] Fine. A very simple assumption—you can agree with it, or you can disagree with it. The assumption is that in the world there are also collective entities and not only individual entities, and collective entities are legal entities in every respect, like a corporation.
[Speaker C] Rabbi, it’s like the example of the ship—if you replace all the planks—
[Rabbi Michael Abraham] The Ship of Theseus, yes. Okay.
[Speaker I] You can—
[Rabbi Michael Abraham] agree, you can disagree, but that—that’s the explanation. I, I—
[Speaker I] choose to keep thinking about it.
[Rabbi Michael Abraham] Okay, I—
[Speaker I] still don’t make decisions that quickly.
[Rabbi Michael Abraham] Very good, a blessed activity.
[Speaker I] Okay, may I ask one more small question? Or is that… yes, is that okay, is that acceptable?
[Rabbi Michael Abraham] Yes, everything’s fine.
[Speaker I] I wanted to ask about the prophets, and I’ll explain my question. Regarding the revelation at Mount Sinai, we have testimony… Rabbi, can you hear me?
[Rabbi Michael Abraham] Yes, yes, I’m with you.
[Speaker I] Regarding the revelation at Mount Sinai, we have testimony passed down from generation to generation, father to son, of six hundred thousand men besides women and children—in short, a very large public. Apparently there was no event like that in history, testimony of an encounter with God. It’s probably the most plausible event that God revealed Himself to people; it’s strong. Now regarding a prophet—let’s take as an example a prophet we relate to less, Jesus. We don’t accept him for a very simple reason: he didn’t prove himself. Meaning, I can’t conduct my life in such a way that anyone who comes and says God spoke to him, I listen to him—even just because of that approach. So my question regarding our prophets is this: true, there is a command, there is a command in the Torah that someone who performs such-and-such a sign, we will listen to him and be obligated to listen to him. My question is not at the level of the command, okay? I understand that that is formal authority even if he did not actually speak truth. My question is in terms of probability: is there really a high probability to think that they were true prophets?
[Rabbi Michael Abraham] And I’ll tell you two things. First, it doesn’t change anything, because the prophets established nothing that is relevant to us; Jewish law comes from the Torah. Laws from prophetic tradition are marginal—very few things. That’s regarding their significance for us. But beyond that, if the Torah says there will be prophets, and afterward prophets come and say that the Holy One, blessed be He, appeared to them, and we test them, then why assume it isn’t true? I don’t understand—the Torah said beforehand that this would happen.
[Speaker I] Wait, I’ll tell the Rabbi why. I watched America’s Got Talent, and what people did there—if that person had come up to me alone in the street and told me that God spoke to him, I would have believed him because of those wonders. I have no doubt about that.
[Rabbi Michael Abraham] But the reasoning I gave you before says something else. It—
[Speaker I] raises the probability that there were prophets, but not that I really trust that every one of the prophets we have spoke truth.
[Rabbi Michael Abraham] If you know in advance that there are prophets because the Torah itself tells you so, and the Holy One, blessed be He, tells you, “I will prophesy to people,” then now when a person comes and says, “Look, the Holy One, blessed be He, prophesied to me,” and he is also tested through various signs, I don’t see a reason to cast doubt on it. If now someone came without the Holy One, blessed be He, having said this in advance, then I would refuse even to listen. By the way, this is somewhat connected to what we discussed today. Suppose that prophet performed signs three times; then the question is whether I have… is this coincidence, or did he really prophesy? Or maybe some ability, some talent, whatever—or did the Holy One, blessed be He, really prophesy? So that’s a good question; you have to decide which of the two explanations is more plausible. But if the Holy One, blessed be He, told me in advance, “Look, I’m going to prophesy to people, and you need to obey them,” then why assume there’s a problem here? The Holy One, blessed be He, will not let people speak in His name if they are not truly speaking, since He Himself requires us to listen to them.
[Speaker I] No, but there were false prophets; people have the ability to lie—
[Rabbi Michael Abraham] and to do—
[Speaker I] sleight of hand.
[Rabbi Michael Abraham] No, no, because if that had happened—if that had happened three times—then it probably would have been true. False prophets are people for whom it apparently didn’t work; they weren’t tested properly.
[Speaker I] Okay, why think that? One could also understand that quite simply a false prophet could have—like, there could have been a false prophet who managed to slip through.
[Rabbi Michael Abraham] You can understand many things, but you know, we say “it can be resolved with difficulty,” not “it can be challenged with difficulty.” You say, “One could understand…”
[Speaker I] No, I really do understand the Rabbi’s argument, only I also think that in a period when people’s knowledge was so limited, it could be that there was a sufficiently talented person—
[Rabbi Michael Abraham] That’s what you said earlier too, but I answered that. If the Holy One, blessed be He, says in advance that He will prophesy to people, and if we test them then we must obey them, and now a person arrives whom we tested, then one must obey him. That’s what is written in the Torah. So the Holy One, blessed be He, presumably must ensure that people do not speak falsely in His name, because He commanded us to obey them. That’s all.
[Speaker I] I understand. Presumably He saw to it that there was a good system.
[Speaker C] Yes, yes. Elihav? I wanted to ask about Occam’s razor. Suppose, for example, that we have one parameter, alpha, that explains all the data, okay? And that’s one model. In a second model we have three parameters—alpha, beta, gamma—that explain all the data. But actually alpha is less plausible than the three other parameters. When you identify the parameters—
[Rabbi Michael Abraham] No. So if you identify them—I intentionally built the model, and we’ll still get to identifying these parameters, I’m still planning to comment on that. But I built the model without identifying the parameters at all, so you have no way to compare which is a relevant parameter and which is not. You just count.
[Speaker C] Okay, but suppose you do identify them—you have alpha, which is an implausible parameter—
[Rabbi Michael Abraham] If alpha is not a plausible parameter, then certainly it could be a theory that I would not accept.
[Speaker C] Even if on the other side there are three parameters? Yes. So your model is not entirely formal?
[Rabbi Michael Abraham] Look, for example, at the a fortiori reasoning that the rule-formulators often bring. Come—am I obligated to put fringes on a doorpost? If a four-cornered garment, which is exempt from mezuzah, is obligated in fringes, then a doorpost, which is obligated in mezuzah—should it not certainly be obligated in fringes? Now make a table, analyze it—the a fortiori argument says yes, correct, we should obligate the doorpost in fringes. So why don’t we do that? Because it’s obvious to us that there is no one parameter shared by the doorpost and fringes. Meaning, where we identify the parameters, or where we don’t really find some intuitive factor that would be a plausible cause—exactly what we discussed today in class—then indeed we won’t go with it. But I’ll still comment on the identification of parameters; that’s still in the plan.
[Speaker C] Okay, and one last question—what Elkhanan said reminded me of this question. Why, in essence, are we not liable to death at the hands of Heaven for all the commandments in the Torah? There is a law that one is liable to death at the hands of Heaven for a commandment that a prophet commands us, right? So why are we not liable to death at the hands of Heaven for all the commandments in the Torah, since it was Moses who gave them to us?
[Rabbi Michael Abraham] Death at the hands of Heaven applies to commandments that only a prophet commands us.
[Speaker C] Right, so Moses—Moses brought them to us.
[Rabbi Michael Abraham] No—commandments that only a prophet commands us, not Torah commandments from the Holy One, blessed be He. Commandments from prophetic tradition. Either from prophetic tradition, or a local command of a prophet—that is, a temporary directive.
[Speaker C] No, but a prophet’s commandment has the status of Torah-level law, doesn’t it?
[Rabbi Michael Abraham] No, prophetic tradition. There are disputes among medieval authorities (Rishonim) about how to relate to prophetic tradition; there are medieval authorities (Rishonim) who argue that with prophetic tradition as well, in a case of doubt one should rule stringently, but it is not Torah-level.
[Speaker C] So it’s only laws that the prophet innovates, so to speak?
[Rabbi Michael Abraham] Yes. And he cannot innovate laws that are permanent, because a prophet is not permitted from now on to introduce anything new.
[Speaker C] Okay, thank you.
[Speaker A] Okay, Sabbath peace, all—
[Rabbi Michael Abraham] the best.