Doubt and Probability—in Halacha, in Thought, and in General—Lesson 18—Rabbi Michael Abraham

Table of Contents

• Rov de-ita kaman and rov de-leita kaman as generalization from a sample
• The presumption of three times: evidence versus habituation, and a dispute among the medieval authorities (Rishonim)
• Specific mu’ad status: species and days
• Maimonides and the Raavad on establishing an ox as forewarned on alternating occasions, and the challenge of generalization
• The process of generalization and its implications for the owner’s duty of supervision
• Kehillot Yaakov: an internal contradiction in Maimonides and proof for habituation
• The lecturer’s interpretation: an evidentiary mechanism of taking the intersection because of doubt and extracting money
• A formal conception of “three times” and comparison of evidence and habituation
• David Hume’s problem of induction and laws of nature as claims about us
• Wittgenstein, sequences, and conventionality as the basis for deciding among generalizations
• The weakness of rov de-leita kaman in the plain sense of the Talmud, and Maimonides’ opposing view
• Majority in monetary law, presumption, and Tosafot on judges
• Reverting from forewarned status back to innocuous status, and combining presumption with monetary possession

Summary

General Overview

The lecture presents the presumption of three times as a halakhic mechanism for generalizing from a sample, and connects it to the distinction between rov de-ita kaman and rov de-leita kaman. Rov de-leita kaman is described as a statistical generalization based on cases, whereas rov de-ita kaman is understood as an a priori reasoning that is not built on experiment and generalization. The discussion focuses on a forewarned ox and the offshoots of “specific forewarned status” by species or by days, placing at the center the dispute between Maimonides and the Raavad and Kehillot Yaakov’s interpretation of Maimonides through the question whether establishing forewarned status is evidence or habituation. From these examples, a fundamental problem is raised in the process of generalization: from the same set of data one can derive many general laws, and deciding between them is not trivial. That leads to David Hume’s problem of induction and to the question why rov de-leita kaman is sometimes seen as weaker, even though Maimonides is presented as holding the opposite.

Rov de-ita kaman and rov de-leita kaman as generalization from a sample

The lecturer states that rov de-leita kaman is a rule based on generalizing from a sample, similar to saying “most women are not aylonit,” which is learned from the impression one gets from a representative sample. He defines rov de-ita kaman as a situation in which all the possibilities are before us, so there is no element of generalization in it—like a piece of meat found in a city with nine kosher butcher shops and one non-kosher one, where the ruling is presented as a priori reasoning and not as the product of controlled observation. He presents the presumption of three times as the halakhic expression of how one deals with sample-based generalizations, and goes on to examine whether this also applies to establishing an ox as forewarned.

The presumption of three times: evidence versus habituation, and a dispute among the medieval authorities (Rishonim)

The lecturer describes a discussion among later authorities (Acharonim) about whether a forewarned ox becomes forewarned by force of evidentiary sampling from three gorings, or by force of habituation created by those very three gorings. He ties this to a dispute between Rabbenu Peretz and Maharam of Rothenburg as later authorities interpret them, and warns that understanding the relationship between them is not simple; he even claims that the truth in classifying the positions is “completely the reverse” of the first impression. He sharpens the point that the practical difference is whether the three gorings are evidence of an existing nature or a process that creates a nature, and only the first possibility is a generalization from a sample.

Specific forewarned status: species and days

The lecturer explains that forewarned status can be narrow—for example, an ox that gored camels three times and thereby becomes forewarned only for camels, or an ox that gores on alternating fixed days and becomes forewarned only for those days. He emphasizes that specific forewarned status can be explained both within the framework of “evidence” and within the framework of “habituation,” because one can say either that the ox has become used to attacking precisely a certain type, or that there is evidence that it has “something against” that type. He also presents an edge case in which the ox gored only camels simply because it did not encounter other animals, and notes that there are disputes about whether in such a case it becomes forewarned for everything or only for camels.

Maimonides and the Raavad on establishing an ox as forewarned on alternating occasions, and the challenge of generalization

The lecturer quotes Maimonides, Laws of Monetary Damages chapter 6, halakhot 9–10, according to whom goring on three days involving different species creates forewarned status “for all,” meaning for those species that were gored, and likewise there is a law of alternating occasions in which the ox becomes forewarned for alternating occasions. He emphasizes that the Raavad disagrees and argues that the wording “for all” means for all animals, but he explains that in Maimonides “for all” refers to the species that were gored, as is implied by the continuation: “And if it gored, on a day for which it is forewarned, one of the three species that it gored on alternating occasions, it is forewarned.” He raises an intuitive difficulty regarding a complex alternating pattern and connects it to the question of a “formula” that can be tailored to any random sequence of days, mentioning Wittgenstein and the claim that one can formulate a rule for any given sequence, and asks how the ox “knows” such a regularity—where the possible answer is that it is not conscious but natural.

The process of generalization and its implications for the owner’s duty of supervision

The lecturer presents the Maimonides-Raavad debate as revealing that from the same data set one can make different generalizations, including a third possibility—that the ox is not forewarned at all, because each species was gored only once. He shifts the focus to the question of what the law demands from the ox’s owner in terms of supervision, and offers a modern parallel: a dog that has bitten only cats many times, and the question whether its owner is also expected to guard against danger to babies. He argues that in modern law there is no sharp “line,” and a judge would decide based on reasonableness, whereas Jewish law draws a formal line of three times, even if three times may sometimes be too few for such a specific inference. Participants raise competing approaches according to which the very fact of attacking teaches us about “general aggressiveness,” and the lecturer answers with examples in which there is a clear regularity in the target of attack, so there is no justification for imposing a universal concern, including an analogy to aggressive behavior toward certain groups and the claim that the label “aggressive” by itself does not determine the duty of caution toward every possible target.

Kehillot Yaakov: an internal contradiction in Maimonides and proof for habituation

The lecturer cites Kehillot Yaakov, who argues that there is an internal contradiction in Maimonides when he limits the forewarned status both to odd-numbered days and to the three species that were gored. Because whichever way you look at it, there would seem to be room to expand it: if the explanation is “days,” then not goring on even-numbered days is not evidence against other species; and if the explanation is “species,” then not goring on even-numbered days results from the fact that those species are not being gored, not from the days. Kehillot Yaakov concludes from this that according to Maimonides, establishing forewarned status is habituation and not evidence, because in habituation, what the ox did not do does not enter the process. The lecturer comments that even under habituation it is hard to understand how three gorings of different species can combine, when each species was gored only once, and argues that the habituation interpretation also does not really resolve Maimonides.

The lecturer’s interpretation: an evidentiary mechanism of taking the intersection because of doubt and extracting money

The lecturer argues that precisely according to the “evidence” approach one can understand Maimonides, because there are two possible interpretive generalizations and no way to decide between them; therefore, we take the minimal intersection on which both possibilities agree. He explains that since forewarned status is a shift from the presumption of innocuousness, and its consequence is extracting money—full damages—the rule applies that “the burden of proof is on the one seeking to extract from another,” and therefore we apply only what is proven with certainty: forewarned status on odd-numbered days and for the three species that were gored. He admits that this still does not solve the basic question of why Maimonides combines gorings of different species into forewarned status for those three species, and he presents that as an independent difficulty in Maimonides, unrelated to Kehillot Yaakov.

A formal conception of “three times” and comparison of evidence and habituation

The lecturer returns to the question of how the Talmud compares a forewarned ox with other presumptions, like the three-year presumption of land ownership, which is certainly evidentiary, and argues that one should not be alarmed by that, because the number three is a formal halakhic line and not some transition from “zero to a hundred” in terms of factual certainty. He gives the example of “He causes the wind to blow,” where habit is measured by ninety repetitions rather than by three, and explains that Jewish law uses the number three typologically in different ways. He brings the example of a girl of three years old whose virginity is restored, including the topic of “an adult who became a minor” following an intercalated year, and explains that the halakhic line is determined by the calendar of the religious court, so the implication works as a formal line, along with discussion of the Shakh and of a mystical versus formal interpretation, and with mention of the Hatam Sofer’s phrase, “the righteous decrees and the Holy One, blessed be He, fulfills.”

David Hume’s problem of induction and laws of nature as claims about us

The lecturer presents David Hume’s claim that generalizations have no real basis in the world but are rather the result of the structure of our thinking, so what happened in the past proves nothing about the future—including the example that the sun has risen until now, but there is no proof that it will rise tomorrow. He describes a view in philosophy of science according to which laws of nature are a way of organizing phenomena according to our conceptual convenience, rather than a binding description of reality itself, and defines this as a claim about the person rather than about the object. He says he finds it difficult to understand how one can live that way, and brings “personal testimony” from conversations with “David Humes” who say they act by habit because there is no better alternative, even in decisions like boarding a plane, and he emphasizes the absurdity he feels in giving no statistical weight to the past.

Wittgenstein, sequences, and conventionality as the basis for deciding among generalizations

The lecturer uses the sequence 3, 5, 7 to show that the next number is not uniquely determined and could be 9 if the rule is odd numbers, or 11 if the rule is primes, or in fact any number by means of a suitable formula, and he attributes this to Wittgenstein’s line on “following a rule.” He argues that psychometric tests measure conventionality rather than talent, because someone who offers an “outside the box” answer with a justification may be smart, but will not align with the language of instruction and the accepted understanding at the university. He distinguishes between the importance of openness and the inability to communicate when generalization is done in a non-conventional way.

The weakness of rov de-leita kaman in the plain sense of the Talmud, and Maimonides’ opposing view

The lecturer connects the problem of induction to the view that rov de-leita kaman is weaker than rov de-ita kaman, and brings the plain sense of the Talmud in Hullin, which derives rov de-ita kaman from “incline after the majority” and then asks, “From where do we know rov de-leita kaman?” so that there seems to be no clear source. He notes that Rashi fills this in in ways such as a law given to Moses at Sinai or an extension of “incline after the majority,” and he cites Rabbi Shimon Shkop in section 3 as presenting rov de-leita kaman as weaker. He presents Maimonides as holding that rov de-leita kaman is actually stronger, and explains that this can be reconciled by saying that in the final analysis, if rov de-leita kaman is also derived from “incline after the majority,” then the hierarchy can shift. He notes that Rabbi Shimon Shkop’s explanation of Maimonides’ view is connected, for him, to the “David Levi effect” discussed earlier in the series.

Majority in monetary law, presumption, and Tosafot on judges

The lecturer addresses the question of “we do not follow the majority in monetary matters” and clarifies that there are still topics of majority in monetary law. He raises a possible distinction among the medieval authorities (Rishonim), according to which in monetary law one might perhaps follow rov de-ita kaman but not rov de-leita kaman, even though Tosafot explicitly say otherwise. He cites Tosafot in Sanhedrin and Bava Kamma 27, who ask from the laws of judges, which are a case of rov de-ita kaman derived from “incline after the majority,” and that implies that on one side we do indeed follow majority. He touches on the relationship between majority and presumption and brings the example of the presumption that a person does not pay before the due date, which extracts money in Bava Batra 5. In the discussion, someone raises the claim of a stronger “statistical necessity” in presumption as opposed to majority, while the lecturer emphasizes that majority includes both 51% and 99%, so the division is not simple, and he mentions distinctions such as a recognizable majority versus an unrecognizable majority.

Reverting from forewarned status back to innocuous status, and combining presumption with monetary possession

At the end, a question is raised about “uprooting” forewarned status back to innocuous status and about the relationship between changing a presumption and extracting money. The lecturer answers that generally stronger evidence is required to move from innocuous to forewarned than to move from forewarned back to innocuous, because in the transition back to innocuous status there is no extraction of money but rather leaving it in its current holder’s possession, even though there is still work to do against an existing presumption. He notes that there are different opinions about returning from forewarned to innocuous status, and connects this as well to the explanations given for the difference between two and three in presumptions, such as the claim that in monetary matters three are needed because of extracting money.

Good evening, Rabbi. Excellent evening, let’s begin. Okay, in the last few sessions I talked about the three-times presumption, and I said that it is basically the halakhic expression, or the halakhic approach, to generalizations from a sample. The claim is that every scientific generalization, or generalizations in general that we make, takes a few particular cases, assumes those cases are a representative sample, and from that creates a general rule about all cases of that type. And I’ll just remind you of the context: we spoke about the difference between a majority that is before us and a majority that is not before us, and my claim was that a majority that is not before us is basically a rule based on generalization from a sample, unlike a majority that is before us, which speaks about a set of options actually present before us, some distribution that is before us with no element of generalization at all. A piece of meat I found in the street, and in the city there are nine kosher shops and one non-kosher one—I assume that this piece came from the kosher shops, although that is not a generalization from a sample. There is no way to do a deliberate, controlled experiment with several examples and try to produce a generalization from that. It is some kind of a priori reasoning. By contrast, “most women are not barren” is a generalization from a sample. I know a hundred women, of whom let’s say ten are barren, so I assume that this sample is representative, and really in the world as a whole ninety percent of women are not barren. That is a majority not before us. And after I clarified this difference between a majority that is before us and one that is not before us—that a majority not before us is a generalization on the basis of a sample—I moved to the three-times presumption, and we saw that this is basically the halakhic treatment of generalizations from a sample. After that, in the previous class, I qualified this a bit and said that the later authorities discuss these three-times presumptions: is this really a generalization from a sample? Because some want to argue that, say, in the case of an ox that is deemed forewarned, if we say it gored three times and from that we create a general rule that this ox is a goring ox, that is a generalization from a sample. Three events happened, and we assume those are specific expressions of a general rule, so that is a generalization from a sample. But some later authorities argue that when an ox becomes forewarned, that is not the result of a generalization from a sample. Those three gorings are not evidence; rather, those three gorings trained it to become a goring ox. It became forewarned because of those three gorings, not that those three gorings prove that it already had a goring nature from the outset. So we saw disputes about this—Rabbeinu Peretz and the Maharam of Rothenburg—which the later authorities interpret in a certain way. I showed that I think the truth is exactly the opposite, but still, the dispute between them—regardless of who says what—is about whether this is evidence or habituation. If it is evidence, that is a generalization from a sample. If it is habituation, it has nothing to do with generalization from a sample; it is something entirely different. So in the previous class that was really mostly a parenthesis. A parenthesis showing that when we decode the dispute between the Maharam of Rothenburg and Rabbeinu Peretz, we need to be careful. In other words, it is not as it seems at first glance. So that was just a conceptual lesson, but it is not really directly related to our series. But I do want to continue for a moment with that point in something that is related. So yes, let’s go back for a moment to the forewarned ox. A forewarned ox basically becomes such after it gores three times. What happens if three times it gored camels, and all the other animals it saw it did not gore? In that case it becomes forewarned for camels. Only for camels. If it gored three camels and met no other animal, then that is already a matter of debate. It could be that it is indeed forewarned for all animals; it only gored camels because those are the only ones it met. But that does not prove it is forewarned only for camels. What happens if it gores, say, every even-numbered day? Only on Monday, Wednesday, and Friday it gores, or once every two days, whatever—like menstrual cycles, basically—then in that case it becomes forewarned for gorings on even-numbered days. Meaning, if it gores on an odd-numbered day, it pays like an innocuous ox. But if it gores on an even-numbered day, it pays like a forewarned ox. The same with the camels I mentioned before: if it gores a camel, it pays like a forewarned ox; if it gores a dog, then it pays like an innocuous ox. So there can be forms of forewarning that are specific. They are not general forewarnings. The concept of forewarned is not necessarily sweeping. Sometimes it is forewarned for certain days, sometimes for certain animals, so that really—meaning, you can say this whether I say the forewarning is evidence or whether I say the forewarning is habituation. Right? So suppose it gored camels three times. Then it simply got used to goring camels. Therefore it is forewarned only for camels. Or alternatively, this is evidence that this ox has something against camels. Meaning, it specifically gores camels. So whether this is evidence or habituation, one can understand specific forewarning—either for specific days or for specific animals. But there is a ruling in Maimonides that Kehillot Yaakov brings, and it somewhat challenges this whole matter. Maimonides says as follows, chapter 6 of Laws of Monetary Damages, halakhah 9: “If it gored an ox today, a donkey tomorrow, and a camel on the third day, it becomes forewarned for all.” Now, as we’ll soon see, “for all” means for these three species, not for literally all animals. The Raavad disagrees with him, but when Maimonides says “for all,” he means these three species. How do I know? You’ll see in a moment. “If it saw an ox today and gored it, and the next day it saw an ox and did not gore it, and on the third day it saw an ox and gored it, and on the fourth it saw an ox and did not gore it, on the fifth it saw an ox and gored it, and on the sixth it saw an ox and did not gore it, it becomes forewarned intermittently for oxen. And so too in any similar case.” Those are the two examples I spoke about earlier. Now look at halakhah 10. “If it saw an ox today and gored it, and the next day it saw a donkey and did not gore it, and on the third day it saw a horse and gored it, and on the fourth day it saw a camel and did not gore it, and on the fifth day it saw a mule and gored it, and on the sixth day it saw a wild donkey and did not gore it, it becomes forewarned intermittently for all.” Okay? Meaning it is forewarned to gore only every two days—but whom is it forewarned to gore? All. As I said earlier, “all” means the three species it gored. The novelty is that although each of these species was only gored once, so seemingly it is not forewarned for anything, Maimonides says no: those three times—if it gored each of those three species once—those occasions combine into forewarning for those same three species. And if that happened intermittently, then it is also once every two days for those same three species. Then Maimonides says as follows: “And if on a day for which it is forewarned it gores one of the three species that it gored intermittently, behold it is forewarned.” Here we see that when he said “forewarned for all,” he meant forewarned for those three species, meaning for all the species that it gored, not forewarned for literally all animals. The Raavad indeed disagrees and argues that it means all animals. But Rabbi, I don’t understand. If we can find some formula—say it gored in such-and-such a pattern—and seemingly it looked chaotic, like yes one time, no one time, many yeses, five yeses, five noes, but the Rabbi is a good mathematician, he’ll sit down and find a formula precisely fitted to it, something like the square root of the square of x times y—so what, now we’ll say the ox did that and is forewarned according to that formula? Good question, yes. That’s following a rule in Wittgenstein, right? For any random sequence of days you give me, I can find a formula that fits those days exactly. So where are we headed? That’s exactly where we’re headed. Again, I don’t think the Sages would have seen it that way; they weren’t aware that even complex structures can be represented by formulas. But at least according to the Sages’ way of thinking, if we apply it to ourselves, then apparently yes—that is, apparently that is what… But how do you explain that the ox knows that? The fact that the Sages knew it I can forgive, but the ox doesn’t know it—how can we think the ox is doing all that calculation? I understand. The ox doesn’t have to know it. It’s not conscious; it’s in its nature. So what, they think there is some biological logic to some such complex formula that causes it to gore every so often? Yes, that’s exactly what I’m… So why then—even if it starts with every other day—how did they get to the wild donkey and all that? That is always the question. That is exactly the question I want to dwell on here a bit: how do you make generalizations? That is really the question here, right? How do you make generalizations? Like the dispute between Maimonides and the Raavad. After it gored on three days, three different species, according to Maimonides it becomes forewarned for those three species. According to the Raavad it becomes forewarned for all animals. I can propose a third option: that it is not forewarned for anything, because each of those three species was gored only once. So you see that from the same set of data one can make many kinds of generalizations. It is a matter of judgment: how do you create the general law from the cases you encountered? It is a very complicated question. I don’t see any simple answer as to what is more correct and what is less correct here. But why is the truth about this ox so important to us? After all, what interests us is not really the ox but its owner. What do we demand of him, what do we expect from how he guards his ox? If an ox gored three times, what do I care whether it identified that this was a wild donkey, a horse, a donkey, or a camel? It gored three times. Because he only has to guard it against those. Guard it, period. Why are we now starting to make formulas? Suddenly when you see a wild donkey nearby—but if I see a sheep nearby, then no, it is not forewarned to gore that? The discussion always starts with the ox; of course the practical implication is for the owner, but the discussion always starts with the ox. In today’s courts, suppose I see a dog that bit. They’ll say, look, I didn’t see that my dog had passed that categorization. So far it only bit a cat. I didn’t think it would bite babies; it just happened. And people will say, what do you mean? You saw that it bites once, twice, certainly three times—then I’m not expected to think the dog at all… Let’s take it more extremely. Suppose the dog bit ten times, only cats. A hundred, fifty times, only cats, okay? Just for the sake of discussion. What do you think—do you have to guard it against babies too? Here there is some logic, okay, even a dog… The question is where the line is, and what if it is ten times and not fifty? The fact is that in today’s courts there is a line. There is no line. My dog chases cats—they’ll say even after a hundred and fifty times. Look, I’m not a lawyer, but in my opinion there is no line. The judge will decide whatever seems reasonable to him. And that is why I say: where you draw the line—in Jewish law the line is drawn at three times. You are right that often three times is too little to infer a specific conclusion from. Meaning, if it gored camels three times, there is logic in saying to him: guard it also against oxen. But Jewish law works in a somewhat more formal way, and from its perspective, if it gored camels, then we have evidence of forewarning for camels. Beyond that, I don’t know. Why is it three times and not ten? Because they fixed it at three times; you have to draw the line somewhere. So I don’t know how to answer those questions of where exactly to draw the line. But I think the line here should be completely, completely clear. The line should be that once an ox has gored—or a dog has bitten—it should make absolutely no difference whom or what: it is aggressive. It is a dog that doesn’t just wander around but attacks, no matter whom or what; from that moment, you should know that here you have a dog that you need to guard. That’s it. That is what you think, but one can certainly also see a different logic here, as I said earlier. Think of a case where… I said earlier, suppose the ox gored only camels fifty times. Only camels, fifty times. It is an ox that needs to be guarded much, much more, because it is an ox that gores, absolutely regardless of whom. Regardless. What, should I now get into the psychology of the ox? How does it decide whom to gore? Obviously there is no question. This ox gores camels. This ox does not behave like a non-aggressive animal. That is not something you grasp? You can’t hear the logic of someone who says, look, this ox has something against camels? It may be, Rabbi, it may be, but what will happen if he guards it better? What disaster will happen if he goes and… is stringent? No, we are not talking about any disaster. The question is whether he is obligated to guard it better or not, that’s all. We are not talking about disasters; the question is what he is obligated to do. We’d do the same with a person who, say, behaves aggressively toward Black people, but it turns out that toward Chinese people he does not behave aggressively. So what? Yes, of course. Of course. Of course he has something against Black people. He has something against Black people—so what? “Aggressive” is just a slogan. This man has something against Black people and nothing against Chinese people, so why guard against him with respect to Chinese people? No, but the point is not whom he has something against. The point is that when he has something against someone and acts on it, he is aggressive. A normal person, when he has something against Black people, is not obligated to attack them. From the moment he sees a Black person and attacks him, he is an aggressive person. Of course he is aggressive, so what? But his aggression is directed only at Black people, so what is the problem? I really cannot understand that logic. I think, look, the Nazis, we still… Yes, Godwin’s law—we’ve reached the Nazis. The Nazis attacked the Jews, right? No, also the Gypsies—no, no, no, they also attacked the Gypsies. The Gypsies, fine, Gypsies, I understand. Gypsies, homosexuals. No, no, not everyone, wait. The homosexuals, the mentally ill—they killed all those people. Ezra, I said that. Ezra, fine, I said it. But now I’m asking another question. So they attacked homosexuals and the mentally ill and Jews and Gypsies. Fine? And if you want, add another five types. Okay? Now imagine such a Nazi walking down the street and next to him passes a perfectly Aryan child. Are you afraid he will attack him? The man is an evil aggressor, a murderer, bloodthirsty. It could be that he thinks this child is… There is no chance. No, he will not attack that child. He will not attack that child. Therefore this label that someone is “aggressive” is just a label. If there is a very clear pattern as to whom he attacks, then that is what I worry about. The label “aggressive” is just a label. Now again, I understand, and I fully agree with you: I too would not draw the line at three. Meaning, if three times it attacked camels, let’s say, I too would suspect general aggression, not only toward camels. But Jewish law works in these somewhat formal ways, and yes, they drew the line at three times. And if there is a pattern in three times, then from the standpoint of Jewish law that is a pattern. I don’t know whether I would draw the line after three times or ten times or fifty times—that can be debated. So the claim in the end is that all the dilemmas around which this dispute revolves are exactly the dilemmas of generalization. You see several cases, and now you ask yourself: what is the general rule? How should you generalize these several cases? There are several possible ways to generalize them. And that is exactly where the disputes are. There can be disputes, and there is no way to decide them. You might be a judge, the Rabbi might be a judge, and someone comes before him, the owner of an ox that attacked, say, a donkey. And now the defense claim will be: I didn’t guard it because there were no donkeys in the area; it attacks only camels. So now is he exempt from paying for the damage to the donkey? As I said before, if there were no donkeys around but only camels, and it attacked the camels, there are views that indeed it becomes forewarned for everything. But if there were donkeys around and it did not attack them, and it attacked only camels, then yes, then it attacks only camels. And you would exempt the owner of the ox from paying damages? I would not exempt him; he would pay as an innocuous ox, not a forewarned ox. Rabbi, the definition of a camel is also a human definition. I’m not sure the ox… that the donkey… that the ox knows how to distinguish. And what if it’s a blond camel? Three times, a blond camel. “An ox knows its owner, and a donkey its master’s crib.” The ox apparently knows how to identify. That is an assumption with no… No, that is not an assumption with no basis; it is an assumption with a basis. If the ox gored camels fifty times, even you would agree, right? There you go. So now the only question is where to draw the line. Whether after three times or after fifty times. Fine. But that’s not true. There are… clearly there are certain animals that can attack a type. The dog doesn’t know these are cats and the others are sheep? It attacks cats, it does not attack sheep. And what bothers me here is that the focus is the donkey and not the owner who is guarding. No, that is not the implication. Yes, but apparently one should be stricter with him. Look, if you have a calm, sweet ox, you raised it from birth—when you decide to be stricter, you can be as strict as you want. A religious court can set rules that go beyond the law. We are discussing the question of what the law determines. A religious court might decide: no, we are raising the bar; any ox that gores three times, from our standpoint its owner must guard it against everything in the world, as an ordinance or something like that. A religious court can establish such a thing, but we are talking about the basic law. Under the basic law, yes, it is an innocuous ox. Anyway, for our purposes, I am dealing here with the question of generalization, not the issue of monetary damages. So let’s talk for a moment about the significance of this for generalization. Look, Maimonides is basically telling us that if the ox gores three species intermittently—and also intermittently by days: on the first day it gored one species, on the second day there was a second species and it did not gore it, on the third day a third species that it did gore, fourth day did not gore, fifth yes, sixth no, okay?—then Maimonides says it becomes forewarned for odd-numbered days and for the three species that it gored. Here this really is something that requires clarification. Why? Why is that the generalization demanded by those data? And here the Kehillot Yaakov brings this Maimonides and argues that there is really an internal contradiction within Maimonides’ words. Why? Because Maimonides is basically saying this: if it is forewarned only for odd-numbered days, then essentially you are saying that the reason it did not gore on the even-numbered days is that on even-numbered days it does not gore, right? That is basically what you are saying. That is why you say it is forewarned only for odd-numbered days. But if so, then why are the animals that it did not gore on the even-numbered days not included in the process of becoming forewarned? Why is it not forewarned for them too? The reason it did not gore them is not that it has no issue with wild donkeys, but because on even-numbered days it rests; it does not gore. You understand? There is an internal contradiction in what Maimonides says. Maimonides says on the one hand that it is forewarned only for odd-numbered days, and on the other hand that even on odd-numbered days it is forewarned only for the three that it gored. And that is contradictory whichever way you look at it: if you say it gores only on odd-numbered days, then the fact that it did not gore other species on the even-numbered days is not because those other species do not annoy it, but because it was an even-numbered day—so it should be forewarned also regarding the species it did not gore. And vice versa: if you say it is forewarned only for those three species, then why is it forewarned only for odd-numbered days? The reason it did not gore on the even-numbered days is because those were species it does not gore. Then it should be forewarned for all days. Therefore, says the Kehillot Yaakov, Maimonides’ words here contradict themselves. You cannot limit the forewarning both to odd-numbered days and to the species—the three species that were gored. Excuse me, Rabbi—according to the side you mentioned that says the gorings habituate it to become a goring ox, then one can understand why we don’t extend it to those it didn’t gore. That is what the Kehillot Yaakov says. He proves from this Maimonides that Maimonides understands the process of becoming forewarned as a process of habituation and not of evidence. Because if it were evidence, then it really would be an internal contradiction as I said before. If you have evidence that it gores only on odd-numbered days, then how do you have evidence that it does not gore the species it did not gore on the even-numbered days? It did not gore them because those were even-numbered days; it does not gore on even-numbered days. Therefore, says the Kehillot Yaakov, we are forced to conclude that Maimonides probably understands that the goring—the process of becoming forewarned—is habituation and not evidence. And then what? Then what it did, it became habituated to. What did it do? It gored those three species on odd-numbered days, so it became habituated to gore those three species on odd-numbered days, and therefore we limited both the species and the days. And that is a bit difficult, because the Talmud compares this to other presumptions where there is no room to say it is habituation. I said in the previous class and also noted it—I’ll return to it shortly. So that is the Kehillot Yaakov’s claim. Now, just as a side note, even if this is habituation, after all on day one it gored a donkey, on day three it gored a camel, and on day five it gored a duck. Fine? Why—why did it become habituated to gore those three species? It gored each of them once. If it takes three times to get used to an action such that it enters the ox’s nature, then it did not perform the same action three times. It did it to three different species. Now if you tell me that it doesn’t matter what animal it gores, then again it should be forewarned on odd-numbered days for all animals. Because if you say it doesn’t matter that each animal was gored only once—if it gored three different ones three times, then that already suffices, then they combine, that is what is called forewarned. Fine, then if so it should be forewarned for all species, not only for those three. But I think that even the habituation claim is incorrect here. Even according to habituation, one cannot understand Maimonides. And I’ll say more than that: according to the mechanism of evidence, one actually can understand Maimonides. In these classes I keep reversing what the later authorities say, like in the previous class. Here too, it is simply the opposite of what the Kehillot Yaakov says. If this is habituation, then it should be forewarned on odd-numbered days for all kinds of animals. Or alternatively, not be forewarned for any of them, because it gored each type only once. So how did it become habituated to gore that type? Now on the other hand, if this is evidence, I don’t understand what bothered him in Maimonides’ words. What did he say there? He said: if you assume that it gores only on odd-numbered days, then what is your evidence that the reason it did not gore on even-numbered days is because those are species it doesn’t gore? It did not gore them because those were even-numbered days. It gores only on odd-numbered days. And vice versa, if you say it gores only those three species—sorry, if you say it gores only those three species—then why with respect to the other species that it didn’t gore did it not become forewarned? It did not gore them because those were even-numbered days. So it should be forewarned for all animals, not only the three it gored. That is the Kehillot Yaakov’s question. But the answer is very simple. I don’t understand the question at all. In the end, what do you have evidence for? What is the minimum about which you have evidence? Clearly it cannot be both, but I don’t know which of the two rules is the correct one. Either it gores all species on every odd-numbered day, or it gores only those species on all days. Right? Those are the two interpretive possibilities here. Agreed? Now what do you do when there are two interpretive possibilities? Remember that forewarning is a change. Meaning, it had the presumption of being innocuous, and you want to apply to it the presumption of being forewarned. Right? You also want to extract more money from it—not half damages but full damages. The burden of proof is on the claimant. So why do I have proof that the ox is forewarned? Only for odd-numbered days and those three species, because that is the intersection between the two different rules, and I don’t know which of them is correct. So what do I do? I say: let’s take the intersection—that is certainly correct. Beyond that I don’t know. Whether to apply it to the other species or not, whether to apply it to the other days or not—one thing I do know: on those three days, for those three species, it is forewarned to gore. That I know. No, but you asked earlier: why should each species itself count as making it forewarned with respect to that species? That question I am not solving. That question I am not solving. That is a question on Maimonides. It has nothing to do with me or with the Kehillot Yaakov. Why does Maimonides think those three species combine, yet it remains limited to those three and not all species? That is a general question on Maimonides; I have no answer to it. But assuming I accept this thesis of Maimonides, how do I understand this strange law that says it is every other day and only the species it actually gored? After all, those are two things that contradict each other. And true, they contradict each other because I don’t know which of the two generalizations is the correct one. I have two possibilities: either it gores on every odd-numbered day whoever it meets, or it gores all those species whenever it meets them; it just happened to meet them on odd-numbered days. Right? Those are the two interpretations I can give to the cases I have encountered. Now what do I do? What general rule, or what presumption, do I apply to this ox? What is the general rule? What is the correct generalization from those cases? I have two possibilities and no way to decide between them. What do we do? We take what is certain. What conforms to both rules there is certainly correct. Everything beyond that, I don’t know. Therefore it is forewarned only on odd-numbered days and only for those three species. Simple. Meaning that if one of those rules becomes clear—if next week it gores intermittently with respect to days the same… the same animal—then the Rabbi says the ruling will be renewed, that it is forewarned for all animals. Correct. A novelty. No, but it also won’t be renewed retroactively, because you need to warn the owner. Certainly, certainly. Even according to the one who says the warning is for the ox and for the owner, yes. So this example basically just shows us how problematic the process of generalization is. I brought it in order to show just how problematic the process of generalization is. Because we have a set of cases we have encountered—what I called a generalization from a sample. That is my sample. And now I want to determine on the basis of those cases a general law. But I have many ways to generate a general law of which those three cases are particular instances. The process is not one-to-one. Take a set of cases—you can generalize them in many, many ways. So what do you do? How do you choose the correct generalization? So Maimonides, for example, says: do the minimal one. But even Maimonides— So why not say: if he already seized payment from him? What? According to Maimonides, if the injured party seized payment, would we take it away from him according to Maimonides? Good question. There is room to discuss that. The question is whether legal doubt allows someone to seize and keep property or not. We won’t get into “a priest who seized property” right now, but yes, there is room to discuss it. A novelty, because Maimonides usually writes explicitly when something is because of doubt. There are several places where Maimonides does not write that, and the commentators on Maimonides say: but one may seize. No, perhaps one could argue that the ox has its original presumption that it is innocuous, and as long as it has not left that, yes, then fine, it depends on the definitions of when seizure is effective. We won’t get into that now. But on the theoretical level, yes, the claim is basically—what you actually mean to ask—is whether Maimonides’ ruling is a ruling out of doubt and not a definite ruling. Correct. And it isn’t definite because of the original presumption. Right. So I’m saying yes, I claim it is a ruling out of doubt. It could be that because of the original presumption we say this doubt remains. Meaning, okay, but still the ruling is a ruling of doubt. Meaning, in the end, because I am uncertain whether the generalization is this or that, I take their intersection. Fine? I have a simple question. If the question of three times is the question of becoming forewarned—Rabbi Yehuda says this is evidence, right? The matter of its gorings. It is evidence, not habituation. No, what Rabbi Yehuda says is part of the dispute between Rabbeinu Peretz and the Maharam of Rothenburg. Fine, I understand that. But when he learns it also from the verses in the Torah, is there any indication that anyone here intends to specify whom it gores? Is there any indication that the Torah even wants to specify which animals it gores? Or does the Torah just talk about one that has gored yesterday and the day before, and that’s it? No, the Torah only talks about that. That is what appears. But from there the reasoning of the Sages enters. What do you mean? The Sages always interpret according to their reasoning. Yes, but ostensibly there is no reason here to go and start specifying the kinds of animals it gores. Why not? There absolutely is. That is the whole point. Once the presumption is that it is an innocuous ox, in order to turn it into a forewarned ox you need proof. Now you have three cases in which it gored. And the question is: why does that constitute proof? What is the rule for which those three cases constitute proof? I have several possibilities. And since the burden of proof is on me when I want to turn it into a forewarned ox, I have not met the burden of proof because I remain in doubt. That methodology you spoke about—the simple way of analyzing things—what was that philosopher’s name? William of Ockham. Yes. Shouldn’t we also apply that here and say, listen, there is a problem of an ox and I need to move it from one state to another. An innocuous ox is one that does not gore. A forewarned ox is one that gored three times, and with that I’ve finished the story. But that’s exactly why I say there is a presumption here. Ockham’s razor does not extract money. There is a presumption here. And now the question is whether evidence based on Ockham’s razor is enough to extract money. You want to extract money from me so that I pay full damages and not half damages, even though this ox just gored a fox now, not even from the species it gored before. And now you say Ockham’s razor says that if it gored three species, it is probably forewarned to gore all of them. Okay—but there is also the possibility that not. Now the question is what advantage the simpler thesis has over the more complex thesis—how much stronger is it? And that matters because when you come to override a presumption and extract money—here it’s both things. You remove the ox from its presumption, from innocuous to forewarned, and you extract money from me. Okay? And in that case the question is whether… Rabbi, Rabbi, Rabbi, the Torah was given to us, right, at Sinai, and at Sinai what was written was what was written in the passage in the plain sense, about the forewarned ox and the innocuous ox. At Sinai that was written, yes, okay. Let’s assume. So the entire chain of transmission from then onward, ostensibly, if it comes to decide here about the conduct of oxen, it should be researching the psychology of oxen. That takes a lot of time. That perhaps would require some experimental psychology that would need to be… I talked about this, I talked about it even in this series. The Sages did not do research, and the Sages also did not do statistics, by the way. The Sages were not aware at all of the need to compare your sensible thesis to reality, yes? Aristotle with heavy and light objects. That was ancient thinking. You ask whether we would do the same today—the answer is no. Fine. I assume that here, even in practical Jewish law, I would nullify the law of the forewarned ox. I would go to people who have knowledge about the nature of an ox, and I would prefer to rely on that rather than on all sorts of three-times presumptions or these rabbinic formalities. Very well, but that is not important, because I am not currently studying monetary damages. So that is a very significant statement with regard to present-day halakhic decisors, if they want to discuss monetary law. Today’s decisors won’t say that. They’ll say fine, the Sages said this in the pre-research approach, whereas today we know better. Today’s decisors won’t say that. Fine. Okay. In relation to what Ezra said about Ockham’s razor, it’s interesting that this is in fact a dispute among the Tannaim between Rabban Shimon ben Gamliel and Rabbi about whether three… Right. And the ruling is three in monetary law and two in prohibitions, which is interesting, because Ockham’s razor already operates on two, and apparently you need a stronger Ockham’s razor to extract in monetary law. Correct, and we also saw this in the signs of an insane person. With the signs of insanity you basically say the simpler explanation is three. And with two it is not enough that it is simpler. Also with two, the explanation… that too is interesting; it really is a question. Because there it is indeed a difficulty, since there it very much concerns prohibitions. That is exactly the indication that the mere fact that simplicity has an advantage does not mean that the evidentiary advantage is absolute. Because there are degrees of simplicity, you know—something a bit simpler than the other is a bit simpler, but maybe not enough evidence to extract money. But if something is much simpler than the other possibility, then it does extract money. Right. No, I’m just asking a question not connected to the reasoning here. In general we know that the law follows Rabbi in prohibitions and Rabban Shimon ben Gamliel in monetary law. Yes, in Bava Metzia there it is not so simple. Never mind. It is not certain the difference is prohibitions versus monetary law. It may be that the difference is in the type of presumptions. The later authorities discuss this. Meaning, it may be about types of presumptions, not necessarily prohibitions versus monetary law. But never mind, that’s not… I even once saw, I think, someone who wanted to argue that one is evidence and the other is habituation. Really? Yes, but fine, I’m not sure that actually stands the test of all the cases; I don’t remember right now. Fine. What? What the Rabbi said earlier may perhaps resolve the question on Maimonides. If we go with the approach of narrowing liability when extracting money—before we obligate a person monetarily, we go with the narrower approach—then one could say that whichever way you look at it: on the side that it gores all species, which is what connects the three species, then in any case he is liable as a forewarned ox. And on the side that it is only those species, then even though each one of those species is only one instance, that already suffices whichever way you look at it to obligate him for them. But what? That is the same question we asked before. Clearly there is some difficulty in Maimonides’ words regardless of the Kehillot Yaakov and all that. There is a difficulty as to why Maimonides chooses to combine three single gorings of different species. I’m saying that what the Rabbi said earlier resolves it, because we go with a narrowing approach. A narrowing approach in extracting money. Now if we go with a narrowing approach, that means: what is the common denominator among all these species? That it gored them all. So on that side, that there is a common denominator among all of them, then he is liable for all of them. But if we go with the narrowing approach that it is only them, then at least it is only them. No, no, I don’t see the explanation here. It is three times. It gored one species each time, each time, each time a different species. Yes, but we have no common denominator to say… Correct, there is no common denominator, and therefore it is innocuous. You are assuming it has to be forewarned, and then asking what the minimal common denominator is. No. If the minimal common denominator does not exist, then it is simply innocuous. That’s it. But if we have no general common denominator, then we must say it is specific; there is no middle option. Specific—so that means either exactly these three or all of them; we have no middle level. So why is it certainly liable? No, it is innocuous. What? There are innocuous oxen in the world too, right? It is innocuous. It gored an ox once, a fox once, and a donkey once. Fine, then it is innocuous, that’s all. If it gores a donkey two more times, it will be forewarned for donkeys. Fine, but in the meantime it is innocuous. That too is an option. And it is not clear why Maimonides ignores that option. Maybe one can say something, but on the face of it that is indeed difficult. I don’t know why. Especially since we are talking about extracting money and moving it out of the presumption of innocuousness. You are doing both: moving the ox from the presumption of innocuousness to the presumption of forewarning, and extracting money from the owner. So the burden of proof is doubly on you. To say that this is so strong that it is forewarned for those three species? I don’t know. It is not clear to me. Anyway, that really is not important for our purposes, because what I wanted was only to use these passages to illustrate the problematics of the process of generalization. Just one note—I do still want to close off the issue of the three-times presumptions, and then we’ll return to the overall line. Daniel, earlier you asked why we compare cases in which there is what? Yonatan, that’s my brother’s computer. Okay. So we’re meeting tomorrow? Right. Okay. So you asked why we compare processes of habituation to processes of evidence. I think the later authorities talk about this a bit, and in fact many of them, by the way, ignore it—which is also strange. They investigate whether this process of forewarning is evidence or habituation, and they completely ignore the comparisons the Talmud makes, for example among the sages of Usha concerning presumptive ownership of houses, where they compare the forewarned ox to the three-year presumption. In the three-year presumption it is certainly evidence. The three-year land presumption is certainly evidence. Now if you say there is an opinion that in the case of the forewarned ox—its process of becoming forewarned—it is habituation, then what is the point of comparing them? And for some reason, again, these are passages I saw a very long time ago. Many later authorities—some note it—but many completely ignore it. I think the Kehillot Yaakov even has a long section in Taharot, section 47 I think, maybe in the old edition—there are two editions of Kehillot Yaakov. And there he has a very long section on all the three-times presumptions, and even there I don’t remember whether he addresses this issue of how one compares habituation to evidence or not. Not sure—I’d have to look there, but I recall that there too I felt that issue was missing. In any case, I want to argue that this too does not bother me, the fact that evidence is compared to habituation. Why? Because in the end, clearly we are talking about a formal determination. Right? It’s not that after three times the evidence is crushing, now it’s 100% true, whereas after two times it’s nothing. Here too, you need to draw a line from the standpoint of Jewish law. So they chose to draw the line after three times. By the way, in saying “He makes the wind blow” it is after ninety times, not three, but that’s… that’s the popular practical difference. What? “He makes the wind blow”? Earlier there was discussion about that. So there too, however, it is not three but ninety. Clearly the number three is some typological number that is used—but three of what? In that case it is three months, ninety times, or three prayers for a month. Or three daily prayers over a month, yes? Three times the prayers of a month, yes, something like that. So clearly we stick to the number three not because that number itself turns it from zero to one hundred. Is there some textual support—well, for three? From the forewarned ox one can bring some… No, because there already he applies it to fields, say, a field from which one can eat the… that is what I recall from Bava Batra. But that is among the sages of Usha. That’s not among the sages of Usha. Right, but still the Talmud sticks to three. No, no—if it’s not among the sages of Usha, then maybe the whole issue of the three-year land presumption has nothing to do with a three-times presumption. Only the sages of Usha are the ones who connect it. In any case, the claim is that once Jewish law draws a formal line, one can certainly understand that both in cases of habituation and in cases of evidence, if I need to choose a line, I draw the line after three times. After all, in either case it is a formal determination. It is not that if after three times it becomes evidence, that means after three times it also truly becomes habituation. It is not that there really is a link between the passages. But if you need an accumulation of things either for evidence or for habituation, and from the standpoint of Jewish law the number three is the determining number, then one can certainly understand that they established it both for evidence and for habituation. Okay? It is true that we rule like Rabban Gamliel in one place and like Rabbi in another—that is indeed a comment on this whole matter. Because seemingly I would expect: Rabbi and Rabban Gamliel, fine. Each one on his own, either two or three—that’s a legitimate dispute. But once I rule in Jewish law, why rule three here and two there? I mean, make a uniform line in the law already. So that is a valid point. But I think nevertheless, clearly the number three—you know, it’s like I mentioned the Shakh, I think, about a three-year-old girl whose virginity can be restored, where he brings the Jerusalem Talmud, yes, that God “finishes it for me,” something—he brings some verse, yes, that nature was handed over to the Sages, and if a religious court intercalates the year, yes, the rule is that a little girl under the age of three whose virginity was torn, it returns. Until age three it returns. After age three, gone. It no longer remains open. Fine? What happens if the girl had relations after age three, but then suddenly the religious court intercalates the year and she becomes younger than three? Yes? The sugya of an adult who became a minor, as they say. Usually we are used to a minor who became an adult, but there are passages about an adult who became a minor. This is one of them, for example. So the Jerusalem Talmud says that indeed the virginity returns. Because the determination of the Sages, the halakhic determination, changed nature—that is seemingly what is written there. And the Shakh brings this and gets very excited about it. Well, these are strange things of course; this doesn’t begin. Meaning, clearly the intent is that the line is a formal line. What is three? There is a girl for whom it will return at three and a half or at four, and there is a girl for whom it happens at two and a quarter. Right? Overall it is around age three, and we need to set a halakhic line because we do not know how to check for each girl how it works. So a halakhic line is set. And that halakhic line is age three. Now what happens when the religious court intercalates the year? Okay, in any event we established a formal halakhic line. We determine the formal halakhic line to be age three according to the Hebrew calendar. Who determines the Hebrew calendar? The religious court. Fine? So therefore the formal line passes at age three, and if the religious court intercalates the year, then yes, her virginity returns. But not because something in the girl’s physiology actually changed; rather, the halakhic assumption is that since she is not yet three years old, we assume that her virginity returns. Fine? That is what the Shakh really means there. Huh? That is what the Shakh really means there. No, I don’t read him that way. But if he means that, then all is well. Rabbi Levi Yitzchak of Berditchev might perhaps interpret the Shakh that way. Maybe. But Hasidim don’t… No, but that really is what the Shakh means there, that he basically connects the monthly cycle with the average interval. Okay, that is indeed the plain sense of the Shakh’s language too—again, I don’t remember at the moment, it’s not in front of me—but that is the plain sense of the Shakh’s language. Also from his excitement there it is pretty clear. I mean, otherwise what is the big deal? What is the novelty? Fine, obviously, because you are saying what determines it is age according to the calendar, not biological age. Fine, obvious—what’s the big deal? All this excitement around the verse and so on. No, because Nachmanides, sorry, brings the Shakh there and says that one cannot say that they spoke correctly—that the sounding of the shofar by the religious court at the start of the month causes it—because it clearly does not cause it. On the contrary, then it is hard to say the intent is simple, that the very establishment of the month causes the… You’re trying to convince me that it’s hard to say. I fully agree. The question is what the Shakh says; one has to read him. And I think that when you read him—I at least, again, years ago, we’d need to read him again—I got the very clear impression that he means that kind of mysticism. He does not mean what I am saying here, but on the contrary, if he does mean this, then he is a sensible Jew and I’d be happy to be in his company. Meaning, if he means this, then excellent, I have support. But I also have support for what I’m saying. In general one can investigate whether it is a sign or a cause. Like two pubic hairs, for example, with regard to the age of maturity. Okay. If I claim this is such a formal determination, how does the Rabbi define it? What is the problem? I mean, I’m trying to understand. It is both a sign and a cause; it doesn’t matter. It doesn’t matter? Everything is a formal line—whether sign or cause, what difference does it make? Okay, so that was just to close the issue of the three-times presumptions, habituation and so on: it is a formal line. Therefore there is no need to panic over differences between one area and another, because we are not really making a substantive comparison between them. We are saying: if you draw the halakhic line at three, then the logic says you should draw it here too at three, because three is your number. Not because it really happens in the same way. There does not really have to be a direct comparison here—derive from it and derive from it, and then return to its own place. Fine, anyway, let me return to us. What I wanted to illustrate through these passages is the problematics of the process of generalization. Now what does that mean? It basically brings us to the problems raised by David Hume. David Hume basically claimed that our generalizations have no real foundation. They are a result of our mental structure. It is not a claim about the world. If I have seen that the sun rose every morning until today, that does not mean it will rise tomorrow morning too. We, as human beings, are used to making generalizations. If it happened until now, apparently it will continue to happen. But you have no proof that it will continue to happen. Not only do you have no proof that it will continue to happen; there is not even any probabilistic calculation of that kind. Meaning, it is simply an assumption of our mode of thought that what has happened until now will apparently continue. It is not certainty, but apparently it will continue. Therefore, says David Hume, generalizations are really acts that create claims about us, not about the world. And from there come various philosophers of science who argue that laws of nature, which are also formed by generalizations from a sample, are claims about us, not about the world. I do not really mean to say that in the world every two massive objects attract one another. Rather, I mean that from the standpoint of my observation it is convenient for me to organize the events I observe by means of this law of nature. Because that fits better with my way of thinking. But I do not presume to claim that this is really what happens in the world itself. It is a claim about the person, not about the object. But I never understood that, really—I just couldn’t understand that point. After all, obviously, didn’t David Hume make generalizations all day every day? He did make generalizations, but he said: I make generalizations because I’m accustomed to it, not because it is true. So he contradicts himself after becoming aware of it and saying, wait a second, how am I going to board a plane? I need to make a billion generalizations for that. So how does he… Those are questions I’ve asked many times. Exactly—but how? So you can’t understand David Hume that way. It just seems to me… No, I’ve spoken with quite a few such David Humes, and I’m telling you from personal experience, direct experience: that is what they tell me. I asked them, how do you board a plane? And he says: because that’s what I’m used to; I have no better option. If I stay on the ground, maybe a plane will crash on my head. I have no way to conduct myself in the world if I seek the absolute truth; it is not accessible to me. So I act according to what I’m used to—what can I do? And the fact that millions of people boarded a plane and landed safely—that doesn’t say something, even statistically? No, because that was in the past. What does that say about the future? That is exactly his argument. It’s really terribly ridiculous. What does it say? Do you have statistics? What does the past say about the future? How would you determine that statistically? What would the calculation be? I don’t see a statistical calculation that would support it. David Hume gets to the terminal at Ben-Gurion and has to decide whether to board a plane to England. Now they ask him, tell me, what does your generalization say? Board the plane. But you say that has no basis in reality. You don’t… what do you think the odds are, how much risk do you think you’re taking? But even if he stays on the ground, if he stays on the ground he might suddenly burn. And I ask now—not that, just that on the ground he’ll arrive safely. I’m saying: if you board the plane, what do you think your chances are of surviving or not surviving? How much money would you bet on arriving safely? Zero. Zero. What? He would say zero money that he’ll fly back safely? Yes. I’m simply telling you from personal testimony. I’m asking—I don’t know if you heard this from me, but you may well have heard it from me more than once. I ask all kinds of people these questions, and that is the answer I get from them. In a moment we’ll get to it—I’ll get to it. In principle, can one just understand what practical difference it makes? Whether the world behaves that way or that’s just how we perceive the world—what difference does it make? I’ll talk about that in a bit. Since there is a practical difference, I think one can decide who is right here. Although it’s not easy to find the practical difference. We’ll talk about that soon. In any case—well, I don’t know if soon, but I do intend to get to it as well. In any case, the problem raised by David Hume, the problem of induction—induction meaning generalization, not mathematical induction but scientific induction—the problem he raised is basically that these generalizations are simply the product of our way of thinking. It cannot be a claim about the world. Okay? Now that is probably what underlies the view that a majority not before us is weak—weaker than a majority before us. Because a majority not before us is the result of a generalization from a sample. And generalizations suffer from the problem David Hume presented. Who knows whether your generalizations are correct? You think in a certain way. Here Maimonides thinks the correct generalization is that it is forewarned to kill a donkey and a camel but not others. The Raavad thinks the generalization is that it is forewarned for all animals. Someone else might think altogether—me, for example, if it were up to me, I would say it is innocuous. It is innocuous. It gored on the odd-numbered days, yes, and it gored three different species. So in my opinion it is innocuous. Okay, so who is right? I don’t know who is right. To each his own generalization. It is simply an expression of the problem David Hume described. You see that when you have a set of data, a collection of cases, facts, observations, however you want to call them, the general law you create from these observations can be many laws; there can be many laws. You do not know what the correct generalization will be. You can define many, many groups of which these cases are particular examples. Okay? The examples mentioned earlier from Wittgenstein—actually it’s not Wittgenstein, I saw it in someone else, but following Wittgenstein. I give you a sequence, a psychometric exam: 3, 5, 7, what is the next number? Any number. We’re used to saying 9. The first thing that comes to mind is 9, right? Why? Because you assume it’s the odd numbers: 3, 5, 7, 9. Someone else could say 11, because these are the primes. 3, 5, 7 are prime; 9 is not prime, 9 is 3 squared. 11 is the next prime. So if the sequence is the primes, then the next is 11. If the sequence is the odd numbers, then the next is 9. And besides that, of course, you can put in whatever number you want—that’s Wittgenstein. Meaning, I can show you a rule that puts negative pi squared as the next number. No problem, I can generate such a rule for you, and that will be the correct number. In psychometric exams, as I usually say in contexts where Wittgenstein comes up, they are not testing talent. Psychometric exams test conventionality. If you think conventionally, you excel. If you think outside the box, you are not admitted. Because someone who says the next number there is negative pi squared is thinking outside the box, but he is no less correct than someone who says it is 9 or 11. He has his rule, and he can show that rule and justify his choice of negative pi squared. Yes, but there’s no point in admitting him to the university; he won’t be able to study. Why? Because his lecturer will say to him, look, with 3 it’s like this, with 5 it’s like this, with 7 it’s like this, and so on. Meaning, understand on your own how it continues. But that fellow’s mind is built differently, so from his standpoint the next number is negative pi squared. So he’ll understand that the next odd number is negative pi squared. His lecturer will teach him about odd numbers and say: 3, 5, 7, and so on. Those are the odd numbers, right? You can’t list all the odd numbers in class; there are infinitely many. Okay, so what do you say? 3, 5, 7, and so on. But what does “and so on” mean? If you have a conventional mind, then yes, you rely on the fact that all the people inside the box will say that means 9, 11, 13, and so on. Okay? There is someone whose mind is outside the box. He is not any stupider than they are, but there’s no point—he won’t be able to study at the university. He won’t understand what is being taught, so rightly he is not admitted. But he is not not admitted because he is less intelligent. That is true at least if the one who gives negative pi squared actually explains it with some rationale. Because if someone just throws it out without a rationale, then he really is stupid. But if someone says to me, look, it is negative pi squared, and shows me the formula that led him there, then he is no less smart than anyone else—maybe smarter than others. Usually the people who fail the psychometric are of the first type, not the second. They throw out answers they cannot justify. It’s not that they have an outside-the-box rationale, a different rationale. And therefore the filtering also filters out fools. But there are some who would be very clever and still be filtered out by the psychometric. They would be filtered out for being outside the box. You must not be too far outside the box. By the way, really, you must not. It’s not good. It’s not good to be outside the box. Because if you are outside the box, you cannot communicate with people; even if you are very smart, it won’t contribute anything to anyone. You cannot speak the same language. But the Rabbi would agree that it is important to keep openness also to what is outside the box, right? That is important. Of course. So maybe, maybe that’s what David Hume meant—that there is no certainty in generalization, no certainty. That there is no certainty is a very small novelty—there is no certainty in generalizations. His claim is that it is subjective, not just that there is no certainty. I mean, nobody says there is certainty in generalizations. What do you mean? Has it never happened to you that your generalization was disproved? It has happened to me quite a bit. Obviously—to all of us. In science too, of course, but outside science. Nobody claims that a generalization is certain. That’s just naïveté. I didn’t quite understand what he is claiming. Is he claiming there are no laws of nature? What determines the way the world behaves? Laws of nature are the way we choose to organize phenomena. But there are no laws of nature? In nature itself there are no fixed laws governing things? So what causes the world to behave? Randomness? Randomness doesn’t cause the world to behave, but there is no cause. Meaning, you don’t know. You don’t know. The fact that the world behaves according to fixed laws… Again, you cannot know how the world behaves. Maybe there are laws, but they are not necessarily your laws, the laws you think. Fine, but there are laws. Does he agree there are laws? No, he doesn’t know whether there are laws or not. We have no way of knowing. Why? It’s obvious that the world behaves according to fixed laws. Everything we think, everything we think derives from our way of thinking. True, but we see that the world acts according to fixed laws and not randomly. It does not accidentally happen that someone threw a ball upward and it kept flying upward. We are forced to see the world as acting according to laws, because our minds cannot grasp a world that does not operate according to laws; we will generate a law that explains even that lawlessness. Because we are compelled to think in terms of laws. That is his claim. That is probably too high for me; I don’t understand it. Okay, next. Either it is too high or it is too low, because you are right. But there are many people who think this way. There are—I’m telling you—I’ve had quite a few arguments with such people; I already have experience. You really stand there astonished. There are people who genuinely cling to this view and declare that they truly believe it. I don’t believe them, but that is what they declare. Fine. In any case, for our purposes, the weakness of a majority not before us is basically rooted in that same ambiguity of the process of generalization. And we saw in the Talmud in Chullin—the straightforward reading of the Talmud is that a majority not before us is weaker than a majority before us, right? Why? Because the Talmud says that a majority before us is learned from “follow the majority.” Then it asks: fine, I know a majority before us, such as the case of nine shops, but from where do we know a majority not before us? And it tries all sorts of things, and in the end remains without a source. Then Rashi there completes it—or says it’s a law transmitted to Moses at Sinai, whatever—he completes it in some strange way. But the Talmud remains without a source, meaning from the Talmud’s perspective, the fact that you have a source for a majority before us still leaves the question of a majority not before us open. And if we follow a majority before us, that still does not mean we will follow a majority not before us. So Rabbi Shimon Shkop says, in Shaarei Yosher, Gate 3, that one sees from there that a majority not before us is weaker. And that is the accepted view among the commentators. Because that is the simple reading of the Talmud. But to see that in monetary law there is no regard at all for a majority before us—in monetary law there is no regard for a majority… Why not? Of course there is. Where is there regard for a majority before us? In the case of the piece of meat and the shops—even if there are monetary implications, there is still a majority there. The question whether we follow the majority in monetary law is another question, but there is a majority there. That is the dispute between Rav and Shmuel. But there is majority in monetary law. What, there are passages about majority in monetary law too. There aren’t, because presumptions—a presumption, a presumption is not like a majority not before us? A majority not before us? It’s not so simple. There is the Pnei Yehoshua, and apparently it is the same thing. But there are distinctions made between them. In the Talmud itself it appears. After all, in the Talmud a presumption does extract money. For example, the presumption that a person does not pay before the due date—in Bava Batra 5—it extracts money, right? So how does that fit with Shmuel saying that in monetary law we do not follow the majority? No, that is a much stronger statistical necessity than an ordinary majority not before us. What do you mean? A majority is a majority—51% and 99%. No, I’m talking about a presumption. Fine, no problem. So Rav disagrees. Does Rav disagree also with the presumption that a person does not pay before the due date? No. Shmuel disagrees. Shmuel would not disagree with that presumption. Why? Because it is a much stronger statistical necessity. Why is it stronger? Because it is a much stronger statistical necessity in the presumption that a person does not pay before the due date. Why? A majority is a majority. This is a majority and that is a majority—what is the difference? Yes, but this is a majority that suffices even at 51%. Even 51% is called a majority. Listen to what your mouth is saying. You say that is 51%, so now you’ve said it is 51%; never mind whether you call it a majority or call it a presumption. The question is, is the difference in the percentages? Yes, it is a semantic difference. And there is a 99% majority—that too is a majority. Maybe that would be called a presumption. No. The distinction is not according to how large the majority is, whether it is 51%. That is called the difference between a noticeable majority and a non-noticeable majority. But that is not the distinction between presumption and majority; those are two different things. And there is a Pnei Yehoshua on this; I don’t remember anymore. I dealt with it once; I’d have to refresh my memory. On the simple level, a majority not before us and a presumption are similar. In any case, for our purposes, the straightforward reading of the Talmud is that a majority not before us is weaker. But of course, as one might expect, Maimonides says it is stronger. Yes, if the Talmud says it is weaker, then obviously Maimonides will say it is stronger, otherwise what would we do? We need to reconcile things, otherwise we’d become unemployed in the yeshiva. So Rabbi Shimon Shkop explains Maimonides’ position there. We spoke about the David Levi effect, if you remember; I explained what the reasoning is that a majority not before us is stronger. And in terms of the sugya, I said that after the conclusion—certainly as Rashi presents it—that in the end we also follow a majority not before us… What do you mean “in the end”? We knew that all along. But also that we found a source for a majority not before us, whether from a law transmitted to Moses at Sinai or from the verse “follow the majority” itself, then there perhaps the hierarchy really changes. And Maimonides says what he says according to the Talmud’s conclusion. In the initial assumption, the Talmud really assumed that a majority not before us is weaker, and therefore the source for a majority before us is insufficient. But in the conclusion, Rashi says that in the end they also learn it from the verse “follow the majority.” How? Without the Talmud saying that at all—only Rashi says it. How? Apparently Rashi understands that according to the Talmud’s conclusion, at least, it is not true that a majority not before us is weaker, and therefore “follow the majority” suffices to teach both kinds of majority. And perhaps that is Maimonides’ view. In any case, if it is a law transmitted to Moses at Sinai, then no. But if it is learned from “follow the majority,” then it seems quite clear like Maimonides—two explanations in Rashi. In any case, for our purposes, what we see here is that there is a reason to resist a majority not before us because it is based on generalizations. Generalizations are always problematic; you never know how to generalize, what to generalize. There are all kinds of generalizations you can make on the basis of the same set of cases. On the other hand, a majority before us is not based on generalization. You have ten shops, they are all before you, you know them directly—it is not a generalization from a sample. You are not talking about all people in the world based on the ten you know; you are talking about ten shops, and you know all ten. That is why many commentators say: therefore a majority before us is much stronger. By the way, for example, with respect to not following the majority in monetary law, some wanted to argue that with a majority before us, yes, we would follow the majority even in monetary law because it is stronger; only with a majority not before us we would not. Tosafot says explicitly not like that, but there are some who wanted to argue it, already among the medieval authorities. In any case, what is Tosafot’s difficulty? Both in Sanhedrin and in Bava Kamma, page 27. Sanhedrin is page 3, there concerning judges. Yes, from judges. Now judges are a majority before us, since “follow the majority” is the source for a majority before us. So you see that with a majority before us, yes, we do follow the majority. But with a majority not before us, we do not follow the majority in monetary law. Therefore there are medieval authorities who want to argue that this is the distinction. This is a majority before us and that is a majority not before us. So again we see that a majority before us is stronger, because in fact it works even in monetary matters where a majority not before us does not. So that is the straightforward view. Interesting, because a majority before us certainly is not statistics. That is a big question. I also think it is not, and I spoke about that in one of the previous classes. I’ll get back to it later. Sorry, sorry—the claim is that Rabbi Shimon Shkop says a majority before us is not statistics, but he says something correct for the wrong reason. His reasoning is nonsense. I spoke about that in one of the previous classes; in my opinion his conclusion is nevertheless correct, that it is not statistics, because you cannot—remember, I explained that you cannot conduct an experiment that would demonstrate that statistic. It is a priori reasoning. There is no way to deliberately lose pieces of meat and afterward check which shop they came from. Well, there is if one plans a very, very sophisticated long-term experiment, but nobody does that. Our reasoning is not based on an experiment. In any case, that is the strength of a majority before us. But—and I’ll only get to this in the next class—I want to argue that in the end there is also a lot of sense in what Maimonides says, that a majority not before us is stronger. And for that we will have to return to Hume’s problem of induction and see how to solve it, and where that solution is relevant and where it is not. Okay, so I’ll stop here. Any comments or questions, if there are any. Yes, in the passage where the Rabbi explained the ox-donkey-camel case, that because of the narrowing interpretation we say it’s only that, there’s actually a problem, because what happens with uprooting the presumption? Meaning it’s not only a narrowing interpretation to avoid extracting money, because with uprooting it, it will basically become… As for uprooting—when you uproot the presumption of forewarning, there are two opposing things here. On the one hand, you are going against the existing presumption, because you want to restore it to being innocuous, but in terms of extracting money, you’re actually not extracting money; you’re retaining money, right? Because you want it to pay half and not full damages. So doing that should be easier than turning it from innocuous to forewarned. I didn’t understand. If afterward there come three times of a wolf, say. So I’m speaking generally first. In general, to move you from innocuous to forewarned requires more unequivocal evidence than to return you from forewarned to innocuous. Okay? Now the question is how much more unequivocal. That is why I prefaced it by saying I don’t have a sharp line, and now one can debate, as they debate in Jewish law, one can also debate on the return. But yes, there are various opinions also on the methods of returning from forewarning to innocuousness. By the way, I now recall that there are also medieval authorities who want to argue this in Yevamot, in the dispute between Rabbi and Rabban Shimon ben Gamliel—whether it is two times or three times. Why in monetary law is it three times? Because in monetary law you extract money. And that is what I wanted to argue—for extracting. Exactly. The point is that stronger proof is required in order to extract money, therefore it needs three. Okay? Fine. Either that is the difference or it is not the difference, but clearly the strength of the evidence is a function of the presumptions against which you are working. If it is the presumption of the ox, then that is one level of evidentiary strength. But if there is also the financial possession of the owner of the ox, that adds another factor, and then perhaps the requirement will be greater in order to extract that money. But in order to keep the money, you only need to leave the ox in its current presumption; as for the money, you are trying to retain it, not extract it. So that will be easier. Good. Okay then, goodbye. Sabbath peace.