Doubt and Probability — in Halakha, in Thought, and in General — Lesson 15
This transcript was generated automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Majority that is before us and majority that is not before us
- A piece of meat from ten stores and a priori reasoning
- Majority, clarification, and how to ask a probability question
- Rabbi Shimon Shkop: majority as sides and formal law
- Separation, fixed status, and the Mordechai in Chullin
- Statistics as a continuation of assumptions, not as their source
- David Hume’s problem of induction and the weakness of a majority that is not before us
- A presumption after three times, an ox forewarned after repeated goring, and signs of insanity
- “There is no presumption for coincidences” and the need for a unifying explanation
Summary
General Overview
The lecture draws a fundamental distinction between a majority that is before us and a majority that is not before us, and argues that one cannot be learned from the other because they rest on different foundations: a majority that is not before us rests on generalization from a sample and induction, whereas a majority that is before us rests on a priori reasoning and on a structure of separation and sources that impose “sides.” The speaker rejects the Sefer HaChinukh’s explanation that the majority in a court is a majority that is not before us because “in most cases the majority is correct,” and instead formulates that the majority in a court resembles the majority among the stores not because of a sample but because of reasoning and a formal structure of sides. He then reads Rabbi Shimon Shkop, critiques his claim that a majority that is before us “is not clarification,” and suggests that it does involve rational clarification, even though a verse is needed to give it normative force. Finally, the lecture turns to the essential weakness of a majority that is not before us through David Hume’s problem of induction, and shows how halakhic discussions of a three-time presumption depend on assumptions about regularity and a unifying explanation, and not on “statistical” calculation itself.
Majority that is before us and majority that is not before us
The speaker states that a majority that is not before us is defined as a majority created by generalization from a sample, the way science arrives at laws of nature, whereas a majority that is before us rests on a priori reasoning that is not the product of sampling. He argues that the Sefer HaChinukh’s understanding of the majority in a court as an empirical claim that “in most cases the majority is correct” is an illusion, because there is no independent way to check in a sample who was right after the fact without relying on the very evidence that was presented to the court. He proposes that the reason to follow two judges against one is reasoning: when the judges are roughly equal in level, logic says the majority is more likely to be right, and this is a majority that is before us.
A piece of meat from ten stores and a priori reasoning
The speaker explains that even in the example of a piece of meat that separated from one of ten stores, nine kosher and one non-kosher, this is not a generalization from a sample, because the Sages did not base the ruling on an empirical experiment of “lost pieces” and tracing their origin. He argues that what looks like “clear statistics” depends on a prior rational assumption of equal chances of separation from the stores in the absence of distinguishing information, and that assumption parallels the assumption of equality among judges for the purpose of majority rule. He emphasizes that the difference does not lie in arriving at a ninety-ten distribution as such, but in how the distribution was produced: by sample or by reasoning.
Majority, clarification, and how to ask a probability question
The speaker critiques the probabilistic mistake that there is no difference between a sequence of “a thousand fives” and any other sequence because every sequence has the same probability, and argues that the correct comparison is between the event “a special result” and the space of “all the other non-special results.” He says that the way one formulates the question determines the result of the calculation, and that many failures in probability stem from assumptions and questions rather than from the mathematics. He applies this to a majority that is before us and argues that the question is not “from which store out of ten,” but rather “from the nine kosher ones or from the one non-kosher one,” and when the question is framed that way the rational case for following the majority becomes decisive.
Rabbi Shimon Shkop: majority as sides and formal law
The speaker quotes Rabbi Shimon Shkop in section 5, who identifies the law of the nine stores with the law of majority among judges by force of “follow the majority,” and explains his language as a formalization of “sides”: each store “generates a legal status” for the meat, and each judge imposes a side on the law, and the majority decides among the sides. The speaker argues that Rabbi Shimon Shkop is right that this is not a generalization from a sample, and that the language of “sides” fits a majority that is before us because of the structure of separation, but he disagrees with Rabbi Shimon Shkop’s conclusion that “in reality there is no clarification here at all.” He says there is rational clarification here, of a kind accepted even outside Jewish law, except that the verse is needed to establish that one may rule normatively on the basis of such clarification and need not be concerned for the minority.
Separation, fixed status, and the Mordechai in Chullin
The speaker brings the Mordechai in Chullin, who asks why we follow the majority in a court even though “anything fixed is considered like half and half,” and quotes his answer that “the judgment or the statement” separated from the judges just as the meat separated from the stores. He acknowledges that the formulation sounds strange on the physical level, but suggests that in essence there is separation here: the law under discussion is “born” from sources that impose sides upon it, and therefore resembles the structure of separation in a majority that is before us. He presents this as an explanation that supports the analogy between stores and judges not as a sample but as a model of sides and sources.
Statistics as a continuation of assumptions, not as their source
The speaker argues that saying “this is statistics” is empty, because every statistical calculation begins only after a distribution has been set, and the distribution itself is created from assumptions, observations, and generalizations. He distinguishes between a distribution that comes from positive information and one that comes from lack of information, and illustrates this with a coin: knowing that a coin is fair versus having no information and still betting on fifty-fifty because there is no basis to prefer one side. He compares this to the distinction in logic between deduction, analogy, and induction, and argues that any argument can be presented as deduction if one makes the implicit assumptions explicit, so the real issue is the quality of the assumptions, not the formal validity of the inference.
David Hume’s problem of induction and the weakness of a majority that is not before us
The speaker presents David Hume’s problem of induction as the claim that the move from past to future and from sample to rule lacks empirical and logical foundation, and that this is the essential weakness of a majority that is not before us. He suggests that anyone who claims that a majority that is not before us is weaker than a majority that is before us is really relying on the Humean concern that generalization from a sample may be unjustified from the outset. He adds that Hume himself lived in practice according to induction but interpreted it as a construction without real validity, similar to claims about the illusion of free choice.
A presumption after three times, an ox forewarned after repeated goring, and signs of insanity
The speaker presents a presumption after three times as a halakhic mechanism of induction: an ox that gores three times becomes forewarned, menstrual cycles are established after three sightings, if brothers died because of circumcision one refrains from circumcising the fourth, and a woman whose husbands died becomes limited in marriage. He cites the Talmud in Chagigah 3b about three signs of insanity and the dispute between Rav Huna and Rabbi Yochanan, and the Talmud’s reasoning that when all the signs appear this is like “one whose ox gored an ox, a donkey, and a camel, and so became forewarned for all.” He brings Rav Chaim’s question why three signs are decisive if each sign has an alternative explanation, and formulates the answer as a preference for one unifying explanation over an accumulation of separate explanations, where three cases provide sufficient normative significance to establish a halakhic status.
“There is no presumption for coincidences” and the need for a unifying explanation
The speaker quotes Mekor Chaim in the laws of Passover about finding three grains of wheat that split open in a pot, and emphasizes its rules: “We do not speak of a three-time presumption unless there is a causal factor such that it is plausible that this should be so,” and “there is no presumption for coincidences.” He concludes that induction depends on the assumption that there is regularity or an explanatory factor that unifies the cases, and if no such factor is found there is no justification for generalization even if the event happened three times. He notes that the case of a woman whose husbands died likewise depends on a hypothesis about the cause of death, and says that later he will discuss a passage in Yevamot that illustrates the problematic nature of induction in Jewish law.
Full Transcript
[Rabbi Michael Abraham] Okay, so we were talking about the distinction between a majority that is before us and a majority that is not before us, and about the course of the Talmudic discussion there, the Talmud’s conclusion, the course of the discussion. We talked about the question of which majority is preferable to which other majority, arguments in both directions. In the previous lecture I finished by explaining why, yes, Rabbi Shimon Shkop’s question, why the majority in a court is considered a majority that is before us, especially according to the Sefer HaChinukh, because the Sefer HaChinukh understands that we follow the majority in a court because in most cases the majority is correct. And we talked about the fact that when you think about it that way, it’s really a majority that is not before us, not a majority that is before us, because we are not looking at the three judges before us and asking ourselves, I don’t know, which one of them separated and asking whether he belongs to the two or to the one. That would have been a classic majority that is before us, like a piece of meat that separated. But there I’m asking what the correct law is, so why should I care that before me there are three judges, two saying one thing and one saying something else? Why is that a majority that is before us? Seemingly, the majority we are talking about relates to the group of all litigations, or all court panels in which there were disagreements of two against one, say courts of three where it was two against one, and the assumption is that in most of those cases the truth was with the two and not with the one. Then I say: in the case before us too, where there are two judges against one, apparently the two are right and not the one. That’s how the Sefer HaChinukh explains it. But that is of course a majority that is not before us, not a majority that is before us, a generalization and all those things. So I explained there, I said that this is not correct. It’s a mistake, an illusion. Because a majority that is not before us—and here exactly comes in the nuance I pointed out earlier—is a majority created by generalization from a sample. And that’s true, it also applies to laws of nature and so on, but the essence is not that it’s laws of nature; the essence is that it’s a generalization from a sample. Usually we arrive at laws of nature by generalization from a sample; that’s how science works. But in fact that is the definition of a majority that is not before us. So then what? When we look at how the majority described by the Sefer HaChinukh is formed, this majority that says that in most panels where there was a dispute between two judges and one judge, the two were right and not the one—that majority was not formed by generalization from a sample. Because we have no way of taking a sample, I don’t know, of fifty cases we encountered, say for the sake of discussion, and checking in those fifty cases in how many the two were right and in how many the one was right. That’s what we would need to do, and then we would reach the conclusion that, say, in thirty out of the fifty the two were right, and then I would say okay, so in general I assume that in all cases in the world usually the two are right and not the one, and in particular the case I’m discussing, the case before me. But it can’t be done that way, because I have no way of taking fifty cases and knowing in how many of them the two were right and in how many the one was right, because I have no way of reaching the correct answer other than through the evidence presented before the court. I have no independent way to check what the correct ruling is, and therefore I can’t know how the success of the two is distributed in the sample. So there’s nothing here from which to generalize. Rather, my claim is that this is reasoning. The reasoning says that if the judges are more or less on the same level, as the Sefer HaChinukh says, then once there are two against one, reason says that most likely the two are right and not the one—but that is reasoning, not generalization from a sample. And if that’s so, then it really is a majority that is before us. Because what happens in a majority that is before us? And then I said that in the case of a piece of meat that separated from one out of ten stores, nine kosher and one non-kosher, I found a piece of meat in the market, and yes, the city gates are locked, meaning it separated from these ten stores, and I ask whether it separated from the nine or from the one. So the claim is that there is a majority that is before us; we assume it separated from the nine. Now this too is not a generalization from a sample. It is not a generalization from a sample because we have no way of conducting an experiment on a sample and checking the distribution of outcomes. How would we conduct the experiment? Tell people to lose pieces of meat when we know from which store each such piece was taken, and then see how many of the lost pieces belong to the kosher stores and how many do not? You understand that you can’t really do such an experiment.
[Speaker B] Why not? Yes. How would you do it?
[Rabbi Michael Abraham] What, you’d instruct people to lose pieces of meat?
[Speaker B] Sure, do it, do a laboratory study, check
[Rabbi Michael Abraham] DNA and see that that’s the case.
[Speaker B] What DNA? I didn’t understand.
[Rabbi Michael Abraham] How? You can, you can artificially create an experiment if you define it that way, put marked pieces of meat into each store, but marked in such a way that the people themselves don’t notice it, maybe with laboratory testing. You could perhaps find a way, yes. On the theoretical level it may be possible to do such an experiment, although even there—how many pieces would get lost, how many you would find, how you would check—but let’s say maybe such an experiment is possible. But you understand that the majority the Sages determined—that the piece before us came from the majority stores—is not based on such an experiment, because no one ever did such an experiment. Therefore this is not a generalization from a sample, even if theoretically such an experiment might be possible, which is itself doubtful.
[Speaker B] But why do you need a sample if the statistics are obvious? Meaning?
[Rabbi Michael Abraham] What obvious statistics are there here?
[Speaker B] That obviously if there are ten stores and a hundred pieces of meat were lost, then most likely they came from the nine and not from the one. Why? How do you—where are you getting that from? Rabbi, don’t you know that statistical law?
[Rabbi Michael Abraham] I don’t know any such statistical law. If there were one, I assume I’d know it. But there isn’t one.
[Speaker B] I see. There are nine identical stores, with no characteristics that distinguish them.
[Rabbi Michael Abraham] You’re making an assumption, an assumption based on reasoning, that the chance of losing something from each store is the same, right? That’s what you’re assuming.
[Speaker B] Maybe.
[Rabbi Michael Abraham] The people who buy in one particular store, the bags given in that store are different, all kinds of things. You’re saying that in the absence of knowledge I assume there is no difference between the stores. Okay, that assumption is that same a priori reasoning I’m talking about. But that same reasoning applies equally to judges. There too the same logic says that if I have two judges equal in wisdom to the third, and the two say Reuven is liable and one says Reuven is exempt, the same logic—you can call it probabilistic reasoning if you want, it doesn’t matter what you call it—the same logic says the majority is right. In that sense the stores and the judges really are similar, right? But they are similar despite the fact that this is not a generalization from a sample but reasoning. Now you ask me why you need generalization from a sample when there is reasoning—fair enough, you really don’t. A majority that is before us is also a majority we rely on, you’re right, even though it is not a generalization from a sample. But it is still a majority of a different character from a majority that is not before us, which is based on generalization from a sample. That’s the claim. The claim is not that we wouldn’t follow the majority in those cases. The claim is that following the majority in those cases stems from a different root, from a different consideration, than the scientific consideration of generalizing from a sample. And because these are two kinds of majority, and we discussed which is stronger and which is weaker, one cannot be learned from the other. And it’s true, we follow both of them. That’s the reasoning you mentioned, and I assume most people would agree that in the absence of other information that’s what I would assume. But I would assume it because it is logic, not because of generalization from a sample. And therefore it is a majority of a different character. But—
[Speaker B] Doesn’t the rabbi feel that in judgment it’s a bit different? For example, let’s say I’m the only one who disagrees with all seventy judges, or the other two judges, or the other twenty-two judges. And I’ve heard them, I know they have the same IQ and the same absolute Torah knowledge, and they say exempt while I am convinced he is liable. But I know the rabbi’s reasoning, I believe in it, I support it, and I say: I can’t now say that I have no rational basis to disagree with them. No, I didn’t understand… how can one relate to this? But we don’t expect a person… if there is—how can one say at all that there is a priori reasoning that the majority is right? With human beings I don’t quite get it, it’s not that intuitive. It’s not so intuitive. There could always be a Newton. Newton didn’t think like everybody else. Until then people thought one thing and he thought something else.
[Rabbi Michael Abraham] Newton—Newton didn’t think like everybody else, but everybody else hadn’t thought like Newton. Meaning, they hadn’t thought through the issue. If they had thought through the issue and said something different from Newton, and you found there several people with Newton’s level of talent—which I very much doubt you would find—then fair enough, you would be right, I really wouldn’t believe him unless I checked it empirically. But that wasn’t the situation there.
[Speaker B] But I can give the rabbi an example, just an example. During COVID I developed an opposite view from the government’s approach of going after children and young people when their risk was seven hundred times lower, and instead I said, invest in the population at risk. And I managed then to meet the health minister, Yuli Edelstein. He sat with me for half an hour, and I explained my theory to him very patiently. Then he asked me a few questions and said, “Very impressive, Dr. Berger, very impressive, but I have a few questions. First question: the whole world thinks differently from you. No one thinks what you’re proposing.” I wasn’t alone; there was a group of scientists and modelers and so on, but a very small minority. I told him, Mr. Edelstein, you—I know this—since you became religious, and I know that you too were a dissident, an opponent of the regime. Abraham our forefather believed in some kind of monotheism—never mind exactly what that means—but he saw around him idol worshipers. So by the logic of the question you are asking, you too did not think like everyone else. You thought differently from all the hundreds of millions…
[Rabbi Michael Abraham] That argument is not an argument. It’s not an argument because Yuli Edelstein here had no—at least he felt he had no tools to really check it. So he said: okay, I have no choice but to follow the majority opinion of the people who understand the issue. So you can’t say that because he was a dissident, that means he should also listen to you even though you’re in the minority. He was a dissident because he knew as much as the regime, he was as smart as they were, and he thought differently from them.
[Speaker B] I didn’t expect him to rule that I was right, Heaven forbid, obviously that would have been irresponsible. But not to dismiss it a priori because the majority doesn’t think like you. He had only heard the opinion, he hadn’t checked it yet. I told him: right now, at this hour, it’s Wednesday, three-thirty in the afternoon. I told him: right now in Holland they’re saying what you—saying the argument the rabbi is saying? That Edelstein is saying? Yes. In Belgium they’re saying it? In every country they’re saying it. So who thought independently? You discover that no one thought independently, because everyone had some—
[Rabbi Michael Abraham] You’re operating on a plane that isn’t relevant. What do you expect a health minister to do when in front of him there are, say, a hundred experts, five of whom say one thing and ninety-five say something else, and his assumption is that he doesn’t have the tools to determine who is right?
[Speaker B] No, that assumption is incorrect. I didn’t expect him to agree with me, of course not; clearly that would be irresponsible. To take it seriously, to present it for brainstorming. What I felt, actually, on the principled level—
[Rabbi Michael Abraham] I’m not going to discuss now whether he was right or wrong, but the very fact that he didn’t accept the argument—if so then there’s no
[Speaker B] dispute—to examine it
[Rabbi Michael Abraham] seriously, fair enough, let him examine it.
[Speaker B] He couldn’t, there was no time, and that wasn’t the issue. What troubled me throughout my whole struggle during COVID was that I felt Netanyahu—this became known to me from internal sources—was preventing it. It suited him; that whole emergency framework was tailor-made for him, and therefore he imposed… people in the Health Ministry told me this from internal sources, and therefore he couldn’t weigh what I was saying because I felt…
[Rabbi Michael Abraham] I’m not sure. But just as an aside, why am I smiling while you’re talking? Because I remembered that Yuli Edelstein said yesterday that the majority decides, but the majority is not always right. He had some sentence like that—meaning, true, the majority decides, but sometimes the minority is right.
[Speaker B] So maybe something got through.
[Rabbi Michael Abraham] That was yesterday, about the committee for appointing judges, he said it there. So it really touches directly on our discussion here. Okay, in any case, let me get back to our issue. So the claim basically is that there are two kinds of majority. One of them is based on generalization from a sample—that is a majority that is not before us. And there is a majority based on a priori reasoning, and that is a majority that is before us. These are two kinds of majority that we follow in both cases, but they are still two kinds of majority of different character. And therefore the Talmud does not derive a majority that is not before us from a majority that is before us, because these are two different majorities, and we discussed Maimonides, who says the hierarchy is the reverse, and we won’t go back to that here. Now I just want to return to Rabbi Shimon Shkop, whom I started reading last time, because he also has some interesting explanation there. I don’t think he means what I’m saying, but it’s not so far away. First of all, I’ll remind you that we read him in section 4, where he said that a majority that is before us is not clarification. Why is it not clarification? Because any store from which you assume the piece of meat separated—there are nine stores against it, so it is not likely that it separated specifically from that one. And since that is true for each of the stores, then a majority that is before us is basically not clarification. That is his claim. I said that this is simply a misunderstanding; it is obviously not correct. Meaning, a majority that is before us in this sense is absolutely clarification, because the question we are asking is not whether it separated from store A or B or C through J, but whether it separated from the nine kosher stores or from the one non-kosher store. And therefore there is certainly a rational consideration in favor of its having separated from the nine stores. This always reminds me of the confusion people get into with the following case: say we roll a die. We roll a die a thousand times and all thousand times it comes up five. Okay? Now someone says: fine, the sequence of a thousand fives is no different from any other sequence like 1, 5, 4, 2, 6, 3, 6, 6, 1—make a vector of a thousand results, each between 1 and 6. Okay? The probability of any such vector is… six to the power of negative one thousand, right? Meaning one-sixth times one-sixth a thousand times. That is the probability of a given sequence. The probability of a thousand fives is also that same probability. So now, if this die comes up five a thousand times, is it correct to infer that the die is not fair? Or maybe not at all—maybe this result is random; any other result would also have had the same tiny probability. So there is nothing special about the result of a thousand fives. So someone who claims that something is fishy about this die, that it’s unfair, is talking nonsense—that’s not true. But it is true. Why is it true? Why would every one of us immediately feel that if it comes up five a thousand times, then the die is not fair? Because we are not asking what the probability is of getting a thousand fives. You have to place two alternatives opposite one another, not six to the thousand alternatives as in that formulation. What are the two alternatives? Either it came up five a thousand times, or it came up with some other result that is not special. You know what, a thousand sixes is also special, a thousand ones is also special, but all the mixed outcomes—that’s six to the thousand minus a discrete number of special outcomes. That is about six to the thousand. Okay? And when I ask whether it came up five a thousand times or some other result that is not special, then obviously the probability of a thousand fives is negligible and the probability of the other side is almost one. Because the other side is not one specific sequence like 3, 4, 6, 2, 1, 1, 6, 5, 6, 5, and so on. No, that is not what stands opposite it, but the collection of all the mixed, non-special outcomes. That is the correct way to ask the question. The moment we ask the right question, the statistical calculation suddenly becomes different. And this is what many people don’t understand: the way we ask the question, we’ll talk about this more later, very often determines the result. Very often failures in probability are not failures in calculation but failures in the assumptions or in the way we asked the question. In most cases that’s how it is. And therefore in our case too, we are not asking what the probability is that it came from store A, B, C through J. We are asking what the probability is that it came from A through I as one option, or what the probability is that it came from J. That is the second option. Once that is the comparison, then clearly the greater probability is that it came from the nine stores and not from the one. Again, under the assumption that the chances are equal for all the stores, and everything I said before. So he is not right in saying that because of that argument it is not a clarifying majority. But as I said before, it is true—I don’t know whether this majority is clarifying or not, in another moment we’ll discuss that—but it is true that this majority is not a generalization from a sample. It is not like laws of nature. That much is true. In that sense this is a majority that is before us and not a majority that is not before us, and judges are like that too. Now when he comes to explain why judges too are like pieces of meat, that’s in section 5. So here, let’s read that now. He has an interesting explanation, a bit formal, but interesting. He says this: “Rather it seems that the matter of the nine stores is like the law of a decisive majority among judges. Since the meat necessarily separated from one of the ten stores, each and every store generates a legal status regarding the meat, placing a doubt on the law of the meat. It follows that regarding the meat there are nine sides generating a side of permissibility and one side generating a side of prohibition, and the Torah said, ‘follow the majority.’ For so too is the law with judges, that the Torah said that the judgment emerging from the majority is what we are to act upon; likewise, the law born from the majority of stores against the minority is a law according to which we are to conduct ourselves, even though in reality there is no clarification here at all. And according to this principle the Talmud said that a majority that is before us is learned from the verse ‘follow the majority.’” End quote. What is he basically saying? He is basically saying that the majority of a piece of meat that separated from ten stores is the same thing as the law decided in a court with three judges. Why? He says like this: basically, this is not clarification—that’s his assumption. A majority that is before us is not clarification, we discussed that earlier. So what is it then? Why is there nevertheless a formal rule here? A formal halakhic rule saying that we follow the majority. What does that mean? Let’s try to translate the formal rule—notice, this is not a statistical calculation according to Rabbi Shimon Shkop, because there is no logic to it in that sense, it is not clarification—but he is trying to formulate the definition of the… So what is the definition? He says this: what happens with judges? Let’s say two judges say that Reuven is liable, and the third judge says that Reuven is exempt. Now I want to ask what the law really is, what the true law is. Is Reuven liable or exempt? So I have three sides: from Judge A’s side, Reuven is liable; from Judge B’s side, Reuven is liable; from Judge C’s side, Reuven is exempt. And therefore I follow the majority of sides. I issue the ruling. Each judge imposes a side as to why we should assume the law is that Reuven is liable or exempt; that is called a “side.” Each judge raises a side. Two judges raise side A and one judge raises side B. Since side A has two judges, there are two sides in its favor, so we follow the majority. That is what “follow the majority” means in a court. He says the same is true with the stores. Why? Because with the stores too, the piece of meat separated. Now I ask myself, where could it have come from? There are ten stores. Each of the stores raises a side regarding the piece of meat, right? This piece of meat separated from store A—it could have separated from store A—that is the side raised by store A; or from store B—that is the side raised by store B, and so on. Now in favor of the possibility that the piece is kosher, there are nine sides leading me to the conclusion that the piece is kosher, and there is one side leading me to the conclusion that the piece is non-kosher. Therefore I follow the majority of sides. Exactly like in a court. He says this is exactly the same thing. But notice: exactly the same not in the statistical sense, but exactly the same in the formal description of what the formal rule of a majority that is before us tells me. If you look at the question and each source imposes a side on it—yes?—you attribute to some source that the conclusion should be such-and-such, to another source that the conclusion should be such-and-such, and I look at how many sources there are for each side, and according to the majority of sides that is what I determine. That is true both in the stores and in the judges. But of course, why do I still think what he says here is interesting? First of all, he is right in this sense—I don’t know if he is right about whether this is clarification or not clarification, on that I’ll comment in a moment—but he is right on the point that there is no generalization from a sample here. This is not statistics in the same sense that a law of nature is statistics. In that sense, yes. This is not clarification in the same way science arrives at a law of nature. Now one can discuss whether the rule—what he calls a formal rule—also has logic in it, whether it is clarifying or not. Fine. But I think he still had good intuition that this really is not similar to a majority that is not before us. In a majority that is not before us, notice, he does not speak the language of sides. Think about a girl standing before me and I ask whether she is an aylonit. And I know that most women in the world are not aylonit. Why shouldn’t you say there too: there is a majority of women in the world, each one imposes a side on the girl before me, and then I say we follow the majority of sides just like in court or in the stores? The answer is no, that’s not right. Because in a majority that is not before us, as I discussed in earlier lectures, there is no process of separation. This woman before us does not yet belong either to the majority or to the minority; she has no status yet. The information I have about a group, about the general group, does not include her herself; it includes other women. And therefore one cannot speak the language of sides. The language of sides describes only a majority that is before us. Because in a majority that is before us there is a very inherent assumption of separation. The thing about which I am uncertain separated from some source, and each possible source imposes a side on it. Where there is no separation, there is no room for Rabbi Shimon Shkop’s description in terms of sides. So in fact he does intuitively grasp the distinction correctly between a majority that is before us and a majority that is not before us. One can of course hesitate about whether a majority that is before us is not clarification or is clarification. He claims that it is not clarification, that it is a decree of Scripture. Here I am not inclined to agree with him. As Shmuel also said earlier, it seems to me that if you ask ordinary people, in the absence of information at the moment—we have no information about the stores and their relations to one another—what would you assume? Is this piece of meat kosher or not kosher? I assume most reasonable people would tell you that the piece is kosher. Which means there is a rational basis for saying the piece is kosher. It is not true that this is a decree of Scripture in the sense that there is no reasoning here. There is reasoning here. And therefore, if you asked me whether this is a clarifying rule, a majority that is before us, I think it is a clarifying rule. It is a clarifying rule. It is true that it is not clarifying in the same way as a majority that is not before us. In that sense I think Rabbi Shimon Shkop is right. But I think he took it too far when he says that this rule is not at all a clarifying rule. But that is a point, a point. This distinction is a significant difference between the two kinds of majority. Because indeed this logic that says a majority that is before us clarifies reality and is a clarifying rule—I think it is a clarifying rule. The fact that rational people use it in contexts not connected to Jewish law at all, and obviously they do—yes, every legal system gives the ruling according to the majority opinion in the court, even though they don’t have verses.
[Speaker C] What element of separation is there in a court?
[Rabbi Michael Abraham] So I’m saying, there’s an element here of separation, in the sense that when I ask myself what the correct ruling is in this case, there are several sources that cast different sides onto it—each of the judges. And those judges cast a side onto the item that separated, each judge according to his own view. So the… not an item that separated, right—the ruling. This is an interesting anecdote: the Mordechai in Hullin asks a different question—we’ll still talk about the law of something fixed—but he says: why do we go after the majority in a court at all? After all, the rule is that if something is fixed in its place, then we do not follow the majority. “Anything fixed is considered like half-and-half.” For example, a piece of meat found inside a store, right? And I don’t know which store it is—there I would not follow the majority. I wouldn’t assume the piece is kosher. It would remain a doubt, half-and-half. There’s a halakhic rule in the laws of doubt that with something fixed, we do not follow the majority—when the thing is fixed in its place. Now he says: the judges are fixed in their place; they sit in the seat of the court. So why on earth should we follow the two against the one? So he says: but the ruling, or the statement, the decision, separated from the judges. The judges remain in place, just as the stores remain in place. But the piece of meat separated from the stores. And so too the court’s ruling—the ruling, when the judges say something, in effect the ruling separated from the court, or something like that. I don’t remember his exact wording anymore.
Now on the face of it, this sounds absurd. What are you saying—the ruling separated? What kind of thing is that? I’m asking: from where did the ruling separate? A horseman without a horse, right, a horseman without a head. Did it separate from Judge A, B, or C? The ruling doesn’t separate from anyone, and nothing of the sort. There are judges debating, as Sefer HaHinukh says, and usually I assume the majority is right. What separated here? What horseman and what nonsense? But according to the way I’m explaining it here, what he says isn’t so far-fetched. Because there really is a process of separation even in a ruling. The separation is not in the sense that something physically separates from the place where the judges are sitting. That’s not the point. The point is that there are certain sources; the matter placed before me, about which I’m deliberating, is the ruling. I’m asking: what is the law? Now the judges are three sources, each of which casts a side onto the question I’m deliberating about—what is the law, whether Reuven is liable or exempt. So you understand that this is basically like separation. In other words, there is something that has separated, and the sources from which it separated are sources that cast sides onto it, or rulings. And therefore, even in court, on the substantive level there is separation. To describe it on the level that the ruling separated from the mouths of the judges—that’s a metaphorical description. I don’t know whether he meant it literally or not, but if he meant it literally then it’s incorrect. But it could be that what he means to say is that there really is, in essence, a process of separation here. This is not generalization from a sample. These are sides that emerge from sources, where the thing you’re deliberating about separated from one of those sources. And therefore there is here a majority of sides.
And in that sense, Rabbi Shimon Shkop’s explanation is a wonderful explanation of what the Mordechai says—which on the face of it sounds like some strange mysticism, it’s unclear what he wants. Now what does this really mean? Because Rabbi Shimon Shkop concludes from here, as I said earlier, that this thing is not clarification at all. But it’s not true that this thing is not clarification. As I said before, reason suggests that this piece really did separate from most of the stores. That makes sense. Even without the verse in the Torah, I would have reached that conclusion. But as I explained in the previous lecture, it could still be that we need the verse in order to tell me that halakhically one may rely on this conclusion and not be concerned for the minority. But the fact that there is clarification here—that is certainly true. We need the verse to tell us that such clarification is sufficient. So the fact that there is clarification here does not mean we don’t need the verse, and the fact that there is a verse does not mean there is no reasoning here, that this is not something clarifying. I said that in the previous lecture.
So therefore the verse merely tells me: rely on this logical reasoning. And in fact people use this kind of reasoning in all sorts of contexts that have nothing to do with verses, or Jewish law, or Judaism בכלל. And other people use this kind of reasoning too, so clearly there is logic in it. In that sense, Rabbi Shimon Shkop’s argument really does not hold water in the sense that this is not clarification. But I just want to clarify an important point in this context. Earlier someone said—yes, Shmuel—he said: what do you mean, but in the case of the stores too it’s obvious to all of us that there’s statistics here; it’s 90 percent likely that it’s kosher, so why shouldn’t we follow the statistics? So look, I’ll give an example that illustrates the point. Or before that I’ll make the claim, and then I’ll give the example.
Everything, after you finish all your assumptions, is statistics. To say that something is statistics is an empty statement. It all depends on what your assumptions are that determined the statistical distribution, and then you make decisions based on that distribution. In the case of generalization from a sample, the generalization created the conclusion that there is a distribution of infertility, right—ten percent infertile and ninety percent not infertile among women in the world—and then I draw a conclusion about the woman before me. That’s statistics. But where did the statistics come from? From the ninety-ten distribution. Where do I know that there is a ninety-ten distribution? Generalization from a sample. Generalization from a sample is not statistics. Generalization from a sample is an assumption: I assume the sample is representative, as we discussed earlier in previous lectures. After all those generalizations, a distribution is created—or some assumption that this is the distribution—and now the statistical calculation begins. The statistical calculation begins only after there is a distribution. But how do you arrive at the distribution? That is always a matter of assumptions, generalizations, observations. There are many ways to arrive at distributions.
And in the context of the stores, how is the distribution ninety-ten kosher versus non-kosher? How did I get there? On the basis of a priori reasoning, not on the basis of generalization from a sample. Now here, generalization from a sample created the distribution; there, reasoning created the distribution. Once I already have a distribution, true, then it’s just statistics—ninety-ten—and so I’ll assume the piece is probably kosher. But it’s no great insight to say that this is statistics. Of course it’s statistics after you’ve assumed that this is indeed the distribution. The more important question is how you know that this really is the distribution. And here there is a difference between an available majority and a non-available majority.
I gave an example of this, if you remember, in one of the previous lectures. Say I toss a coin. If I know the coin is fair, then the distribution between heads and tails is fifty-fifty. What happens if I have no information at all about the coin? I know nothing about it. It could be fair, it could be unfair, it could be biased this way or that, I have no idea. Now they tell me: you have to bet. What’s the chance it lands tails? I assume most of us would bet on fifty percent, right? Now here that fifty percent is created out of an informational vacuum—I have no information. But precisely because I have no information, I have no way to prefer heads over tails or the reverse. So I’ll assume the distribution is fifty-fifty. In the previous case I have positive information: the coin is fair. If I know the coin is fair, then my assumption that it’s fifty-fifty is an assumption based on information. In both cases, at the end of the day, I have a fifty-fifty distribution, and my statistical calculation will say: what is the probability that it falls twice on three? One out of thirty-six, right? That will supposedly be the case in both instances. And in both cases they’ll tell me: wait, that’s statistics. What do you mean? No, it’s not statistics in this simple sense. After there is a distribution, the statistical calculation says one out of thirty-six. But how did you get to the distribution? You got to the distribution in entirely different ways.
Therefore, for example, statisticians will often tell you that the second case isn’t really statistics at all. It’s just pseudo-statistics, not really statistics. Fine—that’s just terminology. But what I’m saying is that to say something is statistics means nothing. Once there is a distribution, then of course the calculation is a mathematical statistical calculation; I can tell you the result for any event in the event space. But where did the distribution come from? The distribution never comes from a statistical consideration. The distribution comes from our assumptions, or generalizations from sample observations, or reasoning as in an available majority, or whatever it may be. The distribution is a product of our reasoning, and after there is a distribution, the mathematics begins.
Why? I’ll give an example of this. Usually in logic one distinguishes between three forms of inference: analogy, induction, and deduction. Deduction is from the general to the particular, right? All chairs have a seat and a backrest; this thing is a chair; therefore this thing has a seat and a backrest. That is deduction, right? If it’s true of all chairs, then in particular it’s true of this specific chair. Analogy is from one particular to another particular: this chair has a seat and a backrest, that one is also a chair, so apparently it too has a seat and a backrest. That’s analogy, right? Induction: this chair has a seat and a backrest; apparently all chairs in the world have a seat and a backrest. That is from the particular to the general. Those are three forms of inference. It’s customary in logic to divide forms of inference into these three: from particular to general, from particular to particular, and from general to particular.
Now inference from the general to the particular is a necessary inference. If all chairs have a seat and a backrest, then this specific thing, which is also a chair, certainly also has a seat and a backrest, because it is one of the chairs. That is necessary. That is logic. Is analogy also logic? This chair has a seat and a backrest, that one is also a chair, so it too has a seat and a backrest. Well, of course that’s semantic. You can call analogy logic too if you want. So I’ll ask a different question: not whether analogy is logic, but why analogy is not deduction. What do I mean? After all, what is analogical inference really based on? I say: if this chair has a seat and a backrest, and that one is also a chair, therefore it too has a seat and a backrest. What is that based on? It is obviously based on the assumption that what exists in one chair exists in all the other chairs too. Right? That is really what I assumed in the subtext. So let’s put that subtext on the table.
Now I present an argument: this chair has a seat and a backrest. Everything that exists in one chair exists in all chairs. Conclusion: that chair too has a seat and a backrest. You understand that now this is deduction? Now this is logic; this is pure, unimpeachable deduction. The same thing with induction. So what nevertheless distinguishes analogy from deduction? In the end both conclude with a valid logical argument whose conclusion follows necessarily from the premises. So what is the difference between analogy and deduction?
[Speaker D] You added another assumption. What? You added another assumption: everything that exists in a chair—
[Rabbi Michael Abraham] Every argument has assumptions. In analogy there are these assumptions; in deduction there are these assumptions.
[Speaker D] In deduction you don’t need that assumption that what exists in one exists in all.
[Rabbi Michael Abraham] No, fine, they’re different arguments, but both are deductive in essence. In both, the conclusion follows necessarily from the premises. A justified argument.
[Speaker D] The difference—
[Rabbi Michael Abraham] —is in the question of how I arrived at the premises. Meaning, when I assume that what exists in one chair exists in all chairs, that is an assumption grounded in induction, right? Therefore I am not certain of that assumption. True, if I adopt that assumption, from that point onward the argument is pure deduction. It is a valid logical argument. But one of the premises on which this valid argument is based is itself not certain; it emerged from induction. Therefore any argument on earth that you bring up here, I can turn into a deduction. How? By adding your implicit premises and formulating them explicitly, putting them on the table. Once I put all the premises on the table, every argument is deduction. There is no argument in the universe that is not deduction.
Once I asked students—I taught critical thinking, I don’t remember exactly what the course was—I asked them: if I say that with a fair die, the probability of getting a five is one-sixth, that’s one claim. A second claim: they ask you, in how many of the rolls will you get a five? So I say: in one-sixth of the rolls. Have I said the same thing? I claim not. The second claim is not necessary; it is not deductive. It’s a hypothesis that could definitely turn out to be false. The first claim is necessarily true; it is deduction. When I say that the probability of getting a five is one-sixth, given that the die is fair, then the probability of getting a five is one-sixth—that is a certain claim. It does not say what will happen in practice when I roll the die. When I roll the die, will I get a result that matches the underlying distribution? Absolutely not. There is the law of large numbers—that if I roll it many, many times, it will approach… toward the limit, right, the central limit theorem—it will approach the probability, the expectation. Okay? But in a specific finite number of rolls, when I say that in one-sixth of the cases it will land on five, that is a statement that is by no means necessarily true. On the contrary, the probability that it will happen exactly that way is very small, almost negligible. So the first is deduction, a necessary proposition, and the second is not, even though they look very similar. “The probability of getting a five is one-sixth,” and “in one-sixth of the times we will get a five.” “The probability of getting a five is one-sixth” is a statement in mathematics. It is not a prediction about reality. It is a statement in mathematics. The question of in how many of the cases I will get a five when I roll the die—that is a question in physics, a question of what will happen in the world.
[Speaker F] But “in one-sixth of the cases I’ll get a five” becomes true the more we roll it, right? Okay, as we approach infinity, basically.
[Rabbi Michael Abraham] In the limit of infinitely many cases, it will be exact.
[Speaker F] But I—
[Rabbi Michael Abraham] When I speak about a finite number of cases, I still—if I had to bet, I would bet that one-sixth of the times it will land on five. Why? Because the probability is one-sixth. Now the fact that the probability is one-sixth is a statement in mathematics, but the claim that in one-sixth of the times it will actually land on five is a hypothesis—that what materializes here will indeed match that mathematical probability. And that hypothesis is far from certain. In short, what I want to claim is that every argument you can think of can be turned into deduction if you add all the implicit premises and put them explicitly on the table. Then every analogy is deduction. I say: this chair has a seat and a backrest, and what exists in one chair exists in all chairs—two premises. Conclusion: that chair also has a seat and a backrest. That is deduction; the conclusion follows necessarily from the premises, even though I described a process that is analogy, not deduction. But what happened? I inserted the assumption of the analogy itself as an explicit premise in the argument. Once I put it in as an explicit premise, the conclusion follows necessarily. If I really adopt that premise, it follows necessarily from the premises. Not that it is necessarily true, but that it follows necessarily from the premises. Do you understand the difference?
Now what I want to claim is that the same thing happens with an available majority and a non-available majority. We’re used to saying, okay, this is statistics—what do you mean, here too it’s ninety percent and there too it’s ninety percent. It’s like saying, well, it’s deduction—it’s definitely true; here too it follows from the premises and there too it follows from the premises. That is a very small insight. Because the question is: what is the quality of my premises? That is what matters. Usually the bug in arguments is not the inference of the conclusion from the premises, but the quality of the premises themselves. Inferring the conclusion from the premises is usually fairly simple. When I attack a position I disagree with, it will usually turn out that I disagree with one of the premises, not that there was an error in the argument. It can happen, but it’s relatively rare. Usually our disagreement is over a premise. Therefore to say that something is logic means nothing. Tell me what premises your logical argument rests on, because the problem may be there—if there is a problem, it will usually be in the premises, not in the argument, not in the inference of the conclusion from the premises.
The same thing with our case. When you tell me that this piece of meat is ninety percent likely to be kosher, you say to me: what do you mean, there’s a ninety-ten distribution, so it’s a mathematical calculation, statistics, clearly ten percent non-kosher, ninety percent kosher. Not true. When the distribution is ninety-ten, I will ask you: how do you know that the distribution is ninety-ten? After you’ve already decided that this is the distribution, from there on it’s statistics, a mathematical calculation. The big question is how you reached the conclusion that this is the distribution. In laws of nature, it’s generalization from a sample; in an available majority, it’s reasoning. Many times, reasoning that stems from lack of information—not positive information but negative information. I have no other information, so I assume all the stores stand on equal footing.
[Speaker D] But that’s an assumption that the Mishnah states: nine stores versus one, and then it set the conditions before you; it didn’t say, take into account that if such-and-such happens—
[Rabbi Michael Abraham] So?
[Speaker D] So what reasoning do I need? That’s the assumption.
[Rabbi Michael Abraham] You need the reasoning that the chance of separation from all the stores is equal.
[Speaker D] So then it is statistics when we have no data at all?
[Rabbi Michael Abraham] No, it’s not statistics. It’s an assumption that leads to a result which is a statistical distribution, ninety-ten. From that point onward the statistics begin. Once there is a distribution, start doing calculations, using the distribution. But arriving at the distribution is never statistics; it is always our assumptions.
You know, I once thought about this: when people say that the probability of something is zero, that’s a distortion—a very nice distortion. Think about it sometime. Maybe now will be that time. When I say that the probability of a certain event is zero, that is never the result of a statistical calculation. Never. In a statistical calculation there will always be sums and products. Right? A certain event is the intersection of several events plus the intersection of several other events, so you get a sum of products. A sum of products of numbers between zero and one never gives zero. To reach a result of zero, one of the factors has to be zero itself. Where do you know that this factor is zero from? Never from statistics. Always from some assumption of yours. You have some knowledge by which you know that the probability of such a thing is zero. But when you say the probability is zero, that is not the result of a calculation. It is an assumption that you are making. Common sense, you… right? Therefore I say: a result of zero is never the result of a statistical calculation. Never. It is always, always our assumption that the probability of something is zero. Because zero is never the result of a calculation that consists of sums and products of positive numbers between zero and one.
[Speaker C] I want to go back for a moment to the issue of the court, the separation. This move of comparing meat that separated from one of the stores, and then turning that into an idea or opinion that separated from the judges—on the face of it, that doesn’t seem entirely right to me. But I want to ask another question. The whole subject of separation, or of reaching… of following the majority because it separated from the stores and so on, all that deals with the formulation of the problem that is brought before the court. There are problems, they are brought before the court, and now we’re giving rules for how the court should rule. Suddenly you transfer that rule to the court itself. What connection is there at all between those two subjects? The court is the one that has to rule. Why are you suddenly…?
[Rabbi Michael Abraham] Really, really, there is no connection. Each judge individually forms his position according to the rules of Jewish law. But now disagreements have arisen between the judges. Now we are on a second-order level, a meta-halakhic level. What do you do when there are disagreements? And here comes the majority.
[Speaker C] I understand that we have to follow the majority, but I don’t understand why we need to take the example from the subject of majority, from meat that separated—
[Rabbi Michael Abraham] —from the stores.
[Speaker C] The reverse… what?
[Rabbi Michael Abraham] The source is the judges, and the piece of meat is learned from the judges. Not—
[Speaker C] The reverse? Not the reverse?
[Rabbi Michael Abraham] The reverse. The source in the Torah is “follow the majority,” and that refers to judges. And that’s the Talmud in Hullin—we saw the Talmud—the Talmud in Hullin says that from this, from the judges, we also learn the majority rule about meat from stores.
[Speaker C] Okay.
[Speaker D] Fine, moving on, moving on. I still didn’t understand why the Rabbi disputes the possibility that this is only policy. From the standpoint of statistics, we know that—what is it… we don’t know… there’s ten percent that it’s non-kosher. If it were poison, you wouldn’t eat it. You eat it because there is a policy that majority—
[Rabbi Michael Abraham] Again, so I’ll repeat what I said in the previous lecture. That’s why we need the verse. I said that the existence of statistical logic and the existence of a verse do not contradict each other. The existence of statistical logic still does not mean that one may rely on it in Jewish law, because with poison, as you said, we would not rely on ten percent.
[Speaker D] So that’s policy. Maybe that’s what he meant when he said it’s policy.
[Rabbi Michael Abraham] Then in an available majority too it’s the same thing. If you had an available majority where ten percent was poison, would you eat it?
[Speaker D] Available majority… you…
[Rabbi Michael Abraham] You’ve repented here, Shmuel. Earlier you explained to me that this is statistics, straightforward reasoning, available majority. Now you’re reverting to saying it’s only policy.
[Speaker D] I deny the continuity of the subject; I’m not standing by that…
[Rabbi Michael Abraham] Okay. Fine. In any case, for our purposes, that is basically the claim, and I think it sharpens very well the difference between an available majority and a non-available majority, and the concept of separation, and the concept of generalization from a sample.
Now I want to begin a bit of the next stage. I want to talk a little about generalizations from a sample, which is really the essential weakness in a non-available majority. Now when we come to discuss generalization from a sample, there is of course… I’ve already mentioned more than once Hume’s problem of induction. Right? Hume basically… and so David Hume basically argues that the fact that you have seen the sun rise every morning does not mean that it will continue to rise every morning from now on, or from tomorrow on. What has happened until now will not necessarily continue. Therefore the assumption that seems so self-evident to us—that if something occurs in the cases we have encountered, then it probably also occurs in all the other cases, future cases or cases we haven’t seen, it doesn’t matter—is an assumption that really has no source, neither logical nor empirical. And therefore David Hume basically argues that induction is some kind of delusion, I don’t know what—some baseless assumption of ours, because it is really a form of speculation.
And I said that whoever claims that a non-available majority is weaker is apparently relying on Hume’s problem of induction. He is basically saying that when you generalize from a sample, you assume that the sample is representative and that you can generalize from it to all cases—and where do you get that from? There is some sort of generalization here. In contrast, in the case of the stores it somehow seems obvious: all the information is before me, I see that there are nine stores here, one non-kosher and nine kosher, I’m making no generalization, no speculation; I’m only making assumptions within the world of knowledge available to me, which is the set of pieces of meat in this city. And therefore it seems stronger. So the weakness of a non-available majority is a weakness that stems from Hume’s problem of induction—from the fact that my ability to generalize from a sample is an ability that really has no true basis. It is a common-sense assumption, but it has no real basis, neither empirical nor logical. Or let’s put it this way: not empirical. And if it’s a logical basis, in Hume’s eyes—he was an empiricist—that’s not enough.
Now where do we see this in Jewish law? In Jewish law there are explicit discussions that deal with induction and the problem of induction. And one example is the issue of an established presumption after three times. We know many cases in which Jewish law says that what happened three times is presumed to continue happening. A few examples: an ox that gores three times is a forewarned ox; the expectation is that it will continue to gore. Menstrual cycles: a woman who saw a cycle three times with some regularity—by date of the month, by interval, it doesn’t matter, an average period—but some fixed regularity, we assume that regularity will continue. The Talmud links the three-year presumption regarding land possession as well to the presumption after three occurrences, at the beginning of the chapter Hezkat HaBatim. If his brothers died because of circumcision—for example, a woman gave birth to children and three children that I circumcised died afterward—the fourth child is no longer circumcised. Because if this happened with three children, then I am concerned that it will happen with the fourth child as well. A woman whose husbands died—three husbands married her and all three died—the fourth is already forbidden to marry her; it’s dangerous. And so on. There are many cases in Jewish law where we rely on a presumption after three occurrences.
This presumption after three occurrences is really induction, right? Something happened once, happened twice, happened three times—I assume it will probably happen in all the other cases too. Of course nothing is certain; in induction nothing is ever certain. But if you ask me what is more probable, it is more probable that it will also happen in future cases. That is basically the rule of induction. Scientific induction, of course, not mathematical induction—mathematical induction is deduction, right? That’s clear; it’s just the same term. Scientific induction means generalization from examples; mathematical induction is not generalization from examples, mathematical induction is a complete proof.
In any case, this generalization on the basis of examples is induction. Now what happens—the nice source on this issue is the well-known Rabbi Chaim in the sugya in Hagigah, right? It’s in Hagigah, I think. For some reason it slipped my mind, I don’t remember anymore. The Talmud discusses a mentally incompetent person—who is considered mentally incompetent? The Talmud brings three signs of such a person. I’m not finding it at the moment. Ah yes, Talmud in Hagigah 3b. The Talmud says there are three signs of a mentally incompetent person. Right, this is the famous Rabbi Chaim. The Rabbis taught: who is a mentally incompetent person? One who goes out alone at night, spends the night in a cemetery, and tears his clothing. Right, three signs. It was stated: Rav Huna said, only if they are all present at once. You need all three signs in order to determine that he is mentally incompetent. Rabbi Yohanan said, even one of them. So it’s enough if he does one of these things to declare him mentally incompetent.
What are the circumstances? The Talmud says: if he does them in a senseless way, then even one is enough. Right? If he does it in a way that has no logic, then one sign is enough to declare him mentally incompetent. If he doesn’t do them in a senseless way, then even all of them are not enough. The case is always one where he does them in a senseless way—but if he sleeps in a cemetery, perhaps he does so in order that an impure spirit may rest upon him. Say someone sleeps in a cemetery. Well, maybe he did it in order that an impure spirit should come upon him. If there is logic behind what he did, then we need not assume he is mentally incompetent. One who goes out alone at night—perhaps he was seized by gendripas, and that’s why he goes out alone at night. And one who tears his clothing—perhaps he is a man deeply preoccupied with his thoughts. Right? He’s lost in thought and tears his clothing. So the Talmud says: once he has done all of them, he is like an ox that gored an ox, a donkey, and a camel, and became forewarned for all. Again, the interesting connection to the goring of an ox, to a forewarned ox. Right? So we see that the Talmud itself connects it to the presumption after three times. And the Talmud says that if he has three signs, then he is mentally incompetent.
Rabbi Chaim asks: so each sign by itself is not enough to determine that you are mentally incompetent. Because if he goes out alone at night—perhaps gendripas seized him. Right? That’s why he goes out alone. Or perhaps an impure spirit came upon him if he sleeps in a cemetery at night. Fine? So he says, two signs are not enough. Why aren’t two signs enough? Say he both slept in a cemetery at night and went out alone. Because this one was due to gendripas and that one due to the impure spirit. So Rabbi Chaim says: then why are three enough? Then say also with three: this one is because of gendripas, this one because he is absorbed in thought, and this one because of an impure spirit. So even three should not be proof. Where is the transition from two to three?
So Rabbi Chaim says as follows: if you have one case, it may be that there is some explanation, and it may be that it happened by chance. If you have two cases, it may be—the probability is already lower—but it could still be that each one separately was coincidental. You have an explanation that unites them both. Right? Say he both went out alone at night and slept in a cemetery. Then you have two possibilities. Either he is mentally incompetent—that is one explanation that explains both behaviors—or he slept in the cemetery because he wanted an impure spirit, and he went out alone at night because gendripas seized him. Each one has some separate explanation. So clearly it is more reasonable to take one explanation that stitches together both cases than two explanations, each of which stitches together one case. The theory stands. But two cases are apparently not distinctive enough.
Rabbi Chaim says, however, that three cases are already distinctive enough. What does that mean? If he also went out alone at night, also slept in a cemetery, and also tears his clothes, then for each case there could be an explanation that it happened for some separate reason. That does not mean he is mentally incompetent, because each one has its own explanation independently. If there were two, one such case is certainly not a sign that he is mentally incompetent. Two such cases are also not a clear sign that he is mentally incompetent, because it could still be that this is because of the impure spirit and that is because of his thoughts. But if all three things happened, then it still could be that this is because of his thoughts, that is because of the impure spirit, and that is because of gendripas. He says no—but if I have one explanation that stitches together all three cases, then that is preferable to three different explanations, each of which stitches together one case. And the Talmud itself compares this to the goring of a forewarned ox. Right? It gored an ox, a donkey, and a camel. What does that mean? The Talmud understands that the case of the mentally incompetent person is actually an example of a presumption after three occurrences. If something happens in three different cases, then probably the explanation that explains all three cases is the correct explanation. You understand that what we have here is basically the principle of induction. If something happened once, happened twice, happened three times, then apparently there is some general rule here. And why—
[Speaker E] Why can’t you apply the same logic to two? To two times?
[Rabbi Michael Abraham] You could have, but it’s not distinctive enough. It relates to the earlier question—just as we said before, if the stores in the city are ninety-ten, that still means I need a verse. Why do I need a verse? Because if ten percent were poison, without a verse would I drink it?
[Speaker E] So it’s for the norm.
[Rabbi Michael Abraham] Exactly. So here too, to establish normatively that he has the legal status of mentally incompetent, I need the distinctiveness of three cases. True, even with two cases there is a decent chance he is mentally incompetent, but it is not enough to establish the legal status of mentally incompetent halakhically. Okay? It is clear to you that the greater the number of cases, the more distinctive it is. It could also have been five cases, because with five cases it’s even more distinctive. So you need the verse, or the halakhic rule, to tell me what level of distinctiveness is sufficient to establish the halakhic rule. And Jewish law says: three. Three cases. That is the required level of distinctiveness.
Which means that what we really have here is a generalization from a sample of a few cases I encountered. Like scientific generalization. And that is a forewarned ox, and also the signs of a mentally incompetent person, and likewise the other examples I mentioned earlier. Now there is a question in the simple understanding—let’s formulate it this way. In the simple understanding, what is the rule of induction? The rule of induction basically says that there are several discrete, individual cases that I encountered, and they are perceived by me as expressions of a law that is a general law. Therefore I turn those cases into a general law—that is induction. Right, that is basically the assumption of induction: that the cases are particular cases that really reflect a general law, or that the cases I saw are a representative sample and I can generalize from them and generate from them a general law.
So for example, if an ox gores three times, then it apparently has a goring nature, and therefore it must be guarded more carefully, and if it gores again I can’t say that I was under duress, right? Because it is a forewarned ox, and I am liable for full damages. Three times that a woman sees menstruation on, say, the same date in the month, then I assume that apparently she has some tendency to see menstruation on that date of the month. And therefore I establish a fixed cycle. The three cases are perceived by me as demonstrations of a general law. Therefore those three cases are really the representative sample, and when I generalize I take those cases and turn them into a general law. Okay? That is basically the halakhic example.
Now come see a consequence of this. Here I’m sharing the Mekor Chaim in the laws of Passover. He discusses some problem in the laws of leaven. We found inside a pot some three wet grains of wheat that had split because of the water, and that essentially means they have become leavened. If they didn’t split, they are not leavened, because the water did not penetrate to where the grain itself, the flour, is. Right? But if it split, then the water is already inside it and it is leaven. Now I found three that split. And I removed them. The question is whether I need to assume that inside this dough there are more such grains. Not only that there are more grains, but that they too split, and therefore they are leaven. That is his discussion, without entering the details.
So he says as follows—I’ll read only the part relevant to us: “Therefore it seems clear to me that we do not say a presumption after three times except where there is a causal factor, such that it is reasonable that it should be so. And intellectual reasoning compels that it should be so. But in a matter that occurs by chance, and there is no sufficiently plausible causal factor, there is no presumption for random events.” Right? The fact that three cases happened does not create a presumption. What is he saying, essentially? He says this: if three cases happened and you have an explanation that can explain all three, then you can make an induction and generate a general law from it. But if you have three cases and you do not find a general logic—a general principle that explains all three cases—then despite the fact that it happened three times, we will not make an induction.
And here you have a wonderful demonstration of the problematic nature of induction. Because the reason I make an induction is only because I assume that behind the facts there is some general law. But that is an assumption, and if I haven’t identified the general law, or I do not see before my eyes some general law, then I will not make an induction. So you understand that induction really rests on some reasoning of mine, some speculation. It is not an empirical result, as many people delude themselves into thinking. The laws of nature are not laws learned empirically. That is a common, general, crude mistake. Not true. The empirical observations create the distribution in the sample. The generalization that I make from the sample to the general law is always the result of my assumption that this is a representative sample of a general law. And only that enables me to make an induction.
Therefore, if I don’t have some explanation of that sort—say there were three such cases of things a person does, and I don’t have any explanation that stitches all three together—then I will infer no conclusion from it, even though it happened three times. In the case of the signs of a mentally incompetent person, it happened three times and I have a shared explanation for all of them: apparently the fellow is mentally incompetent. He does things that mentally incompetent people do. If I have three indications of that, I can establish the general law: the man really is mentally incompetent. Because it is an indication that I have an explanation that stitches together all three of these cases, so apparently that really is the reality—he really is mentally incompetent. But if I had not found an explanation, then even though it happened three times, I would not make the generalization.
For example, a woman whose three husbands died—which is also an example the Talmud brings—then it is forbidden to marry her, because she is dangerous. In the Talmud it’s not so simple, because it depends on the question of what your hypothesis or conjecture is regarding the cause of death. If you do not have such a conjecture, then it would be permitted to marry her even after she killed three husbands. I would assume that it happened by chance. Only if I have some explanation that explains the three cases—only then do I forbid the fourth husband to marry her. And we will see this; he himself brings proof for it from a Talmudic passage in Yevamot. We’ll see that next time, that passage in Yevamot, which is a wonderful demonstration of the problematic nature of the principle of induction.
Okay, so at this stage I’ll stop here. Thoughts or questions? Yes?
[Speaker D] How did the Rabbi explain the doubt that David Hume cast on induction? Did David Hume not act in life according to induction?
[Rabbi Michael Abraham] He did. He acted according to that logic; he just said that it is a construction embedded within us. It has no basis at all. Apparently I have nothing better, so that’s what I do. I have a bitter disagreement with Jeremy Fogel on this issue, yes—the last column I wrote about his book mentions it briefly. But he argues that David Hume does believe in induction. He only claims that it has no empirical basis, therefore it is not certain. And I say that’s nonsense. Of course it isn’t certain. Who says it is certain? You don’t need David Hume for that. David Hume is an empiricist, and if he claims that what does not emerge empirically is not correct—not merely uncertain.
[Speaker D] So how does he nevertheless act according to it?
[Rabbi Michael Abraham] He says: that’s how I’m conditioned. I don’t have anything better to do, so that’s how I act. And you hear answers like that from many skeptics.
[Speaker D] If he lived before Newton, then he wouldn’t rely on the fact that something will fall if he lets it go in the air. That makes no sense.
[Rabbi Michael Abraham] He would rely on it. Why wouldn’t he rely on it?
[Speaker D] Because he wouldn’t have a law, he wouldn’t have… He saw a thousand times that it falls.
[Rabbi Michael Abraham] The fact that things fall to the ground—so what if he doesn’t know the mathematical description of the law? Everyone knows that things fall to the ground; people understood that even before Newton.
[Speaker D] He didn’t believe it would happen again? Really he didn’t believe it would happen again?
[Rabbi Michael Abraham] I’m saying, I think he did believe, but he argued—he explained to you—that no, it’s just a construct. What does it mean that he believed? He had that kind of feeling, but he claimed that this feeling is just a construct, it has no real validity at all. It’s like all those people who deny the whole idea of free choice—determinists. So they’re not denying that they have an experience of choice; they only claim that this experience is an illusion. It’s embedded in us in some way, but it isn’t really true. That doesn’t mean—they go on behaving as if they have choice, everything’s fine—but they explain to themselves that really it’s just a construct, with no real basis. What other wager could he make? What would he do differently? Suppose he doesn’t get on a plane, because, you know, just because a plane didn’t crash three times, or a hundred times, who says that the hundred-and-first time it won’t crash? So he won’t get on a plane. But by the same token, someone who doesn’t get on a plane can die too. Just because it hasn’t happened until now, that doesn’t mean it won’t happen from now on. He has nothing to bet on. You’re living in a completely Kafkaesque world. There’s no way to know how to behave. Any other comment? Another question? Okay then, good night, see you.