Doubt and Probability—in Halakha, in Thought, and in General—Lecture 13
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- The three principles of majority, and the choice to focus on following the majority
- The source of following the majority: “Incline after the majority” and the example of nine stores
- The Talmudic distinction: a majority that is before us versus a majority that is not before us
- The case of a boy and girl in levirate marriage, and the majority that “most women are not infertile and most men are not sterile”
- A conceptual question about source rather than validity: “we have found the law” and “I had not merited”
- What “before us” and “not before us” mean: full information versus generalization from a sample, and the concept of separation
- A representative sample, statistical errors, and election polls as an example
- A law of nature as the basis for generalization in a majority not before us, and its limits
- The strength of the majority: the argument that a majority not before us is weaker versus the argument that it is stronger, and Rabbi Shimon Shkop on Maimonides
- The end of the passage, Rashi, and the tension between the initial assumption and the conclusion
Summary
General Overview
The text presents the rule of following the majority as the central principle among the laws of majority, and distinguishes it from nullification by majority and “most of it is like all of it,” which, he argues, are not matters of statistics but legal rules. It returns to the Hullin passage that seeks a source for the rule “follow the majority,” and distinguishes between a majority that is before us and one that is not before us, emphasizing that the Talmud’s question is about the source of the rule and not about its practical validity. It defines the conceptual difference between the two kinds of majority through the question of the source of the statistical information, through the concept of separation, and through the idea of sampling and generalization, and raises different possibilities regarding the force of a majority not before us as compared with a majority that is before us, based on the Talmud, Rashi, and Maimonides as cited in the name of Rabbi Shimon Shkop.
The three principles of majority, and the choice to focus on following the majority
The text distinguishes among three principles: “anything that separated is presumed to have separated from the majority,” or following the majority; nullification by majority; and “most of it is like all of it.” It attributes the first to the Talmud, the second to the medieval authorities (Rishonim), and the third to the later authorities (Acharonim), all with a general connection to the verse “incline after the majority.” It states that nullification by majority and “most of it is like all of it” are not connected to statistics, and explains that nullification by majority is a legal rule in which the forbidden item “takes on the status” of the permitted one, not a probabilistic calculation. It notes the view of Rashba that dry-mixture nullification does contain an element of following the majority, but places that as a return to the discussion of following the majority rather than as a separate topic.
The source of following the majority: “Incline after the majority” and the example of nine stores
The text brings the Talmud’s question, “From where do we know these words, that the Sages said: follow the majority?” and the basic answer from the verse “incline after the majority,” in the context of deciding in a religious court according to the majority of opinions. It presents as a clear example a piece of meat found in a city with nine kosher stores and one non-kosher one, and emphasizes that in principle we assume the piece is kosher because we follow the majority of stores. It presents the derivation from the verse as a move from majority rule in a religious court to majority rule in matters of prohibition and permission and in other halakhic contexts.
The Talmudic distinction: a majority that is before us versus a majority that is not before us
The text quotes the Talmudic distinction that “a majority that is before us, such as nine stores and the Sanhedrin, is not what troubles us,” and defines a majority that is before us as a majority in which the majority and minority are “before us” in the sense of full information about the entire group. It explains that in the case of stores and in a religious court there is a defined and known group, and the doubt is only to which side a separated unit belongs, and therefore this fits with “incline after the majority.” It emphasizes that the Talmud raises difficulty specifically regarding “a majority that is not before us, such as a boy and a girl—where do we derive it from?”—that is, a majority where the group relied upon is not before a person as a whole body of direct and complete information.
The case of a boy and girl in levirate marriage, and the majority that “most women are not infertile and most men are not sterile”
The text explains that the case of a boy who must perform levirate marriage with a girl raises a severe doubt, because if they are not capable of producing children there may be a forbidden union with a brother’s wife, whose punishment is death, and only where levirate marriage applies is that prohibition removed. It describes the puzzlement over how “they are raised together” despite the possibility that it will turn out that she is infertile or he is sterile, and presents the Talmud’s answer that we follow the majority: most women are not infertile and most men are not sterile. It adds a discussion about the question of “feeding a child prohibition with one’s own hands,” and cites the Pri Megadim as saying that there is also a prohibition regarding minors, even though they are under compulsion and not punishable.
A conceptual question about source rather than validity: “we have found the law” and “I had not merited”
The text states that the wording “from where do we derive it?” does not cast doubt on the very existence of the rule, but rather seeks a conceptual source within the Oral Torah for something that is in any case already practiced. He compares this to the saying of Elazar ben Azariah, “Behold I am like a man of seventy years, and I had not merited that the Exodus from Egypt be mentioned at night until Ben Zoma expounded it,” and explains that “I had not merited” means that the source had not been found until the exposition, even though the law was known and accepted. He notes that the Talmudic phrase “we have found the law” likewise means finding the source of a law, not innovating the law itself.
What “before us” and “not before us” mean: full information versus generalization from a sample, and the concept of separation
The text rejects the understanding that the distinction depends only on whether one physically sees all the particulars, and defines a majority that is before us as a situation in which there is full information about the relevant group, and the unit under discussion is part of that group about which we have information and has merely “separated” from it, thereby creating the doubt. It states that “anything that separated is presumed to have separated from the majority” is the essential definition of a majority that is before us, and ties to it the concept of separation as a criterion, not merely as a formal expression. It defines a majority that is not before us as a situation in which the information about the distribution is created by generalization on the basis of a sample or on the basis of a general assumption, and therefore the application to a new case is a speculative extension of knowledge from one group to a unit that is not included in the direct information.
A representative sample, statistical errors, and election polls as an example
The text describes how generalization from a sample is not free of problems, because the sample may be biased and unrepresentative, and explains that this is the source of many errors in statistics. It gives the example of Knesset election polls and argues that professional samples sometimes use only about 500 people and still manage to produce accurate estimates with deviations of only a few percent, and that the bad reputation of polls comes from the fact that political contests are close, so even a small deviation can flip the result. It states that the real expertise of statistical institutes lies in constructing a representative sample and offsetting biases, not in the calculation itself of multiplying up the sample’s results.
A law of nature as the basis for generalization in a majority not before us, and its limits
The text connects the possibility of extending from a sample to a general population to the assumption that we are dealing with a law of nature or human nature, as in the physiology of women or in the statement “it is better to dwell as two,” as a feature of human nature. It distinguishes between distributions that are not a law of nature, like the number of kosher stores in a city, which gives no reason to project to another city, and distributions understood as a result of nature that are expected to apply similarly to new individuals. It notes that in the time of the Talmud they may have assumed more readily that what was familiar in the nearby environment reflected the world at large, and presents this as a simple working assumption that may become problematic when the sample is biased.
The strength of the majority: the argument that a majority not before us is weaker versus the argument that it is stronger, and Rabbi Shimon Shkop on Maimonides
The text presents the intuitive view that a majority not before us is weaker because it rests on induction and generalization from a sample, and mentions in this context “David Hume’s problem of induction” as an epistemological difficulty. It cites Rabbi Shimon Shkop as saying that Maimonides holds that a majority not before us is actually stronger, and explains this by saying that in a majority based on a law of nature there is an internal reason in each individual case for the decision to go in the direction of the majority, and therefore the majority can be “applied” broadly to every new case. He illustrates this by saying that regarding women there is a natural reason to assume of each and every woman that she is not infertile, whereas with pieces of meat there is no internal “law of nature” pushing each piece toward kashrut, and in a majority that is before us we know with certainty that there is a minority of non-kosher pieces, so deciding by majority necessarily involves certain error in some of the cases.
The end of the passage, Rashi, and the tension between the initial assumption and the conclusion
The text states that the Talmud “remains without an answer” regarding the source of a majority not before us after rejecting various sources, even though it is clear that we continue to rely on it. It brings Rashi, who suggests “it is a law given to Moses at Sinai that we rely on a majority even where it is possible [to clarify],” as a solution to the lack of an explicit source, and also brings Rashi’s second possibility, that “incline after the majority” implies both a majority that is before us and one that is not before us, “for what difference is there between this and that?” It points to a difficulty here, since throughout the discussion the Talmud assumes a sharp distinction between the two types, and therefore it is hard to say at the end “what difference is there” without the Talmud explicitly saying it has changed course, and suggests that this may explain how Maimonides can align the conclusion with the possibility of deriving everything from “incline after the majority.” It concludes with three organized possibilities: to retain the assumption that a majority not before us is weaker; to accept Rashi’s second equation that there is no difference; or to follow Maimonides’ view that a majority not before us is stronger, and is therefore a fortiori from a majority that is before us.
Full Transcript
[Rabbi Michael Abraham] Last time we started dealing with majority, with the principle of majority—or principles of majority—when really majority is the clearest rule that lays claim to the crown of a clarifying rule. Right? It’s basically logical, statistical, it exists in every field of thought, not specifically in Jewish law, and therefore when we deal with statistics or probability and doubts in Jewish law, I think majority is a central topic in that context. So we began to discuss this issue of majority a bit. I said there are a few different principles connected to majority. One of them is “anything that separated is presumed to have separated from the majority,” or to follow the majority, “we go after the majority.” The second rule is nullification by majority, and the third rule is “most of it is like all of it.” I said that the first is written in the Talmud as derived from “incline after the majority,” the second is written in the medieval authorities (Rishonim), and the third is written in the later authorities (Acharonim) as derived from “incline after the majority.” Somehow they connect all of them to the verse “incline after the majority.”
I want to focus right now on the law of following the majority, because both “most of it is like all of it” and nullification by majority are in no way connected to statistics. Meaning, there it’s clear that this is not a statistical matter. With following the majority—because nullification by majority, say, if I have a non-kosher piece of meat that falls into a pot of kosher meat, then it is nullified. The concept of nullification does not mean that I’m making some kind of statistical calculation; rather, nullification is a legal rule. The rule says that the non-kosher item that fell into the pot receives the status of kosher meat, or the prohibitive legal features disappear from it. There is the view of Rashba that in dry mixtures, nullification in a dry mixture is indeed a law of following the majority, but then that takes us back to following the majority, because he says: why is there a law of nullification in a pot? Because if you take out one piece of meat, the assumption is that this is not the non-kosher piece, because most of the pieces here are not the non-kosher one. So essentially, nullification in a dry mixture is just another application of following the majority.
So that’s not important, because for our purposes we’re basically focusing now on following the majority, which can at least belong to questions of statistics, to statistical principles. What is the concept of following the majority? So the clearest, most familiar example is a piece of meat that we find in the street. There are nine kosher stores in the city and one non-kosher one, so in principle I may assume that the piece of meat I found is kosher. Meaning, that’s the law of following the majority: we go after the majority of the stores. That’s the law of following the majority, and we derive it from “incline after the majority,” which is following the majority in a religious court. But that’s the example of following the majority.
We started the passage in Hullin; I want to return to it, because it really deals with the question of the source for this law. The Talmud says: “From where do we know these words, that the Sages said, ‘Follow the majority’?” Where do we learn this principle from, that the Sages say to follow the majority? As it is written—the Talmud says, from where do we know it? From the verse, “incline after the majority.” Meaning, from the verse “incline after the majority.” If there is a dispute in a religious court, and there is a majority of opinions in one direction and a minority of opinions in the other, we rule like the majority view—we go after the majority. So too in matters of prohibition and permission, and in all other halakhic contexts, we should follow the majority, and we derive it from that verse.
The Talmud says: “A majority that is before us, such as nine stores and the Sanhedrin, is not what troubles us. What troubles us is a majority that is not before us, such as a boy and a girl—where do we derive it from?” So the Talmud first of all divides here between two kinds of majority in the law of following the majority. One type is a majority that is before us, which is like stores and the Sanhedrin; those are the two examples the Talmud itself brings. Most of the stores—that’s what I mentioned earlier: you find a piece of meat in the street, there are nine kosher stores and one non-kosher one, you go after the majority of the stores. That’s called a majority that is before us. What does “before us” mean? That it is present before us. We have before us ten stores here in the city, nine of them kosher and one non-kosher. In principle all the stores stand before us, and I need to know to which store this piece belongs, or from which store it came. That is called a majority that is before us.
The Talmud says the same regarding the Sanhedrin, meaning a religious court. When there is a majority in a court—say two against one, or twenty against three in capital cases—we follow the majority, and there too all twenty-three stand before us, and the majority of twenty and the minority of three, everything is before us. Therefore that is a majority that is before us. That, and stores, are the two examples of a majority that is before us.
The Talmud says: so a majority that is before us is not what troubles us. Did you think I was asking where we know a majority that is before us from? No, that’s obvious; we learn it from “incline after the majority.” We derive the majority of the Sanhedrin—which is simply the case of the verse itself—and the majority of the stores, which is the same thing, because it too is a majority that is before us. “What troubles us,” says the Talmud, so what were we actually uncertain about? A majority that is not before us. A majority that is not before us. Such as a boy and a girl. Where do we derive it from? Where do we know that we follow a majority that is not before us?
What is the case of a boy and a girl? A boy who must perform levirate marriage with a girl—both of them, essentially, it is still not known whether they can produce children, because we only find that out when they grow up, mature, and then we know whether she is infertile, whether he is sterile. So when they are minors we still can’t know that. Now, one has to know that in levirate marriage, if they are not capable of producing children, then there is a prohibition here, because essentially he is marrying his brother’s wife. Marrying one’s brother’s wife is a forbidden union. It’s a severe prohibition whose punishment is death. Only in a case where levirate marriage applies is the prohibition of one’s brother’s wife removed. Therefore it is very important to know whether they are capable of producing children—whether she is infertile and he is sterile—or whether they are healthy people, meaning they can produce children. Because if not, then basically it is forbidden for them to live together; it is a forbidden union.
And nevertheless we say that they should grow up together. That’s what we say regarding a minor yavam and yevama: we raise them together. They live together until they become adults, and then it becomes clear whether they are capable of producing children or not. And on the face of it this is very strange. You are putting them into a situation where it may be that they are violating a severe forbidden union. Why not wait and see, when they grow up, and then decide whether they are permitted to live together or not?
The Talmud says that we follow the majority. What majority? Most women are not infertile and most men are not sterile. Meaning, most people can produce children, and that is enough for us to permit this doubtful prohibition, where there may be a prohibition of one’s brother’s wife. So we follow that majority.
[Speaker B] So when the Talmud says that, is that because you’re feeding a prohibition, as it were, directly with your own hands? What? Is this because of feeding a prohibition directly to a minor?
[Rabbi Michael Abraham] What’s the problem with minors violating a prohibition? Well, the Pri Megadim says that there is also a prohibition regarding minors, even though they are under compulsion and there is no punishment. But yes, you could say that it’s from the angle of feeding them prohibition, imposing prohibition directly.
So the claim, in the end, is that there is a majority here of a different kind. It’s not a majority that is before us; it’s a majority that is not before us. What does that mean? When we speak about the majority of women who are not infertile, who is the total group we are talking about? It is all the women in the world. And we assume that among all the women in the world, the majority can produce children, and there is a minority who are infertile, who cannot produce children. And we assume that this girl before us belongs to the majority. That is called following the majority. The majority and minority we are talking about here are a majority that is not before us. It is not before us. All the women of the world are not before us; we do not know all the women of the world. It’s not like judges, where there are three judges and we know who they are, and we know that two think one way and one thinks the other way—or twenty-three, whatever it is—but all of them are before us. And the same is true of the stores: ten stores, nine kosher and one non-kosher. We know all the stores, they are before us, and we know the distribution. Right? How many stores of this type there are and how many of that type there are.
With the women of the world, we have some sort of general information about a group that is not before us. It’s all the women of the world in principle. Therefore this is a different kind of majority—that’s what the Talmud assumes. And since this is a different kind of majority, the Talmud says: where do we know that we follow it? The subtext is: this cannot be learned from “incline after the majority.” Meaning, from “incline after the majority,” which you wanted to use as the source for the law of following the majority, I’m willing to accept that for a majority that is before us. Fine, that we learn from “incline after the majority”: stores and Sanhedrin. But a majority that is not before us—you can’t learn that from there. That’s what the Talmud says. So where do we learn it from? How do we know that we follow a majority that is not before us?
Now here, a few comments.
[Speaker C] Why does that matter? What’s the meaning of the distinction? What? What’s the meaning of the distinction? Why does it matter?
[Rabbi Michael Abraham] I’ll get to that in a moment. So there are a few comments I want to make. First, the wording of the question. It says: “From where do we know this matter, that the Sages said to follow the majority.” Meaning, we are not putting the rule itself into question—that we follow the majority. That’s obvious. The rule is known and agreed upon, everything is fine. All we are asking is a conceptual, theoretical question: what is the source of this rule? It’s not that if we don’t find a source, then there won’t be such a rule. The rule exists and it is correct; it is a clear tradition; no one disputes it. We follow the majority both in a majority that is before us and in a majority that is not before us. What we are asking is whether there is a source.
That somewhat reminds me of what… yes… what Elazar ben Azariah said: “Behold I am like a man of seventy years, and I had not merited that the Exodus from Egypt be mentioned at night until Ben Zoma expounded it.” Right? “All the days of your life”—the days; “all the days of your life”—the nights. What does it mean, “I had not merited that the Exodus from Egypt be mentioned at night”? Usually people think that they did not mention the Exodus from Egypt at night until the point when Ben Zoma expounded it. But that’s very unlikely, because that’s the law of recounting the Exodus from Egypt on the night of the Passover Seder. What, until Ben Zoma they didn’t do that? It’s pretty clear that they did. So what does that mean—what is the meaning of that statement, “I had not merited that the Exodus from Egypt be mentioned at night”? It means: I had not merited to find the source for the fact that they mention the Exodus from Egypt at night, until Ben Zoma taught me the exposition: “the days of your life”—the days; “all the days of your life”—the nights. Now I know what the source is. But the law itself—it was an agreed law. We knew that law; there was no question mark over the law.
By the way, in many places in the Talmud you find the phrase “we have found the law.” “We have found the law” means we have found the source of the law. “We have found” means we have found the source for that law.
[Speaker C] So therefore what does—
[Rabbi Michael Abraham] “I had not merited that the Exodus from Egypt be mentioned at night” means: I didn’t know what the source was for the fact that the Exodus from Egypt is mentioned at night.
[Speaker C] Rabbi, Rabbi, I didn’t really understand. “Incline after the majority”—what’s the other option? Suppose the Torah hadn’t said “incline after the majority,” what would we do in a case of doubt?
[Rabbi Michael Abraham] The laws of doubt. We wouldn’t follow the minority, right, that’s obvious, but we would apply the laws of doubt. There is doubt here, after all. You assume that there’s a situation of fifty-fifty, but if there’s sixty-forty or eighty-twenty, then you follow the majority. Why? Maybe we should leave it in a state of doubt?
[Speaker C] In a dispute between one person and another, would they say it’s doubtful and we’ll wait? What would they do, say, in a monetary dispute?
[Rabbi Michael Abraham] They would leave it in the possession of the current holder; they would apply the laws of doubt.
[Speaker C] By the way, there’s actually a very nice force to the idea that only when they reach unanimity is there any value to all these court discussions. If there isn’t unanimous agreement, then really it was a waste with the lawyers.
[Rabbi Michael Abraham] Without the verse, without the verse of “incline after the majority,” truly we would not follow the majority—that’s what seems to emerge from the Talmud. Only unanimity. Yes. And I brought, in one of the previous lectures, the view of Rabbenu—
[Speaker C] Tam. That—
[Rabbi Michael Abraham] It’s not something practical. I brought the view of Rabbenu Tam in one of the previous lectures.
[Speaker C] Yes, but that’s about communities; that too has to be discussed.
[Rabbi Michael Abraham] What difference does that make? The idea is the same. In a place where we have no source, then the rule is unanimity—we do not follow the majority.
[Speaker C] What legal system could function like that? In every dispute, all it takes is one judge—what’s the problem?
[Rabbi Michael Abraham] There are disputes. Things can remain doubtful, and there are rules for doubt. What’s the problem?
[Speaker C] The whole legal system would have no substance.
[Rabbi Michael Abraham] Of course it would have substance. The judges sit, and if they agree then there is a ruling, and if not then the laws of doubt apply. What’s the problem with that? There are situations of doubt; that’s allowed. In any event, that’s the first comment.
The second comment is: why should there really be a difference between a majority that is before us and a majority that is not before us? What difference does it make? Statistics—we go with statistics: ninety-ten, so the ninety overcomes the ten. Why do I care whether the majority is before me or not before me? What difference does it make if the majority is present before me or not present before me? I’ll put it in an even sharper way. Why is the majority of the women of the world not before us? It too is before us. “Before us” doesn’t mean that I see all of them. The stores in the city—I don’t necessarily see them either, right? It could be a large city with ten butcher shops. I’m standing somewhere in the city. Do I see all the stores? Of course not. I know there are ten stores in the city. So what does it mean that it is “before us”? It doesn’t mean physically before me; rather, I know that there is such a group and the split is nine to one. So why aren’t all the women in the world the same thing? There too, among all the women in the world, the split is basically ninety-ten, let’s say, or something like that, and the whole group of the women of the world is before us.
[Speaker B] In the time of the Talmud, it’s not necessarily clear that… they relied on information. It was based on a law of nature. They said nature proceeds according to its regular course. That’s the natural law. But they don’t have information now about each and every woman.
[Rabbi Michael Abraham] What does information have to do with it? But they know the distribution of births.
[Speaker B] Right, what does it mean they know? They know the distribution.
[Rabbi Michael Abraham] They know that most women give birth. Right. I mean, they know—
[Speaker B] It’s according to some law that they observe.
[Rabbi Michael Abraham] What do you mean, some law that they observe? They simply see that most women give birth. Yes, but—
[Speaker B] They’re making, as it were, a copy over to the rest of the world, which isn’t—
[Rabbi Michael Abraham] You mean from the sample. Yes. What they see is only a sample. So I’m getting to that in a moment. That’s right; I’m getting there in a moment.
I’m saying that, in principle, we need to define better what the difference is between a majority that is before us and a majority that is not before us. There’s a lot of confusion about this among the later authorities, and in my opinion among the medieval and later authorities. There’s a great deal of misunderstanding here. So that’s basically the fundamental question, because in the Talmud itself you see that the Talmud is willing to accept “incline after the majority” as a source for a majority that is before us, but it is not willing to accept it as a source for a majority that is not before us. Meaning, it sees these as different mechanisms, different principles. One cannot be learned from the other. Why not? What difference does it make? It’s ninety in one distribution and ninety in another distribution. If I have a cube—whatever—a cent coin, and I flip heads or tails, it’s fifty-fifty, right? Now I do it with a shekel. That too is fifty-fifty. So if you tell me that with cent coins I should follow the statistics, wouldn’t I understand on my own that with shekel coins I should also follow the statistics? What difference does it make? If there is a ninety-ten statistic, I follow the ninety. What practical difference does it make how that statistic was generated? And what difference does it make whether it is before us or not before us? And in general, what does it mean that it is not before us? It’s before us as well—people in the world too. Meaning, this whole story in the Talmud is very vague.
On the other hand—and maybe I’ll sharpen it even more—the distinction the Talmud makes is not the result of a verse. On the contrary. The Talmud assumes this distinction as something obvious. Therefore, when they bring the verse “incline after the majority” as a source for the law of following the majority, the Talmud is not willing to accept it as a source for a majority that is not before us. Meaning, the Talmud assumes this as self-evident. It’s not that it has some verse that says there is a difference between a majority that is before us and one that is not before us, and this is a scriptural decree. No, it is not a scriptural decree; it is a logical argument. It is a logical argument—and not only that, it is such a strong logical argument that the Talmud is unwilling to accept a source that deals with a majority that is before us as a source for the idea that we also follow the majority when it is not before us. So first of all it is a logical argument, and this argument appears to the Talmud to be decisive, very strong. So the question is: why? What is the reasoning here? Why does it matter where the statistics came from?
So first of all I want to define the concepts better before asking what is stronger and what is weaker. On the conceptual level, a majority that is before us is basically this: I have a group, say, of ten stores. They don’t of course need to be standing before me in the sense that I see them with my eyes. But I know the ten stores. I have complete information about them. I know that nine sell kosher and one sells non-kosher. And now I ask: this piece of meat—it is clear that it came from one of the stores. The only question is from which store it came, right? And I am basically asking a question about a piece of meat that belongs to a group for which I have statistical information about the group. And now I ask: to which of the two groups does the piece of meat belong? To the majority group of kosher meat, or to the minority group of non-kosher meat? It is clear that it belongs to one of the two groups. It’s just that now it has separated—it is not… right, “anything that separated is presumed to have separated from the majority.” So it separated, it is not inside the store, so I cannot know with certainty to which store it belongs, so I follow the majority. “Anything that separated is presumed to have separated from the majority.” That is a majority that is before us.
A majority that is not before us—the non-infertile women—that is essentially a majority that is not before me not because I don’t see the women; I don’t see the stores either. It is not before me because I really do not have information about all the women in the world. That’s simply not true. I have no empirical information about all the women in the world. I have information about those women whom I know. And among the women I know, the majority can produce children and a minority cannot, the infertile minority. Who says that this is also the distribution among all the women in the world? So I make a generalization. I take the sample that I know and generalize on the basis of the sample. Which is exactly what is done in scientific work. I take some sample and I make a generalization based on the sample and establish a general law. Right? I saw… some number of bodies with mass falling toward the earth, and I generalize from that sample and say that apparently all bodies with mass—those I know and those I don’t know—apparently all of them will fall toward the earth. So I make a generalization based on a sample.
Generalization based on a sample is a method that is not free of problems. It is not free of problems because who says that this sample is a representative sample? It could be that the people I know are, for some reason, women who have some tendency to give birth, because this place causes them to be that way, or I don’t know exactly what. Or if it’s a wealthy place, then people only marry women who can give birth, so therefore among us there are only women who can give birth. But in other places maybe the distribution is completely different. How can you know that the sample you know is a representative sample? And we’ll encounter this point quite a bit later on. A great many errors in statistics come from the fact that I use an unrepresentative sample. I have some information about a sample, I conclude that this is also true of the group as a whole, and that conclusion is hasty, because the sample is not representative. The sample is biased.
When we do a sample about voting for the Knesset—one of the amazing things there, I found this out a few years ago, I had no idea—the most professional polling samples they do are on 500 people. That’s nothing. There are 120 members of Knesset; it’s the same order of magnitude. They test 500 people, see their voting distribution, and from that infer conclusions about the whole population, when we’re talking about significance, right, about a deviation of two, three, four percent one way or the other. It’s unbelievable that 500 people can give me such a remarkably accurate estimate. Political polls got a bad name here, really not justifiably. Political polls are super accurate. Super accurate. And it’s amazing how accurate they are. And the most amazing thing is that it’s done on the basis of 500 people. Those are the standard polls. Some do more, but the standard polls are 500 people. And they give you a deviation of only a few percentage points, two, three, four percent one way or the other.
Now why did they get a bad name among us? Because our political contests are usually close in elections. Coalitions are coalitions of sixty-something; there are no longer coalitions of seventy or eighty, almost none—coalitions of seventy or eighty Knesset members. Now in such a situation, many times an error of one percent this way or that way can flip the whole picture. But understand that an error of one percent is a very impressive statistical achievement. The fact that the contests are close, and therefore one percent can flip the picture—fine, that’s true—but that is not the problem of statistics. The statistician also tells you: my sampling error is three percent one way or the other. And usually it falls there, almost always. The achievements of this field are amazing, and it’s amazing how wide the gap is between the achievements of the field and its public image. The public image is as though we’re dealing with some bunch of speculators just making things up as they feel like it. That’s really not true. It’s a very impressive professional field.
Anyway, for our purposes—why is it so impressive? Or how did it manage to become so impressive? It wasn’t like that at the beginning. Because these people developed very sophisticated methods for finding 500 people who will constitute a representative sample. That’s the great wisdom. If you just gather 500 random people in the street, it won’t come out well. You have to offset a lot of things, make sure those 500 people represent different population sectors, divide them in some way, offset the biases. Some people mess with the pollster; voters of certain parties tend to mislead pollsters. So they developed many, many methods for finding a sample of 500 people that will actually be a representative sample. And that’s the whole story.
Meaning, all the important technique—taking 500 people, doing statistics on how they vote, and then deciding what will happen in the election—any idiot can do that. For that you don’t need a statistician. What’s the problem with doing that? Take 500 people, ask them what they’re voting for, multiply the results, adjust them to 120 Knesset members, and there you have the result. Why do you need statistical institutes and experts to run this and so on? The whole thing, entirely, lies in the question of how you determine the sample. That’s the whole story. How do you determine the sample? Do you manage to create a sample that will truly be representative, meaning that the distribution within it will be like the distribution in the whole population? That’s a great art. That’s where the expertise lies. Everything depends on the question of how you determine the sample. That’s the whole story. How do you determine the sample? Because if you succeed in creating a sample that really is representative, meaning that the distribution in it is like the distribution in the whole population, that is a great art. That is where the expertise lies.
And therefore a majority that is not before us is basically a majority that is based on generalization from a sample. What is before me is a sample. A majority that is not before us is basically a majority that is based on generalization from a sample. What is before me is a sample. In a majority that is before us, what is before me is the entire group—the majority and the minority, everything is before me, I have complete information. In a majority that is not before us, what is before me is a sample. That sample has a majority subgroup and a minority subgroup within the sample. The big question is what happens in the general group. For example, in our case, among all the women of the world. I know, let’s say, fifty women, a hundred women; I know that out of them ninety-five out of a hundred, say, managed to produce children, and five did not manage to produce children. Now I want to know what the situation is among all the women in the world. Is it also ninety-five-five there? Maybe in my case it just happens to be an unrepresentative sample; somehow there is bias in the distribution. That’s the big question.
So generalization based on a sample is a step that is speculative in a certain sense. Meaning, it involves many assumptions. Therefore, says the Talmud—at least that’s how I would understand it—even if I have a source for a majority that is before us from “incline after the majority,” who says that one may follow a majority that is not before us? A majority that is not before us is a very problematic majority. It is problematic because the information you have is about a sample group, but you don’t know whether that sample is representative or not. You don’t know what it says about the population as a whole. So who says that in Jewish law one may rely on such a mechanism? Right—that is the problem with a majority that is not before us. Say maybe a point connected to that.
[Speaker D] What? And in this way of thinking about the sample, what happens if I reach a reality that is not according to the sample? Am I supposed to rule the opposite, or should I always—
[Rabbi Michael Abraham] If it’s not according to the sample, then the statistics are not correct. The statistics of the sample do not represent the general statistics.
[Speaker D] Right, right. But if I have a ruling that did go according to this rule of the sample?
[Rabbi Michael Abraham] You’re asking whether we decide questions of majority on the basis of statistical calculations. Meaning, if there’s a statistical bug, would the halakhic ruling of following the majority also change? Exactly. Exactly. That’s one of the things we’ll have to get to. But for that, I want to clarify the concepts of majority, and then we’ll try to see what their relationship is to statistics. Okay, that’s the topic. So first I want to—I’m still in defining the concepts of a majority that is present before us and a majority that is not present before us. I want to say, to look at that same distinction I made earlier from a slightly different angle. Look at the woman, this woman before us whom we want to know about—or the girl, yes?—this one before us, and we want to know whether she is infertile by nature or not, and we decide that on the basis of the majority, since most women in the world are not infertile by nature. Now you have to understand that with this girl there was no process of separation. In the stores, the piece of meat was in some store, and while it was still inside the store I had information about all the stores, statistical information. That information was also information about this very piece of meat itself, right? Let’s say I have ten stores in the city and I know that nine of them sell non-kosher meat and one sells kosher. One sells kosher. As long as the pieces of meat are in the stores, I can tell you everything about all the pieces. I have full information about the whole group. Let’s say there are a hundred pieces, distributed among ten stores. So ninety pieces are kosher and ten pieces are non-kosher. And I can also tell you about each piece whether it is kosher or non-kosher. I have full information about the whole group. Now suddenly I find a piece of meat in the street. Where does the doubt arise? Why does the doubt arise here? The doubt arises because it separated from one of the stores. Because it isn’t in its place, it’s not in the store—it separated. What happens when it separates? The moment it separates, I don’t know which store to assign it to. On the other hand I say, yes, but this piece—before it separated I could have told you its status, right? It was basically supposed to be kosher, okay? If it separated from the kosher store, and there are nine kosher stores and one non-kosher one. So the fact that it separated doesn’t change the situation. Because after all, I have information about a hundred pieces in this city, of which ninety are kosher and ten are non-kosher. This piece is certainly one of the hundred, and I have information about all one hundred. So I want to apply the ninety-ten statistics to this piece as well. Because this piece is included in the information I have. That’s an important point—notice. In the case of the infertile woman, that’s really not the situation. I’ll draw you a different picture. Let’s say I have a million women in the world, for the sake of discussion. Of them, nine hundred thousand are not infertile by nature and a hundred thousand are infertile by nature—ten percent. Okay? And I know—I know, I’ve gone through, I know all the women in the world. I know the full information on all the women in the world. Now a woman comes before me who is either infertile by nature or not infertile by nature, everything is known, and I need to decide her status now. In that situation, that is a majority present before us. It is not a majority not present before us. Even though we’re talking about all the women in the world. Why? Because the information I have also pertains to her. After all, I know all the women in the world, and I know that ninety percent of them are not infertile by nature and ten percent are infertile by nature. Now I ask: where did this woman come from? Did she come from the majority group or from the minority group? When I have full information about all the women in the world, including her, she is part of the group about which I have information. That would be a majority present before us, not a majority not present before us. What is the difference in our case? In our case we are talking about a minor. About this minor we still have no information at all, because it is not yet known whether she is infertile by nature or not. So it’s not that this minor belonged to some group—either to the minority group or the majority group—then separated, and now I don’t know from which group she separated, from the minority or the majority. Because questions of separation are always questions where before the separation I had full information about all the pieces. Now one of the pieces comes before me, and it belongs to the group about which I had full information, including this piece itself, except that now something got mixed up for me, so I don’t know where this piece belongs. So about this piece too I have information—statistical information. I know that this piece belonged to a group of which ninety percent was kosher and ten percent non-kosher. With infertility by nature it isn’t like that, because the little girl is now a new case. She didn’t separate from anywhere. I know all the women in the world, the women who have already been diagnosed—ninety percent are not infertile by nature and ten percent are infertile by nature—but this girl hasn’t been diagnosed at all yet. It’s not that she belongs to one of the two groups. I have no information about her.
[Speaker C] What if I knew the information about all the women in the world with certainty?
[Rabbi Michael Abraham] Yes, even then. Because about her you wouldn’t know, since she’s still a minor.
[Speaker C] But she belongs to the group of women, so what, I don’t know? I know in exactly the same way as before. If I know? Of course I do!
[Rabbi Michael Abraham] Not at all, because she wasn’t included—there is no information about her.
[Speaker C] No, but if I know the definite information about all the women in the world—not a sample, actual definite knowledge. The adults. Adults, but what difference does it make that she now joined the adults? She belongs to that group.
[Rabbi Michael Abraham] No, she doesn’t belong.
[Speaker C] We’re going to say that I don’t know what—
[Rabbi Michael Abraham] No, that’s a mistake. That’s exactly the point. “Now she joined”—that’s the focal point. Why? So what’s the logic of the focal point? Wait, I’ll explain. If I have full information about all the women in the world—a million women—and now one of them went out, then I had information about a group that also included her herself. And she went out from within the group. So now I ask whether she came out of the ninety-percent group or the ten-percent group. And she probably came out of the ninety percent. But this girl, the information I had did not include her. I have information about other women. Now she joined. She grew up and joined the group. Now the question is not where she separated from, but what she is entering into—and that is a completely different question. Since this is not a question where I’m applying information that I also had about this very piece itself, and only now it got mixed up for me so I apply statistics to it. This girl—who told you at all that she is connected to the distribution among all the women in the world? What does that even have to do with it? If one of the women in the world had separated, I would say she probably separated from the ninety percent, obviously. Why? Because the full information was about the group that included her herself too; only now she separated. So I ask where she came from—did she come from the ninety or from the ten? That’s called “anything that separates, separates from the majority.” But that is a majority present before us, and many later authorities don’t understand this. Such a thing is a question of a majority present before us, not a majority not present before us. But the little girl never belonged to the group about which I have the information. I don’t have information about her. Therefore even if I have the information—
[Speaker B] Just—
[Rabbi Michael Abraham] One second. Notice, I’m not making a generalization now on the basis of a sample. I now know with certainty all the adult women in the world. I know exactly what the distribution is: ninety percent not infertile by nature and ten percent infertile by nature. Still, regarding the minor this is a majority not present before us. It is a majority not present before us—why? Because the information I had was about a group that did not include this minor herself, but about a different group. About that group I have the information. I want to apply to her the information I have about that group. What does this application mean? A generalization from a sample. Even though the information about the million is not information based on a generalization from a sample. It is direct information—I know, I know all the women in the world. Okay? But now this girl who comes—when I want to apply to her the certain information I have about all the women in the world, that very application will be a generalization on the basis of a sample. Yes—
[Speaker B] That assumes some law of nature like that.
[Rabbi Michael Abraham] One second, I’ll get to law of nature in just a moment.
[Speaker B] Before the law of nature—the generalization on the basis of a sample.
[Rabbi Michael Abraham] Why? Because the girl is not one of the million women; she was not included in the group about which I have the original information. She is not part of that group. Therefore the information I have about that group is merely a sample, and now I want to apply it to another woman—not a woman who belongs to that group. So that is already a generalization on the basis of a sample. That is a majority not present before us. Do you understand that with the piece of meat I find, I am not doing that? Because with the piece of meat I find in the street, this is not a generalization on the basis of a sample. This piece itself belongs to the group about which I know the information—ninety-ten. I know it directly; it’s not a sample-based generalization. I know that ninety percent of the pieces of meat in this city are kosher pieces and ten percent are non-kosher pieces, and this piece is one of the pieces found in the group about which I have the information. Only now it separated. It separated from that group. “Anything that separates, separates from the majority.” This can be learned from a court. That is “anything that separates, separates from the majority.” But a majority not present before us is not “anything that separates, separates from the majority.” It did not separate; there is no concept of separation here. Therefore “anything that separates, separates from the majority”—many times you see in the medieval authorities (Rishonim) and later authorities (Acharonim) that they use this as some sort of loose expression, as though that’s more or less how the problem arose. No. It belongs intrinsically to the definition of a majority present before us. “Anything that separates, separates from the majority” is the definition of a majority present before us. And therefore separation, the concept of separation, is a very important concept. It isn’t a formalistic concept, it’s a substantive concept. If there is no separation, it is a majority not present before us.
[Speaker B] Wait, did the Rabbi address how—I don’t remember—regarding the court itself, how that counts as separating?
[Rabbi Michael Abraham] Wait, wait, we’ll get there, we’ll get to the court. Not yet, I’ll get to the court. Right now I’m talking about stores versus infertility by nature, okay? Now here another element really enters. The basis—what am I doing—meaning, when I make a generalization on the basis of a sample, why do I assume that what holds in the sample holds in the overall group? That’s an a priori assumption. Where does it come from?
[Speaker E] The sample is taken from the total group.
[Rabbi Michael Abraham] That’s not exactly the assumption. I can’t hear.
[Speaker D] There’s simply no other way, no better way than that.
[Speaker E] The sample is taken from the group.
[Rabbi Michael Abraham] Let’s formulate it differently. Let’s say there are ten stores in my city, nine kosher stores and one non-kosher one. Can I infer that in the whole world there are ninety percent kosher meat stores and ten percent non-kosher meat stores? No. Why not? I have a sample-based generalization, don’t I?
[Speaker C] Here the characteristics are similar—
[Rabbi Michael Abraham] A law of nature—only if this were a matter of a law of nature.
[Speaker D] No, no, specifically with stores you can’t say that.
[Rabbi Michael Abraham] Right, it’s not a natural law about stores. Exactly. Because the distribution among the stores in this city is not a law of nature. Exactly. In this city there are nine stores that chose to sell kosher meat, one store that chose to sell non-kosher meat, but that has nothing to do with a law of nature. Since that’s so, in another city—depending on the customers, depending on whether there are Jews there or not—the distribution will be completely different. There is no reason to assume that the distribution in this city represents the distribution in the world or in another city.
[Speaker B] But—
[Rabbi Michael Abraham] When I’m talking about, say, women, whether they are infertile by nature or not, and I see that in the world there are ninety percent of women not infertile by nature and ten percent infertile by nature, I assume that this is simply the nature of womanhood. A woman’s nature causes her generally to be able to bear children unless there is some malfunction. Okay?
[Speaker D] Here we are—
[Rabbi Michael Abraham] In the domain of a law of nature.
[Speaker D] Does the Rabbi think that in the time of the Talmud this is also what they thought? Meaning, it’s not like today when we know that most of the world is similar. What do you mean, most of the world is similar? Meaning, a sample from my city, a sample from my country, represents the world. But they never flew abroad and they didn’t know what’s beyond the sea. On the contrary.
[Rabbi Michael Abraham] What? On the contrary. In the past they assumed as obvious that the whole world is similar. Today we’re aware that no, that’s not correct—you need a representative sample; not every sample is representative.
[Speaker D] Meaning because of the lack of knowledge—
[Rabbi Michael Abraham] Exactly the opposite of what you said.
[Speaker D] Because of the lack of knowledge they had to assume that the whole world is similar.
[Rabbi Michael Abraham] I don’t know if they had to, but I think they weren’t aware of these statistical nuances. And they did tend to think that if this is what I know around me, then that’s probably the whole world.
[Speaker D] That was their working assumption. Yes, it’s a very simple working assumption, really, yes.
[Rabbi Michael Abraham] Simple, but often problematic. Yes. The important point is that my move from the sample to the overall group stems from the fact that the distribution in the sample is the result of a natural condition, of the laws of nature. And since that is so, if the sample is representative, I have no reason to assume that the distribution in the broader group will be different, because these are laws of nature. Women have female physiology—what difference does it make whether these women or those women? Of course, someone who does a distribution study in a clinic that deals with infertility, and there he checks the distribution of women infertile by nature, won’t get very far. If he makes a generalization on the basis of the sample he finds there, he won’t get very far, because it’s a biased sample. But if I take a sample of women, a random sample of women, my assumption is that the distribution in that sample will also be the distribution in the whole world. And why? Because that distribution is the result of the laws of nature. And if my sample is large enough and representative enough, then that’s probably what is happening in the whole world too, more or less. Therefore the move from the sample to the overall group stems from the fact that the distribution I am dealing with is the result of the laws of nature. And therefore if I now look at all the women in the world, and let’s say I know the distribution, I know that 90% of them are not infertile by nature and 10% are infertile by nature—I know this by personal information, not from a sample-based generalization, I know it all. Okay, and now an adult woman leaves the group about which I had information, and I ask now whether she is infertile by nature or not. That is a majority present before us. Why? Because when I assume she is not infertile by nature, it is not because the laws of nature say that women are not infertile by nature, but because I know that out of 100% of women, 90% are not infertile by nature. I have concrete information about that; I don’t need the laws of nature. Even if these were not laws of nature, and it just happened that in this generation 90% of women are not infertile by nature, still if one of them had separated, I would assume she is not infertile by nature, regardless of whether this is a law of nature. Why? Because the decision about her does not stem from the question of how her physiology works; I am simply asking where she separated from—did she separate from the majority group or the minority group? And if I know that the majority group is women not infertile by nature, then I will assume she too is not infertile by nature, regardless of what the laws of nature say. You don’t need to know anything about the laws of nature. Rabbi, but one second—but if I want to decide about a little girl that I now need to decide about, who did not separate from the full group about which I had the information, then I said this would already be a majority not present before us. Why? All the women are known, it’s a million women before me, I know the information about all of them. Yes, I know the information about all of them, but the woman I am dealing with is not one of the group about which I know all the information. She is outside that group. And when I go out to apply the information in that group to this new woman or this new girl, there will be a generalization from a sample here. How do I know that she too is probably in the 90%? How do I know? If the woman came out from the group of the million, then it’s clear why there is a 90% chance she is not infertile by nature, because this is a random woman coming out of a group in which 90% are not infertile by nature. But if I want to discuss a new woman—if this were not a law of nature—then it would not help me to know that 90% of women are not infertile by nature and 10% are. That would say nothing about this woman. Nothing at all. Only because I know that the ninety-ten information is the result of the laws of nature, and I assume that the laws of nature work on this girl too in the same way, only then do I say that she is probably not infertile by nature. Here I have to assume that we are dealing with laws of nature.
[Speaker C] And everything is laws of nature—what isn’t a law of nature?
[Rabbi Michael Abraham] The stores in the city and what is kosher and non-kosher—that is not a law of nature. That is exactly the distinction we are making.
[Speaker C] To check it all the way down to the root—what brought them to be what they are, and in the end?
[Rabbi Michael Abraham] Not laws of nature, it’s—
[Speaker C] A multiplicity of cases, right?
[Rabbi Michael Abraham] You see that in every city the distribution is different, so there’s nothing to investigate. If you investigate and reach a determinism of how each person chooses, that’s not interesting. Because if you reach that, then you won’t be able to infer anything from this city to other cities; instead you’ll have to do something else—not a sample from this city, but another sample. The sample we make on the basis of the stores in this city has no connection to laws of nature.
[Speaker B] Yes, it comes out as an all-encompassing law of nature. To say that everything is a law of nature—that’s not the problem.
[Rabbi Michael Abraham] Yes, no, that’s not what’s interesting, because that’s not how it works.
[Speaker C] Let’s assume that being infertile by nature or not were a matter of free choice, okay? Not laws of nature. So what then? About this girl—I don’t know whether she has the capacity for choice, I don’t know, we can’t talk about—
[Rabbi Michael Abraham] What she chose—I don’t know.
[Speaker C] So then couldn’t we use the same statistics? Right, it’s not— I agree that this is not present before us, I agree. Actually no, no.
[Rabbi Michael Abraham] Only—only a majority not present—
[Speaker C] Before us.
[Rabbi Michael Abraham] But if I had only a majority present before us, I couldn’t.
[Speaker C] It’s not a sample and it’s highly representative—why isn’t she?
[Rabbi Michael Abraham] So I’m saying, maybe that would be a majority not present before us, but not a majority present before us.
[Speaker C] I accept that, for the minor, okay?
[Rabbi Michael Abraham] No, a majority not present before us would apply to the minor. That’s fine. What— I didn’t understand the claim.
[Speaker C] The division into present before us or not present before us is very nice, and really brilliant, but the law of nature isn’t clear to me. If we are talking about a sample—not about present before us but not present before us—then not present before us is statistics, a sample, what?
[Rabbi Michael Abraham] This statistics is based on—
[Speaker C] Laws of nature—we’re not looking for laws of nature there.
[Rabbi Michael Abraham] Of course we are, of course we are! Only laws of nature! Only laws of nature!
[Speaker C] But people—that’s laws of nature?
[Rabbi Michael Abraham] Listen, only laws of nature. If this were not about laws of nature, all your statistics would not help you. Your statistics would be completely irrelevant. Because the question is why you assume that what happens in this group is also true for someone who is not from the group.
[Speaker C] Right. So I’m saying, subjection to laws of nature covers everything; there’s no case without laws of nature. Even those who choose, supposedly by free choice—it’s the same thing.
[Rabbi Michael Abraham] The number of stores in the city is not a law of nature.
[Speaker C] No, that’s present before us—I’m talking about not present before us.
[Rabbi Michael Abraham] Now we’re going back to not present before us, to an election sample. I’m returning to what I’m saying and putting a question mark at the end. I’m saying: a majority not present before us is laws of nature, right? Yes, yes, that’s what I’m saying. And this claim, in the end, is an important point because I think many people don’t understand it, including halakhic decisors and rabbis—they don’t really understand this distinction properly. And many complications surround various questions of whether this is present before us or not present before us, and they don’t truly understand the difference in the proper way; they look at whether it is before us or not before us. The question is not whether it is before us or not before us; that is not the point at all. That’s not the issue. The question is where the information I have about the full group comes from. Is the information I have about the full group the result of a generalization from a sample, or is it direct information? If it is direct information, that is a majority present before us. If it is the result of a generalization from a sample, that is a majority not present before us. That is the question—how was the ninety-ten statistical distribution created: is it a generalization from a sample, or direct knowledge? That’s the question. Rabbi—
[Speaker D] Last week the Rabbi brought—I don’t remember what this rule is called—that the Talmud says a woman does not like living alone.
[Rabbi Michael Abraham] “Better to dwell as two than to dwell alone,” yes.
[Speaker D] Yes, so what is that?
[Rabbi Michael Abraham] That’s a law of nature.
[Speaker D] They assumed that it was a law of nature?
[Rabbi Michael Abraham] Yes, human nature. Human nature is that she wants a relationship.
[Speaker D] Meaning, they took a sample from their surroundings and assumed that that’s how it is.
[Rabbi Michael Abraham] Not necessarily that they took a sample. Even today, by the way, only a small minority of our statistical determinations are based on a sample. We assume things. We don’t make some sophisticated and professional statistical calculation. In the past no one did that, and today there are already experts who know how to do it professionally. In the past no one did that, but common sense also worked back then.
[Speaker D] Yes, I mean, I assume that at that time it’s clear they didn’t do a sample—some statistician didn’t come and ask people—it was probably just cultural, that a woman doesn’t like to be alone; it was very much embedded in the culture.
[Rabbi Michael Abraham] Right, as an essence. They took a sample, they saw the women around them, and understood that this is the nature of women. Yes.
[Speaker D] So the distinction—
[Rabbi Michael Abraham] Essentially this distinction is the conceptual distinction. Now I ask myself, and I return to the Talmud. In the Talmud itself it says that if there were a verse, “follow the majority,” I would derive from it a majority present before us. And the question is where I would know from there a majority not present before us. I explained this in the course of what I said—this is, apparently, the simple, natural explanation: that a majority not present before us is weaker. Because it assumes some kind of extension on the basis of a sample. One could say that here we have Hume’s problem of induction.
[Speaker B] On the one hand it is weaker, but on the other hand it is also stronger in the sense that it is a law of nature.
[Rabbi Michael Abraham] Wait, one second, you’re getting ahead of me. So from the first side, right now I’m on the first side, apparently it is weaker. Why? Here in the stores we have full information about all the pieces of meat. Right? Our information is complete. Now a piece has separated, and it is reasonable to say that it probably separated from the majority and not from the minority. That sounds like something much stronger than taking some sample of—I don’t know what—fifty or a hundred women that I know, and deciding something about all the women in the world, something very speculative, and drawing a conclusion on that basis about a new woman who comes before me.
[Speaker C] Even though probabilistically that’s not true, because in fact all of probability theory says it could make no difference, or the opposite.
[Rabbi Michael Abraham] No, wait, we’ll still get to probability. First I’m asking just in terms of common sense. On the face of it, there is Hume’s problem of induction here. Yes, induction that says: I know a certain sample and I generalize from it to the whole group. David Hume says: there is no basis for that at all. Why do you assume that what is true of the sample is true of the whole group? There is a large degree of speculation here. Now never mind at the moment how one answers Hume’s difficulties—I’ve dealt with this quite a bit—but I’m saying, this difficulty is probably the basis for what the Talmud is doing here. The Talmud says: if you learned a majority present before us, the question of a majority not present before us still remains open, because the assumption is that a majority not present before us is a weaker majority. And the question whether to proceed also on the basis of a majority not present before us cannot be learned from the verse that deals with a majority present before us.
[Speaker C] The Sages didn’t do induction? What, were they really stammering like that? How did David Hume suddenly wake up here?
[Rabbi Michael Abraham] So I said, I said that the Talmud’s question—this is why I prefaced it—is not whether to use majority, but where the source for using majority comes from. They use majority beforehand. The whole question is only where the source comes from. That’s all. So they say that the source from the verse “follow the majority” cannot be the source, because a majority not present before us is a weaker majority. Right, and they use it.
[Speaker C] Why isn’t it enough to call it logic?
[Rabbi Michael Abraham] Maybe it is, but the Talmud doesn’t bring it from the standpoint of logic. In a moment we’ll see what the conclusion is. But it’s not—again I’m saying—the question is only a question about the source. And if a source is brought for a majority present before us, the Talmud says that cannot help me with a majority not present before us. So you see that a majority not present before us is weaker.
[Speaker B] Rabbi, when the Rabbi says that the problem with the sample is, like, the epistemological question itself? Or is it simply that maybe we made a mistake in the calculation?
[Rabbi Michael Abraham] It’s the same thing.
[Speaker B] Rabbi, and that’s the same thing?
[Rabbi Michael Abraham] It’s the same problem. The question whether the sample is representative or not representative is the same problem as David Hume’s, just from another angle. Even with the most representative sample in the world, from your point of view, I can still ask David Hume’s question: who says this is true for the whole world? And if it isn’t true for the whole world, that means the sample I saw was not representative. You assume there is some universal law of nature here—but that itself is what David Hume asks: where did you get that from?
[Speaker B] Right, right, but I mean David Hume is a much more basic question.
[Rabbi Michael Abraham] Two angles on the same question.
[Speaker B] Because after we answered David Hume, supposedly—after, as the Rabbi himself answered, after we answered that—then it no longer remains weaker, as it were. It’s a problem you need to get past.
[Rabbi Michael Abraham] No, no, why? I can understand why to rely on it, but that doesn’t mean it is stronger than a majority present before us, or not weaker. Why? It is weaker; it’s just that logic says we rely on it as well. Intuition, logic, whatever you want to say. I’m not speaking now about the question whether to rely on majority. I’m saying again: the Talmud is not discussing whether to rely on a majority not present before us; obviously we do. The whole question is what the source is for relying on it.
[Speaker B] No, but I mean it’s simpler to say that this too is a problem of, like, sample calculation, as the Rabbi said—that this is what statisticians are for, to know—
[Rabbi Michael Abraham] I’m saying that even if you have statisticians it won’t help you, because after you have the statisticians, you assume that once they found the most representative sample, then clearly you can draw a conclusion about the majority. David Hume asks: why on earth? Even then.
[Speaker B] Right, right, I agree. I’m only saying that you don’t necessarily have to assume that in order to show that a sample is weaker than present before us—that’s obvious. Because a sample can always make mistakes in the calculations anyway; it’s not free of problems.
[Rabbi Michael Abraham] More than that, even if you—
[Speaker B] The Rabbi is saying, like, the statistics—there’s no problem at all—there will still always be the epistemological problem, as it were.
[Rabbi Michael Abraham] Yes. Fine. So apparently the conclusion that emerges from the Talmud is that a majority not present before us is weaker. Now, Rabbi Shimon Shkop proves from Maimonides that Maimonides holds that a majority not present before us is stronger. There are proofs for this, never mind, we won’t get into the details right now. He discusses this at length in Gate 3, and he argues that according to Maimonides, a majority not present before us is stronger. So first of all I want to explain the reasoning. How this works with the Talmud we’ll see in a moment, if at all. But what is the reasoning for it? So look, in this context there is what I used to call the David Levy effect. What is the David Levy effect? David Levy was—yes—a Likud member; those of the younger generation among us perhaps already don’t remember, or didn’t know, but he was a senior Knesset member from Likud, a minister on behalf of Likud. Now he was often in struggles against the Likud leadership; in the background there were Mizrahim versus Ashkenazim and so on, feelings of discrimination of various kinds and so on. At one point one of David Levy’s claims was that the faction he represented within Likud—there were different factions—there was one faction that he was the leader of, and the faction he represented was not receiving executive positions within Likud or on behalf of Likud. That’s what he claimed; let’s say he had a faction of thirty percent, and they weren’t getting positions. So they told him: what do you want? This is democracy. You vote and the majority decides; vote, and you’ll have whatever power you have. What’s the problem? So he said to them: fools of the world. Meaning, if you go by the majority in the way you are suggesting, then that means that one hundred percent of the positions will be filled by the faction that has fifty-one percent in the party. Right? Because for every position we’ll hold a vote, the fifty-one percent will defeat the forty-nine percent, and one hundred percent of the positions will be filled by the faction with fifty-one percent. And in terms of representation, that is unfair representation, because it comes out that forty-nine percent of the party has no representation in the executive positions. So in short, there’s a failure here—the democracy here is failing; it does not produce good representation in this case. And we talked about this in the previous lesson or the one before, about how to represent what the public wants. Democracy is quite a poor method—maybe the simplest—but it is quite a poor method: going after the majority. So that is what David Levy claimed. Now for our purposes, let’s apply this for a moment, yes—or maybe another example, yes, the Supreme Court. Today this exists less, but once there was the “religious seat” on the Supreme Court. Menachem Elon, Englard—yes, there was always one token religious judge on the Supreme Court and another fourteen normal, regular people. So the claim was that in fact there is no representation; the percentage of religious people in the population is more than one out of fifteen. So this wasn’t right, yes—there was no adequate representation for that population. By the way, you have to take out the Haredim, because then at least they weren’t studying law and weren’t candidates for this at all, but still even among the Religious Zionist public it wasn’t one in fifteen; they were more. Now what happens—today there are more, of course many more. I haven’t counted, but there were stages where it was more than their percentage in the population, the number of religious judges on the Supreme Court. In any case, it’s still not certain that this gives adequate representation to opinions, to the distribution of opinions in the population. And why? Because when panels are set, if in a panel there are always—say there are a third religious, and let’s say that’s the proportion in the population—a third of the population, let’s say, is religious, and that’s not far off, Haredim and religious together let’s say, roughly—let’s say a third of the population, okay? So a third of the Supreme Court judges are religious—five religious judges. Okay? Now in every panel they put together—say a panel of three—statistically there will be two secular judges and one religious judge. So in how many of the rulings will the ruling lean in the religious direction? Zero. Zero percent. Not a third, not thirty-three percent—zero percent. How can you get to a situation where—therefore it doesn’t help that there are five religious judges. If there are five religious judges, so what? At the end of the day the number of rulings that lean in the religious direction will not be a third; it will be much less. How can you improve this? For example, by holding a lottery not over who will sit on the panel, but over whether the panel will have a religious majority or a secular majority. Let’s say in those cases that are relevant to the question of religious or not religious, okay? So in those cases they would hold a lottery, and in one third of those cases a religious majority would sit, and in two thirds a secular majority would sit. That could lead to better representation, more representativeness. Okay? But following the majority brings poor representation. It gives one hundred percent of the power to fifty-one percent of the group. Now why am I bringing this up, beyond the conceptual failure that people often get trapped in on these questions? Because it can illustrate well the difference between a majority present before us and a majority not present before us. Look, with a majority not present before us, every woman who comes before us, yes, we are essentially supposed to assume that she is not infertile by nature, right? Because the law of nature is that women are not infertile by nature. There are some for whom something malfunctioned. But in principle, the law of nature says that a woman is not infertile by nature. And therefore if women were coming before us, then regarding each and every woman there are very good reasons to assume that she is not infertile by nature. Internal reasons within her, not because of belonging to a group, but because of her physiological structure it is much more reasonable to assume she is not infertile by nature. I have mechanistic reasons within this specific woman herself that cause her not to be infertile by nature. And therefore if you asked me, with one hundred percent of the women who come before me I would determine that they are not infertile by nature. Because in each and every woman the law of nature operates in the same way. Now of course this is a statistical law. So ninety percent in effect causes them to be not infertile by nature; ten percent do come out infertile by nature. But in each and every woman there is that ninety percent. And therefore about every single woman for whom the question arises, we are supposed to assume that this woman is not infertile by nature. There are good reasons, a law of nature, that influences all women. About a piece of meat there is no law of nature that says this piece of meat is kosher. The whole question is only where it came from. Therefore I would in no way decide about all one hundred pieces of meat in the city that they are all kosher. After all, I know that ten of them are not kosher, and there is no law of nature within each piece of meat that creates a situation in which the piece is kosher. It is not some natural activity pushing the piece to be kosher. It has nothing to do with a law of nature; it is simply a distribution resulting from the accidental structure of this city, what exists in this city. Therefore in this case, you see, from this perspective a majority present before us is weaker, not stronger. It is weaker because it is actually clear that there is a minority here—a minority of non-kosher pieces before us. Therefore it is impossible to ignore that. You can, you must ignore it—that’s the law of majority—but clearly ignoring it is problematic. We will certainly be wrong in ten percent of the pieces of meat. If all the pieces of meat come before us and we decide about every single piece that it is kosher, we have certainly erred with ten percent of the pieces of meat. In contrast, with the women, in principle there is no certainty that we erred. There is a statistical chance that we erred, but you cannot say that we certainly erred with ten percent of the women. No. In principle all women are supposed to come out not infertile by nature. True, there are malfunctions, and usually it won’t come out that way. But you can’t say that we certainly erred with ten percent of the women. No. Every single woman who comes before us—the logic says to decide that she is not infertile by nature. Her physiology says she will not be infertile by nature. Therefore, from this perspective, this is David Levy turning fifty-one percent into one hundred percent. The result of the fifty-one percent is correct for one hundred percent of the cases. And therefore there is a great deal of logic in applying a majority not present before us to one hundred percent of the cases. It is stronger than a majority present before us from this perspective.
[Speaker C] It comes out that if we had information about all the women, and we knew that ninety percent are not infertile by nature and ten percent are, specific information about all the women, then that would only seemingly detract from—
[Rabbi Michael Abraham] No, it makes no difference at all. Because when I discuss a new little girl, not one who was inside the group about which I had information, then why should I care about the information there? What do you want to extract from there? From the information there you want to extract the law of nature. The law of nature operates on this girl. So this girl is unequivocally not infertile by nature.
[Speaker C] Fine, and if she were an adult, let’s say—not a minor.
[Rabbi Michael Abraham] An adult who came out of that group? Ah, that’s a majority present before us, obviously.
[Speaker C] Then it would already be—even less good.
[Rabbi Michael Abraham] Right. Again, unless what you are hiding behind this is that I already know how the ninety-ten majority was formed—through the laws of nature. But then I am using the laws of nature, not the information of ninety-ten. Therefore this is an important point, and the question is where I know the ninety-ten from. Do I know the ninety-ten on the basis of a generalization from a sample because I know this is a law of nature, or do I know the ninety-ten as immediate information? And precisely in this sense, the immediate information is weaker, not stronger. It is not stronger.
[Speaker B] Yes, because I don’t really understand—one needs to explain a bit why the thing that separates from a ninety-ten group, why it separates from the majority, why that is more— With a law of nature it’s very, as the Rabbi explained, very understandable. But with a majority present before us you first need to understand the reasoning at all.
[Rabbi Michael Abraham] You’re presenting the same question. That is why I say that a majority present before us has a weaker side to it. We’ll see this more sharply later, but for now I’m only dealing with defining the concepts.
[Speaker B] No, I do understand, I just simply don’t understand the reasoning for this thing at all.
[Rabbi Michael Abraham] What do you mean? If you understand that if you found such a piece of meat in the street and you know that nine stores are kosher and one is non-kosher, wouldn’t you decide that it is kosher? Wouldn’t you bet ninety against ten that it is kosher?
[Speaker B] Yes, I would decide, but I don’t understand why. It needs to be defined a little.
[Rabbi Michael Abraham] We’ll talk about that more. We’ll talk about that more, but common sense says yes. Okay? We’ll see. In any case, for our purposes, at least conceptually I can understand Maimonides’ view, which says that a majority that is present before us is weaker, not stronger. Of course, in the Talmud that’s problematic, because the Talmud says that even if I have a source for a majority that is present before us, that still doesn’t mean I would use a majority that is not present before us. A majority that is not present before us is stronger, as Maimonides says, so why doesn’t that follow? It should follow by an a fortiori argument. If the verse tells me that with a majority that is present before us we rely on it, then with a majority that is not present before us all the more so I should rely on it. So here I want to jump to the end of the passage; it’s one page later. In the end, the Talmud is left without an answer. They don’t find a source for following a majority that is not present before us. A majority that is present before us comes from the verse, “incline after the majority.” A majority that is not present before us remains unresolved. You can’t derive it from the verse. The Talmud tries to derive it from here, derive it from there, and it’s left with nothing. All the sources are rejected. And that’s it. But it doesn’t then give a bottom line: okay, so what do we do with that? There’s no source. But on the other hand it’s obvious that nobody would even think not to use a majority that is not present before us. As I said earlier at the beginning, it was clear that we use these majority rules. The whole question is only whether we have a source, or what the source is for them, but obviously we do use them. So Rashi here, on this passage—I said, one page later—yes, Rashi says as follows: “Rather, certainly…” I’m not going into all the details because we skipped the passage itself. “Rather, certainly, it is a law given to Moses at Sinai that we rely on a majority even where it is possible…” What is he saying? Apparently there is a law given to Moses at Sinai here, because on the one hand we don’t find a source, and on the other hand it was obvious to the Talmud from the very start that we do use it. The whole question was only whether there is a source, or what the source is. So the fact that we got stuck regarding the source doesn’t mean we don’t use it. We use it; we just don’t have a source. Rashi says, so apparently we have to conclude that this is a law given to Moses at Sinai, because we didn’t find a source. Another possibility—and this is a strange thing—“Or alternatively, ‘incline after the majority’ implies both a majority that is present before us and a majority that is not present before us, for what difference is there between this one and that one?” Now that is really unbelievable. One possibility is that it’s a law given to Moses at Sinai, fine, you invented a law given to Moses at Sinai. Second possibility: what logic is there to distinguish? A majority that is present and a majority that is not present are both ninety-ten, ninety percent ten percent. If we follow statistics, then we follow statistics. What difference does it make whether it is present before us or not present before us?
[Speaker B] Fine, but to say that the Talmud distinguished in its initial assumption and then in the conclusion with this very same reasoning?
[Rabbi Michael Abraham] Yes, it’s impossible. What do you mean? The Talmud at the beginning says that if I have a source for a majority that is present before us, I still won’t be able to derive from it the majority that is not present before us. Meaning, the Talmud says there is clearly a distinction here. There is clearly a distinction here, and I can’t derive one from the other. The majority that is not present before us is weaker. Let’s leave Maimonides aside for a moment. The majority that is not present before us is weaker. You can’t derive it from there. Now Rashi comes and says—without the Talmud saying this; the Talmud doesn’t say it, the Talmud remains without an answer—“what difference is there between this one and that one,” as if he’s looking at you with a rhetorical question: why make a distinction at all? What do you mean? Didn’t you read the Talmud? The Talmud just spent an entire page of give-and-take only because it was not willing to equate a majority that is not present before us with a majority that is present before us. It’s really strange. Now if you remember the question I asked about Maimonides, according to Maimonides a majority that is not present before us is stronger. So why doesn’t the Talmud say at the beginning that if we learned a majority that is present before us, then all the more so we also have a majority that is not present before us? And from “incline after the majority” you can derive everything. It may be that Maimonides really says what he says only in the conclusion of the passage. In the conclusion of the passage, where we have no source for a majority that is not present before us, yet it is obvious that we use it—the whole question is only whether there is a source, but it is obvious that we use it—how can that be? Maimonides says: apparently the initial assumption, which said that a majority that is not present before us is weaker, is incorrect. A majority that is not present before us is stronger, and the source really is “incline after the majority.” We derive the majority that is present before us, and all the more so also the majority that is not present before us. He learns like the second approach in Rashi. Still, over the course of the Talmudic discussion this is very difficult, because the Talmud should have said something. After all, its whole assumption throughout was that a majority that is not present before us is weaker, and you can’t derive it from the verse. So the Talmud itself should say: okay, we didn’t find a source, I retract, this is actually a stronger majority and it can be derived a fortiori. But it doesn’t say a word. It just remains without an answer and goes home. But in any case, this really is difficult in the Talmud, so I don’t know what to say about it. This passage here really ends somehow in the middle. It’s not clear what is happening here; maybe some section is missing, I don’t know exactly. But in any case, that’s apparently what comes out. And if so, then at least in the conclusion we have three possibilities. We can remain with the view that a majority that is not present before us is weaker, as the Talmud assumes all along, and there is no hint that it retracted from that. We can go with Rashi’s second approach, that in the conclusion of the Talmud a majority that is present before us and a majority that is not present before us are the same thing: what difference is there between this one and that one? That’s a second approach. The third approach is Maimonides’ approach: that in the conclusion of the Talmud, a majority that is not present before us is not only the same as a majority that is present before us, it is stronger than a majority that is present before us. Because if we rely on a majority that is present before us, then all the more so on a majority that is not present before us. Three approaches regarding the relationship between a majority that is not present before us and a majority that is present before us. And what causes this dilemma is basically the reasoning I gave earlier. Right, the reasoning for why a majority that is not present before us is stronger, and why a majority that is not present before us is weaker. Okay, so up to this point I’ve at least presented the concepts and the different sides. Any questions or comments?
[Speaker E] Yes, Rabbi, a question. Why don’t we look at the older women, who all came from young girls, and it turned out over time that most of them were not infertile from birth, and therefore apply that back to all these young girls so that it would count as a majority that is present before us?
[Rabbi Michael Abraham] No. Because this young girl who is before us now is not part of those young girls about whom I have the information. I have information about a group of a million young girls, namely the older women of today when they were young girls. But that group also does not include the young girl who is now before us.
[Speaker E] Right, but I meant, like, with induction.
[Rabbi Michael Abraham] No, that doesn’t help retroactively. If retroactively it would return me to a group that also included this young girl, you’d be right. But it returns me to a group of a million other young girls, and now I want to take them as a sample and apply it to this young girl, so I’m still making a generalization from a sample. Another comment or question?
[Speaker C] Rabbi, the option the Rabbi mentioned where there’s no difference is basically that we’re simply doing statistics, and in that there really is no difference.
[Rabbi Michael Abraham] I’ll sharpen that more next time, but yes. Okay then, goodbye, Sabbath peace. Thank you very much.
[Speaker C] Good news. Amen.