Majority in Halacha and General Principles 2, Lesson 8

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A majority that is present before us and a majority that is not present before us, as probability versus counting possibilities
Rabbi Shimon Shkop and counting sides in a majority that is present before us
Statistical evidence in law: prisoners and buses versus eyewitnesses
The envelope paradox, Monty Hall, and how the calculation depends on information about the mechanism
Background assumptions, induction, and causality as the basis for using probability
Human behavior as non-statistical and its implications for “we do not follow the majority in monetary cases”
A doubt where there is a possible prohibition and a doubt where there may be no prohibition, as a probabilistic distinction
Certain error versus probability of error in comparing statistical conviction to testimony
Determinism, chaos, and the view of probability as lack of information
The law of fixedness: anything fixed is treated as fifty-fifty, and the verse “and he lay in wait for him and rose up against him”
A verse as a source versus the need for explanation and reasoning in scriptural derivations
Non-probabilistic explanations for fixedness and their difficulties: Rabbi Gordin and Moshe Koppel
Reversing the question: why in cases of separation do we follow the majority, and what is the role of “sides”

Summary

General Overview

The text draws a distinction between a majority not present before us as a majority based on probabilistic generalization from empirical data, and a majority present before us as a majority that is not probability at all but rather a counting of possibilities in the absence of information. It applies this distinction to explain why in law one does not convict on the basis of “statistical evidence” such as 99 out of 100 prisoners, but one does convict on the basis of eyewitness testimony even when its reliability is similar. It then offers three complementary explanations for the non-probabilistic nature of certain cases: lack of information about the space of possibilities, the fact that human behavior is not random but the result of decision, and a halakhic distinction between a doubt where there is a possible prohibition and a doubt where there may be no prohibition, as a probabilistic and not a psychological distinction. Finally, it presents the law that anything fixed is treated as half-and-half, rejects or presents as problematic various “legal” explanations of the law, and proposes the conclusion that the real question is not why in a fixed case we do not follow the majority, but why in a case of separation we do follow the majority at all, because that is a novelty of counting sides rather than a probabilistic calculation.

A Majority Present Before Us and a Majority Not Present Before Us as Probability versus Counting Possibilities

A majority not present before us is built from statistical inference: one checks a representative sample, discovers a distribution, and generalizes to a law of nature or a rule about the whole population, and therefore in a new case one decides according to probability supported by information. A majority present before us is described as a majority that does not reflect probability, because there is no information putting the possibilities on equal footing; there is only a count of possibilities, such as nine kosher stores and one non-kosher store, together with the practical assumption that one should “bet” on the majority. The text emphasizes that the statement “there is a ninety percent chance that the meat is kosher” is not really correct as an actual probability without information about the mechanism of separation; rather, it is the result of lack of information and counting sides. The example of a fair die versus a die about which we have no information illustrates that counting faces becomes probability only when it is known that all possibilities carry equal weight. When there is no such knowledge, the bet is not a probabilistic calculation but a practical decision.

Rabbi Shimon Shkop and Counting Sides in a Majority Present Before Us

Rabbi Shimon Shkop is presented as formulating the law of the nine stores as counting sides: the meat “must necessarily have separated from one of the ten stores,” and each store imposes one side of doubt on the meat, so there are nine sides of kashrut against one side of non-kosher status. From this a practical implication is derived: the majority is determined by the number of stores and not by their size, and most halakhic decisors say that the size of the stores makes no difference, because the law is not probabilistic but based on sides. The text sharpens the point that if there were probabilistic information about an equal chance for each piece of meat to reach the street, there might be room to weigh the quantity of meat in each store, but in the absence of such information the counting of possibilities remains “sides” and not probability.

Statistical Evidence in Law: Prisoners and Buses versus Eyewitnesses

The text presents the example of one hundred prisoners attacking a guard, where one did not participate, and the accepted legal principle that one does not convict a particular person on the basis of a 99/100 probability alone. It contrasts this with possible conviction when there are eyewitnesses, even if their reliability is similar. The proposed explanation is that in the statistical case there is not really a 99% probability regarding the concrete individual, because there is no information about the process by which the defendant was selected from the group or about the mechanism connecting that specific person to the event. The text rejects a “formal” explanation that this is “information” and that is “not information,” and argues that the difference is genuinely probabilistic: in one case there is no basis for assigning a probability and therefore one cannot convict, whereas in the case of testimony there is an evidentiary mechanism that generates probability on the basis of information.

The Envelope Paradox, Monty Hall, and Dependence of the Calculation on Information about the Mechanism

The envelope paradox is brought in to show that an expected-value calculation which seems to imply that one should always switch envelopes rests on hidden assumptions about the process by which the sums were set, and when there is no information about the mechanism the calculation is invalid. The text compares this to the principle that in probabilistic calculations one must “take all the information” about the sample space and the process of selection into account, rather than merely count two possibilities as though they were equally weighted. Monty Hall is mentioned as a demonstration that there we do have structural information about the process, and therefore switching really does change the probability.

Background Assumptions, Induction, and Causality as the Basis for Using Probability

The text clarifies that even in probability “based on information,” background assumptions always remain, and compares this to the problem of induction and David Hume’s questions about the principle of causality. It distinguishes between assumptions that are perceived as rational and natural as part of the infrastructure of science, and speculative assumptions, and applies that distinction to the question of when statistics count as information-based and when they are only a methodological bet. From this it argues that the desired distinction is not legal-formal but depends on whether there is real information about the space of possibilities and the mechanism that generates the data.

Human Behavior as Non-Statistical and Its Implications for “We Do Not Follow the Majority in Monetary Cases”

The text offers a second explanation according to which, when human decisions are involved, the phenomenon should not be viewed as random, and therefore probabilistic tools are not appropriate. This is illustrated by the difference between drawing a ball randomly from a container and deliberately choosing a ball after looking. In the halakhic context it brings the topic in tractate Bava Batra about one who sells a goring ox, and the halakhic conclusion according to Shmuel that “we do not follow the majority in monetary cases,” with an explanation cited in Shema’tata in the name of Nachmanides regarding gifts sent to a bride, namely that this is a purposeful decision by the buyer and not a random process. From here it is argued that even in the prisoners example there is no “one in a hundred chance” that a given prisoner did not riot as though this were a law of nature, because the event depends on their choices and not on a random mechanism.

A Doubt Where There Is a Possible Prohibition and a Doubt Where There May Be No Prohibition as a Probabilistic Distinction

The text presents the distinction between a case of two pieces, one kosher and one prohibited, and a case of one piece whose status is unknown, and notes that a provisional guilt-offering is brought only for the first type. It rejects a psychological explanation based on the “presence of the prohibition” and argues that this is a probabilistic difference: when there are two pieces, there is complete information about the space and the 50/50 probability rests on a blind selection mechanism, whereas in the case of one piece the 50/50 is only the result of lack of information and not a real probability. On this basis it is argued that the novelty is that a doubt where no prohibition was established at all is still called a “doubt,” even though there is no probabilistic justification for saying it is truly balanced. The connection to the idea of counting sides sharpens the point that the number of sides allows us to speak about probability only when equal weight is known, or when the Torah innovated that the count itself is to be treated as decisive.

Certain Error versus Probability of Error in Comparing Statistical Conviction to Testimony

The text points out that if all one hundred prisoners were judged according to statistical majority, one would certainly convict at least one innocent person, because it is known that one did not participate. Therefore such a mechanism leads with certainty to a mistaken result. By contrast, conviction based on witnesses who are 99% reliable does not require that in a given case an innocent person be convicted; it merely creates a probability of error, and therefore it is not similar to a mechanism that guarantees error. This distinction is presented as part of the same axis of “using probabilistic tools” where there is no real probability concerning the concrete individual.

Determinism, Chaos, and the View of Probability as Lack of Information

The text argues that throwing a die is not truly random but a deterministic process whose outcome is fixed by initial conditions and Newton’s laws, and that the use of probability stems from extreme sensitivity to initial conditions and lack of information about them, that is, the phenomenon of chaos. It adds that in all fields other than quantum theory, probability is generally a description of ignorance rather than an inherent property of the world, and that human decisions too are not probabilistic but rather “choice.” From this it argues that the human habit of assuming equal weighting in the absence of information is an a priori intuition that also explains the character of a majority present before us.

The Law of Fixedness: Anything Fixed Is Treated as Half-and-Half, and the Verse “And He Lay in Wait for Him and Rose Up Against Him”

The law of fixedness is presented through the distinction between a case of separation, where a piece is found in the street and we follow the majority of stores, and a case where a piece was bought in a store and the doubt arose within the place of mixture, where the law is half-and-half and we do not follow the majority. The example is also brought of throwing a stone into a pit containing nine gentiles and one Jew, where in a fixed case it is treated as fifty-fifty even though there is a gentile majority. The Talmud in Ketubot 15 is brought as the source: “Anything fixed is treated as half-and-half, whether for leniency or for stringency,” and the Torah source is learned from the verse, “and he lay in wait for him and rose up against him,” meaning until he intended him specifically.

A Verse as Source versus the Need for Explanation and Reasoning in Derivations

The text argues that learning from a verse does not exempt us from searching for an explanation, and it criticizes the approach that a “scriptural decree” replaces reasoning. It brings the example of “we do not administer punishment based on logical derivation,” with three “possibilities” analyzed as two explanatory possibilities and one source, in order to show that the verse is the source and not the explanation. From this it argues that every derivation rests on the reasoning of the interpreter, because he could have drawn other contents from the verse, and therefore even in the derivation from “and he lay in wait for him and rose up against him,” there must be some reasoning that distinguishes between fixed and separated cases even before the verse.

Non-Probabilistic Explanations for Fixedness and Their Difficulties: Rabbi Gordin and Moshe Koppel

An explanation is brought in the name of Rabbi Gordin according to which, in a majority not present before us, the question is about the case before me against the background of a known general state, whereas in a majority present before us the question is about “the stores of the city” as a collective determined by the majority, and the piece is merely a derivative. In the law of fixedness, when the doubt arises inside the store, the question focuses on the piece itself and therefore one gets a fifty-fifty result. The text points to difficulties in this explanation, including only partial fit with the cases in the Talmud and the fact that even in a majority not present before us we ask about an individual case and still follow the majority. Another explanation is brought in the name of Moshe Koppel, who formulates the fixed case as a hypothetical question, “what will happen if I take one out,” as opposed to separation, which is a question about a defined piece that has already been taken out. The text notes that this explanation too is problematic, because in practice there is a concrete piece and a defined removal process.

Reversing the Question: Why in Separation Do We Follow the Majority, and What Is the Role of “Sides”

The text concludes by arguing that the real difficulty is not to understand why in a fixed case the law is half-and-half, but to understand why in a case of separation we follow the majority at all, because in a majority present before us there is no probability and no information that justifies 90/10. It presents the answer as a Torah innovation of “counting sides,” as formulated by Rabbi Shimon Shkop, in which the Torah instructs us to decide according to the number of sides when the item has separated and there are sides corresponding to where it came from. In a fixed case there are no sides to count, because the doubt arises about the thing in its place and not as a question of where it came from, and therefore it simply does not fall under the innovation of “incline after the majority” in this sense, and remains half-and-half. On this basis, the verse “and he lay in wait for him and rose up against him” is presented as limiting the operation of majority to the case of separation and excluding the fixed case, and the novelty is that the majority in separation functions not as probability but as a mechanism of sides.

Full Transcript

[Rabbi Michael Abraham] Last time, after we talked about the difference, or the different kinds of majority, a majority present before us and a majority not present before us, I tried to explain the difference between them. We then moved on to statistical assessments, or probabilistic assessments, in the legal world. Let me just briefly remind you: we talked, for example, about the case of a hundred prisoners who attack a guard. One of them is sitting on the side; ninety-nine took part in the incident. We want to judge the person standing before us, one of them. In the legal world it’s accepted to say that you can’t convict him on the basis of that probability of ninety-nine out of a hundred. On the other hand, if there are eyewitnesses that he took part in the incident, even though the reliability of their observation is also something like that, or maybe even a bit less, in that case you can convict. And the question was: why, really? I brought, in quite a detailed discussion, David Enoch’s proposal, this whole business of the sensitivity criterion and information. I’m not going to go through all that again. I’ll send it by email, so maybe anyone who wants can refresh their memory. But in the end my claim was that this can be explained in three ways. I think I already mentioned one or two of them. Three ways.

[Rabbi Michael Abraham] The first way—I’ll remind you again—is that the difference between a majority present before us and one not present before us is that a majority not present before us is based on probability. Meaning, if we want to know—I don’t know—what the chances are that a certain woman gives birth after nine months rather than seven months, then we examine some sample of women, let’s say a representative sample, and we discover that eighty percent of them give birth after nine months and twenty percent give birth after seven months. Then we come to the conclusion that there is some law of nature like that, saying that women generally give birth after nine months, even though there are women who also give birth after seven. But there is such a natural law. And since that’s the case, now if a new case comes before us—some woman regarding whom we need to decide whether she gave birth after nine or after seven—we’ll say she gives birth after nine, because that is the law of nature, that is the probability. That’s how science works, that’s how inference from samples works.

[Rabbi Michael Abraham] In a majority present before us, the claim was that this does not reflect probability. The fact that there are ten stores in town, nine of them kosher and one non-kosher, and I found a piece of meat in the street and need to decide which store it came from—the assumption is that we follow the majority; we learn this from “incline after the majority.” But that is a majority present before us. And the Talmud says that from a majority present before us you cannot derive a majority not present before us. Why? Because a majority present before us is not probability. It is not true to say that this piece of meat has a one-tenth chance of being non-kosher and a nine-tenths chance—ninety percent—of being kosher. Why? Because we have no information here at all. We would still say: if I had to bet on the status of this piece—whether it’s kosher or non-kosher—I would bet that it’s kosher. But that bet is based on lack of information, not on information, unlike the previous case where we have information from a sample and we generalized it to the whole group. In this case we have no empirical basis for this at all, no information whatsoever. What we do is count possibilities. There is a possibility that this piece came from store A, B, C, D, all the way to J. There are nine possibilities that it came from a kosher store and one possibility that it came from a non-kosher store, so I assume it’s kosher. But we have no information telling us that the chance it came from each of the stores is actually equal. Who said that? We have no reason to assume it isn’t, but we also have no knowledge saying that it is.

[Rabbi Michael Abraham] I think I brought an example for this. Suppose I roll a die—a fair die—and I ask you what the chance is that it lands on two. People tell me: one-sixth. Why? Because I know the die is fair. I tried rolling it a few times and saw that more or less the outcomes are distributed equally among one through six. But what happens if I roll before you a die about which we have no information? We don’t know whether it’s fair or unfair, we know nothing. Fine? Now I ask you: what’s the chance it lands on two? If you had to bet, I assume—at least that’s what I would do—you’d still bet on one-sixth if forced to. But you understand that this is arbitrary; it’s not the result of a calculation. Because if the die is unfair, then there is no one-sixth chance that it lands on two. Rather, since I know nothing, I’m in a complete absence of information.

[Speaker B] What do you mean, unfair?

[Rabbi Michael Abraham] Unfair means it has a tendency to fall on a certain face. It doesn’t land with equal probability on all the faces. It’s not a fair die; it’s an unfair die. Right. So in that situation we would still bet that it lands on two with a one-in-six chance, meaning five against one, right? That’s more or less what any person would do. But that is the result of lack of information; it is not the result of information. We have no calculation showing that the chance of this is one-sixth. Rather, there are five possibilities like this and one possibility like that, so the chance is one in five—the de facto chance is one in five, I’ll bet on it in a ratio of one to five. But it’s not correct to say that there really is a twenty percent chance this will happen. That’s simply not true. I have no information about it at all. So not twenty percent—sixteen percent. Therefore, in both cases we follow the majority; in both cases we supposedly make a probabilistic calculation. But in the second case it isn’t really a probabilistic calculation at all, just a counting of possibilities, which is not the same thing.

[Rabbi Michael Abraham] Counting possibilities is this: once I know that all the possibilities carry equal weight—positive information, not that I have no information and therefore assume they carry equal weight, but that I know they carry equal weight, like I know that a die is fair—then counting possibilities turns into probability. Right? If I know that all possibilities are equal, then obviously—how do I calculate probabilities? In general, in combinatorics, how do I calculate probabilities? I count how many possibilities there are and say that the probability of the event is the number of possibilities fitting it out of the total number of possibilities. But that’s only when all possibilities are equally weighted. If the possibilities are not equally weighted, then this is not probability. And still, I think any reasonable person, if they have no information at all, would take that bet. Why? Because I have no information, so in the absence of information, what am I supposed to do? That’s the least bad decision I can make. That’s all. That is a majority present before us. Meaning, a majority present before us is not a majority that is the result of probabilistic calculation, but a counting of possibilities.

[Rabbi Michael Abraham] I’m reminding you—I think I read something from Rabbi Shimon Shkop. When Rabbi Shimon Shkop talks about a majority present before us—let’s see if I have it here, not sure—we read it from his book, but let’s see if I have it here. He really writes that we count possibilities. Yes, here it is: “Rather, it seems that the matter of the nine stores is like the matter of the majority that decides among judges. And it is that since the meat must necessarily have separated from one of the ten stores”—the piece of meat I found in the street came from one of the stores—“each and every store creates a legal status regarding the meat, a doubt about the law regarding the meat.” Right? My doubt about the piece stems from the fact that I have ten possible origins for the piece: store A, B, C, D, up to J. So each store casts some side onto the meat. From this store there is a side that the meat is kosher; from that store another side that it is kosher; from that store there is a side that the meat is non-kosher. I have nine sides that it’s kosher and one side that it’s non-kosher. I count sides, and then I say the chance is ninety percent. But of course not chance—sides. Sides are not chance. Only if the chance of separation from each store is equally weighted does counting sides actually reflect probability.

[Speaker C] And what happens if the stores aren’t the same size?

[Rabbi Michael Abraham] So that—here, for example—is a practical implication. What happens when the stores aren’t the same size? When the stores aren’t the same size, most halakhic decisors say it doesn’t matter. We go by the number of stores, not by the size of each store. And why? This is a very clear reflection of Rabbi Shimon Shkop, because Rabbi Shimon Shkop asks himself: from how many places could it have come? We’re talking about sides, not about probabilistic calculation. Now how many sides are there? There are nine sides that it’s kosher and one side that it’s non-kosher, and therefore we say that this is basically a ninety percent majority, even though that one single store may contain a huge amount of meat. Of course, if we had some information saying that every piece of meat had the same chance of being found lying in the street, this wouldn’t be right. Because probabilistically, if there are many more pieces of meat in the large store than in each of the nine small ones, then who cares that there are nine small ones? But if I count possibilities, then the hypothetical possibilities are either it came from here, or here, or here. Counting possibilities gives nine against one, and therefore the size of the store doesn’t matter. That is exactly the practical implication of this explanation. Here we see that this is not probability. Fine?

[Rabbi Michael Abraham] You know, I’m reminded right now of a famous problem: the envelope paradox. Do you know it?

[Speaker D] Whether to switch to the other one or not? Yes.

[Rabbi Michael Abraham] You get two envelopes, and you know that one of them contains an amount that is double the other. Fine? One contains some sum—you don’t know how much—and the other contains double that sum. Now of course you don’t know which envelope has the larger amount and which has the smaller amount. You open—well, you get two envelopes, and you know that one contains an amount that is double the other. Fine? One has some amount and the second has double. And of course you don’t know which is the larger and which is the smaller. You choose an envelope, fine? Now you have one envelope in your hand and one envelope lying there. And they tell you, listen, if you want, you also have the option to switch. Whoever wants can switch. Is it worth switching?

[Speaker E] Even if you decide to open it.

[Rabbi Michael Abraham] Yes. Even if you’re allowed to open it, that also doesn’t matter, yes. So should you switch or not? Seemingly, what difference does it make? I could just as well have picked up the other one. It doesn’t make sense to say that it’s right to switch. On the face of it, it seems to make no difference. The chances are equal. Not true. Not true. Because if you’re holding the smaller envelope, say it’s 1000 shekels—you opened the envelope. You have 1000 shekels. Now there are two possibilities: either the other envelope is the smaller one and has 500, or the other envelope is the larger one and has 2000. Right? Well then, the expected gain is this: there’s a fifty percent chance you’ll get 2000 and a fifty percent chance you’ll get 500. So the expected value is 1250, and now you’re holding 1000 in your hand. So that means it’s worth switching. Right? But that’s not true. It’s not true. It’s not true. And okay, it’s a somewhat complicated story. It’s not true because in order to say that, you need to know something about the process by which the envelopes were prepared—how the sums were put in the envelopes. If you know nothing, then this is not a probabilistic calculation. Maybe it’s some kind of a priori assumption. And a priori I’d say it is not worth switching. When people present this as a probabilistic calculation, they assume there is information here—that there is information and we’re doing probability calculations. But if you want to use the information, then take all the information: how the envelopes were assigned, how the amounts were determined. It could be that larger sums have lower probability. In the end you reach some amount that they simply wouldn’t put in an envelope. Therefore that calculation is not correct. Look up the envelope paradox—you’ll find it. Gadi Alexandrovich has a post online with a nice explanation for anyone interested.

[Speaker E] And that’s like the Monty Hall problem.

[Rabbi Michael Abraham] Yes, Monty Hall, exactly, that’s it.

[Speaker E] No, but there it really does work. Here you chose one door.

[Rabbi Michael Abraham] There it is worth switching because you’re left with two. Before, you chose one out of three, and now two. That’s Monty Hall.

[Rabbi Michael Abraham] So in short: when we want to talk, when we want to make a probabilistic calculation, we really need to rely on information. Again, every probabilistic calculation is a case where some information is missing, right? I don’t know the status of the piece of meat before me. But if I have some information about the space—the event space or the sample space—then I can make a probabilistic calculation. But in a place where not only do I lack information about the specific piece in front of me, but I also know nothing at all about the space, then the calculation is not probabilistic. It is an a priori assumption. And that’s why I also said that a majority in a religious court, according to Sefer HaChinukh, is basically a majority present before us and not a majority not present before us—even though according to Sefer HaChinukh it would come out as a majority not present before us—because I argued that there too there is no way to know what the probability really is, or the number of cases in which the majority is right. There’s no way to know, because we have no independent means of understanding when a religious court ruled correctly or incorrectly. And therefore the classification of majority in a religious court is like a majority present before us.

[Rabbi Michael Abraham] So if I go back to the case of the rioting prisoners—or, if you remember, the buses: there are 100 buses in the city, 90 red and 10 blue. One of them caused damage. Can I sue the red company? Because it’s larger, so there’s a 90% chance it was a bus from the red company. So I say that in both of these cases, it seems to me the explanation is that in fact we do not have a probabilistic calculation. Meaning, it is not true that we are relying on information when we prosecute that prisoner, and therefore we cannot convict him. Because to convict someone—even if it’s a statistical conviction—that has to be based on information. But here we have no information. Why? Because we don’t know exactly how this particular prisoner who didn’t participate in the event chose to do that, or alternatively how we chose the prisoner who is now standing before us in court. We have a group of 99 prisoners who did it and one prisoner who didn’t. Now I choose one prisoner, put him on trial, and ask whether I can convict him. This process of selection is what matters here. Meaning, if I randomly selected a prisoner belonging to one group or the other, then maybe I could talk about chances. But here it’s not like that. Standing before me is one very specific prisoner, and I have no information about the chance that he belongs to this group or that one. This is not the result of a probabilistic calculation. And therefore one cannot convict.

[Rabbi Michael Abraham] So I return to the formulation that appears in many articles, even though I rejected it—a formulation appearing in many articles—that one may convict only on the basis of information and not when we have something that is not information. But I rejected that because they defined the concept of information in a completely formal way. Now I’m claiming that this is a probabilistic claim. Notice: what I’m saying is a probabilistic claim. It is not a formal claim. People think this is some kind of legal argument: the difference between two kinds of evidence. This one is also 99% and that one is also 99%; why here do we rely on the majority and there we don’t? So they make some formal argument: this is called information and that is not called information. And once it’s “not called information,” everyone asks: why should I care whether it’s called information? Bottom line, it’s ninety-nine percent. What difference does it make whether we call it information? That’s a philosophical, epistemological question—does such a thing count as information? What I’m saying now is that that’s wrong. The answer is probabilistic. There is a probabilistic difference between the cases. Because in the first case it is not true that there is a ninety-nine percent probability that he is guilty. That is simply not true. If I had no choice and I had to bet, I would bet one against ninety-nine—just like with the die about which I know nothing. That’s true. But I don’t have to bet. Here I can say: okay, I have no basis, and I can’t convict him. You don’t have to bet, right? Where I need to make a decision, then if I have a probabilistic calculation, I make it on that basis. If I don’t have a probabilistic calculation, I have no way to make the decision. The difference between the two cases is not that this is ninety-nine percent and that is ninety-nine percent, but that there is some formal issue here that differs between them. No. Here it is not ninety-nine percent. It is a mistake to think it is ninety-nine percent. It is not. It is not correct to say that the chance that this prisoner participated in the events is ninety-nine percent. Yes.

[Speaker E] Even when I do have information, there’s always some further layer in the breakdown of the sample—

[Rabbi Michael Abraham] where—

[Speaker E] where I’m making an a priori assumption that it’s uniform. For example, with the buses: if I had statistics on what percentage of accidents are caused by red buses versus—then we’d call that information or not information. But if you go another layer down—whether the drivers are male or female, this age or that age—you can always—

[Rabbi Michael Abraham] Right, of course in the end you can always—this is like scientific generalization in general. Even in scientific generalization, you know, it’s a bit parallel to questions about the validity of scientific generalization, of induction, David Hume’s questions and things like that. Obviously in the end there are always our assumptions. We also assume the principle of causality; we assume lots of things. But there are certain assumptions that are perceived as assumptions about the nature of the world—I’m not going into where we get them from right now—like the principle of causality. David Hume says we have nowhere to get it from. Where does the principle of causality come from? We assume it, right? But still, it is the infrastructure of science. No one will say, well, then it isn’t rational. Every scientist assumes it. Why? Excellent philosophical question, but that’s what we assume.

[Speaker F] So yes, I still don’t understand. What’s the difference between this and ordinary statistics? I have some medicine and I want to know what percentage of the time it succeeds or something, so you make some sample.

[Rabbi Michael Abraham] But the person before us, to whom we’re giving the—

[Speaker F] the medicine—is he in this category or that one?

[Rabbi Michael Abraham] A similar question to what was asked earlier. If we have some indications that the sample really is a representative sample, then fine. If not, then it really isn’t worth anything. But the assumptions are that the sample is representative, and again, there are always assumptions in the background. It’s clear that this distinction doesn’t go all the way. Even when I talk about statistics based on information, or probability based on information, that’s partial information. Meaning, there are always some assumptions there. Fine, but there are assumptions that are perceived as things I can assume about the world, and there are assumptions that are speculation. So that’s one explanation, and the important point I want to sharpen is that, contrary to what people usually think, the distinction is not a legal distinction or a formal distinction like in the halakhic realm. It’s a genuinely probabilistic distinction. It’s simply a probabilistic difference, contrary to what people think.

A second explanation—I mentioned it last time too—is that when we’re talking about human behavior, we don’t do statistics. Right? Like I mentioned, say a person has a container with ninety-five blue balls and five red balls in it. Okay? Now a person puts his hand into the container, mixes them around, mixes them around, and pulls out one ball. What’s the chance he pulled out a red ball? Five percent. Right? I think red is the minority. Okay, so five percent. Fine? Now you tell the person: okay, look, choose whichever ball you want. He looks, checks, and pulls out a ball. What’s the chance the ball is red? I’d assume half, fifty percent. It depends whether he likes red or likes blue. Assuming the preference for red or blue is distributed more or less evenly, then the chance is half. Why? Because if he wants red, he’ll keep looking until he finds red. He’s not pulling it out randomly, right? So in fact, when you’re talking about behavior—it’s somewhat connected to what I said earlier, there’s a similarity between these two things—when you’re talking about human behavior, you can’t discuss it with probabilistic tools. Probabilistic tools are tools that deal with random behavior, chance behavior. When we’re talking about a human decision, the human decision follows that person’s own considerations.

Now again, if I know nothing, I’ll still bet according to the ratio. Say, for example, we talked about “we do not follow the majority in monetary matters,” in the Talmud in Bava Batra, where the Talmud speaks there about a dispute between Rav and Shmuel regarding a person who sold an ox to someone else and the ox turned out to be a gorer. So the buyer wants to return the ox: give me back my money, I can’t plow my field with this ox because it gores. Okay? So the seller says: what do you want? I sold it to you for slaughter. A goring ox, that doesn’t matter—you slaughter it and that’s that, right? He says no, no, I bought it for plowing. Now, most people in the world buy for plowing. Most oxen in the world are bought—and there’s more need for oxen for plowing than for oxen for meat, for slaughter. Okay? Do we follow the majority in monetary matters? So the Jewish law is like Shmuel, that we do not follow the majority in monetary matters. I talked about there being two possibilities, but that doesn’t matter right now. So the Jewish law is like Shmuel, that we do not follow the majority in monetary matters. Why not? So the Shema’tteta explains, following Nachmanides on engagement gifts—we brought that passage there on engagement gifts—he says that here we’re dealing with a person’s decision. He decides whether to buy for slaughter or to buy for plowing. The fact that most of the world decides, that most of the world usually buys for plowing—so what does that mean? I’m telling you I want an ox for slaughter. Or the opposite, it doesn’t matter, yes? The fact that the majority behaves differently changes nothing. After all, this is a question of decision; it doesn’t just happen. If I were choosing oxen blindly, then you could tell me: yes, usually you probably chose an ox bought for plowing, because most oxen in the world are bought for plowing and not for slaughter. But if I performed a deliberate act based on my own consideration—I need an ox for plowing or an ox for slaughter—then I’m telling you that I needed an ox for slaughter. So what difference does it make that most people buy an ox for plowing? So therefore, therefore not—therefore, Rabbi Shimon Shkop explains, therefore we do not follow the majority in monetary matters. That’s only in a majority of the kind that depends on human behavior.

Here too it’s the same thing, with this prisoner who didn’t riot. What does that mean? It’s not a one-in-a-hundred chance that a particular prisoner wouldn’t riot. That’s how we assume when we think in terms of probability. There is no a priori one-in-a-hundred chance that a prisoner wouldn’t riot. In a group of a hundred other prisoners it could definitely have been different: eighty rioted and twenty didn’t, or eighty didn’t riot and twenty did. So why did it come out ninety-nine and one here? Because that’s how it came out, simply because these are the people, and that’s what they want. So what does probability have to do with it? It’s not that inside every person there’s some tendency to riot, with a ninety-nine percent chance that he won’t riot. That would be a law of nature. If it were like that, it would be a law of nature, and by the way it would be a present majority. Then it would be a present majority. But here it’s simply like the nine stores in the city. In this city there are nine stores of one kind and one of another kind. That doesn’t mean that in the whole world ninety percent of stores are kosher, or that every store has a ninety percent chance of being kosher. It just happened to come out that way here; it’s incidental, not a law of nature. That’s how it came out. Here too with the prisoners. So therefore, once the prisoners’ behavior is the result of a decision—each prisoner decides whether to participate in the riot or not—what does that have to do with probabilities? What sort of probabilities are these? I’m saying: you say there’s a ninety-nine percent probability that I participated in the riot, and I’m telling you that I chose not to participate. I’m an agent making a choice; I’m not chosen for. How can you claim there’s a ninety-nine percent chance that I participated? It’s simply not true. Okay? That’s the second explanation.

The third explanation—and there are connections among all of them—the third explanation is that there are two types of doubt in Jewish law: there is a doubt where prohibited matter is established, and a doubt where prohibited matter is not established. A doubt where prohibited matter is established is when there are two pieces of meat before me, one kosher and one non-kosher, and I take one and eat it. Now there is a fifty percent chance that what I took is kosher, right? And a fifty percent chance that it is non-kosher. That is called a doubt where prohibited matter is established. A doubt where prohibited matter is not established is when there is one piece before me and I don’t know whether it is kosher or non-kosher. That too is a doubt; there are two possibilities, fifty percent, I don’t know whether it’s kosher or non-kosher. There is a difference in Jewish law between these two doubts. For example, the provisional guilt-offering is brought only for the first kind of doubt, only for a doubt where prohibited matter is established. For a doubt where prohibited matter is not established, you don’t bring a provisional guilt-offering. And the question is why.

Usually people say there is some legal or halakhic explanation here, an explanation that is not probabilistic. The probability is fifty-fifty in both cases. So what nonetheless is the difference? Here, when there are two pieces before us, some say this is a psychological explanation. Here, when there are two pieces before us, one of them is in fact prohibited—there is a prohibition here before me, that’s clear. I can’t ignore the possibility that there is a prohibition here; it’s just not certain that I took it. In the case of one piece, there is a possibility that it isn’t prohibited at all and there is no prohibition here in the first place, nothing at all. So where it is clear that there is a prohibition here, only you don’t know whether you took it, that’s not the same as a place where you don’t know whether there is any prohibition. A lot of times when you ask people, they’ll tell you this is a psychological difference—that basically you can’t ignore the possibility that is present before you, even though in both cases it’s fifty-fifty. What fifty-fifty? What? You can say that if I have no information about this piece… Okay, you can say that, so that’s what I’m going to say, just a second. I’m only saying that the accepted explanation is that this is basically a psychological difference. What I want to argue is: not at all. It’s a probabilistic explanation. It’s a probabilistic explanation exactly like the envelopes, by the way. It’s a probabilistic explanation because in a place where there are two pieces before me, and I know this one is kosher and this one is non-kosher, I have complete information about the space of possibilities. I have no information about the piece I took, but I have complete information about the space. When I now say that I took a piece, there is a fifty percent chance it is kosher and a fifty percent chance it is non-kosher—and that chance is probability—because I took one, say I took it blindly, okay? I didn’t look and didn’t choose, and I have no information from among the pieces. So I took it blindly; fifty percent is the result of a probabilistic calculation.

When I take one piece and don’t know whether it’s kosher or non-kosher, it’s fifty percent because of lack of information. Not because of information. I know nothing about this piece; it could be definitely non-kosher, it could be definitely kosher—I simply don’t know. So I have two possibilities: either it’s non-kosher or it’s kosher. As my wife always says, when there are two possibilities it’s fifty-fifty. Okay, fine, so if it’s an unfair coin, then it’s either heads or tails—what else can it be? So it’s fifty-fifty. That’s not how it works. What happens is that you have no information. When you have no information, you make a methodological assumption, a practical assumption, that it’s fifty-fifty, but it’s not really fifty-fifty. There is no probabilistic calculation here.

And my claim is that the difference between a doubt where prohibited matter is established and a doubt where prohibited matter is not established is a probabilistic difference. It’s not a psychological or legal or halakhic rationale; it’s a probabilistic doubt. You bring a provisional guilt-offering for a state where there was a fifty percent chance that you sinned—for that you bring a provisional guilt-offering. You don’t bring a provisional guilt-offering for a case where there is one possibility that you sinned and one possibility that you didn’t—maybe the possibility that you sinned is a tiny minority; you don’t know. Where you don’t know, you don’t bring a provisional guilt-offering. Even though, again, if I had to bet, I’d bet fifty-fifty, because I have one possibility versus another possibility and I don’t know how to make a better decision than that. Okay, but that is the result of lack of information and not of information. Therefore the difference between a doubt where prohibited matter is established and where prohibited matter is not established is basically a probabilistic difference.

On the contrary, there is actually a novelty here: that a doubt where prohibited matter is not established is also called a doubt. People think the novelty is that a doubt where prohibited matter is established is more severe. Why? It’s also fifty-fifty like the other one. I say the opposite: the novelty is that a doubt where prohibited matter is not established is also called a doubt, because really it isn’t a doubt. A doubt is fifty-fifty. It isn’t a doubt because you can’t establish that it’s fifty-fifty; you simply don’t know. This is again Rabbi Shimon saying, with the “sides,” that people count sides and the number of sides determines the probability. That is a present majority.

If I go back to the case of the ten rioters or the buses, actually the ten rioters is stronger; in the buses it may be a bit more problematic. In the ten rioters there is a situation before me in which one prisoner did not riot. Right? One prisoner definitely did not riot. I can’t ignore that possibility—yes, parallel to established and not established prohibited matter. I can’t ignore that possibility; that is, there is a possibility that he didn’t riot. Okay, in the case of, say, two people who saw a certain prisoner, who saw the person rioting—that’s not—there isn’t before me, that’s a non-present majority, that’s a doubt where prohibited matter is not established. There is no prisoner before me who did not riot. Therefore maybe I can decide based on probabilities, because here there is no case present before me that openly contradicts what I think.

Or let me put it another way. If I were judging all the prisoners, then in principle, if I followed the majority, I would convict all of them, right? That’s what I’d have to do. Every one of them who came before me—there’s a ninety-nine percent chance he took part in this riot—and I would convict him. But then it would come out—except for the last prisoner. No, no, all of them. No, that’s the Rashba’s pieces of meat. The Rashba’s pieces of meat are something else. Not something else, but that’s a halakhic issue. I would judge them all and convict them all. But clearly if I convicted them all, then I convicted at least one person who is innocent, because one of them did not participate in this riot, right? By contrast, if I use two witnesses who saw this prisoner and therefore I convict him, and the reliability of their observation is ninety-nine percent. Fine? It is not certain that I will convict an innocent person; there is a probability that I will convict an innocent person. And if I use these witnesses again and again and again a hundred times, and ninety-nine percent of cases they see correctly but in one percent they don’t, then there is a probability that in one case out of a hundred I will convict a person who is innocent. But that still isn’t one hundred percent. Exactly. Therefore I say: here it is not certain that someone innocent will be convicted; this is a probabilistic phenomenon. Okay? In the first case, someone innocent will certainly be convicted, so you can’t use a mechanism that will certainly lead to a mistaken result.

Wait, but with witnesses too, if you convicted the hundred percent and you know that one didn’t riot? No, no, you didn’t convict one hundred percent; the witnesses are testifying about one person. There are no witnesses about each of them; that’s a different case. If there were witnesses about all one hundred, that would be something else; that really would be different. I’m saying, if the witnesses come and testify about one prisoner, not about all the others, we only judge him because about him we have witnesses. And their reliability is ninety-nine percent for their observation. But if these witnesses testify one by one about all one hundred? Well, then that’s something else, because even statistically, if you bring—even if those same witnesses testify about a hundred different cases, it’s still the same order of thing. No, no, you’re right—they would testify about a hundred different cases. But if they testify about a hundred prisoners, that these are the ones, the ten, and ninety-nine percent? Then clearly one of them didn’t participate and you’ll convict all one hundred. Ah, in such a case you’re right, so it isn’t similar. So indeed here, if ninety-nine percent fled and won’t return—No, that doesn’t matter; for me this is only hypothetical. Right, I’m saying, it’s only hypothetical, exactly. I’m saying: such a mechanism, where if I brought all the witnesses one person would certainly be convicted, I’m not willing to use. Obviously that doesn’t have to happen in practice.

So that is the third case here. And really, the third explanation—sorry—and again I think there is some connection among these three explanations, even though they are different explanations. What constantly stands behind them is that there is a certain kind of case in which we use a probabilistic tool even though in truth it is not probability. And therefore the difference is not a formal difference; it really is a probabilistic difference.

Like I once mentioned another case—but since it comes up here, I’ll raise it as an example—suppose I roll a die. And I ask myself what is the chance it will land—a fair die—what is the chance it will land on two. Okay? So I say one-sixth. I use probabilistic tools because there are six equally weighted possibilities since the die is fair, so I say one-sixth. But the truth is that there is nothing random at all in rolling a die. It is a completely deterministic process. If you give me the structure of the die, give me the initial speed, the force I applied to the die, the air density, everything needed, I will tell you which face it will land on, according to Newton’s laws. There is nothing random here; we just use probability. And usually probability deals with a reality in which there is some degree of freedom that you don’t know. Yes, I use it because I don’t know, right? I use probability because I don’t know, but the truth is that reality itself is completely deterministic. This is basically chaos. It’s not essential probability; it’s very high sensitivity to initial conditions. If you throw the die a little differently, it will land on a completely different face. In other words, the connection between the initial conditions and the result is a very weak connection. That’s what is called chaos in mathematics and physics. And in cases like these we use probability, but we use probability even though we are not dealing at all with an event that is random. We are not really counting random possibilities; we are counting deterministic possibilities.

Now understand—this is a complete absurdity. To count deterministic possibilities? So what logic is there in using probability? What makes you think all the possibilities are equally weighted? You don’t know; you have no idea. You don’t know how the person throws the die. Is there an equal probability he’ll throw it this way, this way, this way, or that way? You don’t know—he threw it. Rather, what happens is that you assume the probability is uniform because you have nothing else to assume. You have no information, and in the absence of information you assume all possibilities are equal. And again, this is basically not really probability, even though we use probabilistic tools.

Now if you pay attention, you’ll see—this already connects to the lectures in Petah Tikva, we’ll get to that in a moment—if you pay attention, our use of probability in all fields, except for quantum theory, in all fields, is like this. Whenever we use probability, it is never about random events. Never. Because there is no such thing as random events. After all, the world operates according to deterministic laws, right? Everything in the world has laws of nature, and if you tell me the circumstances, and I know the circumstances fully, I’ll tell you what the result will be. The only place where there is real probability in the world itself—not probability that is only my lack of information—is only in quantum theory. If at all; and even about that there is debate. Human decisions too. No, human decisions too are not probability. Why? That’s choice. Choice is not probability. No, that’s what I’m saying—it’s not probability. All probabilistic things apart from quantum theory are not—on the contrary, on the contrary, on the contrary. Only quantum theory is probabilistic. Everything else is not probabilistic. And human decisions too are not probabilistic. They are not deterministic, but they are not probabilistic. Right, but they are not probabilistic. They are something else. And therefore this is one of the great wonders—I don’t know if it’s a wonder, one of the surprises—that you can use statistics when working in psychology. In psychological research you can also use statistics, which is surprising. There is nothing random there. Human choices are not random. But the assumption is that if you have no information at all, you still use probabilistic tools because it’s not deterministic—or at least I think it isn’t deterministic. That’s my worldview.

Well, in any case, the truth is that they don’t get such amazing results in these fields either. Okay. In any case, for us the claim is basically that sometimes we use probabilistic tools also for situations where there is nothing random at all. And therefore, although we use these tools—and every person does this, not only in Jewish law—every person, if he had to bet and knew nothing about the die, I assume would bet there’s a one-in-six chance it lands on two. Right? So there is logic to that, but the logic is not probabilistic logic. Rather it is some kind of a priori reasoning. And therefore the present majority too is a priori reasoning, and therefore it is a present majority and all that we talked about there, and I think that also explains the non-use of probabilistic evidence in law.

Now I want to show you, in just a moment—what I’m saying is, so in the end a present majority too isn’t really probabilistic? No, I’m saying that assuming the sample is representative—as you asked earlier—assuming the sample is representative, then yes. Of course, we always have—the comment I gave at the end says exactly that, that in fact even what we call a probabilistic majority is not really a probabilistic majority, which is exactly, for example, the principle of causality. It doesn’t come to us from nowhere. Why do we use it? To use it is mysticism; it’s like saying there’s a fairy doing various things. No, there is some assumption that such a thing obviously exists in the world. Why? I don’t know, we see it in some way. I don’t know exactly how. There are assumptions which, even though they are assumptions—we did not observe them, we have no empirical information about them—are still obvious, rational, reasonable assumptions, and we use them. Where the distinction lies and how we know that—that’s an interesting philosophical question. I have a few things to say about it, but not here.

What I want is to use that same principle to talk about another interesting law in the context of the law of majority, and that is the law of fixedness. The law of fixedness is a long-standing mystery, and in the Talmud in tractate Ketubot, on page 15, the Talmud says there: “Returning to the matter itself: Rav Zeira said, anything fixed is considered like half and half, both leniently and stringently.” What does that mean? Suppose I enter a store; say there are nine kosher butcher shops in the city and one that sells non-kosher meat. So if I found a piece of meat in the street, that is called a case of separation. The piece of meat separated from the store, it’s found somewhere in a neutral place, so I follow the majority of stores, and the majority of stores here are kosher. What happens if I entered a store, bought a piece of meat, got home, don’t remember which store I bought it from, and suddenly I think to myself: oh, maybe I entered the non-kosher store? I don’t remember which store I was in. In that case it is fifty-fifty. In that case we do not follow the majority. This is called the law of fixedness. When the item did not leave its place, but the moment the doubt arose was when the item was in its place—not when, after it already came out, I ask where it came from, but rather the question is about the thing while it is in its place—there we do not follow the majority. That is what is called the law of fixedness.

The same thing when I throw a stone into a pit and in that pit there are ten people, nine gentiles and one Jew. Yes, and of course murdering a gentile is a well-known commandment, so therefore when I throw a stone into that pit and the question is whether this makes me liable—the Jew was killed, naturally; Murphy’s law—so the Jew was killed and now they ask me whether I’m liable for execution as a murderer. So I say no, because we follow the majority. When I threw the stone, I threw it into this pit, and inside it were nine gentiles and one Jew. So in effect when I threw the stone I did not perform an act with criminal intent. Criminal intent of course, certainly not “you shall not murder.” In any case, the claim is that there is a majority of gentiles. The Talmud says no. Since the matter is fixed in its place—not that if a person had come out of the pit and I ask what the chance is that he is Jewish, then the chance is one-tenth. Rather, if I throw the stone into the pit and it strikes the person in his place, inside the place of mixture, there it is half-half. Even though ninety percent of the people in the pit are gentiles, we treat it as half-half. So this too is a case of fixedness.

And the Talmud asks: and how do we know this from the Torah itself? How do we know this thing, the law of fixedness? What practical difference does the half-half make? What? Stringently. Stringently. Okay, exactly. For example, maybe a provisional guilt-offering, or the obligation to be stringent. If there is a majority, you don’t have to be stringent. You can shoot at the target for me. With half-half you have to be stringent. Say in the meat example it’s relevant. Regarding the meat example that’s true, because in the meat example you really are allowed to eat. Fine. Okay. But in the end, even though this is fixed, I still have a ninety percent chance that I bought in a kosher store. Okay, fixed is half-half. Jewish law treats it as half-half. Why? Okay, that’s our question.

So the Talmud asks: and how do we know this from the Torah itself? Where do we know this, the law of fixedness, from? It says: the verse says, “and he lay in wait for him and rose up against him”—meaning, he must have intended him specifically. They learn it from the verse: “and he lay in wait for him and rose up against him.” He has to be lying in wait for the person he kills, “and he lay in wait for him,” and only then can he be convicted. And in a situation of fixedness, this is basically a situation where I was not lying in wait for the person from the outset, because I didn’t actually know whom this thing would hit. Never mind—they learn it from the verse.

Now here, a preliminary remark. The fact that they learn it from a verse does not exempt us from looking for an explanation. We’ve already talked about this more than once: there is some sense in the yeshiva world that if there is a verse, then no explanation is needed. So apparently there is no explanation. Maybe if there were an explanation, you wouldn’t need a verse. Yes, I mentioned—I brought this example—from Rabbi Yosef Engel in Atvan De’oraita; the Talmudic Encyclopedia copied it, on the rule “we do not punish based on logical derivation.” Meaning, prohibition A is punished with lashes, prohibition B is more severe than prohibition A, but it isn’t written. Since it’s more severe, then all the more so it is prohibited. And besides, of course, if it is prohibited, then lashes are also given for it. The Talmud says no: we do not punish based on logical derivation. “Logical derivation” means an a fortiori argument. So if you learned something through an a fortiori argument, you do not impose punishment for it. Why not? There are three possibilities—well, really two possibilities. One possibility is that perhaps there is a refutation of the a fortiori argument. Fine, sometimes there are aspects that undermine an a fortiori argument. So you can’t impose punishment, because punishment is something irreversible. A second possibility is that maybe the punishment for prohibition A is not enough to punish for prohibition B, because after all prohibition B is more severe than A. That’s why we made the a fortiori argument. So if the punishment for A is lashes, maybe the punishment for B is death; lashes are not enough. Therefore we do not punish based on logical derivation; we leave the Holy One, blessed be He, to deal with that Jew; we do not punish. A third possibility is that we learn it from a verse. It says “his sister, the daughter of his father or the daughter of his mother,” and we learn by an a fortiori argument that she is also the daughter of both his father and his mother together. So why does the Torah write it? To teach you that we do not punish based on logical derivation. It needs to write it, because if we had learned it by an a fortiori argument, we would not have punished. So those are the three possibilities—and as I already told you, of course they are not three possibilities, they are only two. Even though everybody always repeats in every lecture, “there are three possibilities,” there aren’t three, there are only two. There are two explanatory possibilities, and one is a source. Not three explanations. It’s two explanations and a source. The source is the verse “his sister, the daughter of his father or the daughter of his mother,” and there are two explanations. One explanation is either that there is a refutation of the a fortiori argument, or that the punishment for the lighter case is not enough to punish for the more severe case. So when you bring me a verse, that is not a third explanation. The verse is only the source from which I learned the law. Now when you ask, but why is the law correct, you have two explanations, not three. Okay?

For some reason, somehow, the moment there is a source, we are exempt from giving an explanation. The same thing here: it is commonly accepted to think that the law of fixedness is a textual decree with no explanation. It has no explanation, but that’s okay because there is a verse: “and he rose up against him and lay in wait for him,” we learn it from a verse and everything is fine. But it isn’t all fine. Why? Because think about the sage who expounded this verse. There was a verse written, “and he rose up against him and lay in wait for him.” I could have gotten who knows what out of that. Maybe only at night are you liable, because only then he lies in wait for him there in secret, and only then he is liable for death. What? I could also have said this applies only to murder law. Right, I could have done a million things. Why did the expositor decide to derive from this verse the law of fixedness? How did he even come up with the idea that there is a difference between fixedness and separation, and derive from this verse the law of fixedness, that fixedness is like half and half? Clearly he had some reasoning that said there is a difference between separation and fixedness. That it is less reasonable to follow the majority in fixedness than in separation. It’s just that this reasoning alone would not have been enough to infer a halakhic conclusion. So he says: come, I’ll learn it from the verse. This verse comes to exclude something. Only “and he rose up against him and lay in wait for him”—only then is he liable for death. So I ask myself: what is the verse talking about? Ah, I basically have an obvious distinction. There is fixedness and there is separation, so apparently it is speaking about separation and not about fixedness. Fine? But clearly there is some reasoning here, and every exposition is like this. We talked about this once: there is no exposition without reasoning.

Something that is written explicitly in the Torah—say the Torah says it—I do it even if I don’t know the reasoning. But an exposition always involved reasoning on the part of the expositor. Because if he didn’t have reasoning, maybe he wouldn’t have expounded this; he would have expounded something else. The exposition creates a law that is the product of the expositor. For example, “you shall fear the Lord your God”—to include Torah scholars. Fine? The particle comes to include something. But maybe it includes chairs? Why Torah scholars? Because the expositor decided it made more sense to include Torah scholars than chairs. That means there is some reasoning of the expositor that told him what to do with the exegetical trigger. There is some trigger that tells me to include something, equate something, all sorts of things like that, and I use my reasoning to decide what to include or what to equate. Same here. There is the verse “and he rose up against him and lay in wait for him.” So he says: you need to exclude something. There is something for which one is not liable for death when one does it. So I say: what could that be? I don’t know—maybe when you kill only someone over thirty are you liable for death. I could have learned a million things from here. Why did they decide specifically to make the distinction between fixedness and separation, and why indeed not only in capital punishment but in every halakhic context? Because there is something different here: “and he rose up against him and lay in wait for him,” as though he has to know exactly whom he is striking. Fine, I’m saying I could have offered lots of other explanations. Maybe I need to know him? “And he rose up against him and lay in wait for him” means I need to know him. Only someone I know—only if it’s within the family—is there liability for death. I could suggest many things. Clearly there is some reasoning behind this. Reasoning that says there is a distinction between fixedness and separation.

On the other hand, it doesn’t seem like there can be reasoning, because the difference between fixedness and separation, in the probabilistic sense, does not exist. If you enter the store and take a piece of meat, and afterward you ask yourself, wait, but which store was I in? then the probability is one in nine, right? A piece of meat separated and you ask where it came from—that is the case of separation. There too the probability is one in nine. So how can there be a difference between two cases where in both of them the probability is the same probability? On the one hand, there has to be reasoning, there has to be an explanation. On the other hand, there can’t be an explanation, because it’s the same probability. So what can it be?

So people always try to offer various explanations that are not probabilistic. Let me perhaps bring one or two examples; they’re somewhat related to what I said before. One example—I just looked around a bit at explanations people give for this—there is Rabbi Gordin from Yeshivat Har Etzion. He wants to make the following claim: in a non-present majority, some case or person comes before me and I have to decide its nature. Say whether the woman is infertile or not, or whether the woman gave birth at nine months or at seven months, or all sorts of things of that kind. So I decide this according to the state of the world, that in the world women generally give birth at nine months and not at seven. The discussion I’m engaged in is a discussion about the nature of the person standing before me, not about the nature of the world. The nature of the world I know. I’m just asking, after I know the nature of the world, what is the case before me? What is its nature? Is this such a woman or such a woman? That is the case of a non-present majority.

In a present majority, he says, the situation is the opposite. In a present majority there is a piece of meat that I found in the street. There are nine kosher stores and one non-kosher one. What I’m really asking myself is: what are the stores of this city? This piece came from the stores of the city. The phrasing is “the stores,” not “one of the stores,” but “the stores of the city.” Now the stores of the city are divided: there are nine kosher ones and one non-kosher one. So I say, well, if there are nine kosher and one non-kosher, then as far as I’m concerned, the stores in this city are stores of kosher meat. And therefore, if this piece is lying here and it is from this city, then it is probably kosher meat. So here, he says, the question in a present majority is different from the question in a non-present majority.

That’s his claim. The question in a present majority is a question about all the stores in the city, not about the piece that came before me. The piece that came before me is just a derivative. It is a derivative of deciding what the… We talked in the past about the law that “its majority is as its entirety.” “Its majority is as its entirety” means, for example, the Jewish people need to bring the Passover sacrifice on the fourteenth of Nisan. If there are people who are impure, then it is postponed to the second Passover. Right? So they bring the Passover sacrifice a month later. What happens if most of the community is impure? If most of the community is impure, they bring the sacrifice in impurity. Why? Because impurity is permitted for the community, or pushed aside for the community—permitted for the community. The question is: but that’s only a majority, not all of it. He says yes, but “its majority is as its entirety.” Meaning, if the majority of the community is impure, then as far as I’m concerned the entire community is impure. And I explained that the principle of “its majority is as its entirety” is not nullification in the majority, where the minority is nullified, but rather that when I ask myself a question about the nature of the collective, then if I need to assign one certain character to the whole collective, then the majority will determine it. Right? That’s basically the claim.

So therefore also in the context of a present majority, when I need to know this piece came from one of the city’s stores, I ask myself: what kind of stores are there in the city? Yes-no question, kosher or non-kosher? What kind of stores are there in the city? If I have to answer that as a yes-no question, then I say kosher stores, because nine of them are kosher and one is not. So therefore the discussion in a present majority is not about the piece. The discussion in a present majority is about the stores, about the whole set of stores. And that is the difference between this and a non-present majority. In a non-present majority I know the general situation; I ask what is the nature of the piece before me.

Now he says, so if we now move to the law of fixedness—the law of fixedness, by the way, is said only regarding a present majority. In a non-present majority there is no law of fixedness and separation, only in a present majority. Therefore, for example, the woman about whom I ask whether she gave birth at nine months or at seven—it doesn’t matter whether she is in her house or whether she came to the court and asks the question there. It doesn’t matter whether she is in her fixed place or whether she has separated from her home; that is irrelevant. In the case of nine stores or ten stores, there is the question whether the piece separated from the store or whether it is inside the store. Only there do we make the distinction in a present majority. There are later authorities who will say there is also such a distinction in a non-present majority, but that’s strained. This distinction is said only within a present majority. And why? So that is what Rabbi Gordin says. He says that in a present majority, the question is about the stores, about the set of stores in the city. And that is what the rule of a present majority tells me: assume that all the stores in the city are like the majority of stores. If most of the stores are kosher, then as far as I’m concerned the city’s stores are kosher. And then if this piece separated from the city’s stores, it is kosher. But if I now go to the store and take the piece, then I’m not asking myself what the nature of the stores in the city is. Here the question is about the piece. The question is about the piece: what is this piece?

Moreover, all the stores in the city don’t even interest me; what interests me is this particular store. Why don’t you formulate the question as: what is the store that I entered, and then I judge the nature of the store by the rule, by the collective? Ah, again, because there is nothing special about this store—I mean, I don’t know which store I entered. No, the meat? I understand. But I’m saying there isn’t a particular store. If, say, I knew which store I entered, I just didn’t know whether it belonged to the kosher majority or the minority, you’d be right. But I don’t even know which store I entered. I’m not discussing a store, because there is no store at all before me. Meaning, there wasn’t some hypothetical store and I’m asking about it. So it isn’t to ask about it, but to ask about the piece. And because of that, he says, that’s why it is half-half. Because as far as the piece is concerned, either it is kosher or it is not kosher—that my wife already said. So therefore, either it is kosher or it isn’t. It doesn’t matter now in terms of the majority of stores. That is his claim as an explanation of fixedness.

I say this explanation is a bit problematic in light of cases that appear in the Talmud. First of all, even if I am asking a question about the piece itself, a non-present majority is also a question about the piece itself. And we know that even when you ask a question about the piece itself, you still follow the majority. So if that is the difference between fixedness and separation, then say that fixedness is like a non-present majority. But why in fixedness is it half-half? That it does not explain. Not to mention all sorts of Talmudic cases where the entire mixture is moving, in motion—yes, wagons of Tzipori or something like that. The mixture is moving, so that is called separation, not fixedness. But that is really strange, really hard to understand. So in short, there are difficulties with this explanation.

If I return to the subject where we began, the Passover sacrifice, I say: is all of the Jewish people impure or all of the Jewish people pure? All of the Jewish people are either impure or pure. Now I’ll come to one particular person among them and say: what is my law? Do I now need to purify myself through the red heifer or not? So I say, the majority of Israel. To purify yourself you certainly need to; the question is whether you can bring the Passover sacrifice, that’s the question. No, I’m saying—but maybe this should be considered fixedness? You—I don’t know. Even if ninety percent of the Jewish people—to purify yourself, obviously you’ll need to purify yourself; nobody becomes pure because of the collective. No, he’s in doubt; he says I don’t know if I’m impure or pure. Okay, so there is a law of doubtful impurity; that has nothing to do with fixedness. But we know that ninety percent of the Jewish people are impure or pure, I don’t know. So wouldn’t I derive his status from that? Why? Certainly I would. Certainly I would. A Torah-level doubt is treated stringently. If most of the community is impure, then I’ll assume he too is impure, even though he doesn’t know. Of course I will. If most of the Jewish people are pure, I’ll say he’s pure. No, we follow the majority. But for him, in his case, he is either impure or pure, and he simply doesn’t know. And we follow the majority. No, now you’re saying, if it’s a non-present majority and I apprehend the thing in its place, then we treat it as half-half. Okay, that’s true.

There is another explanation. I saw Moshe Koppel once wrote some explanation of this matter. His claim is as follows. Suppose there is a container with ten balls, nine white and one black. I drew out a ball and I ask what its color is. Ninety percent it is white, ten percent it is black—suppose now I’m talking about drawing it out randomly. Now I ask a different question: if I put my hand into the container and take out a ball, what color will it be? He claims that this is a different question. It’s a different question because at the moment there isn’t even a ball yet that you’re asking about. It’s a little similar to that store. There is no ball here that you are asking about: if I put my hand into the container and take out a ball, what color will it be? That is a hypothetical question, and I don’t know how to answer it—like the attorney general. A hypothetical question he doesn’t answer. In this case there is not yet any ball; what are you asking about? Or in other words, I’ll formulate it somewhat similarly to what I said about statistical evidence: tell me how you carry out the extraction. After you’ve done the extraction, I know how you extracted, or what the characteristics of the act of extraction are, and then I can discuss it statistically. But if you haven’t extracted yet, then that is a question I don’t know how to answer. There is no particular ball here; I don’t know what the mechanism of extraction will be, and therefore I can’t answer that question.

Earlier too the mechanism didn’t affect you. What? Earlier too you didn’t know about the mechanism. No, I knew. If I don’t know about the mechanism, apparently it will be the same. It will be the same. Therefore, for example, I’ll give you a case with the stores. In the store, when you go to the store and take out the meat, then you take it home, so the meat has already separated. So why don’t we then follow the majority? After all, this is separation, not fixedness. Because when the doubt arose, when I was there, it was in its place. I don’t care that afterward it is separation. So in effect Koppel’s claim is that if the piece of meat separated—if the piece of meat separated—then there is a defined piece of meat about which I ask whether it is kosher or non-kosher. And that is called this piece; it is the law of this piece. But if I ask myself, in the place of fixedness, what will happen if I take out a piece of meat—will this piece of meat be kosher or non-kosher—that is a hypothetical question. The question of fixedness is a hypothetical question. That is his claim. The question of fixedness is a hypothetical question.

I think that is problematic, because what do you mean? There is indeed a concrete piece here; after all, I took the piece and removed it. There is a concrete question here; I even know how the extraction process happened, so what? The moment the doubt arose was when I was inside the store. Therefore I say—I’m shortening because we’re already out of time and I want to finish this today—so I say that this too is a problematic explanation. But all these explanations are basically explanations that are not probabilistic explanations, but legal explanations—what the right way is to ask the question, or something like that.

My claim is that this is true with reservations. After all, as I said, the difference between fixedness and separation is stated only in a present majority. And a present majority, as I prefaced, is not probabilistic at all. Therefore in my view the question is not why fixedness is like half and half, as they despaired there, as I said. The question is why in separation we follow the majority. People say: in separation it’s obvious that we follow the majority; in fixedness why is it only half-half—there too go after the majority. I think the question is the reverse. The question is why in separation we follow the majority. There is no probability; you have no information; you can’t know that it is ninety percent, as I said before. So why do you follow the majority? Fine—the Torah innovated that we follow the majority. Why? So I quoted Rabbi Shimon earlier. Rabbi Shimon says: we count sides. Each store contributes a side regarding this piece of meat: either it came from this store or it came from this store or it came from this store, right? So the Torah says there are nine sides versus one that it came from a kosher store, and therefore we follow the majority. This is basically a textual decree. There is no probabilistic calculation here. I can say okay, but sides are like probability—the Torah made that innovation. But that is all in a place where there are sides. In fixedness there are no sides. The fixed item is in its store; it did not separate from some store and I ask from which store it separated. There are no sides there. The question is what the piece is—from the previous explanations, but from a different angle. In such a situation there are no sides; what can you do? So there is no innovation of the Torah that we follow the majority, and in any case it remains half-half. It remains half-half because the question is either that the piece is kosher or it isn’t kosher, and you have no probability, and if you have no information and no probability—half-half.

With sides there is an innovation that even though there is no probabilistic calculation, you still count the sides as though it were probability. What I basically want to say is this: it is true that the explanation of the difference between fixedness and separation is not probabilistic; on that I agree. But even in separation, following the majority is not probabilistic—that is the point I want to introduce here. Even when I follow the majority in separation, it is not a probabilistic majority in any event. So this whole law is not probabilistic; therefore look at what the law says. If the law says to count sides, that is only when there are sides. If there are no sides, there is nothing to count. So it becomes self-evident. In other words, once I understand that a present majority is not a probabilistic majority, the distinction between fixedness and separation is obvious. And that is the reasoning that stood before the expositor when he learned it from “and he rose up against him and lay in wait for him.” The reasoning is simply that if I understand that “follow the majority” means to count sides, then that applies when there are sides; when there are no sides, then not.

And basically what I’m saying—and with this I’ll finish—is that, as I said before, what I’m trying to explain is not at all why in fixedness it is half-half. That is obvious. The question is why in separation we follow the majority. In separation we follow the majority even though there is no probability—why? There is a great novelty here: we follow the majority because we count sides. Fine, with that innovation, then it remains half-half. In other words, contrary to what people think—that separation is the obvious case, and now in fixedness we look for some special explanation, I don’t know, a textual decree, a definition, whatever—I say exactly the opposite. Fixedness is the simple case, and now the question is why in separation we follow the majority. Because the Torah innovated that we count sides, therefore in separation we follow the majority. Why did the Torah need to say “and he rose up against him and lay in wait for him”? That’s the simple case. No, in order to tell you that only in separation do we follow the majority; in fixedness we do not. Sorry—only in fixedness do we not follow the majority; in separation we do. That is the novelty. No, but you’re saying that is the natural thing; the natural thing is that in separation… But after it is written “follow the majority,” you might say we follow the majority in every case. No—only when there are sides.

Majority in Halacha and General Principles 2, Lesson 8

Table of Contents

Summary

General Overview

A Majority Present Before Us and a Majority Not Present Before Us as Probability versus Counting Possibilities

Rabbi Shimon Shkop and Counting Sides in a Majority Present Before Us

Statistical Evidence in Law: Prisoners and Buses versus Eyewitnesses

The Envelope Paradox, Monty Hall, and Dependence of the Calculation on Information about the Mechanism

Background Assumptions, Induction, and Causality as the Basis for Using Probability

Human Behavior as Non-Statistical and Its Implications for “We Do Not Follow the Majority in Monetary Cases”

A Doubt Where There Is a Possible Prohibition and a Doubt Where There May Be No Prohibition as a Probabilistic Distinction

Certain Error versus Probability of Error in Comparing Statistical Conviction to Testimony

Determinism, Chaos, and the View of Probability as Lack of Information

The Law of Fixedness: Anything Fixed Is Treated as Half-and-Half, and the Verse “And He Lay in Wait for Him and Rose Up Against Him”

A Verse as Source versus the Need for Explanation and Reasoning in Derivations

Non-Probabilistic Explanations for Fixedness and Their Difficulties: Rabbi Gordin and Moshe Koppel

Reversing the Question: Why in Separation Do We Follow the Majority, and What Is the Role of “Sides”

Full Transcript

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Table of Contents

Summary

General Overview

A Majority Present Before Us and a Majority Not Present Before Us as Probability versus Counting Possibilities

Rabbi Shimon Shkop and Counting Sides in a Majority Present Before Us

Statistical Evidence in Law: Prisoners and Buses versus Eyewitnesses

The Envelope Paradox, Monty Hall, and Dependence of the Calculation on Information about the Mechanism

Background Assumptions, Induction, and Causality as the Basis for Using Probability

Human Behavior as Non-Statistical and Its Implications for “We Do Not Follow the Majority in Monetary Cases”

A Doubt Where There Is a Possible Prohibition and a Doubt Where There May Be No Prohibition as a Probabilistic Distinction

Certain Error versus Probability of Error in Comparing Statistical Conviction to Testimony

Determinism, Chaos, and the View of Probability as Lack of Information

The Law of Fixedness: Anything Fixed Is Treated as Half-and-Half, and the Verse “And He Lay in Wait for Him and Rose Up Against Him”

A Verse as Source versus the Need for Explanation and Reasoning in Derivations

Non-Probabilistic Explanations for Fixedness and Their Difficulties: Rabbi Gordin and Moshe Koppel

Reversing the Question: Why in Separation Do We Follow the Majority, and What Is the Role of “Sides”

Full Transcript

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