Doubt and Statistics – Lecture 17
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Table of Contents
- Kavua and Parish and the transition from probability to Jewish law
- Possible kinds of explanations for the law of kavua
- Rabbi Goldwicht’s proposal from Alon Shvut (Yeshivat Har Etzion)
- Kavua according to Rabbi Goldwicht and the difficulties in the explanation
- Moshe Koppel’s explanation: a concrete question versus a hypothetical question
- Critical comments on Koppel and on applying the law of kavua
- Intent in “throwing a stone into a group” as a halakhic-legal determination
- The direction of Rabbi Shimon Shkop: a present majority as a rule of conduct, not statistics
- “A majority of sides” and its implication for kavua versus parish
Summary
General overview
The text presents the topic of kavua as an example of the gap between probabilistic calculation and legal-halakhic decision-making, because in kavua the law treats it as fifty-fifty even though apparently the probability is identical to the case of parish, where one follows the majority. It defines kavua versus parish through the example of nine kosher stores and one non-kosher one, and proposes a framework for possible explanations that are not necessarily probabilistic, such as a legal explanation or legal intuition. It then presents two central attempts to explain the law of kavua (that of Rabbi Goldwicht/Gordin and that of Moshe Koppel), examines the difficulties in them, and finally proposes another direction inspired by Rabbi Shimon Shkop, according to which a present majority is not a statistic of information but a rule of conduct based on a “majority of sides,” and from that begins to clarify why the distinction between parish and kavua belongs דווקא there.
Kavua and Parish and the transition from probability to Jewish law
The text states that the topic of kavua illustrates how non-immediate the transition is from probability to law and Jewish law. It presents a case where meat is found in the street in a city that has nine kosher stores and one non-kosher one, and there one follows the majority because the piece separated from its place, and therefore “whatever separated, separated from the majority.” It presents a case where a piece was taken from one of the stores but it is not known which one, and there the law is “whatever is fixed is treated as half-and-half.” It sharpens the point that the central question is why there is a halakhic difference between kavua and parish even though the probabilistic calculation seems identical, and it illustrates the difficulty through a conversation in which it was argued that a real explanation should be one a person would actually be willing to rely on in an existential decision such as drinking poison.
Possible kinds of explanations for the law of kavua
The text distinguishes between a probabilistic explanation and a legal explanation based on systemic consequences, and comments that in the context of kavua “it doesn’t seem like there is that kind of explanation.” It defines “legal intuition” as a determination that seems right or wrong even though it cannot be explained through consequences like certainty and equality, and presents this as a possible explanation that was already demonstrated in topics of legal evidence. It asks the reader to keep these possibilities in the background while discussing the law of kavua.
Rabbi Goldwicht’s proposal from Alon Shvut (Yeshivat Har Etzion)
The text presents Rabbi Goldwicht as beginning with the difficulty that a majority in a religious court is apparently not similar to a majority among stores, because in a religious court the opinion of each judge is known and the question is what the ruling of the collective is. He argues that in both cases the majority is not a matter of statistics but a mechanism for determining the identity or character of a collective, so that in a religious court the majority determines what “the court as a collective thinks,” and among stores the majority determines that the city is a “kosher city.” He compares this to elections, where the opinion of the majority is attributed to the whole, and adds the example of “its majority is like its entirety” regarding the Passover offering in impurity in order to show that the decision mechanism is attributing the characteristic of the majority to the collective. He notes terminologically that the Talmud calls such a mechanism “its majority is like its entirety” and not “following the majority,” and that from the standpoint of the sources of derivation there is no necessity that it is learned from “follow the majority” as a present majority is learned.
Kavua according to Rabbi Goldwicht and the difficulties in the explanation
The text explains that according to Rabbi Goldwicht, when the piece separated into the street, the discussion is about the set of stores and therefore one can determine the character of the collective and project from that onto the piece. He argues that when a piece was taken from a specific store, the discussion is not about the character of the set of stores but about that specific store, and therefore the law of a present majority was not newly stated there and the ordinary laws of doubt apply, from which one gets “kavua is treated as half-and-half.” He adds that this explains why the law of kavua is said only regarding a present majority and not regarding an absent majority, because an absent majority is a probabilistic mechanism of scientific generalization and therefore there is no room there for the distinction between kavua and parish.
The text presents several difficulties: it repeats the comment that the mechanism described resembles “its majority is like its entirety” and not “following the majority.” It asks why in an absent majority one follows the majority even though the question is always about a specific individual case, whereas in kavua it is argued that no majority was introduced because this is a question about an individual case. It suggests that if in a present majority one does not activate the collective mechanism regarding an individual case, one could have activated the statistical mechanism of an absent majority there too, and it presents this as a difficulty. It also argues that one could have applied the same pattern to a particular store within the group (“which store is this?”) and considered it as belonging to the kosher majority, so the distinction that rests on “there is no separation here” seems formalistic and unsatisfying.
Moshe Koppel’s explanation: a concrete question versus a hypothetical question
The text brings from Moshe Koppel a distinction between a concrete question about a ball that has already been drawn from a container and a hypothetical question, “if I were to put in my hand and pull out a ball, what color would it be?” It defines that in the concrete question there is a defined object and the problem is lack of information, so one uses probability; by contrast, in the hypothetical question there is no defined object, and therefore the question is “not well-defined” and may even depend on the method of extraction. It emphasizes that the intuitive answer in both cases may be the same probabilistically, but the nature of the question is different, and in the hypothetical question there is no justification for answering by means of statistics.
The text concludes that according to Koppel, when the question is hypothetical, Jewish law does not allow one to determine an answer on the basis of majority, and therefore the two possibilities are treated as legally equal in weight, and that is “as half-and-half,” which is not probabilistic. It applies this to “throwing a stone into a group” in Ketubot: when there are nine Jews and one gentile in the room, the halakhic question about intention at the moment of the throw is hypothetical with respect to who will die, and therefore there is no room for majority and the law is half-and-half even though in practice a Jew ended up dying. It sharpens the point that the question is not about the identity of the victim after the fact, but about the classification of the intention and the act at the moment of the throw.
Critical comments on Koppel and on applying the law of kavua
The text argues that according to Koppel it is not clear why one should distinguish between a present majority and an absent majority, because even in an absent majority one could formulate the question as a question about “all the women in the world” and then apparently one should also arrive at half-and-half. It raises a particular difficulty from the canonical case of kavua, where a piece of meat is taken from a store, because there there is a defined piece in one’s hand and the question is not hypothetical, and it suggests the strained possibility that the doubt “arises” at the moment of taking and can therefore be described as hypothetical. It argues that the law of kavua is applied in such a strange way by commentators that it is hard to believe there will be one explanation that covers all the cases, and it suggests a description of a process of “formalization” in which a principle born from certain cases expands into applications that do not preserve the original logic. It emphasizes that from its perspective the Talmudic cases require an explanation because they are the canonical cases of kavua, foremost among them taking a piece from the store and throwing a stone into a group.
Intent in “throwing a stone into a group” as a halakhic-legal determination
The text presents a discussion in which it is asked whether one can infer the thrower’s intention from the number of people in the room, and it answers that the question is not factual—what passed through his mind—but rather a halakhic classification of a situation in which a person knows that most of those present are Jews. It suggests that Jewish law can view such an act as the intentional murder of a Jew even if the thrower claims he intended to hit a gentile, because the irresponsibility and knowledge of the risk determine the classification. It raises the implication that even bringing witnesses about a unique intention to harm the gentile would not change the classification, and compares this to examples of shooting into a place with many people and to a parallel discussion about “unintentional” on the Sabbath where there is a distinction between “doesn’t want” and “doesn’t know.”
The direction of Rabbi Shimon Shkop: a present majority as a rule of conduct, not statistics
The text returns to the distinction between a present majority (stores, religious court) and an absent majority (for example, most women give birth at nine months), and stresses that a present majority is not built from generalization from a sample but from an a priori logic of symmetry in the absence of information. It cites Rabbi Shimon Shkop at the beginning of Gate 3 in Sha’arei Yosher, who argues that in the clarification of the nine stores, “this clarification is not truth,” and that there is no clarification of reality here but rather an instruction for conduct learned from the verse “follow the majority.” It notes that in his view Rabbi Shimon Shkop’s reason concerning the inability to attribute separation to a particular store is a statistical mistake, but he adopts the basic conclusion that the law is not “the majority clarifies” but a rule of conduct.
The text proposes a supporting probabilistic formulation: in a present majority there is no distribution learned from information, but rather an answer that arises from ignorance, similar to saying “half” about a coin about which there is no information. It argues that the Torah’s novelty is that one is permitted to decide even on the basis of such a majority, which is not based on objective information but on the structure of the doubt, and therefore the verse is needed. It adds that an absent majority is statistics of scientific information arising from samples and rules, and therefore distinctions like kavua/parish do not exist there.
“A majority of sides” and its implication for kavua versus parish
The text cites Rabbi Shimon Shkop that the majority among stores is similar to the majority among judges because in both one counts “sides” and does not calculate probability, so that each store “generates a legal implication” as a doubt about the meat, and thus nine sides permitting and one side forbidding are created, about which it is said, “follow the majority.” It brings an indication from the words of later authorities who discuss whether one should take into account the quantity of meat in each store and note that “we count stores,” and argues that this is understandable if the mechanism is a “majority of sides” and not statistics of quantities. It concludes that if a present majority is not statistics, then the distinction between kavua and parish is not a contradiction to probabilistic calculation but a question of where the Torah’s novelty of “follow the majority” applies.
Toward the end, the text begins to offer a resolution: in parish there are many sides because the piece could have come from any one of the ten stores, and therefore there is a majority of sides for kashrut; in kavua, when a piece was taken from a specific store, there is no multiplicity of sides of stores, but rather a binary question about one defined store—whether it is kosher or non-kosher—and therefore the law is half-and-half. It states that this is not statistics but an internal distinction in the structure of the “sides,” and announces that the detailed explanation will continue next time.
Full Transcript
[Rabbi Michael Abraham] Okay, let’s begin. We’re in the topic of kavua, and this topic basically comes to illustrate the complexity involved in moving from a statistical consideration to a legal-halakhic consideration and the like. We saw this from various aspects, we saw it when we talked about statistical evidence in law, and I’m continuing that discussion into the topic of kavua. There too, at least in Jewish law, we find that there is a difference in how we relate to a case of kavua as opposed to a case of parish, even though apparently the statistical calculation is identical, or the odds, the probability is identical in both cases, and nevertheless in one of them we follow the majority, we follow the probability, and in kavua it is treated as half-and-half. So this is again an example of how non-immediate the transition is from probabilistic calculation to the legal plane. Now I’ll define again the concept of kavua. We’re basically talking about a piece of meat that I took—say the standard case is that I find a piece of meat in the street. There are ten stores in the city, nine kosher and one non-kosher, so we follow the majority, and therefore the assumption is that the piece is kosher. But if I took the piece from one of the stores and I don’t know which one, I don’t know whether it is kosher or not kosher, in that situation that is called kavua, and whatever is fixed is treated as half-and-half. Kavua means that it is fixed in its place and did not separate from its place, right? The piece in the street separated from the store, from its original place. So whatever separated, separated from the majority, meaning whatever separated—we follow the majority. But if the thing is fixed in its place, then whatever is fixed is treated as half-and-half, it’s like fifty-fifty. And the question is why. And I gave some short introduction to the a priori difficulty of explaining this, or how an explanation for such a thing is even possible. Because my friend kept coming back to me every time with some other proposed explanation for the law of kavua, and I asked him whether he would drink poison on the basis of that explanation, and of course he said no, he would not drink poison on that basis. So I told him, if that’s so, then you have no explanation. Meaning, the problem is that on the one hand I’m looking for an explanation, something that will give me the logic behind the difference between kavua and parish, but on the other hand it’s obvious that probabilistically—at least that’s how it seems—probabilistically it’s the same thing. So if it’s the same thing, how can there be any explanation at all? So we talked about two other kinds of explanation besides the probabilistic explanation: there could be a legal explanation, meaning it has some problematic outcomes or implications, like the fruit of the poisoned tree; in this context it doesn’t seem like there is that kind of explanation. And the third thing is legal intuition. Legal intuition means something that seems to us intuitively that this is not the right way to act or this is the right way to act, not because there are consequences—certainty in law, equality, I don’t know, all kinds of consequences of that type—or concerns like the fruit of the poisoned tree, because there I don’t call that legal intuition, I call that a legal explanation. There is some explanation that is not probabilistic but legal. Legal intuition is something I don’t know how to explain, but there is some sense that this is right, this is the right way to act, and that is not the right way to act. And I argued that an explanation of that kind is also a possible explanation, and we demonstrated that in the topic of legal evidence. And now I want you to keep that in the background, in your minds, as we deal here with the law of kavua. Last time, at the end of last time, I finished with a first proposal to explain the law of kavua, from Rabbi Goldwicht of Alon Shvut, from Yeshivat Har Etzion, and he basically argues the following. He starts with a difficulty—I’m going over it again because we did it rather quickly at the end. He starts with the difficulty that apparently a majority in a religious court is not the same kind of case as a majority of stores. In a majority of stores, when I’m talking about a piece that separated, I’m basically trying to determine the nature of this piece that I found: is it kosher or not kosher? Right? So my subject is the nature of the piece. In a religious court, after all, the opinion of every judge is known. We have no question what Judge A, Judge B, or Judge C thinks. Our question is what the law is. We have three judges, two opinions against one, we follow the majority. And that is called a present majority; we saw that in the Talmud in Hullin. But it’s not like some judge came out to us and we don’t know whether he belongs to the majority camp or the minority camp, and we are discussing what that judge thinks. If that were the case, it would resemble a piece of meat that separated. But in a religious court the discussion is altogether different. Every opinion of every judge is fully known to us. We ask only how the law should be decided, the ruling of the whole court. When two say one thing and one says another, what is the overall ruling? The overall ruling is determined by the majority. It is not a law of following the majority in the sense we know from pieces of meat. We have no doubt about any individual item as to whether it belongs to the majority group or the minority group. We have a question of how to determine the ruling in court. So we already spoke about that difficulty. He starts from that difficulty, and he basically says that in both cases, both in stores and in a religious court, the majority is actually not a matter of statistics at all. The majority comes to clarify the identity of a collective. And in a religious court it is very clear that this is so. We have two judges who say Reuven is liable, one judge says Reuven is exempt. I ask: okay, what does the court as a collective think? That is basically the ruling. The decision that comes out of the court is what the court as a whole says. So I say: if I want to determine the opinion of the whole or the character of the whole, to make some determination about the whole, then what characterizes the majority for me is the characterization of the whole. That is the law, that’s what we see in court. Rabbi Gordin says: the same thing is true in stores. In stores too, we are not searching—we are not really trying to determine the nature of the piece. In the end that is what we want to determine, whether it is kosher or not. But the majority there is not a statistical majority that tells me that because there is a high probability, this piece is kosher. Rather, this majority basically says: once I have ten stores in the city, nine kosher and one non-kosher, then when I ask whether this is a kosher city or a non-kosher city, the answer is that this is a kosher city. Most of the stores are kosher, so the city is kosher. Do you see the similarity to a religious court? It is exactly the same mechanism that we see in following the majority in a religious court. Once the city is a kosher city, then the piece of meat that I found is also presumed kosher, because I have decided that the city is kosher. So my discussion is really about the character of the set of stores or of the city. The implication is for the piece before me. I am not asking about the nature of the specific piece before me. That is basically his claim. And that is how he explains, so far—we haven’t yet gotten to kavua, this is only an introduction—how the majority in a religious court is a present majority exactly like the majority in stores. Okay? As he says, it’s like—I don’t know—when there are elections in a city, we talked about this. There are two parties, they hold elections. If the majority voted for Party A, then that city is ruled by or chose Party A. Right? I am the prime minister of everyone, as each one tells us two minutes after receiving the bitter news that he was elected. So the claim is basically that elections are not meant to determine—we discussed this at length—not meant to determine who is right, not meant to determine anything else; they simply come to determine what the city says. What the city as a city, or the state as a state, says. The claim is that in our eyes, the opinion of the majority is what we attribute to the entire collective. And that is the law of following the majority in a present majority. Therefore, in both these cases, as in elections, we do not use the majority as a statistical tool, but rather to determine the character of the collective when the individuals within it have differing characters. And the claim is that the character of the majority of the individuals is, for us, the character of the collective. That is basically the novelty in following a present majority. You see, we are not doing any calculation; this is not a statistical calculation. We are not discussing the question of what the chance is that this piece is kosher. That is not the point. It is really worth commenting on this, because I think maybe I already did, that from the verse “follow the majority” the Talmud derives the law of majority, a present majority, maybe also an absent majority, of following the majority. But there are other laws of majority, like “its majority is like its entirety.” “Its majority is like its entirety” means, for example, if most of the Jewish people are impure on Passover eve, when the Passover offering has to be brought, then we bring the Passover offering in impurity, because impurity is permitted in the community. But not the whole community is impure, only sixty percent of it. Yes, but for me if sixty percent of the community is impure, then the whole community is impure. That is the character of the majority. Again, I need to determine the character of the whole—sorry—I need to determine what the character of the whole is, so I take the character of the majority and for me that is the character of the whole. You see that this is really what we are seeing here. Even though in the Talmud the terminology is different. That law regarding the Passover offering is called the law of “its majority is like its entirety.” The laws we are dealing with here are laws of following the majority. It’s not the same thing. But in terms of mechanism, in a present majority, what Rabbi Gordin is arguing is that in a present majority we are really dealing with “its majority is like its entirety,” not with following the majority. Because we are not discussing the statistical question of the nature of the piece; we are discussing a whole—what is the nature of the whole when the items within it have different natures? So I say: the nature of the majority is what determines the nature of the whole. That is like saying “its majority is like its entirety.” It is really the law of “its majority is like its entirety” and not the law of following the majority. That is a bit of a comment on his claim, although one can understand what he is saying, but this terminological comment is a real one, because apparently the Talmud uses these as two different principles. More than that: following the majority is learned from “follow the majority”; the law of “its majority is like its entirety”—there are only a few later authorities who argue that this too is learned from “follow the majority.” That does not appear either in the Talmud or in the medieval authorities. So apparently this is really the law of “follow the majority”—it is not learned from “follow the majority,” it is the law of “follow the majority” itself. The law of “follow the majority” is the law of “its majority is like its entirety.” So apparently I would expect it to be completely simple, clear, and agreed upon that yes, it is not learned from “follow the majority”; it is the law of “follow the majority” itself. So these are comments, but they are more stylistic comments. Logically, one can hear what he is saying. As terminological comments, okay—but logically, one can certainly hear what he is saying. Now, what he wants to say is that in light of this, one can also understand the law of kavua. What does that mean? He says as follows: if the piece separated from the store and we find it in the street, then the discussion is really a discussion about the stores, right? I ask what the nature of the stores is, and then I say: fine, the piece separated from those stores—the stores meaning all ten. So if the stores are kosher as a collective, then the piece is also kosher, and if not, then not. So the discussion is a discussion about the stores. But if I took a piece from a specific store and I don’t remember which one, or I don’t remember whether it is kosher or non-kosher, then there is no point discussing, so he argues, the character of the stores. There is one specific store in which the piece was, and I ask: what is the nature of that store? So he says that if I ask what the nature of that store is, then the law of a present majority was not said about that, because this is not determining the character of a collective. In the background, of course, there is some assumption, because I could have said the same thing about the store. I have nine kosher stores and one non-kosher one. This store separated from the groups, right? I am interested in one particular store, and now I ask whether it separated from the nine, whether it belongs to the nine, or whether it is the one non-kosher one. And then I can apply what he said about a separated piece, even when the discussion is about the store rather than the piece. It is true that there is no mechanism of separation here. This store did not separate from anywhere; it was there and it is still there. I ask which store this is, not where it separated from. It did not separate from anywhere. I ask which store this one is. All the more so because it may be that I do not remember which store it is at all. It doesn’t matter. But even if I remember which store it is, I just don’t know whether it is a kosher store or a non-kosher store, then the question is a question of which store this is, not where it separated from. In that sense, maybe one can hear a difference from those cases of “its majority is like its entirety” he spoke about earlier. And therefore he says that in such a situation we do not follow the majority, because here that novelty of following the majority in a present majority was not introduced. Consequently, we have the laws of doubt here. Where the law of majority was introduced, we resolve the doubt by the majority, but where the law of majority was not introduced, then we remain at the starting point: if I have two possibilities, I have a doubt, and we follow the laws of doubt here. Why indeed did we say that the law of kavua is stated only in the context of a present majority and not in an absent majority? Because in an absent majority there is no difference between kavua and parish. Only in a present majority—that is the overwhelming majority of views. There are some who want to say otherwise, but the overwhelming majority of views say this, and this is also the simple logic. Why indeed is that so? Rabbi Gordin says: because in a present majority it is entirely non-probabilistic; it is a law of “its majority is like its entirety.” I say: that law depends on whether you are asking a question about some collective, and then there is a novelty that its majority determines the character of the collective. If you are not asking a question about the collective but about an individual item, then the law of a present majority was not introduced, and the laws of doubt apply. But in an absent majority, such as most women give birth at nine months, then in that case the calculation is statistical; it is not “its majority is like its entirety.” I ask a question: who is this woman? Meaning, did this woman give birth at nine months or at seven months? She did not separate from anywhere and she did not go anywhere; that is irrelevant. I ask questions about the nature of women or about the nature of this woman, and the question whether she gave birth at nine months or seven months is a probabilistic question. A present majority is not probabilistic; it is a question of what determines the character of the majority. The question of an absent majority is a probabilistic question, like any scientific question. I make generalizations from a sample and then apply them afterward to a case that appears before me, and therefore there it does not make sense to distinguish between kavua and parish. That is his claim. Here too this is a problematic story. I’ll tell you a few things that are difficult for me in his explanation. First of all, what I said before, the conceptual comment. Right? On the conceptual level, the law he describes is called by the Talmud “its majority is like its entirety,” not a law of following the majority. So that is only regarding the terminology. A second question: when I look at an absent majority—an absent majority, there is a woman before me, she gave birth, and I ask whether she gave birth at nine months or seven months, okay? Now, this is a discussion not about a collective, but about this particular woman. The collective I know exactly: there are such and such women who give birth at nine months, such and such women who give birth at seven months, everything is fine, the statistics are known. I am now asking about this woman: did she give birth at nine months or seven months? That is a question about a specific woman, not a collective, right? If that is a question about a specific woman, then why do we follow the majority? He says that where the question is about a particular piece, as when we take the piece from the store, right? There he told me this is not a question about the collective of stores, it is a question about this piece of meat or about that store, and in such a situation the law of following the majority was not newly introduced. But in an absent majority that is always the situation. In an absent majority I always ask a question about the individual before me, and I apply the laws of majority to such a question. So why not in a present majority? Now here one can somehow explain it by saying that these are different mechanisms. The absent majority is scientific generalization; it is an ordinary probabilistic mechanism. That we apply even when the question is about a single piece, and maybe especially when the question is about a single piece. Only in a present majority the majority is not probabilistic at all, but rather some novelty of the Torah that the majority determines the character of the collective. And that novelty was said only when I am asking questions about a collective and not about a specific object. And one could come back and ask: fine, so the law of a present majority does not apply when I ask a question about a specific object. Then let’s apply the statistical law to that case, the law of an absent majority. I can apply the statistical law to it, and that I do apply even when I ask a question about a single object. So why don’t I learn from an absent majority to this case? I certainly can apply the mechanisms of majority even when the question is about a single object. Third, as I said before, even when I took the piece from the store, right? Then the discussion is really about the piece and not about all the stores or about the store. So why shouldn’t I relate to the store as something about which the discussion is: from which group of stores did it separate? There are nine kosher stores and one non-kosher one, so the collective of stores is kosher, and so this store is also kosher. Just as he explained regarding a piece of meat that separated—what does he say? I ask what the nature of the city is, whether this city is kosher or not, and if this city is kosher, then this piece that came from one of the totality of kosher stores is also kosher. Well then, why when I’m talking about a store can’t I say the same thing? The collective of stores here is kosher, and therefore this store is also kosher. What is the difference? You tell me, yes, there is no separation here. The store did not separate from anywhere. Fine, so that is a formalistic point—so what if it didn’t separate? What difference does that make? The pattern of thought exists here too. So I don’t know—there are several difficulties here that I think are very problematic. Okay. I want to move on to a second explanation of the law of kavua. This explanation is taken from Moshe Koppel—I hope he’s still with us after all the demonstrations they hold outside his house. And he says as follows. Suppose there is a container with ten balls in it, nine white balls and one black. Now I ask a question. I present two scenarios. First scenario: I put my hand into this container and pull out a ball. Now I ask you—you did not see the ball I pulled out—I ask you what color that ball is. Right, there are nine white and one black; what color is that ball? That is one question. Let’s call it the concrete question. I have a particular ball, and I ask what its color is. I don’t know what its color is, I ask what its color is, but there is a defined ball here and I ask what its color is. Obviously the answer is black or white; the question is well-defined, the possible answers are defined, everything is fine, I just lack information. The second question is hypothetical. I now ask you another question: if I were to put in my hand and pull out a ball, what color would it be? That is a hypothetical question. It looks very similar to the first question, and most people would answer it in the same way. But it’s not exactly the same thing. Intellectually, I mean, not probabilistically. Intellectually it is not the same thing. In the first question, it is a well-defined question. I have a ball in my hand. There is either the answer white or black. Now you can answer me, either it is black or it is white, these odds, those odds—there is room to discuss that. When I ask a hypothetical question, what will happen if I put my hand into the container and pull out a ball, what will its color be? It is not certain that this question even has an answer at all. What does that mean? It depends which ball you pull out. What do you mean, if you pull out a ball what will its color be? There is no particular ball here about which you are asking the question. First let there be a ball, and then one can ask whether its color is this or that. You’re talking to me about—it depends how you pull it out, it depends what you pull out, it depends which ball. I don’t know. How can I answer the question whether the color of something whose identity I don’t even know is black or white? It’s not— In the first case I also have lack of information, so I use probability to compensate for that. So I have ninety percent, and I say fine, ninety percent that it is white, so I assume its color is white. And I may be wrong, maybe not, but that is how I answer. The question is well-defined, and based on the information in my hands I propose an answer. But in the second case the question itself is not well-defined. It is not just that information is missing. When there is a defined ball and I do not know its color, that is lack of information. If you ask me a question about a ball that you haven’t even defined for me, then that is not lack of information—the question is not defined.
[Speaker C] But the way of thinking toward the answer is the same way of thinking, so it’s the same thing.
[Rabbi Michael Abraham] That’s why I said: on the probabilistic level there is no difference. On the probabilistic level, in both cases in the end I’ll use the same tools to answer them. But one has to understand that the nature of the question is different. I said this is a non-probabilistic difference, not a probabilistic explanation, but the nature of the question is different. The first question is well-defined; the second question is basically not defined. Now if they forced me—if they forced me to answer it, I assume I would answer in the same way. Ninety percent white, so I would say white. But basically, that’s just because—in principle I could say the question is not defined.
[Speaker C] So now basically the different character between them is that in the case where I took the ball, I can prove my thesis, and in the second case I can’t. One more time? In the first case, where the ball is there—I chose the ball and it’s in my hand—I can simply prove whether my way of thinking was correct.
[Rabbi Michael Abraham] No, that’s obvious, that’s obvious.
[Speaker C] Fine, but I don’t see any other difference at all.
[Rabbi Michael Abraham] No, you can prove your way of thinking there too. Put your hand into the container, pull out a ball, and check its color.
[Speaker C] נכון. So I don’t really understand the difference between the…
[Rabbi Michael Abraham] I’m saying the difference is not probabilistic, but there is definitely a difference in the essence of the question. The second question really is a kind of hypothetical question. The second question really is a kind of hypothetical question. You’re not asking a question about a specific ball; you’re asking a question about the situation. You’re not asking a question about the ball; there is no ball here. It hasn’t even been born yet—it’s an egg that hasn’t been laid. The ball hasn’t even been born yet. Why are you asking me questions about the color of a ball that doesn’t exist? And in the first question, it is a perfectly well-defined question. There is a specific ball here, and you are asking what color it is. So there definitely is a difference in the character of the question, in the meaning—the meaning of the question.
[Speaker B] So now basically in the second question, is it not a lack of information? I can’t hear. In the second question, the question doesn’t exist, but it’s not a matter of lack of information, right?
[Rabbi Michael Abraham] As I’m saying: in the first question there is a defined ball. The question is well-defined: what is the color of this ball? The only thing is that I don’t know how to answer because I don’t have all the information. I don’t know the color, I haven’t seen it. I don’t have full information; I have information about the circumstances—how many such balls there are, how many such balls there are—so I have indications, I can do statistical calculations, but I lack information regarding this ball. In the second question there is no ball. The question is not defined. It’s not that I lack information about the ball. In the first question the problem is in the answer—the answer I don’t know how to give because I lack information. In the second question the problem is already in the question, before the answer. Which ball are you talking about? About the ball that you’ll pull out? Pull it out and we’ll see. I don’t know. It depends which ball you pull out. If he were asking me what the color of the ball I will pull out will be? It depends which ball you pull out. If you pull out a white one, its color will be white; if you pull out a black one, its color will be black. The question is not defined.
[Speaker D] What does it mean, an undefined question—what does that mean?
[Rabbi Michael Abraham] I didn’t understand—is it not syntactically correct?
[Speaker D] What does it mean—what is the meaning of an undefined question?
[Rabbi Michael Abraham] Not syntactically—what do you mean not syntactically correct? I’m saying it has no defined object for the question. It doesn’t ask a question about a particular ball. You are asking a question about a hypothetical ball. If I were to ask you a question—say, tell me, if I have a child, what will his height be? I don’t know, there is no child here, I don’t know what you want from me. It depends how he is born, it depends what he is—that’s the question. Now if I have a child and I ask you what his height is and you don’t know, then the question is defined, you just don’t know how to answer it. Maybe I can formulate it differently. If, say, you asked me in the second question, what is the color of this ball? Then I would say: that depends very much on which ball you pull out or how you pull out this ball, right? It depends how you choose to pull out the ball. Meaning, I don’t know. By contrast, once you have already pulled out the ball, then you’ve already pulled it out, I have seen everything, everything is known. Now I just don’t know what the color of the ball that came out is. So the answer to the second question can depend not only on the distribution of the balls in the jar or the container, but also on how you conduct the process of taking it out. Will you simply stick your hand in? Will you feel around? Will you choose? Maybe the balls are arranged there somehow, I don’t know. In other words, it depends on what method of extraction you choose. There are various ways one can remove a ball, so the answer can depend on that too. So it does not depend—let’s put it this way—it does not depend only on the question of the distribution of the balls in the container, but also on how you conduct the process of extraction. Okay? Therefore, unlike the first question, where the point is simply that I have already taken out the ball, there is a ball in my hand, and now I ask what its color is—that depends on nothing except how many balls there are, and one has to do the calculation.
[Speaker F] According to what you said, that in the second question it also depends on how I conduct myself in taking out the ball, then one could say the same thing about the first case, where I already chose the ball.
[Rabbi Michael Abraham] The question of how I took it out?
[Speaker F] Yes, how I took it out. And besides that, will we say the same thing about every hypothetical question? That there is no answer that can be given. Right. But to go back to the example you gave: what will the child’s height be—fine, then let’s look at the parents’ height; according to genetics there is a high probability—you’re talking about genetics, fine, I want to compare it to the number of white balls relative to black ones.
[Rabbi Michael Abraham] Even on the second question here, if you forced me, I’d answer that the color is white. That’s clear. But I’m just saying, if you pay attention, the question isn’t well-defined. What does that mean, “not well-defined”? I understand the question, and I also have the answer. Maybe saying the question is not well-defined is an unfortunate expression, or not the best description. I understand what the question is, and I also know how to answer it.
[Speaker F] Would that actually change the answer?
[Rabbi Michael Abraham] No, it wouldn’t change the answer. It changes the character of the question. I said: the answer would be the same for both questions.
[Speaker C] But why is it important, this desire to distinguish between the two kinds of questions?
[Rabbi Michael Abraham] Wait, I’ll explain. Okay. So the claim, basically, in the end, is that when you ask the hypothetical question, there isn’t actually a specific ball that you’re asking about. In that situation, Jewish law tells you: you can’t give an answer. The answer is either black or white. In other words, fifty-fifty. This isn’t a probabilistic fifty-fifty, of course, but a legal fifty-fifty. Meaning: since you can’t answer this question, and you can’t use the rules of probability to determine the answer, then I say fine, if so there are two possibilities: either the ball will be black or the ball will be white. From my perspective that’s fifty-fifty, because majority rules are meant to answer defined questions. When questions aren’t defined, then halakhically you’re really supposed not to answer them. Jewish law is not willing for you to answer hypothetical questions by means of statistics. If the question is hypothetical, then relate to the various possibilities: you have black or white, fifty-fifty. “Anything fixed is regarded as half and half.” Or before we even get to the fixed case—we haven’t yet arrived at fixed—still, it is regarded as half and half.
Now he says, for example: what happens in the case of someone throwing a stone into a group? Right, that’s the case of fixed that appears in the Talmud in Ketubot. Yes? A person threw a stone into a certain room, and inside the room there are nine Jews and one gentile. Now in the end, a Jew was killed. Okay? In the end, a Jew was killed. So the question is not who—it’s already after the Jew was killed, and now I ask whether the murderer is liable to the death penalty. Right? That is basically the question there. So the Talmud makes it depend on the law of majority. What does that mean? Since there were nine Jews and one gentile there, when he threw the stone he was effectively intending to kill a Jew, because we follow the majority. If he intended to kill a Jew and also killed a Jew, then he is liable to the death penalty.
The Talmud says no—there is a law of fixed. What does that mean? When there are nine Jews and one gentile inside the room, and they are all inside the room—it’s not that one went out and I ask whether he is Jewish or gentile—but rather they are all inside the room, and now I throw a stone into the room, what is the question I’m asking? The question I’m asking is: if I throw a stone into such a room, who will be the person who dies? The answer is exactly like with the hypothetical question about the balls. I don’t know. No person has died yet. I can’t ask about him whether he is Jewish or gentile. It depends how you throw, depends what you throw, depends what happens. I have no idea. Either gentile or Jew, half and half. Therefore you basically—now notice this—at the end a Jew died. We know who died in the end. This is not a probabilistic question about whether the person who died in the end was Jewish or gentile. I know: it was a Jew. The question is only the hypothetical question. Meaning: when you were before the throw, and you threw the stone, we ask: if someone throws a stone into such a room, is he intending to kill a Jew or intending to kill a gentile? I don’t know. That’s a hypothetical question, because nobody has yet been killed; there isn’t a person here about whom I’m asking that question. In such a situation I’m basically supposed to treat the two possibilities as equal: either he is Jewish or he is gentile, regarded as half and half.
If there were a defined person here and you asked, say, if I killed someone and I don’t know whether he is Jewish or gentile—now I ask whether the one who was killed is Jewish or gentile—here I would follow the majority, because now there is already a ball in my hand and I’m asking whether it is Jewish or gentile. Here, according to Kopel’s explanation, we do follow the majority. Right? In such a case I would follow the majority. But since the person who was killed is a Jew—that I know. All I’m asking is the hypothetical question before the throw. About that hypothetical question there is no answer; it does not deal with a defined person. The person who was killed in the end is very well-defined, but regarding him I also know that he is Jewish, so there is no question about him. This is a question about some hypothetical person who would die if I throw a stone into this room. A person who is not the person who in fact died, but some abstract person, I don’t know what. Here it’s even much easier to understand the reasoning, much easier than with the balls, because here in fact I know what happened in the end. A Jew died. A Jew. The whole question is only the hypothetical question: what did you intend when you threw the stone? Or what did you know? Or what counts as your intention when you threw the stone? And regarding this hypothetical question, Kopel says, you can’t use probabilistic tools or following the majority. It’s not a defined question; it has two possible answers, either Jew or gentile, they carry equal weight, fifty-fifty. Here you don’t follow the majority.
That is basically his claim regarding the law of fixed. And in the law of fixed, the question is always a hypothetical question. And since it is a hypothetical question, in his formulation, since it is hypothetical, it doesn’t really deal with an object that I’m speaking about at all. It deals with the whole set. In that sense, this is similar to what Rabbi Gordin said earlier. Basically he says: when I have a ball in my hand, the question concerns this specific ball that is in my hand. But if the question is hypothetical, then it isn’t dealing with a specific ball at all; it is dealing with the group of balls. Right? Because that’s just a way of phrasing it—what will happen if I take a ball out of there. But really I’m asking a question about the group of balls, not about a specific ball. It is not relevant to any specific ball.
Yes, it reminds me of Rashi on the portion of Shemot. He brings there the midrash of the Sages: “He turned this way and that way and saw that there was no man, so he struck the Egyptian and hid him in the sand.” Rashi brings the midrash of the Sages: what does “he turned this way and that way and saw that there was no man” mean? He says: he looked to see whether any person would come from this Egyptian who would convert, and he saw that not, and therefore he killed him. So the question is of course—obviously no person who would convert was going to come from him, because in another moment you’re killing him. How could someone come from him who would convert? You created that future; you didn’t foresee that future. With your own hands you created, brought about, that future. After all, by killing him, automatically he can produce nothing at all—not someone who would convert and not someone who wouldn’t convert. You created the very future that you were supposedly observing. That’s no great feat. I know that too; you don’t need to be a prophet for that. I can say that too. Clearly Moses was not asking a question about what would come from him in the future. Moses was asking a question about the nature of this Egyptian in the present. If I leave him alive, what will come from him? That is really the question he asked. That is exactly a hypothetical question. That question does not deal with the son of this Egyptian and what will be with him. That question deals with the Egyptian, not with his son. His son is only the indication that tells me what the father was. If something useful would come from the son, apparently there was also a good side in the father. If nothing at all would come from him, then not. But the discussion is about the father, not the child.
Now exactly the same thing with the balls. I ask the question: what will happen if you put your hand into the container and take out a ball—what will its color be? You understand that this is not a question about any ball. It’s a question about the group of balls in the container. It is not a question about a specific ball. If I took out a ball and I’m now holding it in my hand, then the question is about the ball. I use the properties of the group of balls in the container to answer it. But basically there is a question here about a ball. The hypothetical question is not a question about a ball at all; it is a question about the entirety of the balls in the container. And regarding that, he says: fifty-fifty. If it’s about the entirety, there is a black ball and there is a white ball, fifty-fifty.
Now at first glance, this resembles Gordin’s distinction, but it is completely reversed. Because what Kopel claims is that in such a situation you do not follow the majority. Gordin says that if the question is about the entirety, then you do follow the majority. If the question is about the individual case, then you do not follow the majority. Because majority means “the majority is as the whole,” right? What is the character of the entirety. He says the opposite. If the question is about the entirety, then there are two possible answers, regarded as half and half; I do not use statistics. If the question is about a particular object, then I use statistics to determine the nature of that object. So on the face of it that seems really, really the opposite of Gordin’s answer. But it does not necessarily contradict it. Why? Because the claim is that if the ball separated, if the ball separated from the pile, then it has an independent status, and according to Kopel you are asking a question about the thing that separated. There is a clearly defined object here, and you ask what the nature of this object is. Gordin also agrees that that is the question I want to resolve. He just says I resolve it by looking at the entirety from which the object came. The difference between them is the question of what you look at, but there is no real contradiction between the conceptions, whether this is a question about an individual or a question about an entirety. The whole question is what you look at, and therefore there is not necessarily a contradiction here between the two things, but still these are two different explanations.
I just want to make a few comments. First comment: according to Kopel too, it isn’t clear to me why we should divide between a majority present before us and a majority not present before us. Say when I have women who give birth—a woman giving birth—and I ask whether she gave birth at nine months or at seven months. I can always say that I’m asking the question about all the women in the world, after all I have no information about this particular woman. If I ask a question about all the women in the world, then why in that situation doesn’t he say that it is either nine months or seven months, regarded as half and half? These definitions or this logic exist also in a majority not present before us; it’s not clear why there should be a difference between a majority present before us and a majority not present before us.
More than that: suppose we take a piece of meat from a shop. Right? That is the case the Talmud brings as a case of fixed. I go to a shop, take a piece of meat, don’t remember whether the shop was kosher or non-kosher, and now I ask the question. That is fixed. Here we do not follow the majority. Now here this is not a hypothetical question—I took the piece of meat, after all, I have a piece of meat in my hand, and I ask whether this piece is kosher or not kosher. So how would Kopel explain that this has the law of fixed? It is absolutely not a hypothetical question.
Possibly—he doesn’t address this, I think—but possibly he could explain that really, when does the doubt arise? The doubt arises at the moment I touch this piece while it is still in the shop. A piece that separated—the doubt arises when I encounter it in the street, I find it. The piece that I took from the shop, really the doubt arises at the moment of taking it from the shop. Now at that moment I’m actually asking a hypothetical question. I’m asking: if I were to take a piece from a shop, would this piece be kosher or not kosher? I haven’t yet taken the piece. It’s not like a piece that separated, where there is already a defined piece here and I ask what its status is, whether it is kosher or not kosher. With a piece that did not separate, where I take it from the shop, this somewhat resembles—although not exactly—the hypothetical nature of the second question. I’m asking what will happen if I go to some shop and take a piece: will that piece be kosher or not kosher? And then perhaps one really can say that the question is an undefined question, a hypothetical question. But that seems a bit like evasion, sophistry, dodging, yes, because all in all you go to the shop, take a piece, and now you ask what it is, what the law is: is the piece kosher or not kosher? There is a very well-defined piece here. Why say that this piece is a piece—why say that this question is a hypothetical question?
Now I have to say: the law of fixed is so strange, and is applied in such odd ways by the commentators, that it is hard for me to believe there will be some explanation that covers all the cases to which the law of fixed is applied. It seems quite clear—and here this really is an academic research statement, the kind of thinking I don’t so much like or tend toward, but it seems to me that here it’s hard to avoid—that the law of fixed started from some case, or a few cases, in which the Sages had some logic according to which they distinguished between the law of fixed and the law of separated. After they established the principle that something found in its place is not judged according to the majority, but rather is treated as an even doubt, half and half—after they established that, it is then applied irrespective of the original logic. Now they discuss anything fixed in its place: the rule is that we do not follow the majority, but rather it is regarded as half and half. I think it is very hard to escape that conclusion here.
You can see this in many other places too—for example in a verbal analogy. There’s such a thing there. Verbal analogies have logic in certain cases, but in the end they make of them something so broad that it no longer seems that there is any logic in the application of the verbal analogy. There is indeed such a claim, also by a scholar—his name is Michael Chernick, yes, Chernick exactly—who argues that the early verbal analogies really were logical verbal analogies. After they established that one makes a verbal analogy between two places where there is a similar word, now in every place where there is a similar word they make a verbal analogy, even though the basic logic that existed in the original cases is no longer present in these cases. It’s a process, let’s call it, of formalization of Jewish law. Once you establish a formal principle, you forget the logical infrastructure that stood at its base, and now you apply it literally. I think that in the law of fixed too it is really very hard to assume that we will find some explanation that truly answers all the cases.
Now you need to understand that what matters is really to answer the cases in the Talmud. Because the cases in the Talmud—if it says there that this is fixed, then it is fixed as a matter of law. When medieval authorities and later authorities ask whether some specific thing is fixed or not fixed, I can say: they probably didn’t understand the law of fixed, and I don’t agree with them. This case is not fixed; it is separated. There is no—it’s a bit a question of authority, but it generates substantive distinctions. Meaning, if I am not committed to the determination that a certain case is a case of fixed, then I’m not obligated. The fact that certain medieval authorities said it is fixed does not obligate me to explain it. So if with my explanation of fixed it doesn’t work out, I won’t accept their claim; this is not a law of fixed. But in the Talmud I say: the Talmud’s classification is the basic assumption on which I build my definitions of fixed. If I don’t accept the Talmud itself, then that is more problematic. And even in the Talmud itself, apparently, as scholars always say—and it is probably true—there are different layers. There are early cases in which the law was born, and there it still had some logic. In the Talmud itself it had already undergone some expansion and somewhat lost contact with its logical infrastructure. But I can say that about some incidental cases that come up along the way. But the case of taking a piece of meat from a shop is the case the Talmud brings as the source for the law of fixed. You can’t say, well, that is some later expansion that already detached from the substantive explanation of the law of fixed, and here they apply it because it’s fixed. That is the basic case. Throwing a stone into a group above, and taking a piece of meat from a shop—those are the two basic cases of fixed. Everything else is incidental: whether it is fixed, why it isn’t fixed, why it is fixed. But those are the cases brought as the canonical cases of the law of fixed. So to say that taking a piece of meat from a shop is one of those cases where the logic is no longer present and they are merely applying the rule—that is hard. And to say that it is a hypothetical question is also hard. Therefore this explanation too is a somewhat problematic explanation.
[Speaker C] Regarding a person who throws a stone into the room where there are nine Jews and one gentile—you can explain just once more what the fixed element is here and exactly what determines it, because you keep saying that the question is what the man who threw intended. Did he know how many people were in the room? Yes? Did he know?
[Rabbi Michael Abraham] Yes, yes.
[Speaker C] So you think that in order to know whether his intention was to kill a Jew or kill a gentile, that can derive from the number of people who were in the room? Intention is something personal to him; it has nothing at all to do with what is in the room.
[Rabbi Michael Abraham] This is not a factual claim about what passed through his mind. It is a halakhic question. He knew there were nine Jews and one gentile there. From our point of view, is throwing a stone into such a place considered throwing a stone with intent to kill a Jew? Because after all, he understood that 90% there were Jews. I don’t care right now what in fact passed through his mind; the question is how I halakhically relate to such a situation. Can I say that this is a case of intentional murder, of a person who knows he is killing a Jew and in fact killed him? Regardless, for the moment, of what was really in his mind. That, at least, is how I understand it. It is a legal-halakhic question.
[Speaker C] But still, to go and convict him of murder without really clarifying his intention, but only on the basis of the targets in the room—that’s far-reaching.
[Rabbi Michael Abraham] He had intent to murder. The only question is whether it was the murder of a Jew or the murder of a gentile. And he knew there were ten people there, and he knew that most of them were Jews.
[Speaker C] But the difference is between death and no death. So in any case you need—we are so careful about the matter of intent in criminal law that it seems to me far-reaching.
[Rabbi Michael Abraham] He who lives in a glass house shouldn’t throw stones. Meaning, you can’t say that you’re being unfairly blamed—really, you intended to kill the gentile. You threw a stone into a room with nine Jews and one gentile—no, you intended only to kill the gentile. Even if that’s true, we’ll execute you. Because such an act is an act of intentional murder of a Jew. Don’t tell me stories: I meant the gentile. It may be that in terms of desire you really wanted to kill the gentile, but that doesn’t interest me. The irresponsibility is so glaring that halakhically it is considered intentional murder of a Jew. Again, that is at least how I understand it. I don’t think they are trying to trace the thoughts that were actually in his mind; rather we look at the situation and ask ourselves whether such a situation is called intentional murder of a Jew. Is such a situation considered intentional murder? The intentional murder of a Jew—yes, we discussed the moral question here about the Jew and the gentile.
[Speaker C] And if he comes and brings witnesses who say that he intended to murder that gentile because he has a conflict with him, and that’s why he threw it—then too, are we going to follow the numbers?
[Rabbi Michael Abraham] Here, here there would be a practical difference. According to my explanation, still yes. The fact that you wanted to kill the gentile is very nice. I want to kill a certain person, so I shoot in the street and I know there are lots of people there, but I only want to kill him, I don’t want to kill them, but I kill a hundred people because I’m spraying bullets in the street and I know he is there too. So is your defense claim that I only wanted to kill that one person?
[Speaker C] No, no, it’s not a defense claim. It’s a distinction between death and imprisonment, because the moment—
[Rabbi Michael Abraham] —that you have—
[Speaker C] —a particular target, the punishment is different.
[Rabbi Michael Abraham] But I’m asking you: wouldn’t this still be death, assuming there is a death penalty for murder? Wouldn’t it be death?
[Speaker C] What if I killed—I—
[Rabbi Michael Abraham] I intended to kill only Reuven, but I killed all twelve sons of Jacob because they were there in the same place, and I sprayed bullets into the room.
[Speaker C] No, he would be liable for killing the Jew, but he would not be liable for intentional murder.
[Rabbi Michael Abraham] Yes, yes he would be liable. He would be liable for intentional murder, since he knew the situation. Maybe he didn’t want it, but he knew. This is actually very connected to unintentional action on the Sabbath, where there is a major question of what “unintentional” means: not wanting or not knowing. Those are interesting questions in the context of unintentional action. But here it seems to me that any person—take him to court. Suppose there was someone there, I don’t know, who had threatened his life, okay? Inside the room. Things that sometimes happen, you know: some terrorist is threatening me inside the room, and with that terrorist there are also people who are not guilty of anything, they are in the same room with him. Now I fire a missile into that room, okay? And I intended to kill the terrorist. I could also have killed him with a handgun, doesn’t matter, but I fired a missile—it was more convenient for me, okay? But I really did not want to kill the others, I only wanted to kill him; it was just easier for me with a missile. So they wouldn’t convict me for killing innocents?
[Speaker C] There is—I didn’t want to, what do you mean I didn’t want to? But I knew. For killing, yes; not for intentional murder. I think not. I think not.
[Rabbi Michael Abraham] This wouldn’t be murder?
[Speaker C] Not premeditated murder. It could be homicide at a high level of negligence, but murder—
[Rabbi Michael Abraham] In premeditated murder this is not negligence; he knew they would die.
[Speaker C] No, but he didn’t intend—
[Rabbi Michael Abraham] He knew they would die, but that’s not what he wanted. He knew they would die; he’s not an idiot. You fire a missile into a room.
[Speaker C] I’m not saying he won’t be punished. I just think he wouldn’t reach the level of premeditated murder.
[Rabbi Michael Abraham] As far as I’m concerned, that is full premeditated murder. But again, I’m not a jurist. I would guess—it’s hard for me to believe that that wouldn’t be full premeditated murder. Fine, but I don’t know. Okay, so that is regarding Kopel’s story.
Now I want to propose another resolution. We saw the distinction between a majority present before us and a majority not present before us. A majority present before us is a majority of shops, and a majority not present before us is like most women giving birth at nine months. I went on about this in previous classes. I talked about the fact that a majority present before us is not the result of generalizing from a sample. I have no way to make a sample of pieces that are lost from different shops and do statistics to see how many were lost from each shop. So what is the majority based on? On a priori reasoning. Since there are ten shops here, I have no reason to distinguish among them, so the chance that it was lost from each shop is one tenth. But that’s not really because I have some information, or because I took a sample and generalized from the sample, unlike women who give birth at nine months, where I can look at a hundred women who gave birth and see how many of them gave birth at nine months and how many at seven. After the sample I say, fine, if this is a representative sample, then in the whole world seventy percent of women give birth at nine months and thirty percent at seven. That is generalization from a sample.
With a majority present before us, it is not generalization from a sample; it is basically a priori reasoning. That is also how I explained—if you remember—why the majority in a court is a majority present before us and not a majority not present before us. Because even in court, although the majority is based on the logic of a majority not present before us—that in most judicial panels, the majority is right—I have no way of checking that in most panels the majority is right, because I have no way to check in any given panel whether the majority was right or not. How do I know if it was right? After all, I have no independent way to know whether so-and-so murdered or didn’t murder. How am I going to check whether the majority was right or not right? I have no way to do that check on the sample, and therefore I also can’t make generalizations from that sample to a majority. I can’t check the sample itself. Therefore, I said, the majority in a court is a majority present before us and not a majority not present before us, because it is not a majority built on generalization from a sample.
So what is it built on? Basically there is here—I’m bringing a passage from Rabbi Shimon Shkop at the beginning of Gate 3 in Shaarei Yosher, where he talks about a majority present before us. He says something that always bothered me terribly. And really, when we come to judge in the case of the nine shops, to decide that the meat that separated is from the nine shops that sell slaughtered meat, because it is more common for this case to happen in them—this clarification is not true. And what, then, is statistics? For regarding every one of these ten shops, we can determine that it did not separate from it, since there are nine others against it, and in any event it separated only from one of them. What is he really saying? He says the chance that the piece separated from each shop is one tenth. For any shop that you decide the piece separated from, there are nine other shops from which it is more likely to have separated. So in fact you cannot decide about any shop that the piece separated from it. And in the reality of the separation there is no distinction between slaughtered meat and carrion, and consequently the whole matter of clarification and determination is nullified. And since there is no clarification of reality regarding the very separation of the meat, therefore there is no clarification at all regarding the kashrut of the meat.
And from this he concludes: similarly, the law that emerges from the majority of shops against the minority is a law that we are to conduct ourselves by in that way. It is only a practical directive, even though in reality there is no clarification here at all. And according to this principle, the Talmud says that a majority present before us is learned from the verse “to incline after the many.” Therefore they learn it from a verse, because a verse is needed. It isn’t statistical. There is no statistical clarification here; it is a verse.
Now the reasoning he gives is problematic. It’s the reasoning of people who don’t understand statistics. He says that for every shop you say the piece separated from, I can prove to you that it’s not true, because there are nine others from which it is more likely to have separated. Obviously, I’m not claiming that the piece separated from one particular shop. I’m claiming that it separated from one of the nine kosher shops. After all, that’s what matters to me. I don’t care from which one of them it separated. And when I say that it separated from one of the nine kosher shops, against that there is only one non-kosher shop. You have no proof that that is not true. It is simply a mistake.
But notice: he is basically making the claim—and I want to argue like him—that this really does not describe probability but rather behavior that is the result of, as I said, lack of information. Meaning, we talked for example about a fair coin. I know it is fair. I toss it and ask what the probability is that it will land heads. The answer is one half. Because with a fair coin I have information about the distribution; the answer is half. They bring me a coin, I have no idea whether it is fair or not. Now they toss it and ask me what the probability is that it will land tails, or heads, doesn’t matter. I will also say half. But I will say half not on the basis of information; I will say half on the basis of ignorance. I have no information at all about the coin, so I have no way to prefer heads over tails or vice versa, and I will still say half. But that half is a half that stems from ignorance, not from information. When I know the coin is fair, then when I say half, that is the result of information. When I say I know nothing about the coin, I’ll again say half, but only because I don’t know. It depends what the coin is, depends how I toss it, but I have no way to prefer one side over the other, and therefore this is really a result of ignorance.
Now my claim is that a majority present before us is really also the result of—or an answer that is the result of—ignorance and not of information, unlike a majority not present before us. With a majority not present before us, I have information. I checked a sample, generalized, and reached the conclusion that most women give birth at nine months. So now I have scientific information about the world. Now a woman comes before me and I ask whether she will give birth at nine months or seven, or she gave birth—at nine months or seven? The answer is: she gave birth at nine months, because the nature of the world is that women generally give birth at nine months. So I have information, and on the basis of that information I draw a statistical conclusion. That’s statistics. Statistics gives me a certain distribution, and for every case that comes before me I judge according to the information I have, the distribution I have accumulated. The distribution represents the information in my possession.
The answer regarding a coin about which nothing is known to me is not the result of a distribution; there is no distribution there. I do not know what the distribution is. I simply have total lack of information, and so the symmetry between the two sides tells me to say half. The same is true in every majority present before us. Every majority present before us is really the result of ignorance. Because after all, I have no information at all how this piece separates from each shop. I do not know what the probability is that it separates from this shop, what the probability is that it separates from another shop. I assume the probabilities are equal. How do I assume that? Did I check? No, my reasoning tells me. So that is a priori reasoning. It is not the result of information; it is the result of absence of information. I have no special information regarding any one of the shops, and in the absence of information I assume they are all equivalent. You see the similarity to the question of a coin about which I have no information.
Therefore here, in truth, this really is not statistics. This is no longer a legal explanation; it is a statistical explanation. And that is the interesting point. It is a statistical explanation because the claim here is that one cannot make a probabilistic calculation, because there is no distribution. True, reason says that for symmetry reasons, if I have to bet, I’ll bet that each shop has a one-tenth chance. But that is just a guess, not from knowledge, but simply because I have no other information. If I had some information, I would do it differently.
So the claim is that every majority present before us is not probability at all; it is a novelty of the Torah that one can follow it at all. Because you have no probability; it is merely a priori reasoning. It is like judging a person—I have an a priori notion that all Ashkenazim are criminals, or most Ashkenazim are criminals, or most criminals are Ashkenazim, okay? Now an Ashkenazi defendant comes before me. Am I allowed to judge him on the basis of my assumption that most Ashkenazim are criminals? I have no information, but that’s what my reasoning tells me. So regardless of whether I’m right or not, even if I’m right, I can’t judge him on the basis of my a priori assumption. In contrast, on the basis of presented information that I can defend, can substantiate—yes, that I can. Not because it is truer, but because that is judgment on the basis of information, whereas this is judgment on the basis of ignorance, just my assumptions. My assumptions are not an objective basis on which legal or halakhic decisions can be made, and so on. Decisions can be made on the basis of information. Therefore you need the novelty of the Torah, “to incline after the many,” learned from the verse, that even in a majority present before us, where this is not information and not based on probability, one may still follow the majority. Therefore a verse is needed, because it is a novelty. A majority not present before us perhaps follows from reason. That is how Rabbi Shimon Shkop explains it—not for his reason; the reason he gave above is not correct, but what he said I think is correct: that a majority present before us is not a clarifying majority; it is a rule of conduct. And that is true—I’m claiming it probabilistically.
Now look at what he writes later in the gate. He basically formalizes a bit the principle that we learn from “to incline after the many.” He says this: rather, it appears that the matter of the nine shops is like the law of the majority that decides among judges. Again he returns to the question: what is the connection between the majority among judges and the majority among shops? Since the meat necessarily separated from one of the ten shops—it is clear that this meat came from one of the ten shops, that is clear—each and every shop generates a legal aspect regarding the meat, creates a legal possibility regarding the meat. Right? I now have possible grounds of doubt regarding the meat. What is the question? From which shop did it come? Now I have ten shops. Each shop imposes a legal aspect on the meat. From the perspective of this shop, it is kosher; from the perspective of that shop, it is kosher; from the perspective of that shop, it is kosher; from the perspective of the last shop, it is non-kosher. So I have ten aspects, nine of which say it is kosher and the tenth says it is non-kosher. I follow the majority of the aspects. Notice: this is not statistics. I am simply counting aspects. Right? And it turns out that regarding the meat there are nine aspects producing a basis for permission and one aspect producing a basis for prohibition. And the Torah said, “to incline after the many.” And so too with judges: the Torah said that the law emerging from the majority is what we are to do.
What is he saying? It is the same as with judges. I ask a question: what is the law, does Reuven have to pay Shimon or not? Judge A says yes, so I have one aspect saying yes. Judge B says yes, I have a second aspect saying yes. Judge C says no, I have one aspect saying no. I have two aspects against one, I count aspects. So the law is that Reuven is liable. You see? That is exactly like a majority present before us. This is not statistics. I am simply counting the aspects of doubt. Each such aspect creates doubt for me, and I examine how many aspects lead me in this direction and how many in the other direction, without assuming that all the aspects carry equal weight. Notice: this is not a probabilistic calculation. I am not assuming that all the aspects carry equal weight. I am simply counting aspects.
I’ll give you an indication. Later authorities discuss the question: what happens if there are ten shops in the city but not the same number of pieces in each shop? One shop is a supermarket with many pieces, many pieces of meat, and another shop is a small butcher shop with few pieces of meat. Do I take into account the quantity of pieces, or is ten shops just ten shops? Now many decisors say that you count shops; I don’t care how many pieces of meat there are. Now if the calculation were really probabilistic, that makes no sense whatsoever. Obviously I should count how many kosher pieces there are, not how many kosher shops there are. According to Rabbi Shimon Shkop, this is very understandable, because Rabbi Shimon Shkop claims that I count aspects; this is not statistics. So it could have separated from any one of the ten shops. Each shop contributes an aspect: if it separated from this shop, it is kosher; if it separated from that shop, it is kosher; I have nine aspects saying kosher and one aspect saying non-kosher. So the law is that it is kosher. I don’t care that one shop is a supermarket and the second is a small butcher shop, because I am counting aspects; this is not a probabilistic calculation. How many possibilities are there? I count possibilities. If I have nine possibilities against one, the law follows the nine possibilities, even though the disqualified non-kosher shop has more pieces of meat than all nine kosher ones.
[Speaker F] But that is already an assumption that changes everything. If you decide to relate to the number of shops without taking into account the amount of meat each one produces, that simply changes the whole situation, the whole picture.
[Rabbi Michael Abraham] And that, I’m saying, right.
[Speaker F] Yes, but that’s already an innocent assumption. He has to prove that.
[Rabbi Michael Abraham] Because I would have—
[Speaker F] —said it’s statistics, and he is mistaken to say that you count the shops.
[Rabbi Michael Abraham] The claim I made from the outset is that this is not correct, because there is no statistics here—that is exactly the point. There is no statistics here. This is a statistical determination that I’m making now; it has nothing to do with the reasoning of the later authorities. In such a situation there is no statistics, because you do not know the distribution. It is an a priori assumption. You have no information; it is ignorance. Now Rabbi Shimon says: so what did the Torah innovate when it said “to incline after the many”? Excuse me—it innovated that nevertheless I can follow the majority. But what majority? There is no statistical majority here. He says yes—a majority of aspects. And I bring an indication for this, not a proof but an indication, from those same later authorities who say that it does not depend on the number of pieces of meat in each shop. How can one say such a thing? I show that they too apparently learned like Rabbi Shimon Shkop, that you count aspects and not numbers of pieces; this is not statistics. I’m not bringing a proof. If I had no logic behind it, then I would remain with the same unresolved difficulty regarding them as regarding him. It doesn’t help me that they too think like him. But if I have a logical explanation for what he says, and I see that the later authorities said it too, then that supports it.
[Speaker C] Now come on, that’s true, that’s true, but excuse me—what he is basically saying, as far as I understand, is that factual truth does not interest me. I simply have to rule, so I take a rule of decision and go with it, that’s all. I’m not interested in the truth.
[Rabbi Michael Abraham] More than that. I am interested in the truth, but I have no way of clarifying it.
[Speaker C] Obviously. And therefore I do this.
[Rabbi Michael Abraham] Exactly. Because the claim is that clarification through statistics is not justified here, because this is statistics of ignorance and not statistics of information. Now still, if you asked me what I would bet on regarding such a piece of meat, I would bet that it is kosher. That’s true. Because, as with a coin about which I know nothing, I would still bet that it’s fifty-fifty for heads. But you understand that this is just a guess that results from ignorance. It is not really that the chance there is half. It depends very much on the question of—I don’t know—the nature of the coin, or the nature of the shops, or how I approach the shop, or how pieces of meat are processed from each shop. Maybe they are not processed with equal probability; maybe there are shops whose bags tear more easily. We talked about that when we discussed the distinction between a majority present before us and a majority not present before us. So that is basically Rabbi Shimon Shkop’s claim. Now if that is really so,
[Speaker F] But if one says no, it is not a guess of ignorance—if one says that really one must relate to it, I don’t say like Rabbi Shimon Shkop and the later authorities who say one relates to the number of shops—if one says that it is not necessarily a guess of ignorance, one says the opposite: that there really is a logical reason to relate to statistics. Therefore it is not a guess of ignorance, it is a statistical guess. And what the Talmud says—nine kosher shops and one non-kosher one—is because they are working under conditions of equal weight.
[Rabbi Michael Abraham] I didn’t understand. If you say that, then you don’t understand the passage.
[Speaker F] No, I’m saying that everything the Talmud said, “whatever separates, separates from the majority,” is because it is that kind of statistical guess, because—
[Rabbi Michael Abraham] I’m saying again: I brought proofs that this cannot be correct, both proofs and explanations. The first proof is: what connection does this have to the majority among judges? Is the majority among judges also statistics?
[Speaker F] No, that really is everyone’s difficulty—how one learns one from the other.
[Rabbi Michael Abraham] Exactly, but this is the difficulty that Rav Shimon is coming to answer here. That’s the difficulty he’s addressing. So he argues that with majority among judges, what you’re asking there is: what is the law? Now you have three judges. Each judge says something, and what he says creates a possibility that the law is this way, this way, or this way. You have three possibilities. Two possibilities say that the law is that Reuven is liable; one possibility says that the law is that Reuven is not liable. So we follow the majority of possibilities. If so, then it’s clear why the Talmud also derives from here the majority rule of an immediately present majority in stores, because it’s the same thing there too: there also it’s a majority of possibilities. Otherwise it’s impossible to understand the connection between them. That’s what Rabbi Shimon Shkop argues. Now I said more than that: not only do I have proof from the Talmud, but logic also says this. Because logic says that this kind of statistic is a statistic of ignorance. That really is true. These aren’t forced explanations of the Talmud; that’s genuinely the case. In a non-immediately-present majority, it’s a majority based on information. An immediately present majority is an a priori reasoning. You don’t have information. Right, and then the claim is basically that an immediately present majority is not a statistical rule at all, but rather a novelty of the Torah, that “one must incline after the majority.” And in this Torah novelty we were told to follow the majority of possibilities. Consequently, it also makes no difference how many pieces are in each store. There are all kinds of implications here, and the comparison to a religious court is now much clearer. The comparison between stores and a religious court, and so on.
Now I’ll just say one sentence, because we really have to stop and I need a bit of time, so we’ll continue next time. Just notice: if that really is the case, then already here I can say that the distinction between separated and fixed, which after all is said only regarding an immediately present majority—we saw that—so if that’s true, then there’s no longer any question, because this is the same statistic, so why do we make a distinction? Because an immediately present majority is not statistics at all. It’s a distinction in terms of the Torah’s novelty—what the Torah’s novelty was said about. There is no statistics here. By contrast, in a non-immediately-present majority, which is statistical, there really is no difference between fixed and separated. Because wherever there is statistics, there is statistics; we don’t make distinctions. Only where there is no statistics do we make distinctions between fixed and separated. Of course, we still need to understand—fine, it’s not statistics, but why make a distinction between fixed and separated? There has to be some internal logic that distinguishes between fixed and separated and tells me that the novelty of “one must incline after the majority” was stated only about the law of separated and not about the law of fixed. And in the case of fixed it was not stated. And the question is why.
I’ll already say in one sentence here, but I’ll explain it more next time. When you approach the store and choose a piece—not when the piece separated, but I approach the store and choose a piece—there are no possibilities here at all. What do you mean by possibilities? After all, this piece came from one specific, identifiable store. There’s no question here of ten stores, where each store creates a possibility regarding the piece of meat. That’s why it’s fifty-fifty. That’s why fixed is fifty-fifty. Again, not because of statistics, but because the number of possibilities is either that it is kosher or that it is non-kosher. There are no possibilities of stores here. It came from one particular store, where I was, and I know which one it is. I don’t know whether it is kosher or not, but it is one defined store. The question is not which store this came from, but what is the nature of the store it came from. What is the nature of the store? Either kosher or non-kosher. So therefore here there is no majority of possibilities. When the question is which store did it come from—there are nine kosher stores and one non-kosher one—then there is a majority of possibilities in favor of kashrut. But if the question is: what is the nature of the particular store in which I am standing—is it kosher or non-kosher—then there are no possibilities here; it is either kosher or non-kosher, so it is half and half. Again, this is not a statistical explanation, because the whole majority rule in stores, in the case of an immediately present majority, is not statistical. I’m only explaining why the law newly introduced by the Torah—that we follow the majority of possibilities—applies only in a case of separated and not in a case of fixed. Because in a case of fixed there simply are no possibilities. Or at least there is no majority of possibilities. Fine, we’ll stop here. I’ll continue next time; we’re already nearing the end of this issue of fixed. We’ll continue it next time.
[Speaker E] Thank you very much, Sabbath peace. Thank you very much, Sabbath peace. Goodbye.