Doubt and Probability—in Halakha, in Thought, and in General—Lesson 27 – Rabbi Michael Abraham

Table of Contents

• Reversing the question: why in a case of separation do we follow the majority
• A majority that is before us versus a majority that is not before us: sample-based reasoning versus a priori reasoning
• The difficulty of testing majority rule among judges and the meaning of “follow the majority”
• Rabbi Shimon Shkop: a majority that is before us as a “majority of sides,” not as probabilistic clarification
• Fixed status according to Rabbi Shimon Shkop: two sides, and therefore like fifty-fifty
• Uman/Oren: the difference between random separation and human choice
• Tension with judges, an administrative rule, and the majority of experts
• Conclusion and a historical note about Shimon HaTzaddik and Alexander the Great

Summary

General Overview

The lecture reopens the question of the laws of fixed and separated cases, and proposes reversing the perspective: instead of explaining why in a fixed case we do not follow the majority, we should ask why in a separated case we do follow the majority at all, especially when dealing with a majority that is before us. The speaker defines a fundamental distinction between a majority that is not before us as a scientific generalization based on a sample, and a majority that is before us as an a priori judgment that cannot really be experimentally verified, and from that comes its relative weakness. He then brings Rabbi Shimon Shkop’s view that in a majority that is before us there is no “clarification of reality,” but rather a halakhic rule of a “greater number of sides.” He then goes on to propose another explanation, from Uman/Oren, according to which a fixed case is different because it depends on human choice rather than on a random process.

Reversing the question: why in a case of separation do we follow the majority

The speaker says that until now the effort has gone into explaining why in a fixed case we do not follow the majority, but he suggests asking the reverse: why in a separated case do we follow the majority? He narrows the discussion to a majority that is before us, where the distinction between fixed and separated is relevant, and raises the possibility that logic should actually have led us not to follow such a majority. If so, then the real novelty in need of explanation is דווקא the case of separated. He suggests that maybe the Torah introduced the rule that “anything that separated is presumed to have separated from the majority” specifically in a separated case, and only afterward do we still need to understand why that novelty is limited and does not apply in a fixed case.

A majority that is not before us versus a majority that is before us: sample-based reasoning versus a priori reasoning

The speaker presents Sefer HaChinukh’s explanation that in a religious court we follow the majority because most likely the majority is correct, and he brings Rabbi Shimon Shkop’s question that this sounds like a majority that is not before us, not a majority that is before us. He defines a majority that is not before us as a generalization based on a representative sample, similar to scientific generalization, such as “most women are not incapable of bearing children,” where we infer from what we know to the world at large. He argues that a majority that is before us is not built that way, because you cannot really base it on meaningful experiment and observation. In the case of the stores, for example, there is no practical way to test systematically from which store lost pieces actually come. He concludes that a majority that is before us rests on a priori reasoning—“it seems logical to me”—rather than on empirical statistics, and is therefore weaker. He also notes that there may be distorting factors, such as differences in bags or in walking patterns, that tilt the actual probability.

The difficulty of testing majority rule among judges and the meaning of “follow the majority”

The speaker applies the same claim to judges in a religious court, explaining that there is no way to get independent feedback as to whether the majority was right or wrong, because any such check would again rely on the same evidence that was before the judges in the first place. He adds that even if, theoretically, one could imagine staged trials in order to test the judges’ accuracy, in practice the Jewish law of following the majority does not emerge from such testing but from reasoning. He emphasizes that since a majority that is before us is a priori reasoning, it may be that a verse is needed to authorize using it for halakhic decision-making, and he even raises the possibility that without a verse it would not have been appropriate to rely on such reasoning in serious legal matters.

Rabbi Shimon Shkop: a majority that is before us as a “majority of sides,” not as probabilistic clarification

The speaker quotes Rabbi Shimon Shkop (Gate 3), who argues that in the case of nine stores there is no real “clarification” of reality, because regarding each store one could say that it is more likely the meat did not separate from that store, since there are nine others against it. The speaker rejects that argument and explains that if you measure the correct events—separation from the kosher stores versus separation from the non-kosher one—then the ratio is nine to one. Still, he accepts Rabbi Shimon Shkop’s mechanistic proposal, according to which the verse “follow the majority” defines a rule of decision that is not about probability but about counting sides. He explains that each store “generates a legal status” and contributes one side to the doubt regarding the piece, so that there are nine sides permitting it and one side forbidding it, and the law is to incline after the majority of sides, just as among judges we count opinions as sides. He illustrates that when there is no information about the “distribution,” people can act similarly in everyday life through “counting sides,” using the example of a coin or die about which there is no information whether they are fair, where people still behave as though the division is equal because there is no basis for preferring one side over another.

Fixed status according to Rabbi Shimon Shkop: two sides, and therefore like fifty-fifty

The speaker applies this mechanism of “counting sides” to the law of a fixed case, and explains that when the piece is found inside the store there are not ten sides of “which store did it separate from,” but only two sides: either this store is kosher or it is non-kosher. He presents this as the explanation for why in a fixed case it is “like half and half,” and we do not follow the majority, because the counting is based on the number of relevant sides, not on the number of stores in the city. He addresses the claim that even in a fixed case one could also formulate it as “nine sides against one,” and leaves that as still needing completion, saying that another explanation can also help resolve that difficulty.

Uman/Oren: the difference between random separation and human choice

The speaker brings another explanation, one suggested by Oren and also appearing in an article by Uman, based on the distinction between a random process and intentional choice. He illustrates it with a container holding ninety-nine white balls and one red ball: when a hand is inserted with eyes closed, that is randomness, and the probability is 99% for white; but when someone looks and chooses a ball, statistics no longer have meaning, because the choice depends on preferences. He applies this to the stores and explains that separated is a case where the loss and separation are a random process, so majority considerations have a place, whereas fixed is a case where a person enters a store and chooses to buy there, and human choice is not a “lottery,” so probabilistic rules cannot be applied to it. He also uses the example of a mouse that entered piles of leavened food and matzah, and argues that the mouse chooses according to what it likes, so the doubt is not resolved by the numerical ratio of the piles but remains like 50/50 when its preference is unknown.

Tension with judges, an administrative rule, and the majority of experts

The speaker raises the point that if we explain a fixed case through “human choice,” then we need to ask what the status is of the law of following the majority among judges, since a judge’s ruling is an act of judgment, not a random process. He refers to Mordechai in tractate Hullin, who asks why judges are not considered a fixed case, and answers that the voice “separates,” and he describes the answer as strange, while noting that it is one way to explain why this is not analogous to a fixed case. He then discusses the claim that the verse “follow the majority” could be read as merely an administrative rule, and argues that the Talmud itself applied the verse to the case of stores, meaning that it understood it as a broader principle and not merely a rule for running courts. He agrees that there are cases where the majority is wrong, and cites Rabbi Shach’s letter about the Entebbe operation in order to distinguish between “the greater chance” and the actual outcome. He argues that as a decision rule under a “veil of ignorance,” a reasonable person would bet on the majority opinion, even though that gives no guarantee of truth in every individual case.

Conclusion and a historical note about Shimon HaTzaddik and Alexander the Great

At the end, a comment comes up that is not directly related to the topic, claiming that Alexander the Great did in fact pass through the Land of Israel twice, and that there may have been overlap with Shimon HaTzaddik, contrary to what the speaker said in another lecture. The speaker responds that he is not well versed in the details, that he may have been mistaken, and agrees that the claim is worth checking.

Okay, we’re in the topic of fixed presence. We spoke about two explanations for the idea of fixed presence; I’m not going to go back over them again. I want to get to two additional explanations. The first explanation I want to suggest is based on things we already saw a bit at the beginning of the series. The problem we’re dealing with, really, is the question: what is the logic of not following the majority in a case of fixed presence? That’s really the question. Because seemingly I would expect that we should. Ask any person on the street and he’ll tell you: what difference does it make whether it’s fixed or not fixed? Statistics say there’s a 90% chance the piece of meat is kosher, so what difference does it make whether it’s inside the store or whether it separated from the store? At the end of the day, 90% is 90%, statistics are statistics. And therefore all our effort until now has really been devoted to the question: so why, despite that, in fixed presence do we not follow the majority? But I want to raise the opposite angle and ask, in light of things we’ve already seen: why, in a case of separation, do we follow the majority at all? The question I tried to examine was why in fixed presence we don’t follow the majority, since in separation we do. As if separation is the obvious case, and fixed presence needs explanation. And now I want to reverse the question. And it may be that actually in—and we’re talking about a present majority, because the difference between fixed presence and separation exists only with a present majority, I mentioned that. Then I say: with a present majority, actually the logic says not to follow the majority, like in fixed presence. And what needs explanation is why in separation we do follow the majority.

Now for this we need to go back a bit to things we discussed quite a long time ago already at the start of the series, and go back and try for a moment to understand what a present majority is at all. Is a present majority a statistical consideration? If you remember, I said that Sefer HaChinukh explains that in a religious court we follow the majority because most likely the majority is right and not the minority. Then Rabbi Shimon Shkop asks on that: if so, then the majority in a religious court is an absent majority, not a present majority. Because we’re not talking about these three judges, where one of them is the minority and two are the majority. Rather, we’re talking about the majority of all panels that split two to one, and the claim is that in most cases the two were right and not the one. So that is actually an absent majority, like “most women are not barren,” or things like that, because there isn’t some defined group here; rather there is some natural-world phenomenon that we know, that in the way of the world, when there’s a dispute between two and one, in most cases the two are right and not the one. That’s how Sefer HaChinukh explained it. And if so, it’s an absent majority and not a present majority.

So I said that if you properly understand the difference between a present majority and an absent majority—or at least according to the explanation I suggested for that—then this isn’t correct. So Rabbi Shimon Shkop’s question doesn’t even arise. Why? Because an absent majority, I explained, is basically a generalization on the basis of a sample. We examine a certain number of cases, see in them some kind of representative sample, and then generalize that if the distribution in that sample was, say, 80:20, then apparently in all cases, throughout the whole world, the distribution is also 80:20. For example, barren women. So I say: I know, say, 100 women around me, and suppose among them there are 10 barren women and 90 who are not. So I say: since I have no reason to assume that the 100 women around me are special, apparently that’s what also happens among the rest of the women in the world. Meaning, I assume that the sample I know is a representative sample, and so my assumption is that this 90:10 distribution is not unique to this sample but is probably true of all women. Women with children and those without children—and from that I infer some conclusion about a much broader group regarding which I have no information, other than my assumption that what I know is a representative sample. Okay? That’s how an absent majority is structured. An absent majority is basically a kind of law of nature, like a scientific generalization; and a scientific generalization too is based on some number of observations, and then I say: I assume those observations reflect some general law, and then I generalize from those observations to the general law. Okay? That’s how an absent majority is built; it’s basically a scientific generalization.

Now, with a present majority you can’t really carry out that process. If I now wanted to examine some sample and do a test, experiment, or observation in order to see whether the piece lying in the street is kosher or non-kosher, and I want to measure whether it’s really 90%—how do you do such an experiment? There’s no way to do such an experiment. What am I supposed to do? I’m supposed to intentionally lose pieces and then ask myself which store they came from. If I’m losing them, that’s not intentional; there’s no such thing as losing something intentionally. So therefore I say: on the theoretical level maybe it would be possible to do such an experiment. How? I’d mark all the pieces of meat in all the stores with some hidden marking, invisible ink, indicating which store each one belonged to. Now people would buy that meat, and among them every so often there would be people who lose the piece they bought. Now someone finds it; the moment he finds it, he goes to the police or the religious court, and there they know how to check the hidden marking and can discover which store it belongs to. Then it would be possible to check whether really 90% of the lost pieces come from the kosher stores. So theoretically one could do an experiment and check whether it’s really 90%, but in practice our statement that it’s 90% is not built on an experiment, because we never performed such an experiment. It’s also very hard to carry one out—how do you know who loses things, when they lose them, who says you have a sample of people who lose things, a sufficient sample of people who lose things? If there are ten stores in town, you need who knows what, fifty, a hundred losses at least, for the results to have some significance. A hundred pieces of meat that people lost and that we find and check—you can wait two hundred years. And they’re not even the same pieces that we always marked; they’ve long since been replaced. There’s no real way to do such an experiment.

So really, what is the assumption built on—that if I found a piece of meat, there’s a 90% chance it came from a kosher store? It’s not statistics or a generalization from a sample, so what is it? My logic says this, right? My logic basically says that if there are nine kosher stores and one non-kosher store, then there’s a 90% chance it came from the kosher stores. I can’t check it; there’s no experiment that can make observations confirming that claim. But my reasoning tells me that’s how it is. Which means that a present majority is actually not based on scientific generalization or on a sample; it’s simply based on an a priori intuition, some kind of prior reasoning, before any check, without checking—just, that’s my reasoning. Okay? And therefore a present majority is a different kind of majority from an absent majority, and according to Maimonides it’s even weaker—we talked about that—because the first generalization is a scientific generalization, and the second generalization is just intuition. Usually science is regarded by us as a stronger, more reliable tool. Okay? And here we have some intuition; maybe it’s correct, maybe it’s not correct.

I spoke about the possibility that maybe the bags in one particular store tear more easily, and therefore the pieces of meat that get lost are mostly lost from that store, whereas in the other stores the bags are sturdier, so pieces of meat don’t get lost from people when they buy there. Never mind—it could be a thousand reasons. Or the route we take from that store is harder, and there’s a greater chance the piece of meat will fall when I return from that store, whereas from the other stores the route is easy and there’s no reason for the pieces to fall. There can be lots of differences between the stores. But in the end, the claim is that my reasoning says that if I don’t have some well-defined piece of data—if I know something clearly defined then I know it—but if I have no other concrete information, then I assume there’s a 90% chance it came from a kosher store, and that is an assumption, that is an a priori intuition.

Question: why can’t we say, sort of, expand the definition from meat lost from stores to something more general—like, whenever something separates, whatever separates is presumed to have come from the majority? And on that, it seems to me reality supplies endless proofs, for example: there are more dogs in the city than lions, and we see more dogs than lions, which means that whatever separates comes from the majority. We see more Israelis here than Americans, which means that whatever separates comes from the majority. There are lots of proofs for this in life itself.

First of all, the moment you present it that way—before I even think about the answer—you’ve turned it into an absent majority. You’re basically saying: I’m making a generalization on the basis of my experience. I see that the people I meet are usually Israelis and not Americans. So you understand that this actually turns it into an absent majority, not a present majority. That’s one thing. And second, on the substance of it, I really need to think. My feeling is that there’s some difference on the substance too. When I speak, say, about Americans and Israelis, I think the process is not a process of random separation out of a group. It’s not like pieces of meat coming out of stores. People move around in the city and each one chooses where to walk, so I’m not sure one can infer from here a conclusion about pieces of meat that somehow get lost and separate from a store. I believe one could find examples that really are a case of separation—like if I find in a pool, I don’t know, in some place that’s not part of the city, I find there more often someone who belongs to the majority group of the city, say.

Yes, but again, I’m saying there’s nothing random here. There’s no process of random separation. There’s no separation here. This isn’t separation. Separation means that something comes out of the group randomly, and let’s see which group it came from. I don’t see anything random here. People just move around, and of course there are more Israelis than Americans in the city. Okay, that I know. But when I talk about…

Brother, I didn’t really understand the difference. So what, for example, could count as separation?

That’s what I’m saying—you won’t manage to find a difference, you won’t manage to find an example of it, because every example you find will be an absent majority. The moment the majority is an absent majority, you have no way to test it. That’s the whole idea. In other words, anything you can test will actually be an absent majority. And an present majority is always an assumption; it’s not something you can test.

I illustrated this not only with pieces of meat; now I’ll illustrate it with judges. Okay? What happens with judges? Suppose I go with Sefer HaChinukh’s explanation, and I say that usually the majority of judges are right and not the minority. Now I want to test that, to make an observational sample. How do I do that? I have no way to do it. Suppose I take a hundred cases where there was a split among the judges, two against one, in various religious courts, doesn’t matter, or in this court, no matter. I make a distribution and try to check in what percentage of the cases the two were right and in what percentage the one was right. Right? That’s what I would need to test according to Sefer HaChinukh. There’s no way to test it. Maybe one could test it the way they did with that ox they put on a stage in a TED talk—I don’t remember who did it—where they basically take the opinion of the majority, and the more people there are, the more likely they are to hit the truth.

You’re talking about the wisdom of crowds. That’s something else.

Yes, the wisdom of crowds is something else; that’s because of the law of large numbers. That’s simple. Here it’s unrelated. And with judges it doesn’t work. You can’t test this for the simple reason that suppose I take the sample of those hundred cases. One second, let me remove this lady from here. Suppose I want to take…

Rabbi, I didn’t understand. I didn’t understand—when he talked about the Americans, there it’s definite, I know what the majority in the world is; it’s not like with barren women where I estimate…

Let’s take a person you meet. I assume that what I’ll find is that the majority of the people I’ve met, each one individually, are Israelis. So that’s basically a way to test an absent majority. So I say again: there the problem is that the separation is not random, but I still need to think about it. It’s a good question. I still need to think.

But regarding judges—I’m getting back to judges—with judges I have no way to test it because I have no… Let’s say I look at a particular case where two judges said Reuven is liable and one judge exempted Reuven. Now I want to check whether the two were right. How will I check that? How will I know whether Reuven is really liable or not? All I can do is go by the evidence. But the evidence was also before the judges. I have no independent feedback that tells me whether the judges here were right or wrong.

I think you can do experiments on that too. Meaning, if we broaden the definition to… if say there’s a majority of people making a certain argument and some people oppose it, who’s right? And I think you can check what’s correct, especially in the area of—I don’t know—flat earth, vaccines, corona, the… You can see the debate here.

The moment you test those things, the moment you test those things, first, they become an absent majority, and second, you’re testing laymen, and that’s not interesting. But the moment you test experts, you have no way… you have no way to test it. Because the moment there’s a dispute between experts, then apparently there’s no simple way to know who is right, because otherwise there wouldn’t have been a dispute. Laymen can be wrong. So when you test judges, you have no way to know who’s right. Unless you have some immediate information—you know that Reuven borrowed the money for some reason, you know personally. But… in general, you can’t test your sample and see who was right there, the majority or the minority.

I understand, but I think there is a way to test even professionals through objective tools. For example, physicists who think aliens really landed, I don’t know, or that the earth is flat, or maybe there was no moon landing; or doctors who think…

There are no physicists who think that.

There are. And there are also doctors who think the corona vaccine causes more people to die than… than people who didn’t get vaccinated. You can test that very simply.

No, you can’t… absolutely not, absolutely not, absolutely not test that simply. That is exactly the debate. You can’t test it. You can test a vaccinated population group versus an unvaccinated population group.

No, you can’t test it. I’m telling you, people worked on this—it’s very hard to test. It’s not… not simple at all. The question is: those who didn’t get vaccinated—why didn’t they? What were the background reasons? Are they more careful in other respects? Why did they die? There are a million things. If it were possible to check it so simply, then there wouldn’t be a dispute among doctors. Laymen, sure, there are always laymen. But among doctors there wouldn’t be a dispute—again, except for strange people. But… So I’m saying: I think in general, a dispute among experts you won’t be able to test, and among judges certainly, certainly you can’t test. Because with corona at least you have some measures—you check whether a person had corona and whether he died, and you also need to know whether he died from corona, which is also a question. But with judges you have no way to know if they were right or not, because you have no immediate way to reach the right answer, only through the evidence. And therefore the sample… the sample we have—one second—the sample we have, there’s no way to test it.

So what Sefer HaChinukh says—that usually the majority of judges is the one that is right and not the minority—that is really an a priori intuition and not the result of generalizing from a sample. I’ll say more than that: even if there were a way to test it, the fact is that we didn’t test it. We really didn’t. When Sefer HaChinukh wrote that, it wasn’t because he first did some kind of systematic examination of some representative sample and then reached that conclusion. He wrote it because that was his reasoning. So even if theoretically there were some way to test it—and by the way I can think of some way to test it, by staging mock trials, with cases where I know what the truth will be but the judges don’t, and now I present things before them and I could theoretically test it—even if theoretically I could find a way to test it, in practice, when we reach the conclusion that… that we follow the majority among judges, it isn’t done on the basis of the test, even if such a test exists. And therefore this really is a present majority and not an absent majority. And that’s what the Talmudic text in Chullin says: the majority of judges is really a present majority, not an absent majority. And that’s true even according to Sefer HaChinukh.

Now what this basically means is that a present majority, unlike an absent majority, is not really statistics, not really probability. So what is it? It’s an a priori intuition. What do I mean by intuition? It seems reasonable to me that if there are nine kosher stores and one non-kosher one, then this piece of meat probably came from a kosher store. Or, if the majority of the judges say one thing and the minority says another, then most likely the majority is right and not the minority. But all of these are a priori intuitions. And with a priori intuitions it’s always problematic, because we have all sorts of biases, and all sorts of ways of thinking one way or another, and we really have no way to test it. That’s also why a present majority is a weaker majority than an absent majority. Because an absent majority can be put to the test—yes, a scientific theory that results from a generalization can be subjected to a falsification test. But an a priori intuition is an a priori intuition. Meaning, even if hypothetically I can think of some falsification test I could put it through, I don’t actually do it. I’m not really testing these claims by putting them through falsification. And therefore a present majority is in fact not statistics at all; it’s an a priori intuition.

So once I say that, once I understand it this way, then maybe the whole situation flips. Instead of having to explain why in fixed presence we don’t follow the majority, I actually need to explain the opposite—why in separation we do follow the majority. After all, there are no statistics here, so why follow the majority? So there’s a Torah novelty, that if it’s separation, then whatever separates is presumed to come from the majority, and we follow the majority. It could be that this novelty was said about separation and not about fixed presence. Of course, even after this novelty is said about separation, we still need to ask ourselves why to qualify it, why to say that it’s only in separation and not in fixed presence. Fine, we’ll have to examine that. But I’m saying, notice that now I can suddenly reverse the picture. Instead of looking for explanations for why in fixed presence we don’t follow the majority, I really need to look for explanations for why in separation we do follow the majority.

Now here there is Rabbi Shimon Shkop’s argument—I want to show it to you.

Sorry, Rabbi—why are you backing away from what you said a minute ago, that a present majority is not statistics, right, because you can’t apply it, but rather an intuition?

It’s an intuition.

Right, so I didn’t understand. Then why are you now saying it suddenly becomes a novelty? A present majority is a novelty? It’s an intuition.

What do you mean, “it’s an intuition”? Is there really a greater likelihood that it’s kosher? Yes.

How do you know?

Because, as you said, there are nine kosher stores.

So there are intuitions, but intuitions are very nice; they’re not really something established. The question is whether to follow—say if there were no verse, okay, suppose there were no verse telling me “incline after the majority,” from which we derive this law of present majority—would I follow this majority? Not at all clear. Not at all clear. Because if I follow an absent majority, then an absent majority is like saying: do I trust science? Okay, so I trust science. But from that to infer the conclusion that I should follow the intuition of a present majority—that’s just an intuition. Meaning, who says that this intuition is one I allow myself to rely on in Jewish law, to decide a case on the basis of that intuition, even if it seems right to me? Even if it seems right to me, that doesn’t necessarily mean it’s enough to convict someone in court, for example, or to declare meat non-kosher, or various things of that sort. So even if the intuition is correct, I may still need a verse telling me to use it. But even on the more basic plane: an intuition is an intuition, but I don’t know to what extent I’m really allowed to rely on it, and I need to insert it into some pattern—which could be a legal pattern and not a statistical one. And that’s what I want to show you, and then it will open the door to showing why in fixed presence this explanation doesn’t exist.

According to what you said in previous classes, there’s some trigger like this: the intuition alone wouldn’t be enough, but because there’s an exposition, that’s the trigger and it strengthens the intuition. Once I have an exposition here and it strengthens the intuition, why not use that intuition also in fixed presence?

Because once your source deals with an absent majority—say your source dealt with a present majority, but in separation—then in separation and not in fixed presence. Fine. So in separation they tell me to use this thing. But I’m not sure it can be used in fixed presence, because the fact is that without the verse, the intuition by itself I wouldn’t have used. So now the question is whether the verse was also said about fixed presence and not only about separation.

But I don’t really understand what you said. This intuition isn’t disconnected from reality, from our experience with the probabilities of reality. In our lives, if this weren’t an orderly reality, if reality were miraculous all the time, then we really would feel very insecure in our conduct. But since we’re not in a miraculous reality, but in this kind of statistical random reality, then we know that if there were a million stores—say we know there are a million stores and except for one all of them are non-kosher and one is kosher—don’t we understand, don’t we feel directly from our probabilistic experience of reality that it’s non-kosher?

I don’t think you can call that experience. The connection between that conclusion and the observations on which you’re basing it is very, very remote. It’s a bit like those claims that intuition is actually some kind of accumulated experience. But it’s not accumulated experience in the form of direct scientific measurements. In direct scientific measurements, I do an experiment and on that I build the scientific theory. Intuition is built on lots of experiences that are actually very remote—like training a neural network, right? You train it on all kinds of examples until in the end you assume it gets organized correctly inside you, and now you think correctly, and so also in the new case what you think will probably be correct. But that’s very far from coming directly out of my accumulated experience. There’s an intermediate step of what experience does to the brain along the way. And therefore here there’s room to discuss whether this is true only in separation, because the verse speaks to me about separation and maybe not fixed presence.

Now again—I need to show it. At this point I’ve only made an introduction. In a moment I’ll try to show you some way of looking at what the law of present majority nevertheless rests on, and then explain why in fixed presence that isn’t true. For now I’ve just opened a possibility. I’m saying: since this isn’t probability, then if it isn’t probability and is only intuition, then now there is room for hesitation. Because if it isn’t probability, it could be that the intuition exists in separation and does not exist in fixed presence. So basically the problem is—yes, maybe I found justification for following the majority in separation, but who says you can do that in fixed presence too? And therefore I don’t need an explanation of why in fixed presence one does not follow the majority. I need an explanation of why the intuition that tells me in separation to follow the majority does not exist in fixed presence. Then it will automatically remain the case there that I do not have the novelty that we follow the majority. Okay? I’ve reversed the picture.

Now I’ll try to explain the mechanism. Meaning, what really stands behind this idea of a present majority. Just a second. And then to show the difference between fixed presence and separation. So I’m bringing you here a passage from Rabbi Shimon Shkop, in Sha’ar 3. He says as follows: “And in truth, when we come to judge in the case of nine stores, to determine that the meat that separated came from the nine stores that sell slaughtered meat, because the majority is more commonly found and therefore this event is more likely to have happened with them—this clarification is not true. For with respect to every store among these ten stores, we can conclude that it did not separate from it, since there are nine others against it. And in any case, it separated only from one of them, and in the reality of the separation there is no difference between slaughtered and carcass. And consequently, all this matter of clarification and determination is nullified. And since there is no clarification of reality concerning the act of separation of the meat itself, there is consequently no clarification whatsoever about the kosher status of the meat.”

What is he basically saying? I already said—I think we discussed this in one of the first classes—and I said I don’t agree with him. I agree with the conclusion but not with the reasoning. He basically wants to make the following claim: when we want to determine from which store the meat separated, every store of which I decide that the meat separated from it—I obviously have nine other stores from which it is more likely that it separated. The division is not specifically kosher versus non-kosher, but generally. Any store among the ten from which I want to say the piece separated—it’s not likely, because there are nine other stores from which it is more likely that the piece separated. Since that is so, says Rabbi Shimon Shkop, the claim of present majority—that the piece separated from a kosher store—is not a probabilistic claim. There is no determination or clarification of reality here. That’s what he claims.

Well, of course he’s mistaken. I agree that there is no determination or clarification of reality here, but for the reason I gave earlier, not for the reason he gives. Why? Because it’s true that if I were trying to decide about one specific store—say I claim it came from store number three—then obviously, yes, that’s only 10%, there’s a 90% chance it didn’t. But if I say: what is the probability that it came from one of the nine kosher stores?—then against that statement there is only one store that is an alternative. There are not nine other stores. After all, I don’t care from which of the kosher stores the meat separated. All I want to know is whether it separated from one of the nine kosher stores. So basically the two events whose probabilities I need to measure are: did it separate from the nine kosher stores, or did it separate from the one non-kosher store? And here it’s nine against one. Therefore, even on his own terms, it is probability. I claimed that it’s not probability because we have no way to check that it’s really uniformly distributed—that is, that separations really happen with the same likelihood from all the stores. And therefore you can’t really know. But he says that even if it happens with equal probability from each of the stores, you still can’t determine that the piece is kosher. That’s not correct.

Therefore he goes on and says as follows: “Likewise, the law produced by the majority of stores against the minority is a law that we are required to act upon, even though in reality there is no clarification here at all. And according to this rule, they said in the Talmudic text that a present majority is derived from the verse ‘incline after the majority.’” So that isn’t right, as I said before. But look what he proposes as an explanation, and here I’m already willing to accept the idea.

There he says as follows: yes, we saw that he says a present majority is not probabilistic, it does not clarify, it does not determine. So what is it? How does it nevertheless work? We learned that we have a verse telling us that we do follow a present majority—“incline after the majority.” Okay, so the verse nevertheless tells us to go with it. Why? What is written there? What is the definition that was introduced in this verse if there is no probabilistic reasoning here? So what is there? He says this: “Rather, it appears that the matter of nine stores is like the matter of majority deciding among judges. Namely, since the meat necessarily separated from one of the ten stores, each and every store generates a legal possibility regarding the meat. And it turns out that with regard to the meat there are nine aspects producing the side of permission and one aspect producing the side of prohibition. And the Torah said ‘incline after the majority,’ for so it is with judges, where the Torah said that the ruling emerging from the majority is what we are to do. Likewise, the law produced by the majority of stores against the minority is a law that we are required to act upon, even though in reality there is no clarification here at all. And according to this rule they said in the Talmudic text that a present majority is learned from the verse ‘incline after the majority.’ And Rabbi Meir did not dispute this,” and so on.

What is he saying, basically? He says: if I have ten stores, there is no probability—he said this above—there’s no probabilistic consideration here. Again, I’m not sure there isn’t a probabilistic consideration here, but it is true that I have no way to establish the distribution. Okay? Even though the intuition does say there is something probabilistic here, I have no way to establish the distribution. So this is not probability in the scientific sense. You can’t determine scientifically that the distribution is 90:10. That’s only intuition. But he says it’s not probability at all. Okay? So what is it? He says: once I have ten stores in town, nine of them kosher and one non-kosher, and now I have a piece of meat that separated, I ask myself: what are the possible grounds for this piece to be kosher or non-kosher? If it came from store number one, it’s kosher. If it came from store number two, it’s kosher. Three also, four also, up through nine. If it came from store ten, then it’s non-kosher, right? That’s basically the consideration.

So he basically says this: each store casts a possible side into doubt regarding the piece of meat. Those possibilities are what create the doubt. Yes? What are the possibilities? Did it come from store one, store two, store three, up to store ten? Each of those possibilities is one side in the doubt. Now, if I have nine sides in the doubt in favor of the conclusion that the meat is kosher—it came from kosher stores—and one side in favor of the conclusion that the meat is not kosher, then the Torah says “incline after the majority.” You follow the majority of sides. Notice: this is not probabilistic reasoning. He is not describing a probabilistic consideration here. He is not assuming that the probability of coming from each store is the same; there’s no such assumption in his framework. All he says is: how many sides do I have in favor of the conclusion that the meat is kosher, and how many sides do I have in favor of the conclusion that the meat is non-kosher? If I have nine in favor of the first side and one in favor of the second side, then “incline after the majority” means I go after the majority of sides. And that is not a probabilistic consideration.

His claim is that even though there is no probabilistic clarification or probabilistic determination here, there is a Torah decree that we follow the majority of sides. That’s his claim. He claims the same thing exists in a religious court. By the way, this certainly no longer fits with Sefer HaChinukh’s explanation of “incline after the majority.” He claims that “incline after the majority” works this way too. What does that mean? I have a case before me. Now I ask whether Reuven is liable or exempt. That’s the case. Right. Now I say: let’s see what the sides are. I have three judges: Yissakhar, Zevulun, and Binyamin. Fine? Now Yissakhar says that Reuven is liable, Zevulun says that Reuven is liable, and Binyamin says that Reuven is exempt. Each of the judges casts a side upon the case, a doubtful side. If Zevulun is right, then Reuven is liable. If Yissakhar is right, Reuven is liable. But if Binyamin is right, then Reuven is exempt. So we have two sides in favor of obligating Reuven and one side against obligating Reuven. Notice, all this is because we have no probability. So if there is no probability, we count sides. Once we count sides, we follow the majority of sides. Therefore we learn from “incline after the majority”—we learn the majority among judges, and we learn the majority among stores. Because in both cases, it’s not probability but simply sides. And the novelty of the Torah in “incline after the majority” is that I count sides and follow the majority of sides even though I have no probabilistic determination.

I’ll maybe give an example that sharpens this more.

Still, why are you committed to saying this isn’t probability? Suppose I have infinitely many kosher stores—infinitely many, tending toward infinity—and I know there is only one non-kosher one.

Shmuel, I agree with the intuition.

No, but it has nothing to do with probability. A million.

I agree with the intuition, but it’s an intuition. It’s not a probabilistic calculation. It’s not scientifically grounded. I can’t put it to an experiment. So the question is how much to treat such an intuition as authoritative. The fact is that you need a verse, because intuition alone isn’t enough. For an absent majority there is no verse. Rashi says it’s intuition. Or a law given to Moses at Sinai, doesn’t matter, but there’s no verse. Why? Because it’s intuition. Meaning, the fact is that a present majority needs a verse. So that also means that…

Who says the criterion for probabilistic reasoning is the ability to test it scientifically? Who says? Maybe gambling—if someone in Las Vegas would bet on it and be willing to invest, then it’s obvious he’s making a probabilistic judgment.

My claim is that the Talmudic text said so. Meaning, I’m trying right now to understand the Talmudic text. The Talmudic text says—if I’m right in the explanation—then the Talmudic text itself said it. But I think the Talmudic text learns “incline after the majority” from judges. After all, obviously if it were about poison—if someone thinks that Kabbalah says that if you eat non-kosher food you damage the soul within you—then maybe who cares that there are nine, even the tiniest chance, I don’t want to take the risk of damaging the soul within me or swallowing poison. With an absent majority, yes. Because there I have a scientific estimate. I know about all women that…

There—you yourself are saying a scientific estimate is better. There, you answered yourself.

Fine, it depends for what matter, for what purpose.

It doesn’t matter for what matter. The fact is: on a scientific estimate you’re willing to rely without a verse, and on a non-scientific estimate or intuition you need a verse in order to rely on it.

No, but why don’t I need a verse for a scientific estimate either? Why? How can an absent majority be followed without a verse? How can that be? Why really? There, Rashi says it, right. The Talmudic conclusion is that there is no verse for an absent majority. We saw the sugya in Chullin. We saw it. The Talmudic text looked for a verse, but in the end it didn’t find one, and Rashi says: forget it, why are you looking? It’s intuition.

Is there no room to distinguish between probability and statistics, in the sense that, true, I don’t have statistics regarding what happens when I find a piece of meat—where it came from—but I do have probability. Meaning, you could call it that.

Of course there’s room to distinguish. That’s the distinction I’m making. You can call this a priori intuition “probability,” fine. But as long as it has no statistics at its base, Rabbi Shimon’s claim is that it’s weaker. Not Rabbi Shimon’s—mine. It’s weaker.

What I’m trying to get at is that there are excellent statistics showing that probability works.

No, no, no—you can’t show that. Probability works, of course it works. But you need to decide what the distribution is. And here you decide the distribution by intuition. I explained this in one of the previous classes—ultimately everything is probability. Meaning, once you’ve decided that this is the distribution, you can perform a probabilistic calculation and calculate the probability of each event. The key issue is how to validate the distribution. And here you have nothing; it’s intuition. My intuition says the distribution is 90:10. There are other places where the distribution is 90:10 but on the basis of another intuition, and that won’t validate this intuition.

I think in a coin toss the probability is a priori, and that has nothing to do with what I decide its probability is. The probability of getting fifty-fifty—meaning, if I toss enough times I’ll get to around fifty-fifty—that’s an a priori probability, and still statistics show that it’s valid.

That’s not true. Exactly—go check and you’ll see, it’s not a priori at all.

No, mathematically that’s not true.

In the result of an experiment—a coin toss, the assumption of fifty-fifty in a coin toss—it’s a known finding, it was published some time ago, that it isn’t even. It tends toward one side, even with coins, in all coins. But never mind. Still, with a coin toss I have two options, which means that even if I strip myself of all prior knowledge or all subjective decision…

Ah—wait, wait, wait. Save that; I’ll come back to it in a moment. I’ll get there soon. With an ordinary coin I’m not stripping myself, I have knowledge. I know this is a fair coin, meaning it’s balanced. Or a fair die, or whatever. There’s a difference between that and a die about which I know nothing. I’ll get to that in a moment.

Why can’t I take the verse “incline after the majority” and see in it an administrative rule, a rule telling me how I relate to such cases, without getting into intuitions or probabilities now?

The Talmudic text learns from it the law of majority in stores. So that means it understood that there’s some principle here, and it’s similar too, between judges and stores. The verse itself can be read as an administrative rule, certainly. But the Talmudic text didn’t read it that way; we’re learning the Talmudic text right now.

But look at what kinds of tangles we get into just because the Talmudic text doesn’t want to see it as an administrative rule.

No, and I’ll say more than that: seemingly, why do I really need to look for an intuition behind the verse now? Why? The verse told me how to treat these things. Why do I need to distinguish between domains at all?

So we can know whether we can derive more things from it. What do you mean?

It would make decisions much easier for me, because I myself see… we see…

That’s not true, it doesn’t make it easier. And if there really is a principle behind it—if there is a principle—then maybe it can be applied in other contexts. Now the Talmudic text apparently understood that there is a principle behind it; the proof is that it applies it to stores, where on the face of it I wouldn’t see any connection between stores and judges. As I said, judges maybe are an administrative rule.

Right, exactly. But we’re learning the Talmudic text. The Talmudic text apparently understood there’s some broader idea here, not just a legal or administrative rule. There is some broader idea here, that one follows the majority, and that expresses itself also in prohibitions, also in a piece of meat. So Rabbi Shimon proposes a mechanism—that is, how the Talmudic text understood the Torah. Why the Talmudic text understood it that way, that’s a different discussion; I don’t know. But that’s how the Talmudic text understood the Torah. Okay? We’re learning that right now.

So basically the claim is that you count sides. Okay? Now if that’s so, and I’m now moving toward the law of fixed presence, yes, then in the law of fixed presence we are dealing, basically, with the piece of meat inside the store. Right? It didn’t separate. Okay. So Rabbi Shimon Shkop says there… wait… I think it’s later in that passage… Ah, I don’t have it here, but I think Rabbi Shimon Shkop says there later on that basically his claim is that… his claim is that once I’m talking about a case of fixed presence, meaning the piece did not separate, then the piece is in its place inside the store. So I don’t have… when the piece separated, then the ten stores are in their place, and each one of them casts… think of it as shooting an arrow at the piece, right? It casts a side in the doubt regarding the piece. But all that is only if the piece separated. If the piece separated, I ask where it came from, and every possibility—that it came from store A, store B, store C—is an arrow. I have ten arrows. Each store says, it came from me, it came from me, it came from me. I have nine arrows from kosher stores. But if I ask about the piece while it’s inside the store, the question is not which store it came from—I know; it came from this store. I just don’t know whether this store is kosher or non-kosher. Now here I have two sides: either the store is kosher or it isn’t kosher. So it’s like half and half. Here I no longer have ten sides that I count—nine from here and one from there. I have two sides. Once we have two sides—and again, this isn’t probability, but we’re counting sides, I’m continuing with Rabbi Shimon—then if we’re counting sides, in the context of fixed presence we don’t have ten sides but only two. Once we have only two, then it’s either kosher or non-kosher, and that’s half and half. Therefore, in fixed presence it’s like half and half, and we don’t follow the majority.

Maybe this is wordplay, Rabbi. He knows it’s exactly the same probability, were it not for the human factor, which seems to me the main thing. If we neutralize the human factor—like I said earlier—

Not only does he not know it’s the same probability, even in separation he doesn’t know it’s the same probability.

Fine, maybe there’s a substantive difference. This is just a way of describing the story in the wording he chose. Once it isn’t probability, then the verse is basically telling me a halakhic decision-rule. The halakhic decision-rule, according to how Rabbi Shimon Shkop proposes it, is counting sides. We’re not following probabilities here; we’re counting sides. If so, then one can definitely understand why in fixed presence we have one side this way and one side that way, so it’s like half and half.

But obviously there is intuition here, and he too understands that there is intuition.

He doesn’t speak about intuition, but intuition alone isn’t enough. That’s what I’m saying, which is why I prefaced everything with that whole introduction. Intuition alone is not something we follow, because the fact is that we need the verse telling me “incline after the majority.” So Rabbi Shimon says: what did the verse introduce? The verse introduced—look, probability—but I really don’t understand. The verse is essential. If it were a matter of a reasoning that unquestionably exists and everyone agrees on, then the question of whether we rule on it in Jewish law would depend on… If the world would be destroyed by whether we eat this piece or not, then obviously we would prohibit it. But since the Torah decided that the world won’t be destroyed, therefore it permitted it and introduced the novelty that in such cases we follow the majority. But what does it mean to follow the majority? The question is what it said. Did it say this intuition you have is valid and we’ll rule by it? So I’m saying: you’re proposing that it said something like, that intuition you have is fine, go with it, okay? And Rabbi Shimon Shkop says no. Since he doesn’t accept that intuition at all, he says no: the Torah defined that we follow the majority of sides. That’s a halakhic rule, not a probabilistic rule, and not even really an intuitive rule. It’s a halakhic rule that where there is no scientific probability, you count sides. That’s the claim.

But in fixed presence too, why not formulate it by saying that here too we count sides: I entered one store, I don’t remember which one, and among all ten stores there are nine saying “you entered me”; there are nine sides that I entered one of the kosher stores and only one side that I entered the non-kosher store.

That’s a good question. Wait—this is just a different formulation.

Rabbi, no—that’s a different question from yours.

That’s exactly what I meant. If we find a way to formulate it, we can formulate it.

No, that’s not what you meant. I’ll explain why. What you meant was to ask a different question—the probability really says it’s kosher. He’s asking a different question. He says maybe the probability doesn’t say it’s kosher; the rule really is to count sides, not probability—but here too there are ten sides. That’s what he’s asking. He’s not saying let’s follow the intuition; rather, let’s go with Rabbi Shimon Shkop, but what Rabbi Shimon Shkop said also exists in fixed presence and not only in separation.

I meant both things, both things. I said it’s a matter of formulation, after we accept whatever we accept about the novelty of the verse.

You didn’t mean that; what you asked wasn’t that, you asked something else. Fine, never mind. In a moment I’ll get to another explanation of the law of fixed presence, and it will actually be needed to complete this explanation too because of your question. Okay? I said we have two explanations left. So let’s leave that for a moment; I’m getting to the next explanation in just a second.

So basically the claim is this: if it’s fixed presence, then I have two sides. Once I have two sides, I go with half and half. Now these two sides are not equal in weight. There are nine stores here and one. Fine. But from the standpoint of counting sides, there are only two, because my question is whether it’s kosher or invalid, not which store it came from. It didn’t come from anywhere—it’s in the same store where it was—so there are only two sides here. And if there are two sides, then it’s like half and half, in that sense.

What someone remarked here earlier—I already forgot who it was—we can maybe compare to the example I once gave about a coin. If I toss a coin and I have established information—I checked—that the coin is made symmetrically, okay? Then I assume the chance that it lands heads or tails is fifty-fifty. Okay? Now if I have another coin, and I have no idea how it’s made. No idea. It may be completely asymmetrical. One side may be much heavier and it will always fall on that side, meaning with the other side up. Right? It will always fall that way. But I don’t know; I didn’t examine the coin, and anything could be true—maybe it’s fair, maybe it’s unfair, maybe unfair in favor of heads, maybe unfair in favor of tails. And now they tell me: bet on what will come out. You have to bet. I still bet on fifty-fifty, right? Why? Do you know why? Because I’m counting sides. What can happen? Either it lands heads or it lands tails. And since I have no information at all, from my standpoint I count sides. Now notice, when I count sides here I really can’t say there’s a 50% chance it will land heads or tails—that’s nonsense, I have no information, there is no distribution here. If I know the coin is fair, then I have a distribution; it’s fifty-fifty. Then if I make a bet with someone now on how the coin will land, it makes perfect sense to use that distribution and say it will probably be fifty-fifty. But if I have no information, notice I’ll do exactly the same thing. I’ll still bet fifty-fifty. I have no information; what can I do? But how did I get to fifty-fifty if I have no information? Why fifty-fifty? Maybe thirty-seventy? Because I have two sides. I’m counting sides. Either it will land heads or it will land tails. And since I have no way to prefer heads over tails or tails over heads, I still bet that it’s fifty-fifty.

The same with a die. If I know the die is fair, then the probability that it lands on two is one sixth, right? If I have no information about the die, maybe it isn’t fair. It may always land on one, or always on six, or I don’t know what, or three quarters of the time on five. I have no idea; anything could happen. And they tell me, you have to bet what the chance is that it lands on two. One sixth. Why one sixth? You have no information, you know nothing. Because I have six sides. The sides are one, two, three, four, five, and six, and I count sides. If I have one side against five, then I bet one against five.

Now I think this brings us very close intellectually—not to why there’s no probability there, I explained that earlier—but to why, when we don’t know the probability or when we don’t have probability, we count sides. And you see that we do this in life too. And in that sense, the Torah’s instruction is simply an instruction close to the way we conduct ourselves in life too. We count sides. Now obviously there is still a formal element here, because as you said earlier, you could say: but even when the piece is inside the store there are ten sides; we’ll still count sides, and there too there are nine sides kosher and one non-kosher. So I said, in a moment I’ll try to answer that. But on the principled level, I’m trying to show you—just a second—I’m trying to show you why counting sides is not such an absurd thing. Meaning, if I have no information, then I count sides in life too, not only in Jewish law. And here the claim is that I don’t really have information, not in the scientific sense. I cannot accumulate scientific information here about what the distribution will be. And the Torah tells us, according to Rabbi Shimon Shkop’s proposal, that if I have no scientific information, this is considered a state of no information. And when you are in a state of no information, you count sides.

But this rule we’re talking about, which is brought in the Talmudic text in Chullin and which we also apply to the Sages, the issue is this: we keep talking about ten, about nine against one, nine against one, but this rule also exists when it’s two against one. Meaning, if I have two stores that are non-kosher and one store that is kosher, or the opposite, two kosher and one non-kosher—in other words, I immediately jump from 10% to 33%. And here I count sides too, yes, and it doesn’t matter; you don’t need to reach infinity. Meaning, even with such an intuition I still can’t test it.

Of course, of course. It has nothing to do with whether it’s 90:10 or 66:33.

No, that doesn’t matter. But in principle there is such a reality that even in situations of non-kosher and kosher I can get to fifty-fifty.

I didn’t understand.

Right. So if you get to fifty-fifty, then it’ll be fifty-fifty. What kind of halakhic ruling is that? A doubt. The laws of doubts—what’s the problem? A Torah-level doubt is ruled stringently. Majority applies when it’s not fifty-fifty but fifty-one.

No, because majority relates to the laws of doubt, because with a present majority—meaning, it doesn’t specifically have to get very large, it can also be a little—and then it comes out that really, aside from the Torah rule “incline after the majority,” we have no intuition at all. Nothing. You really can’t decide at all.

Why no intuition at all? If I need to decide whether it’s the 51 or the 49—true, the gap is small, but I’ll still decide in favor of the 51. That’s obvious, yes.

But it comes out from this that really this rule—you can’t test it, you can’t—and that means it really is, as Shmuel said, some sort of administrative rule, a decision rule, and so on. Meaning, you have no intuition in it at all.

No, it’s not an administrative rule. Again, I’m saying: the verse can be read as an administrative rule, but the Talmudic text certainly didn’t read it that way, because the proof is that the Talmudic text applies it broadly.

No, obviously. The Talmudic text searches and doesn’t find; that’s the whole point.

No, it does find! It says it compares it to stores and everything is fine. It doesn’t remain unresolved. That’s how it learned it. And that’s exactly the point. You can read the verse differently; I’m not arguing right now whether the Talmudic text is right. I’m only trying to understand what the Talmudic text says, what its logic is. Later you can argue whether it’s right, whether it can be read differently, why it read it this way. But I’m speaking on a different plane. And in the end I tried to show that counting sides is not such a far-fetched thing. In our lives too, when we have no information, what we do is count sides. That’s all. The only claim is that a present majority counts as a situation—and that’s where the argument here lies—of having no information. And one can argue with that, because Shmuel says we have intuition. So why don’t we have information? Intuition also… So maybe I’d say no, “information” means something one can accumulate scientifically. Fine?

A different question is: then why isn’t it nine sides against one also in fixed presence? And forget the intuition—right, there’s no intuition, we count sides—but still, in fixed presence too there are nine sides against one. So I’ll get to that in a moment. So this is another explanation for the law of fixed presence.

Another explanation is one Oren suggested to me on the website—Oren is the site editor. He once suggested this explanation to me. Someone in the previous class, or the one before that, reminded me of Aumann’s article on this issue. I read it many years ago, so I didn’t remember. Aumann’s article basically suggests this explanation. Meaning, Oren’s explanation is Aumann’s explanation; it’s the same explanation. And the claim is basically the following. And as I said, it completes the previous explanation against your question. What does that mean?

You remember Moshe Koppel’s container with the balls? Yes? Suppose I have a container with 99 white balls and one red ball. Wherever—you put your hand into the container with your eyes closed and pull out a ball. What’s the probability that a white ball comes out? 99, right? Red, 1%. Now I say something else. I look into the box and choose a ball for myself. Fine? Now I ask: what is the probability that a white ball comes out? Fifty.

Fifty? Why fifty? Because you’re choosing.

Exactly! Because if I like a white ball, I’ll take a white one. If I like red—there’s only one red one—but if I like the red one, I’ll take that. I won’t take white. The choice is not random. Once we’re talking about a human act, not a random process, then you cannot apply statistical rules. It isn’t determined by probabilities. I choose according to what I want, not randomly. If it’s not random, then there’s no room to talk about probability. Therefore the claim is that when you’re dealing with a human act, you can’t activate probabilistic rules. That’s the point.

Now I’ll expand on this in a moment—but for our purposes, what he basically wants to say is this: if I entered the store and took a piece from inside the store, and now I’m going home and I’m in doubt which store I was in, yes, where did I come from with this piece—why is that not like separation? The claim is: because separation is a piece that got lost, and the loss of the piece is a random process. We don’t have… it’s not a person deciding to lose a piece or to lose a piece from this store or another store. It happened to him. It’s a random process. Since it’s a random process, I can apply probability or statistics. Okay? But if we’re talking about a human decision—he entered a store and took it from there. If he wants a piece of meat, then it’s not correct to say there was only a 10% chance he entered the non-kosher store. If he likes that store, then he’d enter it 100% of the time. If he wants non-kosher meat. If he wants kosher meat, then 100% of the time he’ll enter the kosher stores, not 90%—100%, because he wants kosher meat. So when the doubt begins from an action that is a human decision, where he chooses the store he enters in order to take the piece, you can’t apply statistics. If the person had fallen onto a store from a spaceship—they threw him down and he found himself in a butcher shop and took a piece from there—then truly one could apply probabilistic rules. But when the person chooses a store and decides to enter it and take a piece of meat, you can’t discuss it by statistical rules. It’s not a lottery. You’re not drawing a store; you’re choosing one.

So then this isn’t present majority; it turns into absent majority.

No, this is present majority. Why not? Because I’m going to some specific place, and from that specific place—meaning, I don’t need to choose all kinds of… there is no majority for me at all here.

No, so it’s ultra-present majority. Even more present than ordinary present majority. In separation too it’s present majority. What you’re saying is that in fixed presence it’s even more present majority. Fine, no problem. But it’s not absent majority; it’s ultra-present majority.

Right, sort of present-present, exactly, twice over. Yes.

If so, then excellent, because if it’s present-present, then it’s even clearer that there are no probabilities here. Because even in an ordinary present majority I said it isn’t probability; here all the more so you can’t apply probabilities. Therefore I’m saying: I don’t know, I don’t remember—if I remembered what my considerations were when I chose a store, then of course the doubt wouldn’t arise. I’d say, look, I chose a kosher store because I eat kosher. Fine, the doubt doesn’t arise. I’m saying: I don’t know what madness came over me, I don’t know how to picture the case, but I don’t know which store I chose. Or, you know what, the mouse entered piles of leaven and unleavened bread, like the Talmudic text in Pesachim. So when the mouse chose a pile of food, that’s not random choice. It chooses the food it likes. So if it likes leaven, it’ll take leaven, even though there are nine piles of matzah. If the mouse likes leaven, it’ll choose leaven. So when I’m in doubt about the question, when the mouse brought me this item and I ask whether it’s leaven or matzah—it’s fifty-fifty, because I don’t know whether the mouse likes leaven or likes matzah. So it’s fifty-fifty. And there that’s really not because we’re counting sides like Rabbi Shimon Shkop. There it genuinely is not distributed as ninety-ten. Really not. Because there’s choice here; it’s an act of choice. And choice depends on my preferences. Once I’m talking about my preferences, there are no probabilities. Probabilities are when there are no preferences. I do a blind random process and the question is what comes out. Then it’s distributed according to how many cases of this kind there are versus how many of that kind there are. But if I’m doing an action, an act of choosing, then there’s no room to talk about probabilities at all.

Therefore, with stores at least one can understand that when I entered a store, I performed some decision-action that I want to enter this store. Right now I don’t remember which store I preferred to enter. Okay? But I preferred this one. You know what? I didn’t know which was kosher and which wasn’t, because otherwise there’s no doubt. If I eat kosher, then obviously I entered a kosher store. But say I didn’t know there was a non-kosher store here; I thought all were kosher. Fine? But I chose this store because it had wonderful air conditioning, or it was very convenient to shop there, or the prices were low, or I don’t know what. For some reason I had a preference for this store. Now at the moment I don’t remember which store I preferred. You understand that there’s no room to discuss ninety-ten here; it’s simply irrelevant. The question is what I like, which stores I like. So what’s the point of discussing ninety-ten? It’s completely irrelevant. Therefore in such a case there’s no reason to follow the majority. That’s actually very sensible.

Except that when you move to other cases of fixed presence, with stores I explained it now, but when you move to other cases of fixed presence, it starts to limp more.

Sorry, Rabbi, sorry for interrupting. Sorry. I understand the additional layer in the explanation you’re giving, but according to Rabbi Shimon, who already rejects probability in present majority, then you can’t say that in fixed presence, because there’s randomness, you can’t apply probabilities—because you can’t apply probability at all.

Correct, correct. So according to Rabbi Shimon there is no distinction. I understand. I don’t agree with Rabbi Shimon Shkop, and I’m going with Shmuel. We do have an a priori intuition that there is an advantage to the stores, so I’m willing to accept that intuition. The question is why the verse “incline after the majority” doesn’t tell me to use that intuition. The answer is that this intuition is not relevant when I go to the store. And now this is a very sensible distinction.

Now the question is: what happens with judges? Judges too are a present majority that… But what happens with judges? Mordechai in chapter 1 of Chullin asks: why do we follow the majority with judges? Isn’t that a case of fixed presence, since the judges are sitting in their place? And his answer is that their voice separates, their voice comes out from… which is a kind of strange argument. I once explained it, but never mind, I won’t get into it here.

What—is this accepted?

What do you mean by accepted? That’s what Mordechai says. I don’t know what accepted or not accepted means.

No, the question is whether they addressed this in practical Jewish law.

He’s answering a difficulty, so what does “in practical Jewish law” mean? There’s no practical ruling here. The practical ruling is that this is a present majority and we follow the majority. He has a question why this isn’t fixed presence. Obviously, as a matter of Jewish law it is not fixed presence—there’s no question. The question is what the explanation is for why it’s not fixed presence. So what does “for practical Jewish law” mean? Practically, you follow the majority. The question of why this is not fixed presence is just a difficulty. How one answers a difficulty—everyone can answer however he wants.

But this isn’t clear to me. Why is it fixed presence? Why on earth would judges be fixed presence?

They’re sitting in their place, the judges.

But we’re not interested in their sitting. We’re interested in what they say.

Exactly. Right. That’s why this Mordechai is strange. This Mordechai is strange. But still, when I now look at the judges, okay, then why indeed is the case of judges more similar to separation than to fixed presence? And leave aside that they’re sitting in their place. According to the explanation I gave earlier, why is it more similar to separation than to fixed presence? After all, with judges we do follow the majority.

Suppose all ten stores were identical, totally identical. From the standpoint of the person choosing, yes? Then here too it wouldn’t make sense to speak of fixed presence. The considerations of fixed presence… So with judges it’s exactly the same. How is it connected to fixed presence at all?

No, let’s try to understand what happens with judges. With judges I’m basically saying that… I’m continuing with Rabbi Shimon Shkop. The judges cast sides onto the case. Okay, they cast sides onto the case. But according to Oren’s or Aumann’s explanation, the claim is that in every case of “whatever separates comes from the majority” there is probability. However, in fixed presence there’s no point in applying probability because it’s human action. Fine? So now the question is how to apply probability to judges. Is it like Sefer HaChinukh, that basically in most cases where there’s a majority versus minority dispute, the majority was right and not the minority—is that the intuition we have regarding judges? Or does it concern these three judges themselves—the majority being two judges against one who is the minority? Because what happens there, when a judge forms a view, is not a lottery. And when I ask what the true Jewish law is, it’s not a lottery when I ask myself whether I drew judge A, B, or C. It is an exercise of judgment. Now if one judge exercised judgment correctly and the other two exercised judgment incorrectly, then he’s right and they’re wrong. There’s nothing random here where you can ask yourself, okay, so what’s the probability that the two are right? Because the probability that they’re right or wrong isn’t random. What they do is ultra-rational judgment. Much more so than a person choosing a store. A person choosing a store is according to one preference or another. Judges are really exercising judgment and reaching a reasoned conclusion. So it’s hard to see…

So we count sides with judges too?

No, but what do you mean… say we also… yes, but what sides are there? That Reuven is liable or that Reuven is exempt. Right, what they cast onto the litigant. Again, according to Rabbi Shimon Shkop you’re right, because according to him they cast sides. But now we’re saying, forget sides, we’re talking statistics. But if this is human action, then you can’t apply statistics. That’s the previous explanation you’re talking about. I’m speaking about the current explanation. Okay, so we don’t apply statistics when the action is human action. Is it correct to apply statistics to judges? No. No. After all, what they’re doing is rational, intelligent judgment. They’re Torah scholars, skilled. Now of course they too can err. But I don’t see why statistics should work here. Unless you go to Sefer HaChinukh’s statistics, that in most cases the majority is right and not the minority—but then again we’re back to all the previous discussions. But if the basis is… if Rabbi Shimon Shkop’s basis is sides, then this isn’t at all…

No, again, according to Rabbi Shimon Shkop I do understand it. I explained that earlier. No, no, I want to say that Aumann’s thesis is not relevant here, because Aumann’s thesis speaks where there is statistics.

Correct. But here there are no statistics.

Correct. Exactly. That’s exactly what I’m explaining. No, I want to say that Aumann’s thesis is not relevant here, because Aumann’s thesis speaks where there is statistics, but here there are no statistics, which is what Rabbi Shimon Shkop says.

Wait, wait, wait, wait, wait. I’m explaining. No, it’s the same thing, all of you are saying the same thing. This is an alternative answer. Again, the previous explanation of Rabbi Shimon Shkop is one explanation, and according to that explanation I understand judges. I’m now talking about Aumann’s explanation, which doesn’t talk about counting sides. He says a present majority is probabilistic; he ignores everything we said before—it’s probabilistic. But when there is human action, it is not correct to apply probability. Now I’m asking, according to Aumann, not according to Rabbi Shimon Shkop: are judges more similar to fixed presence or to separation? On the face of it, they seem to me more similar to fixed presence—not because of what Mordechai says, that they’re sitting in place. No. Rather because this is human action, and the question is not a random question. When you ask who is right, that is a question of judgment, not a question of lotteries.

But why is it similar to fixed presence?

It’s similar to fixed presence in the sense that there is here intelligent human action, and you can’t apply probabilities to it.

One second, one second, Rabbi. Come on. I went to a store, chose meat, came out, don’t remember which store. I go with this meat to the Sages, I enter the religious court, I ask, gentlemen, what do I do? They tell me, listen, where was it? We’re talking about the store, so it’s fixed presence. Now they determine some Jewish law for me. That law—after the majority, after the majority, never mind what. But I—as Shmuel said—why should I care where they are sitting? They are discussing my case.

Again, I’ll explain. You’re asking whether the situation is a case of fixed presence. I’m talking about whether the logic is the logic of fixed presence. The logic of fixed presence according to Aumann is not connected to the question whether you are in place or not in place.

No, I understood. It depends on whether you have human action or random action, whether it’s judgment or random action—that’s what…

Judgment is fixed presence; random action is separation.

Fine, understood. Now I understand. So here I’m saying: in a religious court it’s hard to understand why we follow the majority—why is that separation?

But I don’t understand why you’re willing to apply Aumann here. You yourself say that Aumann’s thesis talks as if judges are operating according to statistics in principle. But according to Aumann’s thesis, you can’t apply statistics here, because each one chose for himself the things he chose.

Okay. I don’t accept that statistics works with judges; it doesn’t work with judges. The statistics doesn’t work. Only Rabbi Shimon Shkop’s thesis works. If all three judges are Torah scholars and two of them reached the conclusion that Reuven is liable and one reached the conclusion that Reuven is exempt, then surely there is room for the intuition that most likely he is liable. Why not? That’s exactly the statistic.

No. Like the intuition with the stores, what’s the problem? Most likely Reuven is liable.

You’re attached to the rule, you’re attached to the rule that one follows the majority.

Not the rule. Now I’m talking about logic. Ask a person on the street and he’ll tell you most likely the majority is right. What do you mean? It’s a simple human intuition, just like they’d tell you about the majority of stores, that most likely it came from the kosher stores. Same thing.

That really doesn’t sound logical at all. In reality we see that the majority is wrong, and hugely wrong, in all kinds of areas of life—on the contrary.

We were talking about most likely.

No, no—most likely the opposite. Usually the majority is wrong.

I had a thesis about this, and in the end I retracted it in light of a comment by Ari Shatzky—that this isn’t correct. Most likely the majority is right. I also agree with Shmuel: today there are so many things the majority does and the majority…

No, you’re talking about a majority of experts. Again, I’m not talking about a majority of fools versus a few experts. Sefer HaChinukh himself, when he speaks about it, says that if there is one great Torah scholar, he can outweigh two who are less wise than he is. Right, because majority is said where the level of wisdom is more or less similar. That’s also how Maimonides brings it in Guide for the Perplexed. Okay.

Fine. So let me just finish. Ah—I still owe you an answer. I’ll finish. The question on Rabbi Shimon Shkop, as you said, is that if I enter the store, there are still nine sides that it’s kosher and one that it’s non-kosher, because there are nine such stores. So I say no, because when I entered the store, I’m not… there’s no… the process of separation is the random process. Something separated, it happened, and then I start talking about sides. But when I enter the store—I’m using Aumann’s answer to rescue Rabbi Shimon Shkop—when I enter the store, either I chose a kosher store or a non-kosher store. There are only two sides. So I don’t care that there are nine kosher stores, because if I want a kosher store I’ll choose one; if I want a non-kosher store, even if it’s one against a hundred I’ll go to the non-kosher one, because I chose it. So I’m saying the fourth answer can also rescue Rabbi Shimon’s third answer. Okay? Fine, that’s it. If there are comments or questions?

Rabbi, doesn’t it feel like the majority really doesn’t determine much? What do I know? Why? Look, I’m saying again: most of the rabbis on the Chief Rabbinate Council oppose ordaining women as rabbis. Rabbi Avraham this week was with…

But that’s an evaluative dispute. That’s not a dispute in interpretive judgment of sources. Those are conservative values, from a value standpoint. Fine?

Rabbi, the ability to separate values from interpretation of sources is really not obvious at all.

Okay, not obvious. But still, there is such a difference. Reality is exactly the opposite. I’m hardly someone suspected of saying the majority is usually right. But I think that if I have a list of experts and I have no information about the situation at all, and the experts tell me—nine experts tell me Reuven is liable and one tells me Reuven is exempt—the assumption is, if I have to bet, I bet that he is liable.

Let’s take the opposite example. A thousand years ago all the experts claimed the earth was flat. So they were wrong, that’s all. So if you had lived then, Rabbi, you would have said, “I’ll say the majority is right”?

Correct. And I would also have been right, because in the end if you have no information, you go after the majority. That doesn’t mean you’ll always be right. It means that in most cases you’ll be right. So don’t bring me examples where the majority was wrong. Of course there are such examples. The question is what most examples show, and in most examples the majority is right. That’s the claim.

In all fields our understandings change, in all fields. The famous letter of Rabbi Shach that I’m very fond of—he talks about the Entebbe operation. Yes, as is known he opposed launching the Entebbe operation, because he said, listen, you’re endangering soldiers, and the chance of success is very small, and it’s not worth paying the price of soldiers’ lives for a small chance of saving the hostages. That was the claim. Now they carried out the operation and it succeeded. Yoni was killed, yes, but overall it was a great success. Okay, so afterward people came to Rabbi Shach—they say this letter is in one of his collections of letters—and they said to him: so, Rabbi, you see? You were wrong. The operation succeeded. So now what? That proves nothing. Meaning, I claimed that given the data I had then, most likely the operation would fail. When I say that most likely the operation would fail, that doesn’t mean it can’t succeed. So yes, a lucky case happened and it succeeded. Does that refute what I said—that it was just a lucky case? Meaning, I say that with the data we had, most likely it would fail, and I stand by that opinion even today.

The same thing here. I claim that in most cases the majority is right. True, there are cases where you’ll find the majority was wrong. But the important question is how many such cases there are versus the opposite cases—not whether such cases exist. Of course there are cases where the majority was wrong. But when I formulate a sweeping legal rule, I need to be blind, what is called behind a veil of ignorance. I say: I look at this with complete blindness, suppose I know nothing, I have no position of my own, nothing. I have to determine. There is a majority in the religious court saying X and a minority saying Y. Okay? Now I know nothing about it, I have no position of my own and nothing. What do I bet on? I think any reasonable person would bet on X, even though there can be cases where he’ll be wrong, true. But if I need to bet and formulate a sweeping rule, the sweeping rule makes sense to set on X rather than Y. Very sensible. I don’t see any problem with that.

So maybe that also answers our question about judges. We’re not talking about what reality is, but rather what is correct to rule given the data presented before the judges. So in that situation the majority determines not because reality is such, but because—and then the human factor is no longer all that important. We’re reflecting on it from outside and saying that’s what we… we neutralize the human factor because we’re not talking about what the true reality is.

But then you turned it into a legal rule, an administrative rule, what was suggested earlier. But then there’s nothing to learn from that for stores. After all, in judicial procedure we follow the majority because it gives legal certainty, or order, or something—I don’t know, there’s a lot of logic to that. But what does that have to do with stores? When the Talmudic text learned from that to stores, it apparently understood that there is some principle here that isn’t tied specifically to the world of law: that we follow a present majority. People come to the judges and they rule that the piece is kosher. We don’t know in reality whether it is kosher, but the majority ruled that it is kosher, and if this is a great novelty that one may rely on that—even though seemingly this may damage the soul—we take the risk and eat it with appetite. And then naturally they say: why not make an analogy from that also to stores? Then the human factor doesn’t interest us, because here it’s not…

No, not administrative in the sense of managing religious courts, but in the sense that when we come to fulfill the Torah’s commandments, seemingly we could have treated this as poison in every transgression, and therefore be stringent in every doubt in the world and not follow the majority, because here it’s poison. And what is introduced, “administrative” in the broad sense, is for the whole management of human life.

So then you’re saying, fine, what was introduced in “incline after the majority” is that one follows the majority and doesn’t worry about the minority, but this was introduced only in separation and not in fixed presence. In fixed presence—certainly in fixed presence—there’s a human factor. But the question is entirely different. So there is a human factor, and once there’s a human factor, with judges too there is a human factor.

No, but with judges the human factor is in the question whether he really murdered or didn’t murder, but that’s not the question. The question is what is correct to do, not whether he murdered. No, no—I’m talking about the judgment exercised by the judge, not the judgment of the murderer. The judge exercises intelligent judgment, not a lottery. Yes, but I’m not betting on what… I’m asking myself what do I do with a majority of nine judges against one, or two against one. So I’m not investigating what the truth in reality was; rather, what I need to do among them. Therefore here…

He claims you do need to investigate the truth in reality. He claims that in stores, the reality is that the meat is kosher—except when the meat is inside the store, in fixed presence, where that’s not true, because that is human action and therefore one cannot apply probabilities here. And then I remark: if so, then apparently with judges too it should be like that.

Fine. Aumann offers another proposal. Fine, he’s talking about Aumann’s passage. No, because the question of—I agree with Aumann’s idea. We already talked about it before he said it—that the question there is generally about a human factor and not about what the piece is. But here with judges we know—there is a reality, there is a written ruling, nine rulings of liable and one exempt. But each one exercised judgment and reached his own conclusion. He isn’t making a lottery, right? So who says here it resembles separation? Maybe it resembles fixed presence because these are acts of judgment, not random things.

But if I had needed to choose among them, then I’d say—but I… I don’t know. The question of truth doesn’t interest me here. The question of truth doesn’t interest me, because look, I’ll tell you something: earlier you said, and I say the same thing, I agree on this point—also with stores I would say it’s kosher. If you ask what the intuition is, what I would say by intuition—with all due respect to Aumann’s intuitions and his distinctions—I would say it’s kosher. If most stores are kosher, then it’s kosher. So if you already accept that nevertheless, although the intuition says that, there is this pattern, this pattern of what? Of fixed presence, Rabbi means?

Yes. No—what do you mean, why not? If a person comes, a person who… when a person comes and chooses, and he has the considerations of kashrut, then can I say because there are nine non-kosher stores I’ll say… Ask a regular person on the street, an intelligent person. Ask him on the street. A person enters one store in town, whichever one, and we don’t remember which store. There are nine—you know what—nine hundred ninety-nine kosher stores and one non-kosher one, okay? Is it not more likely that he entered a kosher one? You have no further information. He’ll tell you yes, he probably entered a kosher one. This a priori logic, this a priori intuition, exists here too. And if you nevertheless say yes, but if this is human action, I’m not satisfied with that; here I don’t apply those rules—then if so, the same with judges. There too the logic says the majority is right, as with stores. But if we go with these halakhic patterns—that this is human action and you don’t apply probability—then I think with judges too it should be like that. Fine, there’s room to think about this issue.

Okay.

Rabbi?

Yes.

I wanted to ask a question not connected to Jewish law at all. I heard you say that Shimon HaTzaddik didn’t meet Alexander the Great because he wasn’t in the Land of Israel. But Alexander the Great was in the Land of Israel twice, and in those years where there’s a dispute between scholarship and Torah there are always a few years where they overlap. He came down from the war in Syria against… to Egypt to build Alexandria, and afterward went back to the war in Turkey until he went up to India and died there. Twice he passed through the Land of Israel.

I’m not expert in the matter, I don’t know. You may be right. What I read was that he was not in the Land of Israel.

No, no, that’s what I wanted to tell you—I heard that.

Then I’m mistaken. We need to check it.

No, because you asked why the Sages used Greek…

In any case, they also weren’t from the same period.

Ah, that’s what I… According to scholarship and according to Torah there are a few years that were lost. That’s known. All of academia talks about the fact that there is a discrepancy in the years. Specifically between Shimon HaTzaddik and Alexander the Great there are a few years where they overlap, and it may be that during those years they met.

So it may be that I was mistaken. I don’t know. That’s what I read, but I didn’t delve into it.

No, no, I heard—I missed Tuesday’s class, and when I listened to it online suddenly I said wow, I immediately went and checked it.

Okay, fine. I studied this in history, so it’s worth checking, because you said something there.

Okay, in any case, thank you very much. Goodbye, Sabbath peace.

Sabbath peace. Thank you.