Doubt and Probability—in Halakha, in Thought, and in General—Lesson 32 – Rabbi Michael Abraham
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
🔗 Link to the original lecture
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Table of Contents
- Statistical evidence versus eyewitness testimony, and the difference between direct and circumstantial evidence
- Rov de-ita kaman and rov de-leita kaman as a first explanation
- “We do not follow the majority in monetary matters” and Rabbi Shimon Shkop as a second explanation
- Moving from the group to the individual, and the claim that group probability is not probability about an individual
- A qualifying note: random picking from one hundred prisoners and restoring the 99% probability
- Doubt involving one piece versus doubt involving one of two pieces as a third explanation
- Public examples: a hostage deal, a flashlight inside the swallowing cavity on the Sabbath, and the Entebbe operation
- Risk, public responsibility, and the distinction between certain risk and a suicide mission
Summary
General Overview
The lecture presents the difficulty of convicting on the basis of statistical evidence even when the probability appears very high, and distinguishes between direct and circumstantial evidence, between different kinds of majority, and between random events and the chosen actions of human beings. Halakhic sources are brought, such as Maimonides’ view that one does not convict in capital cases on the basis of circumstantial evidence, and Rabbi Shimon Shkop’s explanation of “we do not follow the majority in monetary matters” when what is at issue is a person’s decision rather than randomness. Later, a halakhic-conceptual distinction is proposed between doubt involving “one piece” and doubt involving “one of two pieces,” in order to explain why an apparently identical probability does not carry the same weight when it is known with certainty that there is an innocent minority within the mixture. The discussion then broadens to public and moral examples involving risk and expected value, such as a hostage deal, checking a weapon on the Sabbath, and military operations, in order to illustrate the tension between statistical expectation and making a determination about an individual.
Statistical evidence versus eyewitness testimony, and the difference between direct and circumstantial evidence
Conviction does not rest only on the probability of being right, because the “hundred prisoners” case creates a probability of ninety-nine percent for each defendant, and nevertheless legal systems do not convict on that basis. By contrast, conviction based on eyewitness testimony is accepted even though there is some possibility of error, because testimony is direct evidence of the act, whereas in the prisoners case there is no direct evidence regarding any individual person, only statistical evidence, which is circumstantial with respect to the individual. Maimonides is brought as an example that even very strong circumstantial evidence—such as a pursuer entering a ruin with a knife and then later being found there with a blood-dripping knife and a victim bleeding out, with no other exit—still is not enough for conviction in capital law, because the problem is the type of evidence, not its probabilistic strength.
Rov de-ita kaman and rov de-leita kaman as a first explanation
A distinction is proposed between rov de-ita kaman and rov de-leita kaman, where rov de-ita kaman is described as a working assumption arising from ignorance rather than positive probabilistic knowledge. In the example of the stores and the meat, there is no known distribution from which percentages are derived; rather, there is lack of knowledge, which leads to equal treatment of the possibilities and then to following the majority. Rov de-leita kaman, by contrast, is presented as a generalization from sample and observation and therefore as a probabilistic majority grounded in knowledge. The prisoners case is associated with rov de-ita kaman, because the ninety-nine versus one distribution is not a “law of nature” but a local fact from which an assumption of equality among the suspects is derived. Therefore, it is argued that there is not really a 99% probability here in the sense of knowledge, but only a working assumption, and that is not enough for conviction.
“We do not follow the majority in monetary matters” and Rabbi Shimon Shkop as a second explanation
The topic of “we do not follow the majority in monetary matters” is brought through Nachmanides and the examples of wedding gifts and “most oxen are for plowing,” along with the dispute between Rav and Shmuel and the ruling that we do not follow the majority in monetary cases. Rabbi Shimon Shkop explains that when the event is not random but the result of human decision, there is no justification for deciding according to a distribution, because each person can claim that he belongs to the existing minority. The example of an urn with ninety-nine white balls and one red one makes clear that a 99% probability exists only when there is blind drawing, but when there is conscious choice the distribution is irrelevant and the question becomes, “Which color does he like?” This explanation is applied to the prisoners by claiming that the attack was a deliberate decision, and therefore each prisoner can argue that he is the one who chose not to participate, and there is no way to convict him by virtue of the group majority.
Moving from the group to the individual, and the claim that group probability is not probability about an individual
It is said that when one looks after the fact at the whole group, one may say that in ninety-nine out of one hundred acquittals there will be a mistake, but from that one cannot infer that in each individual trial there is “99% guilt.” It is argued that moving from a distribution over a group to a probabilistic claim about a single person requires an assumption of relevant equality among all the individuals, and that assumption is not justified because there may be real differences between people. The example from psychology is described as statistics that predict a distribution in a group but do not determine the probability of a decision by an individual, because the individual chooses how to act. Alongside this, the claim returns that the laws of majority operate in a case of doubt, and when there is knowledge or decision, relying on majority has no meaning.
A qualifying note: random picking from one hundred prisoners and restoring the 99% probability
A case is presented in which a police officer randomly chooses one prisoner out of a hundred and brings him first to trial, and then the chance that the chosen prisoner belongs to the ninety-nine really does come out to 99%, because genuine random “picking” has been created. It is argued that the earlier explanations are not sufficient when the situation is formulated this way, because here one gets a real probability and still no one convicts on the basis of the statistical fact. A distinction is then drawn between a situation in which a prisoner is caught because he happened to remain or was caught for a non-random reason, in which case there is no justification for assuming this is a random sample because there may be correlation between the reason for capture and guilt. An image is brought of a “lottery” that does not look fair, and there is a hint to the “ship paradox,” where the question arises whether force or natural circumstances that determine who is thrown into the sea count as a lottery.
Doubt involving one piece versus doubt involving one of two pieces as a third explanation
A halakhic distinction is brought between doubt involving one piece, where there is one piece that is possibly forbidden fat and possibly permitted fat and one does not bring a provisional guilt offering, and doubt involving one of two pieces, where it is known that one is forbidden fat and one is permitted fat but it is not known which is which, and there one does bring a provisional guilt offering. It is argued that in the one-piece case there is not really “fifty-fifty” as probabilistic knowledge, but rather a working assumption arising from ignorance, similar to betting on a coin when one has no information whether it is fair, whereas in the two-piece case there is real knowledge about the composition of the mixture, so the fifty-fifty is a fact. The distinction is applied to the difference between eyewitness testimony and the prisoners case: with eyewitnesses there is a chance of error, but there is no certainty that there is “an innocent person in the mixture” right before our eyes, whereas with the prisoners it is known with certainty that there is one innocent among the hundred, and therefore one cannot “nullify the minority” when it is known to be right here. The argument is that the gap lies not in the percentages themselves but in the question whether the minority is certainly present within the mixture, or only a statistical possibility that will materialize on average over many cases.
Public examples: a hostage deal, a flashlight inside the swallowing cavity on the Sabbath, and the Entebbe operation
An argument is presented against a hostage deal, according to which saving a certain number now will on average cause a larger number of deaths in the future, and the speaker rejects that argument as statistical expectation that is not equivalent to placing “concrete dead people” before our eyes. He suggests a formulation in which the deal imposes on each person a very small future risk, and such a risk can be taken in order to save definite lives now, even though by the law of large numbers many are expected to be harmed. A ruling by Rabbi Mordechai Eliyahu is brought, permitting one to turn on a flashlight on the Sabbath in order to check a weapon inside the swallowing cavity, even though the risk in each individual case is very small, because in a large public and over many events this accumulates into a meaningful doubt of danger to life, while emphasizing that in the laws of the Sabbath even a doubt involving danger to life overrides the Sabbath when it is significant enough. The story is also brought about Rabbi Shach regarding the Entebbe operation: according to him, success after the fact does not prove that the initial judgment was reasonable if the probability of failure had been high, and the decision must be evaluated according to the information available at the time, not by the outcome.
Risk, public responsibility, and the distinction between certain risk and a suicide mission
It is argued that there is a difference between requiring a soldier to take a risk in war and ordering him on a mission of certain suicide, and the case of Mitla is brought, where a volunteer was asked to drive in a way that exposed firing positions. The distinction is presented as a principle according to which one may require a person to bear future risk as part of a social system of sharing risks, but there is no legitimacy in imposing certain death on him even for the public good. The discussion compares this to thinking in terms of statistical expectation, where people “will certainly” be harmed in the aggregate, yet refuses to translate that into a decision that treats those future harms as if they were concrete present harms. In conclusion it is said that consequentialist accounting is not necessarily the only consideration, and that there are additional value-based considerations, but the examples are brought in order to clarify the principled distinctions between probability about a group and making a determination about an individual.
Full Transcript
[Rabbi Michael Abraham] Okay,
[Speaker B] In the last few
[Rabbi Michael Abraham] times we dealt with statistical evidence in law, and the case through which we approached this issue was the prisoners case, right? A hundred prisoners in the prison yard, ninety-nine of them attack the guard and kill him, and now we put them on trial. Each one who stands trial, apparently, has a ninety-nine percent chance of having participated in the act, and nevertheless it is accepted in all legal systems that you do not convict in such a situation. By contrast, if two witnesses come and say that so-and-so murdered so-and-so, and there is some chance that the witnesses did not see well and missed something, or that what they say is wrong for various reasons, and still let’s say it’s ninety-five percent, we still convict on the basis of eyewitness testimony. That means conviction is not based on the probability, not only on the probability that I’m right. In other words, the probability that I’m right by itself is still not enough. Something else is required, and that is what is called the issue of statistical evidence. Meaning, if the evidence comes from witnesses, that is direct evidence: the witnesses saw you murder. True, it may be that they didn’t see well, but the evidence is direct evidence. With the prisoners there is no direct evidence at all that you participated in the act; we have statistical evidence, meaning ninety-nine out of a hundred participated in the act, so apparently there is a ninety-nine percent chance that you too participated in the act. But that is not direct evidence about you; it is circumstantial evidence. We saw halakhic examples of this from Maimonides, yes, with the fellow who saw a pursuer enter a ruin with a knife, and afterward went in after him and saw the victim bleeding and that fellow holding a blood-dripping knife in his hand, with nobody else around, no additional entrance, nothing—and still, according to Maimonides, we do not convict. We do not convict because the evidence is circumstantial evidence. And I explained that circumstantial evidence is not accepted in a trial involving the death penalty—yes, in a criminal trial one could say this more or less—but not because of the quality of the evidence, meaning not because of the probability that I might be mistaken. Circumstantial evidence is not necessarily weaker than direct evidence; it is a different kind of evidence, and here, according to Maimonides, the problem is a problem of type and not of the quality of the evidence. Meaning, circumstantial evidence is not accepted by virtue of being circumstantial, regardless for the moment of how likely it is to be correct or incorrect. So at the end of last time I proposed a first explanation for this difference, and I said that I made a distinction between rov de-ita kaman and rov de-leita kaman, and I claimed that rov de-ita kaman is basically not really a probabilistic majority. It is not probabilistic because I don’t have some information by virtue of which—say, in the case of stores, where I have nine kosher stores in town and one non-kosher one, and I found a piece of meat—I don’t really have a ninety-percent distribution of the chances that this piece came from a kosher store. I am ignorant; I don’t know. Since I don’t know and there are ten stores, I assume the chance for each one is equal, and therefore I reach the conclusion that it’s ninety percent. By contrast, rov de-leita kaman is basically a generalization from a sample, which is understood the way it is in scientific contexts. It is seen as positive knowledge—not ignorance, but the result of positive knowledge, admittedly from a representative sample and not from all reality, and that is why there is a generalization here, but it begins from information, observations, knowledge, and so on. Therefore rov de-leita kaman is a probabilistic majority. And the claim—my claim—was that in the prisoners case we are dealing with rov de-ita kaman. True, we are dealing with a hundred prisoners standing before us, ninety-nine of whom participated in the act and one did not, so the ninety-nine to one distribution is not the result of the nature of the world; it is not some law of nature that ninety-nine percent of all people are murderers. Rather, in this specific case I know that ninety-nine out of the hundred participated, and therefore in this specific case I assume that the chance for each one is ninety-nine percent. In that sense it is exactly similar to the case of the stores, the piece of meat and the stores, because the majority under discussion is rov de-ita kaman. And I said that if rov de-ita kaman is really not a probabilistic majority at all, but some sort of working assumption born of ignorance, then in such a situation the claim is that I cannot convict. And I noted that at first glance this looks like a legal explanation and not a probabilistic one—you remember we spoke about several possible types of explanation? But on further consideration you can definitely see a probabilistic aspect or explanation here as well, because the claim is that it really is not ninety-nine percent. It really is not ninety-nine percent. The fact that I assume it is ninety-nine percent is merely a working assumption, and it is not really the result of knowledge that there is a ninety-nine percent chance that he murdered or participated in the murder. And therefore, yes, so that was the first explanation.
The second explanation I want to propose—we spoke about this last time—the second explanation I want to propose is, maybe here I should already make some qualified remark—no, let’s leave the remark for another moment, I’ll get to it. A qualifying remark, not a qualified one. The second explanation is, apparently, a legal explanation and not a probabilistic one. If the first is probabilistic, the second is legal. I remind you of the topic we saw a few lectures ago about “we do not follow the majority in monetary matters.” And there we saw, yes, Nachmanides on wedding gifts, or “most oxen are for plowing”—most people who buy an ox buy it for plowing, not for slaughter. And the dispute between Rav and Shmuel, and in Jewish law we rule that we do not follow the majority in monetary matters. Meaning, even if most people buy an ox for plowing and not for slaughter, he cannot claim by virtue of that majority that he bought it for plowing, or that the other person sold it to him for plowing. The other person says, no, I sold it for slaughter. Why not? So we saw that Rabbi Shimon Shkop explains that when we are talking about an event that is not random, an event that is the result of human decision—someone decides whether he wants to buy an ox for plowing or an ox for slaughter—in such a situation it is incorrect to go by a distribution. Meaning, even if in the world ninety percent of people who buy an ox buy it for plowing and only ten percent buy it for slaughter, I can always claim that I belong to the ten percent who bought the ox for slaughter. Or, I sold the ox for slaughter. Why? Because there are such people, and I claim that I am one of them. Meaning, there is nothing random here.
I want to compare this to my previous argument and say that when a piece of meat falls from the stores, the process is random. The piece of meat fell unintentionally, and that happened. Therefore there is room there to talk about using the distribution. Meaning, I want to know the chance that it came from a kosher store—say ninety percent. So earlier we saw that this ninety percent is a working assumption and not a distribution, but the case itself really happened in a random way. Meaning, a piece fell; it was not a person’s decision to lose a piece. The question whether the distribution is relevant or not relevant—whether it represents positive knowledge or only ignorance, a working assumption born of ignorance—that we discussed in the previous explanation. But in terms of the case itself, it is a random case. Therefore, if there were a distribution, then certainly one should use the distribution to analyze this case. By contrast, in the case of selling an ox for slaughter or for plowing, in that situation the person decides that he wants an ox for slaughter. So what do you tell him—that most people decide they want an ox for plowing? So what? I want an ox for slaughter. What kind of claim is that—that I’m lying because I say I bought this ox for slaughter? What do you mean? After all, ten percent of people buy an ox for slaughter, and I claim that I am one of those ten percent.
Again, if someone had taken me randomly out of a thousand people and asked himself, tell me, are you one of those who buy oxen for plowing or one of those who buy oxen for slaughter? Which are you? Okay? Then I would say there is a ten percent chance he is one of those who buy an ox for slaughter and a ninety percent chance he is one of those who buy an ox for plowing. Why? Because the picking—when I took him from the group—really was a random process. I didn’t know whom I was drawing; I drew someone randomly. Then, if the distribution is ninety-ten, I can assume that the chance that I drew someone from the majority group is ninety percent. Because the act I performed was random. But here it is not like that. I did not take a random person from the group of people in the city—say that in this city people are distributed such that ninety percent buy oxen for plowing and ten percent buy oxen for slaughter. So if I had just pulled a random person out of the city and asked myself to which of the two groups he belongs, then it would be reasonable to say that there is a 90% chance that he belongs to the group that buys an ox for plowing and not for slaughter. But here I did not—there was no such situation of picking, right? I did not randomly pull a person from the group of people in the city. Rather, what happened is that a case occurred, a legal dispute arose, the two people came before me, and now the person claims: what do you want from me? I belong to the group that buys an ox for slaughter and not for plowing. There is such a group, after all. Ten percent of the people in this city are like that. Why do you claim that I am not one of those people? After all, the choice is in my hands; I decided that I am buying an ox for slaughter. This was not a random act of drawing someone from the population. Once it is not a random act, there is no point in referring to distributions.
Yes, I remind you again of the example that accompanied us in the previous sessions. Suppose there is an urn full of balls, and inside it there are ninety-nine white balls and one red ball. Now the person puts his hand into the urn and blindly pulls out a ball, so the chance that he will pull out a white ball is ninety-nine percent, okay? Now a different case: the person puts his hand into the urn but he is looking. He has to choose a ball. He sees which ball he is taking. And now I ask: what is the chance that he will take a white ball? The answer is fifty percent, even though there are ninety-nine white balls and one red one. Why? Because if he likes white, then he will take a white ball; if he likes red, then what does it matter that there is only one red ball? He will look for it and take it. Therefore the distribution is not relevant to the question which ball will come out; the question I should ask is: which color does he like? But which color he likes is either white or red. If I don’t know, then it’s fifty-fifty. Assuming he likes white, he will take white; assuming he likes red, he will take red. So what difference does it make to me that there are ninety-nine white balls and one red ball in the urn? It is relevant only where I am doing random picking, taking out some ball without looking. Fine—if it was without looking, random, then apparently the chance is, for our purposes, equal, and there is a ninety-nine percent chance it will be a white ball and a one percent chance it will be a red ball, because the chance of taking any one of the balls is equal for the sake of discussion. But all that is only when I take a ball at random. If I choose the ball, you can’t say to me: look, I’m saying I took one out and now I claim that I took a red ball—I’m hiding it and not showing you—do you assume that I’m lying because after all there is a ninety-nine percent chance that the ball I took is white? No, of course not. After all, I took out a red ball because I like red. So there is no reason to assume that I’m lying even if you don’t see the color of the ball. If I tell you that I took out a red ball, then probably I took out a red ball—what’s the problem? Because I chose it. There is no random process here, and therefore there is no reason to refer to distributions.
Yes, I remind you of the story from the beginning of the series, more or less, about Rabbi Yonatan Eybeschutz, when the priest came to him and said: why don’t you follow us, after all we Christians are the majority, we are the majority, and it says in the Torah, “follow the majority.” So Rabbi Yonatan Eybeschutz said to him: I follow the majority where I am in doubt. If I’m not in doubt, I don’t follow the majority. In a place where I don’t know, it may be that I would go after the majority, and the majority are Christians. But if I have a clear position that Judaism seems correct to me, then what do I care that most people think otherwise? Meaning, the laws of majority were created for someone who is in doubt. If you are in doubt, go after the majority. If you are not in doubt, I have no need of the laws of majority. The law of majority is guidance for what to do when I don’t know. But if I do know, then what difference does it make? Yes, like I said about the piece of meat found in the market where there are ten kosher stores and one non-kosher one, but this piece of meat has a kosher seal on it. Now I found the piece of meat—nine non-kosher and one kosher store? No, let me put it properly: nine non-kosher and one kosher store in the city, and now I ask whether I should assume that this piece is non-kosher because there are nine non-kosher stores out of ten in the city. Of course not. Why not? Because I know that the piece is kosher—there is a seal. If I didn’t know, it would be a random matter and I would follow the distribution: ninety percent non-kosher stores, apparently this piece is non-kosher, ninety percent that it is non-kosher. But if it has a seal on it, then I am not in doubt, and if I’m not in doubt, why should I follow the majority? The law of following the majority was said in a case of doubt.
So something like that I want to say here as well. Meaning, the laws of doubts or probabilities were said about events that happen randomly. But events that occur intentionally, deliberately, by human decision—there there is no point in discussing them according to distributions. What the person decided is what he will do, assuming he is able to do what he decides. Okay? And we already spoke about the fact that in psychology and in human decisions we nevertheless do use statistics, and the question is how that fits with what I said here, but those are matters we already discussed in previous lectures.
I return to our discussion, yes, about the prisoners—how to explain the fact that we do not follow statistical evidence. So basically the claim I want to make is that if a prisoner stands before me and I now want to judge him, and I have statistical evidence against him—ninety-nine prisoners out of a hundred attacked and one prisoner did not attack—then apparently there is a ninety-nine percent chance that he is guilty. But since we are dealing here with a deliberate decision—he either decided to attack or he decided not to attack—where we are talking about a deliberate human decision, I don’t care that ninety-nine out of a hundred people decided to attack. He claims that he is the one who decided not to attack. And of course every one of them claims that. We are not talking about one particular person; each of them can claim that he is the one who decided not to attack. So you cannot decide about me by virtue of the majority of the ninety-nine. Now it is clear that if they all claim that, then ninety-nine of them are lying. All true. But you cannot come with complaints against any one of them, because each one says: what do you want from me? I’m the one who is telling the truth. So there is no way to convict any one of them. There is no way to convict any one of them because the probability—even though there is a probability of ninety-nine, as if there is a ninety-nine percent chance—but the event we are dealing with is not a random event. If it is not a random event, then there is no point in referring to chances and distributions, exactly as we saw regarding wedding gifts or the ox for slaughter and plowing.
Now, what is this explanation—a legal explanation or a probabilistic one? Apparently, from a probabilistic point of view the chance is still one in a hundred. So perhaps the explanation is legal and not probabilistic. But that is not right, or at least not necessary. As I said in the previous explanation, my claim is that there really is no ninety-nine percent chance that I’m guilty. There is no ninety-nine percent chance that I’m guilty, because if it is an act I chose to do, not a random act, an act that I chose to do, then it cannot be judged according to a distribution. So therefore it is really not true that there is a ninety-nine percent chance that I am guilty. It is true that after I judge all the prisoners, then in ninety-nine out of a hundred I probably made a mistake if I acquit them all. That is true. But with each prisoner separately, when I judge him, I really cannot say that there is a ninety-nine percent chance that he is guilty. That is simply not true, since this is an act, a deliberate decision and not a random decision. In a deliberate decision there is no point in judging by the distribution.
Now notice: this explanation now, after I made this correction, is actually quite similar to the previous explanation. It basically says: listen, you don’t really have a ninety-nine percent distribution that he is guilty. But the previous explanation tied that to the fact that this is rov de-ita kaman and not rov de-leita kaman, while now I am tying it to the fact that this is a deliberate decision and not a random process. So the bottom line is similar, but the reason why I claim there is no probability here is different. Before I said it was because it is rov de-ita kaman, and here I am saying it is because this is a deliberate act. So in the end these are different explanations even though they end up sounding similar. But I do want to make one remark nonetheless, and here this is the remark I intended to make earlier—a remark on both kinds of explanation.
[Speaker C] Sorry, Rabbi, sorry Rabbi, before—if I can add something. Can you hear me? Sorry, if possible, before—if I can interrupt you. Yes. But here it is very, very different, because true, it comes from initiative and therefore we do not count the principle of distributions. But when each and every prisoner says, I am the one who was not among the ninety-nine, anyone who says that is undermined by the other one who says the same thing.
[Rabbi Michael Abraham] Right, and you can’t choose whom to convict.
[Speaker C] Yes, so I want to say that this brings us back to a more legal argument than a probabilistic one. Because when you say about the box with a hundred balls, and I see what I choose, fine, then you don’t apply distributions. When I bought an ox—and by the way I wanted to ask you—that’s exactly the same argument as fixed location and something taken from it.
[Rabbi Michael Abraham] That was in the previous lecture. There is indeed a similarity to the difference between fixed location and separation.
[Speaker C] Yes, and I also wanted to say that the same argument to explain fixed location that you gave explains the fact that we don’t—okay, what I want to say is that when there are a hundred, there are ninety-nine people who all attacked the guard.
[Rabbi Michael Abraham] Yes, I understand, but I’ll tell you—the point is, and this is also a point we discussed in one of the previous lectures, you are right that after I have finished judging all one hundred prisoners, and let’s say I acquitted them all, yes? Now clearly ninety-nine percent of them are guilty, I acquitted them for nothing. So in that sense you are right that ninety-nine percent of the prisoners were acquitted not despite wrongdoing—well, of course, despite wrongdoing. Meaning, there are ninety-nine percent for whom I was mistaken. But I still insist on saying that in each specific trial, with a particular prisoner standing here before the court, it is really true that there is no ninety-nine percent. It is not true that there is a ninety-nine percent chance that he is guilty. That is simply not true. Probabilistically, it is not true.
And I spoke about this one of the previous times, when I spoke about the difference between using psychological statistics and the fact that with intentional actions we do not work with statistics. I said there that psychology’s statistics say nothing about the individual person. Meaning, they tell me what the distribution in the group as a whole will be. So in the group as a whole I know that if they are frustrated, then they will react more violently than the group that is not frustrated. Okay? But for the individual person, assuming he is frustrated, I cannot say that now there is a ninety percent chance that he will be violent. No. Because it is his decision whether to be violent or not. You are right that overall some distribution is formed across the whole group—that I discussed there. And now I am answering you the same way here. Here too, when a particular prisoner comes before me and now stands trial, it is not true to say that there is a ninety-nine percent chance that he is guilty. It simply is not true. You are right that after I look at one hundred prisoners, obviously ninety-nine of them are guilty. Yes, that is true. But how that is distributed—that is, who is the one and who is not—it is not true that the chance of each of the hundred being the one innocent person is the same. No, because I, for example, am righteous, so therefore, let’s say—yes, in my character I am righteous—so there is a greater chance that I am the one who did not participate, while the others are wild people, and therefore it is less likely that they did not participate. So you decide that the one percent who is innocent is divided equally among all the souls. And here you are moving from a distribution over the group as a whole to a claim about the individual person standing before us here for judgment. And I say that this move must not be made. Because the individual person…
[Speaker D] Fine, but here for each one it’s fifty-fifty. What?
[Rabbi Michael Abraham] Each and every one… let’s not exaggerate. I wouldn’t say it’s fifty-fifty, but I can’t say it’s ninety-nine. Meaning, I don’t know.
[Speaker D] No, from the judge’s point of view, when he looks at the person, he says either liable or not, either guilty or not.
[Rabbi Michael Abraham] No, obviously there are two possibilities, but that does not mean the two possibilities carry equal weight. I don’t know. This is ignorance; I don’t know what to say about it. But it is certainly not ninety-nine percent. Okay? So that is actually the claim. Now I…
[Speaker E] Under what halakhic definition does this fall?
[Rabbi Michael Abraham] What? I can’t hear.
[Speaker E] Does this fall under some halakhic definition? Is it…
[Rabbi Michael Abraham] What am I claiming? That here we do not follow the majority, just as we do not follow the majority in monetary matters. Because an act that is the result of a person’s decision is not judged according to the majority.
[Speaker E] I’m asking whether there is some halakhic source for this, like in the Talmud or…
[Rabbi Michael Abraham] The halakhic source is that we do not follow the majority in monetary matters, according to Rabbi Shimon Shkop. But yes, why not? Call it reasoning. If that is the reasoning, that is what I say even without a source. Here, now there is a halakhic source—I said it. If I write it down, then there will be a halakhic source.
[Speaker D] No, but here we’re talking about lives, not money. What? Here we’re talking about life and death. Doesn’t matter.
[Rabbi Michael Abraham] According to Rabbi Shimon Shkop’s explanation, it has nothing to do with money at all.
[Speaker D] No, I understand,
[Rabbi Michael Abraham] The point is that this is a type of majority that we do not follow, because it concerns a person’s free choice. It is not specifically about money. He claims the difference is between types of majority, not between monetary matters and something else—that is his whole argument.
[Speaker D] No, why don’t they say that in capital law too? Say that it’s…
[Rabbi Michael Abraham] Here I am saying it in capital law too. If there is a case of this type, if there is a case of the type of “most are for plowing,” then in capital matters too it would be the same, and in monetary matters too, and in everything else.
[Speaker D] The Talmud says monetary matters, monetary matters, monetary matters. This isn’t monetary matters; it’s a court in general.
[Rabbi Michael Abraham] That’s exactly what I’m saying. Rabbi Shimon Shkop claims that the fact that we do not follow the majority in monetary matters is not a rule about monetary law; it is simply that the majority in question is a kind of majority that one does not follow. If there were such a majority in capital cases, one would not follow it there either. It is simply a pathological majority, because the event is
[Speaker D] not
[Rabbi Michael Abraham] a random event; it is an event that is a person’s decision. So this is actually a mistaken formulation.
[Speaker E] I didn’t understand. It is a mistaken formulation to say
[Rabbi Michael Abraham] that we do not follow the majority in monetary matters. Correct. That “we do not follow the majority in monetary matters” means that in these monetary topics we do not follow the majority because the majority is something else. Yes, that is the claim. Just so I understand—if I may ask—this is of course not agreed upon. There is a dispute about this among Tosafot, and also between Tosafot in Bava Kamma and Tosafot in Sanhedrin, but even Rabbi Shimon’s explanation of Tosafot in Sanhedrin is only Rabbi Shimon’s explanation. Meaning, I’m not saying I have here some solid halakhic foundation. But I claim that I don’t need a solid halakhic foundation. It is a matter of reasoning.
[Speaker D] But the reasoning is strong. Both in a religious court and in a civil court they won’t convict a person.
[Rabbi Michael Abraham] I think so, yes, it seems to me. Now we’ll still get to what happens with people who don’t understand this reasoning. I’ll comment on that later, in a moment. I just want to note. Yes?
[Speaker G] Just so we understand in general, both in separation and in fixed location, regardless—what exactly does it mean about a person, what does it mean when we say about a person that he is 99% guilty or 99% innocent? What does that 99% mean? I didn’t understand the question. I mean, I think the definition of, say, when I say about someone that he is 99% guilty, is that if one hundred cases exactly similar to this case came before me, 99% of them…
[Rabbi Michael Abraham] That is exactly what not. So what is the definition?
[Speaker G] Exactly. So what is the definition, then?
[Rabbi Michael Abraham] That’s the answer I gave earlier: it is not correct to infer from a distribution in a group of people to a distribution about a single individual. In a place where you do say there is 99% about the individual, then that will also be the distribution among one hundred people—ninety-nine out of the hundred will be like this and one will be otherwise. But the reverse is not true. Meaning, if you tell me that in a group of people ninety-nine percent will be such-and-such and one percent otherwise, that still does not mean that for each individual person there is a ninety-nine percent chance. Because you would have to assume that all the people have equal standing in that group, and that is not true.
[Speaker G] Okay. So when I say in separation, for example, where there I do say that I can say that there is a 99% chance the person is guilty, say, or a 90% chance the meat came from a kosher store—what does that 90% mean?
[Rabbi Michael Abraham] No, that has nothing to do with separation at all. What does that have to do with separation? Separation is an act done randomly. An act done randomly—I follow the distribution. The piece of meat that separated, separated randomly. It was not a person’s decision. Because of that I follow the distribution. In the case of rov de-ita kaman, by the way, I claim that there too there is no distribution, but that is another argument. But I am saying that if there were a distribution, then here there would be room to apply it, because this is a random event. But a person’s decision is not a random event, so even if there were a distribution I would not follow it. Interesting. And when there is a random distribution,
[Speaker G] then I say—when there is a random distribution, I say about this piece that there is a 90% chance it is kosher? Yes?
[Rabbi Michael Abraham] I’m not… that 90% is not correct. In rov de-ita kaman there aren’t really percentages, but it’s a working assumption. Most likely, let’s say. What does it mean, most likely it is kosher? Again, in rov de-ita kaman, with a piece that separated randomly… no, no, I’ll explain again. No. In rov de-ita kaman I claimed that it is not correct that this is a probabilistic distribution. Not correct. It is a working assumption that I treat as if there were 90% here, but since this is a random case, then once there is a distribution or a working assumption, it doesn’t matter—I use it in order to judge the case before me, because it is a random case. But if the case is not random, I do not judge it by a distribution, whether there is a distribution or not, because it is not relevant.
[Speaker D] If it’s not random, then it’s not a doubt.
[Rabbi Michael Abraham] Exactly. The example of someone who is not in doubt—exactly.
[Speaker D] Right, so it’s not…
[Rabbi Michael Abraham] The discussion will be completely different.
[Speaker G] Okay, and when the piece did separate, why do I actually say that it is kosher, that it is most likely kosher?
[Rabbi Michael Abraham] Because what? Because it came from such a group?
[Speaker G] I’m saying, there is
[Rabbi Michael Abraham] a working assumption—that is rov de-ita kaman, that is the novelty of rov de-ita kaman: there is a working assumption that if you have ten possibilities and you are in complete ignorance about them, behind a veil of ignorance, yes? You are in complete ignorance regarding the ten possibilities, then you assign them all equal probability. That is an assumption. But there is no real basis of knowledge in that. It is the result of lack of knowledge, of ignorance. Therefore I claim it is a working assumption, not a distribution.
[Speaker D] But that is how Jewish law is actually ruled in practice.
[Rabbi Michael Abraham] Correct, and that is the novelty we learned from “follow the majority,” in rov de-ita kaman. But I am saying that even after that novelty, whether I apply a distribution or a working assumption that I rely on as if it were a distribution, all that is relevant to cases that are random cases. But if it is something that is the result of a decision, then neither rov de-ita kaman nor rov de-leita kaman nor anything of the sort is relevant. It is simply that distributions, whether they exist or not, I do not apply them to something
[Speaker I] where it’s a person’s decision, not a random event. I just want to make one qualifying remark now about the two explanations I’ve given so far. I can present this in a certain way, in a form that is probabilistic after all—not that it is probabilistic in itself, but that on the probabilistic level it really is ninety-nine percent. Why? Let’s think about the prisoners. Say I now do something like this: the hundred prisoners are standing in line for the courthouse, and now a police officer, or whoever brings them into the courthouse, chooses someone at random from those hundred and brings him in to be tried; he is first. After that he chooses another one, brings him in to be tried; he is second, and so on. If I now do a random picking of a person from the hundred people standing at the entrance to the courthouse, what is the chance that I’m holding a murderer in my hand? Here it really is ninety-nine percent, right? Yes. Because the event is a random event. That is, now there is picking, right? It’s not a person who came before me in judgment—I don’t know how he got here—but a person is standing before me in judgment. Now I ask: what is the chance that he murdered? I say: here there is no distribution, because whether he murdered or did not murder is his decision. There are ninety-nine who murdered and one who did not, that’s true, but with respect to the individual person, since this is an act of decision and not a random event, I do not apply the distribution to it, because there is no picking event here at all; it is simply an act of decision. But I can present this situation as a situation in which there is picking. If I now, as I said, take a random person from the hundred people, pull out some person—just like that, you’re first in line, go stand before the judge. Okay? Now the judge says to himself: wait a second, I pulled one person from a group of a hundred, and in that group of a hundred there are ninety-nine murderers and one innocent person; I pulled one person at random, and now I ask: what is the chance that I’m holding a murderer? Here it already is ninety-nine percent, right? Because I pulled him at random; here there already is picking. Okay.
[Rabbi Michael Abraham] Very much so. Here there’s already picking going on, okay? So in that case I can no longer say that this is a probabilistic explanation, because here there’s a ninety-nine percent chance. And then I can say, fine, maybe we need some kind of legal explanation, but the probabilistic explanation I suggested isn’t correct. The probabilistic explanation I suggested is correct if there is a person standing before me—say all the prisoners escaped from the prison, and now I caught one, just one, while all the others scattered in every direction. I caught one prisoner and I bring him to trial, okay? When I bring him to trial and now I want to convict him, I can’t convict him, because it’s not true that the probability that he murdered is ninety-nine percent. Why? Because I’m judging a particular person, and I’m asking whether this person chose to murder or chose not to murder. Since this is an act of choice, not random picking, I can’t apply the distributions. But if the case is that all one hundred are standing here, and now I randomly pull one out of the hundred, when I ask myself what the probability is that this one murdered, that really is ninety-nine percent. Here it’s already clear that there is a probabilistic chance of ninety-nine percent. And still, that isn’t enough. What is he hearing? And still that isn’t enough to convict. No, I know it isn’t enough, but—right, that is, de facto we do not convict in such a case. But the question is why. In other words, the explanation I’ve given so far is not enough to explain this. Apparently because of that same effect you have, say, in trolley experiments, where even with the same probabilities of death for a certain number of people and saving a certain number of people, there are things the instinct allows and things the instinct doesn’t allow, regardless of how many people you save versus how many people you kill. Here too, maybe in those same… instinct is all very nice, but I’m looking for justifications, not instincts. Instincts are a description of a psychological state; I’m asking a philosophical question, not a psychological one. I’m not asking what a person will do, I’m asking what ought to be done. Why is that psychology? It’s mathematical altogether. What do you mean? No, the question is, you can use mathematics, but you have to give it some kind of status, and the status of mathematics is a philosophical claim. In other words, if the chance is ninety-nine percent, I convict. The fact that it’s ninety-nine percent is a mathematical calculation, but the fact that we convict when it’s ninety-nine percent is a philosophical claim. Okay? Okay. So the claim, ultimately, is that if I treat this as random selection, as picking a person out of the group of one hundred, then the previous explanations won’t help me. I need to look for an additional explanation, or say that in such a case we really would convict. But if we assume that we do not convict in such a case, then I need to look for another explanation. So I’ll suggest one more explanation. Excuse me, Rabbi, excuse me, Rabbi, I didn’t understand the difference at all—if all one hundred escaped and you only catch one, then here we’re talking about judging him, so you can’t accuse him, you can’t say. Because the case where ninety-nine escaped and one remained—the one who remained is not a random selection of one person out of a hundred. There wasn’t someone here who pulled this one out and extracted him from the group of one hundred. It could be that he stayed here precisely because he was innocent and wasn’t afraid, so he didn’t run. I don’t know—there was no random selection of a person here. One person remained here, but the result that one person is here is not the result of some random picking, but the result of something else, and I don’t know how that something else operates. Therefore I can’t know whether it’s ninety-nine percent or not. In the case where I pull out a person, all one hundred are standing here in the room before me, and now I say, you standing over there, come with me, we’re going to the judge—I chose a person randomly. Here there’s a ninety-nine percent chance he is a murderer. Yes, I would say the same thing about the case where in the end I happened to succeed in catching this prisoner. No, but it isn’t by chance that you succeeded in catching him. Who says it was by chance? You didn’t have a choice whom to catch, right? It’s not that you had a choice whom to catch and then chose to chase after him. If that were the case, you’d be right, because that would be like taking one out of the hundred. But here I’m saying ninety-nine escaped and only he remained; he just stayed there in the room, he didn’t run. Yes, yes, what I meant was that even about the fact that I caught him, okay, I caught this one—but even about him I have to ask the same question: what is the chance that the one I caught is one of the murderers? And here I have no way to answer that. It could be that he stayed here because he was innocent and therefore wasn’t afraid, so he stayed here—so what’s the chance he’s one of the murderers? Zero. Because the fact that he stayed here is because he didn’t murder. I’m just throwing out a possibility. I’m saying: you can’t know. In other words, in the case where I pull someone out, all one hundred are there; I could have taken any of the hundred, and I chose one of them randomly, so the chance is one out of a hundred. Right? Because I had the possibility of choosing all of them, and I chose one out of the hundred. But here the selection of the one out of the hundred wasn’t made by a process of picking. He decided not to run; he stayed here. And why not treat that as picking? What, because… why should that be picking? There wasn’t any picking here. By the way, this connects to an issue we’ll talk about later, about the ship—the ship paradox, a ship that sailed from Brighton, I think, from England to the United States. I once wrote a column about it; we’ll talk about it later in this series. This is exactly the point. I mean, there, yes, maybe I’ll say it already here, if I remember correctly—I need to reconstruct it. Say there are people, a ship sank, and the passengers got onto a lifeboat. Now there are one hundred people on this boat, and the boat can’t carry them all; they’ll all drown. So what do you do? You need to draw lots. Draw lots to decide which ten we throw overboard, yes, like Jonah the prophet. Which ten we throw into the sea, because the boat can carry only ninety. Now instead of that, one person comes and says: I’m throwing ten people into the sea by force, and that’s my lottery. Now that sounds unfair to us, right? That’s not a fair lottery. Hold a lottery and let’s see which ten get thrown into the sea. He says: what do you want? The lottery is that I’m a bully and they aren’t bullies. Nature held a lottery: it made me a bully, or more of a bully than they are, and therefore I succeed in throwing them out and they don’t succeed in throwing me out. That’s also a lottery. What difference does it make that nature held the lottery and we didn’t do it here by throwing dice? That is basically the question. Do you see that it’s the same question as what we’re talking about here? Because the question is whether every time someone remains here and everyone else runs away, that’s like a lottery—a lottery that nature ran, not a person. No, that’s not correct. Because behind it… we’ll also discuss there why it’s not correct, but here too I’m saying: the fact that you remained here may have many reasons. It’s not a random selection of the one who remained while everyone else ran away. It’s not that there was someone here who held a lottery and decided you’ll stay and everyone else will run. Rather, you decided, for some reason, to remain. That’s not the same as my taking one person out of the hundred and deciding to take him. That’s picking. Okay. Rabbi, suppose you phrase it this way, that part stayed—if the hundred had fled, and the one you happened to catch, not that he remained on his own, but the one you succeeded in catching was one of the hundred. I still wouldn’t say that. Because it could be that he ran slowly because… that’s why I succeeded in catching him. So what? He ran slowly, and because of that he also didn’t take part in the murder—he isn’t as much of a bully and athlete as the others, so he didn’t take part in the murder. I can offer you lots of explanations. Therefore, once there are explanations, you can no longer assume that the distribution will hold. But when I choose a person—just like that, I chose a person, I could have chosen any other and with my eyes closed I chose one person—there the chance is one out of a hundred. That’s obvious, because there’s a process of random picking here. We need to be precise: really, the definition of something that is not picking is if I know there’s no correlation between the reason that particular one came into my hands and the producing mechanism. The opposite. If I don’t know that there is a correlation, not if I know there isn’t. No, but if I know there isn’t, that’s picking. That’s obvious. If I know there isn’t, then it’s not picking. If I know there’s no correlation, then you can’t know anything. If I know there is a correlation, then it’s picking. But if I don’t know whether there is or isn’t a correlation, then even then I can’t judge him. From the possibility that there is a correlation—that’s exactly my worry here. Okay, so I want to offer a third explanation, and this third explanation—I’ll start maybe from a halakhic / of Jewish law difference. In Jewish law there are two kinds of doubts. A doubt involving one piece, and a doubt involving one piece out of two pieces, yes? This is called a fixed prohibition and not a fixed prohibition, an established prohibition—sometimes they call it this, sometimes that. I have a piece of meat in front of me and I don’t know whether it is forbidden fat or permitted fat. Permitted fat may be eaten—what is it? Wait, just a second, I see something here, I thought someone was waiting in the room. Fine. So there is a piece before me that is possibly forbidden fat, possibly permitted fat, and the question is whether I may eat it. So I’m in doubt; since I’m in doubt, a Torah-level doubt is treated stringently, and I’m forbidden to eat it. If I ate it, I violated the prohibition of doubt. So I violated a prohibition, but for such a prohibition I do not bring a provisional guilt-offering. Why? Because this is a doubt involving one piece. But what happens in another kind of doubt? I have two pieces before me; I know one is forbidden fat and one is permitted fat, but I don’t know which is the forbidden fat and which is the permitted fat. Again, I’m forbidden to eat either one of them, right? Because there’s a fifty percent chance that I’d be eating the forbidden fat. So I’m forbidden to eat either one of them. I took one and ate it. Again, I violated—there’s a fifty percent chance I violated a prohibition. But if I violated that prohibition, I do bring a provisional guilt-offering. Why? Because it’s a doubt of one piece out of two pieces, not of one piece. Okay, so there is a difference here: in both cases a Torah-level doubt is treated stringently, in both cases it’s fifty-fifty, and still regarding the provisional guilt-offering, in a case of one piece you do not bring a provisional guilt-offering, and in a case of one piece out of two pieces you do. But the second case is a double doubt. Why? Because you have a doubt whether it’s either this piece or that piece, and the second doubt is whether it’s permitted fat or forbidden fat. No, no, what are you talking about? It’s the same doubt—what do you mean? I have a doubt whether it’s forbidden fat or permitted fat; what is this about this piece or that piece? I took a piece, and my doubt is whether it was forbidden fat or permitted fat—only one doubt. Oh, I thought you had doubt with two pieces. No, no, I have two pieces, and I know that one is forbidden fat and one is permitted fat, that’s clear. Now I just don’t know which is which. Okay. So that’s the halakhic / of Jewish law difference. Now what exactly is the difference between the two situations? You have half-certainty here; in the case of the two pieces there is half-certainty of prohibition. Okay, so what? But still it’s fifty percent that I violated and fifty percent that I didn’t. What’s the difference? So I claim that in the case of one piece, it is not true that there is a fifty percent chance that I violated. How do you know it’s fifty percent that it’s forbidden fat or permitted fat? You just don’t know whether it’s forbidden fat or permitted fat. Again, this is ignorance, not a distribution of fifty percent based on knowledge. In the case of one piece out of two pieces, I have knowledge that there is fifty percent forbidden fat and fifty percent permitted fat here. If I took one piece, I know there is a fifty percent doubt that I took forbidden fat. But if it’s a doubt involving one piece, I don’t know the distribution of pieces in the world, I have no idea—and not in the surroundings here either. Rather what? It could be forbidden fat, it could be permitted fat. I have two possibilities. Since I have two possibilities, the working assumption is—like a majority that is present before us, yes—the working assumption is that it’s fifty-fifty, because I have no way to measure, to weigh, the different possibilities. I know there are two possibilities, but I have no knowledge about them. If I have no knowledge about them, then I have no way to weigh them. So the working assumption is that it’s fifty-fifty, but that assumption stems from ignorance. I simply don’t know, that’s all. Because of that I still assume it’s fifty-fifty. Excuse me, Rabbi, and when you find one piece, if you know for certain that it could be forbidden fat, then should it be less? You know for certain that it could be forbidden fat. So, like this: if you find one piece and you just think it could be forbidden fat or could be permitted fat, then it’s really as you say. Okay. But if you have knowledge… what knowledge? What knowledge? Describe the case to me. No, between knowing and not knowing it’s fifty-fifty, right? Give me the case, give me a third case. Out of one hundred percent. If I find a piece, yes, and I see that it’s something white or yellow. Now I don’t know whether it’s permitted fat or forbidden fat and I ate it. Okay. Your case, right? Good. Now in the case where you find a piece that you know could be a piece of forbidden fat. What do you mean, know it could be? That’s the first case. In other words, they sell there pieces of meat with forbidden fat. So what? That’s the first case. That’s the first case; therefore I have a doubt whether it’s forbidden fat or permitted fat, because they also sell pieces of forbidden fat and also pieces of permitted fat. So how is that different from this? It isn’t different, not different, it’s the same thing. No, in the case of the two pieces. No, the case of the two pieces is something else. Before me is a piece of forbidden fat and a piece of permitted fat. And I know that one of them is forbidden fat and one of them is permitted fat. In other words, probabilistically, it’s fifty and fifty. Right. The difference should only be in the choosing. No, the difference is—I claim the difference is that the first one is really not fifty-fifty. That’s not true. Why? So I’m explaining. In the first case I assume it’s fifty-fifty out of ignorance, not out of knowledge. Since there are two possibilities and I have no way to weigh each of the two possibilities, I have no choice but to assume they have equal weight. So I say it’s fifty-fifty. But it isn’t really because I know that the probability is equal in the two directions. It’s simply that I know nothing. Is this the case of absence and presence? What? Is this absence and presence? It doesn’t matter, absence and presence—a piece in front of me right now. It doesn’t matter; in both cases it’s absence. You have no knowledge about stores and all those things. No, but I know that generally in the world there is both forbidden fat and permitted fat. So I claim that this is… I’ve already brought this example more than once. I have a coin and I want to toss heads or tails. Okay? So I toss the coin, and I know that the coin is fair. I spoke to the manufacturer. The manufacturer made it in a completely symmetrical way. I know it’s fair. Okay? Now I say there is a fifty percent chance it lands on heads and a fifty percent chance it lands on tails. By the way, that’s not exact—I think I mentioned that a study was published not long ago showing that there is almost no coin in the world that is really exactly fifty-fifty. There is always some slight bias. Never mind. But say I know the coin is fair, so the probability is fifty-fifty. Then in my betting I’ll bet fifty percent on heads and fifty percent on tails. What happens if I have a coin about which I have no information whatsoever? I don’t know—fair, unfair, leaning toward heads, leaning toward tails—I have no idea. I have no information at all about this coin. Now someone puts a gun to my head, I have to bet. Okay? What will I assume in my bet? I assume we’d all agree: I assume fifty-fifty, right? I have no way to compare or weigh differently the possibility of heads and the possibility of tails. So I still assume it’s fifty-fifty. But you understand that this is just a working assumption. There isn’t really a fifty percent chance it’s this way and a fifty percent chance it’s that way. It isn’t the result of knowledge; it’s the result of ignorance. Since I know nothing, I have no way to weigh, so I say, okay, fifty-fifty. By contrast, when I know the coin is fair, I know the probability is fifty here and fifty there. It’s not that I’m assuming there are two possibilities and I have no way to weigh them. I do have a way to weigh them, and I know their weights are equal. Do you understand the difference? That’s the difference between a doubt where the prohibition is present and a doubt where the prohibition is not present. Now look, in both cases I treat it as fifty-fifty. In both cases. But again, that’s a way of treating it, it’s a working assumption, it’s not really the situation. So what happens in our case, what I want to claim, is that in the case of the prisoners, there were before us—there are before us—one hundred prisoners, and it is clear that among them one is innocent. It’s clear that one is innocent, right? That’s not the same as the case of eyewitnesses. In the case of eyewitnesses, the eyewitnesses say that Reuven murdered, and there is a five percent chance that they were mistaken, they didn’t see well, and he didn’t really murder. So that’s a doubt involving one piece. Why? Because there isn’t really one who murdered and one who didn’t murder, and I just don’t know who the murderer is and who isn’t. I have one person, and I don’t know whether he murdered or not, okay? Because I have a doubt regarding the witnesses’ observation. And the doubt is not fifty-fifty, but ninety-five-five. Never mind; but the doubt is of the type of one-piece doubt, not one-piece-out-of-two-pieces. By contrast, in the case of the prisoners, I have before me one hundred prisoners and I know one is innocent, ninety-nine are not and one is. In such a case, when I take one of the prisoners—and now yes, I’m doing picking—I take one of the prisoners, okay? randomly. Then at the probabilistic level, it really is ninety-nine percent that I picked up a murderer, not an innocent person, right? But on the other hand, it is clear that there is one person here whom I will convict for nothing, who really is innocent. After I do this with all these prisoners, it’s obvious that there is one here whom I will convict for nothing. Therefore this is not the same as the case of the two witnesses, in which it is generally true that witnesses don’t see one hundred percent accurately, only ninety-five percent. But there is no concrete case here in which I know there will be a false conviction. I can only say that probabilistically, if I look at many cases in which I convict on the basis of witnesses, then five percent of the cases will probably be false convictions. But I can’t say that there will definitely be someone here who is falsely convicted. I can’t say such a thing. I can say that probabilistically there will probably be such people. And notice—here the probability is the same. In other words, this is ninety-five versus five, and that is ninety-five versus five. The difference is only the question whether this is a probability on the group or a probability on the individual person. Again, the same distinction I made earlier. Because in the case of the prisoners, there is certainty that one person will be convicted unjustly—certainty, if I convict on the basis of statistical evidence. Okay? In the case of the witnesses, there is no such certainty. On average, the expected value of the matter will be that five percent are convicted for nothing. But I don’t know, maybe not. There is no certainty; it’s only the expectation for a large group of people, yes? Therefore in the case of the prisoners I cannot ignore the possibility that there is an innocent prisoner here. I cannot nullify that possibility against the possibility of the ninety-nine prisoners who are not innocent. In the case of the witnesses, the eyewitnesses, I can ignore the possibility that there is an innocent person here, because there isn’t an innocent person actually standing before my eyes. This isn’t one piece out of two pieces; there is no piece here that is definitely forbidden fat. Rather what? There is a chance that this piece is forbidden fat. In that situation I am allowed to ignore minority possibilities. I cannot ignore the minority if there definitely is such a minority here—I just don’t know whether I encountered it. But there definitely is such a minority. But if there is only some chance that I will hit the minority, that possibility I can ignore. That is basically the claim. Now this reasoning is legal, not probabilistic. Okay? In this case I cannot—the chance is still ninety-five versus five, but when the five are definitely present inside the mixture, definitely here before me, I cannot ignore the possibility that I landed on those five percent and not on the ninety-five. Maybe I’ll give you another example. In the debate over hostage deals that we’ve had here in recent months, one of the common claims raised against a hostage deal was that right now we are saving, I don’t know, say twenty people who are there in captivity, and we are saving their lives by means of this deal, because otherwise they die. But the terrorists we release will, on average, kill, I don’t know, one hundred people and not twenty. Therefore you cannot prefer the twenty hostages now over one hundred Israelis who will be murdered in the future by the terrorists we are releasing. Now let’s assume for the moment that these assessments are realistic and correct assumptions; I’m not going to argue about the facts right now. Okay? Let’s assume for the sake of discussion that it’s true, that accumulated experience really shows this. Is this argument a decisive one? I claim it is not. I claim not only that it isn’t decisive, I also don’t agree with it. I was against these deals in general, but not because of this argument. In my opinion this argument is not correct. Why not? Again, you can argue—I understand those who think this way. Again, one can argue. I understand those who think otherwise, but I want to present one side of why one can also think this way, yes? My claim is that it is true that on average one hundred Israelis will be killed. But that’s on average. Meaning, it could also be that nobody will be killed. If right now you have definite human lives that you are going to save, and there is some future risk to more people, to one hundred people, not twenty—since this is only a future chance that may not materialize, even though on average the law of large numbers says that it will materialize. But, but since it is only probabilistic, I prefer the definite lives of twenty over the doubtful lives of one hundred. The doubtful lives of a million, whose expectation is that one hundred will be killed. Okay? So this is a bit similar to what I said before. Because here I have human lives definitely before my eyes that are in danger, and I’m saving them now through this deal. Here I am endangering certain people in the future, and probabilistically it will probably happen. But that’s only probabilistically. I’ll put it differently, maybe. I’d say this: in practice, when I release the terrorists now in exchange for the hostages, I am putting all ten million residents of the State of Israel at risk. But each person has a very, very small risk, say one in one hundred thousand. Okay? Therefore on average one hundred out of the ten million will be killed. Right? Because the chance for each person is one in one hundred thousand. So really what I’m looking at now is not one hundred future deaths versus twenty lives I save now; rather I say: I am willing definitely to save twenty lives now and take upon myself a risk of one in one hundred thousand that I will die in the future. And each one of us takes upon himself a risk of one in one hundred thousand that he will die in the future in order definitely to save the lives of twenty people now. Do you understand that one can definitely hear such a consideration, right? It’s not an absurd argument. I think it’s correct too, but I’m saying there are people who disagree with it. But it isn’t an absurd argument. After all, on average—just a second—after all, on average there are twenty on one side of the scale and one hundred on the other side, and it will probably happen; there is the law of large numbers. So it will probably happen. My claim is not that it won’t happen. My claim is that it’s probabilistic. These are not concrete people; they are people who will be selected in some random way. Therefore if you look at the concrete individuals, then what this means is that in order to save the twenty people now, I am taking a risk of one in one hundred thousand that I will be murdered. I am willing to take that risk in order to save the lives of twenty people now. And each one of us is taking that risk now. On average there is almost no doubt that one hundred of us will indeed be murdered later. That is, the risk for each one of us is one in one hundred thousand, a very small risk. It’s worth it to me to take that risk in order definitely to save twenty people. Yes. Yes, I think once you mentioned a line of reasoning that somewhat contradicts this. You once brought a question that a soldier asked some rabbi about checking with a flashlight inside the weapon chamber to make sure it was emptied, just in case, yes? So it’s almost negligible that a bullet remained inside, but because the probability is one in one hundred thousand or something like that, then definitely there will be some soldier who gets hurt if you don’t do it. So here they look at the final result of the civilians who, Heaven forbid, will be murdered. Good question. I think there is a difference. Here in our case, we are comparing life against life. In other words, saving twenty hostages now in exchange for each one of us bearing a risk of dying in the future, one in one hundred thousand, okay? In such a situation I claim that the definite lives of now are preferable to a small future risk for each one of us, even though if you multiply that risk by the number of people, more people will really die than I am saving today. Because in practice, what I am paying now is not those one hundred people. What I am paying now is the risk I take upon myself, and it is a very small risk, one in one hundred thousand. And each one of us is willing to take that risk upon himself in order to save the twenty people. In the end, one hundred of us will pay the price. But right now, we are not talking about some concrete person, and each one of us is talking only about a chance of one in one hundred thousand. That I am willing to pay in order to save twenty hostages. Now in the case of the flashlight, that was a ruling of Rabbi Eliyahu, Rabbi Mordechai Eliyahu. An officer asked him whether on the Sabbath it is permissible for an officer to inspect the weapon chamber after the soldiers’ shift—the officer must inspect with a flashlight inside the chamber to see that no bullet remained there. Now the chance that a bullet remained there and that it would discharge and endanger life is negligible. And now you’re going to violate the Sabbath for this. So Rabbi Eliyahu said that he thought the flashlight should be turned on according to army procedures. Why? Because once you give such an instruction to the entire army and to all the guards and officers and in all these situations, then even though the risk is a very, very small risk, since there are very many people and very many cases, statistically in the end it will indeed happen. That is. For an individual it is a negligible risk. But when you talk about the public as a whole, then in practice it will happen. All right? So basically what you’re asking is that there we do make expectation calculations and look at the expectation as if it were concrete—as if now people are being killed. So I claim that in a situation of saving life versus the Sabbath, even a doubtful saving of life overrides the Sabbath. Okay? Now true, an extremely tiny doubt does not override the Sabbath. I don’t know where the line is, but that’s obvious. Yes, like Rabbi Ben Zion Abba Shaul said—they once asked him about leavened food on Passover; after all, leavened food on Passover is forbidden even in the slightest amount. So the question was whether one may drink water from the Kinneret. Yes, you know all those people who put cloths on the faucet to filter the water from the Kinneret because leavened food on Passover is forbidden even in the slightest amount. So Rabbi Ben Zion Abba Shaul said: yes, but even “the slightest amount” has a measure. In other words, all right, there is some common sense here—a slice of bread in the entire Kinneret is not “the slightest amount.” And neither is a whole loaf of bread in the entire Kinneret. Okay? So here too I claim the same thing. If a single individual had come and asked Rabbi Elyashiv, he would have told him: you are forbidden to use a flashlight. Because the risk you are taking is negligible. Yes? And true, a doubtful saving of life overrides the Sabbath, but not such a doubt. Even a doubtful saving of life means some level of chance, five percent. Fine, but not one hundredth of a percent. Okay? That’s not a risk for which you violate the Sabbath. But if we are talking about a million people each taking a risk of one hundredth of a percent, then yes, that justifies violating the Sabbath because it is considered a doubtful saving of life. I do not see that as certainty; I see it as doubt—that’s the difference. But with respect to the Sabbath, even a doubtful saving of life overrides the Sabbath. So all I need to do there is decide that the doubt is significant enough. But in our case, what I need to do is not to say that the doubt is significant enough, but to say that I see those one hundred people as if they are actually being murdered. Not as if this is a significant doubt. Now, that isn’t correct. I am not willing to see those one hundred people as if they are being murdered now in actuality, and then it is not equivalent to releasing twenty and losing one hundred. But in the laws of Sabbath, what I have to do is not know that one hundred people are dying now. I have to know that the risk is a significant risk in order to count as a doubtful saving of life. And once it is significant enough to count as a doubtful saving of life, then it overrides the Sabbath, because even doubt overrides the Sabbath. There I do not need to assume that the people who may be harmed in the future are as if they have already been harmed concretely right now. What difference does it make whether it’s now or not? What? What difference does it make whether it’s now or not? I’m saying again: I violate the Sabbath not so that people in the future won’t die. I don’t violate the Sabbath for that. I violate the Sabbath so that the people of now won’t enter a state of doubtful danger to life. Do you understand? The expression of the fact that we are now in doubtful danger to life is that in the future some of us will die. But what overrides the Sabbath now is not that people will die in the future. That’s just an indication of it. What overrides the Sabbath now is that right now there are people in doubtful danger to life. But that depends on whether the doubt is significant or not. An insignificant doubt does not override the Sabbath. A significant doubt does. I think checking with a flashlight is a very significant doubt, much more. For an individual clearly not. No, for an individual yes, but when you talk about the army and in general—in general, when I come down from guard duty at night in dangerous places where everyone is carrying, then the doubt becomes much greater. Yes, but again I’m saying: the difference is this—for an individual I’d say the same thing. No, because if we look at probability, doubt, the doubt is not small. So again I say: for an individual such a doubt does not override the Sabbath. It’s a sufficiently small doubt that it does not override the Sabbath, and that’s the whole point. The point is that when you move to large numbers, the small doubt becomes a significant doubt. Not that the future murdered people become concretely murdered people—that’s not correct. Rather, the small doubt becomes a significant doubt. Yes, no murdered people are needed. In our case I need to assume not that the doubt is significant, because a doubt of one in one hundred thousand is not significant. And a doubtful saving of life does not override another person’s definite saving of life. Therefore it won’t help me to say that the doubt is now significant. I need to decide that the one hundred future murdered people are as if I lost them right now, and I released twenty people and paid with the lives of one hundred. If that is the situation, then we do not release the twenty. But that is not a decision I make. This reminds me of something else. People always say, yes, now they’re talking about a commission of inquiry. Yes, where should the commission of inquiry begin? From the Oslo Accords? Or, I don’t know—yes, someone said from the Exodus from Egypt; why not begin from the Exodus from Egypt? So the claim that it begins from the Oslo Accords is because, you see, that’s where Hamas began to gain its standing, even though it didn’t quite yet—it came about maybe half a year later, but never mind. Or the disengagement, sorry, not the Oslo Accords—the disengagement. So that’s where Hamas really got its power, and because of that we got what we got. Therefore obviously the lesson for the future is not to do more disengagements and not to do more things like that. This stupid claim ignores something very basic: October 7 would not have happened if we had not messed up. The fact that they have weapons and control and all kinds of things did not bring October 7 upon us. What brought October 7 upon us was our failure. If we had not failed, it would not have happened. Now true, it is a necessary condition—if Hamas had had no power, it would not have happened, I agree. But even if Hamas did have power, it still would not have happened if we had not failed. Therefore don’t tell me that if Hamas is armed there will be another October 7. Not true. We need to draw the lessons and not fail again as we failed then. And do you see that this is the same reasoning as what I said before? Because this reasoning too basically says: there is a future risk, it could be that we will fail—after all, people sometimes fail. What is that? It can happen, yes? It even did happen, not only can happen. But I’m saying: people sometimes fail. That can happen again too, true. But it depends on us. And in the end it is only a chance that perhaps there will be a future failure. The chance that perhaps there will be a future failure is translated by some people into a present danger. And that translation is problematic, because it is not a present danger. Translating it into a present danger also assumes that we will certainly fail. And that is not true. Therefore there is a risk, with some probability, that something problematic will happen. And you can tell me that in large numbers, at some point we really will fail too—over the next hundred years, at some point there really will be a failure. Okay, but these are all just chances. In the end it is only a risk that by the law of large numbers may eventually happen. But it’s a risk. And the question is whether I now treat such a risk as though it were concrete and had actually happened now, or whether I say no, this is a future risk, I need to try to prevent it as much as I can. You can tell me that statistically I won’t succeed in preventing it for the entire next hundred years; at some point it can happen. Maybe. But since it is only a risk, I say no—the task is on me to try, and if I fail, I fail. But I am not willing to treat it as if it were an event that has already happened now. And this bringing of the future into the present—and this goes back, by the way, all the time to the same distinction we talked about before. The distinction that says there is a difference between what happens in large numbers and the translation of the probabilities onto the individual person who stands before me right now. In other words, the individual person standing before me right now—the risk to him is one in one hundred thousand that he will be murdered by the terrorists released in the deal, okay? True, we are ten million people in the country, so if the chance is one in one hundred thousand then one hundred people will be murdered. Okay? But that is the risk in large numbers. In other words, in large numbers, out of the ten million people, one hundred will be murdered. That is true statistically for the group. Does that mean that I myself have a one in one hundred thousand chance of being murdered? I don’t know—maybe yes, maybe no. On average, if you translate it per person, then yes. But that translation is problematic. I am taking the distribution in the group and applying it to an individual. And these transitions from the individual to the group—you see that they pop up at every stage of our discussion, each time from a different angle. Yes, but it’s not right to define this as something like one in one hundred thousand. Because we are looking here at twenty versus one hundred, which will definitely happen only by the law of large numbers. Okay, so—I didn’t understand. It might never happen. It’s not one in one hundred thousand. One in one hundred thousand is in relation to me. In relation to me, right now there is no issue at all. As an individual person, you ask me whether I’m willing to do a hostage deal? The answer is yes. I’m willing to take upon myself a risk of one in one hundred thousand in order to save the lives of twenty people. Now if you ask every other person in Israel, he too will tell you the same thing. So each one of us is willing to put himself at a risk of one in one hundred thousand in order definitely to save the lives of twenty people now. But the government has public responsibility and it has to examine twenty against one hundred. It has public responsibility, and it needs to listen to the public. And the public agrees, so everything is fine. No, also if you ask the question that way—the government sends the army to defend civilians even though the army is endangered. The army is endangered, okay. But to send the soldier on a certain suicide mission—we will not send him even in order to protect civilians. Yes, I once spoke about what happened at Mitla, yes? with Yehuda Ken-Dror. After they parachuted into Mitla there was an Egyptian ambush they had not expected, and they began shooting, and it was very dangerous, yes? They were dug in there and camouflaged, and the paratroopers there did not know where the Egyptians were. So there was a need—the commander there, Davidi I think it was, Aharon Davidi I think—he decided that someone had to be sent in a jeep. The Egyptians would shoot at him, and once they fired, the paratroopers there would be able to see where the sources of fire were and thus discover where the Egyptians were dug in. Because otherwise they were simply shooting at them all the time, they couldn’t raise their heads, they didn’t know where the Egyptian was—they couldn’t fight them. And then what happened was, he asked for a volunteer, and a man named Yehuda Ken-Dror volunteered, and he drove the jeep on a certain suicide mission. It was clear to everyone that he was not coming back. He drove the jeep, and of course was very, very badly wounded, and by a miracle stayed alive for several months, which was far beyond expectations, but in the end he really died. And the IDF ethical code states—and Aharon Davidi also did this then, but afterward they also, I think, conceptualized it more—that you cannot give an order to a soldier to go out on such a mission. Even though all the time you order a soldier to go out to war and that endangers him, he may lose his life. And that is certainly a lawful order. That is what the soldier is there for, to fight. But when the risk is a certain risk, you cannot give such an order. Even though, what do you mean? otherwise we’ll lose the battle or lose the war. We’ll lose the war, but you cannot give me an order of certain suicide in order to win the war. Why? Because if I go into battle, I have some future risk that maybe I’ll get hurt. That risk is something each one of us is supposed to take, because otherwise we will all be wiped out. The state cannot survive without an army; each one in turn takes upon himself the risk and goes to war. Okay? Therefore it’s obvious that we have to take some future risk. None of us agrees to sacrifice his life now, for certain, for victory in the war. No. I am willing to take a risk of one in a thousand that I will die in the war. Now, even though the risk of one in a thousand that I will die in war—if you multiply it by one hundred thousand soldiers—that means one hundred will die. But true, the risk each one takes is only a future risk; it’s not certain that it will happen. And that is something we are willing to take in the present situation. That’s another example that just came to mind—simply another example of the difference between expectation calculations that in the end will happen, the law of large numbers works, meaning in the end people will die in war, it’s not that they won’t die. But because this concrete person is not being sent on a suicide mission, even though he knows that out of a thousand people one hundred won’t come back. Okay? Fine—but I don’t know which hundred. So there is a ten percent risk that I take; that is a lawful order, that can be demanded of me. That sounds emotional, not rational. I disagree. Because there is no logic in a government agreeing to send nine hundred soldiers to their deaths in order to save one hundred—that’s not logical. Not true. True, they weren’t sent to death with one hundred percent certainty, but if the government knew that nine hundred soldiers would die and did it in order to save one hundred, that isn’t worthwhile. I understand, and I disagree with you. Not true. I don’t see where the logic is in that. The logic is that we have a division of roles in the state. And the division of roles says that each person devotes three years and then reserve duty in turn to defend the civilians. And at the stage when he is in that situation, his life is worth less than a civilian’s life. And the benefit he gets from that is that when he is a civilian there will be others, soldiers, who will take the risks for him. Otherwise we won’t succeed in living here. Even though in the end, obviously, I wouldn’t want to die. If in the end I died, then it will emerge retroactively that my agreement was not on that understanding. Fine—but therefore, since in the agreement I only took a risk, in the end it materialized, but in the agreement I only took a risk—that is a legitimate agreement. Chances of twenty percent, of ten percent—that is something normal. But when we talk about the law of large numbers where for certain—I’m no longer talking right now about the number of percentages, so I don’t care if it’s ten percent, it doesn’t matter, I’m talking about the principled issue. Even ten percent, when a million soldiers go into battle, ten percent means one hundred thousand will die. Fine, that’s my personal calculation, but when there is a government that has to decide—no, that’s the point, you claim it is not a personal calculation, you claim that one hundred thousand will die, so why should I care that for me it’s only a ten percent chance, right? No, so I claim no—it is, that is the calculation, the calculation is indeed personal, and this isn’t emotion, okay? this is logic—my logic. Again, there are people who disagree. I’m only claiming that such a consideration is certainly a possible one; it is not absurd at all. But I’m not talking about your personal consideration. When a government has a decision of twenty civilians versus one hundred, the government makes the decision in the name of the citizens. Fine, but the government makes the decision by virtue of the fact that the citizens appointed it to make the decision, gave it the mandate to make the decision, and therefore when it makes a decision, that means the citizens basically made the decision through it. And how do I make the decision? Because I am willing to take this risk for the sake of the goal. But it’s a collective decision—you can’t say twenty. As a citizen, you wouldn’t want to take risks for others like that, just as you wouldn’t want there to be an operation to save. To save a thousand people, if that would require the sacrifice of one hundred thousand soldiers, say—we as citizens also wouldn’t want that. Not sure. Not sure. There may be proportions where maybe not. Fine, so present it that way. The price is not a thousand against—a thousand against a million may be no. But a thousand against two thousand maybe yes. So I think that is exactly what the citizens here tried to say—at least some of them—because that is exactly the question. There’s no point separating citizens and government. I didn’t claim there is no opposing position. There is an opposing position. It was also present in the public discourse. No, but according to your claim, if there is—no, if there is an opposing position then even if in principle you don’t think like it, you still have to agree with it de facto because your whole arrangement is based on the idea that citizens don’t make mistakes. Leave it, leave it—that takes us into another discussion. It isn’t relevant. I’m talking about this principled question: not whether my argument is correct, but whether it is absurd. I claim it is not absurd. There are people who do not accept it, perfectly fine, we have an argument. I claim that this argument is not absurd. That’s my claim. Not that it is certainly correct, but this can be discussed. Okay? That’s my claim—that this kind of consideration is a relevant kind of consideration. It is a rational kind of consideration. You can accept it, you can reject it, that’s fine, there is a dispute about it. I agree. But if they explicitly told the citizens and said to them, listen, such a war is—this has turned a bit from majority and so on into politics, soldiers and so on. No, fine, never mind, the discussion is really the principled discussion. So what if it is conducted in the political field? On the contrary, let’s extract the precious from the worthless. Even from political arguments you can extract interesting ideas. We already took these ideas when each one did reserve duty. No, I don’t think so. In my opinion people did not really conceptualize these arguments for themselves. For and against. And I’m saying again: I’m not claiming that my position is certainly right and the others are plainly mistaken. I am claiming that this is a legitimate position. I also think it is correct, but it is certainly not an absurd position. In other words, there is definitely room for such considerations. No, I agree, I didn’t come to say it’s absurd. If that’s the case, then we have a dispute. And also in connection with what the Rabbi said about the Oslo commission, it’s the same thing with the suitcases of money Netanyahu transferred to Hamas—that basically, from the Rabbi’s perspective, was that basically okay? What do you mean, okay? That like the Oslo agreement, basically they made the right decision for the time. What does “right for the time” mean? I may disagree, but it’s a legitimate decision. It’s a completely legitimate decision. If you think that’s the right decision, then do it. It was obvious to everyone that some future risk was being taken, and in this case the risk materialized. It also materialized because of our failure as I said, never mind, but even if not—the risk materialized, fine, there are always risks, what can you do. But the decision at the time was a decision made because that was how they thought it was right to act, okay? legitimate. But basically the suitcases of money were also a decision for the time? Yes, absolutely. By the way, this too is doubt and probability. Exactly for making such decisions. Right, absolutely, unequivocally. About the suitcases of money—today everyone is wise after the fact. Again, I don’t think I was in favor of it in real time, I no longer remember, I think not. But fine, I can understand a person who thinks that suitcases of money should be transferred to Hamas because it will bring such-and-such benefit. A completely legitimate consideration. The fact that in the end it turned out he was mistaken—fine, a politician is allowed to be mistaken. By the way, do you know someone named Rotnerossi? Yes. Yes? I once heard someone ask him that question, and he said that in the case of when looking at one act everyone disagrees, but over most years people took a certain risk and probability that it would work, and that’s how things worked out in the world. Yes, yes, that really is so. That’s Rabbi Shach. I once brought Rabbi Shach in one of his letters, I think letter 2 in one of the volumes of his letters, about the Entebbe operation. I think I mentioned it too. Right, yes. That he said it wouldn’t succeed. He said it wouldn’t succeed; he opposed carrying out such an operation because you endanger soldiers and the chance of succeeding in saving the hostages is very small. And in the end it succeeded. So they came back to him and said, look, Rabbi, well, it succeeded, you were mistaken. So he said no, I was not mistaken. I think that at the time the consideration was not right, but obviously the consideration was not right because there was a large chance they would not succeed. But there was also a chance that they would succeed, and in this case that also materialized. What does that prove? The fact that something happened after the fact does not mean—the question is what the considerations were at the time. And if at the time it did not seem reasonable, then the fact that it succeeded in the end proves nothing. But on the basis of what expertise could he say that? It doesn’t matter. You can argue about that, it doesn’t matter; he consulted, I don’t know exactly. I’m only talking about the principled claim. But what is the relation to the law of large numbers? Is the law of large numbers treated like certainty, like majority? The law of large numbers is not certainty; there is no certainty. But the law of large numbers is highly probable. In other words, with very high probability, the larger the number, the higher the probability of getting the result. So here there is near certainty of one hundred versus twenty? So what is the logic? What is the consideration? Future near certainty. You’re repeating the same question and I’ll repeat the same answer; we won’t make progress. In other words, we don’t agree. Fine, that’s allowed. I just can’t understand what the point of disagreement is. The disagreement is that I look at the question of what risk I am taking now, and not at the question… But personally, I personally have no risk even in the case that twenty die. Personally I have no risk that the twenty hostages who are now there will die. Right, and nevertheless I am willing—I don’t know—I am nevertheless willing to put one chance in one hundred thousand of my life at risk in order definitely to save their lives. That’s all. But if they tell you that on that basis another one hundred will also die? Still. What do you mean, if they tell me? They told me, and I still say this. So where’s the logic? It’s not… It’s that each one takes a risk of one in one hundred thousand. It’s not a risk, it’s the certainty of the law of large numbers that one hundred will die. No, it’s a risk, it’s not certain. A risk that is highly likely. No, it’s a tiny risk that will very likely materialize for one hundred people. So what? But not for me. The chance regarding me is very small, and I am willing to take a risk for them. But whether for me or not for me—the twenty who will die are also not for me. Right, but that’s precisely why—but they are in certain mortal danger, and in order to save them from certain mortal danger, I am willing to take a risk for them. I’m altruistic. Well, Akiva, you have certainty versus uncertainty. Exactly like that. You have certainty—that twenty will definitely die—and by the law of large numbers it is also certainty. No, that’s uncertainty, because maybe it won’t happen either. Right, so therefore it isn’t certain it will happen. No, no, maybe it won’t happen, but with a very small chance. The law of large numbers in large numbers works. That is… yes, fine, okay, large numbers take time before they arrive. Yes. I think that… I came in late today, but I think this accounting and this consequentialism is not necessary. It can be logical, but it certainly isn’t necessary. This consideration that one hundred will die or twenty is not necessarily the only consideration. There is a value issue. A person decides for himself that my life is worth risking—as the Rabbi says, one in a million, or even one in a hundred, or even certainly—for the child who was kidnapped. I have many additional considerations with respect to a hostage deal. I spoke only about one of them because it touches on our issue. No, no, I’m talking about this specific issue. The accounting need not even reach the matter of the numbers. Right, the law of large numbers is correct, that it is almost certain that one hundred will die, and here we save twenty. Our lives have a purpose; they are not lives for themselves. And our purpose is to do great things with them, and this is one of the things our lives are worth doing. Therefore the accounting here isn’t all that interesting. But I return to what I said: that’s another consideration. Fine, there are many other considerations surrounding a hostage deal. As it happens, I have many considerations against a hostage deal, but I do not agree with that particular consideration against the hostage deal. Fine, but I’m not discussing the hostage deal; I’m discussing this aspect of the argument, because that aspect touches our lesson. I think the Rabbi’s formulation is not far from what I’m saying. When the Rabbi says that each person finds it worthwhile to take the one-in-one-hundred-thousand chance that he will be killed in order definitely to save—that’s another formulation of what I’m saying. That’s how I think. Okay, so if that’s the case, then everything is fine, then we’re saying something similar. Okay, friends, good night then, Sabbath peace. Good night.