Probability and Statistics – Lecture 30
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- The wisdom of crowds and the law of large numbers
- The transition from statistics to doubt in Jewish law
- Majority, dependence, and the story of Rabbi Yonatan Eybeschutz
- Types of doubt: lack of information, established prohibition, and the suspended guilt-offering
- Laws of doubt as rules of conduct rather than rules of decision
- Utility function, Pascal's Wager, and insurance
- Rabbinic-level doubt leniently, nullification by majority, and something that will become permitted later
- A utility-based proposal for nullification by majority and its implications for “spiritual dulling”
Summary
General overview
The lecture completes a remark on what is called the wisdom of crowds and grounds it in the law of large numbers only under conditions of independence and symmetry of errors around the correct value, while warning that following the majority of public opinion is sometimes a weak and even misleading indication because of dependence, charisma, and herd behavior. It then draws a seam between “uncertainty,” which can be decided using rational tools like majority and statistics, and “doubt” in the halakhic sense, where no decision is possible and so rules of conduct come into play, such as Torah-level doubt stringently and rabbinic-level doubt leniently. It then argues for a connection between the laws of doubt and utility-function considerations, through a discussion of something that will become permitted later and nullification by majority, and proposes that some of these leniencies are best understood as practical accommodations that protect against loss rather than as fully clear-cut permission.
The wisdom of crowds and the law of large numbers
The speaker assumes that when most of the world thinks something, that is usually a mistake unless proven otherwise, and explains that a majority creates psychological pull and can imitate real deliberation through an artificial majority produced by dependence. As an example he cites the order of speaking in a religious court in capital cases, where they begin with the junior judge in order to prevent automatic following of the senior one, and he parallels this to any case where there is correlation between positions. He notes the Rema’s rule that in the case of an error in a Torah scroll one follows the majority of Torah scrolls, but only when the scrolls are independent, and he applies the same principle to checking textual versions in books among philologists and scholars. He defines the wisdom of crowds as a phenomenon in which the average of independent estimates converges on the correct value by force of the law of large numbers, and not as proof that the majority is “right,” and he emphasizes that it works only when there is independence and when errors are symmetric around the expectation, which is the true number. He adds an example of communal singing, including the Koolulam project, and suggests that the absence of collective off-key singing is explained as an averaging of errors around “correct singing,” with the reservation that in complicated songs this may not hold.
The transition from statistics to doubt in Jewish law
The speaker distinguishes between a situation of uncertainty, where there are tools for rational decision such as probability, statistics, and following the majority, and a situation where one cannot manage to decide, and then the laws of doubt come into play. He defines doubt in the context in which he is using it as a state of equally balanced possibilities with no ability to decide using statistical tools or other decision rules, and describes it as fifty-fifty or an equal split among more than two options. He qualifies this by saying that the definition of doubt is not agreed upon, and cites a dispute regarding doubt of impurity in the public domain where there is a majority for impurity: whether an 80-20 case is still called doubt for purposes of the rule that doubt of impurity in the public domain is pure, or whether when there is a majority there is no “doubt” and therefore no room for that rule. For purposes of the continuation of the series, he settles on treating doubt as a case in which the laws of doubt apply according to all opinions, meaning an even balance with no majority decision.
Majority, dependence, and the story of Rabbi Yonatan Eybeschutz
The speaker tells the story of Rabbi Yonatan Eybeschutz, to whom a priest said, “Incline after the majority,” and therefore one should follow the Christians, who are the majority; and Rabbi Yonatan Eybeschutz answered that one follows the majority only when one is in doubt. He notes that even if there were doubt, such a majority is not meaningful because it is not independent, since public positions are formed within an atmosphere and under the influence of opinion leaders, and the public is drawn more by charisma than by substantive examination. He illustrates the halakhic principle with the example of a piece of meat bearing a kosher seal in a city whose shops are mostly non-kosher, where one does not follow the majority because there is no doubt about the specific piece. He notes that the conception according to which one must first define the present case as doubt and only then apply the majority rule strengthens the possibility of viewing even a majority case as one type of doubt conceptually, although in practice the laws of doubt do not apply when there is a majority.
Types of doubt: lack of information, established prohibition, and the suspended guilt-offering
The speaker distinguishes between doubt created by a total lack of information about the surroundings and doubt created by a positive consideration that leads to an even balance, such as a city with five kosher shops and five non-kosher ones. He presents the distinction between doubt where no prohibition was established and doubt where a prohibition was established through the example of one unidentified piece versus two known pieces, one kosher and one non-kosher, where one of them was eaten. He states that a suspended guilt-offering is brought only for doubt where a prohibition was established and not for doubt where no prohibition was established, even though both can be described statistically as fifty-fifty, and explains this by saying that in the former there is a positive reason to doubt. He suggests that in the case of a city with five and five there may be room to argue that one ought to bring a suspended guilt-offering because there is a positive reason for doubt, but notes that this is a separate discussion.
Laws of doubt as rules of conduct rather than rules of decision
The speaker states that rules of doubt such as Torah-level doubt stringently and rabbinic-level doubt leniently do not decide “what is true,” but rather guide how to act in the absence of a decision, and therefore they are rules of conduct and not rules of decision. He says that in this sense the connection between the statistics section and the doubt section is mainly sequential: when the statistical tools of decision are not effective, the rules of doubt enter. He adds the claim that there is also a “statistical” dimension in the sense of utility considerations—not in the sense of calculating probabilities, but in the sense of the significance of outcomes.
Utility function, Pascal's Wager, and insurance
The speaker introduces the concept of a utility function and explains that probability alone is not enough for decision-making, because one must also weigh the price, harm, or benefit of each outcome. He cites Pascal's Wager, in which a small chance that God exists is multiplied by the infinite benefit of reward or the infinite punishment of eternal loss, and therefore leads to keeping the commandments as an expected-value consideration, and he comments that in his view the problem there is the use of expectation as the metric. He illustrates with car insurance and home insurance, where the expected monetary gain from insurance is usually negative, yet it is rational when one is protecting against a worst-case scenario that a person cannot withstand, and he presents his own considerations in not taking comprehensive car insurance as opposed to taking home insurance.
Rabbinic-level doubt leniently, nullification by majority, and something that will become permitted later
The speaker raises the question whether rabbinic-level doubt leniently is a certain permission or only permission to be lenient, such that a conscientious person should still be stringent, and parallels this to the question whether nullification by majority is complete permission or whether one really ought to be stringent. He argues that the law of something that will become permitted later provides an indication that these leniencies are not fully “glatt,” because for something that will become permitted later one is stringent even in rabbinic-level doubt, on the reasoning, “Instead of eating it now in prohibition, eat it later in permission,” as with leavened food on Passover, where one can wait until after Passover. He notes that the principle of something that will become permitted later also applies to nullification by majority, so that if one can wait and eat without relying on nullification, one is not permitted to rely on nullification. In parentheses he mentions the Ran’s approach in tractate Hullin, which explains something that will become permitted later in the context of nullification by majority in terms of the laws of nullification of like into like, rather than by the reasoning “Instead of eating it now in prohibition,” and he notes that most of the medieval authorities (Rishonim) explain nullification by majority as well with that same reasoning.
A utility-based proposal for nullification by majority and its implications for “spiritual dulling”
The speaker proposes understanding nullification by majority as a consideration of expectation or utility in which Jewish law “protects the property of Israel,” so that it does not require a great financial loss of permitted food in order to avoid eating a small amount of prohibited food, whereas in a one-against-one case there is no room to be lenient. He addresses the difficulty that one is willing to spend any amount of money in order not to violate a prohibition, and answers that when there is nullification by majority this is not the usual prohibition of pork but a different halakhic state in which there is no halakhic prohibition, and only perhaps something that is not proper to eat. He discusses the question of spiritual dulling and notes disputes among halakhic decisors as to whether spiritual dulling depends on the halakhic prohibition or on the physical reality of the food even when there is no prohibition, and gives as an example the passage about nursing from a non-Jewish woman in tractate Ketubot 60a and the later discussion that reached Yoreh De'ah. He concludes that two connections link the laws of doubt to the statistics series: the rules come into play when the statistical tools of decision run out, and on the other hand they reflect utility-function considerations. After that he concludes and announces a transition to dealing with the laws of doubt themselves.
Full Transcript
[Rabbi Michael Abraham] Okay, we’re in a series on statistics and doubt, and up to now I’ve basically been dealing with statistics, different aspects of it, and now I want to move on to the topic of doubts. Maybe just one small completion that I didn’t get to. Right, I didn’t talk about the wisdom of crowds, which is also a statistical effect that’s worth a sentence or two. There’s some kind of conception, feeling—I don’t know what to call it—that people have, that usually the masses tend to be right, that there’s some kind of wisdom, something in the crowd beyond the intelligence of each of the individuals who make it up, and so somehow if the whole public says something, it’s probably true. Not because there are great sages there, but because there’s something about quantity that improves our thinking performance. At least that’s how some people tend to think. And about that I just want to say a word, because it’s also connected to the law of large numbers, and that’s how it connects to the previous topic of statistics. My simple assumption is that it usually works the other way around. Meaning, if the majority says something, it’s probably a mistake unless proven otherwise. That’s my starting point—that usually when most of the world thinks something, it’s a mistake.
[Speaker B] Why is that your starting point? Sorry for interrupting.
[Rabbi Michael Abraham] Because it seems to me that that’s simply how it is in practice, experientially, factually. At least that’s my impression. Usually when most of the world thinks something, it’s a mistake.
[Speaker C] The truth is, if you have a majority then you have a kind of psychological element that automatically causes the average person to be drawn to that opinion.
[Rabbi Michael Abraham] Okay, and it could be that this intensifies the effect of error, because that majority is actually created artificially. That’s why, for example, in Jewish law—at least in capital cases—they begin with the junior judge. Meaning, when a religious court sits and judges capital cases, the first one to speak is the least senior of them all, and the most senior speaks last. And the reason is so that not everyone will just follow him, because then you don’t really have a genuine discussion, you don’t have any real brainstorming or an honest examination of different alternatives, because everyone is following the senior authority. And that really is true in many places: when there is correlation between people, or between the different positions, then it is not correct to follow the majority. Right, even in the laws of a Torah scroll—if they find some error in a Torah scroll, one scroll is written this way and another scroll that way, and now I want to know which one is correct—then the rule is, it appears in the Rema, that one follows the majority. Meaning, you check the majority of Torah scrolls, and the wording that appears in the majority of Torah scrolls is the wording that is halakhically binding. But the halakhic decisors write that this is only if these are independent Torah scrolls. If they were copied one from another, then the fact that there is a majority here has no significance at all, because that majority is basically just the replication of the same thing several times. The same is true in checking textual versions in books. Ask philologists or academic researchers who study different texts: the fact that most texts look a certain way is meaningful only if that majority is made up of independent texts. But if one copied from another, it has no significance at all. In any event, for our purposes, the claim is that—
[Speaker B] But sorry—in the court, that means that people tend to follow someone who is greater than they are, because they perceive his wisdom, and here, public opinion leaders, intellectuals, thinkers, and so on, they influence the public as a whole and tilt their views one way or another. It’s not that their opinions are based on factors that really examined things substantively along with the text?
[Rabbi Michael Abraham] Well, but there are factors that examined things substantively and say this way, and factors that examined things substantively and say that way. So whom will the public follow? The one who is more charismatic.
[Speaker B] And those are usually the people who are more mistaken.
[Rabbi Michael Abraham] I don’t know, but it certainly isn’t an indication that they are more right. I think—again, I phrased it in my provocative way—but I think there’s even, yes, Haym Soloveitchik actually talks about this in his book. But yes, I really do think that the majority has some kind of—I think maybe—when the majority expresses conscious positions, I really don’t tend to give that any weight at all, and many times it’s actually the opposite. In any event, for our purposes, leave that aside. Our topic isn’t why the majority is wrong; our topic is why the majority is not right. In my view the majority is also usually wrong, but let’s focus on the weaker claim: why the majority is not necessarily right. So here we really need to examine this concept of the wisdom of crowds and where it comes from. It came from a set of situations, even tested experimentally, where what is really at work is simply the law of large numbers. For example, if I want to know how many leaves there are on a tree, or how many cows are grazing in a field—okay, there are lots of cows and I want to know how many there are—so I ask a lot of people. Each one throws out a number; we can’t count, so each one gives a number and I take the average. Or the number of leaves on a tree—like the well-known story about Maharil Diskin, that with one glance he could say how many leaves were on the tree. That’s the legend. Not that I believe that legend, and not only because I don’t know who afterward bothered to count the leaves and check that he was right; it doesn’t sound to me like there was anyone like that. But the point is that when people estimate the number of leaves or the number of cows or something like that, then often there is a distribution around the real number, with the possibility of error in one direction or the other. Okay, let’s assume it’s Gaussian. The chance of hitting the exact correct number is distributed like a Gaussian whose expectation is indeed the real number. That sounds plausible, at least for quite a few situations. Now if that’s really the case, then when we take lots of people, each one will make a mistake, but when we average over many people, the law of large numbers will tell me that we get the average, and the average really is the correct number. So the law of large numbers is simply what says the wisdom of crowds. The wisdom of crowds is nothing other than the law of large numbers. And where it holds, it really does hold; where it doesn’t hold, it won’t happen. For example, we discussed that the law of large numbers does not hold when there is dependence between the events. And here exactly, what was noted earlier—if I remember right, Toar noted it earlier—what happens when we are drawn after someone more charismatic, or someone who shapes public opinion, or something like that. That creates dependence between the different positions. The moment there is dependence between the different positions, the law of large numbers no longer works. The law of large numbers requires independence. And when, for example, I’m checking the number of leaves on a tree or the number of animals in a field, even there I need to ask each person separately, without his knowing what the others answered. Otherwise, again, you get tangled up and you won’t arrive at the correct answer—or at least there’s a good chance you won’t. But if you ask people independently, each one gives an answer, and then you collect them, then in many cases you really will get a number that is even better than the estimates of experts. Because the law of large numbers works. When the numbers are large, we really do get close to the expectation. And if the expectation of the distribution is the real number—which is not always true, but if it is—then the wisdom of crowds really will work. And again, it’s not because the number of opinions—that it’s not that one improves the other, and not because lots of people hold that opinion, because when I did the averaging, each person said a different number. It’s not a majority in the sense that most people say there are a thousand cows here and the minority say there are eight hundred. Rather, each person says a different number, and I average all the statements or all the opinions. That is not following the majority in the sense that the majority is right; it is averaging many opinions and getting a correct result. That’s really not the same thing. And therefore one has to be very careful with this mantra of the wisdom of crowds, because it works only in very, very specific cases: when the people are independent of one another, when the distribution of each person’s errors is symmetric around the center, and when the center is, on average, the real number or the correct number. Okay? So that’s the point I wanted to add about the wisdom of crowds, because it is connected to the law of large numbers, which we dealt with quite a bit. And just as an aside—an interesting remark someone brought to my attention some time ago, I don’t remember if it was a year or two ago—someone pointed this out and suddenly it caught my ear. Have you noticed that usually when a group sings, it isn’t off-key? Even in a synagogue, which usually isn’t such a huge group. An average synagogue, I don’t know, fifty people, a hundred people—that’s already a big congregation. When they sing, usually there isn’t off-key singing. When you hear the singing, it’s pretty amazing. I mean, not to mention Koolulam—what do they call it? There’s some sort of project like that where they go to various places, gather many thousands of people to sing together. Both well-known songs and they also teach one song, and the result is very impressive, very impressive.
[Speaker D] Rabbi, it’s called Koolulam. Koolulam? Yes.
[Rabbi Michael Abraham] In any event, it’s pretty interesting—you should listen to it sometime. In my opinion it’s also, of course, based on the law of large numbers. Because in the end, when each person sings, there are many who are off this way, off that way, but if everyone sings together, then what I get is the average multiplied by the number of people. And if all of our singing ability is distributed around the correct singing, with errors symmetrically in both directions, then when lots and lots of people sing, they will sing correctly. It’s exactly the same thing as the wisdom of crowds. Now I don’t know if it’s always like that, and with complicated songs it may not be like that—I haven’t examined it deeply—but someone pointed it out, I don’t remember who, and it really caught my ear, and it’s a good observation. Afterward I noticed it. I went to various synagogues and so on, especially on the High Holidays. You hear that when there’s a lot of communal singing, the public usually is not off-key. It’s quite interesting. And again, it’s connected to the law of large numbers and to what is called the wisdom of crowds, but you have to place it in the context where it is relevant, not take it to places where it is not relevant. That’s just a concluding remark regarding the law of large numbers. Now I want to move on to doubts. Up to now we’ve been talking about statistics. What is the situation of doubt, really? And here I want to create the seam between the first part of the series and the current part of the series, which will be shorter. The first part of the series basically dealt with statistics, probability, statistics. What does that mean? I’m basically in some state of uncertainty. You can call it doubt, but that’s not the concept of doubt in its halakhic sense. It’s some state of uncertainty, and in that state I’m trying to decide using sensible, rational tools. That is, statistics and probability. In the case of Jewish law, usually this is what is called following the majority. And we talked about a present majority, an absent majority, all the types of majority and their meanings—we discussed that at length. But what does that majority mean? That majority is basically one kind of statistical tool or another. We discussed whether it’s statistical or not; it doesn’t matter—
[Speaker E] —at the moment.
[Rabbi Michael Abraham] Some logical tool for making a decision between different possibilities in a state of uncertainty. When we talk about the laws of doubts in Jewish law, it always deals with a situation in which we did not manage to reach a decision. We didn’t manage to reach a decision. The simple case is that there is no majority for either side. Say the issue is whether a woman is aylonit or not an aylonit, or whether a piece of meat is kosher or not kosher, and there are five shops this way and five shops that way—there’s no majority. The moment there is no majority, statistics won’t give me a tool to resolve my uncertainty, to choose one option out of the possible options. So where the tools of decision are not relevant or not effective—in other words, statistics has nothing to say, nothing to help me with—then I move from the concept of situations of uncertainty to what in Jewish law is called doubt. Doubt is not a situation in which I don’t know what the truth is. That is not the definition of the concept of doubt. The definition of the concept of doubt in Jewish law is a situation in which I have several—statistical tools help me choose an option that is of course not certainly correct, but I have sensible, rational ways of choosing one of the options among those possible in this situation. That’s what I called a state of uncertainty, and there I use statistics to try and conduct myself in a reasonable, sensible, rational way. When statistics doesn’t work—in other words, there is no statistical edge; it’s fifty-fifty. There is statistics; fifty-fifty is also a distribution. But once I’ve reached the conclusion of fifty-fifty, meaning I can’t use statistics to choose one of the two options, then we move from the first part of the series, which dealt with statistics, to the second part of the series, which deals with doubts. Meaning, in Jewish law one must understand that doubt is not a situation in which I don’t know what the truth is. In Jewish law, doubt is a situation in which I have several possibilities, two or more, that are equally balanced, and I have no way to decide between them using statistical tools or majority or any other tool. There are also practical tools, and I said that there are also practical decision tools, but I’m not going into all those stories again right now. I have no rules of decision—sorry, not statistical and not others. That is what creates the state of doubt. I’ll just note parenthetically that what I just said is the sense of the term doubt that I’m going to use here. From the standpoint of Jewish law there are disputes about this. Why? For example, there are special rules in Jewish law regarding certain laws of doubt—for example, doubt of impurity. Doubt of impurity in the public domain is pure, even though it’s a Torah-level doubt, where I should have been stringent. Doubt of impurity in the private domain is impure. That’s the rule. Doubt of impurity is not like a regular doubt of prohibition. Okay, it depends on the domain. Now, what happens if I’m in the public domain and I have a majority toward impurity? I’m unsure whether something is impure or not in the public domain, and there’s an eighty percent chance it’s impure. That’s not fifty-fifty; that’s eighty-twenty. There is a dispute among later commentators—there is a dispute. That dispute depends on the question whether an eighty-twenty situation is also called a situation of doubt, in which case the rule is that doubt of impurity in the public domain is pure, or whether the moment I have a majority—because eighty-twenty is not fifty-fifty—then it isn’t even called a situation of doubt at all. It’s a situation in which I know what the truth is—again, halakhically know—I know because the eighty percent is what determines it, and if so there is no reason to apply the rule that doubt of impurity in the public domain is pure, because this is not a situation of doubt. So the dispute on this question is really rooted in how I view an eighty-twenty or sixty-forty case. I assumed earlier that an eighty-twenty case is not what Jewish law calls doubt, and certainly the rule Torah-level doubt stringently—the ordinary rule of the laws of doubt—does not apply to it, because one follows the majority. But still, there are commentators who claim that such a case is indeed called a situation of doubt for purposes of other doubt-rules, like doubt of impurity in the public domain and the like, because they basically say that even such a case is doubt. They define doubt as any situation in which I do not have certainty regarding the question of what the truth is. That is called certainty, of course, at a reasonable level. What is the truth? And then it is called doubt. Now true, if there is a majority then one follows the majority and decides, but that does not mean that I am in a state of certainty. I don’t have certainty. I’m just following the majority. Therefore, if you ask for the definition of such a situation, it is still defined as a situation of doubt. And the practical difference is that, for example, in doubt of impurity, if it is in the public domain, we would go leniently even though the majority points stringently, because this is called a situation of doubt and the rule is that for doubt of impurity in the public domain one goes leniently. Therefore I qualify what I said earlier. Earlier I said that doubt in Jewish law is only a fifty-fifty situation. That is the common conception, but not everyone agrees. There are those who claim that a situation of doubt also includes a situation decided by majority. But for me that’s semantics. When I now deal in the second part of the series with the concept of doubt, I’m dealing with it in this sense—in the sense where I have fifty-fifty, or thirty-three, thirty-three, thirty-three, depending on the case. And then I have no possibility of deciding with tools of decision, statistical or others, and then the laws of doubt come into play. There is—yes, I think I already mentioned this nice story about Rabbi Yonatan Eybeschutz, like all the nice stories about Rabbi Yonatan Eybeschutz, where a priest comes to him and says, why don’t you follow us Christians? After all, it says in the Torah, “Incline after the majority.” We are the majority. This is connected to the wisdom of crowds. Yes, we are the majority. So by the way, why indeed don’t we apply the wisdom of crowds here—in Christianity versus Judaism, say, or Islam versus Judaism, or I don’t know, Hinduism versus Judaism? Because that really isn’t independent. This great majority did not form its opinion independently, one from another. And therefore a majority has no significance in such a case. It’s simply an environment, and someone who is inside it apparently lives in that atmosphere. That doesn’t mean they are wrong, but it also doesn’t mean they are right. A majority has no significance in that situation. And in the case of Rabbi Yonatan Eybeschutz—or what was supposed to have happened with Rabbi Yonatan Eybeschutz—they asked him, the priest asked him, why don’t you follow us? So he said: I follow the majority when I am in doubt. But if I am not in doubt, why should I follow the majority? And therefore there is no reason to be Christian if I am not in doubt between Judaism and Christianity. If I were in doubt, maybe I would follow the majority. What I said earlier is that even that is not correct, since this is a majority whose members are dependent on one another, and therefore such a majority has no significance. One need not follow the majority even if I really am in a state of doubt.
[Speaker E] But—
[Speaker F] Is there really a reality in which there is no doubt about something? Can you say about anything that it is absolutely certain?
[Rabbi Michael Abraham] I can’t hear.
[Speaker F] Is there really a situation with no doubt, where one can say about something that it is absolutely certain?
[Rabbi Michael Abraham] No—I said doubt, and I qualified this earlier. When I say there is no doubt, I mean for all practical purposes—that is, beyond a reasonable doubt, as lawyers say.
[Speaker C] But is there a reality in which there’s no doubt, for example that I’m now seeing some particular thing? Say, the senses. That I exist, for example. Things like that—basic things of being.
[Rabbi Michael Abraham] So about that there’s no doubt, right? No—even there you can argue that the senses sometimes mislead us. There’s a mirage, there are—our senses can sometimes mislead us. You don’t have complete certainty even about sensory appearance. True, I very, very strongly think that if I see something then it’s probably there, but who knows—it could be a mistake; such things have happened.
[Speaker C] No, it could be that it’s not there, but I can’t cast doubt on the fact that I’m seeing it, do you understand what I mean?
[Rabbi Michael Abraham] All right, but that’s not interesting. I’m talking about claims about the world. Okay. I also can’t doubt that I’m now saying the sentence “I can’t doubt.” Fine, okay, that’s not the point—I’m talking about claims about the world; that’s the issue we’re dealing with. In any case, for our purposes, although the discussion about the cogito can raise doubts even about that, even when I’m talking about the question of whether I doubt or not. But we’re not going into that philosophical hair-splitting right now. For our purposes, what I’m basically claiming is that yes, Rabbi Yonatan Eybeschutz is really saying: only when I am in doubt do I follow the majority. If I am not in doubt, why should I follow the majority? That is basically his claim. Now, this, by the way, is not a joke; it’s a serious argument. Meaning, say I find a piece of meat in the marketplace, and in the city there are nine non-kosher butcher shops and one kosher one, but this piece of meat is sealed with a premium kosher certification stamp—should I be concerned that it isn’t kosher because there are nine non-kosher shops here? Obviously not. Why not? Because if this piece has a kosher seal, then I’m not in doubt about it. If I’m not in doubt about it, why should I follow the majority? Following the majority is a rule that tells me what to do when I am in doubt, but if I’m not in doubt, there is no reason at all to follow the majority. And that is a serious claim, not a joke. Meaning, it’s certainly true. Yes, many times people say: wait, but most of these and these are such-and-such—most academics are left-wing, most academics are secular, most—I don’t know—various claims of that kind. So what? Why should that interest me? Meaning, if I were in doubt, then maybe I would take that into account. And even then, as I said earlier, the argument is that even that is not correct, since this is a majority in which there is dependence between the cases, so such a majority has no significance; you don’t need to follow that majority even if you are in a state of doubt. But if I know, I don’t need to resort to those rules. So again, this form of relating to it shows us that truly, even a situation where we have a majority is called a situation of doubt. First I need to define that situation as a situation of doubt, and then the rule of majority comes and tells me what to do in that situation. That somewhat reinforces the claim of those commentators I mentioned earlier, who see even a case of majority as one of the types of doubtful situations. Okay? But for our purposes, as I said before, that is not important, because when I speak from here on about doubt, I mean a situation in which the laws of doubt apply, and according to all opinions that is only in a 50-50 case. If there is a majority, then the laws of doubt do not apply, even if the situation can be defined as one of doubt; but the laws of doubt certainly do not apply in such a situation. I am speaking about a situation where the laws of doubt apply, and that is a situation where I am at 50-50. As I think I already mentioned, a 50-50 situation can arise in two ways. Say I find a piece of meat lying here and I have no information at all about the surroundings. I don’t know what’s going on around it, how many shops of this kind there are, how many of that kind there are. In that case it is definitely reasonable to define it as a 50-50 doubtful situation. Not because I know there is a 50 percent probability that it is kosher and a 50 percent probability that it is not kosher, but because I know nothing. And if I know nothing, then again the two possibilities—kosher and non-kosher—have equal weight. That too is a state of doubt. There are situations of doubt where I have a positive calculation that leads me to 50-50—for example, a city in which there are five non-kosher shops and five kosher shops. There too I relate to this piece of meat as a doubtful piece, 50-50, but there the doubt is born from a positive consideration. In the previous case, the doubt was born from lack of information; that is doubt arising from a negative consideration. I spoke about that when I discussed a majority that is present before us versus a majority that is not present before us. I said that a majority present before us is really such a case, a case of negative doubt—here I used it in the opposite sense, no matter, I’m only illustrating. So in any case, for our purposes, both of these situations are situations of doubt, and the rules of doubt apply there. By the way, they are not identical situations. For example, with regard to a provisional guilt-offering: someone who ate something whose intentional violation incurs karet and whose unintentional violation requires a sin-offering, and he ate it while in a state of doubt, then he brings a provisional guilt-offering for that until it becomes clear to him what happened, and then it may be that he will have to bring a sin-offering. But at the first stage he brings a provisional guilt-offering. What is a provisional guilt-offering? It is something you bring for violating doubtful prohibitions. You violated a doubtful prohibition—you should have been stringent because of the doubt, you were not stringent—you bring a provisional guilt-offering. Okay, now as a matter of Jewish law, a provisional guilt-offering is brought only for a doubt in which a prohibition was established, not for a doubt in which a prohibition was not established. What does that mean? Say I have a piece of meat, and there is a 50 percent chance it is kosher and a 50 percent chance it is non-kosher—that is a doubt in which a prohibition was not established: 50-50, but I have no reason to assume it is 50-50, I just don’t know. Okay? What happens if I have two pieces, one kosher and one non-kosher—I know that—and both are before me, only I don’t know which one is kosher and which one is non-kosher, and I took one and ate it. That is called a doubt in which a prohibition was established. Sometimes they call it an established presumption of prohibition, but really, a prohibition was established. What does that mean? Here there is a positive reason for the doubt. After all, I know there are two pieces here, one kosher and one non-kosher; the only question is which of them I ate. That is not the same thing as the previous case, which is called the doubt of one piece. Here it is a piece out of two pieces; the earlier doubt is the doubt of one piece. For the doubt of one piece out of two pieces, one brings a provisional guilt-offering. For the doubt of one piece, one does not bring a provisional guilt-offering, even though statistically this is 50-50 and that is 50-50. Why? Because one piece out of two pieces is 50-50 from a positive consideration. I have here a positive fifty percent in favor of the possibility that I violated a prohibition. In contrast, one piece—a doubt about one piece where I simply don’t know what it is—I do not have a positive fifty percent; I simply have absence of information. From absence of information I assume it’s fifty percent kosher, fifty percent not. I have nothing better than that. And therefore I basically assume it is fifty-fifty; I do not have information that it is fifty-fifty. For that one does not bring a provisional guilt-offering. Now by the way, it is commonly thought that doubt in a city with five kosher shops and five non-kosher shops is not called an established prohibition. For that one does not bring a provisional guilt-offering, because it is not a piece out of two pieces. I think one should bring a provisional guilt-offering for that too, because there is a positive reason to be in doubt. There are five non-kosher shops in the city; I have reason to doubt that this piece came from there. But that is another discussion. In any case, for our purposes, it is true that there is a difference between the two kinds of doubts, for example with regard to a provisional guilt-offering, but for our purposes these are both states of doubt. I relate to both of them as a fifty-fifty doubt. Since I mentioned this distinction at an earlier stage in the series, I talked about what happens with a fair die. With a fair die, I know there is a one-sixth chance for each face. There are unfair dice in the world, and then the distribution is of course different. What happens if there is a die and I have no idea whether it is fair or not? I have no information about it. Even then, if I had to bet, I would probably assume a one-sixth chance for each face, because I have nothing better than that on grounds of symmetry. But it is very hard to say that there is here a positive consideration of one-sixth that it will land on the number five. It is simply because of the lack of information that I assume the chances for all faces are equal, but I have no positive reason to assume that. That is basically parallel to the difference between established prohibition and non-established prohibition, or between doubt with a positive reason and doubt from a negative reason. In any case, for our purposes both of those situations are called situations of doubt. So if we cannot decide it with statistical tools or decision tools, following the majority and the like, then we activate the laws of doubt. And from this you can understand that the laws of doubt are basically rules of conduct, not rules of decision. The rules of doubt—Torah-level doubt requires stringency—do not tell me that now I ate a prohibition. If they did tell me that, I would have to be flogged. They do not say that I have now eaten a prohibition. They say that I need to be stringent as if there were a prohibition here. But that is a rule of conduct, not a rule of decision. It is not a rule that decides for me what the truth is. It is a rule that tells me what to do in the absence of information about the truth. Therefore, in the standard classification of halakhic rules into rules of decision and rules of conduct, the laws of doubt are rules of conduct, not rules of decision. I am supposed to be stringent in a Torah-level doubt, and one may be lenient in a rabbinic-level doubt, but not because it is more likely to be prohibited than not prohibited, but because there is a rule of conduct telling me to be stringent. So in that respect, it is a rule of conduct. If so, then in practice there is not much of a real connection between the first part of our series and the second part of our series. The first part of our series talked about situations of uncertainty and different ways to decide the uncertainty or make decisions using statistical tools. Here we are talking about a situation in which there is no way to decide using statistical tools, and nevertheless Jewish law gives me a practical rule about what to do in a situation where I have no decision. Those tools are not connected to statistics. But there is still a contextual connection, yes? Meaning, this basically complements the statistical tools. Once you cannot work with statistical tools, the rules of doubt come into play. So in that sense it still belongs to the same series, but these are two different parts. Now I want to argue a claim that goes one step further. There is also a statistical dimension within the rules of doubt. And I will explain what I mean, in a very particular sense. I want to make that claim, and here I want to raise a different question, and then I will come back to this point. Maybe I’ll say one sentence first. I want to introduce a bit the concept of expected-value considerations, or the utility function. Okay? The utility function is defined in game theory, or generally defined, as the… price, or positive or negative price, yes, the benefit or the harm in each of the options. Say when we handle a problem statistically, we basically assume there are various options here with certain weights. Say if it is a fair die, these are equal weights, and I can calculate what the probability is that I will get a number greater than or equal to five—the probability is one-third. Why? Because I count: there are two possibilities out of six total, so the probability is one-third. Okay, here the question of what it means for me to get five or six on this throw of the die does not enter at all; I ask only what came out. That is a purely statistical question. But many times—maybe even in most cases where we use statistics—statistics is only part of the picture, because statistics only tells me the probability that each result will occur, but besides the probability I also need to take into account the significance of each of the results. The significance of each result means: what its price is for me. Yes, we talked about—don’t remember if we talked about Pascal’s Wager? I don’t remember; for some reason I have the impression we did, but I no longer remember.
[Speaker G] In the faith series we talked about it.
[Rabbi Michael Abraham] I didn’t talk about it here? I’ll say it briefly. Pascal basically makes the following argument. He says to the atheist—yes, he was a believing Christian, and by the way one of the fathers of statistics, Pascal—and he makes the argument against the atheist, his famous wager. Let us assume that the probability that God exists is very, very small, I don’t know, one in a million, fine? A very small probability. So the atheist says—after all, the atheist cannot say that the probability is zero; you cannot know with certainty that there is no God, only that the probability is very, very small, one in a million, let’s say. Pascal says: yes, but if you make the utility calculation, if you calculate with your utility function, then you will see that on the assumption that there is a God and you observed all His commandments, you receive infinite reward. If you committed sins and there is a God and you committed sins, you receive terrible and eternal punishment. Okay? If there is no God, you have a little benefit here, a little harm there, nothing significant. Therefore, he says, basically the calculation of the utility function—or expected profit, if you want—says that you should observe the commandments even if you are an atheist. You should observe the commandments because the one-in-a-million chance that there is a God has to be multiplied by an infinite expected gain. Infinite expected gain times a one-in-a-million chance still gives you infinite gain, yes, or very large gain, and therefore utility considerations should lead you to observe the commandments. Now this is basically an argument that shows us, or illustrates for us, that when we make decisions using statistical tools, the statistical calculation is not enough. The statistical calculation—what is the probability that there is a God or that there isn’t a God—that may be some statistical datum, but in order to reach a conclusion about what I should do, it is not enough for me to know the probability that there is a God or the probability that there isn’t; the question is what will happen, or what the harm or benefit will be, in each of the possibilities. That is of course not a statistical consideration; it is something each person will have to work out, I don’t know, with whatever tools he accepts, but it is part of our decision-making. You cannot make decisions with statistics alone; you need to make decisions while taking into account what each possibility means. Yes, say an insurance company—I insure my car, okay? And I insure my car, and obviously my expected gain is negative. My expected gain is negative; broadly speaking, most people lose money on their insurance. Think about it over a lifetime, on average over everyone: for most people, the expected gain is negative in an insurance transaction. And still it is not right to say that it is irrational to buy insurance. Why? Because although the probability that something will happen to my car is small, if it does happen, the damage I will suffer will be very, very large, and I want to insure myself even against a very rare possibility, since if it happens then it is very problematic. Therefore it is not correct to say that buying insurance is irrational, even though the expected gain of the transaction is negative. Unless you also include the peace of mind it gives as part of your utility function, and then of course you complete the picture. But in principle the claim is that the statistical calculation by itself is not enough to give me the tool for how to decide, how to behave. I also need to take into account the significance of each of the possibilities, or the price, harm, or benefit of each of the possibilities, and that is what is called the utility function. So for example I personally, just as an example, do not insure something I can afford. For example, for a car I don’t buy comprehensive insurance. I don’t buy comprehensive insurance. I don’t buy comprehensive insurance because at worst the car will be stolen or I don’t know what will happen to it, but that’s not—I can handle it. In contrast, a house—if my house is gone, I can’t handle that. It would bring me to a situation where I could, but it would bring me to a situation where I would live in a way that would be very, very problematic for me. And in order to close off that option, even though it is very rare, I am willing to enter into a deal whose expected gain is negative. So for me the criterion is whether I can handle the worst case. That is a reason to buy insurance. But if I can handle it, then at least I do not think that I—I generally do not insure in such a case, since the expected gain is negative, so over a lifetime I will gain. And if I can also handle the losses, why should I do it? Okay? What I’m saying is not completely precise. I’m bringing it here only as an illustration; it’s very rough, it isn’t always exactly true, but we won’t get into that here. At one point I looked into it a bit. But we won’t get into that here. In any case, as an illustration, what I want to say is basically this claim: that the utility function is important, and therefore when we speak about rational decision-making, beyond statistics there is also game theory. Or in other words, there are the calculations of the benefit and harm of each of the possibilities, and that usually has to be taken into account in addition to the probabilities of each of the possibilities. You multiply them, add them up, and so on, and you arrive at a measure of expectation. The expectation measure is not always a good measure—for example in Pascal’s Wager. We won’t get into that here, but in Pascal’s Wager, in my view, the mistake is precisely the use of the expectation function. I think expectation is the wrong measure there. But never mind. For our purposes, the claim is that in order to make decisions, it is not enough to make a statistical calculation; you also need to take into account the significance of the possibilities. Why am I bringing all this? Because I want to argue that the laws of doubt really, although they do not belong to pure statistics, because they are activated only where there is no statistical calculation and it remains fifty-fifty, still they are connected to the utility function. In that sense there is a connection, if not to statistics then to game theory. It is connected to the utility function. And in that sense it is not completely detached from statistical thinking, because the utility function is indeed the business of statisticians, even if it is not statistics in the narrow sense of the term. What do I mean? Let me illustrate this through another question raised by the commentators regarding the laws of doubt. The commentators wonder whether, when they tell me that in a rabbinic-level doubt one may be lenient, is that a definite permission? Meaning, is it fitting for a conscientious person to be stringent? You are allowed to be lenient, but it is fitting to be stringent. Or not? Once it is permitted according to Jewish law, there is no reason at all to be stringent. Are you being stringent because you don’t want to violate a prohibition? There is no prohibition. The question is whether this is a full permission, or merely permission to do it, while a conscientious person ought to be stringent. Fine, a question various commentators ask regarding the laws of doubt. The same thing can be asked regarding nullification by majority. There too, in nullification by majority, you are basically eating a prohibition; there perhaps it even dulls the soul—prohibitions, I don’t know exactly. So what happens if there is nullification by majority? Is it still fitting to be stringent, only one is allowed not to be stringent, allowed to be lenient? Or not—there is no point at all in being stringent once it is permitted; why be stringent? So the commentators discuss this in both directions, and there is no consensus. It is a dispute. I want to argue that in the topic of something that will later become permitted—I’ll explain this in a moment—there is a fairly good indication in favor of the thesis that this is not a full permission. What do I mean? We know the rule: Torah-level doubt requires stringency, and rabbinic-level doubt allows leniency. That is the basic halakhic rule in the laws of doubt. But there is a qualification. In tractate Beitzah on page 4 and in other places, the Talmud qualifies this by saying that with something that will later become permitted, one must be stringent even in a rabbinic-level doubt. What does that mean? For example, if I have a doubt—say, I don’t know what—in the prohibition of set-aside items. Fine? Leavened food—each of those, by the way, probably is not an example of something that will later become permitted, but never mind, these are examples. So say leavened food, fine? I have a doubt regarding leavened food. This doubt is during Passover. After Passover, even if it is leavened food, I am allowed to eat it. Leavened food over which Passover has passed is a rabbinic prohibition; I am ignoring that right now. In terms of the core laws of leavened food, one may eat the leavened food after Passover. Okay? So basically, when I find something during Passover and I don’t know whether it is leavened food or not, then I am in doubt. Now let’s assume this is only rabbinic-level leavened food. Fine? Rabbinic-level leavened food. So if it is rabbinic-level leavened food and I am in doubt, then ostensibly I may eat it. They tell me no. Why? Because it is something that will later become permitted. Wait until after Passover and you can eat it certainly, not just on the basis of doubt. Or in the language of some of the medieval authorities (Rishonim): instead of eating it in prohibition, eat it in permission. Why should we permit you to eat it in prohibition during Passover? Wait until after Passover, and after Passover it is certainly permitted even if it is leavened food, and therefore you can eat it freely. So why should we permit you to eat it during Passover on the basis of doubt? That is the standard explanation among the medieval authorities for this stringency regarding something that will later become permitted. Why are we stringent with something that will later become permitted? Even though usually the accepted halakhic view is that if something will later become permitted, that is a reason to be lenient. Because it means its prohibition is not intrinsic. It is only a prohibition dependent on time. There will be a certain time when it will not be prohibited, so it is a prohibition on the person, not on the object itself. And very often that is specifically a reason to be lenient. But in the case of the laws of doubt it is specifically a reason to be stringent. And why? Not because it is more severe, but because there is no reason to be lenient if you can eat it later without needing leniency. Okay? That is the accepted explanation. The big problem that arises here—or before the problem, another example of the law of something that will later become permitted is with regard to nullification by majority. Regarding doubts, the law of something that will later become permitted applies to a rabbinic-level doubt. Torah-level doubt goes stringently even if it is not something that will later become permitted. Rabbinic-level doubt in principle goes leniently. And if it is something that will later become permitted, then one must be stringent. In nullification by majority it is the same thing, but there it applies even at the Torah level, because nullification by majority works even for Torah-level prohibitions. Okay? Now if a piece of prohibited food fell into a majority of permitted food, let’s leave aside for the moment the question of taste, which on the face of it is only rabbinic, but if a prohibited item fell into a majority of permitted items, then the prohibited item is nullified. I am allowed to eat it. There is nullification by majority. And here too the question arises whether this is permitted, or whether it is fitting for a conscientious person to be stringent, or whether there is no reason at all to be stringent because a permitted thing is permitted. And on that too they disagreed. Now the Talmud there in Beitzah applies the principle of something that will later become permitted also to nullification by majority, not only to the laws of doubt. And even nullification by majority of something that will later become permitted—meaning that it can be eaten at a later time without relying on the rule of nullification by majority, because there is no problem—then they did not permit you to eat it by relying on nullification by majority. That is the stringency of something that will later become permitted. This applies both in rabbinic-level doubt, where instead of leniency we go stringently, and also in nullification by majority in Torah-level prohibitions, where one must be stringent and may not rely on the nullification. Okay? Now I return to the question I asked earlier. Are these laws—both rabbinic-level doubt and nullification by majority at the Torah level—a full permission, with no point at all in being stringent? Or is it permitted, but if someone wants to be stringent, all the better? After all, you are still eating some kind of prohibition; they only permitted it, they enabled you to be lenient. But clearly, ideally one should avoid it as much as possible. So I am saying that the law of something that will later become permitted apparently points toward the second possibility. Why? Because what are they basically telling me? Instead of eating it in prohibition, eat it in permission. Why permit you to rely on rabbinic-level doubt leniency or on nullification by majority? Wait until after Passover and eat it without needing special permissions. Now I say: if this permission is a full permission… then what difference does it make whether I need it now in order to eat it, or whether I wait until after Passover? Even now I am eating something fully permitted. This consideration indicates that even if during Passover I can rely on nullification by majority or on rabbinic-level doubt leniency, it is not perfectly clean. It is permitted; they are accommodating me, allowing me to be lenient. But ideally it would be proper to be stringent. Therefore, where I have the option not to violate the prohibition and I do not need these special permissions, then indeed they do not issue them to me. They do not give me these permissions. I think this topic is a strong indication—if not absolutely compelling, but I think it is a strong indication—for the view that these permissions, like the laws of doubt or leniency in rabbinic-level doubt and nullification by majority and the like, are not full permissions. If someone wants to be stringent, all the better; it is fitting to be stringent.
[Speaker B] I don’t understand—what is the doubt here? In nullification by majority, what is the doubt?
[Rabbi Michael Abraham] What do you mean, what is the doubt?
[Speaker B] The Rabbi is comparing it to doubts, and I’m asking.
[Rabbi Michael Abraham] I am comparing it to doubts in the sense that Jewish law allows me to rely on nullification by majority and eat a prohibited thing. Now the question is whether this rule, which allows me to eat the mixture, is a rule for the ideal case or whether ideally one should be stringent.
[Speaker B] Yes, but why is that—why compare it to doubt? Why is there doubt here?
[Rabbi Michael Abraham] I’m not comparing it to doubt. There are two rules, and regarding both of them one asks whether these are rules that turn the thing into a full permission, or whether they merely allow me to be lenient, while ideally I should be stringent. I ask that about both.
[Speaker B] When there is doubt, then we say there are rules—rabbinic-level doubt allows leniency. Here we say it’s a matter of doubt because in reality we don’t know what is going on here; here we do know what is going on in reality—we know there is a prohibition here—and they permit us because it is nullified by majority.
[Rabbi Michael Abraham] Fine, but still there is a prohibition inside the mixture and Jewish law permits me to eat it, right? Now the question is whether this permission to eat the prohibition is a perfectly clean permission, or whether ideally one should be stringent even though you are allowed to be lenient. What is the problem? It’s a very good question. Just as I ask it about doubts, I can ask it about nullification.
[Speaker B] Yes, but I don’t know whether you can infer one from the other.
[Rabbi Michael Abraham] I am not trying to infer. Two separate questions. I haven’t inferred anything yet. I ask regarding this, and I ask regarding that.
[Speaker B] Okay, fine.
[Rabbi Michael Abraham] Now I’m saying that from the topic of something that will later become permitted, it emerges that the answer to both questions is that we are not dealing with something perfectly clean. Why? Because the rule of something that will later become permitted is basically founded on the idea that instead of eating it in prohibition, eat it in permission. But after all, according to the view that this is a perfectly clean permission, I am not eating it in prohibition. So why is it better to wait until after Passover and not eat it now? Even now it is perfectly clean. There is no prohibition in it. Unless it isn’t—unless it is not perfectly clean. They permit you, fine; they don’t want to burden you. But clearly, ideally one should be stringent, and in a place where this is not burdensome because you can later eat it in permission, then indeed they did not permit you to rely on this permission. I’m not inferring the law of nullification by majority from the law of doubt; rather, I learn both from the topic of something that will later become permitted. Two independent questions, but both are decided by that same topic. Now I ask: if indeed there is some concern here, then I am violating a Torah prohibition, right? A piece of pork fell into kosher meat, fine? Now this is a Torah prohibition, but they permit me ideally to be lenient and eat the mixture. But they expect a conscientious person to be stringent, and therefore in a case of something that will later become permitted they indeed do not permit anyone to eat it either. By the way, maybe in parentheses I’ll add the view of the Ran in Chullin, namely that regarding nullification by majority, the law of something that will later become permitted is not based on the reasoning “instead of eating it in prohibition, eat it in permission,” but rather on the laws of nullification. He says: this is same-kind with same-kind; something that will later become permitted is in its own kind permitted, so it comes out that you have permitted food nullified within permitted food, and same-kind with same-kind is not nullified. So that is an explanation that is completely different from the explanation in the laws of doubt. According to the Ran, you cannot reach this conclusion regarding nullification by majority, only regarding doubts. But the view of most of the medieval authorities (Rishonim)—Rashi, for example, in Beitzah that I mentioned, and others—most of the medieval authorities do not go like the Ran. Even in the Ran himself, in other places, you see that he explains differently. Most of the medieval authorities explain the same explanation in nullification by majority as well: instead of eating it in prohibition, eat it in permission. And then you see that these are laws that accommodate me and try to make things easier for me. But ideally one should be stringent. Now I ask: what does it mean to make things easier? There is pork here. So you say there is pork here; if there is pork here, then why be lenient? What is the idea behind this? So I want to suggest a possibility. I want to claim—think, for example, about a piece of pork that fell into a majority, into pieces of permitted meat, yes? Now say there is one piece of pork and one piece of kosher meat in the pot. Now I don’t know which is which, so the whole mixture becomes prohibited, because there is no nullification by majority here; it is one against one. Okay? But if there are two or more kosher pieces, then the prohibited piece is nullified and everything can be eaten—or one should leave one piece, or leave two pieces, there is a dispute among the halakhic authorities, but there are authorities who say you can even eat all of it. And even according to those who say not, according to most opinions this is only a rabbinic prohibition; there are opinions that say it is also a Torah prohibition, but let us go for the moment with the majority view. So it is permitted to eat it if it is nullified by majority. Why? I want to claim that this is an expected-value consideration. Here expected value enters. What does that mean? They tell me this: basically you need to be careful not to eat pork. But what is the logic of not allowing me to eat kosher meat—which is fit to be eaten completely lawfully—just because there is prohibited meat next to it? Why do I have to lose meat that I am permitted to eat in order to avoid that prohibition, the eating of that prohibited meat? So the Talmud says—or the Torah tells us, or Jewish law tells me—like this: if the piece that you will lose, the permitted piece that you will lose because of the prohibition, is only one piece—meaning, if your loss is like the value of the prohibition that you would eat—then that is what is demanded of you. But if the number of permitted pieces is greater, two or more, the Torah does not demand that you give up great wealth in order to avoid eating a little bit of prohibition. It has pity on you. Now if you are wealthy, or if you want to invest and still be stringent, all the better. If it is something that will later become permitted and you can eat it after Passover, then you will lose nothing at all—not the permitted pieces nor the prohibited piece, you will lose nothing—then of course there is no reason to permit it to you. But if, when it is prohibited to you, it comes out that you will lose the permitted pieces in order not to eat the prohibited one, then the Torah has pity on the property of the Jewish people, and therefore they tell you there is nullification by majority. That is the suggestion I am making. Maybe that is how this law of nullification by majority can be understood. If that is indeed so, then it may be that, yes, one piece against one piece is doubt; it is not a majority, and there one must be stringent at the Torah level. Why? Because there the expected gain is equal to the expected loss. Right? Meaning, if they forbid me to eat both pieces, then what I have lost is one permitted piece, but what I would have gained by eating the prohibition is also one piece. So that is the threshold at which the laws of nullification begin. And therefore the Torah has pity on the property of the Jewish people. If it is a lot of money, then they do not obligate me to give it up, but if the money is only equal to the prohibition, then they do obligate me to give it up. Okay? That is the threshold demanded of me in order not to violate the prohibition, and that is basically a kind of expected-value or utility consideration. Right? Because they are basically telling me: let’s calculate what will happen if you eat and what will happen if you do not eat. So if the mixture is ten kosher pieces against one non-kosher piece, fine? If I don’t eat, I lose ten kosher pieces—that is a lot of money. If I do eat, I have eaten one prohibited piece. So the utility calculation that the Torah makes—not us, yes?—but the Torah tells me: I have pity on the property of the Jewish people; you may be lenient, you can eat the whole mixture. If you want to be stringent, all the better. It’s not that it is perfectly clean; it is not perfectly clean. But there is pity for the property of the Jewish people. If it is something that will later become permitted, meaning you can wait and then eat everything entirely without any problem, then indeed they will not permit it to you. Why? Because the whole idea of the permission is that otherwise you are going to lose all the permitted pieces. But if you can wait another two days or a few days and you will not lose anything from the permitted pieces, then there is no problem. You can wait and lose nothing, so there is no reason to permit you to eat the prohibition, because you gain nothing permitted from it. And therefore I want to claim that the considerations behind the laws of doubt are really utility or expected-value considerations. This is the obvious question—Menachem asked it here. If you already asked it, I wanted to ignore it, but since you asked, I’ll answer it anyway. Menachem asked a good question. He says: according to how I am presenting it here, it comes out that the Torah permits me to eat pork in order not to lose two pieces of kosher meat, but after all, in order not to violate a prohibition, a person is supposed to spend all his money. So what is the issue with losing two permitted pieces? I am supposed to lose all my property in order not to eat one piece of pork. Clearly, when the piece of pork is mixed into kosher pieces, it is already no longer the ordinary prohibition of pork. That is obvious. The only question is whether it is a full permission, like those views that hold it is a full permission, or whether there is still a value in being stringent. And that value in being stringent is not being stringent because of the prohibition of pork—there is no prohibition of pork here. There is some value in being stringent—dulling of the soul, or I don’t know exactly what, some sort of consideration that it is not fitting to do this. It does not obligate me to spend all my money, only according to the laws of majority, or if it is balanced or a majority. If it were a real prohibition, then of course a person would have to spend all his money in order not to violate the prohibition. Okay?
[Speaker H] Rabbi, isn’t that a proof against this whole idea of dulling the soul and all this mysticism? After all, it is obvious that if there is a thirty percent dulling of the soul, then you won’t do it.
[Rabbi Michael Abraham] You won’t do it—fine, then don’t do it. But who said there has to be a prohibition? Let each person make his own calculation. If you want to dull your soul, dull it; if you don’t want to, don’t. The Torah doesn’t…
[Speaker I] Meaning it’s just some kind of health recommendation? A recommendation—the Torah prohibition has nothing to do with dulling the soul; it’s just some recommendation, some kind of gastroenterological recommendation.
[Rabbi Michael Abraham] I am suggesting a possibility here in order to show that what you concluded is not necessary. You may be right, but it is not necessary. You said this is a proof against mystical conceptions of dulling the soul. I am saying: a proof, no. It can be understood this way, and it can also be understood otherwise. And in practice there are disputes—disputes among the halakhic authorities. In Ketubot on page 60 there is a topic about a nursing infant and a non-Jewish woman—whether an infant may nurse from a non-Jewish woman who eats prohibited foods. Okay, now there is no halakhic prohibition in that matter, but still it may be that ideally one should be stringent. And then the halakhic authorities there discuss what happens when there is no halakhic prohibition: is there dulling of the soul where there is no halakhic prohibition? And this reaches the Arukh there in that place—he discusses it there in Ketubot—and it reaches the Shulchan Arukh in Yoreh De’ah, and all the commentaries deal with this issue: does dulling of the soul go together with prohibition, or is dulling of the soul independent of prohibition? Meaning, is it a reality—if you ate pork, does it dull your soul even if that eating involves no prohibition, for example a sick person who ate pork? Does that dull his soul or not? Not that I understand how one decides such a thing, or who even knows that it dulls the soul; I am speaking now in the conventional halakhic terminology without getting into the question of what my personal opinion is about these conceptions and whether they are actually true. I very much doubt that they are true, but that is another discussion. So what I basically want to claim is that although the connection of the laws of doubt to the discussion of statistics that we have had until now is double: first, where the statistical tools end, that is where the rules of doubt begin, and therefore this complements the picture or the discussion about statistics. True, it is not a use of statistical tools, but it completes the statistical picture in a situation of uncertainty in which statistical tools did not help you decide it—that is the situation called doubt, and here the laws of doubt apply. And the additional connection that I argued exists is the connection of the utility function. I want to claim that the laws of doubt fundamentally assume a utility-function calculation, and therefore they claim that I need to be stringent in Torah-level doubt because the utility function does not justify permitting the prohibition. What I would gain if they permitted the prohibition does not justify permitting it. And in that sense there is another connection between the laws of doubt and considerations of game theory or statistics—not of the statistical calculation itself, but of the utility function that one takes into account in statistical calculations. Okay? So that is basically the claim. And from here on I will try to get a bit more into the topic of the laws of doubt. Until now I mainly talked about its connection to the topic of statistics, and now we’ll talk a bit about it itself, about the laws of doubt themselves. Okay, up to here—if there are questions or comments. Okay then, have a peaceful Sabbath, goodbye. There’s also a class tomorrow for anyone who didn’t notice, Friday morning tomorrow. Okay, goodbye.
[Speaker J] Rabbi, may I ask just about what the Rabbi said earlier—that the pork becomes, the pork becomes a different kind of prohibition? Meaning, the Rabbi understands that this isn’t the ordinary prohibition of pork—so what is it then?
[Rabbi Michael Abraham] No, it’s also—it’s probably not a prohibition at all in the halakhic sense. But it is still something that is not fitting to eat. If you want, it’s dulling of the soul.
[Speaker J] Meaning, in terms of the nullification of the prohibition, it is certainly completely nullified. There are just some other considerations here not to eat it, for various reasons.
[Rabbi Michael Abraham] Yes, and that enters Jewish law, at least on the rabbinic plane, in the law of something that will later become permitted.
[Speaker J] I understand, but the prohibition—but it isn’t—
[Rabbi Michael Abraham] Not really a prohibition, rabbinically.
[Speaker J] But the nullification of the original prohibition is complete nullification; by majority it is simply nullified and there is no prohibition at all. Right.
[Rabbi Michael Abraham] I understand. But the reason for the prohibition is not nullified. After all, the prohibition was originally imposed because there is something problematic about pork. That problematic thing that exists in pork remains there even if the pork is nullified by majority. It’s just that you are allowed to take the—not correct to say take the risk—but you are allowed to dull your soul if you want, if we speak in that language. There is no halakhic prohibition. If you want, be careful, but Jewish law does not require that of you. Understood.
[Speaker E] Thank you very much.
[Rabbi Michael Abraham] Goodbye, have a peaceful Sabbath. Goodbye.