Doubt and Probability — In Halacha, in Thought, and in General — Lesson 22 — 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
🔗 Link to the transcript on Sofer.AI
Table of Contents
- [0:00] Differences between probabilistic questions in legal judgment
- [3:17] The difference involving conditional probability in medical science
- [5:57] The effect of the rarity of a disease on test results
- [10:39] The reliability of legal testimony and its connection to the rarity of crime
- [12:05] The quality of a judge versus the reliability of the ruling
- [19:25] Preliminary filtering by the prosecution and its effect on evidentiary value
- [29:00] Postmodern critique of determining truth
- [30:23] The connection between statistics and morality
Summary
General Overview
The lecture returns to doubt and probability and sharpens a critical distinction between two similar questions that people tend to confuse: given that the correct law is X, what is the chance that the judge will rule X, versus given that the judge ruled X, what is the chance that X is in fact the correct law. The claim is that the second question depends heavily on how common the phenomenon under discussion is, and therefore the high reliability of a test, a piece of evidence, or a judge is not enough to guarantee that the conclusion itself is highly reliable in practice. The practical solution is preliminary filtering, which reduces the field of possibilities and changes the relevant “rarity,” and in principle Bayes’s formula explains the relationship between these conditional probabilities. Along the way, the discussion also touches on postmodernism, the distinction between the legitimate stage of asking questions and an answer that erases truth, and the difference between fields where there truly is no single truth and fields where there is a truth but it may be hard to persuade others of it.
Two Different Questions About the Reliability of a Judge and a religious court
The central distinction is between a question that measures the quality of a judge by the likelihood that he will rule correctly when the law is known, and a question that measures the reliability of the ruling after it has been given. Confusing the two leads to error in evaluating rulings, especially when the type of case under discussion is very rare. The calculations attributed to Nadav Shnerb about the quality of different panels of a religious court are based on the first question, and therefore do not directly give the probability that the ruling actually issued is correct.
Medical Diagnosis and the Difference Between Test Reliability and Result Reliability
A medical test with ninety-five percent reliability means that if a person is sick, there is a ninety-five percent chance that the test will identify it, assuming symmetry of errors in both directions. When the disease is very rare, for example one in a million, such a test will generate a huge number of false positives, so that out of fifty thousand positive results only one will be a real patient. The conclusion is that the question “I tested positive, what is the chance that I am really sick” is not answered by the “reliability of the test” alone, but by combining that reliability with the rarity of the disease, and the gap between the two probabilities can be dramatic.
Legal Evidence: Reliability of a Witness Versus Reliability of Testimony
In the case of identification testimony with ninety-five percent reliability, the point is made that the reliability of the witness is not identical with the reliability of the conclusion that the defendant is the murderer, because the number of murderers in the population is very small. The distinction is between “in how many cases the witness will testify correctly” and “given this testimony, in how many cases it will actually be correct.” It is argued that this same probabilistic mistake may lead to wrongful convictions, and that even in Jewish law there is room to ask similar questions, despite the very high evidentiary threshold in criminal law, with a note about prior warning and possibilities such as confinement in a cell.
Rarity of a Phenomenon and the Need for Preliminary Filtering
The claim is that if you examine evidence or tests without prior filtering, they may be almost completely worthless when the phenomenon is rare. In the legal world, an example is given in which circumstantial suspicions such as motive and opportunity are not enough for conviction, but they narrow the suspect group from a million people to five, thereby changing “one in a million” into “one in five,” at which point a stronger piece of evidence becomes meaningful. In medicine, initial symptoms play a parallel role, and the accurate test becomes effective only after the relevant prevalence is no longer tiny; in the coronavirus example, it is argued that sending the entire population to be tested without any indication makes the test worthless, whereas testing in response to symptoms is meaningful.
Conditional Probability and the Mathematical Formulation of the Two Questions
The explanation uses conditional probability—P of B given A versus P of A given B—to show that reversing the condition changes both the question and the answer. The die example shows that the probability of “rolling a five” is one-sixth, but the probability of “rolling a five” given that the result is known to be odd is one-third, whereas the probability of “odd” given that a five was rolled is one. The claim is that once you formulate the question precisely, “you’ve done three-quarters of the work,” and that many statistical paradoxes arise from a poorly formulated question.
Bayes’s Formula as the Connection Between the Probabilities
The connection between the two conditional probabilities is presented through Bayes’s formula, which follows from the equality of two ways of calculating the probability of A and B together. It is emphasized that the relation between P of B given A and P of A given B also depends on the base probability of A and of B, and therefore the prevalence of the phenomenon is a decisive parameter in evaluating the reliability of a conclusion after it has been reached. The claim is that this is exactly why the quality of the judge alone cannot determine the reliability of the ruling in practice.
The Example of Eilam Gross, God, and Bayesian Calculations (Column 506)
A quotation is brought from column 506 on the website, describing a lunch at a conference in 2007 about the statistics of hypotheses in the search for the Higgs particle and a discussion of a book called The Probability of God. It is argued that Eilam Gross confused the question “what is the probability of God’s existence given the universe” with the reverse question, and attributed to a preacher for religion a mistaken claim as though he were equating the two, and even asserted that the probability that “given God, the product is an amazing butterfly” is one hundred percent. The lecturer says that in the quoted passage “there aren’t two words here that connect to each other into a correct statement,” and that the source of the mistake is a prior assumption that of course there is no God.
Formulating a Physico-Theological Argument Using Bayes
Event A is defined as “God exists” and event B as “a complex world exists,” and the probability of B is taken as one because the given world exists and is complex. It is argued that there is no way to know P of B given A, but there is a claim that one can maintain that P of B given not-A is very small, meaning that if there is no God the probability of a complex world is tiny. From this is derived the conclusion that the probability that God exists given a complex world is “almost one,” and according to the claim this is the mathematical representation of the argument that the chance of the spontaneous emergence of complexity is tiny. The lecturer announces that there is “another formulation” that will be presented next time to show how “begging the question” can enter into the calculation.
Postmodernism, Foucault, Truth, and the Distinction Between Questions and Answers
A position is presented according to which postmodernism seemingly has two stages, and the critical question-raising stage is excellent and not postmodern at all, whereas the problem lies in the answer stage, which declares that the two possibilities are always equivalent and there is no way to know. It is argued that there are fields in which there is a systematic way to reach good conclusions, and therefore one should not infer that “nothing is true,” alongside an acknowledgment that there are cases in which there really is no way to reach an answer. There is also a discussion of Foucault and the claim that the concept of “illness” is a value-laden and not an objective concept even in physical medicine, with mention of a debate with Yoram Yovel, Makor Rishon, and columns 25 and 26, as well as a Copernican example according to which, kinematically, there is no truth to the question of who revolves around whom, because it depends on the choice of coordinate system.
Conclusion: Questions About Fifty Percent and Biases Versus Assumptions
At the end, the question is raised whether judges always have fifty percent because there are only two possibilities, and the response is that two possibilities do not imply equal probabilities, just as with a biased coin. An example is raised in which the same “proof” can affect different people differently, and the lecturer reduces the explanation to just two possibilities: illegitimate bias or different underlying assumptions. The debate also concerns the distinction between emotion and intuition, with the lecturer claiming that intuition is cognitive rather than emotional, and the discussion closes by returning to the claim that there is no third option beyond bias or differing assumptions.
Full Transcript
[Rabbi Michael Abraham] Okay, hello everyone. I see we survived the holidays, or maybe “after the holidays” has finally arrived, as Kishon writes—at some point even that arrives. So we return to our topic, doubt and probability, and last time I tried to sharpen the difference between two questions that look similar on the face of it, but are actually different. One question is: assuming that the law in this case is X, what is the chance that the judge will rule X? That’s one question. The second question—yes, this really points to the quality of the judge, how likely he is to hit upon the halakhic truth. The second question is the reverse one: assuming that the judge ruled X, what is the chance that this really is the correct law? Okay? Now the question looks very similar, and when we examine the quality of judges we often switch between these two questions, and what I want to argue is that it’s very important not to confuse them. I brought Nadav’s calculation—Nadav Shnerb’s—regarding the quality of different compositions of a religious court. Yes, he talks about the… I also sent the screenshot on WhatsApp. I think I got it once from Yossi Eitan, if I remember correctly, who once sent me the original. In any case, he calculates there how the quality of the religious court changes if I add judges. It turns out it doesn’t always improve; even if you add good judges, you may actually make things worse. If there’s one excellent judge and you add two good judges, the quality of the ruling may go down. Meaning, the number of cases you miss may become larger. But all the calculations there are calculations based on the first type of question. Meaning, given that this is the correct law, what is the chance that the panel, or the judge, or the religious court will indeed rule that law. In other words, assuming the law is X, what is the chance that the panel will rule X? Okay? But there is another question that looks very similar, but it’s not the same thing. And that is: assuming the panel ruled X, what is the chance that this really is the correct ruling? That this really is the correct law in this case. That is a different question. And to clarify this point I brought several examples. I said I needed to think some more about how to sharpen it further, so it seems to me I can sharpen it in a relatively simple way. So we talked—the examples I brought were from medical diagnosis and legal evidence. Yes, the claim is that suppose we have some disease, any disease, and I want to know whether a certain person has that disease. So I send him to take a test. And let’s say the reliability of that test is ninety-five percent. In five percent of cases it’s wrong. Both false positive and false negative, meaning in both directions. In other words, it can miss that you’re sick, and it can miss that you’re not sick. Okay, for simplicity I’m assuming the errors are symmetric. That’s not always so. In any case, let’s assume the quality of the test is ninety-five percent. What does that mean? That in ninety-five percent of cases the test will diagnose correctly. Meaning, if you are sick, there is a ninety-five percent chance that the test will say you are sick. Now I ask the reverse question: I went to get tested, and the test said I’m sick. Now I ask: what is the chance that I really am sick? That is not the question, given that I am sick, what is the chance that the test will diagnose it, but rather: if the test diagnosed it, what is the chance that it diagnosed correctly—that I really am sick? That is the reverse question. And I talked about this—I said that basically what we have here is conditional probability. Conditional probability means: given A, what is the chance of B. Yes, we denote it as P of B slash A, P of B given A. Okay? So basically, if you formulate these two questions, you can call them P of B given A or P of A given B. Right? Say A is: I have disease X. And B: the test says I’m sick with X. Fine? So P of B given A means: assuming I’m sick, what is the chance that the test will say I’m sick. P of A given B means: the test said I’m sick, what is the chance that I really am sick? In other words, what is the chance that I really am sick given that the test said I’m sick—which is a different question. Therefore, if I now ask: the test has ninety-five percent reliability. And now I ask: I went to take the test, I tested positive. What is the chance that I really am sick? An intuitive answer that many people will give is ninety-five percent—that’s the reliability of the test. Wrong. And to clarify this, I think I used this example: suppose there are a million people in the population, and only one in a million has this disease. So we have a million people in the population, one person is actually sick. Okay? Now I give all one million people the test. Out of the million people, how many will come out positive? Fifty thousand.
[Speaker B] Five percent.
[Rabbi Michael Abraham] Five percent, right, fifty thousand. Okay? Because a very large number of healthy people will test positive—five percent of the healthy people. There are a million healthy people, one sick person, so there are a million healthy people, and out of those million healthy people the test will miss fifty thousand of them—that’s five percent. So fifty thousand will come out positive. Okay? Now notice: if I now put all one million people through the test, there are fifty thousand who come out positive. How many of them are actually sick? One. Meaning that if I tested positive on this test, I can go home happy and cheerful—there’s no chance I’m sick. And I’m talking about a test with ninety-five percent reliability. And why is that? Because the disease in question is a very rare disease. And the reliability of the test has to stand in some proportion to the rarity of the phenomenon I’m trying to test for. Meaning, if the disease occurs in fifty percent of the population, then a test with ninety-five percent reliability is a good test for it. But if the disease occurs in one percent of the population, then a test with ninety-five percent quality is not much. It won’t give me good results. The chance that I’m sick is around twenty percent, meaning one out of five. Okay? Meaning, that’s okay, it’s no longer negligible, but it’s still very far from being ninety-five percent, as the quality of the test might make it sound. So in effect, the relationship between these two probabilities, P of B given A and P of A given B, depends on P of A—on the disease itself, on how rare the disease itself is, what the chance is that people are sick at all. And if that probability is very, very small, there can be a dramatic difference between P of B given A and P of A given B. Okay? Without doing the mathematics, I think in this calculation you can see it very easily. I also said the same thing regarding legal evidence. Just as doctors have to learn this, lawyers also need to learn it, because when evidence is brought before the court that is ninety-five percent reliable that I committed the murder—I, the defendant—they bring evidence that is ninety-five percent reliable that I committed the murder. There are two witnesses who saw me, but it was from a distance such that the reliability of whether they identified me correctly is ninety-five percent. For the sake of discussion, okay? What is the chance that I really am the murderer? The reliability of the evidence is ninety-five percent, like the reliability of the medical test. But notice: how many murderers are there in the population? Very few. Therefore think—if those same two witnesses were to look at all the people in the universe, they would find five percent of them to be murderers. Which is—
[Speaker B] But that doesn’t relate to it.
[Rabbi Michael Abraham] What? I didn’t hear.
[Speaker B] That doesn’t relate to it.
[Rabbi Michael Abraham] What do you mean it doesn’t relate to it?
[Speaker B] It relates only—the eyewitness testimony relates specifically to a particular person, unlike the medical test, which relates to all the sick people.
[Rabbi Michael Abraham] No, no, with a medical test too you can send just one person to take the test. When I talk about a million people, that’s just a way of doing the calculation. Instead of talking in probabilities, I’m talking in numbers. I could have done it with probabilities and it would come out the same. I’m just talking in numbers because it’s much more tangible, that’s all. Mathematically you’re right, but… Five percent—that means fifty thousand people. Right? How many of them actually… how many of them actually murdered someone here? One. Meaning, the testimony is worth nothing. Now, this means there is a difference between the reliability of the witness and the reliability of the testimony. The reliability of the witness means: in how many cases the witness will testify correctly. The reliability of the testimony means: assuming this is the testimony, in how many cases will it be correct. That is a different question. Okay? And the same thing if I now return to judges—now it’s very easy to see. Suppose I have a judge whose reliability is ninety percent. A good judge: in ninety percent of cases he will hit upon the correct law. Okay? We said the worst judge possible is fifty percent, right? Because he could just toss a coin. So a ninety-percent judge is a good judge. Let’s say that for the sake of discussion. I hope so, at least—there’s no way to know it. We saw there’s no way to know that, which is why we rely on an accessible majority, the majority in a religious court. I explained that in one of the previous lectures. But let’s say that’s my estimate: this judge has a quality of ninety percent. What does the quality of the judge mean? That in ninety percent of the cases I brought before him when I tested him—yes?—that’s what determined… what grade did he get on the exam. What is the grade he got on the exam? Out of a hundred cases presented to him, in ninety he gave the correct answer. Right? That is the quality of the judge. Meaning, that’s the grade he got on the ordination exam for judges. So this judge is of quality 0.9, ninety percent. Now I ask: this judge said—ruled, after everything was brought before him—that Reuven murdered. What is the chance that Reuven really murdered? Negligible. A ninety-percent judge, an excellent judge—negligible. There is almost no chance that Reuven murdered, because the number of murderers in the population is very small. We talked about… yes, about Munchausen syndrome; let’s not go back to that again, yes, I gave examples last time. So what does this actually mean? It means that a judge needs to pay attention, just as he needs to pay attention to the quality of the evidence and the quality… and a doctor needs to pay attention to the quality of the test, they also need to pay attention to the rarity of the phenomenon. And the quality of the evidence or the test is not enough to determine the quality of the ruling or the doctor’s diagnosis and the judge’s ruling. Okay? You need to know how rare the phenomenon is. Now how… how do we deal with this? Because if that’s really the case, then all legal rulings aren’t worth a penny. Since there is almost no chance that judges have before them evidence at the level of ninety-nine point nine percent. The number of murderers in the population is very small. One-tenth of a percent would already be an enormous number of murderers. There aren’t a tenth of a percent murderers in the population. So if the evidence is of quality ninety-nine point nine, it’s worthless in a murder trial. Is there a doubt here at a higher level of certainty than that? There isn’t.
[Speaker B] Is that with respect to civil law or to Jewish law? It doesn’t matter. No, I’ll tell you why. In Jewish law you need prior warning. So there, no… there’s no such thing as judging a person based on evidence. In the secular legal system, yes, judges relate to the person, the witness.
[Rabbi Michael Abraham] Even… even the prior warning can be challenged. Who says he heard you well? Who says you heard him well? It’s not only the witnesses that can be challenged. That’s true, but that same person—
[Speaker B] He has to be there.
[Rabbi Michael Abraham] Fine, so what? Maybe he didn’t murder? Maybe he didn’t hear you? And more than that—even if… if two witnesses come and testify that Reuven murdered and they didn’t give him prior warning—
[Speaker B] Then no, you can’t judge him.
[Rabbi Michael Abraham] Not true. You may not execute him, but you might put him in confinement.
[Speaker B] Oh, that’s something else.
[Rabbi Michael Abraham] So I’m saying, there definitely is room in Jewish law too to ask these questions. It’s not as though this doesn’t exist in the halakhic context. True, Jewish law sets a very, very high bar, a very high evidentiary bar in criminal law. But there is still certainly room to ask these questions there as well.
[Speaker D] Rabbi, doesn’t this give a nice explanation for why, once adulterers became common, the bitter waters stopped? Because it really wasn’t a test; the Sages also knew it wasn’t really… and the Torah also didn’t think it was a reliable test.
[Rabbi Michael Abraham] No, on the contrary, I would have expected the opposite—once adulterers became common, the test should become better.
[Speaker D] No, but apparently those bitter waters never did anything, no woman apparently ever had that happen to her, it was just ordinary water. So since everyone was pure and most people were just suspicious husbands who brought them—
[Rabbi Michael Abraham] Because if now you’re not catching adulterers, then apparently you really are worth nothing. Okay, you’re a pessimist. Fine, anyway—or a rationalist, I don’t know what to call it.
[Speaker C] In any case, Rabbi, the two fields are very different, really, because in the case of the medicine there are no elements—right, what will determine things is the percentage rarity of the disease. But in the case of testimony, there are elements that strengthen the claim despite the rarity—if there are witnesses and interrogations and all kinds of things.
[Rabbi Michael Abraham] Wait, that’s my next sentence. Okay, how do we solve this problem on the practical level? Because on the face of it, this means all doctors and judges may as well resign. Everything they say now is worth—
[Speaker D] Nothing, at least—
[Rabbi Michael Abraham] nothing, at least in the context of things that are somewhat rare, let’s say. Everyday simple things maybe, but somewhat rare things—what they do has no significance. But that’s not so. Why not? There is—I may have mentioned this, I don’t remember anymore—in the legal world, for example, they do not convict based on self-incrimination. Like, “a person does not render himself wicked,” so in the legal world too they don’t accept self-incrimination unless there is some additional element, some small additional piece of evidence besides the confession, besides the fact that the person comes and admits that he committed the offense. What does that additional element do? So that additional element—now I’m not talking in the specific context of self-incrimination, though it can be connected to that too—I’m talking now about what happens when there is some additional element in the kinds of cases I described earlier. For example, a man stands accused of murder, and two witnesses come and testify: “Yes, we saw him commit the murder.” Why was he put on trial? Why was he put on trial in the first place? Before the witnesses came, we didn’t know anything yet. Why was he put on trial? Because he was suspected. Why? He had a motive, he had an opportunity, he was hanging around in the area, I don’t know, something like that, okay? So there are already things that make him suspicious. Now they put him on trial, and then two witnesses come and testify: “Yes, we saw him, he’s the murderer.” Now that’s already something entirely different. Why? Because without the witnesses, all those circumstantial things aren’t worth much; of course I can’t convict a person on that basis. So what do those things do? What they do is this: they say that the number of potential people who could be suspects in this murder has dropped from a million to five. Only five people were in the area and had the opportunity and the means to carry out this crime. There weren’t more than that. All the rest of the people in the population of the State of Israel weren’t in the area; they’re irrelevant. Now among those five, one of them is the murderer. The rarity of the phenomenon has suddenly changed from one in a million to one in five. One in five is still very weak evidence—no one is going to convict for murder based on twenty percent, okay? But now when ninety-five percent evidence comes along, when the rarity of the phenomenon is one-fifth and not one in a million, now that’s good evidence. Meaning that even though this initial circumstantial filtering is weak filtering, its effect is very important for the legal process, very important. And therefore, by the way, the prosecution also has to go over the evidence and check the case very carefully before bringing charges. On the face of it, what’s the problem? Send everyone to court, the court will examine the evidence, if everything is fine he’ll be acquitted and if not, not. Why do you need the intermediate stage of the prosecution? So you’ll tell me it’s to streamline the process, the court can’t sit on all these cases, it won’t manage. That’s not the point. Okay, that’s also a point, but it’s not the essential point. The essential point is what I said here. Someone who has passed through the prosecution’s filter leaves us with a very limited number of people who could have committed this crime. Now if good evidence is brought before the court, it will already be meaningful evidence. Because the rarity of the phenomenon is no longer relative to the entire population of the State of Israel, but relative to those who passed the prosecution’s filter. And that’s already fine. The same thing applies to a doctor and disease. When someone comes to the doctor, the doctor doesn’t just casually send him, “Go take a medical test, maybe you have some… I don’t know, some rare disease.” Obviously he sends him because there are some indications, such-and-such symptoms, I don’t know, something. Now those indications in themselves—ten percent, twenty percent—that means they’re not enough to make a diagnosis. But once you have those indications, and on their basis you sent him for the test, then a ninety-five percent test becomes a good test, because the rarity of the phenomenon being tested is no longer one in a million but one in five or one in ten. And therefore these initial filters are very, very important, even though people tend to dismiss them. These initial filters are very important, no less important than the test itself. The test itself is worth nothing without them. Even though the test is ninety-five percent and these filters are ten percent reliable, twenty percent reliable—not worth much. Yes, but those ten or twenty percent reliability figures turn the rarity of the phenomenon into something much less rare, and then the test can already be effective. Therefore in real life, medical tests and legal evidence are fine—they do the job, they really do the job—provided that an important preliminary screening is indeed done. Because if, for example, I sent all the Jewish people to get a coronavirus test with no suspicion at all, the whole Jewish people get a coronavirus test, that test would be worth nothing, nothing at all. Because if there was no indication about me that led you to send me for the test, then what is the chance that I’m sick? Let’s say, I don’t know, one percent of the population is sick. You’d need a test with reliability of at least ninety-nine point nine before we could even begin to take it seriously.
[Speaker B] But there is a difference, an essential difference, between these things.
[Rabbi Michael Abraham] What do you mean?
[Speaker B] Judges sit and examine, and these are human beings who go over it. Now when you spoke about the device, it’s a device checking a person.
[Rabbi Michael Abraham] Human beings can make mistakes too, what do you mean?
[Speaker B] No, exactly the opposite, exactly the opposite. Through majority rule we got… the point is, when you have several people examining something, it could be that the force of a court process, a person who has gone through prosecution, supposedly has much more force than what you’re describing in medicine, because the machinery can’t grasp—it’s impossible to treat machinery like human beings.
[Rabbi Michael Abraham] No, but in medicine too, the initial check is not done by machinery.
[Speaker B] The initial check—you hear—
[Rabbi Michael Abraham] from me that I have symptoms, it looks suspicious for such-and-such disease, and then he sends me for a test. Exactly like the prosecution’s screening.
[Speaker B] Yes, but in that test, I’m speaking a bit mathematically, in that test millions go through it, you can’t filter them. I mean, I’m referring to what you said about P of A, P of B, P of B given A, P of A given B. Many go through, and then you have no way to check it.
[Rabbi Michael Abraham] Again, if—
[Speaker B] if you send all the people—
[Rabbi Michael Abraham] if you send all the people without symptoms or initial indications, then you’re completely right. There it’s worth nothing. But if you send me because I have coronavirus symptoms—you just don’t know until the test comes back, but I do have symptoms—then the test is already meaningful. That’s exactly the point. There is a very big difference between sending the whole population to get tested for coronavirus—that’s worth nothing, nothing at all—and sending someone about whom you have some suspicion, based on one clinical phenomenon or another, and you say to him, okay, take a test so we can see what the situation is. That is already meaningful. That is the parallel to the prosecution’s preliminary screening. It’s like if two witnesses came who saw a murder, and I put all the residents of the State of Israel before them in a lineup.
[Speaker B] It doesn’t apply. They simply wouldn’t identify anyone.
[Rabbi Michael Abraham] That is parallel to sending all the Jewish people to get a coronavirus test. It’s the same thing. But if you put before them only the five people who were in the area and had the opportunity and ability to commit the murder, that’s fine, because then the rarity of the phenomenon is one in five, not one in a million. Therefore, in practice, on the ground, it works—but one has to be very, very careful. Last time I brought the examples of Munchausen syndrome and all kinds of things of that sort, where people were convicted and sat in prison, all because of this mistake, and many medical diagnoses also fall into this failure, at least until people became aware of the problematic nature of it. And even today I’m not sure how aware everyone is of this. In any case, let’s think now in the same way about the quality of a judge. I said I had a criticism of the calculations Nadav made, because he was basically checking the quality of the religious court in terms of in what percentage of cases they would be right. Meaning, assuming you committed the murder, what is the chance that the religious court will indeed rule that you are a murderer? That’s what defines the reliability. Let’s talk about a judge, not a court. One judge. So let’s say he has reliability of ninety percent. Okay? The judge’s ninety percent reliability basically means that if I committed the murder, there is a ninety percent chance that he will indeed declare me a murderer. But the important question when we come to examine the reliability of the ruling—not of the judge. After all, what matters to me is that the judge has now declared me a murderer. Now what matters to me, or what matters to the public, is whether I can accept the ruling of the judge. That’s really what matters. The given in the problem is the reliability of the judge, but the datum that interests us is the reliability of the ruling, not of the judge. And we want to infer from the judge’s reliability to the reliability of the ruling, and that has to be done very carefully. Because if we now do it without preliminary signs—say we take the whole thing, we passed all the Jewish people before this judge, and he declared so-and-so a murderer, and he has reliability of ninety percent—the chance that this person is a murderer is zero. Even though the judge’s reliability is ninety percent. Therefore the important question is not in how many cases the religious court will hit upon the correct law, but in how many cases the correct law will match what the religious court ruled. And that is a completely different question. And the calculations Nadav makes are calculations of the first type, not the second. When I want to know what the chance is that the religious court was right, what the chance is that I didn’t convict an innocent person here, that is not directly connected to the quality of the judge. It is affected by the quality of the judge, but it is definitely not the only parameter. It is not the only thing that can teach me the quality of the ruling, how much I can rely on the ruling. Okay, so that’s about the point I said I still wanted to clarify today, because last time I felt it hadn’t come out clearly enough. What is happening here. Rabbi? Yes.
[Speaker D] Could it be that the explanation the rabbi just gave actually gives us a better formulation of the postmodern claim that it’s impossible to know the truth about reality and that it’s basically our narrative? Because we use some kind of tool, we try to argue and explain rationally, but it depends on our underlying assumption about the prevalence of the phenomenon, and that’s not something we checked. We assume, we feel, and therefore if we feel that everyone around us is a murderer then we determine one thing, but if I feel that everyone is righteous then all our diagnostic tools look different.
[Rabbi Michael Abraham] No, but I’m saying: we have other diagnostic tools that are not built on assumptions. We have diagnostic tools—precisely the preliminary filtering I talked about—with clinical symptoms for a doctor, or opportunity and means for a judge. And that is something objective. Therefore it’s not all based on assumptions. Today I posted a column on the website in which I explained that postmodernism apparently has two stages, that the postmodern move has two stages. The first stage is the stage of questions. Who says you’re right? Maybe the opposite is true? The stage of questions is an excellent stage. It’s not postmodern at all. It’s very important to be critical and think maybe what you’re saying is wrong, maybe the opposite is true. Postmodernism lies in the second stage, in the stage of the answer, not in the stage of the question. And their answer is that the two possibilities are always equivalent, neither one is truer than the other. To raise the question—maybe another possibility is true and not this one—that is critical thinking, not postmodernism. It is definitely important, and also not new. Postmodernism takes the question mark and turns it into an exclamation mark. Nobody is right, because the opposite is just as true as what you are saying. There is no way to know who is right.
[Speaker B] And what—
[Rabbi Michael Abraham] What you raised earlier—I accept that the question is a good one. One needs to think about how reliable court rulings are, or doctors’ diagnoses, and so on. But on the other hand, the line of thought I proposed here also gives an answer; it doesn’t remain at the question stage and therefore conclude that nothing is true and no one is genuine, as you wanted to claim. No. It only means one has to be more careful when reaching conclusions. But there is a systematic, rational way to arrive at good conclusions.
[Speaker D] But again, Rabbi, we’re now examining reality. We ask ourselves whether it seems to us that the State of Israel is currently carrying out genocide, or has until now carried out genocide, or not. Now supposedly people are having a rational argument about this. I argue with people about it. People give me arguments. Based on the underlying assumption, how I feel, about basically the prevalence of the phenomenon in the population, and then I see that suddenly it all completely depends on the underlying assumption, and really—
[Rabbi Michael Abraham] I don’t agree at all. Here you have questions that are not statistical at all. What does that have to do with statistics? There is no question here of the frequency of phenomena. You can argue about the question of whether, I don’t know, killing two civilians for every terrorist is called genocide or not called genocide. Fine—that’s a question and everyone can decide as he decides. But it has nothing to do with the prevalence of a phenomenon or the problems of probabilistic calculations.
[Speaker D] Fine, so maybe that’s not a good example. I mean in general, when you come to examine reality you bring a whole set of rational arguments that converge on some test, let’s call it that, and you say, here, this proves something. The other person tells you: my underlying assumption about the prevalence of the phenomenon is completely different, and therefore my proof regarding reality is different.
[Rabbi Michael Abraham] That’s such a general statement. I can’t do anything with it. If you bring a specific example and show me that it really all depends on the prevalence of the phenomenon—in a moment I’ll bring such an example, where it all depends on the prevalence of the phenomenon—then you’ll be right. I’ll really say: here there truly is no way to get to the truth. But it’s not true that all cases are like that. And there are cases in which there absolutely is a way to move forward, like I said earlier regarding medical diagnosis and legal rulings. That doesn’t mean that in every case we have such a way, but it also doesn’t mean that in every case we don’t have such a way. Rather, we have a systematic way to advance, and sometimes we won’t succeed in reaching an answer. At least, as rational people, we’ll be aware that in this case we really have no way to reach an answer. Fine—that isn’t postmodernism. It’s simply sober thinking. Postmodernism means that in no question and in no situation do we have a way to reach the truth. That is simply not true. It’s the opposite of what… maybe more…
[Speaker D] For example, there is a book by Foucault—the rabbi surely knows it—about madness and the distinctions of the courts—
[Rabbi Michael Abraham] Madness and Civilization. Yes. Exactly.
[Speaker D] So again, it depends on the assumption… So clearly psychiatrists have DSMs, criteria for diagnosing various illnesses, but all this depends first of all on the very definition of the illness. Right, it depends on the definition and not on the prevalence.
[Rabbi Michael Abraham] But again, it depends on the definition and not on the frequency; one hundred percent, I agree. By the way, I completely agree with Foucault. Unlike postmodernism, which I have major criticism of, with Foucault I completely agree.
[Speaker D] That has nothing to do with postmodernism at all.
[Rabbi Michael Abraham] It’s a sober way of thinking that is simply aware that there are underlying assumptions at the base of our determinations. Very true, absolutely. Completely true.
[Speaker D] And the underlying assumptions depend on us. Right. On our feeling.
[Rabbi Michael Abraham] Right. That’s why I’m saying… no…
[Speaker D] But why doesn’t the Rabbi accept that only regarding madness and not regarding everything?
[Rabbi Michael Abraham] After all, his books embrace the whole—
[Speaker D] human phenomenon.
[Rabbi Michael Abraham] So I’ll explain. No, that’s not true; that’s exactly the postmodern leap. Here I accept Foucault and disagree with postmodernism, and the dependence of one on the other is incorrect. Because when you’re talking to me about statistical problems, or even philosophical questions like the law of causality, the principle of causality, whether everything has a cause—then I have a basic assumption that everything has a cause, I believe in the principle of causality. Let’s say, for the sake of argument, that you don’t believe it. Okay? So what? All I’m claiming is that there is truth here, but yes, I probably won’t have a way to convince you. Okay? But there is truth here. It depends on the basic assumptions. But—but excuse me—not that it depends on the basic assumptions, rather there is truth here and we have no way to reach it. In Foucault’s case, my claim is that there is no truth. There is no truth because the question whether your criterion for mental illness is a Protestant criterion or some Jewish criterion or another criterion—it doesn’t matter—lack of functioning, yes, Max Weber’s thesis also goes in that direction and so on—that really is a value-laden criterion. Meaning, everyone has his own values. But that’s not…
[Speaker D] But the Rabbi thinks there are correct values—
[Rabbi Michael Abraham] —and incorrect values. What I said—I added a sentence here, you stopped me. I’m not talking about values in the moral sense. Values in the sense of what is called sane. Suppose someone wants to die, okay? And now he has cancer. Is he sick or not sick? I claim he is not sick. Because his condition fits what he wants. He is not sick. Meaning, he wants to be like this, so what’s the problem? Illness is when there’s something bothering you, something you don’t want. That’s illness.
[Speaker D] Ecclesiastes says to the Rabbi that even if a person is healthy he’s basically… right. It makes sense to want to die that way.
[Rabbi Michael Abraham] Fine, okay, exactly. So if a healthy person wants to die, then on the contrary, he is sick. Because he’s not sick. His healthy state is to be sick and die. And I mean this seriously. That’s why I’ve written about this more than once and spoken about it more than once. The concept of illness is a concept that is entirely value-laden—not value-laden in the moral sense. A concept of, I don’t know what to call it, worldviews, outlooks, not facts. It has nothing to do with facts. It is impossible to define illnesses, neither in psychiatry nor in medicine—yes, physical medicine either—in any objective way whatsoever. I had some argument with Yoram Yovel—yes, part of it spilled over onto my website, in Makor Rishon, and afterward we continued both privately and on my site in columns 25 and 26. You can look there. And I think in the end he admitted it. But this is something entirely different, because there really is no truth there. It’s like the other example I gave, yes, where people often criticize religious thinking for thinking that the earth is at the center and the sun revolves around the earth. “You primitives, Copernicus already taught us 500 years ago that this isn’t true.” That’s nonsense, of course. Copernicus didn’t teach us anything. There is no way to determine who revolves around whom—whether the earth revolves around the sun or the sun revolves around the earth. Kinematically there is no way at all to determine it. Dynamically there are various definitions, but those are physicists’ definitions. Definitions you can accept, you can reject. Kinematically there is no possibility of distinguishing between these two things. The question is where your coordinate origin is. If your coordinate origin is the earth, then the sun is the one revolving. If your coordinate origin is the sun, then the earth is the one revolving. There is no truth and falsehood here. What Copernicus discovered is that there is a simpler coordinate system to work with. If you put the center at the sun and not the earth, the equations look simpler, because the paths are simple ellipses. That’s all. But there is no truth and falsehood here. So for example, in the Copernican context, דווקא in the Copernican context, I am postmodern. I am postmodern in that sense because there is no truth in that particular question. But that is not postmodernism. There really is no truth here. Postmodernism says there is no truth in any question. That is postmodernism, and that I do not accept.
[Speaker D] But again, regarding illness and health, the Rabbi agrees there is no truth?
[Rabbi Michael Abraham] Completely. Meaning, there is truth, only the truth depends on what the person wants.
[Speaker D] Then there is no truth. It depends on what truth I’m willing to accept. No, not willing to accept—it has nothing to do with being willing to accept. He determines whether he is sick or not. Only he determines it. There is absolute truth. I’ll ask him and then I’ll know whether he is sick or not. But there is no definition of it that you can come to me with instruments and establish. It depends on what he wants. Why isn’t that true of all the phenomena of life?
[Rabbi Michael Abraham] All the phenomena that we can experience from life? I don’t know what “experience” means. Causality isn’t like that. Either causality is true or it isn’t true. It may be that I won’t succeed in proving to you that it is true, but either it is true or it isn’t. Here there is truth. It’s not like Copernicus, where there is no truth.
[Speaker D] When the Rabbi gets to free choice, suddenly all of causality gets undermined.
[Rabbi Michael Abraham] Right. Fine, we won’t get into the argument about causality now; I’m only bringing it as an example here, I don’t want to get into that argument now. But yes, free choice is the same. Either we have free choice or we don’t; there is truth here. It’s not that there is no truth here. Maybe I have no way to prove it, or you have no way to prove it to me, it doesn’t matter—but there is truth. It’s not like Copernicus. With Copernicus there is no truth. There are simply two equivalent possibilities. It’s like Fermat’s principle in optics, yes? The question whether optics is geometric—yes, Snell’s law with refraction and transition from one medium to another—the question is whether you describe it that way or through Fermat’s principle, that light chooses the shortest path to reach its goal. It turns out the two possibilities are equivalent, even though one is teleological and purposive and the other is causal. They are completely equivalent. Everything that comes out this way comes out that way too. So who is right? Nobody is right. These are two forms of description. A Cartesian system and a polar system for a point in a two-dimensional plane. Who is right? Is x equal to one and y equal to one, or is the distance root two and the angle 45 degrees? This is a Cartesian description and this is a polar description of the same thing. There’s no right and wrong here. These are just two ways of describing it, that’s all. Okay, back to our topic. So basically what I claimed is that when I want to examine the quality of the judge or the quality of the religious court—meaning the quality of the court’s rulings—the datum of the judge’s quality is not enough. The datum of the judge’s quality is only one of the parameters in calculating the quality of the ruling. And now to understand this a bit more, I’ll go into a discussion I mentioned in the example I gave. Look, I once had a debate with Professor Eilam Gross, a very well-known physicist, about God, belief in God, and so on. And before that debate, I read some article of his in Odyssey, I think it was, where he talked about God and Bayesian probabilistic calculations and so on, the existence of God. They brought there—he and some friends of his at some conference—he told a story there about how he and some friends at a conference discussed some argument in someone’s book that proved the existence of God and so on, and they mocked it and the like. So following our debate I also wrote a column or columns on the site, and there I analyzed it. In the debate I only mentioned briefly the mistake in his article, but on the site I brought it in greater detail. So I want to present it to you so that you can really see the meaning of the difference between these two questions. Right, so I’ll bring you the quote here. It’s column 506 on my website. “In 2007 five physicists sat down for lunch as part of a conference on statistical testing of hypotheses regarding the search for the Higgs particle”—yes, the God particle that in Yediot Aharonot is called the God particle. “We talked about a book called The Probability of God, which had just come out and purported to calculate by means of Bayes’ formula the probability of the existence of God. Although we all regarded the book as absolute nonsense”—very important, pay attention, because here I’m getting to your question, Shmuel, from before, about basic assumptions—“the conversation developed and we found ourselves sliding into a heated discussion. After hours we reached a kind of agreement on the issue of what the scientist’s God is.” Fine? Now I’ll skip the question of the God of the gaps; that’s less important to me right now. Or—let’s talk about conditional probability. Conditional probability, what I also described earlier, basically means—it is based on the fact that the probability of some event is not an objective datum. It depends on the information I have. Suppose I ask: what is the probability that a die will land on the number five? There is no answer to that question. If the die is fair, then the probability is one-sixth. But if the die is something else, I don’t know—you need information about the die in order to answer the question whether that probability is one-sixth, or what the probability is that we’ll get a five. But now we may have additional information. Suppose I have information that this die has already been rolled and the result that came out was odd. And now they ask: what is the chance that the result was five, assuming a fair die. What is the answer now?
[Speaker B] Well, thirty-three?
[Rabbi Michael Abraham] One-third, yes, correct. There are three odd outcomes—one, three, and five. Assuming the die is fair and all three are equally likely, that means the chance is one-third. So decide: is the chance one-third or one-sixth? It depends on what information I have when I ask the question. If the information I have is only that the die is fair and that’s it, I know nothing else beyond that, then the probability is one-sixth. If I have additional information, for example that the result was odd, then the probability can be different—one-third. By the way, the more information I have, the greater the probability will be, right? I’ll be able to estimate the result more confidently. Additional information always helps me estimate the result, okay? Or if I have information, I don’t know, that the result was greater than two. Okay, then what is the chance that it came out five? Twenty-five? One-quarter. Right? Four outcomes are greater. So there is a twenty-five percent chance it was five. Meaning, it depends; the answer to the question what the probability of a certain thing is depends on what information I have. And therefore statisticians or mathematicians define the concept of conditional probability. There is a probability of event A, and there is a probability of event A if information B is known. That’s P of A given B. P is probability, yes? P of A is the probability of A. P of A given B means P of A if I know B. For example, if I know that the result was odd, yes? What is the chance that it was five? Then A is “it was five,” B is “the result was odd.” So P of A is one-sixth. But P of A given B is one-third. Fine? The chance that it was five given that the result is odd—P of A given B—is one-third. But unconditioned P of A, P of A itself, is one-sixth. The chance of five is one-sixth. Okay.
[Speaker B] But that’s now post factum, and that’s before.
[Rabbi Michael Abraham] Yes, it doesn’t matter. I have information. I need it to be post factum in order to use the information. I could have drawn—suppose I know that this die lands only on odd faces. Now roll it tomorrow.
[Speaker B] It’s just any information, any information—
[Rabbi Michael Abraham] It doesn’t matter, that’s just the illustration I found, it doesn’t matter. So okay. That is basically the meaning of conditional probability. Conditional probability is the mathematical way to take into account the information I have in probability calculations. I want to calculate the probability of event A when I have information B, so I calculate P of A given B, and it won’t be the same as P of A. I can of course ask the reverse question: given that it came out five, what is the chance that the result was odd?
[Speaker B] One in six? It’s one. One. Right, it’s one. But out of six. Well, a hundred percent. A hundred percent.
[Rabbi Michael Abraham] One meaning 1.0, one hundred percent. After all, it came out five; five is odd.
[Speaker B] Ah, if it already came out.
[Rabbi Michael Abraham] Yes, I’m saying given. Okay.
[Speaker B] Now—
[Rabbi Michael Abraham] I’m asking P of B given A. Before, I calculated P of A given B. What is the chance that it came out five if I know that it came out odd? The answer is one-third, right? Now I’m asking the reverse question. What is the chance that it came out odd given the fact that it came out five? The answer is one.
[Speaker C] One hundred percent, yes.
[Rabbi Michael Abraham] Right? You see that one-third is not one. Meaning P of A given B is not P of B given A. It’s not the same thing. Different questions that have different answers, or can have different answers, exactly like with the test or with the judge. Meaning, if I murdered someone, what is the chance that the judge will rule that I’m a murderer—that’s P of A given B. But if the judge ruled that I’m a murderer, what is the chance that I really did murder—that’s P of B given A. And the answer is not necessarily the same answer. It could be that P of A given B is excellent but P of B given A is small.
[Speaker B] And that’s not connected to murder; that’s true in every decision of a judge. Okay.
[Rabbi Michael Abraham] Absolutely. No, no, of course. I’m saying murder is just an example.
[Speaker B] Yes, it’s just an example.
[Rabbi Michael Abraham] A loan, yes, it doesn’t matter. So the claim I’m making here is that it’s very important to formulate our parameters properly: what are the events A and B, what is the probability, what is the question I am asking. And statisticians know that the moment you ask the question precisely, you’ve done three-quarters of the work. Meaning, now it’s just calculation. That’s already not—it’s the easy part. The problems are always in the fact that you simply didn’t ask the right question, or didn’t ask it precisely. If you ask the question precisely—“a wise question is ninety percent of the answer.” Okay? And in statistics this is very common. Meaning all kinds of statistical paradoxes and things of that sort always basically stem from the fact that you didn’t ask the question correctly or didn’t narrow it down, yes? You didn’t formalize precisely the question you were asking. Now let’s see the connection between these two questions. The way to get to the connection is Bayes’ formula. Suppose on one die roll a five came out, and now I rolled again and again a five came out. Okay? What’s the chance that both on the first roll a five came out and on the second roll a five came out? So if the rolls are independent, then it’s the product of the probabilities. Right? One-sixth times one-sixth, one over thirty-six. Okay? But if there is dependence between the rolls, then you’re not allowed to multiply probabilities. And then what you do is basically say this: I calculate the chance that a five came out, and then I multiply it by the chance that a five came out again given that a five already came out. If the question is—if those probabilities depend on each other, then the way—look now at the formula here, do you see the formula? P of A and B together, do you see, this is it. On the left side of the formula, P of A and B. P that both A and B happened. If they are independent, then it’s simply the product of the probabilities. But if they are dependent, then you have to do it—there are two ways to do it: either it’s the probability that A occurred, whatever occurred occurred, times the probability that B occurred given that A occurred first. Alternatively, it is the probability that B occurred times the probability that A occurred given that B occurred. It’s the same thing.
[Speaker B] It’s the same thing, because mathematically it’s the same thing.
[Rabbi Michael Abraham] Right. Both of them basically give me the chance that both A and B occurred. Why is that interesting? Because now I ignore the left side of the formula and look only at these two. These two are equal, right? If they are equal, then there you see—we have found the connection between P of B given A and P of A given B. The connection between them depends on P of A and P of B. There, we have a formula. That’s Bayes’ formula. You see, if for example the judge—the quality of the judge—is P of B given A. Okay? Given that A happened, what is the chance that he will output A? Meaning—sorry—given that X happened, that was event A. Event B means the judge ruled that X happened. Fine? That is event B. Now, what does P of B given A represent? The quality of the judge. Right? What does that mean? Given that X happened, what is the chance that the judge indeed rules X? Right? In how many of the cases does he rule correctly? He will hit the correct answer. In contrast, this probability, P of A given B, says: assuming the judge ruled that X happened—that’s B—what is the chance that X really happened? Okay? Now what is the relation between these two questions? You see, there is no equality between them. No equality. The question is what P of A is and what P of B is. What is P of A? It’s how many murderers there are, right? What is the chance that a certain person murdered—how many murderers there are. P of B is basically one, because P of B is: the judge ruled, the judge ruled X. Now I’m asking what is the chance that if he ruled X, then X really happened. So the fact that he ruled X—that is already probability one, it happened. Post factum, what you said earlier. Okay? So basically you see that this depends on P of A. This basically represents the phenomenon I described to you earlier, that the rarity of the phenomenon affects the relation between the two conditional probabilities. Or in medical diagnosis, if I want to know what is the chance that the test will classify me as sick—that’s B—assuming I really am sick, that’s P of B given A, and I know that if I am sick the test classifies me as sick with a probability of ninety percent or ninety-five percent—it depends on P of A, depends on what the chance of being sick is, how many sick people there are. You understand that basically Bayes’ formula says what I told you above, what I told you earlier. That’s Bayes’ formula. Now let’s move to Eilam Gross. I’m quoting here from the article he wrote in Odyssey. “The hypothesis of the existence of God is supposed to be examined by the scientist by answering the following question”—yes, this is the continuation of his meeting with those same five physicist friends; I remind you this was a conference on statistical testing of hypotheses. That was his mistake. Statistically—theirs, not his, of all five. They fell here into a really elementary statistical mistake. From all the mockery of the fellow who wrote the book, they fell into a silly mistake and he was right. Five professors at a very high level at a statistics conference. This teaches you the importance of assumptions, of starting points. “Given the data we have—the earth, sun, moon, stars, etc.—what is the probability of the existence of God?” Right? What is proof of the existence of God? I receive as input reality, right? That is the data, and I ask what is the chance that there is a God. Okay? Let’s say that is P of B given A. Given reality A, what is the chance that there is a God? That’s P of B given A. Fine?
[Speaker D] How many worlds did you examine? I don’t understand the question at all.
[Rabbi Michael Abraham] No, no, leave aside how many worlds I examined. I’m formulating the question formally right now. I’m not getting into how one finds that probability. But this is how I formulate the question. I’m looking for P of B given A. That’s what I’m looking for. “We need to formulate our questions in a way that they can be answered. And in both cases, physics and theology, the questions are as follows: assuming there is a Higgs particle, to what extent do the collision data fit its existence?” That’s the scientific question, not important right now. Or: “assuming there is a God, to what extent does the amazing universe that surrounds us indeed fit the fact of His existence?” You notice that the question has been reversed. Right? Assuming there is a God, what is the probability that this would be the universe. The previous question was: assuming this is the universe, what is the probability that there is a God. Okay. “In mathematical language one can also ask thus: what is the probability of the existence of the universe assuming God exists? This is of course a trivial question whose answer is one hundred percent. This is not the question that interests us. The question that interests us is the reverse: what is the probability of the existence of God given the universe as we understand it?” Okay, up to here everything is fine, except for one thing of course. The answer is not one hundred percent. That’s not true. What, if there is a God, that means there necessarily will be a world? What if He decides not to create the world? Or to create a different world?
[Speaker C] He means that that was the question. If so, if that was the original question, then if we already have the answer about God’s existence, it doesn’t interest us.
[Rabbi Michael Abraham] No, he doesn’t mean anything like that. He says it’s a trivial question whose answer—
[Speaker B] —is one hundred percent.
[Rabbi Michael Abraham] But that isn’t true. That’s an assumption altogether, not a question. No, it is a question, but the answer to it is not one hundred percent. We have no way of knowing the answer to it.
[Speaker B] Of course it’s not one hundred percent, but it’s also not a question; he’s assuming some answer, a question he answers with one hundred percent, even though it’s not even fifty.
[Rabbi Michael Abraham] No, again, you’re mixing up two things. The question is a question. His answer to that question is incorrect, that’s all. But the question is a question. Fine? Assuming there is a God, what is the chance that there will be a world?
[Speaker B] I don’t know how to answer that.
[Rabbi Michael Abraham] Assuming, assuming, yes.
[Speaker B] He framed it as an assumption.
[Rabbi Michael Abraham] The probability here rests on an assumption; here it’s conditional probability. Given that there is a God—that’s A—what is the chance that there will be a world? P of B given A.
[Speaker B] P of B given A, yes, that’s the question.
[Rabbi Michael Abraham] Okay. Now that is basically what he says. Now he says: “The classic argument of the outreach rabbi says”—meaning the distinction he made above is a correct distinction. These really are two different questions. The theological question is: given a world, what is the chance that there is a God. The question: given that there is a God, what is the chance that there will be such a world—that is a completely different question, and you cannot learn one from the other. Up to here I completely agree. I do not agree that it’s one hundred percent, but that’s less important for our purposes here. “The classic argument of the outreach rabbi says: see how beautiful the butterfly is, see how complex the human being is—could these have arisen by chance? Certainly not. And there you have proof of the existence of God.” Okay. Up to here, correct. That is the argument of the outreach rabbi—again, in a very simplistic form, but that is the argument. “This argument relies, of course, on a common mistake in statistics,” and here is the key sentence: “namely that the probability that, given the amazing butterfly, God exists, is equal to the probability that, given God, the outcome is an amazing butterfly. The latter probability equals one hundred percent, but of course the former does not.” In those twenty-three words there are not two words—words that connect to each other into a correct statement. There are none, you won’t find them. There isn’t even half a sentence here that is correct. I don’t know how he managed to pack so many mistakes into three lines. Full of mistakes. Unbelievable. “The probability that, given the amazing butterfly, God exists, is equal to the probability that, given God, the outcome is an amazing butterfly.” Is that the assumption of the outreach rabbi? Exactly the opposite. The outreach rabbi asks the first question: if the butterfly is amazing, what is the chance that God exists? Where did he connect that to the question that if there is a God then there is a butterfly? Second, if there is a God then there is a butterfly—the probability is one hundred percent? Absolutely not. That is not correct. Maybe God will decide not to produce a butterfly. What does that have to do with it? Does the outreach rabbi learn from this one hundred percent to the second one hundred percent? The outreach rabbi also does not think that this is one hundred percent. Does the existence of a wondrous butterfly mean that there is a one hundred percent chance that there is a God? No. It means it is much more likely that there is than that there isn’t. But it is not one hundred percent. There isn’t a sentence here, there isn’t a word here that is correct. Now that is simply unbelievable. The man made the correct distinctions, he is speaking in the context of a statistics conference, he is not suspect as someone who doesn’t know Bayes’ theorem. Okay? Bizarre. Where does all this come from, of course? From that same assumption that it is obvious there is no God. That is the assumption he is making, of course—the context of assumptions, what Shmuel raised earlier. Now look, I have two formulations. When he says, “Bayes’ theorem gives us the connection between the two probabilities. The probability that the butterfly is beautiful given God must be multiplied by the probability that God exists at all, for if there is no God there is no point in the whole probabilistic discussion. The probability that…” You notice? After all, according to his view God does not exist, so the probability is zero; therefore this product comes out zero. Which means, of course, that he himself is begging the question, not the outreach rabbi. He is begging the question; he assumes there is no God and therefore the probability comes out that there is no God. Thank you very much. “The probability that the existence of the universe points to the existence of God equals the probability that, given God, the universe exists—but only on condition that there indeed is a God.” That too is not true. Simply not true. Nothing here is correct. It’s unbelievable. And all of this is the mistake of mixing up the two questions, exactly as we spoke about earlier regarding the judge and all the other things. But here you see where the assumptions come in, and now you’ll see even more where my assumptions about the probability of God’s existence come in. Look. I’ll start with a first formulation, okay? Claim A is “God exists,” fine? Claim B is “a complex world exists,” or “a wondrous butterfly exists,” it doesn’t matter, okay? Now, the absolute probability that God exists is P of A, right? We don’t know it, of course. Eilam Gross knows—it’s zero, yes? But we don’t know it. We come to the question tabula rasa, and we basically want to clarify what’s going on here. The probability that a complex world exists is P of B, equal to one, right? We know—there is a world before us and it is complex. Here there are no probabilities. The absolute probability, not the conditional one, is known to us: it is one. Okay? Regarding the conditional probabilities, what we are actually looking for is P of A given B, right? Given that a complex world exists, what is the chance that God exists? Right? That is basically the question of the outreach rabbi. In the term “outreach rabbi” itself you can already see the a priori attitude here. But okay. In contrast, the reverse conditional probability, P of B given A—what is that? Assuming there is a God, A, what is the chance that a complex world exists? I have no way of knowing that. So what do we do? I’m looking for it, okay? I want to use Bayes’ formula, I want to use Bayes’ formula, but I don’t know this. I don’t know this either. P of B is one, but I don’t know this. I have no way of knowing it—contrary to Eilam Gross’s one hundred percent. Not true, there is no way to know it. So now what do I do? I do the following trick. What do I know? I know that if God does not exist, there is no chance we would have such a complex world, right? Or the chance is very small. That I do know. Okay? So basically what I know is this: P of B given not-A. I don’t know P of B given A, I know P of B given not-A, right? Meaning if God does not exist, the chance that a complex world B exists is something—some x, where x is a number. A very, very small number. Fine? Now, what matters to us is to calculate this: what is the chance that God does not exist given that the world is complex? Why is that important? Because if I know what the chance is that God does not exist, one minus that is the chance that He does exist. Okay? So that’s it. Pay attention. Yes, after all what I’m looking for is the chance that, given there is a complex world, God exists. So I say like this: P of B given not-A times P of not-A equals P of—anyway just look at it, not important right now, I won’t read it. It’s Bayes’ formula, only instead of A I wrote not-A. Fine? The event is not-A, what difference does it make? That’s my event.
[Speaker B] So it should be minus A, so to speak, yes?
[Rabbi Michael Abraham] Yes, exactly. Meaning, it does not exist. Okay? I’m allowed to; Bayes’ formula applies to any event I want, so both the event “God exists” and the event “God does not exist,” it makes no difference. Bayes’ formula is always true. Okay? Now what interests me, of course, is this. Right? What is the chance that God exists given that there is a complex world? But that thing is simply, as you see from here, P of A given B—the chance that God exists given a world—is one minus the chance that God does not exist given a world. Right? And that I calculate from Bayes’ formula. Therefore the result comes out like this: the chance that God exists given a complex world is one minus x times P of not-A. Okay?
[Speaker C] That—
[Speaker B] means it comes out a number—
[Speaker C] that is a very small number.
[Rabbi Michael Abraham] Right. Because P of not-A is a number between zero and one, so no matter what you assume—P of not-A is a number between zero and one, a probability. Okay? So what is written here, x times that, is something smaller than x, and x itself is very small.
[Speaker B] Like, it’s a world but not complex, so to speak. What? A world but not complex.
[Rabbi Michael Abraham] No, it is complex.
[Speaker B] But it’s small, so to speak.
[Rabbi Michael Abraham] No, no, the chance of it. The chance that God exists given a complex world is one minus a very, very small number. So the result is almost—
[Speaker C] one. Because your assumption is that x is a very small number. Yes. Since there isn’t much chance that existence exists without God.
[Rabbi Michael Abraham] That is the claim of the outreach rabbi. That’s what he claims. Not what Eilam Gross puts in his mouth. I claim that a complex thing does not arise on its own, does not arise spontaneously. That is the claim. Now you can argue about that, no problem. But don’t tell me that his argument is statistically incorrect; it is completely statistically correct. That’s what I just proved to you now. This is basically the mathematical representation of the physico-theological argument. The physico-theological argument basically says that for a complex thing, the chance that it is formed spontaneously is tiny, very small. And that basically means that if we have a complex world, then the chance that there is a God is almost one. Okay?
[Speaker B] So how does Eilam Gross not know that? What? Eilam Gross doesn’t know that?
[Rabbi Michael Abraham] Of course he knows that.
[Speaker B] No, but like—
[Rabbi Michael Abraham] It teaches you what biases can do to a smart person. Well, that’s exactly the point.
[Speaker B] A complex world is one hundred percent, meaning it’s always one.
[Rabbi Michael Abraham] Right. P of B is one; we know it in this case. Good. By the way, from this you can also derive P of A. Right. P of A given B is a very large number times P of B, which is one, so the result is almost one. So P of A is almost one.
[Speaker B] Because in the end we always get one.
[Rabbi Michael Abraham] Almost one, yes. Meaning it is very, very likely—that’s the point. Now there is another formulation that I won’t have time to get to here; I’d like to do it next time. Why is it important to me? Because there I’ll show you how begging the question enters into the calculation, and why Eilam Gross will beg the question and arrive at the conclusion that there is no God, while I won’t assume anything and will arrive at the conclusion that there is. And therefore he is the one begging the question, not the outreach rabbi. But for that I need the second formulation, and there isn’t time to get into it right now; we’ll do it next time. Look at column 506 if you want to read it more calmly. So maybe I’ll send it as a link on WhatsApp. Okay, I’ll stop here. Any comments or questions?
[Speaker B] Yes, regarding a discussion that judges are supposedly judging—after all, the probability that they are right is always fifty percent.
[Rabbi Michael Abraham] Why?
[Speaker B] Because their decisions always move between one opinion and another opinion. Meaning, supposedly you can’t determine that what he said is certainly true, and there isn’t any more—wait, I’ll explain—supposedly you can’t determine that what he said is definitely true, and there isn’t any further…
[Rabbi Michael Abraham] But why fifty percent? So—
[Speaker B] What?
[Rabbi Michael Abraham] The fact that there are two possibilities doesn’t mean the probability of each is fifty percent. Only if the probabilities are equal. But who says the probability of his making a mistake and his being right are equal?
[Speaker B] No, we’re not talking about the conditional; we’re saying for sure it’s always post factum, because when they come to a hearing it’s always after all the—
[Rabbi Michael Abraham] After the event happened. Right. Now I ask what the judge will rule. So who said it’s fifty-fifty? You say it’s either one or zero. So what? But the probabilities of one and zero are not equal. Say you have a biased coin. Then it can come up heads or tails, and it’s not fair. So the probabilities of heads and tails are not equal. It could be that the probability of heads is ninety percent and the probability of tails is ten percent, even though there are only two possible outcomes. In order to get to fifty percent, you have to assume that the probability of each of the two outcomes is equal. That doesn’t hold for a good judge. A good judge has a greater chance of being right than of making a mistake. Ah, like…
[Speaker B] But how can you know who’s good and who’s not good?
[Rabbi Michael Abraham] Meaning, that’s—
[Speaker B] dependent on your assumptions.
[Rabbi Michael Abraham] That’s another discussion, another discussion. We spoke about that in previous lessons, that there is proof, and therefore this is a majority that is before us. But regarding the—
[Speaker D] After all, we know—the Rabbi knows this better than all of us—that those same proofs for the existence of God, for example, affect one person deeply, and he is full of wonder and faith and runs to accept upon himself the yoke of the kingdom of Heaven and the yoke of Torah and commandments, and for another it just passes right by him even though they have the same IQ. And you ask yourself: after all, both of them understand and examined the same arguments and proofs at the same depth, and arrived at a different way of life. How can that be? But exactly what the Rabbi showed us today—if a person comes, let’s say, to Rabbi Kook, who lives God entirely, and we bring him the weakest proof imaginable, he’ll see it like the splitting of the sea, and it’s truth…
[Rabbi Michael Abraham] You’re talking to me about psychology; I’m talking to you about logic.
[Speaker D] Yes, but it explains very well why from the very same proofs one person can arrive at—
[Rabbi Michael Abraham] Psychological tendencies, of course. Biases—we all have them, we’re human beings, that’s obvious.
[Speaker D] It’s not only that. You can formulate it not merely in a psychological way. When the Rabbi comes and says what is the chance that I’m feeling something that has no connection to reality—that too is some kind of epistemology.
[Rabbi Michael Abraham] There are two possibilities to explain what you described at the beginning. One possibility is biases. Two people equally smart, with the same data, are presented—
[Speaker D] No, but I’m trying to formulate the biases in a less flattening way. I’m saying, when I come to Rabbi Kook and Rabbi Kook says to me, listen, the chance that I’m constantly feeling divinity and there’s nothing there, in my view, is very small, not high. And then they bring me some proof and I’m full of wonder and singing the Song at the Sea. The other person really feels the opposite, and they bring him the same proof…
[Rabbi Michael Abraham] Okay, so that’s the second possibility I wanted to mention. One possibility is that these are biases. The second possibility is that they have different underlying assumptions, and every argument is built on underlying assumptions. For example, if someone comes and says, look, a complex thing really can arise spontaneously, the probability is not small, okay? Then this argument collapses. But if he really doesn’t think that—and I think most people, if they are honest with themselves, do not think that—then he cannot argue with this argument, so this argument is correct.
[Speaker D] What I tried—
[Rabbi Michael Abraham] to do—
[Speaker D] I simply tried to bring the psychological factor, or the biases, however you want to call it, into that same field of statistics in the sense of how we think there is some… what is the reliability of this test. We feel that something exists, we think of ourselves as—
[Rabbi Michael Abraham] That is the proof I brought here. What’s the problem with the proof I brought here?
[Speaker D] What, now at the end? Yes. It’s too complex. I’m saying, I tried to simplify it in order to explain—and in a way that won’t just flatten it into psychology—why the same proof can cause one person to reach the conclusion—
[Rabbi Michael Abraham] I said there are only one of two possibilities: either bias or a different underlying assumption. And then maybe it isn’t bias. A person can tell me, I think… I think that something spontaneous arising by chance is not a thing.
[Speaker D] No, I’m saying the word “bias” is a critical word, right? It’s not just a neutral word. So I’m saying you can turn it into something less critical. It’s not just criticism. I’m coming with some kind of epistemology, some kind of test—why turn it into that?
[Rabbi Michael Abraham] There is the possibility—
[Speaker D] —the second one, that there are different underlying assumptions here. No, that’s certain; on that we don’t disagree. That there are different underlying assumptions is definitely true. That’s it, those are the two possibilities.
[Rabbi Michael Abraham] You can’t turn bias into something else.
[Speaker D] No, but “bias” has criticism built into it, right? When we say to someone, listen, you reached that conclusion because of bias, that’s criticism.
[Rabbi Michael Abraham] Bias really is irrelevant to the issue, but if there are different underlying assumptions, that is relevant. Fine, so then we have a real disagreement.
[Speaker D] Again, I come to Rav Kook, and he tells me: in my sense, in my tools of sensing reality, I have eyes, I have ears, and I have some feeling that senses reality. I feel that there is God here, I see Him before me every morning. And then when I come—and this test has some degree of reliability, right? I don’t know what it is, but it has some degree of reliability in my eyes, a fairly high one—and then I come and they prove to me—
[Rabbi Michael Abraham] —some proof out of the various proofs that exist, so I accept it and it fits for me. The other person comes with… Try to square the circle, Shmuel. In the end there are only two possibilities: either bias or a different underlying assumption. What you just described is simply a different assumption. You’re basically saying: there’s an argument here that brings me, say, to belief in the existence of God at seventy percent, for the sake of discussion. Now another person says, I have no additional support for this matter, so for him seventy percent isn’t enough. Someone else says yes, I do have additional support for this matter—my intuitive sense—and therefore for me it’s already ninety percent, not seventy percent, and therefore I do accept it. No problem, that’s perfectly fine. But both of them agree that this argument is worth seventy percent. Their final conclusion is different because they have some other additional assumption that…
[Speaker D] Exactly, that’s what I wanted to say.
[Rabbi Michael Abraham] There’s no disagreement. So I’m saying again: there’s no point taking biases and turning them into something else. There are two possibilities: either bias or a different underlying assumption; there is no third possibility. Bias is something invalid. Of course we all fall into it from time to time, but in principle one should try to avoid it. Different underlying assumptions definitely can exist, absolutely. In our case, for example, the only way to argue with the argument I presented here is simply to say that something complex can arise spontaneously, that the probability of that is not small.
[Speaker D] But what brings about those assumptions? Also something—a sense of reality. He’s not just bringing them out of nowhere. Intuition, as the Rabbi calls it. Intuition, yes.
[Speaker B] But where is there room for feeling and emotion in a case where we’re talking about probability and logic? Why should emotion be involved in this at all?
[Rabbi Michael Abraham] No, but there are assumptions.
[Speaker B] An assumption—an assumption is not emotion. The fact that there’s emotion here, or that this is…
[Rabbi Michael Abraham] No, I’m not talking about emotion. Emotion belongs in the realm of biases. No, the fellow…
[Speaker B] Intuition is—
[Rabbi Michael Abraham] —assumptions.
[Speaker B] The fellow who spoke said, I have emotion, I feel.
[Speaker D] But here we’re talking about probability, because an underlying assumption is intuition, and intuition is emotion in my opinion.
[Rabbi Michael Abraham] The dispute—no, he thinks intuition and emotion are the same thing; I think they’re not. So that’s it, we have an old dispute about that. All right.
[Speaker B] I—
[Rabbi Michael Abraham] —think that emotion—
[Speaker B] —doesn’t play a role here when we’re talking about probability, A, B, as it were.
[Rabbi Michael Abraham] I agree, but let’s not open that up here again because we’re already…
[Speaker C] Intuition is cognitive. Yes. Okay, fine.
[Rabbi Michael Abraham] Goodbye, Sabbath peace.
[Speaker C] Thank you very much. Thank you very much.
[Rabbi Michael Abraham] Thank you very much.