Uncertainty and Probability—in Halakha, in Thought, and in General—Lesson 23 – Rabbi Michael Abraham

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[Rabbi Michael Abraham] It’s clear that sharpness and intelligence help you reach correct conclusions, but there are things that can get in the way. In other words, good character traits plus sharpness—that’s the best combination. And there’s some kind of interplay between them: if you have good character traits, then you can be a little less sharp and still reach better results. If you’re a complete fool with good character traits, it could still be that you’ll be less correct. I don’t know how to formulate a general rule. There’s a passage in tractate Bava Kamma that I found—20a, in the topic of “this one benefits and that one does not lose.” We spoke about it in the past. The Talmud says this—and look, these really are very beautiful ideas, so I’ll allow myself to devote a few sentences to it. The Talmud says as follows: Rav Chisda said to Rami bar Chama, “You weren’t with us in the evening in the study area, and we raised some excellent points.” Right—you weren’t with us there in the evening, and you missed out; in the study hall there were wonderful things. He said: “What excellent points?” What wonderful things did you have there? He said to him: “If someone lives in another person’s courtyard without his knowledge, must he pay rent, or need he not pay?” That was the question asked in the study hall. And then it goes on to describe the discussion. It says: What are the circumstances? What case are we talking about? If it’s a courtyard not ordinarily rented out, and a man who does not ordinarily rent—then this one does not benefit and that one does not lose. Right? We’re talking about a courtyard that isn’t for rent, and a person who doesn’t need housing—he has housing of his own. Someone entered another person’s courtyard and lived there without permission. The question is whether he has to pay. Now, if the courtyard isn’t meant to be rented out, then the owner of the courtyard didn’t lose anything. I lived in his courtyard, but he wasn’t planning to rent it to someone else. So he didn’t lose. But I am someone who doesn’t need to rent—I don’t need housing, I have my own house—so I didn’t gain either. Therefore this is a case of “this one does not benefit and that one does not lose”: I didn’t benefit because I have housing, and he didn’t lose anything because it wasn’t for rent. But if it’s a courtyard that is ordinarily rented out, and a man who ordinarily rents—well that can’t be it either, because then this one benefits and that one loses. So if I benefited and he lost, obviously I have to pay. If I didn’t benefit and he didn’t lose, then obviously I don’t have to pay. So what case is it after all? The Talmud says: No, it’s needed for the case of a courtyard that is not ordinarily rented out, and a man who ordinarily rents. We’re talking about a courtyard that isn’t for rent—in other words, you didn’t lose anything, you’re not lacking—but I need housing, I went in there to live, so I gained, I benefited, while you did not lose. And about that the question was asked: does he have to pay or not? Right? What then? What—“What did I cause you to lose?” Can he say to him: look, what did I deprive you of? You haven’t lost anything, so why should I pay you? Or perhaps he can say to him: but you did benefit—after all, you benefited, so even if I didn’t lose, pay. Or in other words, he’s basically saying to him: is the obligation to pay determined by my benefit? Do I have to pay because I benefited? Or do I have to pay because you lost? What is the relevant factor for payment liability—my benefit or your loss? So if there’s both benefit and loss, obviously I have to pay according to both sides. If there’s neither benefit nor loss, obviously I don’t have to pay according to both sides. The practical difference will be in two cases: either I benefit and you do not lose, or you lose and I do not benefit—which only comes up in the medieval authorities (Rishonim); here it’s a dispute between Tosafot and the Rif. But in the Talmud it comes up when I benefit and you do not lose. So if loss is what causes the payment, then I don’t have to pay, because you didn’t lose. If benefit causes the payment, then I benefited, so I have to pay. That’s what the Talmud says. He said to him—so Rami bar Chama hears this enthusiastic description of the Talmud, of what happened in the study hall—and he says to him: what are you getting so excited about? It’s in the Mishnah—it’s an explicit Mishnah. The Talmud says: Which Mishnah? What Mishnah is that? He answered him—listen, there was such a beautiful analytical discussion in the study hall, we were all so excited—and he says: come on, it’s an explicit Mishnah, what are you all splitting hairs about here? He said to him: “When you serve me, then I’ll tell you.” I won’t tell you until you serve me. So he took his cloak and wrapped it around him—right, he dressed him with the cloak, served him. Then he granted his request and told him what the Mishnah was from which the question could be resolved. What Mishnah? “If it benefited, it pays for what it benefited.” Right? An animal that fell into a garden—okay, in the category of damage by eating or trampling—so if it benefited, say if this happened in the public domain, then it’s exempt from damages, but if it benefited—if it ate, for example—then it pays for the benefit it received. Rava said: how unhealthy and unsound is a man whose master helps him—what kind of foolish proof is he bringing from the Mishnah? Even though it isn’t similar to the Mishnah, he accepted it from him! There, it is “this one benefits and that one loses,” while here it is “this one benefits and that one does not lose.” In the Mishnah, what does it say? The animal falls into a garden and eats the fruits. In terms of loss and benefit, what do we have there? The animal benefited—it ate—and the owner of the fruits lost. And there, obviously it has to pay for the benefit, because there’s both benefit and loss. So why did you want to resolve from that Mishnah the question of “this one benefits and that one does not lose”? That’s a completely different question. And not only that, but after he brings him the Mishnah, the other one is silent—this is Rav Chisda, I think—yes, Rav Chisda is silent. As if he doesn’t say to him: listen, Rami bar Chama, what nonsense are you saying? It’s not similar at all. No—he was so captivated by him that he didn’t even notice what nonsense he was being fed. The Talmud asks: But Rami bar Chama—what did Rami bar Chama himself think when he brought this Mishnah? Didn’t he notice that it’s “this one benefits and that one loses”? They say: “Ordinary fruits left in the public domain are considered ownerless.” What does that mean? He put the fruits in the public domain, the animal fell on them or ate them, benefited from them—so on the face of it this is a case of “this one benefits and that one loses.” That was the question. The Talmud says no—this is a case of “this one benefits and that one does not lose.” Why? Because when he puts the fruits in the public domain, it’s as if he rendered them ownerless. And if he rendered them ownerless, then he didn’t lose the fruits. So the animal benefited and he did not lose. Now, that plainly cannot literally be what’s meant, because if that’s so then what’s the question? If you didn’t lose, why should I pay you? You made them ownerless. Why should I pay you for fruits you abandoned? Clearly the Talmud means to say this isn’t actual abandonment. The fruits were his; he didn’t really abandon them. But if he put them in the public domain, then he bears contributory blame. You put them there—you should have taken into account that animals could pass by there and eat the fruits. And because of that, it’s considered as though he did not lose. But the fruits are still his. Therefore there is room for discussion whether one has to pay him for the benefit the animal got, or does not have to pay him for the benefit the animal got. And that is the proof from the Mishnah. So yes, the proof from the Mishnah is in fact a good proof. Because what? The proof from the Mishnah really is speaking about a case like “this one benefits and that one does not lose,” and it says they must pay. From here there is proof that in a case of “this one benefits and that one does not lose,” one must pay. That is the flow of the Talmudic discussion.

Now there are several interesting points here. First, I also have a column about this on the site. I once brought this up in some panel at the National Library. First: why is he so excited about these “excellent points”? What is so special about this topic that he got so excited—what excellent things we had in our study hall? There I argued that in this topic something is formulated almost like an analytical inquiry of the later authorities (Acharonim). How would Rabbi Chaim write his little piece on this topic? He would say something like this: “And we must investigate whether the obligation to pay is due to the loss of the injured party, or due to the benefit of the damager.” What causes the payment obligation? The practical difference is in a case where there is loss but no benefit, or no loss but there is benefit. That’s the practical difference. And then you bring proof from the Mishnah, and so on. This is really a very Rabbi-Chaim-style move, right? Two sides, a conceptual inquiry, a practical difference that resolves the inquiry. This is very uncommon in the Talmud. The Talmud usually brings a case and compares it to another case. It doesn’t usually have this kind of inquiry that sets up two sides, understands practical differences, and resolves which of the two theoretical sides is correct. And that’s why he got excited. The excitement is about something we’re already so used to that we don’t get excited by it. But when the Talmud sees a move of Rabbi Chaim, or Rabbi Akiva Eiger, or whatever—a move characteristic of the later authorities—it gets very excited. It’s something brilliant, something analytically sophisticated, something the Talmud wasn’t used to in this form of thinking. That’s why he’s excited.

Now, he says to him: you can bring proof for this from a Mishnah—Rami bar Chama. So Rav Chisda says to him: which Mishnah? And he says: first serve me, serve me. Why? So Rabbi Shimon Shkop says in the introduction to Shaarei Yosher that he demanded service because he wanted to see whether Rav Chisda valued him. Meaning: if Rav Chisda values Rami bar Chama, then Rami bar Chama is willing to teach him. If you don’t value me, there’s no point in my teaching you. Why? Because if you hear something from me that you agree with, then you’ll agree—but you knew it already anyway, so you learned nothing from me. And if you hear from me something you don’t agree with, you’ll immediately throw it away and reject it. So practically speaking, you won’t be able to learn anything from me. After learning from me, you’ll remain with all the things you thought were true beforehand, and nothing will change for you—learning from me won’t help you if you don’t value me. By contrast, if you do value me, then even if you hear from me something that doesn’t seem reasonable to you, you’ll think twice, and maybe you’ll find that it is reasonable and learn something new. Maybe not, but maybe yes. And therefore, Rabbi Shimon Shkop says—he brings this Talmudic passage—and he says: whoever does not value me… because in Shaarei Yosher there are many strange things. And if, when you hear something there that doesn’t sound reasonable to you, you just throw it away immediately because it doesn’t make sense to you, then don’t open the book. You won’t learn anything. Only someone who values me, and when he hears something strange will think about it again and again, and only then form an opinion—like Beit Hillel with Beit Shammai—only such a person should study my book. That’s what he says there.

Now look how the passage continues. After he served him, he brings him the proof from the Mishnah. And then Rava, standing on the side, says: tell me, you two are a pair of fools. What, don’t you see that the Mishnah isn’t similar to our case? The Mishnah is “this one benefits and that one loses.” We’re talking about “this one benefits and that one does not lose.” Now both Rami bar Chama and Rav Chisda were hypnotized. They didn’t notice something that every first-grader would notice. And here’s the connection to us. How can that be? What, you don’t see that this is a case of “this one benefits and that one loses”? Any child learning this would immediately tell you: why are you bringing me proofs from the Mishnah? That’s “this one benefits and that one loses.” How did they not notice? Fine, so Rav Chisda was hypnotized by Rami bar Chama. But what was Rami bar Chama thinking? That’s what the Talmud asks. And then it says that “ordinary fruits in the public domain are considered ownerless.” Meaning: on the face of it, the whole thing sounds like complete nonsense. And Rava remains with the view that this is complete nonsense. Why? Because Rava doesn’t value Rami bar Chama. And when he hears from Rami bar Chama something that doesn’t sound reasonable to him, he says to him: you’re an idiot—sorry for the low language, but that’s basically what he’s saying. Forget it, you don’t interest me, you’re talking nonsense. But Rav Chisda—he served Rami bar Chama. He values him. So when he hears from Rami bar Chama something implausible, he thinks twice before rejecting it. And Rav Chisda thought about it and understood that although at first glance it sounds implausible—“ordinary fruits in the public domain are considered ownerless”—therefore it really is a case like “this one benefits and that one does not lose,” not like “this one benefits and that one loses.” But for that you have to think twice, because on the face of it, it sounds stupid. And that is done only by someone who serves his rabbi and understands or values his rabbi enough that even if he hears from him something implausible, he will think twice before forming an opinion about it. And it’s very יפה, because after this introduction of “serve me,” something really strange does indeed come. Without having served him, he would not have accepted it. And the proof is right there: Rava, standing on the side. Rav Chisda served him, so he accepted it. Rava did not serve Rami bar Chama, so he says: Rami bar Chama, you’re talking nonsense. Meaning, in the end we see—and that’s why I brought all this, it’s a bit long, but I think it’s beautiful, and it raises a lot of questions.

[Speaker C] Rabbi, Rabbi, that’s not an example. The Rabbi sometimes likes to say there’s no point in studying aggadic literature, no point in studying this stuff, because whatever you came in with is what you’ll come out with. If it doesn’t fit your morality, you won’t accept it—and if you won’t accept it… But when we approach the aggadot of the Talmud and study the Tannaim and Amoraim, and we respect them very, very, very deeply and value them, and also the heroes of the Hebrew Bible (Tanakh), then even when we face something that seems to us like nonsense or contradicts our morality…

[Rabbi Michael Abraham] I’ll answer. My remark is a factual remark. My remark is factual. In practice, all those who study aggadot and greatly, greatly value the Amoraim still don’t learn anything new there either. So you can’t buy that just on the level of my valuing the Amoraim.

[Speaker C] Does the Rabbi really think that if the Rabbi’s children had never learned any aggadot, didn’t know anything at all about the figures of Abraham, Isaac, Jacob, Joseph, David—all stories—and had learned only Jewish law, Jewish law from age three until today, they would be the same people they are today after they did learn those things? I have no idea, but that wouldn’t be a result of learning.

[Rabbi Michael Abraham] But again, we’re entering here into a topic that requires a long clarification. I’ve written quite a bit about it, so it’s better—I’d suggest—not to get into it now. That’s not learning. They heard the stories as children in kindergarten; yes, that built some kind of consciousness in them. That’s not what I call learning. Not that it isn’t Torah—it isn’t learning. It’s something else, it’s an influence of some other kind. Fine, but let’s leave that now. What I want to take from here is this: look how a smart person can arrive at a mistaken judgment because he is biased. Or alternatively, in the case of valuing one’s rabbi, this is a kind of bias—a corrective bias. Something sounds like nonsense to you, but you’re biased because you think this rabbi is a wise person, so you think about it twice, and suddenly you discover that it isn’t nonsense. And many times, valuation—this is what’s called the principle of charity—when you hear an argument from someone who disagrees with you, don’t seize on some point he missed or didn’t formulate precisely. Try… formulate his argument for him in the best possible way, and only then begin the discussion. Because catching him on some point he formulated carelessly—fine, you’ll come out the winner, but what did that help you? You’ll remain with the position you came to the discussion with. If you really want to learn, then you have to think carefully about the opposing position, and only then form an opinion about it. If you value the person who holds that position, then of course you’ll do that. If you think the person standing opposite you is an idiot, then you won’t do it. There really is no point in trying to erect some majestic position here if you have no appreciation for the one expressing that position. But in the end, with Beit Shammai and Beit Hillel, of course both sides were Torah scholars; no one there was an idiot. So Beit Shammai were sharper or more incisive, but precisely because of that Beit Hillel valued Beit Shammai, and therefore they weighed Beit Shammai’s doctrine carefully before formulating their own. And that caused it so that even though Beit Hillel were less sharp, they reached better, more correct conclusions.

And if I return to our issue—yes, this is a moral lesson, not related to statistics, but I think it’s very important, and that’s why I’ve taken up a bit of your time with it now. Many times, very sharp people, because they are unwilling to listen to the other side, reach incorrect conclusions: “From an over-sharp mouth comes error.” And sometimes it’s because of their sharpness. Their sharpness leads to error on two different planes. One plane: if you’re a sharp person, you can justify anything. You can always present an argument in favor of whatever conclusion you want. Someone who is sharp can prove whatever he wants. And on the other hand, the fact that you’re sharp also leads you to belittle your opponent and not weigh his words seriously, not to listen to his words. I have a question. There are two reasons why precisely the sharper people err more than those who are less sharp. Two reasons: first, contempt for the other and lack of listening; and second, sharpness enables me to prove anything. Therefore, as—who was it, not Oscar Wilde, also British, never mind—said: there are mistakes so great that only academics can produce them, things only academics are capable of saying. We see this with our own eyes, day by day. I mean, there are things so bizarre that come out of the mouths of smart people. Clearly this is some kind of bias, some kind of hubris, some kind of—I don’t know—you can attribute it to various things of that sort. And it’s because of the wisdom, not despite the wisdom. It’s because of the wisdom.

[Speaker D] I remember that Ilam Gross, at a certain point in his article, says the assumption that if God exists, then certainly there would be a world. And I wanted to ask: isn’t that assumption by itself enough to reach this mistaken conclusion? Meaning, even if the statistical calculation were completely correct, but it includes that assumption. No? Not enough?

[Rabbi Michael Abraham] No. Look at my column—no, it’s not enough. Okay. In any case, yes, so this is just an answer to the question of how smart people can reach such problematic conclusions. Okay, so I return to our topic. Basically what we discover here is that if I look at this in Bayesian terms, what this argument is actually doing is saying the following: given that my starting point is that the probability that there is a God is one-half, and the probability that there is no God is also one-half—the situation is evenly balanced, two equal possibilities—the physicotheological argument leads me to increase the weight of the probability that God does exist. Meaning, the probability that God exists, P of A, is one-half, but P of A given B is 0.99. In other words, the conditional probability is much stronger than the unconditional probability. Now why is that important? Because conditional probability is always probability on the basis of more information. We talked about this; I gave examples in the previous lesson. Suppose I throw a die. So I ask: what’s the probability it lands on five? A fair die: one-sixth. But if I know that the result will be odd, then the probability is one-third. Meaning, if I have more information about the possible outcomes, I can narrow the outcomes that can occur, and therefore the probability grows.

Now in our case, the discussion of whether or not there is a God is a discussion in the air. The atheists think there isn’t one, and I think there is. But it’s up in the air. Let’s see—but we do have data; it isn’t just floating in the air. There is a world here; a complex world exists here. What does that datum do? Which way does it move the needle? Does it increase the probability that there is a God, or not? That is basically the meaning of a physicotheological proof, and the answer is that it does increase it—significantly. If I start from the point of departure that it’s one-half, then once I also take into account the fact that there is a world, I suddenly get to 0.99—or I’m just throwing out a number—but much higher. Okay? So that is the meaning of a physicotheological proof. Therefore, when we look at probability, the physicotheological proof does not rest content with the probability that there is a God. That’s just begging the question. If you assume there isn’t, then there isn’t; if you assume there is, then there is. That’s a trivial case of assuming the conclusion. But the physicotheological probability argument says: forget what you think a priori; take more information into account. There is a world here, and the world is complex. Does that not change the probabilistic weights for you? The answer is that it does. And that is what this calculation does. So the meaning of the shift from absolute probability to conditional probability basically tells me that if I take into account more information or more data, the result—the probabilities of the result—can change. They can increase or decrease, doesn’t matter, but they can change. The probability that there is no God decreases; the probability that there is a God increases. As more information is added, it can change the probabilistic calculation, because the probabilistic calculation of someone who has a lot of information is not the same as that of someone who has no information or less information. Probability is a function of how much information I have. Because probability is always decision-making under conditions of uncertainty—but the question is how great my uncertainty is. If I have very little information, great uncertainty, then it’s like an a priori probability. If I have a lot of information, it may be very different from the a priori probability. And I need to do calculations of conditional probabilities, as we saw in examples in earlier lessons as well.

So basically I want perhaps to understand another example in the same context. When people bring the physicotheological proof, let’s focus for a moment on the origin of life. The claim is that a living being is a very special being. And again, low entropy—this is objectively special. It’s not in the eye of the beholder. So this is a very special being, and therefore it is improbable that it came into being without a guiding hand. Therefore there is a God—this is one formulation of the physicotheological proof. You could call it a biologico-theological proof. So that’s the formulation. Now this is really the role that evolution plays in this discussion. Why? Because evolution is basically trying to offer me an alternative mechanism, without assuming the existence of God, and still explain how in a spontaneous way a sophisticated being, a special being, can arise. How? Through evolutionary processes. Okay—natural selection and genetics and the formation of mutations; mutations arise, natural selection preserves the more survivable or fitter mutations, and genetics passes them on to the next generations. That’s the genetic path, the evolutionary path. And this basically says that we have a completely natural explanation for the origin of life. Therefore the assumption that a complex thing cannot arise spontaneously without the possibility of a guiding hand—that assumption is false. That assumption has fallen. And therefore the physicotheological proof has fallen. That is essentially the whole polemic around evolution.

Now I’ve also spoken about this more than once, and written about it. Where’s the mistake here? The mistake is that you’re looking at the problem from within the laws. Given the laws of nature, I can show you that life can arise without anyone being involved. The big question, of course, is who created these laws of nature within which life can arise spontaneously? If the laws of nature were different, then life would not arise spontaneously. Even the tiniest change whatsoever would destroy the possibility of biology existing at all—chemistry, biology, everything needed on the way to living organisms. Therefore the question is not whether you have a scientific explanation for the origin of life. That’s “God of the gaps.” Right? Meaning: if you don’t have an explanation, that means there is God. That’s the God of the gaps, yes? The moment there’s a gap in scientific knowledge, that means there is God. “The believer’s celebrations are always faithfully held whenever the weather forecaster was wrong”—that’s always the example standing before me. Whenever the weather forecaster is wrong, they celebrate. Yated Ne’eman declares a holiday. Why? Because from their point of view, if science is right then there is no God; if science is wrong then there is God. That is exactly an expression of the God of the gaps—proving the existence of God from our gaps or scientific misunderstandings. And on that many atheists rightly claim that one should not bring proofs for the existence of God from gaps in scientific knowledge. Gaps in scientific knowledge get closed through scientific research. Five hundred years ago there was much more God, because we had many more gaps in scientific knowledge. That has closed. So the gaps that exist today may also close in the future. You can’t build any conclusion on the existence of those gaps. Maybe it’s simply because we haven’t finished investigating. We’ll investigate more, and we’ll know that too. Therefore, God of the gaps is not a valid proof for the existence of God.

But when I speak about proof from the laws—what I call it—I mean that I prove the existence of God not from the origin of life, but from the origin of the laws within which life can arise spontaneously. And precisely because the system of laws is like this and not even slightly different. If it were even a tiny bit different, this could not happen. Now here you can no longer talk to me about evolution; there is no evolution of the coming-into-being of systems of laws. So you’ll say: fine, then they’ll find some other scientific field that explains how the laws came into existence. That is still God of the gaps. You are basically telling me: I don’t understand something scientifically, therefore there is a God. That’s God of the gaps. I say no. Why no? Because even if they find a scientific explanation for the laws that govern the world, that scientific explanation itself will also rely on some laws—meta-laws—that govern the formation of laws. Then I will ask: who created the meta-laws? What will you tell me—turtles all the way down? In other words, at some point there is some initial command, yes, which is the basic law—the unified field theory, as Einstein called it, searched for desperately and didn’t find. And to this day there is hope of finding it. But even that unified field theory will be one law from which everything is derived. And the question will still remain: who created that law? And this cannot be closed by scientific research, because scientific research at most discovers more scientific laws. But here you need some explanation without scientific laws. There is no scientific explanation without scientific laws. Therefore here this is an essential claim; it is not God of the gaps. I claim that the existence of the laws is the proof for the existence of God, not the origin of life. The origin of life, given that these are the laws—fine, of course. But why these laws?

Now in the last formulation I gave, you understand that this is exactly the difference between probability and conditional probability. The original creationists bring a proof in terms of conditional probability, a proof from within the laws. They say: how can life arise without a guiding hand? There’s no chance life could arise without a guiding hand. The answer is: not true. Evolution shows us that there is such a possibility. There is a possibility for life to arise without a guiding hand, through the laws—through behavior according to these laws, life will eventually arise. But that process is a conditional process. Given that these are the laws, what is the probability that life will arise? The answer is one. And now I ask: what is the probability that life will arise unconditionally—not given that these are the laws? What is the probability that life will arise? Or in other words, what is the probability that these will be the laws? If this is P of A given B, then you have to multiply it by P of B. Meaning: P of A given B is one. But what about P of B? B is that these are the laws, and A is that life arises. Given that these are the laws, then life arises—the conditional probability is one. But what is the probability that these would be the laws? Why assume that these would be the laws? What is the probability they came into being just like that? Here the probability is very small, and that is what proves the existence of God—not the conditional probability. Precisely the absolute probability proves the existence of God. So here the mistake is the opposite mistake. Instead of looking at the absolute probability, you look at the conditional probability. The conditional probability is high, that’s true, but the a priori probability is tiny. So again, moving from conditional probability to unconditional probability—given that these are the laws, which is the extra information I have—what is the probability that life will arise? The answer is one, or almost one. Okay? But that is conditional probability. I’m asking: what is the probability that life will arise, period? Or what is the probability that laws will arise that allow the spontaneous emergence of life? That probability is very small, and on this point it is not God of the gaps. Here I really can infer the conclusion that there is a God, because without God such a thing could not have happened.

[Speaker C] Another claim of yours—the complexity drops out of the picture; right now we’re talking about the most basic fundamental law.

[Rabbi Michael Abraham] No, he’s answering—the complexity does not drop out of the picture. Suppose the law…

[Speaker C] No, no, I’m talking about the law itself—what does it contain?

[Rabbi Michael Abraham] What? No, that’s the complexity of the law. The complexity of the law is that this law produces very, very complex beings. If this simple law were a linear law, y = ax + b, you have two parameters a and b—that’s the unified field law. But a has to be exactly pi over four. If you deviate a tiny bit to the right or a tiny bit to the left, nothing will come into being. That is a special law, even though its formula is very simple. It is a very special law. And the question remains the same question: how did a come out exactly pi over four? The complexity remains; it doesn’t matter how much you simplify the system of laws.

[Speaker C] Its outputs would be complex. I don’t know—there are infinitely many worlds, there are infinitely many worlds, infinite… No, I don’t mean—I don’t understand—some event happened and some…

[Rabbi Michael Abraham] That’s a different argument. I’m willing to argue with you about that too—I’ve written about it as well. But that’s a different argument. I’m trying to illustrate the difference…

[Speaker C] No, how can one determine the…

[Rabbi Michael Abraham] The statistics?

[Speaker C] I’m asking the Rabbi: what is the most fundamental law of the universe? Suppose the Rabbi defines it for me. It’s terribly, terribly simple. I don’t know—let’s just describe it schematically: two hydrogen molecules, I don’t know, connect. I’m just saying some nonsense. The simplest thing in the world, and that causes the Big Bang and then it rolls forward. Now, there’s no—this very fact that two hydrogen molecules connected is, let’s say, very simple to explain. Now, the fact that there is… no, it’s not simple.

[Rabbi Michael Abraham] No, no, no, no, no. I’m stopping you there. What does “simple to explain” mean? There is no explaining it. That is the law; it explains other things. It itself cannot be explained. I’m not explaining—what is the explanation for a law?

[Speaker C] The law itself is simple; its consequences are very complex. It led to the Big Bang, which rolled…

[Rabbi Michael Abraham] Exactly. But that law is a very special law. If you just drew a random law, it would not have complex consequences. So that law is a very special law, and it requires an explanation.

[Speaker C] But how can one determine the probability that such a thing would happen?

[Rabbi Michael Abraham] Well, by… think about it: if you draw laws completely at random, how many of the systems of laws you draw will produce a world with this level of complexity? The answer is: almost none. That is the specialness of the system; that is what defines the specialness of the system.

[Speaker C] Wait, aren’t there infinitely many other laws that would create other worlds?

[Rabbi Michael Abraham] No. And if there are infinitely many, it is still an infinity that is very small compared to that infinity. Think of the natural numbers versus the real numbers. Still probability zero. It doesn’t matter that there are infinitely many; that isn’t important. There are infinitely many. Meaning, if you increase all the physical constants in the same proportion—that is, keep the ratios between them—every such system of constants would create a complex world like ours. Human beings would just be smaller, bigger, or fatter. But it would still create the same complexity. There are infinitely many laws that create that, but that infinity of laws is such a tiny infinity compared to the totality of all possible laws that it is still negligible. The probability is zero. What? Think of drawing a real number—what is the probability it comes out an integer? There are infinitely many integers. Zero. Do you understand? It doesn’t matter that there are infinitely many integers.

Anyway, once again, I’m bringing here an example from another angle of the need to be careful not to confuse conditional probability with absolute probability. In this case it’s the opposite confusion. Meaning, the atheist uses conditional probability and the believer uses absolute probability. In the case of the physicotheological proof, it was the believer who used conditional probability. Okay? But still, these confusions are confusions that show up in a great many arguments. Even in arguments where people do calculations, and with numbers—as the advertisements say—you can’t argue. Well, actually you can argue with numbers even more than with logical arguments. Because behind the numbers there are always all kinds of assumptions. And for some reason, when you focus on the numbers it blinds people; they think there’s an argument here that can’t be disputed.

I’ll perhaps bring another example that illustrates this point. We’ve talked about it in the past as well. We know there is a rule that “the burden of proof is on the one who seeks to take property from another.” If someone sues me over some item of property that is in my possession, then he is the one who needs to bring evidence in order to take it from me. If he brings no proof, it stays with me. What is the logic behind this rule? There are later authorities (Acharonim), and it’s also commonly thought in the world, that the logic is possession—the presumption that what is under a person’s control is his. There is such a presumption in the Talmud: what is under a person’s control is his. Usually, if it is with me, it is probably mine. So if now you sue me and I say you’re wrong, the burden of proof is on you. Why? Because in the ordinary state of affairs, if it is with me, it is probably mine. That is the common explanation. Except that it is not the correct explanation, and it is incorrect for the very same reason we are talking about here: because this involves conditional probability and not absolute probability.

What do I mean? Think, for example, of a situation in which we go through all the objects in the world, in all the houses of all people, and we record for each one whether it is with its owner or not with its owner. We will get an overwhelming majority of objects that are with their owners. Right? That is obvious. Meaning, if an object is found in a certain place, usually it is with its owner. In other words, most objects are with their owners. Okay. But now I ask another question. If someone comes and sues me over, say, this phone here, okay, which is in my possession, and he claims that I stole it from him and I claim nothing of the sort—can one say that this phone is probably mine because what is in my possession is usually mine? The answer is no—or not necessarily. Why? Because the statistics I described earlier were done over all objects in the world. If you go over all the objects in the world, in most cases the object is with its owner. Okay? But if you focus on the subset of objects over which there is a legal dispute—let’s look only at that subset—then in that subset there is no reason to assume that plaintiffs are bigger liars than possessors, right? The plaintiff has a presumption of integrity, and the possessor has a presumption of integrity. There is no reason to assume the plaintiff is lying and the possessor is not. The conclusion is that if you focus on the group of objects over which a legal dispute is being waged, the probability that it is mine or yours is fifty-fifty. Even though, over all the objects in the world, clearly there is an overwhelming majority of objects that are with their owners. So what does that mean? It means that if I look at the absolute probability and say: given an object, what is the probability that it is with its owner—what is the probability that the one holding it is its owner? The answer is ninety-five percent. But now I look at a conditional probability: given that there is a dispute over this object—and there are only very few such objects in the world, objects over which there is legal dispute—given that this is the case, what is the probability that the one holding the object is the owner? Fifty percent. That is the difference between absolute probability and conditional probability. As I said, conditional probability is always a probability that focuses on a subspace, yes, on part of my event space. I’m not looking at all the objects in the world, but only the disputed objects. I’m not looking at all worlds, but only the complex worlds. I’m not looking at all systems of laws, but only at the special legal system that is here. And now I try to infer conclusions. So conditional probability basically means narrowing the gaze to a subgroup or subpart of my event space.

[Speaker D] Can’t one treat this conditional probability as the product of the honesty or credibility of the two sides, which is, say, one-half, together with the absolute probability—that ninety-five percent really are under their owners’ control—and then it would still come out…? Why not?

[Rabbi Michael Abraham] What? Of course not. What do you mean, product?

[Speaker D] Because the general argument is also relevant, no? The general argument suddenly isn’t relevant?

[Rabbi Michael Abraham] It’s not relevant at all. Why not? There is no product here. A product applies when you need both things to occur, and each one separately has a certain probability, and they are independent—then you can multiply the probabilities. But here there is dependence. If I am lying, that means the object is not mine. The question whether I am lying or not and the question whether the object is with me or not are not two independent questions. If I’m lying, that means the object is not mine. You can’t multiply probabilities when the variables are dependent. What you would have to multiply now is probabilities in the following way: you would have to say what is the probability that this object is mine, times the probability that I am not lying, times the probability that I am not lying given that it is with me—like Bayes’ formula. Do you understand? You can’t multiply the probability that the object is with its owner, the general probability, by the general probability that a person lies. You need to multiply an absolute probability by a probability…

[Speaker C] I don’t understand, but that’s just begging the question again. The object belongs to this category of objects that are in legal dispute—that’s what we’re trying to determine. Obviously that’s influenced by credibility. Suppose we’re in some country—not Israel, some other country—where there are no liars. They have some illness like that, they don’t lie; some virus infected everyone, they don’t lie. It’s very rare that someone—some mutation, some oddity—actually lies. Then we see—right, not exactly, but to say that they lie, there’s no such thing. It’s very rare, really an unusual phenomenon. So then I really would use the general probability. So we do see that we look at the general population and say: most people… If we’re in Sodom—no—but there you’d be right—

[Rabbi Michael Abraham] But there indeed the relevant probability would be the general probability, that’s obvious. But we don’t live in such a world.

[Speaker D] Why? But on both sides they don’t lie, but—

[Speaker C] We are influenced by that, we are influenced by what happens in the general population. If we’re in Sodom, where everyone steals from everyone, then we aren’t influenced by anything.

[Rabbi Michael Abraham] Our world is a world in which people do lie. Our world is a world where, when two people are arguing, a very reasonable assumption is that one of them is lying, not that one of them is mistaken.

[Speaker C] No, okay, I said that was just an example I brought.

[Rabbi Michael Abraham] And then we can relate to the absolute probability.

[Speaker C] But there’s no difference, for example, if we’re discussing it—there’s a presumption—if you come to Sodom, where everyone steals from everyone systematically and that’s obvious, and you come to Israel, where that’s not the case. Does that presumption exist? Right, and here it would. In Israel it would, because people steal less, the general population steals less.

[Rabbi Michael Abraham] Not only because of that. That presumption exists here because there are legal reasons for that presumption, not probabilistic reasons. The probabilistic reasons don’t exist. There is no probabilistic consideration in favor of the current possessor. There is a legal consideration. A sensible legal order says that in order for the religious court to take action, you have to persuade it; otherwise it doesn’t intervene, and the object will therefore remain with the person holding it. But that’s a legal consideration, not a probabilistic one. Probabilistically, the chance is fifty-fifty that it’s yours.

[Speaker C] But if, Rabbi, we were really betting on it, we’d say it can be clarified, we’d be able to determine it with certainty in the end—the Rabbi wouldn’t, if he were a person who came to some organized country, I don’t know, to Sweden, to Norway, let’s say everyone there is honest, and I make a bet with the Rabbi, a wager, then—

[Rabbi Michael Abraham] The Rabbi would say—

[Speaker C] —that it belongs to the possessor?

[Rabbi Michael Abraham] Obviously, but—

[Speaker C] That’s a different country.

[Rabbi Michael Abraham] We don’t live in that reality. And Hazal didn’t live in that reality either. It’s not a matter of the decline of the generations.

[Speaker D] But is there no possibility of a situation where in fact neither side is lying, but one is mistaken?

[Rabbi Michael Abraham] In cases of mistaken perception, yes.

[Speaker D] I mean also in a reality where there is an equal presumption of reliability for both sides, where each of them lies half the time and tells the truth half the time—on the possibility that they’re mistaken, don’t we still have to take the overall absolute probability into account?

[Rabbi Michael Abraham] Of course we do, and that’s what I said earlier. In a world where no one lies, and if there’s a dispute then apparently one of them is mistaken, not lying, then I would use the general probability there, without a doubt.

[Speaker D] But I’m asking: in a world where people do lie, is there still no chance that here no one lied, and we still need to take into account the possibility that someone is mistaken?

[Rabbi Michael Abraham] And in fact, in situations where the possibility of mistaken perception arises, the law really does change. For example, migo does not apply against mistaken perception. Because migo proves that you’re not lying, but if my concern is that you’re mistaken, then what does it help me that you have migo? Usually the assumption is that when there’s a dispute, one side is lying. If there’s a possibility that one side is only imagining things, as in identifying the dead, yes, in permitting agunot and so on, then there is mistaken perception, and the rules really are different. Okay, so I’ll stop here. If there are questions or comments? Rabbi, Rabbi, maybe…

[Speaker C] The Rabbi said that he doesn’t like talking about aggadic literature and that we don’t derive things from aggadic literature and so on and so on, but when the Rabbi does end up talking about aggadic literature, somehow it comes out extremely well, like today, in today’s class. Maybe the Rabbi will consider in the future doing some kind of series, I don’t know…

[Rabbi Michael Abraham] But aggadic literature here is the narrative framework for Jewish law; this is a halakhic discussion. One benefits and the other doesn’t lose.

[Speaker C] No, but I mean drawing philosophical values דווקא from aggadic literature, like he does at Bar-Ilan on topics in the Talmud. Just a suggestion for the future, because it came out very successfully; this aggadic passage seems very fundamental in this explanation.

[Rabbi Michael Abraham] Yes, well, maybe. But you understand that this still fits my rules, because it leads to a conclusion that I already identify with in advance. It’s not that I disagreed, but because it says so in the Talmud I changed my mind. The Talmud served me as a nice illustration of a principle that was actually clear to me even beforehand.

[Speaker C] Right, but if the Rabbi had told me—or us, I don’t know, at least me—the lesson beforehand, just some seemingly basic lesson like he said, as opposed to when he described it… it hit me much more strongly. Very differently, completely—it changes things, it’s tremendously important in the end. That’s also the lesson of aggadic literature, that kind of human impact.

[Rabbi Michael Abraham] Yes. Okay. It has rhetorical value, I agree. Okay then, Sabbath peace, and may we hear good news.