A Look at Torah and Torah Study – Lesson 11 – 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

[Rabbi Michael Abraham] This is simpler. Right? A straight line seems simpler to us. And you can debate whether a straight line really is simpler, or whether we’re just built in such a way that, for us, a straight line is simple. And as far as someone who is built differently, whose way of perceiving is different, a straight line is not necessarily the simplest line from that person’s point of view. Right? It has to do with the structure of our mind, meaning how we think. Okay? But fine, we have some principle that the simplest thing is probably the correct generalization. Or at least that’s our starting assumption: we choose the simplest possibility unless something forces us to give it up. Say suddenly there’s a result like this. Then I can no longer choose the simplest result, right? Because it doesn’t fit the line. Assuming, of course, that it’s not an experimental error, but if there are enough results that deviate from the straight line, I’ll reach the conclusion that apparently the straight line is not the correct line. Okay? So that’s the first question that comes up in this context. Meaning: how can we arrive at the correct generalization when there are actually infinitely many possible generalizations? More than that: usually, in logic, we distinguish between three forms of inference: analogy, induction, and deduction. Analogy is a comparison between, say, one particular case and another particular case. Induction is moving from particulars to a general rule. And deduction is applying a general rule to particulars. For example: if all tables are brown, and this thing is a table, the conclusion is that this thing is brown. That’s deduction. Because I begin with a general statement and infer from it a conclusion about a particular case included within the scope of that statement. Okay? Induction means: this table is brown, and this table is also brown, and this one is brown too, so apparently all tables are brown. That’s the move from particulars to the general rule. And analogy means: this is a table and that is a table; if this one is brown, then apparently that one is brown too. That’s the move from one particular to another particular. Okay? Now, in science people often talk about scientific induction. Scientific induction is… I conduct experiments in certain cases and try to derive a general law from them. But the truth is, that’s basically what I did here, right? I have four cases, and the continuous line is basically the general law. And I’m looking for what the general law is based on the particular cases. And then I said: the general law could be this, but it could also be this, and it could also be the blue one. All these are different proposals for what the general law might be. Okay? But that’s not entirely accurate, because here I’m talking about induction. And what science actually does is abduction. Abduction means producing a theory that explains the cases, not connecting them with a line. Connecting them with a line is a generalization on the phenomenological level, meaning how it behaves. But I’m asking: what ideas cause this thing to behave this way? And as part of the theory, for example, I identify theoretical entities. I say: there is an electron, and there are electric fields, and this and that, and assuming I make all these crazy assumptions, I can explain various phenomena in the world. That’s no longer just a generalization like drawing a straight line through points. Rather, I’m inventing all sorts of concepts altogether, creating a theory through them, and that theory is the explanation for the cases I observed. That is called abduction. In other words, induction is moving from particulars to a general law; abduction is moving from particulars to a theory, not to a general law. The theory is something that explains the general law. It is not the general law itself. Okay? It’s what explains the general law. Now, in our context too, we can talk, in the Torah context, about generalizing the cases, giving some definition, and I can talk about the theory that explains why that really ought to be the generalization. What defines the giving here specifically this way and not otherwise? And in that sense, we always really need to do two jobs. First, to make a generalization, to give some definition that covers all the cases. And second, to find a theory that explains why the generalization is specifically this one. Why is it specifically like this? Why here is it specifically a straight line? So you need to find some theory that explains why the relation between force and acceleration is a straight line. That’s Newton’s second law, right? The mass is the slope of the line. Okay? So that’s one type of problem with these transitions from particulars to the general. There’s another kind of problem. A philosophical problem. Up to this point I was talking about the question of how I know it’s true in the first place. But now I’m saying: suppose I know it’s true. Fine? Usually we relate to finding a scientific theory, or to scientific research, as an act that tries to look for explanations, tries to explain phenomena. Right? Now it’s not so clear why a scientific theory constitutes an explanation. In what sense does it constitute an explanation? When we talk about explanations generally, explanation means reducing something to the familiar. Right? If there’s something I don’t understand, what does it mean to explain it? To show that it follows from principles that I do understand. Right? I reduce the unfamiliar thing to principles familiar to me, and that’s how I understand it, that’s how I explain it. Okay? So for example, if there’s a plane crash, a plane went down. Now there’s a commission of inquiry of experts and so on who are checking why it happened. So we have a phenomenon we don’t understand—the plane crashed—and what are they looking for? They’re looking for an explanation. What would the explanation be? The explanation would be, for example, that there was a crack in the wing. And then it couldn’t withstand the load and the air pressure, the wing collapsed, and without a wing the plane falls. All of these are aerodynamic laws and we understand them. Okay? So when I’m looking for an explanation for this poorly understood phenomenon, I find an explanation for it in terms of principles that are familiar to me. Through those principles I know how to explain the phenomenon. But finding a scientific theory is not that kind of process. Think about Newton, who saw the paths of the stars, and he saw tides, and he saw that bodies fall to the earth, that bodies with mass fall to the earth. And then he reached the conclusion that there is a law called the law of gravitation. The law of gravitation—attraction. That is, every two masses attract each other with a force that varies as one over the square of the distance between them. Fine? That’s Newton’s law of gravitation. Does something like that constitute an explanation? No. Why not? Because we know the phenomena. We all know that there are tides; we know that bodies fall to the earth. But until Newton, we did not know the law of gravitation. So in fact this explanation is an explanation of the type of reducing to the unfamiliar, not reducing to the familiar. I take phenomena that I know and explain them, in quotation marks, by means of a theory that is new, that I am now presenting for the first time. In other words, I explain them in terms of something unfamiliar. So in what sense… why is such a thing called an explanation? Why is it an explanation? Explanation is supposed to clarify something for me. To clarify something is to use things I know in order to explain something I don’t know. Here they take things I do know and explain them by means of something I don’t know. Why is that an explanation? Now on this I have a big argument with all sorts of atheists on these matters. Yes—whether the Holy One, blessed be He, is an explanation for the fact that the world is complex. The physico-theological argument. If the world is complex, that means it has a composer, and therefore there is the Holy One, blessed be He. Now the claim is: what kind of explanation is that? You take something you are trying to explain, and you invent something nobody has heard of and nobody knows about, and you think that explains the phenomenon before you. That is reducing to the unfamiliar; it’s not an explanation. And the answer I give them is: every proposal of a scientific theory is an explanation of exactly that type. It is reducing to the unfamiliar. Now what’s going on here behind all this is basically a debate in the philosophy of science. Karl Popper, one of the most important philosophers of science in the twentieth century, maybe the most important of them, argued that a scientific theory is not something we prove; it’s not even something that can be proved. A scientific theory is a theory that can be falsified. That is, suppose I have a theory that all ravens are black. Okay? How would I prove such a theory? There’s no way. I can see one raven, and another raven, and another raven, but I’ll never know that I’ve seen all ravens. Right? I also don’t know what will happen with future ravens that don’t yet exist. So I can’t really prove the theory that all ravens are black. More than that—even if, say, I trap all the ravens in one huge net, I catch them all, I conclude that this is all the ravens, and indeed they’re all black, I go through them one by one, all black, and now I destroy them so there will be no more ravens in the future, then it’s certain. But then it’s no longer a scientific theory; it’s just facts I observed. A scientific theory is always something general that gives me information also about situations I have not observed. In other words, a theory that merely summarizes what I know is not called a scientific theory. It’s an efficient summary of what I know, okay? A scientific theory is when I draw conclusions from what I know that are relevant to situations I do not know, and from the theory I can try to think about what will happen in those situations. Okay? So basically Popper told us that a scientific theory cannot be proved, but it can be falsified. If I bring one white raven, then the theory that all ravens are black has been falsified, right? You can falsify a scientific theory; you cannot prove it. What? No—then the theory is not correct. You falsified the theory. The theory says that all ravens are black; that’s what the theory says. You can now correct the theory—that’s already what people call articulation, refinement, correction of the theory, and there are problems with ad hoc corrections and so on—I’m not getting into all the details here in the philosophy of science. I want to give some general introduction because it will be important for our purposes. Now this is not the end of the story, because many attacked Popper over this, saying his description is too simplistic. Surely he was right, but the description is too simplistic, because Popper essentially reached the conclusion that we cannot know anything about a scientific theory except that it has not yet been falsified. That’s all. Every future experiment will subject it to another test of falsification. Suppose it passes safely—still, there are many other experiments I can do. All I can say about a theory is only something negative: that it has not yet been falsified. That’s all. And we all understand that this does not exhaust the matter. There are scientific theories about which we have a very high degree of conviction that they are correct, and not merely that they have not yet been falsified. Now true, there is no certainty; some future experiment may falsify the theory and change the picture. But you can’t say we are in a total vacuum, meaning that all we have is ‘it hasn’t been falsified.’ The theory that all fairies have two wings also hasn’t been falsified. Okay? But of course it also can’t be falsified, because there is no way to observe fairies. Therefore it is not a scientific theory. A scientific theory is only a theory that can be subjected to a test of falsification. Okay? That is why people continue to speak of the concept of confirmation. What is confirmation? The more and more ravens I find—of different types, different species, from different continents, as varied as possible—and all of them are black, the more my belief grows stronger that the theory ‘all ravens are black’ is correct. Fine? So this basically means: true, I can never know for sure; maybe in another minute a pink raven will arrive and knock the whole thing down. But I become more and more confident in the theory as I’ve seen more cases and they are more diverse. That’s called the process of confirmation, as distinct from proof. There is no proof for a scientific theory, but there is confirmation. Okay? So now basically we have two things we can do following an experiment. We subject a theory to an experiment, and we have two possibilities. Either the experiment falsifies the theory—that is, the prediction… the theory’s prediction fails, the experiment shows it is not correct, and then the theory falls. Or it confirms the theory, confirms the theory. What does that mean? If the theory passed the experiment successfully, that does not mean it is true. It means my confidence in it is now greater. The more experiments it passes safely, the more my confidence in that theory grows. Okay? Therefore it has been confirmed. Fine? Now, one might say here: but it is obvious that the moment there is one experiment that fails, the theory falls. In other words, surely a theory can be falsified. It probably cannot be proved. It probably can be confirmed. That’s debatable, but never mind. But it is clear that a theory can be falsified, and if you subject it to a test of falsification, then it falls. Then comes Thomas Kuhn, who was basically a sociologist of science, a philosopher of science, never mind, also in the twentieth century, and he presents the following criticism of Popper. He basically says that the fact is that when a theory fails to predict the results of a few experiments, we still do not throw it out. Factually, the scientific community does not immediately throw out a good theory. A successful theory is not discarded so quickly. So that means that this conception which says that if one experiment doesn’t work, the theory has fallen—that is a naive conception. Now notice: I’m not talking only about the possibility that there was an experimental error. That can always happen. So you repeat the experiment. A scientific experiment also has to be repeatable, so that one can repeat it in different places and get the same results. A non-repeatable experiment is not a scientific experiment. Okay? A scientific experiment is an experiment such that if you give me the apparatus, I can carry it out again in my own lab and I’m supposed to get the same results. Otherwise your result is worthless. Okay? It is supposed to be something that can be reproduced. Fine? So I’m not talking about mistakes in the experiment. There are no mistakes in the experiment, and one can repeat it in different places and at different times, and we always get the same result. It contradicts the theory, and still the theory has not fallen. Why? Because the theory explains so many cases, so many cases, that I am not willing to overthrow it on the basis of one situation it doesn’t explain. Here I’ll begin to move into maybe articulations, to say these are exceptional cases, and to try to explain why they are exceptional cases and why in the other cases the theory is in fact correct. I won’t give up the theory so quickly, even though it fails in a certain experiment. Then Thomas Kuhn says: there is some threshold, some number of experiments that the theory fails to explain, beyond which we say, okay, now we throw out the theory. A single experiment won’t do it, but there is some level, some minimal threshold, such that if the theory fails to explain too many situations, then it probably is no longer correct, and there is no point continuing to hold on to it. Okay? And that, of course, depends. The number of such situations depends very much on the question of how convinced we are that the theory is correct. The more convinced we are, the more situations in which it doesn’t work we will want to see before giving it up. Okay? If it explains a huge number of facts, then it is strong. And even if there are ten facts it doesn’t explain, still—how do you explain the fact that it does explain a thousand facts? In other words, there is something there. Now we need to look for why, in those ten facts, it does not explain them. But we do not give up the theory even though it doesn’t work in some of the cases.

[Speaker F] Unless there’s a better theory.

[Rabbi Michael Abraham] No, no, I’m not talking about a competitor. We go out to look for the competitor. But first I want to know: this theory doesn’t work. So now I’m looking for an alternative. But for that I first have to decide that this theory doesn’t work. Therefore that decision is disconnected from the competitor. I want to know whether I have lost confidence in this theory. If I have, I’ll look for a replacement theory. Fine? But in order to decide that I have lost confidence, enough experiments or enough situations have to occur that the theory does not explain. Think, for example, in non-scientific contexts. There are various difficulties with faith. Fine? Somebody says that the phrase עד עצם היום הזה means the Torah was not given at Sinai, because clearly it was written later. Or whatever, or various kinds of source criticism, the documentary hypothesis in the Bible, and all sorts of things of that type, and archaeology, and the Exodus, and all sorts of one difficulty or another. Now usually, when we have one such difficulty, someone who truly believes in that tradition—if he has one such difficulty and no answer to it, the age of the world, whatever, he has no answer, fine?—we do not immediately abandon faith. Why not? Because we’re irrational? No; in science too it works that way. Since if we have strong trust in a belief, one difficulty does not bring it down. As they say about Rabbi Akiva Eiger—do you know the joke about Rabbi Akiva Eiger? Someone comes to the rabbi with a difficulty. So the rabbi says: look in Rabbi Akiva Eiger on Ketubot on page such-and-such—I’m just throwing out a random page. He goes there and sees it’s not connected at all—what does that have to do with his question? He comes back to the rabbi, and the rabbi says: Rabbi Akiva Eiger there has a note on Tosafot: ‘requires further analysis,’ and after that he has a note on the next Tosafot as well: ‘requires further analysis.’ You see that after he had ‘requires further analysis’ on this Tosafot, he moved on to the next Tosafot. That’s all. I have no answer for you. So there’s no answer—move on. Fine. What happened? Nobody dies from a difficulty. What does that mean? The claim is that if I have a theory in which I have a high degree of confidence, one difficulty will not bring it down. It won’t bring it down because I’ll think: fine, so I haven’t thought deeply enough, I’m not smart enough, maybe the theory needs a bit of refinement, but I’m not giving up that theory so quickly. Okay. But if there are already, I don’t know, a thousand difficulties attacking the faith from every direction—the Bible was not given at Sinai and in general was composed by people, and nothing there makes sense, and it’s not moral, and nothing works; in short, the Exodus never happened at all, and everything is under attack from all directions—then a person with intellectual honesty ought to abandon the faith, right? That is, then he says that apparently I was holding on to a false belief. One has to be honest. Okay, so what—conversion? Or deconversion, whatever; for me that is what it means to abandon it. So the point is that the higher your degree of confidence in the theory or the belief in question, the more difficulties you need in order to give it up, right? In other words, you do not give it up immediately. Now Thomas Kuhn basically says: that is exactly how science proceeds. What does that mean? A certain theory was proposed on the basis of the facts known at the time. That theory works well, it explains a great many things and works well, it has become well established, everything is fine—Newtonian mechanics. Okay. Now suddenly some point arises that Newtonian mechanics cannot explain. We do not give up Newtonian mechanics, because it explained so many things in such an elegant way that we have very great confidence that it is correct. Okay? It’s not plausible that it is incorrect. So what—this one thing it doesn’t explain? Fine, then apparently this is some anomaly I haven’t yet understood, I’m not smart enough, I need to think about it. Maybe someone else will discover the answer, I don’t know. But I do not give up so quickly the theory I had been holding. Now another difficulty comes, and another, and another. At some point people realize: Newtonian mechanics apparently is, after all, not correct. Despite all its power and despite everything it gave us up to now, apparently it is not correct. Then a paradigmatic crisis is created, as Thomas Kuhn says. That is, up to that stage we work within the paradigm. At some point a crisis is created. The paradigm does not work; it is clear that the paradigm must be replaced. Then people look for a new paradigm. A paradigm is a conceptual framework, a theory. Fine? A new conceptual framework. Until they find the new conceptual framework, and then they continue to work within it—and that is work within the paradigm—until it too fails the test, because there are enough experiments that do not confirm it, that falsify it, and then once again the paradigm has to be replaced, and so on. That is how he describes the scientific process. Until Elijah comes. Until Elijah comes, or until something explains everything. So what happens within the paradigm is basically explanations of reducing to the familiar. Right? If someone says to me: I don’t know, let’s look for an explanation for the tides. And I already know Newton’s law of gravitation. Then I understand that the moon pulls the water—I don’t know exactly how—and I understand that this is what causes the tides. That really is reducing to the familiar, right? Because I take the tides, which I don’t understand why they happen, and Newton’s law of gravitation I already know; we’re talking after Newton, so we already know the law of gravitation, and we use the law of gravitation to explain the phenomenon of tides. That is called reducing to the familiar. I take something I understand and use it to explain something I do not understand, like the plane crash. Okay. But at the stage of a paradigmatic crisis, when Newton’s theory falls because there are many facts with which it does not fit, okay, now I am looking for a new theory. When I find that theory, how will I test it? By seeing whether it explains all the facts in which the previous theory failed, which it did not explain, right? But that will already be an act of reducing to the unfamiliar. Because I take the facts I know and explain them in terms of a theory that is new; I do not know it. That is basically an explanation of reducing to the unfamiliar. Now if we were always using only explanations of reducing to the familiar, then science would never advance; today we would still be at the level of Adam, scientifically speaking—with all due respect. Right? Because what would that mean, basically? Every time that… I’ll give you an example. Back in the yeshiva there was a student—when I was at Gush, there was a student in the yeshiva. A bit older than me, who got hepatitis, today he’s a well-known figure. He had hepatitis for about half a year. And he didn’t get out of it. Fine? We had a mutual friend; I wasn’t close with him, but I have a good friend who was also his friend, and he went to visit him in the hospital and was in touch with him. One day he comes back and tells me that some kind of witch came there with pigeons to the hospital, put them on him—you know this thing?

[Speaker C] That she put the pigeons on him,

[Rabbi Michael Abraham] the pigeons on his belly button.

[Speaker C] Yes, I did that, I did that.

[Rabbi Michael Abraham] Okay. So in short, she put the pigeons on him, the pigeons died, died, they drew out the bilirubin or whatever exactly, and after a few days he went back to the yeshiva. Right? A true story. I came back, I came back—you sound enthusiastic. I would have believed it too; I saw it myself. I saw it and I still don’t believe it, but we’ll see in a moment. I went back to my parents in Elkana and told them what had happened in the yeshiva. My parents didn’t understand—hesder yeshiva, wow, the yeshiva, those benighted people in the yeshiva are messing with your head, ruining your mind, what is this darkness? Obviously there’s some scientific issue here; this can’t work, pigeons don’t cure jaundice. And I told them: look, I understand that rational thinking means trying to explain everything. Totally fine. But refusing to accept something just because you don’t have an explanation for it—that’s rationalistic thinking, not rational thinking. And it’s destructive thinking, because that kind of thinking basically leaves you forever with the theory you currently have, since any fact that doesn’t fit that theory—you just won’t accept it. If you don’t accept it, then nothing can threaten that theory, and you’ll never replace it. You’ll be stuck with the theory you have now your whole life. Being rational doesn’t mean refusing to accept something I can’t explain. Being rational means accepting a fact if it really is a fact—you need to verify that it was actually observed, that it’s significant, that everything is in order—and then looking for an explanation. There may be a new explanation, but still an explanation. Someone who clings all the time only to what’s already established, who looks only for explanations on the basis of the existing theory, will be stuck with that existing theory forever; it will never be refuted. You’ll never advance; you’ll remain at the level of scientific understanding of Adam. Okay?

Why did I say that I don’t really believe it? Because later it was published that Rabbi Tau did some sort of study on it. We did it afterward with my son too, and indeed a few pigeons died there. But afterward I didn’t see that he was cured by it, though they did die. Then I read some study that Rabbi Tau did—he apparently checked the matter systematically—and his conclusion was, that’s the claim, that’s what I read from him, that pigeons have some breathing opening in the back, and if you take—what, from the rear, I don’t know exactly where in the back somewhere—when you take the pigeon and press it to the navel, yes, as they always do there, you simply suffocate it. It can’t breathe, and that’s why it dies. So how do they get cured? Because people sometimes recover from things on their own. There’s spontaneous healing, there’s placebo, there are lots of healing phenomena. And therefore the fact is—by the way, I once heard that Meir Hospital used pigeons to cure jaundice. People say: factually, if it worked, then it worked. So what if I don’t understand it? Fine. I think that’s fair enough if they did it. But today they don’t do it there anymore, nor anywhere else as far as I know, because apparently—I don’t know, I didn’t check—but apparently they already checked it and understood that there’s nothing real there. It’s Bnei Brak folklore.

Anyway, to our subject—I’m coming back to us—what I want to say is that if it really had worked, and I had checked it in a clear-cut way, then yes, I would have had to change my paradigm and understand that pigeons somehow do cure jaundice, and then look for an explanation. If I’m a rational person, then yes, I would try to look for an explanation and not attribute it to miracles. But I am willing to accept facts even if they contradict my existing paradigm. Okay? That’s really the claim.

Now, how do I find the new paradigm? Right—through explanations of science regarding the unfamiliar. How do I find the new paradigm? I look at the new facts, including those that the previous theory doesn’t explain, and I try to understand from them—yes, exactly what I did here—I now have another x, another fact that the straight line doesn’t explain, so I look for another line that will explain it. Okay? But as you can also see here, even if you add another point, there are still infinitely many lines that will produce generalizations.

A second point: this is also a problem in the philosophy of science that I saw in two independent places—one probably didn’t know about the other—one a historian and the other a philosopher of science. The historian is Carr—E. H. Carr—What Is History?, he has a book by that name, early twentieth century, a well-known British historian. He writes a book on historical methodology, how one studies history. And among other things he says there: suppose we want to understand how Napoleon lost the Battle of Waterloo. In Russia? No, no, Waterloo is in Belgium. Yes, somewhere over there, I don’t know exactly where. So why, how did he lose the Battle of Waterloo?

Now what does Francis Bacon basically say to him? Francis Bacon was essentially the herald of the new scientific philosophy in the sixteenth century, and he basically said: there is a collection of facts, you make observations, and from the facts you try to extract a theory, okay? The big question is: which facts do you collect? Because there are infinitely many facts. How many soldiers did each side have, what was their average height, what color was their skin, what was the name of the mother of the adjutant of the twelfth regiment, what was the height of the deputy company commander of Company C in the fifty-eighth battalion? Yes? There are infinitely many facts. Which facts should you look at? You look at the relevant facts, right? But what are the relevant facts? Relevance is theory-dependent. If the explanation for the victory is this, then certain facts are relevant. For example, if the victory was due to a difference in morale—the morale of the Prussians and the British was higher than that of the French, and therefore they won—wait, then if the theory is that it was morale, I can try to check facts that bear on morale. For example, how many duels took place the night before? Mutual quarrels among the soldiers in each army, or how much wine they drank and whether they got drunk, or I don’t know exactly what, all sorts of things like that, okay? How much the soldiers were abused. All these are relevant facts for seeing whose morale was higher. But for that I need to know in advance that morale is what determined the outcome of the battle. But if I’m looking for the theory, and certainly if I’m a blank slate, I know nothing about military theory, I’m a tabula rasa, I’m just now beginning to build my military knowledge—then I start looking for facts, but which facts should I look for? I have no idea. I need to know what the theory is in order to know which facts to look at. But I can know the theory only after I’ve observed the facts and extracted the theory from them. So it’s a loop. How do you start? The chicken and the egg, right? How do we begin, how do we start moving forward in this matter? Okay? Yes, that fact is no worse than any other fact—the mother of the adjutant is no less relevant.

The second example is taken from a book by Carl Hempel, also a philosopher of science, and he talks about an Austrian-Hungarian Jewish doctor named Semmelweis at a hospital in Vienna. He was head of the maternity ward in a hospital in Vienna. And there was another maternity ward there—there were two maternity wards. Have I already told this here in this series? Okay, so maybe I just don’t remember. But in any case it’s the same idea. They were looking for the facts responsible for the mortality of the mothers in his ward, which was much higher than in the other ward. But they had no idea which facts to look at. Which direction the windows faced, from which side the priest entered, what the pitch of his bell was—they had no clue. It was completely a shot in the dark. And at some stage they discovered that the students came straight from dissecting corpses and didn’t wash their hands, and that was apparently what caused it. But they arrived at that fact entirely by chance, because there were infinitely many other facts they could have wandered among. And again the question is: if you don’t know what causes maternal mortality, how do you know which facts to look at? Which facts to collect? The relevance of the facts is determined by the theory that those facts express. But you don’t know the theory until you’ve collected the facts. So you can’t begin scientific research.

And in both cases the conclusion is that apparently you have some sort of intuition as to what the theory might be, and from that you can understand which facts may be relevant and which may not. Very often you’ll be wrong, and often not, but it isn’t a complete shot in the dark. In other words, you have certain intuitions that tell you where to look. All right? Then you begin, and then you test the theory. It doesn’t work, because it doesn’t stand up to some factual test, so you refine the theory, you change it, you check another fact. It’s this back-and-forth movement between the facts and the theory; all the time there’s some sort of interplay back and forth.

And that is exactly the game of abduction. The game of abduction basically says: I collect facts, and from them I derive a theory. And then the theory comes back and tells me: look, check another fact—maybe that will refute the theory. I check another fact; maybe I’ll change or refine the theory, or replace it entirely if it’s a paradigmatic crisis, and so on. Okay? So it’s a very winding process of moving from facts to theory. It’s not really a straightforward move from facts to theory; rather, I have an idea about the theory, I check the facts, project back onto the theory, return to the facts, and so on. And that’s how one advances—two steps forward, one step back, like in a folk dance. In the end, somehow, I do move forward. That is the scientific process, and it’s the same in analytical Talmud study. In analytical study too it works exactly the same way: you take the cases, you try to derive from them a theory that explains those cases. But that theory may not work with other cases, so you need to replace it, refine it, and so on. Okay? That is called explanation. The explanations we are looking for are really explanations of science about the unfamiliar. It’s not science about the familiar. We’re looking for a theory that will explain the cases—for example, the cases that appear in the Talmud and represent the delivery of a bill of divorce. We’re looking for a theory that will explain those cases. Why in these cases is the giving valid and proper, and in those cases the giving is invalid? Why? How—how can I arrive at a definition of giving? That’s really what I’m doing when I study analytically, just like in scientific research, with all the problems of scientific research.

Now I want to bring one more point, and here we’ll leave the scientific introduction, but I want to sharpen this a bit further, and then we’ll enter a little into the giving of a bill of divorce. Why indeed is science’s explanation of the familiar considered an explanation? That’s the philosophical question I asked. Right? Why is this an explanation? To explain something, I explain things by means of something I understand. There is something I don’t understand; I take things I do understand and by means of them I explain it. And I said that there are scientific explanations of the unfamiliar when there are things I can’t understand by means of the existing theory, so I need to look for another theory that will explain those cases. In what sense will that other theory count as an explanation? Okay? That’s the question.

It reminds me—there’s a piece in Kishon’s book The Fox in the Chicken Coop. Nothing beats me. The Fox in the Chicken Coop—yes, of course it’s a humorous sketch. I don’t know, maybe some of you don’t know Kishon; that’s already a matter of age. In The Fox in the Chicken Coop he tells there about some union functionary—what was his name, it slipped my mind? Doesn’t matter, I forgot. A union operative who goes to some little settlement in the Galilee and builds himself a magnificent villa there with horse stables and an Olympic swimming pool. Tax investigators come to him and say: tell us, from the salary of a union clerk you don’t build an empire like this. Where did the money come from? So he says: you’re right, excellent question, I have a wonderful explanation for you—you won’t believe it. About a year ago I had a dream at night. Elijah the Prophet appeared to me and told me: go to a certain tree on a hill in the Galilee, walk exactly one hundred steps north, say three times “cock-a-doodle-doo,” go fifty steps east, say “tootoreetoo,” then jump three times in place, and then dig at the spot you’ve reached, and you’ll see wonders. And you won’t believe it—the next night, exactly at midnight, I went there to the tree, walked one hundred, cock-a-doodle-doo, tootoreetoo, dug, and found a treasure: a chest full of precious stones and pearls, and with that I built my villa. So they tell him: that’s a fantastic story. Do you have any evidence for this fantastic story? He says: look at the villa—how could I have built the villa if I didn’t have the money? So yes, that’s his proof. That’s usually what explanations of science about the unfamiliar look like.

In any case, what I want to say is that an explanation of science about the unfamiliar is an explanation because of its economy. That’s why it’s called an explanation. What do I mean? Suppose I have a hundred cases. If I can formulate a theory composed of three principles, and it explains all one hundred cases, then I call that an explanation. Because I’ve basically economized on the number of independent facts. I’ve reduced the dimension of my space, if you want to put it in mathematical terms. Okay. In other words, I’ve grounded all the facts on the basis of three elements. So for me that is the complexity of the matter, and therefore there is an explanatory dimension here.

Think about it, I don’t know, say a two-dimensional sheet of paper. There are lots of spatial points in a two-dimensional space. I can draw a coordinate system, right? An x-axis and a y-axis. Every point will be indicated by its x-value and its y-value—its projection on the x-axis and its projection on the y-axis. Okay? What I’ve essentially done is taken all the points in the plane and “explained” them, in quotation marks, in terms of two quantities: the x-value and the y-value. Right? So in that sense this is called an explanation. If you want, you can also look at polar coordinates—distance and angle. Doesn’t matter. But you always need two numbers because it’s a two-dimensional object. Okay? So that means that the most economical theory is one that will need two independent elements to explain this space. Fine? That is called explanation. Explanation means something economical.

Now look. Suppose I give you a sequence of numbers: one, three, five, seven, nine, and so on, and I want to explain it. What does it mean to explain it? I give you one principle that describes the whole series: odd numbers. One, three, five, seven, nine, eleven, thirteen, and so on. Right, yes. So I’m saying: one principle—instead of giving you all the numbers, I give you a so-called explanation in terms of one principle that explains the whole series. And since it’s only one principle, it’s economical, so I see such a thing as an explanation of the series. Yes? In the psychometric exam, whenever you get a sequence to complete—what’s the next term in the series?—okay, usually that goes by way of some kind of explanation. Right? You look for what characterizes all the terms that appear, and if you’ve found an explanation, then you know what the next term should be. Okay? And every such continuation, every such induction, actually hides abduction behind it. You’re looking for a theory that explains the facts, and after you have the theory, you know what will happen also in the fact you haven’t observed yet, in the new fact. Exactly what is done in science.

By the way, on that point let me already tell you something. Take the series three, five, seven, and so on. What comes next? Nine. One person says eleven, one person says nine. Who is right? Both are right. Correct? Yes. Nine—if you assume the explanation is that these are odd numbers: three, five, seven, nine. And eleven—if you assume the explanation is prime numbers: three, five, seven, eleven. Because nine isn’t prime. Okay? So there can be two continuations; in fact there can of course be infinitely many continuations. That’s Wittgenstein. There can be infinitely many continuations. It’s Wittgenstein’s argument about what’s called “following a rule.” In any case, coming back to us, let’s now look at another series: one, three, eight, nineteen, twenty, thirty, thirty-three, thirty-seven, and so on. Now I ask you: what is the next term? You probably won’t know, because there’s no simple pattern. Okay? I just threw out numbers. Yes? There’s always some ad hoc way to arrange it, but there’s nothing natural. I didn’t do anything here; I just threw out numbers.

What do you think of the following explanation? Look. Take the number one, add two, and of course you get three. Then add five, you get eight. Then add eleven, you get nineteen. Then add eleven again, you get twenty, add ten, you get thirty. There—you have an explanation for the whole series. Good explanation, no? What’s wrong with that explanation? That it isn’t economical. It’s not one principle by which I explain the whole series. The number of principles is almost the same as the number of facts I’m trying to explain. So what did I gain from that theory? In other words, a theory that grounds the unfamiliar—again, a theory that grounds the familiar is no problem. You can explain with as many principles as you like. But a theory that grounds the unfamiliar—if the theory needs a number of principles roughly equal to the number of facts it came to explain, then that theory is worth nothing. The explanatory power of an unfamiliar theory is always in its economy. That means: if a small number of principles explains a great many facts, then you say you have a good theory. It explains, it’s economical, it has explanatory power. Okay? But if the number of principles or entities the theory contains is like the number of facts it explains, then we haven’t done anything. We’ve merely translated the problem into another language, but the problem remains exactly where it was.

With us, for example, you’ll see that an explanation of that sort won’t help you complete the next number in the series, right? Now what remains? Okay, I gave you an explanation: take one, add two, get three. Add five, get eight. Add eleven, get nineteen. Eleven again, get twenty, and so on. What comes after twenty? No, there’s no way to calculate it. What are you going to calculate? I didn’t tell you the rule governing the differences. Each time it’s a different difference, but what’s the pattern, how do you choose the differences? There is no way. And therefore this is another indication that what I gave you here is not an explanation. It explains nothing. I merely described the facts I wanted to explain in another language; I translated it from Hebrew to English. Thank you very much. How does that help me? Okay, that’s not an explanation in any sense.

Why am I saying this? Because now I’m moving to the giving of a bill of divorce. Because with the giving of a bill of divorce, as I’ll try to show you in a moment, the explanation proposed for the collection of facts that appear in the Talmud contains roughly as many principles as there are cases, as many facts, and therefore it is worthless. That explanation isn’t worth much. Okay, that’s really the bottom line with which I want to set out.

Now, when we want to define the concept of giving a bill of divorce—I’ll come back to this whole introduction, it’s important—when we want to define the process of giving a bill of divorce, we look at different examples. The Talmud gives us examples and determines regarding them whether this counts as giving or not as valid giving, and so on. And the medieval authorities (Rishonim) and later authorities (Acharonim) take the examples and try to derive from them a theory, exactly like scientific work. They take the cases and try to understand what theory explains the cases. Now, as is their way, the medieval authorities do this briefly. The later authorities do it in a more analytical, systematic, broad way; they look at all the cases and try to derive a general definition of giving a bill of divorce. Now this is an extremely difficult intellectual task. As I said, there are dozens and dozens of cases, maybe even hundreds. Just in the Talmud, even before the medieval authorities. And the question is how from all this one extracts an economical theory that, on the basis of a small number of principles, manages to explain all these cases, and all the cases in which the bill of divorce is invalid, all the valid cases and all the invalid ones.

The most detailed case I know of among the later authorities who tries to do this is the Kehillot Yaakov on tractate Gittin, sections 14 to 17—four long sections devoted to this issue. What I’ll try to show you here is half of the second section, and even that only in broad outline, just so you understand the scale of things. So in principle this already begins with the Ketzot, and the simplest definition that emerges from the verse itself—what would you say “giving” means? Giving a bill of divorce. “And he shall write her a scroll of severance and place it in her hand.” What is that called? What needs to be done? Right: take something and physically put it into the woman’s hand, right? That’s the simple definition I would derive from the verse.

Now when I come to the Talmud, I discover that this definition doesn’t stand the test of reality. Why? For example, he places the bill of divorce in a courtyard and transfers ownership of the courtyard to her. The bill of divorce is valid. Now here there was no physical giving of the bill of divorce from his hand—the bill of divorce didn’t move from its place; it was lying in the courtyard, it was in the courtyard and remained in the courtyard. I transfer the courtyard to her. Transfer it. She has to know, everything is fine. But still, I say: I transfer the courtyard to her, and this is a valid bill of divorce. The Talmud says it’s a valid bill of divorce. That means the definition is not physical giving from the husband’s hand to the woman’s hand, right? So there’s a first example.

Now I say, fine, so maybe the rule is that he must transfer ownership of the bill of divorce to her. Acquisition. That fits better. Why? Because even the cases where he simply gives her the bill of divorce physically also fall under the definition of transfer of ownership, because there is acquisition by lifting, by handing over, by drawing toward oneself—these are also kinds of acquisition. So maybe the act of handing over merely comes to say: when the Torah said, “and he shall write her a scroll of severance and place it in her hand,” it meant to say: transfer ownership of the bill of divorce to her. Giving is one of the ways to transfer ownership of a bill of divorce. You can transfer it by transferring ownership of the courtyard in which the bill of divorce is sitting, you can transfer it in various ways. Okay? So it could be that valid giving is simply transfer of ownership. Again, a simple definition. Not handing over—we already saw it’s not handing over—transfer of ownership.

But that doesn’t work either. The Ketzot already notes this, and says that if the bill of divorce is written on something from which benefit is forbidden, it is valid. There is a dispute among the medieval authorities whether there is ownership over things from which benefit is forbidden. Some of the medieval authorities say that once benefit from it is forbidden, there is no ownership over it. Once it is forbidden for benefit, I am not its owner. Now if I write the bill of divorce on something from which benefit is forbidden and give it to the woman, then if the definition of giving were transfer of ownership of the bill of divorce, that would be impossible with something from which benefit is forbidden. With such prohibited-benefit items you can’t own them, so how can you transfer ownership of the bill of divorce to the woman? It’s written on something from which benefit is forbidden. So transfer of ownership can’t be the answer either. So what is? In short, it can’t be physical handing over and it can’t be transfer of ownership. So what is it? Then all kinds of combinations begin: it’s a handing over that includes transfer of ownership, or transfer of ownership that includes handing over, or all sorts of gimmicks like that—and they don’t get anywhere. They don’t get anywhere, because understand: since there are so many cases, every definition—you bring another case and you have to shave the definition down a little more, then another case and shave it down a little more. In the end, the number of refinements, the number of patches you’ve put on your theory, is roughly the same as the number of cases. And then the theory has no economical value at all. Because it’s not a small number of principles explaining the whole array of cases that appear in the Talmud; rather the number of principles in the theory is roughly like the number of cases—each case adds another principle. Epicycles and deferents. So it has no explanatory value; that is, it’s worth nothing.

So for example, look at an example from the Kehillot Yaakov that I brought. He says: “Here is your bill of divorce, but the paper is still mine.” He gives her the bill of divorce but does not transfer ownership of the paper to her. So the verse implies that she is not divorced. She is not divorced—apparently because the paper is his, he didn’t transfer it. But we saw that he doesn’t need to transfer it, because if it’s written on something from which benefit is forbidden, it is valid.

[Speaker C] What exactly are you transferring there?

[Rabbi Michael Abraham] So what do you do? So they say: no, this isn’t handing over. But physical handing over isn’t required either, right? The problem here isn’t physical; physically I did hand it over. Physically I handed her the bill of divorce; it’s just that ownership of the paper of the bill of divorce remained with him. Remained mine. So it’s a kind of transfer of ownership that merely expresses some type of handing over, or something like that. And then he goes on there—for example, yes, the Rashash says that these are letters floating in the air. In other words, the problem isn’t that there is an ownership issue here, but that nothing was actually given; there is nothing tangible that was given, because the letters are floating in the air. But why was nothing given? I gave her the paper; ownership of the paper remained mine, but I gave it. So yes, transfer of ownership plays some sort of role here. So you need handing over and not transfer of ownership, but without transfer of ownership it isn’t handing over. So you understand that the story gets complicated here.

Then he says that someone who wrote the bill of divorce on the hand of a slave or the horn of a cow and gave her only the horn without the slave or the cow—that too is invalid. Why invalid? Here too he is already giving it to her, because it’s attached to something that is mine. So what then? Is the problem again transfer of ownership? Is it not giving? How exactly do you define this thing? Afterward he does indeed talk about someone who wrote the bill of divorce in his courtyard and transferred the courtyard to her, what I mentioned earlier. Then he brings this as a difficulty: an agent for delivery cannot become an agent for receipt, because the agency doesn’t revert back to the husband—so how in the case of a courtyard does that happen? In short, there’s no getting out of this.

I’ll read you one small passage from the middle of section 15. This passage summarizes, as I said, half of the second of the four sections he devotes to the matter. And look at the level of complexity in just one-eighth of the material. It says: “For certainly transferring ownership of the bill of divorce itself is not enough to count as giving, for we require that besides transferring ownership of the bill of divorce, the husband assist in the act of acquisition involved in receiving the bill of divorce. But transferring ownership of the courtyard, which serves as a hand for receiving the bill of divorce, is indeed considered assistance in the act of acquisition of receiving the bill of divorce, since without his transfer there would be no act of acquisition here; and it is through his transfer that it becomes the woman’s courtyard-acquisition. But in every case of ‘take your bill of divorce from atop the ground,’ even without the husband’s transfer, the woman herself is also performing the act of acquisition, since it is already in her hand; only the matter of legal entitlement requires his transfer. But when the husband transfers the courtyard in which the bill of divorce is located, it is only through his transfer that the woman’s act of acquisition comes into being.”

So the woman acquires—not good enough; the husband gives—not enough either. But if the husband is a partner in the proprietary action by which the woman acquires the bill of divorce, or some kind of definition like that—now, what counts as being a partner? There too I still haven’t defined what partnership means. When he transfers to her the courtyard in which the bill of divorce is located, that counts as his being a partner. But if he says, “Take your bill of divorce from atop the ground and acquire it,” then he is not a partner. You can see the intuition that there is a difference between these two things, but defining it is very difficult.

And afterward, if you continue with all the cases there, in the end he arrives at a definition whose number of components is roughly equal to the number of cases you came to explain. In short, the theory you arrived at has no explanatory value at all. All right? After four packed, long, and very exhausting sections, that is in the end the conclusion.

So as I said at the beginning of the lesson, the first question that arises here is: why doesn’t the Talmud itself give me the rule? Why does it bring so many examples and complicate my life with the attempt to extract the rule from the examples? Let it just give me the rule. Apparently the Talmud itself did not believe that there is some rule here that can be formulated. And I said—there I spoke about the casuistry of the Talmud—that the Talmud believes in cases and not in principles. So the Talmud itself basically doesn’t believe in this, and therefore it tries to convey the idea to me through examples.

It conveys the idea to me through examples, and then the opposite question arises: so why do I—or the Kehillot Yaakov, it doesn’t matter, any one of us approaching the passage—why do we nevertheless try to derive a theory, rules that explain all the examples? If the Talmud itself had such a rule, it would have given it to me. It doesn’t have such a rule, right? It doesn’t give me one. So why do I keep trying this all the time, when of course in the end I fail? So what have I done? I’ve wasted Torah study over four sections of the Kehillot Yaakov. The whole thing seems completely absurd. You labor and labor, collect all the cases, try to reinvent the wheel when the Talmud itself told you there is no wheel, and in the end you discover that indeed there is no wheel. In other words, you arrived at something that isn’t really a theory, it’s worth nothing. So what do we do?

Rabbi Ovadia would tell you that this is Ashkenazi hair-splitting, a waste of Torah study. Okay? And I, alas, want to disagree with him, and I want to make the following claim: when we want to understand a phenomenon like the delivery of a bill of divorce—a phenomenon that apparently is very hard to define—we as human beings, our thinking is structured in such a way that we always think through rules. We can’t think about one case and compare it to another case. Behind that there sits some kind of rule, right? When I say to you one, three, five, seven, nine—what is the next number? You say eleven. Why? You didn’t just say eleven for no reason; you understand that we’re dealing with odd numbers. One, three, five, seven, nine, so presumably the next is eleven. Okay? And we don’t just move arbitrarily from case to case. Behind the move, behind the analogy we make from case to case, there is always some rule that we have concluded is probably the right rule.

And in our conception, when we explain something, the explanation will always be in terms of rules. We don’t explain one case by means of another case. We explain the comparison between two cases on the basis of a rule. Explanation is always bound up with rules. We cannot think without rules. Thinking means placing the thing into a pattern of rules—broad rules. That is what thinking is called. Sometimes there is another rule and another rule and it gets complicated, but we cannot think otherwise. There is no such thing as thinking about a case. Thinking about a case always means understanding which rules find expression in it. That is what it means to think about the case. Okay? I can’t think about the case as such. What am I supposed to think about the case? She received the bill of divorce in a courtyard and he transferred the courtyard to her, and therefore it is a bill of divorce. Okay, let’s think about the case. What exactly am I supposed to think there? What am I supposed to do now with that case? I can now try to formulate rules in my head. Maybe a bill of divorce is handing over. I see here that it’s not handing over. Maybe it’s acquisition? Yes, here that could work. But I see that when it’s written on something from which benefit is forbidden, there I see that it’s not acquisition. So you see—I propose a rule, and reject it by means of a counterexample. You can see the scientific process of refutation. I propose a scientific hypothesis, a scientific theory, and I reject it by means of a refuting experiment. Right? Which in this context is basically an example from the Talmud that doesn’t fit the theory. I try a more sophisticated theory, refute that too. Really a scientific process.

Okay? We are basically trying to generate the scientific theory from the cases. Except—what?—that we don’t succeed. Science is a relatively simple world. Difficult, but relatively simple. That is, there is a certain number of rules by means of which one can explain a great many examples. In other words, nature is on the whole simple. You need to be smart to understand that, but in the end it is simple. Okay? Life is more complicated—at least that’s how it seems. We don’t succeed. Why does psychology get so tangled up, and why doesn’t it manage to become a science? Because it doesn’t manage to become a science, yes, because it’s terribly complicated. Right? That is, you can’t take a set of, I don’t know, five rules and explain all human behavior by means of five rules. It simply doesn’t work.

My sister once studied criminology here. Did I tell this? So she told me that almost every one of their courses began with a definition of what science is. When I studied physics, nobody began any course with a definition of what science is. I mean, yes—even she didn’t need me to tell her that. She told me this precisely for that reason. That is, she understood that it wasn’t a science, and that’s exactly why they kept explaining to her why it is a science. Because whoever is secure in being a science doesn’t explain to anyone that he is a science; everybody knows. In other words, it’s the same here. And why not? Because there is no small set of rules that has explanatory value and can describe the whole range of psychological phenomena. There’s no such way. It’s not because psychologists are stupid. It’s not that physicists would know how to do it better. Physicists wouldn’t do it better either. Because the field is apparently—this is what I think, I don’t know, one can try—but this is what I think: the field itself is of a kind that does not respond to scientific patterns, to rules, to these general principles. Okay? And physics is more responsive to that kind of thinking.

So basically the point is that Talmud too, or law, or whatever—things like that—also do not respond to thinking in terms of rules. Thinking in terms of rules is too simplistic. Reality, the world, is too complicated for us to succeed in describing it by means of a closed set of a small number of rules. It can’t happen. But when we think—so why does psychology still try to define rules that never work? It doesn’t matter, it tries to define rules. Why? Because we cannot think without rules. Even in a field that does not submit to rule-based thought, when we come to think about it, we have nothing else. That is the tool we have. We think with rules. There’s no help for it.

How do we do that? We propose a hypothesis, some kind of rule, which we test against the facts. We’ll see that it doesn’t work. That is, there are facts that contradict it. Then I say, okay, so I have another hypothesis. I test the facts; that too doesn’t work. Okay, then I’ll make some expansion of them, some combination of them, I don’t know exactly what; I test that, it doesn’t work either. And so on. Slowly I arrive at something more and more and more complicated—combinations with lots of principles. The number of principles is like the number of cases. In the end I’ve finished the matter; I’ve “explained,” in quotation marks, all the cases. Only the theory I’m using is so uneconomical that the number of principles in it is roughly the same as the number of cases. Now the question is: what am I left holding? And my answer is—and here I return to the neuron model—my answer is that this theory isn’t worth the paper it’s written on. And yet the whole process was a very important process. Why? Because what I’ve done here is a kind of explanation through hollowing out. You know what hollowing out is? When I write on the Sabbath—or with writing in a bill of divorce there is also a discussion—writing on the Sabbath: I can write by simply writing, and I can erase around so that a letter remains. Say, for example, on a weekday—I can carve around and leave what remains. So is that called writing or not called writing? Because I didn’t touch the letter itself; I only removed everything around it. So it’s like they always say that the statue already existed inside the stone before the sculptor came; he only removed what prevented you from seeing it. Right? So who made the statue? Did the sculptor make the statue? So the Talmud says yes: hollowing out counts as writing.

Here too there are sometimes explanations that are explanations by hollowing out. What does that mean? I eliminate all kinds of rules—here I come to negative attributes. I eliminate all kinds of rules because I understand that they don’t work. But you understand that after I’ve eliminated all the rules, something remains that I don’t know how to formulate—certainly not economically. But what remains is basically an intuitive understanding of what the giving of a bill of divorce is. And after I’ve understood that it is not handing over, and not acquisition, and not a combination of them, and not this combination of them, because every time another case—slowly there is formed in my mind some pattern that can identify what valid giving is.

If you ask me, okay, formulate it—I don’t know how to formulate it, certainly not economically. I know how to say what the Kehillot Yaakov said—to give you a list of eighty rules, which correspond to roughly eighty cases in the Talmud: eighty rules, and with that this is valid giving. That’s nonsense; I don’t think that’s the point in the end. The claim is that after I’ve examined many, many cases, after I’ve examined very many cases, some intuitive understanding has formed within me of what giving a bill of divorce is. Now I can throw the whole theory of the Kehillot Yaakov in the trash; it doesn’t matter. What mattered was the path. Because along the path, when I rejected this theory and rejected that theory and rejected another theory, rejected everything, what remained in me at the end was something that is an understanding of what the giving of a bill of divorce is. And that is what the Talmud really wanted to convey to me when it wrote a hundred different cases of valid givings and invalid givings. Because it basically expected me to try to define rules for all the cases, reject them on the basis of other cases, define again, reject again, define, reject, define, reject constantly. In the end I won’t be left with a theory, as one expects in science—to remain with some general law or general theory that explains the facts. No. I’ll be left with some unformulated intuitive understanding, but one that is already very well built inside me. And that is really the goal of study.

The goal of study is to try to understand what the giving of a bill of divorce is—but not understand in the sense of formulation. Rather, the different formulations that I ultimately reject leave behind in me an intuitive understanding of what the giving of a bill of divorce is. Now if a new case comes before me, I won’t go through the whole Kehillot Yaakov. Rather, if I have internalized this process well and it has built within me a healthy sense of what valid giving is and what it isn’t, I’ll immediately say whether this is valid giving or invalid giving. I won’t need to justify it and I won’t need to explain it, and I won’t say this resembles that and that resembles the other. Rather, some understanding has been built within me that can already directly say: this is valid giving and this is invalid giving.

[Speaker E] But is that actually reliable?

[Rabbi Michael Abraham] I don’t know. I have no independent way to measure it. How would I test it? I can take a person and ask him about the Talmudic cases, because there I have an answer—the Talmud gave the answer. But I trained him on those examples, so that proves nothing; on those examples he’ll give the right answer. You see that this is really, really a neural network, right? Completely. I mean, for anyone who doesn’t know, what’s the difference between a neural network and a classical program? A classical program—if you want, say, I don’t know, to make a program identify a face. Let’s say they want to train a program to identify my face—in summer, in winter, in shadow, in light, whatever—but every time it sees me it will know it’s me, and if it’s someone else it will know it’s someone else. Right, face recognition, facial recognition. How would you train a classical program? You can’t. You have to define my features for it positively. He has a nose like this of such-and-such a length, and if the light comes from here then there will be this kind of shadow, and if the light comes from there… In other words, you have to define it, and then it will apply that and identify me, carry out the instructions and manage to identify me. You get nowhere that way. You just don’t get there with that. Okay? Why? Because you’re trying to work with rules. Okay, if the light comes like this, and if it’s like this and this, now let’s go through all those cases. And that’s only to identify me. What about identifying every person? Comparing between two people? No chance with a classical program. When do you start making progress? When you move to the model of a neural network. What’s a neural network? A neural network is some kind of miracle that apparently nobody fully understands, in which, within that framework, we have a collection of points connected to one another by links, okay? And those links have some sort of weight—the details don’t matter, that’s not the main point—and I can control the weights that connect the elements, okay? Now what happens is that I feed input into the network, I put in, I don’t know, say a picture of me into the network, its numerical representation, doesn’t matter, and the network processes it and outputs an answer: yes or no. Yes if it’s me, no if it’s not me. Okay? That’s the point. Now I want to train the network so it knows how to identify me. I don’t tell it how to identify me, what the length of my nose is like in a classical program, right? And what the size of my head is, and if the light comes from here what the shadow will be—I tell it none of that. I simply show it a collection of a great many pictures of me. I tell it, this is yes; a great many pictures that aren’t mine, and I tell it no for those. With each answer like that, the network arranges its internal weights so that the computation will produce yes in the right places and no in the right places. And you have enough parameters that you can arrange them so that it fits all the examples presented to the network. And it turns out, to our astonishment, that now if we present the network with a picture of me that it has never seen, it will identify it with very high probability. And a picture that isn’t mine it will also identify with very high probability as not mine. And the more examples we train it on, the more reliable the identification will be. Now notice: the network doesn’t think at all the way we think—wait a second, he has this kind of nose and this comes from here and that comes from there and so on. No, not at all. It arranges some internal weights, performs some calculation, and it’s not at all clear what the connection is between that and the thought processes that happen consciously in us. Right, in the head we also have such processes, but in the intellect, not in the brain. In the intellect we think according to principles. Okay? It’s not at all clear what the relation is between this and that. And it outputs answers that are more or less correct. Why? Because the examples it received with feedback—say this is what they call supervised learning—in other words, it’s learning that receives the answer of correct and incorrect, and according to that it organizes itself, because it adapts itself to the correct answer. So I’m saying that’s exactly what we’re doing here in the process of giving a bill of divorce. Here I say: the bill is in her hand and the pulling is in her hand—the answer is yes; sorry, the answer is no, that’s not a valid connection. He placed the bill in the courtyard and transferred ownership of the courtyard to her—the answer is yes. I don’t explain at all why. There’s no need to explain why. I give a set of examples: for these the answer is yes, for these the answer is no. The neural network will already arrange itself so that when it sees a new example, its answer about that new example will, with very high reliability, be a good answer, a correct answer. Even though if you ask it, what’s the explanation for why you’re saying this transfer is valid and this one isn’t, it has no idea, it won’t know how to answer. That’s not what matters. It doesn’t pass through explanations. Somehow, from the examples, in a very abstract way, it extracts unformulated principles and applies them to cases it has not encountered. Of course, the cases it has encountered—there’s no point testing it on those; it trained on them. I’m talking about cases it hasn’t encountered. That’s why in the Talmud it’s hard to do this. So if we want to test ourselves in the Talmud, the only way—say there are a hundred examples—the only way is to train on ninety of them. And then test ourselves on the remaining ten and see whether we matched the Talmud’s answer or not. Okay? My assumption is that the more examples you train on, the more you’ll also hit the additional examples. You’ll hit them with a high level of reliability—there’s no certainty here. With a high degree of reliability you’ll get the next examples right. In other words, the Talmud teaches us exactly the way someone trains a neural network. And not like a classical program, where you explain to it: if so then do this, and if so then do that, and do this calculation, do that calculation, and give me the result. That’s like a pocket calculator. In other words, do a calculation, right, that I tell you exactly how to do. That’s the difference between artificial intelligence and a computer. Artificial intelligence is not a computer. A computer has no intelligence. A computer does what it was programmed to do. Artificial intelligence does something it was not programmed to do—not in the classical sense of the concept of programming. It can perform complex tasks and decide for itself on methods of action, based of course on a great, great deal of information that was fed into it and the training it underwent, but that is already intelligence and not just calculation.

[Speaker B] And that’s not theory. What? Right, exactly.

[Rabbi Michael Abraham] In our human thinking, we move through understandings and theories, and we reject theories, and so on.

[Speaker B] But really, really, we—

[Rabbi Michael Abraham] We don’t actually end up with a theory that we work with. Rather, rejecting theories, proposing theories and rejecting them—that actually trains our internal network to identify correctly what is a valid transfer and what is not a valid transfer. And what that really means is that analytic study, what it does, is simply take the abstract principles of the Torah that we don’t know how to formulate, and just internalize them within us. This doesn’t pass through our cognition. Cognition is an auxiliary tool. In other words, conscious thought is an auxiliary tool. In the end, our neural network is supposed to organize itself in a way that contains, in some abstract fashion, what is called Torah in its abstract sense. We talked about abstractions. And therefore this is absolutely not neglect of Torah study. If there’s anything here that is not neglect of Torah study, it’s what Kehillot Yaakov did here. Because what Kehillot Yaakov did here, essentially, was take that same abstract thing that I said later appears in the laws and all the rest, which we don’t know how to formulate and don’t know anything about—and what do we do? We internalize it within ourselves through the cases and the situations and the rules and everything. In the end, we are putting the abstract Torah somewhere inside us—not the formulated version, but into our inner selves. We don’t even know how to formulate it. But it’s there. That’s literally cleaving, literally cleaving to the Holy One, blessed be He—physically, in the plain literal sense. Okay? That is the meaning of Torah study in the sense we spoke about there.

[Speaker E] Look, in some cases there are disputes, so that’s why I put it into NLP.

[Rabbi Michael Abraham] You understand that there are two sides—

[Speaker E] And I don’t know whether it’s yes or no.

[Rabbi Michael Abraham] You can train a neural network to say: in this case there is a dispute. It has two sides. There’s a side that says this is Michael Abraham, and a side that says this is not Michael Abraham. This is an image for which there is room to hesitate. Because someone else—say if they photograph you from a certain angle and me from another angle—it could be that the same image comes out, even though we’re different. You understand? And then there really are two correct answers here. Not because there’s a mistake in one direction. There really are two correct answers here, because the image doesn’t contain all the information. It contains me from a very specific angle and with very specific lighting, and you from another angle with different lighting, and somehow it comes out the same. So then you would train the program to answer: in a case like this, it could be either Yaron or Michael Abraham. Okay?

[Speaker G] And in learning, then, when there’s, say, a dispute in Tosafot, I don’t know, Abaye and Rava, or something where I don’t know what the Jewish law is here or where the law follows—then basically I also need, sort of intuitively, to understand that here there is a dispute.

[Rabbi Michael Abraham] Correct. There are two sides here, and each has the possibility that Jewish law could be ruled in accordance with it. It really does grasp a correct meaning of the passage. Yes, we didn’t talk about “these and those are the words of the living God,” but it’s connected to “these and those are the words of the living God.” In other words, yes, like the well-known parable of the elephant: if you look at the elephant from the front and they ask you what an elephant looks like, you say it has two eyes, it has two legs very close together, and a trunk. And when you look at it from the side and they ask you what an elephant looks like, you say it has one eye, it has two legs very far from each other, and a trunk. Now who’s right? Both are right. There is an angle from which the elephant looks like this, and an angle from which the elephant looks like that. And every person sees Jewish law and reality from a certain angle, and the assumption is that the totality of angles is the full truth. But each angle is a correct angle—in other words, you’re not mistaken. Okay?

[Speaker H] On the other side they say: let it stand unresolved.

[Rabbi Michael Abraham] Yes, that’s the opposite. It’s not another side; it means there’s no way to decide, the two answers remain evenly balanced. When we decide there, you could say, look, in the end there really is a mistake, because one side really is right. Precisely the case of let it stand unresolved fits my description better. Because a case of let it stand unresolved means the two answers are both correct; there isn’t a correct and incorrect answer here. Okay. One acted in accordance with this master and did well, and one acted in accordance with that master and did well. That’s even more than an unresolved case; in fact both can even be followed in practice. In an unresolved case we still apply the laws of doubt, but in “one acted in accordance with this master and did well, and one acted in accordance with that master and did well,” we rule like both views. Like Rabbi Yehuda and the Sages regarding the afternoon prayer and the evening prayer and various other things as well. So therefore I’m saying that this form of learning—that I’m closing some sort of circle here—and I want to say that the purpose of analytic study, in the end, is to retrace the process of concretization, to carry out a process of abstraction. The process of concretization that I spoke about at the beginning of the semester, where the Torah descends from abstract ideas and is formulated in words and situations from our world and in halakhic rulings and so on—and basically we now take the rulings, that in a bill of divorce like this the transfer is valid, like that the transfer is not valid—those are rulings. But the claim is that this expresses some more general abstract ideas; I don’t know how to formulate them. So what do I do? I put them inside myself; they are now inside me. Through the cases I internalize them into my neural network. Okay? And basically, in a certain sense, I have inserted the Torah in its completely abstract sense into myself. And the words and the principles and the different cases I dealt with are only the tools through which I did this. Exactly like in a neural network. And now you suddenly see, almost visually, why the cases are the means to understanding, and not that understanding is a means for knowing what happens in the cases. I use the cases as training for the neural network, when my goal is for the neural network to absorb into itself the abstract form of thought called Torah. And the cases are the way to do that. In other words, only through the cases can I do it, because I have no formulation. I can’t do it directly through a formulation of principles; I have to go through the cases. Okay? So I think this is a very nice demonstration of why the cases are the means and the theory is the goal. The cases serve the goal, which is understanding the theory. And understanding the theory does not mean formulated understanding. I don’t know how to formulate the theory at the end, but it is inside me. And now when you ask me—right, they always say this in yeshivot—that if the Rosh brings proof for his view, you can argue. This proof doesn’t seem right to me, I have counter-evidence, I have another line of reasoning. But if the Rosh says “it seems to me,” then it’s game over. “It seems to me” that this is so—there’s nothing to argue about, then that’s how it is. Because if he says “it seems to me,” that basically means his neural network is saying it. The totality of all the training he has undergone until now says that this is so. He doesn’t have this proof or that proof, but it’s clear to him; his whole Torah is basically standing behind it. Okay? When he brings proof, then he says: I have proof. Fine, proof that can be debated, good proof, not good proof. That doesn’t come from the neural network; that comes from here. From here—meaning that the neural network is also inside there—it comes from the…

[Speaker B] So how does that fit with Rabbi Kook’s idea—Rabbi Kook says that one needs to teach the depth of the principles, I think, when there’s distortion?

[Rabbi Michael Abraham] You’d have to ask him.

[Speaker B] To teach? No, it’s an explicit passage there.

[Rabbi Michael Abraham] I don’t know.